معرفی چند منبع در زمینه آموزش برنامه نویسی MATLABیا متلب کتاب های به زبان انگلیسی عنوانMatlab, Third Edition: A Practical Introduction to : Programming and Problem Solving ترجمه عنوان :متلب :مقدمه ای عملی بر برنامه نويسی و حل مساله ،چاپ سوم مولفینStormy Attaway : سال چاپ2013 : انتشاراتButterworth-Heinemann : کتاب های به زبان فارسی عنوان :اصول و مبانی متلب برای علوم مهندسی مولفین :برايان هان ،دانیل تی ،والنتین مترجمین :رامین موالنا پور ،سارا موالناپور ،نینا اسدی پور انتشارات :سها دانش لینک دسترسی :لینک لینک دسترسی :لینک عنوانMATLAB For Dummies : ترجمه عنوان :تلب به زبان ساده مولفینJim Sizemore, John Paul Mueller : سال چاپ2014 : انتشاراتFor Dummies : عنوان :کاربرد MATLABدر علوم مهندسی مولفین :حیدرعلی شايانفر ،حسین شايقی انتشارات :ياوريان لینک دسترسی :لینک لینک دسترسی :لینک عنوانEssential MATLAB for Engineers and Scientists : عنوان :برنامه نويسی MATLABبرای مهندسان ترجمه عنوان :آنچه بايد مهندسین و دانشمندان از متلب بدانند مولفین :محمود کشاورز مهر ،بهزاد عبدی مولفینBrian Hahn, Daniel Valentine: سال چاپ2013 : انتشاراتAcademic Press : انتشارات :نوپردازان لینک دسترسی :لینک لینک دسترسی :لینک عنوانMATLAB: An Introduction with Applications : عنوان :آموزش کاربردی مباحث پیشرفته با MATLAB ترجمه عنوان :مقدمه ای بر متلب و کاربردهای آن مولفین :نیما جمشیدی ،علی ابويی مهريزی ،رسول مواليی مولفAmos Gilat : انتشارات :عابد سال چاپ2014 : انتشاراتWiley : لینک دسترسی :لینک لینک دسترسی :لینک عنوانMATLAB For Beginners: A Gentle Approach: عنوان :کاملترين مرجع آموزشی و کاربردی MATLAB ترجمه عنوان :متلب برای افراد مبتدی با يک رويکرد تدريجی مولفین :علی اکبر علمداری ،نسرين علمداری مولفPeter I. Kattan: انتشارات :نگارنده دانش سال چاپ2008 : انتشاراتCreateSpace Independent Publishing Platform : لینک دسترسی :لینک لینک دسترسی :لینک عنوانMATLAB for Engineers : عنوان :برنامه نويسی MATLABبرای مهندسین ترجمه عنوان :متلب برای مهندسین مولف :استفن چاپمن مولفHolly Moore : سال چاپ2011 : انتشاراتPrentice Hall : لینک دسترسی :لینک عنوانMastering MATLAB : ترجمه عنوان :تسلط بر متلب مولفینDuane C. Hanselman, Bruce L. Littlefield : سال چاپ2011 : انتشاراتPrentice Hall : لینک دسترسی :لینک مترجم :سعدان زکائی انتشارات :دانشگاه صنعتی خواجه نصیرالدين طوسی لینک دسترسی :لینک عنوان :آموزش گام به گام محاسبات عددی با متلب مولف :کلیو مولر مترجم :رسول نصیری انتشارات :نشر گستر لینک دسترسی :لینک منابع آموزشی آنالین عنوان :مجموعه فرادرسهای برنامهنويسی متلب مدرس :دکتر سید مصطفی کالمی هريس مدت زمان ۹ :ساعت و ۳دقیقه زبان :فارسی ارائه دهنده :فرادرس لینک دسترسی :لینک عنوان :مجموعه فرادرسهای متلب برای علوم و مهندسی مدرس :دکتر سید مصطفی کالمی هريس مدت زمان 14 :ساعت و 2۲دقیقه زبان :فارسی ارائه دهنده :فرادرس لینک دسترسی :لینک عنوان :مجموعه فرادرسهای برنامه نويسی متلب پیشرفته مدرس :دکتر سید مصطفی کالمی هريس مدت زمان ۲ :ساعت و 12دقیقه زبان :فارسی ارائه دهنده :فرادرس لینک دسترسی :لینک عنوانIntroduction to Programming with MATLAB : ترجمه عنوان :آشنايی با برنامهنويسی متلب مدرسینAkos Ledeczi, Michael Fitzpatrick, Robert Tairas : زبان :انگلیسی ارائه دهندهVanderbilt University : لینک دسترسی :لینک عنوانIntroduction to MATLAB : ترجمه عنوان :مقدمهای بر متلب مدرسDanilo Šćepanović : زبان :انگلیسی ارائه دهندهMIT OCW : لینک دسترسی :لینک عنوانUp and Running with MATLAB : ترجمه عنوان :شروع سريع کار با متلب مدرسPatrick Royal : زبان :انگلیسی ارائه دهندهlynda.com : لینک دسترسی :لینک عنوانModelling and Simulation using MATLAB : ترجمه عنوان :مدلسازی و شبیهسازی با استفاده از متلب مدرسین Prof. Dr.-Ing. Georg Fries :و دیگران زبان :انگلیسی ارائه دهندهiversity.org : لینک دسترسی :لینک Fixed-Point Designer™ Reference R2013b www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان How to Contact MathWorks Web Newsgroup www.mathworks.com/contact_TS.html Technical Support www.mathworks.com comp.soft-sys.matlab [email protected] [email protected] [email protected] [email protected] [email protected] Product enhancement suggestions Bug reports Documentation error reports Order status, license renewals, passcodes Sales, pricing, and general information 508-647-7000 (Phone) 508-647-7001 (Fax) The MathWorks, Inc. 3 Apple Hill Drive Natick, MA 01760-2098 For contact information about worldwide offices, see the MathWorks Web site. Fixed-Point Designer™ Reference © COPYRIGHT 2013 by The MathWorks, Inc. The software described in this document is furnished under a license agreement. The software may be used or copied only under the terms of the license agreement. No part of this manual may be photocopied or reproduced in any form without prior written consent from The MathWorks, Inc. FEDERAL ACQUISITION: This provision applies to all acquisitions of the Program and Documentation by, for, or through the federal government of the United States. By accepting delivery of the Program or Documentation, the government hereby agrees that this software or documentation qualifies as commercial computer software or commercial computer software documentation as such terms are used or defined in FAR 12.212, DFARS Part 227.72, and DFARS 252.227-7014. Accordingly, the terms and conditions of this Agreement and only those rights specified in this Agreement, shall pertain to and govern the use, modification, reproduction, release, performance, display, and disclosure of the Program and Documentation by the federal government (or other entity acquiring for or through the federal government) and shall supersede any conflicting contractual terms or conditions. 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Revision History March 2013 Online only September 2013 Online only New for Version 4.0 (R2013a) Revised for Version 4.1 (R2013b) www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان Contents Property Reference 1 fi Object Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . bin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . dec . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . double . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . fimath . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . hex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . NumericType . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . oct . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-2 1-2 1-2 1-2 1-2 1-2 1-3 1-3 1-3 fimath Object Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . CastBeforeSum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . MaxProductWordLength . . . . . . . . . . . . . . . . . . . . . . . . . . . MaxSumWordLength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . OverflowAction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ProductBias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ProductFixedExponent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ProductFractionLength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ProductMode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ProductSlope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ProductSlopeAdjustmentFactor . . . . . . . . . . . . . . . . . . . . . . ProductWordLength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . RoundingMethod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SumBias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SumFixedExponent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SumFractionLength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SumMode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SumSlope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SumSlopeAdjustmentFactor . . . . . . . . . . . . . . . . . . . . . . . . . SumWordLength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-4 1-4 1-4 1-4 1-4 1-5 1-5 1-5 1-5 1-7 1-7 1-7 1-8 1-8 1-8 1-9 1-9 1-11 1-11 1-11 fipref Object Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . DataTypeOverride . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . DataTypeOverrideAppliesTo . . . . . . . . . . . . . . . . . . . . . . . . FimathDisplay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-12 1-12 1-12 1-12 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان iii iv Contents LoggingMode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . NumericTypeDisplay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . NumberDisplay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-13 1-13 1-14 numerictype Object Properties . . . . . . . . . . . . . . . . . . . . . Bias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . DataType . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . DataTypeMode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . DataTypeOverride . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . FixedExponent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . FractionLength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Signed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Signedness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Slope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SlopeAdjustmentFactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . WordLength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-15 1-15 1-15 1-15 1-16 1-16 1-17 1-17 1-17 1-18 1-18 1-19 1-19 quantizer Object Properties . . . . . . . . . . . . . . . . . . . . . . . . DataMode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . OverflowAction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . RoundingMethod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-20 1-20 1-20 1-21 1-22 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان Functions — Alphabetical List 2 Glossary Selected Bibliography A Index www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان v ﻣﺘﻠﺐ ﺳﺎﯾﺖ | www.MatlabSite.com ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان Contents vi 1 Property Reference • “fi Object Properties” on page 1-2 • “fimath Object Properties” on page 1-4 • “fipref Object Properties” on page 1-12 • “numerictype Object Properties” on page 1-15 • “quantizer Object Properties” on page 1-20 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 1 Property Reference fi Object Properties The properties associated with fi objects are described in the following sections in alphabetical order. Note The fimath properties and numerictype properties are also properties of the fi object. Refer to “fimath Object Properties” on page 1-4 and “numerictype Object Properties” on page 1-15 for more information. bin Stored integer value of a fi object in binary. data Numerical real-world value of a fi object. dec Stored integer value of a fi object in decimal. double Real-world value of a fi object stored as a MATLAB® double. fimath fimath properties associated with a fi object. fimath properties determine the rules for performing fixed-point arithmetic operations on fi objects. fi objects get their fimath properties from a local fimath object or from default values. The factory-default fimath values have the following settings: RoundingMethod: OverflowAction: ProductMode: SumMode: 1-2 Nearest Saturate FullPrecision FullPrecision www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان fi Object Properties To learn more about fimath objects, refer to “fimath Object Construction”. For more information about each of the fimath object properties, refer to “fimath Object Properties”. hex Stored integer value of a fi object in hexadecimal. NumericType The numerictype object contains all the data type and scaling attributes of a fixed-point object. The numerictype object behaves like any MATLAB structure, except that it only lets you set valid values for defined fields. For a table of the possible settings of each field of the structure, see “Valid Values for numerictype Structure Properties” in the Fixed-Point Designer™ User’s Guide. Note You cannot change the numerictype properties of a fi object after fi object creation. oct Stored integer value of a fi object in octal. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 1-3 1 Property Reference fimath Object Properties The properties associated with fimath objects are described in the following sections in alphabetical order. CastBeforeSum Whether both operands are cast to the sum data type before addition. Possible values of this property are 1 (cast before sum) and 0 (do not cast before sum). The MATLAB factory default value of this property is 1 (true). This property is hidden when the SumMode is set to FullPrecision. MaxProductWordLength Maximum allowable word length for the product data type. The MATLAB factory default value of this property is 65535. MaxSumWordLength Maximum allowable word length for the sum data type. The MATLAB factory default value of this property is 65535. OverflowAction Overflow-handling action. The value of the OverflowAction property can be one of the following strings: • Saturate — Saturate to maximum or minimum value of the fixed-point range on overflow. • Wrap — Wrap on overflow. This mode is also known as two’s complement overflow. The MATLAB factory default value of this property is Saturate. 1-4 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان fimath Object Properties ProductBias Bias of the product data type. This value can be any floating-point number. The product data type defines the data type of the result of a multiplication of two fi objects. The MATLAB factory default value of this property is 0. ProductFixedExponent Fixed exponent of the product data type. This value can be any positive or negative integer. The product data type defines the data type of the result of a multiplication of two fi objects. ProductSlope = ProductSlopeAdjustmentFactor × 2 ProductFixedExponent . Changing one of these properties changes the others. The ProductFixedExponent is the negative of the ProductFractionLength. Changing one property changes the other. The MATLAB factory default value of this property is -30. ProductFractionLength Fraction length, in bits, of the product data type. This value can be any positive or negative integer. The product data type defines the data type of the result of a multiplication of two fi objects. The ProductFractionLength is the negative of the ProductFixedExponent. Changing one property changes the other. The MATLAB factory default value of this property is 30. ProductMode Defines how the product data type is determined. In the following descriptions, let A and B be real operands, with [word length, fraction length] pairs [Wa Fa] and [Wb Fb], respectively. Wp is the product data type word length and Fp is the product data type fraction length. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 1-5 1 Property Reference • FullPrecision — The full precision of the result is kept. An error is generated if the calculated word length is greater than MaxProductWordLength. Wp = Wa + Wb Fp = Fa + Fb • KeepLSB — Keep least significant bits. You specify the product data type word length, while the fraction length is set to maintain the least significant bits of the product. In this mode, full precision is kept, but overflow is possible. This behavior models the C language integer operations. Wp = specified in the ProductWordLength property Fp = Fa + Fb • KeepMSB — Keep most significant bits. You specify the product data type word length, while the fraction length is set to maintain the most significant bits of the product. In this mode, overflow is prevented, but precision may be lost. Wp = specified in the ProductWordLength property Fp = Wp − integer length where integer length = (Wa + Wb ) − ( Fa − Fb ) • SpecifyPrecision — You specify both the word length and fraction length of the product data type. Wp = specified in the ProductWordLength property Fp = specified in the ProductFractionLength property For [Slope Bias] math, you specify both the slope and bias of the product data type. S p = specified in the ProductSlope property B p = specified in the ProductBias property 1-6 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان fimath Object Properties [Slope Bias] math is only defined for products when ProductMode is set to SpecifyPrecision. The MATLAB factory default value of this property is FullPrecision. ProductSlope Slope of the product data type. This value can be any floating-point number. The product data type defines the data type of the result of a multiplication of two fi objects. ProductSlope = ProductSlopeAdjustmentFactor × 2 ProductFixedExponent . Changing one of these properties changes the others. The MATLAB factory default value of this property is 9.3132e-010. ProductSlopeAdjustmentFactor Slope adjustment factor of the product data type. This value can be any floating-point number greater than or equal to 1 and less than 2. The product data type defines the data type of the result of a multiplication of two fi objects. ProductSlope = ProductSlopeAdjustmentFactor × 2 ProductFixedExponent . Changing one of these properties changes the others. The MATLAB factory default value of this property is 1. ProductWordLength Word length, in bits, of the product data type. This value must be a positive integer. The product data type defines the data type of the result of a multiplication of two fi objects. The MATLAB factory default value of this property is 32. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 1-7 1 Property Reference RoundingMethod The rounding method. The value of the RoundingMethod property can be one of the following strings: • Ceiling — Round toward positive infinity. • Convergent — Round toward nearest. Ties round to the nearest even stored integer. This is the least biased rounding method provided by Fixed-Point Designer software. • Zero — Round toward zero. • Floor — Round toward negative infinity. • Nearest — Round toward nearest. Ties round toward positive infinity. • Round — Round toward nearest. Ties round toward negative infinity for negative numbers, and toward positive infinity for positive numbers. The MATLAB factory default value of this property is Nnearest. See “Rounding Methods” in the Fixed-Point Designer User’s Guide for more information. SumBias The bias of the sum data type. This value can be any floating-point number. The sum data type defines the data type of the result of a sum of two fi objects. The MATLAB factory default value of this property is 0. SumFixedExponent The fixed exponent of the sum data type. This value can be any positive or negative integer. The sum data type defines the data type of the result of a sum of two fi objects SumSlope = SumSlopeAdjustmentFactor × 2 SumFixedExponent . Changing one of these properties changes the others. 1-8 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان fimath Object Properties The SumFixedExponent is the negative of the SumFractionLength. Changing one property changes the other. The MATLAB factory default value of this property is -30. SumFractionLength The fraction length, in bits, of the sum data type. This value can be any positive or negative integer. The sum data type defines the data type of the result of a sum of two fi objects. The SumFractionLength is the negative of the SumFixedExponent. Changing one property changes the other. The MATLAB factory default value of this property is 30 . SumMode Defines how the sum data type is determined. In the following descriptions, let A and B be real operands, with [word length, fraction length] pairs [Wa Fa] and [Wb Fb], respectively. Ws is the sum data type word length and Fs is the sum data type fraction length. Note In the case where there are two operands, as in A + B, NumberOfSummands is 2, and ceil(log2(NumberOfSummands)) = 1. In sum(A) where A is a matrix, the NumberOfSummands is size(A,1). In sum(A) where A is a vector, the NumberOfSummands is length(A). • FullPrecision — The full precision of the result is kept. An error is generated if the calculated word length is greater than MaxSumWordLength. Ws = integer length + Fs where integer length = max ( Wa − Fa , Wb − Fb ) + ceil ( log 2 ( NumberOfSummands ) ) www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 1-9 1 Property Reference Fs = max( Fa , Fb ) • KeepLSB — Keep least significant bits. You specify the sum data type word length, while the fraction length is set to maintain the least significant bits of the sum. In this mode, full precision is kept, but overflow is possible. This behavior models the C language integer operations. Ws = specified in the SumWordLength property Fs = max( Fa , Fb ) • KeepMSB — Keep most significant bits. You specify the sum data type word length, while the fraction length is set to maintain the most significant bits of the sum and no more fractional bits than necessary. In this mode, overflow is prevented, but precision may be lost. Ws = specified in the SumWordLength property Fs = Ws − integer length where integer length = max ( Wa − Fa , Wb − Fb ) + ceil ( log 2 ( NumberOfSummands ) ) • SpecifyPrecision — You specify both the word length and fraction length of the sum data type. Ws = specified in the SumWordLength property Fs = specified in the SumFractionLength property For [Slope Bias] math, you specify both the slope and bias of the sum data type. Ss = specified in the SumSlope property Bs = specified in the Su umBias property [Slope Bias] math is only defined for sums when SumMode is set to SpecifyPrecision. The MATLAB factory default value of this property is FullPrecision. 1-10 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان fimath Object Properties SumSlope The slope of the sum data type. This value can be any floating-point number. The sum data type defines the data type of the result of a sum of two fi objects. SumSlope = SumSlopeAdjustmentFactor × 2 SumFixedExponent . Changing one of these properties changes the others. The MATLAB factory default value of this property is 9.3132e-010. SumSlopeAdjustmentFactor The slope adjustment factor of the sum data type. This value can be any floating-point number greater than or equal to 1 and less than 2. The sum data type defines the data type of the result of a sum of two fi objects. SumSlope = SumSlopeAdjustmentFactor × 2 SumFixedExponent . Changing one of these properties changes the others. The MATLAB factory default value of this property is 1. SumWordLength The word length, in bits, of the sum data type. This value must be a positive integer. The sum data type defines the data type of the result of a sum of two fi objects. The MATLAB factory default value of this property is 32. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 1-11 1 Property Reference fipref Object Properties The properties associated with fipref objects are described in the following sections in alphabetical order. DataTypeOverride Data type override options for fi objects • ForceOff — No data type override • ScaledDoubles — Override with scaled doubles • TrueDoubles — Override with doubles • TrueSingles — Override with singles Data type override only occurs when the fi constructor function is called. The default value of this property is ForceOff. DataTypeOverrideAppliesTo Data type override application to fi objects • AllNumericTypes — Apply data type override to all fi data types • Fixed-Point — Apply data type override only to fixed-point data types • Floating-Point — Apply data type override only to floating-point fi data types DataTypeOverrideAppliesTo displays only if DataTypeOverride is not set to ForceOff. The default value of this property is AllNumericTypes. FimathDisplay Display options for the fimath attributes of a fi object • full — Displays all of the fimath attributes of a fixed-point object 1-12 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان fipref Object Properties • none — None of the fimath attributes are displayed The default value of this property is full. LoggingMode Logging options for operations performed on fi objects • off — No logging • on — Information is logged for future operations Overflows and underflows for assignment, plus, minus, and multiplication operations are logged as warnings when LoggingMode is set to on. When LoggingMode is on, you can also use the following functions to return logged information about assignment and creation operations to the MATLAB command line: • maxlog — Returns the maximum real-world value • minlog — Returns the minimum value • noverflows — Returns the number of overflows • nunderflows — Returns the number of underflows LoggingMode must be set to on before you perform any operation in order to log information about it. To clear the log, use the function resetlog. The default value of this property of off. NumericTypeDisplay Display options for the numerictype attributes of a fi object • full — Displays all the numerictype attributes of a fixed-point object • none — None of the numerictype attributes are displayed. • short — Displays an abbreviated notation of the fixed-point data type and scaling of a fixed-point object in the format xWL,FL where www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 1-13 1 Property Reference - x is s for signed and u for unsigned. WL is the word length. FL is the fraction length. The default value of this property is full. NumberDisplay Display options for the value of a fi object • bin — Displays the stored integer value in binary format • dec — Displays the stored integer value in unsigned decimal format • RealWorldValue — Displays the stored integer value in the format specified by the MATLAB format function • hex — Displays the stored integer value in hexadecimal format • int — Displays the stored integer value in signed decimal format • none — No value is displayed. The default value of this property is RealWorldValue. In this mode, the value of a fi object is displayed in the format specified by the MATLAB format function: +, bank, compact, hex, long, long e, long g, loose, rat, short, short e, or short g. fi objects in rat format are displayed according to (2 1-14 1 fixed- point exponent ) × stored integer www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان numerictype Object Properties numerictype Object Properties This section describes the properties associated with numerictype objects. Bias The bias is part of the numerical representation used to interpret a fixed-point number. Along with the slope, the bias forms the scaling of the number. Fixed-point numbers can be represented as real-world value = (slope × stored integer) + bias where the slope can be expressed as slope = fractional slope × 2 fixed exponent DataType The possible value of the DataType property are: • boolean — Built-in MATLAB boolean data type • double — Built-in MATLAB double data type • Fixed — Fixed-point or integer data type • ScaledDouble — Scaled double data type • single — Built-in MATLAB single data type The default value of this property is Fixed. DataTypeMode Data type and scaling associated with the object. The possible values of this property are: • Boolean — Built-in boolean • Double — Built-in double www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 1-15 1 Property Reference • Fixed-point: binary point scaling — Fixed-point data type and scaling defined by the word length and fraction length • Fixed-point: slope and bias scaling — Fixed-point data type and scaling defined by the slope and bias • Fixed-point: unspecified scaling — Fixed-point data type with unspecified scaling • Scaled double: binary point scaling — Double data type with fixed-point word length and fraction length information retained • Scaled double: slope and bias scaling — Double data type with fixed-point slope and bias information retained • Scaled double: unspecified scaling — Double data type with unspecified fixed-point scaling • Single — Built-in single The default value of this property is Fixed-point: binary point scaling. DataTypeOverride Data type override for applying fipref data type override settings to fi objects. This property provides a convenient way to ignore a global fipref data type override setting. This property is not visible when its value is the default, Inherit. The possible values of this property are: • Inherit — fi object uses the fipref DataTypeOverride setting. • Off — fi object uses the numerictype data type settings and ignores fipref settings The default value of this property is Inherit. FixedExponent Fixed-point exponent associated with the object. The exponent is part of the numerical representation used to express a fixed-point number. Fixed-point numbers can be represented as real-world value = (slope × stored integer) + bias 1-16 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان numerictype Object Properties where the slope can be expressed as slope = fractional slope × 2 fixed exponent The exponent of a fixed-point number is equal to the negative of the fraction length: fixed exponent = − fraction length FixedExponent must an integer. FractionLength Fraction length of the stored integer value of the object, in bits. The fraction length can be any integer value. This property automatically defaults to the best precision possible based on the value of the word length and the real-world value of the fi object. Scaling Scaling mode of the object. The possible values of this property are: • BinaryPoint — Scaling for the fi object is defined by the fraction length. • SlopeBias — Scaling for the fi object is defined by the slope and bias. • Unspecified — A temporary setting that is only allowed at fi object creation, to allow for the automatic assignment of a binary point best-precision scaling. The default value of this property is BinaryPoint. Signed Whether the object is signed. The possible values of this property are: • 1 — signed • 0 — unsigned www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 1-17 1 Property Reference • true — signed • false — unsigned • [] — auto The default value of this property is true. Note Although the Signed property is still supported, the Signedness property always appears in the numerictype object display. If you choose to change or set the signedness of your numerictype objects using the Signed property, MATLAB updates the corresponding value of the Signedness property. Signedness Whether the object is signed, unsigned, or has an unspecified sign. The possible values of this property are: • Signed — signed • Unsigned — unsigned • Auto — unspecified sign The default value of this property is Signed. All numerictype object properties of a fi object must be specified at the time of fi object creation. If this property is set to Auto at the time of fi object creation, the property automatically defaults to Signed. Slope Slope associated with the object. The slope is part of the numerical representation used to express a fixed-point number. Along with the bias, the slope forms the scaling of a fixed-point number. Fixed-point numbers can be represented as real-world value = (slope × stored integer) + bias 1-18 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان numerictype Object Properties where the slope can be expressed as slope = fractional slope × 2 fixed exponent SlopeAdjustmentFactor Slope adjustment associated with the object. The slope adjustment is equivalent to the fractional slope of a fixed-point number. The fractional slope is part of the numerical representation used to express a fixed-point number. Fixed-point numbers can be represented as real-world value = (slope × stored integer) + bias where the slope can be expressed as slope = fractional slope × 2 fixed exponent SlopeAdjustmentFactor must be greater than or equal to 1 and less than 2. WordLength Word length of the stored integer value of the object, in bits. The word length can be any positive integer value. The default value of this property is 16. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 1-19 1 Property Reference quantizer Object Properties The properties associated with quantizer objects are described in the following sections in alphabetical order. DataMode Type of arithmetic used in quantization. This property can have the following values: • fixed — Signed fixed-point calculations • float — User-specified floating-point calculations • double — Double-precision floating-point calculations • single — Single-precision floating-point calculations • ufixed — Unsigned fixed-point calculations The default value of this property is fixed. When you set the DataMode property value to double or single, the Format property value becomes read only. Format Data format of a quantizer object. The interpretation of this property value depends on the value of the DataMode property. For example, whether you specify the DataMode property with fixed- or floating-point arithmetic affects the interpretation of the data format property. For some DataMode property values, the data format property is read only. The following table shows you how to interpret the values for the Format property value when you specify it, or how it is specified in read-only cases. 1-20 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان quantizer Object Properties DataMode Property Value fixed or ufixed Interpreting the Format Property Values You specify the Format property value as a vector. The number of bits for the quantizer object word length is the first entry of this vector, and the number of bits for the quantizer object fraction length is the second entry. The word length can range from 2 to the limits of memory on your PC. The fraction length can range from 0 to one less than the word length. float You specify the Format property value as a vector. The number of bits you want for the quantizer object word length is the first entry of this vector, and the number of bits you want for the quantizer object exponent length is the second entry. The word length can range from 2 to the limits of memory on your PC. The exponent length can range from 0 to 11. double The Format property value is specified automatically (is read only) when you set the DataMode property to double. The value is [64 11], specifying the word length and exponent length, respectively. single The Format property value is specified automatically (is read only) when you set the DataMode property to single. The value is [32 8], specifying the word length and exponent length, respectively. OverflowAction Overflow-handling mode. The value of the OverflowAction property can be one of the following strings: • Saturate — Overflows saturate. When the values of data to be quantized lie outside the range of the largest and smallest representable numbers (as specified by the data format properties), these values are quantized to the value of either the largest or smallest representable value, depending on which is closest. • Wrap — Overflows wrap to the range of representable values. When the values of data to be quantized lie outside the range of the largest and smallest representable numbers (as specified by the data format www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 1-21 1 Property Reference properties), these values are wrapped back into that range using modular arithmetic relative to the smallest representable number. The default value of this property is Saturate. Note Floating-point numbers that extend beyond the dynamic range overflow to ±inf. The OverflowMode property value is set to saturate and becomes a read-only property when you set the value of the DataMode property to float, double, or single. RoundingMethod Rounding method. The value of the RoundingMethod property can be one of the following strings: • Ceiling — Round up to the next allowable quantized value. • Convergent — Round to the nearest allowable quantized value. Numbers that are exactly halfway between the two nearest allowable quantized values are rounded up only if the least significant bit (after rounding) would be set to 0. • Zero — Round negative numbers up and positive numbers down to the next allowable quantized value. • Floor — Round down to the next allowable quantized value. • Nearest — Round to the nearest allowable quantized value. Numbers that are halfway between the two nearest allowable quantized values are rounded up. The default value of this property is Floor. 1-22 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2 Functions — Alphabetical List www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان abs Purpose Absolute value of fi object Syntax c c c c Description c = abs(a) returns the absolute value of fi object a with the same numerictype object as a. Intermediate quantities are calculated using the fimath associated with a. The output fi object c has the same local fimath as a. = = = = abs(a) abs(a,T) abs(a,F) abs(a,T,F) c = abs(a,T) returns a fi object with a value equal to the absolute value of a and numerictype object T. Intermediate quantities are calculated using the fimath associated with a and the output fi object c has the same local fimath as a. See “Data Type Propagation Rules” on page 2-3. c = abs(a,F) returns a fi object with a value equal to the absolute value of a and the same numerictype object as a. Intermediate quantities are calculated using the fimath object F. The output fi object c has no local fimath. c = abs(a,T,F) returns a fi object with a value equal to the absolute value of a and the numerictype object T. Intermediate quantities are calculated using the fimath object F. The output fi object c has no local fimath. See “Data Type Propagation Rules” on page 2-3. Note When the Signedness of the input numerictype object T is Auto, the abs function always returns an Unsigned fi object. abs only supports fi objects with [Slope Bias] scaling when the bias is zero and the fractional slope is one. abs does not support complex fi objects of data type Boolean. When the object a is real and has a signed data type, the absolute value of the most negative value is problematic since it is not representable. 2-2 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان abs In this case, the absolute value saturates to the most positive value representable by the data type if the OverflowMode property is set to saturate. If OverflowMode is wrap, the absolute value of the most negative value has no effect. Data Type Propagation Rules For syntaxes for which you specify a numerictype object T, the abs function follows the data type propagation rules listed in the following table. In general, these rules can be summarized as “floating-point data types are propagated.” This allows you to write code that can be used with both fixed-point and floating-point inputs. Data Type of Input fi Object a Data Type of numerictype object T Data Type of Output c fi Fixed fi Fixed Data type of numerictype object T fi ScaledDouble fi Fixed ScaledDouble with properties of numerictype object T Examples fi double fi Fixed fi double fi single fi Fixed fi single Any fi data type fi double fi double Any fi data type fi single fi single Example 1 The following example shows the difference between the absolute value results for the most negative value representable by a signed data type when OverflowMode is saturate or wrap. P = fipref('NumericTypeDisplay','full',... 'FimathDisplay','full'); a = fi(-128) www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-3 abs a = -128 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 16 8 abs(a) ans = 127.9961 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 16 8 a.OverflowMode = 'wrap' a = -128 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 16 8 RoundingMethod: OverflowAction: ProductMode: SumMode: Nearest Wrap FullPrecision FullPrecision abs(a) 2-4 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان abs ans = -128 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 16 8 RoundingMethod: OverflowAction: ProductMode: SumMode: Nearest Wrap FullPrecision FullPrecision Example 2 The following example shows the difference between the absolute value results for complex and real fi inputs that have the most negative value representable by a signed data type when OverflowMode is wrap. re = fi(-1,1,16,15) re = -1 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 16 15 im = fi(0,1,16,15) im = 0 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-5 abs DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 16 15 a = complex(re,im) a = -1 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 16 15 abs(a,re.numerictype,fimath('OverflowMode','wrap')) ans = 1.0000 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 16 15 abs(re,re.numerictype,fimath('OverflowMode','wrap')) ans = -1 DataTypeMode: Fixed-point: binary point scaling Signedness: Signed WordLength: 16 2-6 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان abs FractionLength: 15 Example 3 The following example shows how to specify numerictype and fimath objects as optional arguments to control the result of the abs function for real inputs. When you specify a fimath object as an argument, that fimath object is used to compute intermediate quantities, and the resulting fi object has no local fimath. a = fi(-1,1,6,5,'OverflowMode','wrap') a = -1 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 6 5 RoundingMethod: OverflowAction: ProductMode: SumMode: Nearest Wrap FullPrecision FullPrecision DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 6 5 abs(a) ans = -1 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-7 abs RoundingMethod: OverflowAction: ProductMode: SumMode: Nearest Wrap FullPrecision FullPrecision f = fimath('OverflowMode','saturate') f = RoundingMethod: OverflowAction: ProductMode: SumMode: Nearest Wrap FullPrecision FullPrecision abs(a,f) ans = 0.9688 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 6 5 t = numerictype(a.numerictype, 'Signed', false) t = DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Unsigned 6 5 abs(a,t,f) 2-8 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان abs ans = 1 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Unsigned 6 5 Example 4 The following example shows how to specify numerictype and fimath objects as optional arguments to control the result of the abs function for complex inputs. a = fi(-1-i,1,16,15,'OverflowMode','wrap') a = -1.0000 - 1.0000i DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 16 15 RoundingMethod: OverflowAction: ProductMode: SumMode: Nearest Wrap FullPrecision FullPrecision t = numerictype(a.numerictype,'Signed',false) t = www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-9 abs DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Unsigned 16 15 abs(a,t) ans = 1.4142 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Unsigned 16 15 RoundingMethod: OverflowAction: ProductMode: SumMode: Nearest Wrap FullPrecision FullPrecision f = fimath('OverflowMode','saturate','SumMode',... 'keepLSB','SumWordLength',a.WordLength,... 'ProductMode','specifyprecision',... 'ProductWordLength',a.WordLength,... 'ProductFractionLength',a.FractionLength) f = RoundingMethod: OverflowAction: ProductMode: ProductWordLength: ProductFractionLength: SumMode: 2-10 Nearest Saturate SpecifyPrecision 16 15 KeepLSB www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان abs SumWordLength: 16 CastBeforeSum: true abs(a,t,f) ans = 1.4142 DataTypeMode: Signedness: WordLength: FractionLength: Algorithms Fixed-point: binary point scaling Unsigned 16 15 The absolute value y of a real input a is defined as follows: y = a if a >= 0 y = -a if a < 0 The absolute value y of a complex input a is related to its real and imaginary parts as follows: y = sqrt(real(a)*real(a) + imag(a)*imag(a)) The abs function computes the absolute value of complex inputs as follows: 1 Calculate the real and imaginary parts of a using the following equations: re = real(a) im = imag(a) 2 Compute the squares of re and im using one of the following objects: www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-11 abs • The fimath object F if F is specified as an argument. • The fimath associated with a if F is not specified as an argument. 3 Cast the squares of re and im to unsigned types if the input is signed. 4 Add the squares of re and im using one of the following objects: • The fimath object F if F is specified as an argument. • The fimath object associated with a if F is not specified as an argument. 5 Compute the square root of the sum computed in step four using the sqrt function with the following additional arguments: • The numerictype object T if T is specified, or the numerictype object of a otherwise. • The fimath object F if F is specified, or the fimath object associated with a otherwise. Note Step three prevents the sum of the squares of the real and imaginary components from being negative. This is important because if either re or im has the maximum negative value and the OverflowMode property is set to wrap then an error will occur when taking the square root in step five. 2-12 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان accumneg Purpose Subtract two fi objects or values Syntax c = accumneg(a,b) c = accumneg(a,b,RoundingMethod) c = accumneg(a,b,RoundingMethod,OverflowAction) Description c = accumneg(a,b) subtracts b from a using a’s data type. b is cast into a’s data type. If a is a fi object, the default 'Floor' rounding method and default 'Wrap' overflow action are used. The fimath properties of a and b are ignored. c = accumneg(a,b,RoundingMethod) uses the rounding method specified in RoundingMethod. c = accumneg(a,b,RoundingMethod,OverflowAction) uses the overflow action specified in OverflowAction. Input Arguments a Number from which to subtract. a can be fi object or double, single, logical, or integer value. The data type of a is used to compute the output data type. b Number to subtract. b can be fi object or double, single, logical, or integer value. . RoundingMethod Rounding method to use if a is a fi object. Valid values are 'Ceiling', 'Convergent', 'Floor', 'Nearest', 'Round' and 'Zero'. Default: Floor OverflowAction Overflow action to take if a is a fi object. Valid values are 'Saturate' and 'Wrap', www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-13 accumneg Default: Wrap Output Arguments c Examples Subtract fi numbers using default accumneg settings and then, using non-default rounding method and overflow action. Result of subtracting input b from input a. a = fi(pi,1,16,13); b = fi(1.5,1,16,14); subtr_default = accumneg(a,b); subtr_custom = accumneg(a,b,'Nearest','Saturate'); 2-14 See Also accumpos Related Examples • “Avoid Multiword Operations in Generated Code” www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان accumpos Purpose Add two fi objects or values Syntax c = accumpos(a,b) c = accumpos(a,b,RoundingMethod) c = accumpos(a,b,RoundingMethod,OverflowAction) Description c = accumpos(a,b) adds a and b using the a’s data type. b is cast into a’s data type. If a is a fi object, the default 'Floor' rounding method and default 'Wrap' overflow action are used. The fimath properties of a and b are ignored. c = accumpos(a,b,RoundingMethod) uses the rounding method specified in RoundingMethod. c = accumpos(a,b,RoundingMethod,OverflowAction) uses the overflow action specified in OverflowAction. Input Arguments a Number to add. a can be fi object or double, single, logical, or integer value. The data type of a is used to compute the output data type. b Number to add. b can be fi object or double, single, logical, or integer value. RoundingMethod Rounding method to use if a is a fi object. Valid values are 'Ceiling', 'Convergent', 'Floor', 'Nearest', 'Round', and 'Zero'. Default: Floor OverflowAction Overflow action to take if a is a fi object. Valid values are 'Saturate' and 'Wrap'. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-15 accumpos Default: Wrap Output Arguments c Examples Add two fi numbers using default accumpos settings and then, using nondefault rounding method and overflow action. Result of adding the a and b inputs. a = fi(pi,1,16,13); b = fi(1.5,1,16,14); add_default = accumpos(a,b); add_custom = accumpos(a,b,'Nearest','Saturate'); 2-16 See Also accumneg Related Examples • “Avoid Multiword Operations in Generated Code” www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان add Purpose Add two objects using fimath object Syntax c = F.add(a,b) Description c = F.add(a,b) adds objects a and b using fimath object F. This is helpful in cases when you want to override the fimath objects of a and b, or if the fimath properties associated with a and b are different. The output fi object c has no local fimath. a and b must both be fi objects and must have the same dimensions unless one is a scalar. If either a or b is scalar, then c has the dimensions of the nonscalar object. Examples In this example, c is the 32-bit sum of a and b with fraction length 16: a = fi(pi); b = fi(exp(1)); F = fimath('SumMode','SpecifyPrecision',... 'SumWordLength',32,'SumFractionLength',16); c = F.add(a,b) c = 5.8599 DataTypeMode: Signedness: WordLength: FractionLength: Algorithms Fixed-point: binary point scaling Signed 32 16 c = F.add(a,b) is similar to a.fimath = F; b.fimath = F; c = a + b c = www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-17 add 5.8599 DataTypeMode: Signedness: WordLength: FractionLength: RoundMode: OverflowMode: ProductMode: MaxProductWordLength: SumMode: SumWordLength: SumFractionLength: CastBeforeSum: Fixed-point: binary point scaling Signed 32 16 nearest saturate FullPrecision 128 SpecifyPrecision 32 16 true but not identical. When you use add, the fimath properties of a and b are not modified, and the output fi object c has no local fimath. When you use the syntax c = a + b, where a and b have their own fimath objects, the output fi object c gets assigned the same fimath object as inputs a and b. See “fimath Rules for Fixed-Point Arithmetic” in the Fixed-Point Designer User’s Guide for more information. See Also 2-18 divide | fi | fimath | mpy | mrdivide | numerictype | rdivide | sub | sum www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان all Purpose Determine whether all array elements are nonzero Description Refer to the MATLAB all reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-19 and 2-20 Purpose Find logical AND of array or scalar inputs Description Refer to the MATLAB and reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان any Purpose Determine whether any array elements are nonzero Description Refer to the MATLAB any reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-21 area 2-22 Purpose Create filled area 2-D plot Description Refer to the MATLAB area reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان assignmentquantizer Purpose Assignment quantizer object of fi object Syntax q = assignmentquantizer(a) Description q = assignmentquantizer(a) returns the quantizer object q that is used in assignment operations for the fi object a. See Also quantize | quantizer www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-23 atan2 Purpose Four-quadrant inverse tangent of fixed-point values Syntax z = atan2(y,x) Description z = atan2(y,x) returns the four-quadrant arctangent of fi input y/x Input Arguments y,x using a table-lookup algorithm. y and x can be real-valued, signed or unsigned scalars, vectors, matrices, or N-dimensional arrays containing fixed-point angle values in radians. The lengths of y and x must be the same. If they are not the same size, at least one input must be a scalar value. Valid data types of y and x are: • fi single • fi double • fi fixed-point with binary point scaling • fi scaled double with binary point scaling Output Arguments z z is the four-quadrant arctangent of y/x. The numerictype of z depends on the signedness of y and x: • If either y or x is signed, z is a signed, fixed-point number in the range [–pi,pi]. It has a 16-bit word length and 13-bit fraction length (numerictype(1,16,13)). • If both y and x are unsigned, z is an unsigned, fixed-point number in the range [0,pi/2]. It has a 16-bit word length and 15-bit fraction length (numerictype(0,16,15)). This arctangent calculation is accurate only to within the top 16 most-significant bits of the input. 2-24 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان atan2 Definitions Four-Quadrant Arctangent The four-quadrant arctangent is defined as follows, with respect to the atan function: y atan x y atan x y atan2( y, x) atan x 2 2 0 Examples x0 y 0, x 0 y 0, x 0 y 0, x 0 y 0, x 0 y 0, x 0 Calculate the arctangent of unsigned and signed fixed-point input values. The first example uses unsigned, 16-bit word length values. The second example uses signed, 16-bit word length values. y = fi(0.125,0,16); x = fi(0.5,0,16); z = atan2(y,x) z = 0.2450 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Unsigned 16 15 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-25 atan2 y = fi(-0.1,1,16); x = fi(-0.9,1,16); z = atan2(y,x) z = -3.0309 DataTypeMode: Signedness: WordLength: FractionLength: Algorithms Fixed-point: binary point scaling Signed 16 13 The atan2 function computes the four-quadrant arctangent of fixed-point inputs using an 8-bit lookup table as follows: 1 Divide the input absolute values to get an unsigned, fractional, fixed-point, 16-bit ratio between 0 and 1. The absolute values of y and x determine which value is the divisor. The signs of the y and x inputs determine in what quadrant their ratio lies. The input with the larger absolute value is used as the demoninator, thus producing a value between 0 and 1. 2-26 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان atan2 2 Compute the table index, based on the 16-bit, unsigned, stored integer value: a Use the 8 most-significant bits to obtain the first value from the table. b Use the next-greater table value as the second value. 3 Use the 8 least-significant bits to interpolate between the first and second values using nearest neighbor linear interpolation. This interpolation produces a value in the range [0, pi/4). 4 Perform octant correction on the resulting angle, based on the values of the original y and x inputs. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-27 atan2 sin | angle | cos ﻣﺘﻠﺐ ﺳﺎﯾﺖ | www.MatlabSite.com ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان See Also 2-28 autofixexp Purpose Automatically change scaling of fixed-point data types Syntax autofixexp Description The autofixexp script automatically changes the scaling for model objects that specify fixed-point data types. However, if an object’s Lock output data type setting against changes by the fixed-point tools parameter is selected, the script refrains from scaling that object. This script collects range data for model objects, either from design minimum and maximum values that objects specify explicitly, or from logged minimum and maximum values that occur during simulation. Based on these values, the tool changes the scaling of fixed-point data types in a model so as to maximize precision and cover the range. You can specify design minimum and maximum values for model objects using parameters typically titled Output minimum and Output maximum. See “Blocks That Allow Signal Range Specification” for a list of Simulink® blocks that permit you to specify these values. In the autoscaling procedure that the autofixexp script executes, design minimum and maximum values take precedence over the simulation range. If you intend to scale fixed-point data types using simulation minimum and maximum values, the script yields meaningful results when exercising the full range of values over which your design is meant to run. Therefore, the simulation you run prior to using autofixexp must simulate your design over its full intended operating range. It is especially important that you use simulation inputs with appropriate speed and amplitude profiles for dynamic systems. The response of a linear dynamic system is frequency dependent. For example, a bandpass filter will show almost no response to very slow and very fast sinusoid inputs, whereas the signal of a sinusoid input with a frequency in the passband will be passed or even significantly amplified. The response of nonlinear dynamic systems can have complicated dependence on both the signal speed and amplitude. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-29 autofixexp Note If you already know the simulation range you need to cover, you can use an alternate autoscaling technique described in the fixptbestprec reference page. To control the parameters associated with automatic scaling, such as safety margins, use the Fixed-Point Tool. For more information, see “Fixed-Point Tool”. To learn how to use the Fixed-Point Tool, refer to “Propose Fraction Lengths Using Simulation Range Data”. See Also 2-30 fxptdlg www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان bar Purpose Create vertical bar graph Description Refer to the MATLAB bar reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-31 barh 2-32 Purpose Create horizontal bar graph Description Refer to the MATLAB barh reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان bin Purpose Binary representation of stored integer of fi object Syntax bin(a) Description bin(a) returns the stored integer of fi object a in unsigned binary format as a string. bin(a) is equivalent to a.bin. Fixed-point numbers can be represented as real-world value = 2− fraction length × stored integer or, equivalently as real-world value = (slope × stored integer) + bias The stored integer is the raw binary number, in which the binary point is assumed to be at the far right of the word. Examples The following code a = fi([-1 1],1,8,7); y = bin(a) z = a.bin returns y = 10000000 01111111 z = 10000000 See Also 01111111 dec | hex | storedInteger | oct www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-33 bin2num Purpose Convert two’s complement binary string to number using quantizer object Syntax y = bin2num(q,b) Description y = bin2num(q,b) uses the properties of quantizer object q to convert binary string b to numeric array y. When b is a cell array containing binary strings, y is a cell array of the same dimension containing numeric arrays. The fixed-point binary representation is two’s complement. The floating-point binary representation is in IEEE® Standard 754 style. bin2num and num2bin are inverses of one another. Note that num2bin always returns the strings in a column. Examples Create a quantizer object and an array of numeric strings. Convert the numeric strings to binary strings, then use bin2num to convert them back to numeric strings. q=quantizer([4 3]); [a,b]=range(q); x=(b:-eps(q):a)'; b = num2bin(q,x) b = 0111 0110 0101 0100 0011 0010 0001 0000 1111 1110 1101 2-34 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان bin2num 1100 1011 1010 1001 1000 bin2num performs the inverse operation of num2bin. y=bin2num(q,b) y = 0.8750 0.7500 0.6250 0.5000 0.3750 0.2500 0.1250 0 -0.1250 -0.2500 -0.3750 -0.5000 -0.6250 -0.7500 -0.8750 -1.0000 See Also hex2num | num2bin | num2hex | num2int www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-35 bitand Purpose Bitwise AND of two fi objects Syntax c = bitand(a, b) Description c = bitand(a, b) returns the bitwise AND of fi objects a and b. The numerictype properties associated with a and b must be identical. If both inputs have a local fimath object, the fimath objects must be identical. If the numerictype is signed, then the bit representation of the stored integer is in two’s complement representation. a and b must have the same dimensions unless one is a scalar. bitand only supports fi objects with fixed-point data types. See Also 2-36 bitcmp | bitget | bitor | bitset | bitxor www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان bitandreduce Purpose Bitwise AND operation of consecutive range of bits Syntax c = bitandreduce(a) c = bitandreduce(a, lidx) c = bitandreduce(a, lidx, ridx) Description c = bitandreduce(a) performs a bitwise AND operation on the entire set of bits in the fixed-point input, a, and returns the result as an unsigned integer of word length 1. c = bitandreduce(a, lidx) performs a bitwise AND operation on a consecutive range of bits, starting at position lidx and ending at the LSB (the bit at position 1). c = bitandreduce(a, lidx, ridx) performs a bitwise AND operation on a consecutive range of bits, starting at position lidx and ending at position ridx. The bitandreduce arguments must satisfy the following condition: a.WordLength >= lidx >= ridx >= 1 Input Arguments a - Input array scalar | vector | matrix | multidimensional array Input array, specified as a scalar, vector, matrix, or multidimensional array of fi objects. bitandreduce supports both signed and unsigned inputs with arbitrary scaling. The sign and scaling properties do not affect the result type and value. bitandreduce performs the operation on a two’s complement bit representation of the stored integer. Data Types: fixed-point fi lidx - Start position of range scalar www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-37 bitandreduce Start position of range specified as a scalar of built-in type. lidx represents the position in the range closest to the MSB. Data Types: fi|single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 ridx - End position of range scalar End position of range specified as a scalar of built-in type. ridx represents the position in the range closest to the LSB (the bit at position 1). Data Types: fi|single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 Output Arguments c - Output array scalar | vector | matrix | multidimensional array Output array, specified as a scalar, vector, matrix, or multidimensional array of fixed-point fi objects. c is unsigned with word length 1. Examples Perform Bitwise AND Operation on an Entire Set of Bits Create a fixed-point number. a = fi(73,0,8,0); disp(bin(a)) 01001001 Perform a bitwise AND operation on the entire set of bits in a. c=bitandreduce(a) c = 0 DataTypeMode: Fixed-point: binary point scaling 2-38 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان bitandreduce Signedness: Unsigned WordLength: 1 FractionLength: 0 Because the bits of a do not all have a value of 1, the output has a value of 0. Perform Bitwise AND Operation on a Range of Bits in a Vector Create a fixed-point vector. a=fi([12,4,8,15],0,8,0); disp(bin(a)) 00001100 00000100 00001000 00001111 Perform a bitwise AND operation on the bits of each element of a, starting at position fi(4). c=bitandreduce(a,fi(4)) c = 0 0 0 1 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Unsigned 1 0 The only entry in output c with a value of 1 is the 4th entry. This is because only entry 4 of a had only 1’s between positions fi(4) and 1. Perform Bitwise AND Operation on a Range of Bits in a Matrix Create a fixed-point matrix. a=fi([7,8,1;5,9,5;8,37,2],0,8,0); www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-39 bitandreduce disp(bin(a)) 00000111 00000101 00001000 00001000 00001001 00100101 00000001 00000101 00000010 Perform a bitwise AND operation on the bits of each element of matrix a beginning at position 3 and ending at position 1. c=bitandreduce(a,3,1) c = 1 0 0 0 0 0 0 0 0 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Unsigned 1 0 There is only one entry in output c with a value of 1. This condition occurs because the corresponding entry in a is the only entry with only 1’s between positions 3 and 1. See Also 2-40 bitconcat | bitorreduce | bitsliceget | bitxorreduce www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان bitcmp Purpose Bitwise complement of fi object Syntax c = bitcmp(a) Description c = bitcmp(a) returns the bitwise complement of fi object a. If a has a signed numerictype, the bit representation of the stored integer is in two’s complement representation. bitcmp only supports fi objects with fixed-point data types. a can be a scalar fi object or a vector fi object. Examples This example shows how to get the bitwise complement of a fi object. Consider the following unsigned fixed-point fi object with a value of 10, word length 4, and fraction length 0: a = fi(10,0,4,0); disp(bin(a)) 1010 Complement the values of the bits in a: c = bitcmp(a); disp(bin(c)) 0101 See Also bitand | bitget | bitor | bitset | bitxor www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-41 bitconcat Purpose Concatenate bits of fi objects Syntax y = bitconcat(a) y = bitconcat (a, b, ...) Description y = bitconcat(a) concatenates the bits of the elements of fixed-point fi input array, a. y = bitconcat (a, b, ...) concatenates the bits of the fixed–point fi inputs. Input Arguments a - Input array scalar | vector | matrix | multidimensional array Input array, specified as a scalar, vector, matrix, or multidimensional array of fixed-point fi objects. When a is the only input, length(a) must be greater than 1. bitconcat accepts varargin number of inputs for concatenation. Data Types: fixed-point fi b - Input array scalar | vector | matrix | multidimensional array Input array, specified as a scalar, vector, matrix, or multidimensional array of fixed-point fi objects. If b is nonscalar, it must have the same dimension as the other inputs. Data Types: fixed-point fi Output Arguments y - Output array scalar | vector | matrix | multidimensional array Output array, specified as a scalar, vector, matrix, or multidimensional array of unsigned fixed-point fi objects. The output array has word length equal to the sum of the word lengths of the inputs and a fraction length of zero. The bit representation of the 2-42 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان bitconcat stored integer is in two’s complement representation. Scaling does not affect the result type and value. If the inputs are all scalar, then bitconcat concatenates the bits of the inputs and returns a scalar. If the inputs are all arrays of the same size, then bitconcat performs element-wise concatenation of the bits and returns an array of the same size. Examples Concatenate the Elements of a Vector Create a fixed-point vector. a=fi([1,2,5,7],0,4,0); disp(bin(a)) 0001 0010 0101 0111 Concatenate the bits of the elements of a. y=bitconcat(a) y = 4695 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Unsigned 16 0 disp(bin(y)) 0001001001010111 The WordLength of output, y, equals the sum of the word lengths of each element of a. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-43 bitconcat Concatenate the Bits of Two fi Objects Create two fixed-point numbers. a = fi(5,0,4,0); disp(bin(a)) 0101 b = fi(10,0,4,0); disp(bin(b)) 1010 Concatenate the bits of the two inputs. y = bitconcat(a,b) y = 90 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Unsigned 8 0 disp(bin(y)) 01011010 The output, y, is unsigned with WordLength equal to the sum of the word lengths of the two inputs, and a fraction length of 0. Perform Element-by-Element Concatenation of Two Vectors When a and b are both vectors of the same size, bitconcat performs element-wise concatenation of the two vectors and returns a vector. Create two fixed-point vectors of the same size. 2-44 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان bitconcat a=fi([1,2,5,7],0,4,0); disp(bin(a)) 0001 0010 0101 0111 b=fi([7,4,3,1],0,4,0); disp(bin(b)) 0111 0100 0011 0001 Concatenate the elements of a and b. y=bitconcat(a,b) y = 23 36 83 113 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Unsigned 8 0 disp(bin(y)) 00010111 00100100 01010011 01110001 The output, y, is a vector of the same length as the input vectors, and with WordLength equal to the sum of the word lengths of the two input vectors. Perform Element-by-Element Concatenation of Two Matrices When the inputs are both matrices of the same size, bitconcat performs element-wise concatenation of the two matrices and returns a matrix of the same size. Create two fixed-point matrices. a=fi([1 2 5;7 4 5;3 1 12],0,4,0); www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-45 bitconcat disp(bin(a)) 0001 0111 0011 0010 0100 0001 0101 0101 1100 b=fi([6 1 7;7 8 1; 9 7 8],0,4,0); disp(bin(b)) 0110 0111 1001 0001 1000 0111 0111 0001 1000 Perform element-by-element concatenation of the bits of a and b. y=bitconcat(a,b) y = 22 119 57 33 72 23 87 81 200 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Unsigned 8 0 disp(bin(y)) 00010110 01110111 00111001 00100001 01001000 00010111 01010111 01010001 11001000 The output, y, is a matrix with WordLength equal to the sum of the word lengths of a and b. 2-46 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان bitconcat See Also bitand | bitcmp | bitor | bitreplicate | bitget | bitset | bitsliceget | bitxor www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-47 bitget Purpose Get bits at certain positions Syntax c = bitget(a, bit) Description c = bitget(a, bit) returns the values of the bits at positions bit in a Input Arguments a - Input array as unsigned integers of word length 1. scalar | vector | matrix | multidimensional array Input array, specified as a scalar, vector, matrix, or multidimensional array of fixed-point fi objects. If a and bit are both nonscalar, they must have the same dimension. If a has a signed numerictype, the bit representation of the stored integer is in two’s complement representation. Data Types: fixed-point fi bit - Bit index scalar | vector | matrix | multidimensional array Bit index, specified as a scalar, vector, matrix or multidimensional array of built-in data types. If a and bit are both nonscalar, they must have the same dimension. bit must contain integer values between 1 and the word length of a, inclusive. bit does not need to be a vector of sequential bit positions; it can also be a variable index value. Data Types: fi|single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 Output Arguments c - Output array scalar | vector | matrix | multidimensional array Output array, specified as an unsigned scalar, vector, matrix, or multidimensional array with WordLength 1. If a is an array and bit is a scalar, c is an unsigned array with word length 1. This unsigned array comprises the values of the bits at position bit in each fixed-point element in a. 2-48 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان bitget If a is a scalar and bit is an array, c is an unsigned array with word length 1. This unsigned array comprises the values of the bits in a at the positions specified in bit. Examples Get Bit When Input and Index Are Both Scalar Consider the following unsigned fixed-point fi number with a value of 85, word length 8, and fraction length 0: a = fi(85,0,8,0); disp(bin(a)) 01010101 Get the binary representation of the bit at position 4: c = bitget(a,4); c = 0 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Unsigned 1 0 MATLAB returns the bit at position 4 in the binary representation of a. Get Bit When Input Is a Matrix and the Index Is a fi Begin with a signed fixed-point 3-by-3 matrix with word length 4 and fraction length 0. a=fi([2 3 4;6 8 2;3 5 1],0,4,0); disp(bin(a)) 0010 0110 0011 1000 0100 0010 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-49 bitget 0011 0101 0001 Get the binary representation of the bits at a specified position. c=bitget(a,fi(2)) c = 1 1 1 1 0 0 0 1 0 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Unsigned 1 0 MATLAB returns a matrix of the bits in position fi(2) of a. The output matrix has the same dimensions as a, and WordLength 1. Get Bit When Both Input and Index Are Vectors Begin with a signed fixed-point vector with word length 16, fraction length 4: a=fi([86 6 53 8 1],0,16,4); disp(bin(a)) 0000010101100000 0000000001100000 0000001101010000 0000000010000000 Create a vector that specifies the positions of the bits you want to get. bit=[1, 2, 5, 7, 4] bit = 1 2-50 2 5 7 4 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان bitget Get the binary representation of the bits of a at the positions specified in bit. c=bitget(a,bit); c = 0 0 1 0 DataTypeMode: Signedness: WordLength: FractionLength: 0 Fixed-point: binary point scaling Unsigned 1 0 MATLAB returns a vector of the bits of a at the positions specified in bit. The output vector has the same length as inputs, a and bit, and WordLength 1. Get Bit When Input Is Scalar and Index Is a Vector Create a default fi object with a value of pi. a=fi(pi); disp(bin(a)) 0110010010001000 The default object is signed with a word length of 16. Create a vector of the positions of the bits you want to get in a, and get the binary representation of those bits. bit=fi([15,3,8,2]); c=bitget(a,bit) c = 1 0 1 0 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-51 bitget DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Unsigned 1 0 MATLAB returns a vector of the bits in a at the positions specified by the index vector, bit. See Also 2-52 bitand | bitcmp | bitor | bitset | bitxor www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان bitor Purpose Bitwise OR of two fi objects Syntax c = bitor(a,b) Description c = bitor(a,b) returns the bitwise OR of fi objects a and b. The output is determined as follows: • Elements in the output array c are assigned a value of 1 when the corresponding bit in either input array has a value of 1. • Elements in the output array c are assigned a value of 0 when the corresponding bit in both input arrays has a value of 0. The numerictype properties associated with a and b must be identical. If both inputs have a local fimath, their local fimath properties must be identical. If the numerictype is signed, then the bit representation of the stored integer is in two’s complement representation. a and b must have the same dimensions unless one is a scalar. bitor only supports fi objects with fixed-point data types. Examples The following example finds the bitwise OR of fi objects a and b. a = fi(-30,1,6,0); b = fi(12, 1, 6, 0); c = bitor(a,b) c = -18 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 6 0 You can verify the result by examining the binary representations of a, b and c. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-53 bitor binary_a = a.bin binary_b = b.bin binary_c = c.bin binary_a = 100010 binary_b = 001100 binary_c = 101110 See Also 2-54 bitand | bitcmp | bitget | bitset | bitxor www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان bitorreduce Purpose Bitwise OR operation of consecutive range of bits Syntax c = bitorreduce(a) c = bitorreduce(a, lidx) c = bitorreduce(a, lidx, ridx) Description c = bitorreduce(a) performs a bitwise OR operation on the entire set of bits in the fixed-point input, a, and returns the result as an unsigned integer of word length 1. c = bitorreduce(a, lidx) performs a bitwise OR operation on a consecutive range of bits, starting at position lidx and ending at the LSB (the bit at position 1). c = bitorreduce(a, lidx, ridx) performs a bitwise OR operation on a consecutive range of bits, starting at position lidx and ending at position ridx. The bitorreduce arguments must satisfy the following condition: a.WordLength >= lidx >= ridx >= 1 Input Arguments a - Input array scalar | vector | matrix | multidimensional array Input array, specified as a scalar, vector, matrix, or multidimensional array of fixed-point fi objects. bitorreduce supports both signed and unsigned inputs with arbitrary scaling. The sign and scaling properties do not affect the result type and value. bitorreduce performs the operation on a two’s complement bit representation of the stored integer. Data Types: fixed-point fi lidx - Start position of range scalar www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-55 bitorreduce Start position of range specified as a scalar of built-in type. lidx represents the position in the range closest to the MSB. Data Types: fi|single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 ridx - End position of range scalar End position of range specified as a scalar of built-in type. ridx represents the position in the range closest to the LSB (the bit at position 1). Data Types: fi|single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 Output Arguments c - Output array scalar | vector | matrix | multidimensional array Output array, specified as a scalar, vector, matrix, or multidimensional array of fixed-point fi objects. c is unsigned with word length 1. Examples Perform Bitwise OR Operation on an Entire Set of Bits Create a fixed-point number. a = fi(73,0,8,0); disp(bin(a)) 01001001 Perform a bitwise OR operation on the entire set of bits in a. c=bitorreduce(a) c = 1 DataTypeMode: Fixed-point: binary point scaling 2-56 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان bitorreduce Signedness: Unsigned WordLength: 1 FractionLength: 0 Because there is at least one bit in a with a value of 1, the output has a value of 1 . Perform Bitwise OR Operation on a Range of Bits in a Vector Create a fixed-point vector. a=fi([12,4,8,15],0,8,0); disp(bin(a)) 00001100 00000100 00001000 00001111 Perform a bitwise OR operation on the bits of each element of a, starting at position fi(4). c=bitorreduce(a,fi(4)) c = 1 1 1 1 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Unsigned 1 0 All of the entries of output c have a value of 1 because all of the entries of a have at least one bit with a value of 1 between the positions fi(4) and 1. Perform Bitwise OR Operation on a Range of Bits in a Matrix Create a fixed-point matrix. a=fi([7,8,1;5,9,5;8,37,2],0,8,0); disp(bin(a)) www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-57 bitorreduce 00000111 00000101 00001000 00001000 00001001 00100101 00000001 00000101 00000010 Perform a bitwise OR operation on the bits of each element of matrix a beginning at position 5, and ending at position 2. c=bitorreduce(a,5,2) c = 1 1 1 1 1 1 0 1 1 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Unsigned 1 0 There is only one entry in output c that does not have a value of 1. This condition occurs because the corresponding entry in a is the only entry of a that does not have any bits with a value of 1 between positions 5 and 2. See Also 2-58 bitandreduce | bitconcat | bitsliceget | bitxorreduce www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان bitreplicate Purpose Replicate and concatenate bits of fi object Syntax c = bitreplicate(a,n) Description c = bitreplicate(a,n) concatenates the bits in fi object a n times and returns an unsigned fixed-point value. The word length of the output fi object c is equal to n times the word length of a and the fraction length of c is zero. The bit representation of the stored integer is in two’s complement representation. The input fi object can be signed or unsigned. bitreplicate concatenates signed and unsigned bits the same way. bitreplicate only supports fi objects with fixed-point data types. bitreplicate does not support inputs with complex data types. Sign and scaling of the input fi object does not affect the result type and value. Examples The following example uses bitreplicate to replicate and concatenate the bits of fi object a. a = fi(14,0,6,0); a_binary = a.bin c = bitreplicate(a,2); c_binary = c.bin MATLAB returns the following: a_binary = 001110 c_binary = 001110001110 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-59 bitreplicate See Also 2-60 bitand | bitconcat | bitget | bitset | bitor | bitsliceget | bitxor www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان bitrol Purpose Bitwise rotate left Syntax c = bitrol(a, k) Description c = bitrol(a, k) returns the value of the fixed-point fi object, a, rotated left by k bits. bitrol rotates bits from the most significant bit (MSB) side into the least significant bit (LSB) side. It performs the rotate left operation on the stored integer bits of a. bitrol does not check overflow or underflow. It ignores fimath properties such as RoundingMode and OverflowAction. a and c have the same fimath and numerictype properties. Input Arguments a - Data that you want to rotate scalar | vector | matrix | multidimensional array Data that you want to rotate, specified as a scalar, vector, matrix, or multidimensional array of fi objects. a can be signed or unsigned. Data Types: fixed-point fi Complex Number Support: Yes k - Number of bits to rotate non-negative, integer-valued scalar Number of bits to rotate, specified as a non-negative integer-valued scalar fi object or built-in numeric type. k can be greater than the word length of a. This value is always normalized to mod(a.WordLength,k). Data Types: fi |single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 Examples Rotate the Bits of a fi Object Left Create an unsigned fixed-point fi object with a value of 10, word length 4, and fraction length 0. a = fi(10,0,4,0); www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-61 bitrol disp(bin(a)) 1010 Rotate a left 1 bit. disp(bin(bitrol(a,1))) 0101 Rotate a left 2 bits. disp(bin(bitrol(a,2))) 1010 Rotate Bits in a Vector Left Create a vector of fi objects. a=fi([1,2,5,7],0,4,0) disp(bin(a)) 0001 0010 0101 0111 Rotate the bits in vector a left 1 bit. disp(bin(bitrol(a,1))) 0010 0100 1010 1110 Rotate Bits Left Using fi to Specify Number of Bits to Rotate Create an unsigned fixed-point fi object with a value 5, word length 4, and fraction length 0. a = fi(10,0,4,0); disp(bin(a)) 1010 2-62 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان bitrol Rotate a left 1 bit where k is a fi object. disp(bin(bitrol(a,fi(1)))) 0101 See Also bitconcat | bitror | bitshift | bitsliceget | bitsll | bitsra | bitsrl www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-63 bitror Purpose Bitwise rotate right Syntax c = bitror(a, k) Description c = bitror(a, k) returns the value of the fixed-point fi object, a, rotated right by k bits. bitror rotates bits from the least significant bit (LSB) side into the most significant bit (MSB) side. It performs the rotate right operation on the stored integer bits of a. bitror does not check overflow or underflow. It ignores fimath properties such as RoundingMode and OverflowAction. a and c have the same fimath and numerictype properties. Input Arguments a - Data that you want to rotate scalar | vector | matrix | multidimensional array Data that you want to rotate, specified as a scalar, vector, matrix, or multidimensional array of fi objects. a can be signed or unsigned. Data Types: fixed-point fi Complex Number Support: Yes k - Number of bits to rotate non-negative, integer-valued scalar Number of bits to rotate, specified as a non-negative integer-valued scalar fi object or built-in numeric type. k can be greater than the word length of a. This value is always normalized to mod(a.WordLength,k). Data Types: fi |single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 Examples Rotate Bits of a fi Object Right Create an unsigned fixed-point fi object with a value 5, word length 4, and fraction length 0. a = fi(5,0,4,0); 2-64 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان bitror disp(bin(a)) 0101 Rotate a right 1 bit. disp(bin(bitror(a,1))) 1010 Rotate a right 2 bits. disp(bin(bitror(a,2))) 0101 Rotate Bits in a Vector Right Create a vector of fi objects. a=fi([1,2,5,7],0,4,0); disp(bin(a)) 0001 0010 0101 0111 Rotate the bits in vector a right 1 bit. disp(bin(bitror(a,fi(1)))) 1000 0001 1010 1011 Rotate Bits Right Using fi to Specify Number of Bits to Rotate Create an unsigned fixed-point fi object with a value 5, word length 4, and fraction length 0. a = fi(5,0,4,0); disp(bin(a)) 0101 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-65 bitror Rotate a right 1 bit where k is a fi object. disp(bin(bitror(a,fi(1)))) 1010 See Also 2-66 bitrol | bitconcat | bitshift | bitsliceget | bitsll | bitsra | bitsrl www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان bitset Purpose Set bits at certain positions Syntax c = bitset(a, bit) c = bitset(a, bit, v) Description c = bitset(a, bit) returns the value of a with position bit set to 1 (on). c = bitset(a, bit, v) returns the value of a with position bit set to v. Input Arguments a - Input array scalar | vector | matrix | multidimensional array Input array, specified as a scalar, vector, matrix, or multidimensional array of fixed-point fi objects. If a has a signed numerictype, the bit representation of the stored integer is in two’s complement representation. Data Types: fixed-point fi bit - Bit index scalar | vector | matrix | multidimensional array Bit index, specified as a scalar, vector, matrix, or multidimensional array of built-in data types. bit must be a number between 1 and the word length of a, inclusive. Data Types: fi|single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 v - Bit value scalar | vector | matrix | multidimensional array Bit value of a at index bit, specified as a scalar, vector, matrix, or multidimensional array of built-in data types. v can have values of 0, or 1. Any value other than 0 is automatically set to 1. When v is nonscalar, it must have the same dimensions as one of the other inputs. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-67 bitset Data Types: fi|single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 Output Arguments c - Output array scalar | vector | matrix | multidimensional array Output array, specified as a scalar, vector, matrix, or multidimensional array of fi objects. Examples Set the Bit at a Certain Position Begin with an unsigned fixed-point fi number with a value of 5, word length 4, and fraction length 0. a = fi(5,0,4,0); disp(bin(a)) 0101 Set the bit at position 4 to 1 (on). c = bitset(a,4); disp(bin(c)) 1101 Set the Bit at a Certain Position in a Vector Consider the following fixed-point vector with word length 4 and fraction length 0. a = fi([0 1 8 2 4],0,4,0); disp(bin(a)) 0000 0001 1000 0010 0100 In each element of vector a, set the bits at position 2 to 1. c = bitset(a,2,1); disp(bin(c)) 2-68 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان bitset 0010 0011 1010 0010 0110 Set the Bit at a Certain Position with Fixed Point Index Consider the following fixed-point scalar with a value of 5. a = fi(5,0,4,0); disp(bin(a)) 0101 Set the bit at position fi(2) to 1. c = bitset(a,fi(2),1); disp(bin(c)) 0111 Set the Bit When Index Is a Vector Create a fi object with a value of pi. a=fi(pi); disp(bin(a)) 0110010010001000 In this case, a is signed with a word length of 16. Create a vector of the bit positions in a that you want to set to on. Then, get the binary representation of the resulting fi vector. bit=fi([15,3,8,2]); c=bitset(a,bit); disp(bin(c)) 0110010010001000 See Also 0110010010001100 0110010010001000 0110010010001 bitand | bitcmp | bitget | bitor | bitxor www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-69 bitshift Purpose Shift bits specified number of places Syntax c = bitshift(a, k) Description c = bitshift(a, k) returns the value of a shifted by k bits. The input fi object a may be a scalar value or a vector and can be any fixed-point numeric type. The output fi object c has the same numeric type as a. k must be a scalar value and a MATLAB built-in numeric type. The OverflowAction property of a is obeyed, but the RoundingMethod is always Floor. If obeying the RoundingMethod property of a is important, try using the pow2 function. When the overflow action is Saturate the sign bit is always preserved. The sign bit is also preserved when the overflow action is Wrap, and k is negative. When the overflow action is Wrap and k is positive, the sign bit is not preserved. • When k is positive, 0-valued bits are shifted in on the right. • When k is negative, and a is unsigned, or a signed and positive fi object, 0-valued bits are shifted in on the left. • When k is negative and a is a signed and negative fi object, 1-valued bits are shifted in on the left. Examples This example highlights how changing the OverflowAction property of the fimath object can change the results returned by the bitshift function. Consider the following signed fixed-point fi object with a value of 3, word length 16, and fraction length 0: a = fi(3,1,16,0); By default, the OverflowAction fimath property is Saturate. When a is shifted such that it overflows, it is saturated to the maximum possible value: for k=0:16,b=bitshift(a,k);... disp([num2str(k,'%02d'),'. ',bin(b)]);end 2-70 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان bitshift 00. 01. 02. 03. 04. 05. 06. 07. 08. 09. 10. 11. 12. 13. 14. 15. 16. 0000000000000011 0000000000000110 0000000000001100 0000000000011000 0000000000110000 0000000001100000 0000000011000000 0000000110000000 0000001100000000 0000011000000000 0000110000000000 0001100000000000 0011000000000000 0110000000000000 0111111111111111 0111111111111111 0111111111111111 Now change OverflowAction to Wrap. In this case, most significant bits shift off the “top” of a until the value is zero: a = fi(3,1,16,0,'OverflowAction','Wrap'); for k=0:16,b=bitshift(a,k);... disp([num2str(k,'%02d'),'. ',bin(b)]);end 00. 01. 02. 03. 04. 05. 06. 07. 08. 09. 10. 11. 0000000000000011 0000000000000110 0000000000001100 0000000000011000 0000000000110000 0000000001100000 0000000011000000 0000000110000000 0000001100000000 0000011000000000 0000110000000000 0001100000000000 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-71 bitshift 12. 13. 14. 15. 16. See Also 2-72 0011000000000000 0110000000000000 1100000000000000 1000000000000000 0000000000000000 bitand | bitcmp | bitget | bitor | bitset | bitsll | bitsra | bitsrl | bitxor | pow2 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان bitsliceget Purpose Get consecutive slice of bits Syntax c = bitsliceget(a) c = bitsliceget(a, lidx) c = bitsliceget(a, lidx, ridx) Description c = bitsliceget(a) returns the entire set of bits in the fixed-point input a. c = bitsliceget(a, lidx) returns a consecutive slice of bits from a, starting at position lidx and ending at the LSB (the bit at position 1). c = bitsliceget(a, lidx, ridx) returns a consecutive slice of bits from a, starting at position lidx and ending at position ridx. The bitsliceget arguments must satisfy the following condition: a.WordLength >= lidx >= ridx >= 1 Input Arguments a - Input array scalar | vector | matrix | multidimensional array Input array, specified as a scalar, vector, matrix, or multidimensional array of fixed-point fi objects. If a has a signed numerictype, the bit representation of the stored integer is in two’s complement representation. Data Types: fixed-point fi lidx - Start position for slice scalar Start position of slice specified as a scalar of built-in type. lidx represents the position in the slice closest to the MSB. Data Types: fi|single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-73 bitsliceget ridx - End position for slice scalar End position of slice specified as a scalar of built-in type. ridx represents the position in the slice closest to the LSB (the bit at position 1). Data Types: fi|single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 Output Arguments c - Output array scalar | vector | matrix | multidimensional array Fixed-point fi output, specified as a scalar, vector, matrix, or multidimensional array with no scaling. The word length is equal to slice length, lidx-ridx+1. If lidx and ridx are equal, bitsliceget only slices one bit, and bitsliceget(a, lidx, ridx) is the same as bitget(a, lidx). Examples Get Entire Set of Bits Begin with the following fixed-point number. a=fi(85,0,8,0); disp(bin(a)) 01010101 Get the entire set of bits of a. c = bitsliceget(a); disp(bin(c)) 01010101 Get a Slice of Consecutive Bits with Unspecified Endpoint Begin with the following fixed-point number. 2-74 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان bitsliceget a = fi(85,0,8,0); disp(bin(a)) 01010101 Get the binary representation of the consecutive bits, starting at position 6. c = bitsliceget(a,6); disp(bin(c)) 010101 Get a Slice of Consecutive Bits with Fixed-Point Indexes Begin with the following fixed-point number. a = fi(85,0,8,0); disp(bin(a)) 01010101 Get the binary representation of the consecutive bits from fi(6) to fi(2). c = bitsliceget(a,fi(6),fi(2)); disp(bin(c)) 01010 Get a Specified Set of Consecutive Bits from Each Element of a Matrix Begin with the following unsigned fixed-point 3-by-3 matrix. a=fi([2 3 4;6 8 2;3 5 1],0,4,0); disp(bin(a)) 0010 0110 0011 1000 0100 0010 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-75 bitsliceget 0011 0101 0001 Get the binary representation of a consecutive set of bits of matrix a. For each element, start at position 4 and end at position 2. c = bitsliceget(a, 4, 2); disp(bin(c)) 001 011 001 See Also 2-76 001 100 010 010 001 000 bitand | bitcmp | bitget | bitor | bitset | bitxor www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان bitsll Purpose Bit shift left logical Syntax c = bitsll(a, k) Description c = bitsll(a, k) returns the result of a logical left shift by k bits on input a for fixed-point operations. bitsll shifts zeros into the positions of bits that it shifts left. The function does not check overflow or underflow. For floating-point operations, bitsll performs a multiply by 2k. bitsll ignores fimath properties such as RoundingMode and OverflowAction. When a is a fi object, a and c have the same associated fimath and numerictype objects. Input Arguments a - Data that you want to shift scalar | vector | matrix | multidimensional array Data that you want to shift, specified as a scalar, vector, matrix, or multidimensional array of fi objects or built-in numeric types. Data Types: fi | single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 Complex Number Support: Yes k - Number of bits to shift non-negative integer-valued scalar Number of bits to shift, specified as a non-negative integer-valued scalar fi object or built-in numeric type. Data Types: fi | single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 Examples Shift Left a Signed fi Input Shift a signed fi input left by 1 bit. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-77 bitsll Create a fi object, and display its binary value. a = fi(10,0,4,0); disp(bin(a)) 1010 Shift a left by 1 bit, and display its binary value. disp(bin(bitsll(a,1))) 0100 Shift a left by 1 more bit. disp(bin(bitsll(a,2))) 1000 Shift Left Using a fi Shift Value Shift left a built-in int8 input using a fi shift value. k=fi(2); a = int8(16); bitsll(a,k) ans = 64 Shift Left a Built-in int8 Input Use bitsll to shift an int8 input left by 2 bits. a = int8(4); bitsll(a,2) ans = 16 2-78 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان bitsll Shift Left a Floating-Point Input Scale a floating-point double input by 23. a = double(16); bitsll(a,3) ans = 128 See Also bitsrl | bitsra | bitshift | pow2 | bitconcat | bitrol | bitror www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-79 bitsra Purpose Bit shift right arithmetic Syntax c=bitsra(a,k) Description c=bitsra(a,k) returns the result of an arithmetic right shift by k bits on input a for fixed-point operations. For floating-point operations, it performs a multiply by 2-k. If the input is unsigned, bitsra shifts zeros into the positions of bits that it shifts right. If the input is signed, bitsra shifts the most significant bit (MSB) into the positions of bits that it shifts right. bitsra ignores fimath properties such as RoundingMode and OverflowAction. When a is a fi object, a and c have the same associated fimath and numerictype objects. Input Arguments a - Data that you want to shift scalar | vector | matrix | multidimensional array Data that you want to shift, specified as a scalar, vector, matrix, or multidimensional array of fi objects or built-in numeric types. Data Types: fi |single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 Complex Number Support: Yes k - Number of bits to shift non-negative integer-valued scalar Number of bits to shift, specified as a non-negative integer-valued scalar fi object or built-in numeric type. Data Types: fi |single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 2-80 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان bitsra Examples Shift Right a Signed fi Input Create a signed fixed-point fi object with a value of –8, word length 4, and fraction length 0. Then display the binary value of the object. a = fi(-8,1,4,0); disp(bin(a)) 1000 Shift a right by 1 bit. disp(bin(bitsra(a,1))) 1100 bitsra shifts the MSB into the position of the bit that it shifts right. Shift Right a Built-in int8 Input Use bitsra to shift an int8 input right by 2 bits. a = int8(64); bitsra(a,2) ans = 16 Shift Right Using a fi Shift Value Shift right a built-in int8 input using a fi shift value. k=fi(2); a = int8(64); bitsra(a,k) ans = 16 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-81 bitsra Shift Right a Floating-Point Input Scale a floating-point double input by 2–3. a = double(128); bitsra(a,3) ans = 16 See Also 2-82 bitsll | bitsrl | bitshift | pow2 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان bitsrl Purpose Bit shift right logical Syntax c = bitsrl(a, k) Description c = bitsrl(a, k) returns the result of a logical right shift by k bits on input a for fixed-point operations. bitsrl shifts zeros into the positions of bits that it shifts right. It does not check overflow or underflow. bitsrl ignores fimath properties such as RoundingMode and OverflowAction. When a is a fi object, a and c have the same associated fimath and numerictype objects. Input Arguments a - Data that you want to shift scalar | vector | matrix | multidimensional array Data that you want to shift, specified as a scalar, vector, matrix, or multidimensional array. Data Types: fi | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 Complex Number Support: Yes k - Number of bits to shift non-negative integer-valued scalar Number of bits to shift, specified as a non-negative integer-valued scalar. Data Types: fi|single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 Examples Shift Right a Signed fi Input Shift a signed fi input right by 1 bit. Create a signed fixed-point fi object with a value of –8, word length 4, and fraction length 0 and display its binary value. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-83 bitsrl a = fi(-8,1,4,0); disp(bin(a)) 1000 Shift a right by 1 bit, and display the binary value. disp(bin(bitsrl(a,1))) 0100 bitsrl shifts a zero into the position of the bit that it shifts right. Shift right using a fi shift value Shift right a built-in int8 input using a fi shift value. k=fi(2); a = int8(64); bitsrl(a,k) ans = 16 Shift right a built-in uint8 input Use bitsrl to shift an uint8 input right by 2 bits. a = uint8(64); bitsrl(a,2) ans = 16 See Also 2-84 bitconcat | bitrol | bitror | bitshift | bitsliceget | bitsll | bitsra | pow2 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان bitxor Purpose Bitwise exclusive OR of two fi objects Syntax c = bitxor(a,b) Description c = bitxor(a,b) returns the bitwise exclusive OR of fi objects a and b. The output is determined as follows: • Elements in the output array c are assigned a value of 1 when exactly one of the corresponding bits in the input arrays has a value of 1. • Elements in the output array c are assigned a value of 0 when the corresponding bits in the input arrays have the same value (e.g. both 1’s or both 0’s). The numerictype properties associated with a and b must be identical. If both inputs have a local fimath, their local fimath properties must be identical. If the numerictype is signed, then the bit representation of the stored integer is in two’s complement representation. a and b must have the same dimensions unless one is a scalar. bitxor only supports fi objects with fixed-point data types. Examples The following example finds the bitwise exclusive OR of fi objects a and b. a = fi(-28,1,6,0); b = fi(12, 1, 6, 0); c = bitxor(a,b) c = -24 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 6 0 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-85 bitxor You can verify the result by examining the binary representations of a, b and c. binary_a = a.bin binary_b = b.bin binary_c = c.bin binary_a = 100100 binary_b = 001100 binary_c = 101000 See Also 2-86 bitand | bitcmp | bitget | bitor | bitset www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان bitxorreduce Purpose Bitwise exclusive OR operation of consecutive range of bits Syntax c = bitxorreduce(a) c = bitxorreduce(a, lidx) c = bitxorreduce(a, lidx, ridx) Description c = bitxorreduce(a) performs a bitwise exclusive OR operation on the entire set of bits in the fixed-point input, a. It returns the result as an unsigned integer of word length 1. c = bitxorreduce(a, lidx) performs a bitwise exclusive OR operation on a consecutive range of bits. This operation starts at position lidx and ends at the LSB (the bit at position 1). c = bitxorreduce(a, lidx, ridx) performs a bitwise exclusive OR operation on a consecutive range of bits, starting at position lidx and ending at position ridx. The bitxorreduce arguments must satisfy the following condition: a.WordLength >= lidx >= ridx >= 1 Input Arguments a - Input array scalar | vector | matrix | multidimensional array Input array, specified as a scalar, vector, matrix, or multidimensional array of fixed-point fi objects. bitxorreduce supports both signed and unsigned inputs with arbitrary scaling. The sign and scaling properties do not affect the result type and value. bitxorreduce performs the operation on a two’s complement bit representation of the stored integer. Data Types: fixed-point fi lidx - Start position of range scalar www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-87 bitxorreduce Start position of range specified as a scalar of built-in type. lidx represents the position in the range closest to the MSB. Data Types: fi | single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 ridx - End position of range scalar End position of range specified as a scalar of built-in type. ridx represents the position in the range closest to the LSB (the bit at position 1). Data Types: fi|single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 Output Arguments c - Output array scalar | vector | matrix | multidimensional array Output array, specified as a scalar, vector, matrix, or multidimensional array of fixed-point fi objects. c is unsigned with word length 1. Examples Perform Bitwise Exclusive OR Operation on an Entire Set of Bits Create a fixed-point number. a = fi(73,0,8,0); disp(bin(a)) 01001001 Perform a bitwise exclusive OR operation on the entire set of bits in a. c=bitxorreduce(a) c = 1 2-88 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان bitxorreduce DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Unsigned 1 0 Perform Bitwise Exclusive OR Operation on a Range of Bits in a Vector Create a fixed-point vector. a=fi([12,4,8,15],0,8,0); disp(bin(a)) 00001100 00000100 00001000 00001111 Perform a bitwise exclusive OR operation on the bits of each element of a, starting at position fi(4). c=bitxorreduce(a,fi(4)) c = 0 1 1 0 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Unsigned 1 0 Perform a Bitwise Exclusive OR Operation on a Range of Bits in a Matrix Create a fixed-point matrix. a=fi([7,8,1;5,9,5;8,37,2],0,8,0); disp(bin(a)) 00000111 00000101 00001000 00001000 00001001 00100101 00000001 00000101 00000010 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-89 bitxorreduce Perform a bitwise exclusive OR operation on the bits of each element of matrix a beginning at position 5 and ending at position 2. c=bitxorreduce(a,5,2) c = 0 1 1 1 1 1 0 1 1 DataTypeMode: Signedness: WordLength: FractionLength: See Also 2-90 Fixed-point: binary point scaling Unsigned 1 0 bitandreduce | bitconcat | bitorreduce | bitsliceget www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان buffer Purpose Buffer signal vector into matrix of data frames Description Refer to the DSP System Toolbox™ buffer function reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-91 buildInstrumentedMex Purpose Generate compiled C code function including logging instrumentation Syntax buildInstrumentedMex fcn -options Description buildInstrumentedMex fcn -options translates the MATLAB file fcn.m to a MEX function and enables instrumentation for logging minimum and maximum values of all named and intermediate variables. Optionally, you can enable instrumentation for log2 histograms of all named, intermediate and expression values. Tips • Arrays of structures are not logged. Only scalar (1x1) structures are logged. • You cannot instrument MATLAB functions provided with the software. If your top-level function is such a MATLAB function, nothing is logged. You also cannot instrument scripts. • Instrumentation results are accumulated every time the instrumented MEX function is called. Use clearInstrumentationResults to clear previous results in the log. • Some coding patterns pass a significant amount of data, but only use a small portion of that data. In such cases, you may see degraded performance when using buildInstrumentedMex. In the following pattern, subfun only uses one element of input array, A. For normal execution, the amount of time to execute subfun once remians constant regardless of the size of A. The function topfun calls subfun N times, and thus the total time to execute topfun is proportional to N. When instrumented, however, the time to execute subfun once becomes proportional to N^2. This change occurs because the minimum and maximum data are calculated over the entire array. When A is large, the calculations can lead to significant performance degradation. Therefore, whenever possible, you should pass only the data that the function actually needs. function A = topfun(A) N = numel(A); for i=1:N 2-92 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان buildInstrumentedMex A(i) = subfun(A,i); end end function b = subfun(A,i) b = 0.5 * A(i); end function A = topfun(A) N = numel(A); for i=1:N A(i) = subfun(A(i)); end end function b = subfun(a) b = 0.5 * a; end Input Arguments fcn MATLAB function to be instrumented. fcn must be suitable for code generation. For more information, see “Making the MATLAB Code Suitable for Code Generation”. options Choice of compiler options. buildInstrumentedMex gives precedence to individual command-line options over options specified using a configuration object. If command-line options conflict, the rightmost option prevails. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-93 buildInstrumentedMex -args example_inputs Define the size, class, and complexity of all MATLAB function inputs. Use the values in example_inputs to define these properties. example_inputs must be a cell array that specifies the same number and order of inputs as the MATLAB function. -coder Use MATLAB Coder™ software to compile the MEX file, instead of the default Fixed-Point Designer fiaccel function. This option removes fiaccel restrictions and allows for full code generation support. You must have a MATLAB Coder license to use this option. -config config_object Specify MEX generation parameters, based on config_object, defined as a MATLAB variable using coder.mexconfig. For example: cfg = coder.mexconfig; -d out_folder Store generated files in the absolute or relative path specified by out_folder. If the folder specified by out_folder does not exist, buildInstrumentedMex creates it for you. If you do not specify the folder location, buildInstrumentedMex generates files in the default folder: 2-94 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان buildInstrumentedMex fiaccel/mex/fcn. fcn is the name of the MATLAB function specified at the command line. The function does not support the following characters in folder names: asterisk (*), question-mark (?), dollar ($), and pound (#). Compiles the MEX function in debug mode, with optimization turned off. If not specified, -g buildinstrumentedMex generates the MEX function in optimized mode. -global global_values Specify initial values for global variables in MATLAB file. Use the values in cell array global_values to initialize global variables in the function you compile. The cell array should provide the name and initial value of each global variable. You must initialize global variables before compiling with buildInstrumentedMex. If you do not provide initial values for global variables using the -global option, buildInstrumentedMex checks for the variable in the MATLAB global workspace. If you do not supply an initial www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-95 buildInstrumentedMex value, buildInstrumentedMex generates an error. The generated MEX code and MATLAB each have their own copies of global data. To ensure consistency, you must synchronize their global data whenever the two interact. If you do not synchronize the data, their global variables might differ. -histogram Compute the log2 histogram for all named, intermediate and expression values. A histogram column appears in the code generation report table. -I include_path Add include_path to the beginning of the code generation path. buildInstrumentedMex searches the code generation path first when converting MATLAB code to MEX code. -launchreport Generate and open a code generation report. If you do not specify this option, buildInstrumentedMex generates a report only if error or warning messages occur or you specify the -report option. 2-96 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان buildInstrumentedMex -o output_file_name Generate the MEX function with the base name output_file_name plus a platform-specific extension. output_file_name can be a file name or include an existing path. If you do not specify an output file name, the base name is fcn_mex, which allows you to run the original MATLAB function and the MEX function and compare the results. -O optimization_option Optimize generated MEX code, based on the value of optimization_option: • enable:inline — Enable function inlining • disable:inline — Disable function inlining If not specified, buildInstrumentedMex uses inlining for optimization. -report Examples Generate a code generation report. If you do not specify this option, buildInstrumentedMex generates a report only if error or warning messages occur or you specify the -launchreport option. Create an instrumented MEX function. Run a test bench, then view logged results. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-97 buildInstrumentedMex 1 Create a temporary directory, then import an example function from Fixed-Point Designer. tempdirObj=fidemo.fiTempdir('buildInstrumentedMex') copyfile(fullfile(matlabroot,'toolbox','fixedpoint',... 'fidemos','fi_m_radix2fft_withscaling.m'),... 'testfft.m','f') 2 Define prototype input arguments. n = 128; x = complex(zeros(n,1)); W = coder.Constant(fidemo.fi_radix2twiddles(n)); 3 Generate an instrumented MEX function. Use the -o option to specify the MEX function name. Use the -histogram option to compute histograms. (If you have a MATLAB Coder license, you may want to also add the -coder option. In this case, use buildInstrumentedMex testfft -coder -o testfft_instrumented -args {x,W} instead of the following line of code.) Note Like fiaccel, buildInstrumentedMex generates a MEX function. To generate C code, see the MATLAB Codercodegen function. buildInstrumentedMex testfft -o testfft_instrumented... -args {x,W} -histogram 4 Run a test file to record instrumentation results. Call showInstrumentationResults to open the Code Generation Report. View the simulation minimum and maximum values and whole number status by hovering over a variable in the report. You can also see proposed data types for double precision numbers in the table. for i=1:20 y = testfft_instrumented(randn(size(x))); 2-98 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان buildInstrumentedMex end showInstrumentationResults testfft_instrumented 5 View the histogram for a variable by clicking in the Variables tab. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-99 buildInstrumentedMex For information on the figure, refer to the NumericTypeScope reference page. 6 Close the histogram display and then, clear the results log. 2-100 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان buildInstrumentedMex clearInstrumentationResults testfft_instrumented; 7 Clear the MEX function, then delete temporary files. clear testfft_instrumented; tempdirObj.cleanUp; See Also fiaccel | clearInstrumentationResults | showInstrumentationResults | NumericTypeScope | codegen | mex www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-101 cast Purpose Cast variable to different data type Syntax b = cast(a,'like',p) Description b = cast(a,'like',p) converts a to the same numerictype, complexity (real or complex), and fimath as p. If a and p are both real, then b is also real. Otherwise, b is complex. Input Arguments a - Variable that you want to cast to a different data type fi object | numeric variable Variable, specified as a fi object or numeric variable. Complex Number Support: Yes p - Prototype fi object | numeric variable Prototype, specified as a fi object or numeric variable. To use the prototype to specify a complex object, you must specify a value for the prototype. Otherwise, you do not need to specify a value. Complex Number Support: Yes Tips Using the b = cast(a,'like',p) syntax to specify data types separately from algorithm code allows you to: • Reuse your algorithm code with different data types. • Keep your algorithm uncluttered with data type specifications and switch statements for different data types. • Improve readability of your algorithm code. • Switch between fixed-point and floating-point data types to compare baselines. • Switch between variations of fixed-point settings without changing the algorithm code. 2-102 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان cast Examples Convert an int8 Value to Fixed Point Define a scalar 8–bit integer. a = int8(5); Create a signed fi object with word length of 24 and fraction length of 12. p = fi([],1,24,12); Convert a to fixed point with numerictype, complexity (real or complex), and fimath of the specified fi object, p. b = cast(a, 'like', p) b = 5 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 24 12 Match Data Type and Complex Nature of p Define a complex fi object. p = fi( [1+2i 3i],1,24,12); Define a scalar 8–bit integer. a = int8(5); Convert a to the same data type and complexity as p. b = cast(a,'like',p) b = www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-103 cast 5.0000 + 0.0000i DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 24 12 Convert an Array to Fixed Point Define a 2-by-3 matrix of ones. A = ones(2,3); Create a signed fi object with word length of 16 and fraction length of 8. p = fi([],1,16,8); Convert A to the same data type and complexity (real or complex) as p. B = cast(A,'like',p) B = 1 1 1 1 1 1 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 16 8 Write MATLAB Code That Is Independent of Data Types Write a MATLAB algorithm that you can run with different data types without changing the algorithm itself. To reuse the algorithm, define the data types separately from the algorithm. This approach allows you to define a baseline by running the algorithm with floating-point data types. You can then test the algorithm with 2-104 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان cast different fixed-point data types and compare the fixed-point behavior to the baseline without making any modifications to the original MATLAB code. Write a MATLAB function, my_filter, that takes an input parameter, T, which is a structure that defines the data types of the coefficients and the input and output data. function [y,z] = my_filter(b,a,x,z,T) % Cast the coefficients to the coefficient type b = cast(b,'like',T.coeffs); a = cast(a,'like',T.coeffs); % Create the output using zeros with the data type y = zeros(size(x),'like',T.data); for i=1:length(x) y(i) = b(1)*x(i) + z(1); z(1) = b(2)*x(i) + z(2) - a(2) * y(i); z(2) = b(3)*x(i) - a(3) * y(i); end end Write a MATLAB function, zeros_ones_cast_example, that calls my_filter with a floating-point step input and a fixed-point step input, and then compares the results. function zeros_ones_cast_example % % b a Define coefficients for a filter with specification [b,a] = butter(2,0.25) = [0.097631072937818 0.195262145875635 0.097631072937818]; = [1.000000000000000 -0.942809041582063 0.333333333333333]; % Define floating-point types T_float.coeffs = double([]); T_float.data = double([]); % Create a step input using ones with the www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-105 cast % floating-point data type t = 0:20; x_float = ones(size(t),'like',T_float.data); % Initialize the states using zeros with the % floating-point data type z_float = zeros(1,2,'like',T_float.data); % Run the floating-point algorithm y_float = my_filter(b,a,x_float,z_float,T_float); % Define fixed-point types T_fixed.coeffs = fi([],true,8,6); T_fixed.data = fi([],true,8,6); % Create a step input using ones with the % fixed-point data type x_fixed = ones(size(t),'like',T_fixed.data); % Initialize the states using zeros with the % fixed-point data type z_fixed = zeros(1,2,'like',T_fixed.data); % Run the fixed-point algorithm y_fixed = my_filter(b,a,x_fixed,z_fixed,T_fixed); % Compare the results coder.extrinsic('clf','subplot','plot','legend'); clf subplot(211) plot(t,y_float,'co-',t,y_fixed,'kx-') legend('Floating-point output','Fixed-point output'); title('Step response'); subplot(212) plot(t,y_float - double(y_fixed),'rs-') legend('Error') figure(gcf) 2-106 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان cast end See Also ones | zeros | cast Related Examples • “Implement FIR Filter Algorithm for Floating-Point and Fixed-Point Types using cast and zeros” Concepts • “Command-Line Fixed-Point Conversion Workflow” • “Command-Line Fixed-Point Conversion Best Practices” www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-107 ceil Purpose Round toward positive infinity Syntax y = ceil(a) Description y = ceil(a) rounds fi object a to the nearest integer in the direction of positive infinity and returns the result in fi object y. y and a have the same fimath object and DataType property. When the DataType property of a is single, double, or boolean, the numerictype of y is the same as that of a. When the fraction length of a is zero or negative, a is already an integer, and the numerictype of y is the same as that of a. When the fraction length of a is positive, the fraction length of y is 0, its sign is the same as that of a, and its word length is the difference between the word length and the fraction length of a plus one bit. If a is signed, then the minimum word length of y is 2. If a is unsigned, then the minimum word length of y is 1. For complex fi objects, the imaginary and real parts are rounded independently. ceil does not support fi objects with nontrivial slope and bias scaling. Slope and bias scaling is trivial when the slope is an integer power of 2 and the bias is 0. Examples Example 1 The following example demonstrates how the ceil function affects the numerictype properties of a signed fi object with a word length of 8 and a fraction length of 3. a = fi(pi, 1, 8, 3) a = 3.1250 2-108 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان ceil DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 8 3 y = ceil(a) y = 4 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 6 0 Example 2 The following example demonstrates how the ceil function affects the numerictype properties of a signed fi object with a word length of 8 and a fraction length of 12. a = fi(0.025,1,8,12) a = 0.0249 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 8 12 y = ceil(a) y = www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-109 ceil 1 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 2 0 Example 3 The functions ceil, fix, and floor differ in the way they round fi objects: • The ceil function rounds values to the nearest integer toward positive infinity • The fix function rounds values toward zero • The floor function rounds values to the nearest integer toward negative infinity The following table illustrates these differences for a given fi object a. a See Also 2-110 ceil(a) fix(a) floor(a) – 2.5 –2 –2 –3 –1.75 –1 –1 –2 –1.25 –1 –1 –2 –0.5 0 0 –1 0.5 1 0 0 1.25 2 1 1 1.75 2 1 1 2.5 3 2 2 convergent | fix | floor | nearest | round www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان clabel Purpose Create contour plot elevation labels Description Refer to the MATLAB clabel reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-111 clearInstrumentationResults Purpose Clear results logged by instrumented, compiled C code function Syntax clearInstrumentationResults('mex_fcn') clearInstrumentationResults mex_fcn clearInstrumentationResults all Description clearInstrumentationResults('mex_fcn') clears the results logged from calling the instrumented MEX function mex_fcn. clearInstrumentationResults mex_fcn is alternative syntax for clearing the log. clearInstrumentationResults all clears the results from all instrumented MEX functions. Input Arguments mex_fcn Examples Run a test bench to log instrumentation, then use clearInstrumentationResults to clear the log. Instrumented MEX function created using buildInstrumentedMex. 1 Create a temporary directory, then import an example function from Fixed-Point Designer. tempdirObj=fidemo.fiTempdir('showInstrumentationResults') copyfile(fullfile(matlabroot,'toolbox','fixedpoint',... 'fidemos','fi_m_radix2fft_withscaling.m'),... 'testfft.m','f') 2 Define prototype input arguments. n = 128; x = complex(fi(zeros(n,1),'DataType','ScaledDouble')); W = coder.Constant(fi(fidemo.fi_radix2twiddles(n))); 3 Generate an instrumented MEX function. Use the -o option to specify the MEX function name. 2-112 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان clearInstrumentationResults buildInstrumentedMex testfft -o testfft_instrumented -args {x,W} 4 Run a test bench to record instrumentation results. Call showInstrumentationResults to open the Code Generation Report. View the simulation minimum and maximum values and whole number status by hovering over a variable in the report. for i=1:20 y = testfft_instrumented(cast(2*rand(size(x))-1,'like',x)); end showInstrumentationResults testfft_instrumented 5 Clear the results log. clearInstrumentationResults testfft_instrumented www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-113 clearInstrumentationResults 6 Run a different test bench, then view the new instrumentation results. for i=1:20 y = testfft_instrumented(cast(rand(size(x))-0.5,'like',x)); end showInstrumentationResults testfft_instrumented 7 Clear the MEX function and delete temporary files. clear testfft_instrumented; tempdirObj.cleanUp; 2-114 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان clearInstrumentationResults See Also fiaccel | showInstrumentationResults | buildInstrumentedMex | codegen | mex www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-115 coder.allowpcode Purpose Control code generation from protected MATLAB files Syntax coder.allowpcode('plain') Description coder.allowpcode('plain') allows you to generate protected MATLAB code (P-code) that you can then compile into optimized MEX functions or embeddable C/C++ code. This function does not obfuscate the generated MEX functions or embeddable C/C++ code. With this capability, you can distribute algorithms as protected P-files that provide code generation optimizations, providing intellectual property protection for your source MATLAB code. Call this function in the top-level function before control-flow statements, such as if, while, switch, and function calls. MATLAB functions can call P-code. When the .m and .p versions of a file exist in the same folder, the P-file takes precedence. coder.allowpcode is ignored outside of code generation. Examples Generate optimized embeddable code from protected MATLAB code: 1 Write an function p_abs that returns the absolute value of its input: function out = p_abs(in) %#codegen % The directive %#codegen indicates that the function % is intended for code generation coder.allowpcode('plain'); out = abs(in); 2 Generate protected P-code. At the MATLAB prompt, enter: pcode p_abs The P-file, p_abs.p, appears in the current folder. 2-116 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.allowpcode 3 Generate a MEX function for p_abs.p, using the -args option to specify the size, class, and complexity of the input parameter (requires a MATLAB Coder license). At the MATLAB prompt, enter: codegen p_abs -args { int32(0) } codegen generates a MEX function in the current folder. 4 Generate embeddable C code for p_abs.p (requires a MATLAB Coder license). At the MATLAB prompt, enter: codegen p_abs -config:lib -args { int32(0) }; codegen generates C library code in the codegen\lib\p_abs folder. See Also pcode | codegen www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-117 coder.ArrayType Purpose Represent set of MATLAB arrays Description Specifies the set of arrays that the generated code accepts. Use only with the fiaccel -args option. Do not pass as an input to a generated MEX function. Construction coder.ArrayType is an abstract class. You cannot create instances of it directly. You can create coder.EnumType, coder.FiType, coder.PrimitiveType, and coder.StructType objects that derive from this class. Properties ClassName Class of values in this set SizeVector The upper-bound size of arrays in this set. VariableDims A vector specifying whether each dimension of the array is fixed or variable size. If a vector element is true, the corresponding dimension is variable size. Copy Semantics 2-118 Value. To learn how value classes affect copy operations, see Copying Objects in the MATLAB documentation. | | | | | | | coder.Type | coder.EnumType | coder.FiType | coder.PrimitiveType | coder.StructType | coder.newtype | coder.typeof | coder.resize | | fiaccel www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.const Purpose Fold expressions into constants in generated code Syntax out = coder.const(expression) [out1,...,outN] = coder.const(handle,arg1,...,argN) Description out = coder.const(expression) evaluates expression and replaces out with the result of the evaluation in generated code. [out1,...,outN] = coder.const(handle,arg1,...,argN) evaluates the multi-output function having handle handle. It then replaces out1,...,outN with the results of the evaluation in the generated code. Input Arguments expression - MATLAB expression or user-written function Expression with constants | Single-output function with constant arguments MATLAB expression or user-defined single-output function. The expression must have compile-time constants only. The function must take constant arguments only. For instance, the following code leads to a code generation error, because x is not a compile-time constant. function y=func(x) y=coder.const(log10(x)); To fix the error, assign x to a constant in the MATLAB code. Alternatively, during code generation, you can use coder.Constant to define input type as follows: codegen -config:lib func -args coder.Constant(10) Example: 2*pi, factorial(10) handle - Function handle Function handle Handle to built-in or user-written function. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-119 coder.const Example: @log, @sin Data Types function_handle arg1,...,argN - Arguments to the function with handle handle Function arguments that are constants Arguments to the function with handle handle. The arguments must be compile-time constants. For instance, the following code leads to a code generation error, because x and y are not compile-time constants. function y=func(x,y) y=coder.const(@nchoosek,x,y); To fix the error, assign x and y to constants in the MATLAB code. Alternatively, during code generation, you can use coder.Constant to define input type as follows: codegen -config:lib func -args {coder.Constant(10),coder.Constant(2)} Output Arguments out - Value of expression Value of the evaluated expression Value of expression. In the generated code, MATLAB Coder replaces occurrences of out with the value of expression. out1,...,outN - Outputs of the function with handle handle Values of the outputs of the function with handle handle Outputs of the function with handle handle.MATLAB Coder evaluates the function and replaces occurrences of out1,...,outN with constants in the generated code. Examples Specify Constants in Generated Code This example shows how to specify constants in generated code using coder.const. 2-120 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.const Write a function AddShift that takes an input Shift and adds it to the elements of a vector. The vector consists of the square of the first 10 natural numbers. AddShift generates this vector. function y = AddShift(Shift) %#codegen y = (1:10).^2+Shift; Generate code for AddShift using the codegen command. Open the Code Generation Report. codegen -config:lib -launchreport AddShift -args 0 The code generation software generates code for creating the vector. It adds Shift to each element of the vector during vector creation. The definition of AddShift in generated code looks as follows: void AddShift(double Shift, double y[10]) { int k; for (k = 0; k < 10; k++) { y[k] = (double)((1 + k) * (1 + k)) + Shift; } } Replace the statement y = (1:10).^2+Shift; with y = coder.const((1:10).^2)+Shift; Generate code for AddShift using the codegen command. Open the Code Generation Report. codegen -config:lib -launchreport AddShift -args 0 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-121 coder.const The code generation software creates the vector containing the squares of the first 10 natural numbers. In the generated code, it adds Shift to each element of this vector. The definition of AddShift in generated code looks as follows: void AddShift(double Shift, double y[10]) { int i0; static const signed char iv0[10] = { 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 }; for (i0 = 0; i0 < 10; i0++) { y[i0] = (double)iv0[i0] + Shift; } } Create Lookup Table in Generated Code This example shows how to fold a user-written function into a constant in generated code. Write a function getsine that takes an input index and returns the element referred to by index from a lookup table of sines. The function getsine creates the lookup table using another function gettable. function y = getsine(index) %#codegen assert(isa(index, 'int32')); persistent tbl; if isempty(tbl) tbl = gettable(1024); end y = tbl(index); function y = gettable(n) y = zeros(1,n); for i = 1:n y(i) = sin((i-1)/(2*pi*n)); end 2-122 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.const Generate code for getsine using an argument of type int32. Open the Code Generation Report. codegen -config:lib -launchreport getsine -args int32(0) The generated code contains instructions for creating the lookup table. Replace the statement: tbl = gettable(1024); with: tbl = coder.const(gettable(1024)); Generate code for getsine using an argument of type int32. Open the Code Generation Report. The generated code contains the lookup table itself. coder.const forces the expression gettable(1024) to be evaluated during code generation. The generated code does not contain instructions for the evaluation. The generated code contains the result of the evaluation itself. Specify Constants in Generated Code Using Multi-Output Function This example shows how to specify constants in generated code using a multi-output function in a coder.const statement. Write a function MultiplyConst that takes an input factor and multiplies every element of two vectors vec1 and vec2 with factor. The function generates vec1 and vec2 using another function EvalConsts. function [y1,y2] = MultiplyConst(factor) %#codegen [vec1,vec2]=EvalConsts(pi.*(1./2.^(1:10)),2); y1=vec1.*factor; y2=vec2.*factor; function [f1,f2]=EvalConsts(z,n) www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-123 coder.const f1=z.^(2*n)/factorial(2*n); f2=z.^(2*n+1)/factorial(2*n+1); Generate code for MultiplyConst using the codegen command. Open the Code Generation Report. codegen -config:lib -launchreport MultiplyConst -args 0 The code generation software generates code for creating the vectors. Replace the statement [vec1,vec2]=EvalConsts(pi.*(1./2.^(1:10)),2); with [vec1,vec2]=coder.const(@EvalConsts,pi.*(1./2.^(1:10)),2); Generate code for MultiplyConst using the codegen command. Open the Code Generation Report. codegen -config:lib -launchreport MultiplyConst -args 0 The code generation software does not generate code for creating the vectors. Instead, it calculates the vectors and specifies the calculated vectors in generated code. Read Constants by Processing XML File This example shows how to call an extrinsic function using coder.const. Write an XML file MyParams.xml containing the following statements: <params> <param name="hello" value="17"/> <param name="world" value="42"/> </params> Save MyParams.xml in the current folder. 2-124 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.const Write a MATLAB function xml2struct that reads an XML file. The function identifies the XML tag param inside another tag params. After identifying param, the function assigns the value of its attribute name to the field name of a structure s. The function also assigns the value of attribute value to the value of the field. function s = xml2struct(file) s = doc els for struct(); = xmlread(file); = doc.getElementsByTagName('params'); i = 0:els.getLength-1 it = els.item(i); ps = it.getElementsByTagName('param'); for j = 0:ps.getLength-1 param = ps.item(j); paramName = char(param.getAttribute('name')); paramValue = char(param.getAttribute('value')); paramValue = evalin('base', paramValue); s.(paramName) = paramValue; end end Save xml2struct in the current folder. Write a MATLAB function MyFunc that reads the XML file MyParams.xml into a structure s using the function xml2struct. Declare xml2struct as extrinsic using coder.extrinsic and call it in a coder.const statement. function y = MyFunc(u) %#codegen assert(isa(u, 'double')); coder.extrinsic('xml2struct'); s = coder.const(xml2struct('MyParams.xml')); y = s.hello + s.world + u; www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-125 coder.const Generate code for MyFunc using the codegen command. Open the Code Generation Report. codegen -config:dll -launchreport MyFunc -args 0 The code generation software executes the call to xml2struct during code generation. It replaces the structure fields s.hello and s.world with the values 17 and 42 in generated code. Tips 2-126 • The code generation software constant-folds expressions automatically when possible. Typically, automatic constant-folding occurs for expressions with scalars only. Use coder.const when the code generation software does not constant-fold expressions on its own. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.Constant Superclasses Type Purpose Represent set containing one MATLAB value Description Use a coder.Constant object to define values that should be treated as constant during code generation. Use only with the fiaccel -args options. Do not pass as an input to a generated MEX function. Construction const_type=coder.Constant(v) creates a coder.Constant type from the value v. const_type=coder.newtype('constant', v) creates a coder.Constant type from the value v. Input Arguments v Constant value used to construct the type. Properties Value The actual value of the constant. Copy Semantics Value. To learn how value classes affect copy operations, see Copying Objects in the MATLAB documentation. Examples Generate code for a MATLAB function, fcn, specialized to the case where the input is exactly 42. k = coder.Constant(42); Create a new constant type for use in code generation. k = coder.newtype('constant', 42); | coder.Type | coder.newtype | fiaccel www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-127 coder.cstructname Purpose Specify structure name in generated code Syntax coder.cstructname(structVar,'structName') coder.cstructname(structVar,'structName','extern') coder.cstructname(structVar,'structName','extern',Name,Value) coder.cstructname(structType,'structName') coder.cstructname(structType,'structName','extern') coder.cstructname(structType,'structName','extern',Name, Value) Description coder.cstructname(structVar,'structName') allows you to specify the name of a structure in generated code. structVar is the structure variable. structName specifies the name to use for the structure variable structVar in the generated code. Use coder.cstructname(structVar, 'structName') in a function that is compiled using fiaccel. Before the first use of the structure variable in your function, you must call coder.cstructname. coder.cstructname(structVar,'structName','extern') declares an externally defined structure. It does not generate the definition of the structure type. Provide the definition in a custom include file. coder.cstructname(structVar,'structName','extern',Name,Value) uses additional options specified by one or more Name,Value pair arguments. coder.cstructname(structType,'structName') returns a coder.StructType with the name structName. When the first argument is structType, coder.cstructname is a MATLAB function. You cannot use coder.cstructname(structType, 'structName') in a function that is compiled using fiaccel. Use the returned type with the fiaccel -args option. coder.cstructname(structType,'structName','extern') returns a coder.StructType that uses an externally defined structure. Provide the structure definition in a custom include file. 2-128 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.cstructname coder.cstructname(structType,'structName','extern',Name, Value) uses additional options specified by one or more Name,Value pair arguments. Tips • coder.cstructname(structVar, 'structName') is ignored outside of code generation. Using coder.cstructname at the MATLAB command line, and then calling codegen does not assign a name to a structure in the generated code. For example, if function foo does not use coder.cstructname to assign a name to structure S, the following commands do not assign the name myStruct to the structure variable S in generated code. coder.cstructname(S,'myStruct'); codegen foo -args {S} • To assign a structure name outside of code generation, use coder.cstructname(structType, 'structName'). coder.cstructname returns a coder.StructType object you can use with the -args option. For more information, see “Create a coder.StructType Object” on page 2-133. • To use coder.cstructname on arrays, use single indexing. For example, you cannot use coder.cstructname(x(1,2)). Instead, use single indexing, for example coder.cstructname(x(n)). • Use of coder.cstructname with global variables is not supported. • If you use coder.cstructname on an array, it sets the name of the base type of the array, not the name of the array. Therefore, you cannot use coder.cstructname on the base element and then on the array. For example, the following code does not work. The second coder.cstructname attempts to set the name of the base type to myStructArrayName, which conflicts with the previous coder.cstructname, myStructName. % Define scalar structure with field a myStruct = struct('a', 0); coder.cstructname(mystruct,'myStructName'); % Define array of structure with field a www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-129 coder.cstructname myStructArray = repmat(myStruct,k,n); coder.cstructname(myStructArray,'myStructArrayName'); • If you are using custom structure types, specify the name of the header file that includes the external definition of the structure. Use the HeaderFile input argument. • If you have an Embedded Coder® license and use Code Replacement Libraries (CRLs), the CRLs provide the ability to align data objects passed into a replacement function to a specified boundary. To take advantage of target-specific function implementations that require data to be aligned, use the Alignment input argument. • You can also use coder.cstructname to assign a name to a substructure, which is a structure that appears as a field of another structure. For more information, see “Assign a Name to a SubStructure” on page 2-132. Input Arguments structName The name to use for the structure in the generated code. structType coder.StructType object. structVar Structure variable. Name-Value Pair Arguments Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN. 2-130 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.cstructname ’Alignment’ The run-time memory alignment of structures of this type in bytes. If you have an Embedded Coder license and use Code Replacement Libraries (CRLs), the CRLs provide the ability to align data objects passed into a replacement function to a specified boundary. This capability allows you to take advantage of target-specific function implementations that require data to be aligned. By default, the structure is not aligned on a specific boundary. Hence it is not matched by CRL functions that require alignment. Alignment must be either -1 or a power of 2 that is not greater than 128. Default: -1 ’HeaderFile’ Name of the header file that contains the external definition of the structure, for example, "mystruct.h". By default, the generated code contains #include statements for custom header files after the standard header files. If a standard header file refers to the custom structure type, then the compilation fails. By specifying the HeaderFile option, MATLAB Coder includes that header file exactly at the point where it is required. Must be a non-empty string. Examples Apply coder.cstructname to Top-Level Inputs Generate code for a MATLAB function that takes structure inputs. 1 Write a MATLAB function, topfun, that assigns the name MyStruct to its input parameter. %#codegen function y = topfun(x) % Assign the name 'MyStruct' to the input variable in % the generated code coder.cstructname(x, 'MyStruct'); y = x; www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-131 coder.cstructname end 2 Declare a structure s in MATLAB. s is the structure definition for the input variable x. s = struct('a',42,'b',4711); 3 Generate a MEX function for topfun, using the -args option to specify that the input parameter is a structure. fiaccel topfun.m -args { s } codegen generates a MEX function in the default folder codegen\mex\topfun. In this folder, the structure definition is in topfun_types.h. typedef struct { double a; double b; } MyStruct; Assign a Name to a SubStructure Use coder.cstructname to assign a name to a substructure. 1 Define a MATLAB structure, top, that has another structure, lower, as a field. % Define structure top with field lower, % which is a structure with fields a and b top.lower = struct('a',1,'b',1); top.c = 1; 2 Define a function, MyFunc, which takes an argument, TopVar, as input. Mark the function for code generation using %#codegen. function out = MyFunc(TopVar) %#codegen 3 Inside MyFunc, include the following lines 2-132 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.cstructname coder.cstructname(TopVar,'topType'); coder.cstructname(TopVar.lower,'lowerType'); 4 Generate C code for MyFunc with an argument having the same type as top. This ensures that TopVar has the same type as top. codegen -config:lib MyFunc -args coder.typeof(top) In the generated C code, the field variable TopVar.lower is assigned the type name lowerType. For instance, the structure declaration of the variable TopVar.lower appears in the C code as: typedef struct { /* Definitions of a and b appear here */ } lowerType; and the structure declaration of the variable TopVar appears as: typedef struct { lowerType lower; /* Definition of c appears here */ } topType; Create a coder.StructType Object Create a coder.StructType object and pass it as argument. . S = struct('a',double(0),'b',single(0)) T = coder.typeof(S); T = coder.cstructname(T,'mytype'); codegen -config:lib MyFile -args T In this example, you create a coder.StructType object T. The object is passed as a codegen argument. However, because of the coder.cstructname statement, T is replaced with mytype in the generated C code. For instance, the declaration of T appears in the C code as: www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-133 coder.cstructname typedef struct { /* Field definitions appear here */ } mytype; Create a coder.StructType Object Using an Externally Defined Type Create a C header file, MyFile.h, containing the definition of a structure, mytype. /* Structure definition */ struct mytype { /* Field definitions */ double a; float b; }; Save the file in the folder, C:\MyHeaders. Define a coder.StructType object, T, with the same fields as mytype. T = coder.typeof(struct('a',double(0),'b',single(0))); Using coder.cstructname, rename T as mytype. Specify that the definition of mytype is in MyFile.h. T = coder.cstructname(T,'mytype','extern','HeaderFile','MyFile.h'); Generate code for MATLAB function, MyFunc, which takes a structure of type, T, as input argument. Add the folder, C:\MyHeaders, to the include path during code generation. codegen -config:lib MyFunc -args T -I C:\MyHeaders In the generated code, the structure, T, is assigned the name, mytype. The code generation software does not generate the definition of mytype. Instead the software includes the header file, MyFile.h, in the generated code. 2-134 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.cstructname | | fiaccel | | | coder.StructType How To • “Structures” www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-135 coder.EnumType Superclasses ArrayType Purpose Represent set of MATLAB enumerations Description Specifies the set of MATLAB enumerations that the generated code should accept. Use only with the fiaccel -args options. Do not pass as an input to a generated MEX function. Construction enum_type = coder.typeof(enum_value) creates a coder.EnumType object representing a set of enumeration values of class (enum_value). enum_type = coder.typeof(enum_value, sz, variable_dims) returns a modified copy of coder.typeof(enum_value) with (upper bound) size specified by sz and variable dimensions variable_dims. If sz specifies inf for a dimension, then the size of the dimension is unbounded and the dimension is variable size. When sz is [], the (upper bound) sizes of v do not change. If you do not specify variable_dims, the bounded dimensions of the type are fixed; the unbounded dimensions are variable size. When variable_dims is a scalar, it applies to bounded dimensions that are not 1 or 0 (which are fixed). enum_type = coder.newtype(enum_name,sz,variable_dims) creates a coder.EnumType object that has variable size with (upper bound) sizes sz and variable dimensions variable_dims. If sz specifies inf for a dimension, then the size of the dimension is unbounded and the dimension is variable size. If you do not specify variable_dims, the bounded dimensions of the type are fixed. When variable_dims is a scalar, it applies to bounded dimensions that are not 1 or 0 (which are fixed). Input Arguments enum_value Enumeration value defined in a file on the MATLAB path. sz Size vector specifying each dimension of type object. 2-136 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.EnumType Default: [1 1] for coder.newtype variable_dims Logical vector that specifies whether each dimension is variable size (true) or fixed size (false). Default: false(size(sz)) | sz==Inf for coder.newtype enum_name Name of a numeration defined in a file on the MATLAB path. Properties ClassName Class of values in the set. SizeVector The upper-bound size of arrays in the set. VariableDims A vector specifying whether each dimension of the array is fixed or variable size. If a vector element is true, the corresponding dimension is variable size. Copy Semantics Value. To learn how value classes affect copy operations, see Copying Objects in the MATLAB documentation. Examples Create a coder.EnumType object using a value from an existing MATLAB enumeration. 1 Define an enumeration MyColors. On the MATLAB path, create a file named ’MyColors’ containing: classdef(Enumeration) MyColors < int32 enumeration green(1), red(2), www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-137 coder.EnumType end end 2 Create a coder.EnumType object from this enumeration. t = coder.typeof(MyColors.red); Create a coder.EnumType object using the name of an existing MATLAB enumeration. 1 Define an enumeration MyColors. On the MATLAB path, create a file named ’MyColors’ containing: classdef(Enumeration) MyColors < int32 enumeration green(1), red(2), end end 2 Create a coder.EnumType object from this enumeration. t = coder.newtype('MyColors'); | | | | coder.Type | coder.ArrayType | coder.typeof | coder.newtype | coder.resize | fiaccel How To 2-138 • “Enumerated Data” www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.extrinsic Purpose Declare extrinsic function or functions Syntax coder.extrinsic('function_name'); coder.extrinsic('function_name_1', ... 'function_name_n'); , coder.extrinsic('-sync:on', 'function_name'); coder.extrinsic('-sync:on', 'function_name_1', ... 'function_name_n'); , coder.extrinsic('-sync:off','function_name'); coder.extrinsic('-sync:off', 'function_name_1', ... 'function_name_n'); Arguments , function_name function_name_1, ... , function_name_n Declares function_name or function_name_1 through function_name_n as extrinsic functions. –sync:on function_name or function_name_1 through function_name_n. By default, this option enables synchronization of global data between MATLAB and MEX functions at MEX function entry and exit, and before and after extrinsic calls. Use this option for maximum consistency between MATLAB and the MEX functions. If most extrinsic calls do not modify global data, but a few do, you can turn off synchronization before and after extrinsic calls. To do so, change the global synchronization mode to At MEX-function entry and exit. Use the –sync:on option to turn on synchronization for extrinsic calls that do modify global data. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-139 coder.extrinsic –sync:off Disables synchronization of global data between MATLAB and MEX functions before and after calls to the extrinsic functions, function_name or function_name_1 through function_name_n. If most extrinsic calls modify global data, but a few do not, you can use the –sync:off option to turn off synchronization for the extrinsic calls that do not modify global data. Description coder.extrinsic declares extrinsic functions. During simulation, the code generation software generates code for the call to an extrinsic function, but does not generate the function’s internal code. Therefore, simulation can run only on platforms where MATLAB software is installed. During standalone code generation, MATLAB attempts to determine whether the extrinsic function affects the output of the function in which it is called — for example by returning mxArrays to an output variable. Provided that there is no change to the output, MATLAB proceeds with code generation, but excludes the extrinsic function from the generated code. Otherwise, compilation errors occur. You cannot use coder.ceval on functions that you declare extrinsic by using coder.extrinsic. coder.extrinsic is ignored outside of code generation. Tips • The code generation software detects calls to many common visualization functions, such as plot, disp, and figure. The software treats these functions like extrinsic functions but you do not have to declare them extrinsic using the coder.extrinsic function. • Use the coder.screener function to detect which functions you should declare extrinsic. This function opens the code generations readiness tool that detects code generation issues in your MATLAB code. During code generation, MATLAB attempts to determine whether the extrinsic function affects the output of the function in which it is called — for example by returning mxArrays to an output variable. Provided that there is no change to the output, MATLAB proceeds 2-140 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.extrinsic with code generation, but excludes the extrinsic function from the generated code. Otherwise, a compiler error is issued from MATLAB. Examples The following code declares the MATLAB functions patch and axis extrinsic in the MATLAB local function create_plot: function c = pythagoras(a,b,color) %#codegen % Calculates the hypotenuse of a right triangle % and displays the triangle as a patch object. c = sqrt(a^2 + b^2); create_plot(a, b, color); function create_plot(a, b, color) %Declare patch and axis as extrinsic coder.extrinsic('patch', 'axis'); x = [0;a;a]; y = [0;0;b]; patch(x, y, color); axis('equal'); By declaring these functions extrinsic, you instruct the software not to compile or generate code for patch and axis. Instead it dispatches these functions to MATLAB for execution. | | | coder.screener • • • “Resolution of Function Calls in MATLAB Generated Code” • • • “Restrictions on Extrinsic Functions for Code Generation” www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-141 coder.FiType Superclasses ArrayType Purpose Represent set of MATLAB fixed-point arrays Description Specifies the set of fixed-point array values that the generated code should accept. Use only with the fiaccel -args options. Do not pass as an input to the generated MEX function. Construction t=coder.typeof(v) creates a coder.FiType object representing a set of fixed-point values whose properties are based on the fixed-point input v. t=coder.typeof(v, sz, variable_dims) returns a modified copy of coder.typeof(v) with (upper bound) size specified by sz and variable dimensions variable_dims. If sz specifies inf for a dimension, then the size of the dimension is unbounded and the dimension is variable size. When sz is [], the (upper bound) sizes of v do not change. If you do not specify the variable_dims input parameter, the bounded dimensions of the type are fixed. When variable_dims is a scalar, it applies to the bounded dimensions that are not 1 or 0 (which are fixed). t=coder.newtype('embedded.fi', numerictype, sz, variable_dims) creates a coder.Type object representing a set of fixed-point values with numerictype and (upper bound) sizes sz and variable dimensions variable_dims. If sz specifies inf for a dimension, then the size of the dimension is unbounded and the dimension is variable size. When you do not specify variable_dims, the bounded dimensions of the type are fixed. When variable_dims is a scalar, it applies to the bounded dimensions that are not 1 or 0 (which are fixed). t=coder.newtype('embedded.fi', numerictype, sz, variable_dims, Name, Value) creates a coder.Type object representing a set of fixed-point values with numerictype and additional options specified by one or more Name, Value pair arguments. Name can also be a property name and Value is the corresponding value. Name must appear inside single quotes (''). You can specify several name-value pair arguments in any order as Name1,Value1, ,NameN,ValueN. 2-142 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.FiType Input Arguments v Fixed-point value used to create new coder.FiType object. sz Size vector specifying each dimension of type object. Default: [1 1] for coder.newtype variable_dims Logical vector that specifies whether each dimension is variable size (true) or fixed size (false). Default: false(size(sz)) | sz ==Inf for coder.newtype Name-Value Pair Arguments Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN. complex Set complex to true to create a coder.Type object that can represent complex values. The type must support complex data. Default: false fimath Specify local fimath. If not, uses default fimath. Properties ClassName Class of values in the set. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-143 coder.FiType Complex Indicates whether fixed-point arrays in the set are real (false) or complex (true). Fimath Local fimath that the fixed-point arrays in the set use. NumericType numerictype that the fixed-point arrays in the set use. SizeVector The upper-bound size of arrays in the set. VariableDims A vector specifying whether each dimension of the array is fixed or variable size. If a vector element is true, the corresponding dimension is variable size. Copy Semantics Value. To learn how value classes affect copy operations, see Copying Objects in the MATLAB documentation. Examples Create a new fixed-point type t. t = coder.typeof(fi(1)); % Returns % coder.FiType % 1x1 embedded.fi % DataTypeMode:Fixed-point: binary point scaling % Signedness:Signed % WordLength:16 % FractionLength:14 Create a new fixed-point type for use in code generation. The fixed-point type uses the default fimath. 2-144 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.FiType t = coder.newtype('embedded.fi',numerictype(1, 16, 15), [1 2]) t = % Returns % coder.FiType % 1x2 embedded.fi % DataTypeMode: Fixed-point: binary point scaling % Signedness: Signed % WordLength: 16 % FractionLength: 15 This new type uses the default fimath. | | | | coder.Type | coder.ArrayType | coder.typeof | coder.resize | coder.newtype | fiaccel www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-145 coder.inline Purpose Control inlining in generated code Syntax coder.inline('always') coder.inline('never') coder.inline('default') Description coder.inline('always') forces inlining of the current function in generated code. coder.inline('never') prevents inlining of the current function in generated code. For example, you may want to prevent inlining to simplify the mapping between the MATLAB source code and the generated code. coder.inline('default') uses internal heuristics to determine whether or not to inline the current function. In most cases, the heuristics used produce highly optimized code. Use coder.inline only when you need to fine-tune these optimizations. Place the coder.inline directive inside the function to which it applies. MATLAB CoderFixed-Point Designer does not inline entry-point functions. coder.inline('always') does not inline functions called from parfor-loops. MATLAB Coder does not inline functions into parfor-loops. Examples • “Preventing Function Inlining” on page 2-146 • “Using coder.inline In Control Flow Statements” on page 2-147 Preventing Function Inlining In this example, function foo is not inlined in the generated code: function y = foo(x) coder.inline('never'); y = x; end 2-146 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.inline Using coder.inline In Control Flow Statements You can use coder.inline in control flow code. If the software detects contradictory coder.inline directives, the generated code uses the default inlining heuristic and issues a warning. Suppose you want to generate code for a division function that will be embedded in a system with limited memory. To optimize memory use in the generated code, the following function, inline_division, manually controls inlining based on whether it performs scalar division or vector division: function y = inline_division(dividend, divisor) % For scalar division, inlining produces smaller code % than the function call itself. if isscalar(dividend) && isscalar(divisor) coder.inline('always'); else % Vector division produces a for-loop. % Prohibit inlining to reduce code size. coder.inline('never'); end if any(divisor == 0) error('Can not divide by 0'); end y = dividend / divisor; www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-147 coder.load Purpose Load compile-time constants from MAT-file or ASCII file into caller workspace Syntax S S S S S S S Description = = = = = = = coder.load(filename) coder.load(filename,var1,...,varN) coder.load(filename,'-regexp',expr1,...,exprN) coder.load(filename,'-ascii') coder.load(filename,'-mat') coder.load(filename,'-mat',var1,...,varN) coder.load(filename,'-mat','-regexp', expr1,...,exprN) S = coder.load(filename) loads compile-time constants from filename. • If filename is a MAT-file, then coder.load loads variables from the MAT-file into a structure array. • If filename is an ASCII file, then coder.load loads data into a double-precision array. S = coder.load(filename,var1,...,varN) loads only the specified variables from the MAT-file filename. S = coder.load(filename,'-regexp',expr1,...,exprN) loads only the variables that match the specified regular expressions. S = coder.load(filename,'-ascii') treats filename as an ASCII file, regardless of the file extension. S = coder.load(filename,'-mat') treats filename as a MAT-file, regardless of the file extension. S = coder.load(filename,'-mat',var1,...,varN) treats filename as a MAT-file and loads only the specified variables from the file. 2-148 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.load S = coder.load(filename,'-mat','-regexp', expr1,...,exprN) treats filename as a MAT-file and loads only the variables that match the specified regular expressions. Input Arguments filename - Name of file string Name of file, specified as a string constant. filename can include a file extension and a full or partial path. If filename has no extension, load looks for a file named filename.mat. If filename has an extension other than .mat, load treats the file as ASCII data. ASCII files must contain a rectangular table of numbers, with an equal number of elements in each row. The file delimiter (the character between elements in each row) can be a blank, comma, semicolon, or tab character. The file can contain MATLAB comments (lines that begin with a percent sign, %). Example: 'myFile.mat' Data Types char var1,...,varN - Names of variables to load string Names of variables, specified as string constants. Use the * wildcard to match patterns. Example: load('myFile.mat','A*') loads all variables in the file whose names start with A. Data Types char expr1,...,exprN - Regular expressions indicating which variables to load string www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-149 coder.load Regular expressions indicating which variables to load, specified as string constants. Example: load('myFile.mat', '^A', '^B') loads only variables whose names begin with A or B. Data Types char Output Arguments S - Loaded variables or data structure array | m-by-n array If filename is a MAT-file, S is a structure array. If filename is an ASCII file, S is an m-by-n array of type double. m is the number of lines in the file and n is the number of values on a line. Examples Load compile-time constants from MAT-file Generate code for a function edgeDetect1 which given a normalized image, returns an image where the edges are detected with respect to the threshold value. edgeDetect1 uses coder.load to load the edge detection kernel from a MAT-file at compile time. Save the Sobel edge-detection kernel in a MAT-file. k = [1 2 1; 0 0 0; -1 -2 -1]; save('sobel.mat','k'); Write the function edgeDetect1. function edgeImage = edgeDetect1(originalImage, threshold) %#codegen assert(all(size(originalImage) <= [1024 1024])); assert(isa(originalImage, 'double')); assert(isa(threshold, 'double')); S = coder.load('sobel.mat','k'); H = conv2(double(originalImage),S.k, 'same'); V = conv2(double(originalImage),S.k','same'); 2-150 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.load E = sqrt(H.*H + V.*V); edgeImage = uint8((E > threshold) * 255); Create a code generation configuration object for a static library. cfg = coder.config('lib'); Generate a static library for edgeDetect1. codegen -report -config cfg edgeDetect1 codegen generates C code in the codegen\lib\edgeDetect1 folder. Load compile-time constants from ASCII file Generate code for a function edgeDetect2 which given a normalized image, returns an image where the edges are detected with respect to the threshold value. edgeDetect2 uses coder.load to load the edge detection kernel from an ASCII file at compile time. Save the Sobel edge-detection kernel in an ASCII file. k = [1 2 1; 0 0 0; -1 -2 -1]; save('sobel.dat', 'k', '-ascii'); Write the function edgeDetect2. function edgeImage = edgeDetect2(originalImage, threshold) %#codegen assert(all(size(originalImage) <= [1024 1024])); assert(isa(originalImage, 'double')); assert(isa(threshold, 'double')); k = coder.load('sobel.dat'); H = conv2(double(originalImage),k, 'same'); V = conv2(double(originalImage),k','same'); E = sqrt(H.*H + V.*V); edgeImage = uint8((E > threshold) * 255); Create a code generation configuration object for a static library. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-151 coder.load cfg = coder.config('lib'); Generate a static library for edgeDetect2. codegen -report -config cfg edgeDetect2 codegen generates C code in the codegen\lib\edgeDetect2 folder. Limitations • coder.load does not support loading objects. • Arguments to coder.load must be compile-time constant strings. • The output S must be the name of a structure or array without any subscripting. For example, S[i] = coder.load('myFile.mat') is not allowed. • You cannot use save to save workspace data to a file inside a function intended for code generation. The code generation software does not support the save function. Furthermore, you cannot use coder.extrinsic with save. Prior to generating code, you can use save to save workspace data to a file. Tips • coder.load loads data at compile time, not at run time. If you are generating MEX code or code for Simulink simulation, you can use the MATLAB function load to load run-time values. • If the MAT-file contains unsupported constructs, use coder.load(filename,var1,...,varN) to load only the supported constructs. • If you generate code in a MATLAB Coder project, the code generation software practices incremental code generation for the coder.load function. When the MAT-file or ASCII file used by coder.load changes, the software rebuilds the code. See Also matfile | regexp | save Concepts • “Regular Expressions” 2-152 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.mexconfig Purpose Code acceleration configuration object Syntax config_obj = coder.mexconfig Description config_obj = coder.mexconfig creates a coder.MexConfig code generation configuration object for use with fiaccel, which generates a MEX function. Output Arguments config_obj Examples Create a configuration object to disable run-time checks Code generation configuration object for use when generating MEX functions using fiaccel. cfg = coder.mexconfig % Turn off Integrity Checks, Extrinsic Calls, % and Responsiveness Checks cfg.IntegrityChecks = false; cfg.ExtrinsicCalls = false; cfg.ResponsivenessChecks = false; % Use fiaccel to generate a MEX function for file foo.m fiaccel -config cfg foo See Also coder.ArrayType | coder.Constant | coder.EnumType | coder.FiType | coder.MexConfig | coder.PrimitiveType | coder.StructType | coder.Type | coder.newtype | coder.resize | coder.typeof | fiaccel www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-153 coder.MexConfig Purpose Code acceleration configuration object for use with fiaccel Description A coder.MexConfig object contains all the configuration parameters that the fiaccel function uses when accelerating fixed-point code via a generated MEX function. To use this object, first create it using the lowercase coder.mexconfig function and then, pass it to the fiaccel function using the -config option. Construction cfg = coder.mexconfig creates a coder.MexConfig object, cfg, for fiaccel MEX function generation. Properties ConstantFoldingTimeout Maximum number of constant folder instructions Specify, as a positive integer, the maximum number of instructions to be executed by the constant folder. Default: 10000 DynamicMemoryAllocation Dynamic memory allocation for variable-size data By default, when this property is set to 'Threshold' , dynamic memory allocation is enabled for all variable-size arrays whose size is greater than DynamicMemoryAllocationThreshold and fiaccel allocates memory for this variable-size data dynamically on the heap. Set this property to 'Off' to allocate memory statically on the stack. Set it to'AllVariableSizeArrays' to allocate memory for all variable-size arrays dynamically on the heap . You must use dynamic memory allocation for all unbounded variable-size data. This property, DynamicMemoryAllocation, is enabled only when EnableVariableSizing is true. When you set DynamicMemoryAllocation to `Threshold', it enables the DynamicMemoryAllocationThreshold property. 2-154 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.MexConfig Default: Threshold DynamicMemoryAllocationThreshold Memory allocation threshold Specify the integer size of the threshold for variable-size arrays above which fiaccel allocates memory on the heap. Default: 65536 EchoExpressions Show results of code not terminated with semicolons Set this property to true to have the results of code instructions that do not terminate with a semicolon appear in the MATLAB Command Window. If you set this property to false, code results do not appear in the MATLAB Command Window. Default: true EnableDebugging Compile generated code in debug mode Set this property to true to compile the generated code in debug mode. Set this property to false to compile the code in normal mode. Default: false EnableVariableSizing Variable-sized arrays support Set this property to true to enable support for variable-sized arrays and to enable the DynamicMemoryAllocation property. If you set this property to false, variable-sized arrays are not supported. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-155 coder.MexConfig Default: true ExtrinsicCalls Extrinsic function calls An extrinsic function is a function on the MATLAB path that the generated code dispatches to MATLAB software for execution. fiaccel does not compile or generate code for extrinsic functions. Set this property to true to have fiaccel generate code for the call to a MATLAB function, but not generate the function’s internal code. Set this property to false to have fiaccel ignore the extrinsic function and not generate code for the call to the MATLAB function. If the extrinsic function affects the output of fiaccel, a compiler error occurs. ExtrinsicCalls affects how MEX functions built by fiaccel generate random numbers when using the MATLAB rand, randi, and randn functions. If extrinsic calls are enabled, the generated mex function uses the MATLAB global random number stream to generate random numbers. If extrinsic calls are not enabled, the MEX function built with fiaccel uses a self-contained random number generator. Default: true GenerateReport Code generation report Set this property to true to create an HTML code generation report. Set this property to false to not create the report. Default: false GlobalDataSyncMethod MEX function global data synchronization with MATLAB global workspace 2-156 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.MexConfig Set this property to SyncAlways so synchronize global data at MEX function entry and exit and for all extrinsic calls to ensure maximum consistency between MATLAB and the generated MEX function. If the extrinsic calls do not affect global data, use this option in conjunction with the coder.extrinsic -sync:off option to turn off synchronization for these calls to maximize performance. If you set this property to SyncAtEntryAndExits, global data is synchronized only at MEX function entry and exit. If your code contains extrinsic calls, but only a few affect global data, use this option in conjunction with the coder.extrinsic -sync:on option to turn on synchronization for these calls to maximize performance. If you set this property to NoSync, no synchronization occurs. Ensure that your MEX function does not interact with MATLAB globals before disabling synchronization otherwise inconsistencies between MATLAB and the MEX function might occur. Default: SyncAlways InlineStackLimit Stack size for inlined functions Specify, as a positive integer, the stack size limit on inlined functions. Default: 4000 InlineThreshold Maximum size of functions to be inlined Specify, as a positive integer, the maximum size of functions to be inlined. Default: 10 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-157 coder.MexConfig InlineThresholdMax Maximum size of functions after inlining Specify, as a positive integer, the maximum size of functions after inlining. Default: 200 IntegrityChecks Memory integrity Sset this property to true to detect any violations of memory integrity in code generated for MATLAB. When a violation is detected, execution stops and a diagnostic message displays. Set this property to false to disable both memory integrity checks and the runtime stack. Default: true LaunchReport Code generation report display Set this property to true to open the HTML code generation report automatically when code generation completes. Set this property to false to disable displaying the report automatically. This property applies only if you set the GenerateReport property to true. Default: true ResponsivenessChecks Responsiveness checks Set this property to true to turn on responsiveness checks. Set this property to false to disable responsiveness checks. Default: true 2-158 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.MexConfig SaturateOnIntegerOverflow Integer overflow action Overflows saturate to either the minimum or maximum value that the data type can represent. Set this property to true to have overflows saturate. Set this property to false to have overflows wrap to the appropriate value representable by the data type. Default: true StackUsageMax Maximum stack usage per application Specify, as a positive integer, the maximum stack usage per application in bytes. Set a limit that is lower than the available stack size. Otherwise, a runtime stack overflow might occur. Overflows are detected and reported by the C compiler, not by fiaccel. Default: 200000 Copy Semantics Handle. To learn how handle classes affect copy operations, see Copying Objects in the MATLAB documentation. Examples Use the lowercase coder.mexconfig function to create a coder.MexConfig configuration object. Set this object to disable run-time checks. cfg = coder.mexconfig % Turn off Integrity Checks, Extrinsic Calls, % and Responsiveness Checks cfg.IntegrityChecks = false; cfg.ExtrinsicCalls = false; cfg.ResponsivenessChecks = false; % Use fiaccel to generate a MEX function for file foo.m fiaccel -config cfg foo www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-159 coder.MexConfig See Also 2-160 coder.ArrayType | coder.Constant | coder.EnumType | coder.FiType | coder.mexconfig | coder.PrimitiveType | coder.StructType | coder.Type | coder.newtype | coder.resize | coder.typeof | fiaccel www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.newtype Purpose Create a new coder.Type object Syntax t=coder.newtype(numeric_class, sz, variable_dims) t=coder.newtype(numeric_class, sz, variable_dims, Name, Value) t=coder.newtype('constant', value) t=coder.newtype('struct', struct_fields, sz, variable_dims) t=coder.newtype('embedded.fi', numerictype, sz, variable_dims, Name, Value) t=coder.newtype(enum_value, sz, variable_dims) Description Note coder.newtype is an advanced function. Consider using coder.typeof instead. t=coder.newtype(numeric_class, sz, variable_dims) creates a coder.Type object representing values of class numeric_class with (upper bound) sizes sz and variable dimensions variable_dims. If sz specifies inf for a dimension, then the size of the dimension is unbounded and the dimension is variable size. When variable_dims is not specified, the dimensions of the type are fixed except for those that are unbounded. When variable_dims is a scalar, it is applied to dimensions of the type that are not 1 or 0, which are fixed. t=coder.newtype(numeric_class, sz, variable_dims, Name, Value) creates a coder.Type object with additional options specified by one or more Name, Value pair arguments. t=coder.newtype('constant', value) creates a coder.Constant object representing a single value. Use this type to specify a value that should be treated as a constant in the generated code. t=coder.newtype('struct', struct_fields, sz, variable_dims) creates a coder.StructType object for an array of structures of the given sz and variable_dims information with the same fields as the scalar structure struct_fields. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-161 coder.newtype t=coder.newtype('embedded.fi', numerictype, sz, variable_dims, Name, Value) creates a coder.FiType object representing a set of fixed-point values with numerictype and additional options specified by one or more Name, Value pair arguments. t=coder.newtype(enum_value, sz, variable_dims) creates a coder.Type object representing a set of enumeration values of class enum_value. Input Arguments numeric_class Class of the set of values represented by the type object struct_fields Scalar structure used to specify the fields in a new structure type sz Size vector specifying each dimension of type object Default: [1 1] variable_dims Logical vector that specifies whether each dimension is variable size (true) or fixed size (false) Default: false(size(sz)) | sz==Inf Name-Value Pair Arguments Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN. ’complex’ 2-162 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.newtype Set complex to true to create a coder.Type object that can represent complex values. The type must support complex data. Default: false ’fimath’ Specify local fimath. If fimath is not specified, uses default fimath values. Use only with t=coder.newtype(’embedded.fi’, numerictype,sz, variable_dims, Name, Value). ’sparse’ Set sparse to true to create a coder.Type object representing sparse data. The type must support sparse data. Not for use with t=coder.newtype(’embedded.fi’, numerictype,sz, variable_dims, Name, Value) Default: false Output Arguments t Examples Create a new type for use in code generation. New coder.Type object. t=coder.newtype('double',[2 3 4],[1 1 0]) % Returns double :2x:3x4 % ':' indicates variable-size dimensions Create a type for a matrix of doubles, first dimension unbounded, second dimension with fixed size coder.newtype('double',[inf,3]) % returns double:inf x 3 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-163 coder.newtype coder.newtype('double', [inf, 3], [1 0]) % also returns double :inf x3 % ':' indicates variable-size dimensions Create a type for a matrix of doubles, first dimension unbounded, second dimension with variable size with an upper bound of 3 coder.newtype('double', [inf,3],[0 1]) % returns double :inf x :3 % ':' indicates variable-size dimensions Create a new structure type for use in code generation. ta = coder.newtype('int8',[1 1]); tb = coder.newtype('double',[1 2],[1 1]); coder.newtype('struct',struct('a',ta,'b',tb)) % returns struct 1x1 % a: int8 1x1 % b: double :1x:2 % ':' indicates variable-size dimensions Create a new constant type for use in code generation. k % % % % % 2-164 = coder.newtype('constant', 42); Returns k = coder.Constant 42 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.newtype Create a coder.EnumType object using the name of an existing MATLAB enumeration. 1 Define an enumeration MyColors. On the MATLAB path, create a file named ’MyColors’ containing: classdef(Enumeration) MyColors < int32 enumeration green(1), red(2), end end 2 Create a coder.EnumType object from this enumeration. t = coder.newtype('MyColors'); Create a new fixed-point type for use in code generation. The fixed-point type uses default fimath values. t = coder.newtype('embedded.fi',... numerictype(1, 16, 15), [1 2]) t = % Returns % coder.FiType % 1x2 embedded.fi % DataTypeMode: Fixed-point: binary point scaling % Signedness: Signed % WordLength: 16 % FractionLength: 15 Alternatives coder.typeof www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-165 coder.newtype | | | | | | coder.resize | coder.Type | coder.ArrayType | coder.EnumType | coder.FiType | coder.PrimitiveType | coder.StructType | fiaccel 2-166 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.nullcopy Purpose Declare uninitialized variables Syntax X = coder.nullcopy(A) Description X = coder.nullcopy(A) copies type, size, and complexity of A to X, but does not copy element values. Preallocates memory for X without incurring the overhead of initializing memory. coder.nullcopy does not support MATLAB classes as inputs. Use With Caution Use this function with caution. See “How to Eliminate Redundant Copies by Defining Uninitialized Variables”. Examples The following example shows how to declare variable X as a 1-by-5 vector of real doubles without performing an unnecessary initialization: function X = foo N = 5; X = coder.nullcopy(zeros(1,N)); for i = 1:N if mod(i,2) == 0 X(i) = i; else X(i) = 0; end end Using coder.nullcopy with zeros lets you specify the size of vector X without initializing each element to zero. How To • • “Eliminate Redundant Copies of Variables in Generated Code” • www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-167 coder.PrimitiveType Superclasses ArrayType Purpose Represent set of logical, numeric, or char arrays Description Specifies the set of logical, numeric, or char values that the generated code should accept. Supported classes are double,single,int8,uint8,int16,uint16,int32,uint32,int64,uint64, char, and logical. Use only with the fiaccel -args option. Do not pass as an input to a generated MEX function. Construction t=coder.typeof(v) creates a coder.PrimitiveType object denoting the smallest non-constant type that contains v. v must be a MATLAB numeric, logical or char. t=coder.typeof(v, sz, variable_dims) returns a modified copy of coder.typeof(v) with (upper bound) size specified by sz and variable dimensions variable_dims. If sz specifies inf for a dimension, then the size of the dimension is assumed to be unbounded and the dimension is assumed to be variable sized. When sz is [], the (upper bound) sizes of v remain unchanged. When variable_dims is not specified, the dimensions of the type are assumed to be fixed except for those that are unbounded. When variable_dims is a scalar, it is applied to bounded dimensions that are not 1 or 0 (which are assumed to be fixed). t=coder.newtype(numeric_class, sz, variable_dims) creates a coder.PrimitiveType object representing values of class numeric_class with (upper bound) sizes sz and variable dimensions variable_dims. If sz specifies inf for a dimension, then the size of the dimension is assumed to be unbounded and the dimension is assumed to be variable sized. When variable_dims is not specified, the dimensions of the type are assumed to be fixed except for those that are unbounded. When variable_dims is a scalar, it is applied to the dimensions of the type that are not 1 or 0 (which are assumed to be fixed). t=coder.newtype(numeric_class, sz, variable_dims, Name, Value) creates a coder.PrimitiveType object with additional options specified by one or more Name, Value pair arguments. Name can also be a property name and Value is the corresponding value. Name must 2-168 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.PrimitiveType appear inside single quotes (''). You can specify several name-value pair arguments in any order as Name1,Value1, ,NameN,ValueN. Input Arguments v Input that is not a coder.Type object sz Size for corresponding dimension of type object. Size must be a valid size vector. Default: [1 1] for coder.newtype variable_dims Logical vector that specifies whether each dimension is variable size (true) or fixed size (false). Default: false(size(sz)) | sz==Inf for coder.newtype numeric_class Class of type object. Name-Value Pair Arguments Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN. complex Set complex to true to create a coder.PrimitiveType object that can represent complex values. The type must support complex data. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-169 coder.PrimitiveType Default: false sparse Set sparse to true to create a coder.PrimitiveType object representing sparse data. The type must support sparse data. Default: false Properties ClassName Class of values in this set Complex Indicates whether the values in this set are real (false) or complex (true) SizeVector The upper-bound size of arrays in this set. Sparse Indicates whether the values in this set are sparse arrays (true) VariableDims A vector used to specify whether each dimension of the array is fixed or variable size. If a vector element is true, the corresponding dimension is variable size. Copy Semantics Value. To learn how value classes affect copy operations, see Copying Objects in the MATLAB documentation. Examples Create a coder.PrimitiveType object. z = coder.typeof(0,[2 3 4],[1 1 0]) % returns double :2x:3x4 % ':' indicates variable-size dimensions | | | | coder.Type | coder.ArrayType | coder.newtype | coder.typeof | coder.resize | fiaccel 2-170 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.resize Purpose Resize a coder.Type object Syntax t_out t_out t_out t_out t_out Description t_out = coder.resize(t, sz, variable_dims) returns a modified copy of coder.Type t with upper-bound size sz, and variable dimensions variable_dims. If variable_dims or sz are scalars, they are applied to all dimensions of t. By default, variable_dims does not apply to dimensions where sz is 0 or 1, which are fixed. Use the ’uniform’ option to override this special case. coder.resize ignores variable_dims for dimensions with size inf. These dimensions are always variable size. t can be a cell array, in which case, coder.resize resizes all elements of the cell array. = = = = = coder.resize(t, sz, variable_dims) coder.resize(t, sz) coder.resize(t,[],variable_dims) coder.resize(t, sz, variable_dims, Name, Value) coder.resize(t, 'sizelimits', limits) t_out = coder.resize(t, sz) resizes t to have size sz. t_out = coder.resize(t,[],variable_dims) changes t to have variable dimensions variable_dims while leaving the size unchanged. t_out = coder.resize(t, sz, variable_dims, Name, Value) resizes t using additional options specified by one or more Name, Value pair arguments. t_out = coder.resize(t, 'sizelimits', limits) resizes t with dimensions automatically becoming variable based on the limits vector. When the size S of a dimension is greater than or equal to the first threshold defined in limits, the dimension becomes variable size with upper bound S. When the size S of a dimension is greater than or equal to the second threshold defined in limits, the dimension becomes unbounded variable size. Input Arguments limits Two-element vector (or a scalar-expanded one-element vector) of variable-sizing thresholds. If the size sz of a dimension of t is greater www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-171 coder.resize than or equal to the first threshold, the dimension becomes variable size with upper bound sz. If the size sz of a dimension of t is greater than or equal to the second threshold, the dimension becomes unbounded variable size. sz New size for coder.Type object, t_out t coder.Type object that you want to resize variable_dims Specify whether each dimension of t_out should be fixed or variable size. Name-Value Pair Arguments Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN. ’recursive’ Setting recursive to true resizes t and all types contained within it Default: false ’uniform’ Setting uniform to true resizes t but does not apply the heuristic for dimensions of size one. Default: false Output Arguments 2-172 t_out Resized coder.Type object www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.resize Examples Change a fixed-size array to a bounded variable-size array t = coder.typeof(ones(3,3)) % t is 3x3 coder.resize(t, [4 5], 1) % returns :4 x :5 % ':' indicates variable-size dimensions Change a fixed-size array to an unbounded variable-size array t = coder.typeof(ones(3,3)) % t is 3x3 coder.resize(t, inf) % returns :inf x :inf % ':' indicates variable-size dimensions % 'inf' indicates unbounded dimensions Resize a structure field ts = coder.typeof(struct('a', ones(3, 3))) % returns field a as 3x3 coder.resize(ts, [5, 5], 'recursive', 1) % returns field a as 5x5 Make a fixed-sized array variable size based on bounded and unbounded thresholds t = coder.typeof(ones(100,200)) % t is 100x200 coder.resize(t,'sizelimits', [99 199]) % returns :100x:inf % ':' indicates variable-size dimensions % :inf is unbounded variable size www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-173 coder.resize | coder.typeof | coder.newtype | fiaccel 2-174 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.screener Purpose Determine if function is suitable for code generation Syntax coder.screener(fcn) coder.screener(fcn_1,...,fcn_n ) Description coder.screener(fcn) analyzes the entry-point MATLAB function, fcn. It identifies unsupported functions and language features, such as recursion, cell arrays, nested functions, and function handles as code generation compliance issues and displays them in a report. If fcn calls other functions directly or indirectly that are not MathWorks® functions, coder.screener analyzes these functions too. It does not analyze MathWorks functions. coder.screener might not detect all code generation issues. Under certain circumstances, it might report false errors. coder.screener(fcn_1,...,fcn_n ) analyzes entry-point functions (fcn_1,...,fcn_n). Tips • Before using coder.screener, fix issues identified by the code analyzer. • Before generating code, use coder.screener to check that a function is suitable for code generation. Fix all the issues that it detects. Input Arguments fcn Name of entry-point MATLAB function that you want to analyze. fcn_1,...,fcn_n Comma-separated list of names of entry-point MATLAB functions that you want to analyze. Examples Identify Unsupported Functions The coder.screener function identifies calls to functions that are not supported for code generation. It checks both the entry-point function, foo1, and the function foo2 that foo1 calls. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-175 coder.screener Analyze the MATLAB function foo1 that calls foo2. function out = foo1(in) out = foo2(in); disp(out); end function out = foo2(in) out = eval(in); end coder.screener('foo1') The code generation readiness report opens. It provides a summary of the unsupported MATLAB function calls. The function foo2 calls one unsupported MATLAB function. 2-176 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.screener In the report, click the Code Structure tab and select Show MATLAB functions. This tab displays a pie chart showing the relative size of each file and how suitable each file is for code generation. In this case, the report: www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-177 coder.screener • Colors foo1.m green to indicate that it is suitable for code generation. • Colors foo2.m yellow to indicate that some significant changes are required. • Assigns foo1.m a code generation readiness score of 4 and foo2.m a score of 3. The score is based on a scale of 1 to 5. 1 indicates that significant changes are required; 5 indicates that the code generation readiness tool cannot detect issues. • Displays a call tree. 2-178 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.screener The report Summary tab indicates that foo2.m contains one call to the eval function which is not supported for code generation. To generate a MEX function for foo2.m, modify the code to make the call to eval extrinsic. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-179 coder.screener function out = foo2(in) coder.extrinsic('eval'); out = eval(in); end Rerun the code generation readiness tool. coder.screener('foo1') The report no longer flags that the eval function is not supported for code generation. When you generate a MEX function for foo1, the code generation software automatically calls out to MATLAB for eval. For standalone code generation, it does not generate code for it. Identify Unsupported Data Types The coder.screener function identifies data types that are not supported for code generation. Analyze the MATLAB function foo3 that uses unsupported data types. function [outSparse, outCategorical] = foo3(inVal,inString1,inString2) outSparse = sparse(inVal); cellArray = {inString1,inString2}; outCategorical = categorical(cellArray); end coder.screener('foo3') The code generation readiness report opens. It provides a summary of the unsupported data types. 2-180 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.screener The report assigns the code a code readiness score of 2, indicating that the code requires extensive changes. Before generating code, you must fix the reported issues. Determine code generation readiness for multiple entry-point functions The coder.screener function identifies calls to functions that are not supported for code generation. It checks the entry-point functions foo4 and foo5. Analyze the MATLAB functions foo4 and foo5. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-181 coder.screener function out = foo4(in) out = in; disp(out); end function out = foo5(in) out = eval(in); end coder.screener('foo4', 'foo5') The code generation readiness report opens. It provides a summary of the unsupported MATLAB function calls. The function foo5 calls one unsupported MATLAB function. 2-182 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.screener In the report, click the Code Structure tab and select Show MATLAB functions. This tab displays a pie chart showing the relative size of each file and how suitable each file is for code generation. In this case, the report: www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-183 coder.screener • Colors foo1.m green to indicate that it is suitable for code generation. • Colors foo2.m yellow to indicate that some significant changes are required. • Assigns foo1.m a code generation readiness score of 4 and foo2.m a score of 3. The score is based on a scale of 1 to 5. 1 indicates that significant changes are required; 5 indicates that the code generation readiness tool cannot detect issues. • Displays a call tree. 2-184 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.screener Alternatives See Also • “Run the Code Generation Readiness Tool From the Current Folder Browser” fiaccel www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-185 coder.screener Concepts 2-186 • “Functions Supported for Code Acceleration or C Code Generation” • “Code Generation Readiness Tool” www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.StructType Superclasses ArrayType Purpose Represent set of MATLAB structure arrays Description Specifies the set of structure arrays that the generated code should accept. Use only with the fiaccel -args option. Do not pass as an input to a generated MEX function. Construction t=coder.typeof(struct_v) creates a coder.StructType object for a structure with the same fields as the scalar structure struct_v. t=coder.typeof(struct_v, sz, variable_dims) returns a modified copy of coder.typeof(struct_v) with (upper bound) size specified by sz and variable dimensions variable_dims. If sz specifies inf for a dimension, then the size of the dimension is assumed to be unbounded and the dimension is assumed to be variable sized. When sz is [], the (upper bound) sizes of struct_v remain unchanged. If the variable_dims input parameter is not specified, the dimensions of the type are assumed to be fixed except for those that are unbounded. When variable_dims is a scalar, it is applied to the bounded dimensions that are not 1 or 0 (which are assumed to be fixed). t=coder.newtype('struct', struct_v, sz, variable_dims) creates a coder.StructType object for an array of structures with the same fields as the scalar structure struct_v and (upper bound) size sz and variable dimensions variable_dims. If sz specifies inf for a dimension, then the size of the dimension is assumed to be unbounded and the dimension is assumed to be variable sized. When variable_dims is not specified, the dimensions of the type are assumed to be fixed except for those that are unbounded. When variable_dims is a scalar, it is applied to the dimensions of the type, except if the dimension is 1 or 0, which is assumed to be fixed. Input Arguments struct_v Scalar structure used to specify the fields in a new structure type. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-187 coder.StructType sz Size vector specifying each dimension of type object. Default: [1 1] for coder.newtype variable_dims Logical vector that specifies whether each dimension is variable size (true) or fixed size (false). Default: false(size(sz)) | sz==Inf for coder.newtype Properties Alignment The run-time memory alignment of structures of this type in bytes. If you have an Embedded Coder license and use Code Replacement Libraries (CRLs), the CRLs provide the ability to align data objects passed into a replacement function to a specified boundary. This capability allows you to take advantage of target-specific function implementations that require data to be aligned. By default, the structure is not aligned on a specific boundary so it will not be matched by CRL functions that require alignment. Alignment must be either -1 or a power of 2 that is no more than 128. ClassName Class of values in this set. Extern Whether the structure type is externally defined. Fields A structure giving the coder.Type of each field in the structure. HeaderFile 2-188 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.StructType If the structure type is externally defined, name of the header file that contains the external definition of the structure, for example, "mystruct.h". By default, the generated code contains #include statements for custom header files after the standard header files. If a standard header file refers to the custom structure type, then the compilation fails. By specifying the HeaderFile option, MATLAB Coder includes that header file exactly at the point where it is required. Must be a non-empty string. SizeVector The upper-bound size of arrays in this set. VariableDims A vector used to specify whether each dimension of the array is fixed or variable size. If a vector element is true, the corresponding dimension is variable size. Copy Semantics Value. To learn how value classes affect copy operations, see Copying Objects in the MATLAB documentation. Examples Create a type for a structure with a variable-size field. x.a = coder.typeof(0,[3 5],1); x.b = magic(3); coder.typeof(x) % Returns % coder.StructType % 1x1 struct % a: :3x:5 double % b: 3x3 double % ':' indicates variable-size dimensions www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-189 coder.StructType Create a coder.StructType object that uses an externally-defined structure type. 1 Create a type that uses an externally-defined structure type. S.a S.b T = T = = coder.typeof(double(0)); = coder.typeof(single(0)); coder.typeof(S); coder.cstructname(T,'mytype','extern','HeaderFile','myheader.h'); T = coder.StructType 1x1 extern mytype (myheader.h) struct a: 1x1 double b: 1x1 single 2 View the types of the structure fields. T.Fields ans = a: [1x1 coder.PrimitiveType] b: [1x1 coder.PrimitiveType] | | | | | | | | coder.Type | coder.PrimitiveType | coder.EnumType | coder.FiType | coder.Constant | coder.ArrayType | coder.newtype | coder.typeof | coder.resize | coder | fiaccel | 2-190 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.target Purpose Determine if code generation target is specified target Syntax tf = coder.target(target) Description tf = coder.target(target) returns true (1) if the code generation target is target. Otherwise, it returns false (0). If you generate code for MATLAB classes, MATLAB computes class initial values at class loading time before code generation. If you use coder.target in MATLAB class property initialization, coder.target('MATLAB') returns true. Input Arguments target - code generation target string Code generation target specified as one of the following strings: 'MATLAB' Running in MATLAB (not generating code) 'MEX' Generating a MEX function 'Sfun' Simulating a Simulink model 'Rtw' Generating a LIB, DLL, or EXE target 'HDL ' Generating an HDL target 'Custom' Generating a custom target Example: tf = coder.target('MATLAB') Data Types char Examples Use coder.target to parameterize a MATLAB function Parameterize a MATLAB function so that it works in MATLAB or generated code. When the function runs in MATLAB, it calls the MATLAB function myabsval. The generated code, however, calls a C library function myabsval. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-191 coder.target Write a MATLAB function myabsval. function y = myabsval(u) y = abs(u); %#codegen Generate the C library for myabsval.m, using the -args option to specify the size, type, and complexity of the input parameter. codegen -config:lib myabsval -args {0.0} codegen creates the library myabsval.lib and header file myabsval.h in the folder /codegen/lib/myabsval. It also generates the functions myabsval_initialize and myabsval_terminate in the same folder. Write a MATLAB function to call the generated C library function using coder.ceval. function y = callmyabsval %#codegen y = -2.75; % Check the target. Do not use coder.ceval if callmyabsval is % executing in MATLAB if coder.target('MATLAB') % Executing in MATLAB, call function myabsval y = myabsval(y); else % Executing in the generated code. % Call the initialize function before calling the % C function for the first time coder.ceval('myabsval_initialize'); % Call the generated C library function myabsval y = coder.ceval('myabsval',y); % Call the terminate function after % calling the C function for the last time coder.ceval('myabsval_terminate'); end 2-192 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.target Convert callmyabsval.m to the MEX function callmyabsval_mex. codegen -config:mex callmyabsval codegen/lib/myabsval/myabsval.lib... codegen/lib/myabsval/myabsval.h Run the MATLAB function callmyabsval . callmyabsval ans = 2.7500 Run the MEX function callmyabsval_mex which calls the library function myabsval. callmyabsval_mex ans = 2.7500 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-193 coder.Type Purpose Represent set of MATLAB values Description Specifies the set of values that the generated code should accept. Use only with the fiaccel -args option. Do not pass as an input to a generated MEX function. Construction coder.Type is an abstract class, and you cannot create instances of it directly. You can create coder.Constant, coder.EnumType, coder.FiType, coder.PrimitiveType, and coder.StructType objects that are derived from this class. Properties ClassName Class of values in this set Copy Semantics 2-194 Value. To learn how value classes affect copy operations, see Copying Objects in the MATLAB documentation. fiaccel | | | | | | | | coder.typeof | coder.newtype | coder.ArrayType | coder.Constant | coder.EnumType | coder.FiType | coder.PrimitiveType | coder.StructType www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.typeof Purpose Convert MATLAB value into its canonical type Syntax t=coder.typeof(v) t=coder.typeof(v, sz, variable_dims) t=coder.typeof(t) Description t=coder.typeof(v) creates a coder.Type object denoting the smallest nonconstant type that contains v. v must be a MATLAB numeric, logical, char, enumeration or fixed-point array, or a struct constructed from the preceding types. Use coder.typeof to specify only input parameter types. For example, use it with the fiaccel function -args option. Do not use it in MATLAB code from which you intend to generate a MEX function. t=coder.typeof(v, sz, variable_dims) returns a modified copy of t=coder.typeof(v) with (upper bound) size specified by sz and variable dimensions variable_dims. If sz specifies inf for a dimension, then the size of the dimension is unbounded and the dimension is variable size. When sz is [], the (upper bound) sizes of v remain unchanged. If you do not specify the variable_dims input parameter, the bounded dimensions of the type are fixed. When variable_dims is a scalar, it is applied to bounded dimensions or dimensions that are 1 or 0, which are fixed. t=coder.typeof(t), where t is a coder.Type object, returns t itself. Input Arguments sz Size vector specifying each dimension of type object t coder.Type object v MATLAB expression that describes the set of values represented by this type. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-195 coder.typeof v must be a MATLAB numeric, logical, char, enumeration or fixed-point array, or a struct constructed from the preceding types. variable_dims Logical vector that specifies whether each dimension is variable size (true) or fixed size (false). Default: false(size(sz)) | sz==Inf Output Arguments t Examples Create a type for a simple fixed-size 5x6 matrix of doubles. coder.Type object coder.typeof(ones(5, 6)) % returns 5x6 double coder.typeof(0, [5 6]) % also returns 5x6 double Create a type for a variable-size matrix of doubles. coder.typeof(ones(3,3), [], 1) % returns :3 x :3 double % ':' indicates variable-size dimensions Create a type for a structure with a variable-size field. x.a = coder.typeof(0,[3 5],1); x.b = magic(3); coder.typeof(x) % Returns % coder.StructType % 1x1 struct % a: :3x:5 double 2-196 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.typeof % b: 3x3 double % ':' indicates variable-size dimensions Create a type for a matrix with fixed-size and variable-size dimensions. coder.typeof(0, [2,3,4], [1 0 1]); % Returns :2x3x:4 double % ':' indicates variable-size dimensions coder.typeof(10, [1 5], 1) % returns double 1 x :5 % ':' indicates variable-size dimensions Create a type for a matrix of doubles, first dimension unbounded, second dimension with fixed size. coder.typeof(10,[inf,3]) % returns double:inf x 3 % ':' indicates variable-size dimensions Create a type for a matrix of doubles, first dimension unbounded, second dimension with variable size with an upper bound of 3. coder.typeof(10, [inf,3],[0 1]) % returns double :inf x :3 % ':' indicates variable-size dimensions Convert a fixed-sized matrix to a variable-sized matrix. coder.typeof(ones(5,5), [], 1) % returns double :5x:5 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-197 coder.typeof % ':' indicates variable-size dimensions Create a nested structure (a structure as a field of another structure). S = struct('a',double(0),'b',single(0)) SuperS.x = coder.typeof(S) SuperS.y = single(0) coder.typeof(SuperS) % Returns % coder.StructType % SuperS: 1x1 struct % with fields % x: 1x1 struct % with fields % a: 1x1 double % b: 1x1 single % y: 1x1 single Create a structure containing a variable-size array of structures as a field. S = struct('a',double(0),'b',single(0)) SuperS.x = coder.typeof(S,[1 inf],[0 1]) SuperS.y = single(0) coder.typeof(SuperS) % Returns % coder.StructType % SuperS: 1x1 struct % with fields % x: 1x:inf struct % with fields % a: 1x1 double % b: 1x1 single % y: 1x1 single 2-198 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.typeof % ':' indicates variable-size dimensions Tips • If you are already specifying the type of an input variable using a type function, do not use coder.typeof unless you also want to specify the size. For instance, instead of coder.typeof(single(0)), use the syntax single(0). | coder.newtype | coder.resize | fiaccel www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-199 coder.unroll Purpose Copy body of for-loop in generated code for each iteration Syntax for i = coder.unroll(range) for i = coder.unroll(range,flag) Description for i = coder.unroll(range) copies the body of a for-loop (unrolls a for-loop) in generated code for each iteration specified by the bounds in range. i is the loop counter variable. for i = coder.unroll(range,flag) unrolls a for-loop as specified in range if flag is true. You must use coder.unroll in a for-loop header. coder.unroll modifies the generated code, but does not change the computed results. coder.unroll must be able to evaluate the bounds of the for-loop at compile time. The number of iterations cannot exceed 1024; unrolling large loops can increase compile time significantly and generate inefficient code This function is ignored outside of code generation. Input Arguments flag Boolean expression that indicates whether to unroll the for-loop: true Unroll the for-loop false Do not unroll the for-loop range Specifies the bounds of the for-loop iteration: 2-200 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.unroll init_val : end_val Iterate from init_val to end_val, using an increment of 1 init_val : end_val step_val : Iterate from init_val to end_val, using step_val as an increment if positive or as a decrement if negative Matrix variable Examples Iterate for a number of times equal to the number of columns in the matrix To limit the number of times to copy the body of a for-loop in generated code: 1 Write a MATLAB function getrand(n) that uses a for-loop to generate a vector of length n and assign random numbers to specific elements. Add a test function test_unroll. This function calls getrand(n) with n equal to values both less than and greater than the threshold for copying the for-loop in generated code. function [y1, y2] = test_unroll() %#codegen % The directive %#codegen indicates that the function % is intended for code generation % Calling getrand 8 times triggers unroll y1 = getrand(8); % Calling getrand 50 times does not trigger unroll y2 = getrand(50); function y = getrand(n) % Turn off inlining to make % generated code easier to read coder.inline('never'); % Set flag variable dounroll to repeat loop body % only for fewer than 10 iterations dounroll = n < 10; www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-201 coder.unroll % Declare size, class, and complexity % of variable y by assignment y = zeros(n, 1); % Loop body begins for i = coder.unroll(1:2:n, dounroll) if (i > 2) && (i < n-2) y(i) = rand(); end; end; % Loop body ends 2 In the default output folder, codegen/lib/test_unroll, generate C static library code for test_unroll : codegen -config:lib test_unroll In test_unroll.c, the generated C code for getrand(8) repeats the body of the for-loop (unrolls the loop) because the number of iterations is less than 10: static void getrand(double y[8]) { /* Turn off inlining to make */ /* generated code easier to read */ /* Set flag variable dounroll to repeat loop body */ /* only for fewer than 10 iterations */ /* Declare size, class, and complexity */ /* of variable y by assignment */ memset(&y[0], 0, sizeof(double) << 3); /* Loop body begins */ y[2] = b_rand(); y[4] = b_rand(); /* Loop body ends */ } 2-202 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.unroll The generated C code for getrand(50) does not unroll the for-loop because the number of iterations is greater than 10: static void b_getrand(double y[50]) { int i; int b_i; /* Turn off inlining to make */ /* generated code easier to read */ /* Set flag variable dounroll to repeat loop body */ /* only for fewer than 10 iterations */ /* Declare size, class, and complexity */ /* of variable y by assignment */ memset(&y[0], 0, 50U * sizeof(double)); /* Loop body begins */ for (i = 0; i < 25; i++) { b_i = (i << 1) + 1; if ((b_i > 2) && (b_i < 48)) { y[b_i - 1] = b_rand(); } } See Also coder.inline | | coder.nullcopy | | for How To • “Using Logicals in Array Indexing” • www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-203 coder.varsize Purpose Declare variable-size data Syntax coder.varsize('var1', coder.varsize('var1', coder.varsize('var1', coder.varsize('var1', Description coder.varsize('var1', 'var2', ...) declares one or more variables 'var2', 'var2', 'var2', 'var2', ...) ..., ubound) ..., ubound, dims) ..., [], dims) as variable-size data, allowing subsequent assignments to extend their size. Each 'varn' must be a quoted string that represents a variable or structure field. If the structure field belongs to an array of structures, use colon (:) as the index expression to make the field variable-size for all elements of the array. For example, the expression coder.varsize('data(:).A') declares that the field A inside each element of data is variable sized. coder.varsize('var1', 'var2', ..., ubound) declares one or more variables as variable-size data with an explicit upper bound specified in ubound. The argument ubound must be a constant, integer-valued vector of upper bound sizes for every dimension of each 'varn'. If you specify more than one 'varn', each variable must have the same number of dimensions. coder.varsize('var1', 'var2', ..., ubound, dims) declares one or more variables as variable-sized with an explicit upper bound and a mix of fixed and varying dimensions specified in dims. The argument dims is a logical vector, or double vector containing only zeros and ones. Dimensions that correspond to zeros or false in dims have fixed size; dimensions that correspond to ones or true vary in size. If you specify more than one variable, each fixed dimension must have the same value across all 'varn'. coder.varsize('var1', 'var2', ..., [], dims) declares one or more variables as variable-sized with a mix of fixed and varying dimensions. The empty vector [] means that you do not specify an explicit upper bound. When you do not specify ubound, the upper bound is computed for each 'varn' in generated code. 2-204 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.varsize When you do not specify dims, dimensions are assumed to be variable except the singleton ones. A singleton dimension is a dimension for which size(A,dim) = 1. You must add the coder.varsize declaration before each 'varn' is used (read). You may add the declaration before the first assignment to each 'varn'. coder.varsize cannot be applied to global variables. coder.varsize is not supported for MATLAB class properties. You cannot use coder.varsize outside the MATLAB code intended for code generation. For example, the following code does not declare the variable, var, as variable-size data: coder.varsize('var',10); codegen -config:lib MyFile -args var Instead, include the coder.varsize statement inside MyFile to declare var as variable-size data. Alternatively you can use coder.typeof to declare var as variable-size outsideMyFile. It can then be passed to MyFile during code generation using the -args option. For more information, see coder.typeof. Examples Develop a simple stack that varies in size up to 32 elements as you push and pop data at run time. Write primary function test_stack to issue commands for pushing data on and popping data from a stack. function test_stack %#codegen % The directive %#codegen indicates that the function % is intended for code generation stack('init', 32); for i = 1 : 20 stack('push', i); end for i = 1 : 10 value = stack('pop'); www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-205 coder.varsize % Display popped value value end end Write local function stack to execute the push and pop commands. function y = stack(command, varargin) persistent data; if isempty(data) data = ones(1,0); end y = 0; switch (command) case {'init'} coder.varsize('data', [1, varargin{1}], [0 1]); data = ones(1,0); case {'pop'} y = data(1); data = data(2:size(data, 2)); case {'push'} data = [varargin{1}, data]; otherwise assert(false, ['Wrong command: ', command]); end end The variable data is the stack. The statement coder.varsize('data', [1, varargin{1}], [0 1]) declares that: • data is a row vector • Its first dimension has a fixed size • Its second dimension can grow to an upper bound of 32 Generate a MEX function for test_stack: codegen -config:mex test_stack 2-206 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.varsize codegen generates a MEX function in the current folder. Run test_stack to get these results: value = 20 value = 19 value = 18 value = 17 value = 16 value = 15 value = 14 value = 13 value = 12 value = 11 At run time, the number of items in the stack grows from zero to 20, and then shrinks to 10. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-207 coder.varsize Declare a variable-size structure field. Write a function struct_example that declares an array data, where each element is a structure that contains a variable-size field: function y=struct_example() %#codegen d = struct('values', zeros(1,0), 'color', 0); data = repmat(d, [3 3]); coder.varsize('data(:).values'); for i = 1:numel(data) data(i).color = rand-0.5; data(i).values = 1:i; end y = 0; for i = 1:numel(data) if data(i).color > 0 y = y + sum(data(i).values); end; end The statement coder.varsize('data(:).values') marks as variable-size the field values inside each element of the matrix data. Generate a MEX function for struct_example: codegen -config:mex struct_example Run struct_example. Each time you run struct_example you get a different answer because the function loads the array with random numbers. Tips 2-208 • If you use input variables (or result of a computation using input variables) to specify the size of an array, it is declared as variable-size www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coder.varsize in the generated code. Do not use coder.varsize on the array again, unless you also want to specify an upper bound for its size. • Using coder.varsize on an array without explicit upper bounds causes dynamic memory allocation of the array. This can reduce speed of generated code. To avoid this, use the syntax coder.varsize('var1', 'var2', ..., ubound) to specify an upper bound for the array size (if you know it in advance). See Also assert | | fiaccel | size | varargin • “Variable-Size Data Definition for Code Generation” • • “Defining Variable-Size Structure Fields” • • “Compilation Directive %#codegen” • • • • “Incompatibilities with MATLAB in Variable-Size Support for Code Generation” www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-209 colon Purpose Create vectors, array subscripting Syntax y = j:k y = j:i:k Description y = j:k returns a regularly-spaced vector, [j, j+1 ,..., k]. j:k is empty when j > k. At least one of the colon operands must be a fi object. All colon operands must have integer values. All the fixed-point operands must be binary-point scaled. Slope-bias scaling is not supported. If any of the operands is complex, the colon function generates a warning and uses only the real part of the operands. y = colon(j,k) is the same as y = j:k. y = j:i:k returns a regularly-spaced vector, [j,j+i,j+2i, ...,j+m*i], where m = fix((k-j)/i). y = j:i:k returns an empty matrix wheni == 0, i > 0 and j > k, or i < 0 and j < k. Input Arguments j - Beginning operand real scalar Beginning operand, specified as a real scalar integer-valued fi object or built-in numeric type. If you specify non-scalar arrays, MATLAB interprets j:i:k as j(1):i(1):k(1). Data Types: fi |single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 i - Increment 1 (default) | real scalar Increment, specified as a real scalar integer-valued fi object or built-in numeric type. Even if the beginning and end operands, j and k, are both unsigned, the increment operand i can be negative. 2-210 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان colon Data Types: fi |single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 k - Ending operand real scalar Ending operand, specified as a real scalar integer-valued fi object or built-in numeric type. Data Types: fi |single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 Output Arguments y - Regularly-spaced vector real vector Fixed-Point Designer determines the data type of the y using the following rules: • The data type covers the union of the ranges of the fixed-point types of the input operands. • If either the beginning or ending operand is signed, the resulting data type is signed. Otherwise, the resulting data type is unsigned. • The word length of y is the smallest value such that the fraction length is 0 and the real-world value of the least-significant bit is 1. • If any of the operands is floating-point, the word length and signedness of y is derived from the fi operand. • If any of the operands is a scaled double, y is a scaled double. • The fimath of y is the same as the fimath of the input operands. • If all the fi objects are of data type double, the data type of y is double. If all the fi objects are of data type single, the data type of y is single. If there are both double and single inputs, and no fixed-point inputs, the output data type is single. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-211 colon Examples Use fi as a Colon Operator When you use fi as a colon operator, all colon operands must have integer values. a b c x = = = = fi(1,0,3,0); fi(2,0,8,0); fi(12,0,8,0); a:b:c x = 1 3 5 DataTypeMode: Signedness: WordLength: FractionLength: 7 9 11 Fixed-point: binary point scaling Unsigned 8 0 Because all the input operands are unsigned, x is unsigned and the word length is 8. The fraction length of the resulting vector is always 0. Use the colon Operator With Signed and Unsigned Operands a= fi(int8(-1)); b = uint8(255); c = a:b; len = c.WordLength signedness = c.Signedness len = 9 signedness = Signed 2-212 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان colon The word length of c requires an additional bit to handle the intersection of the ranges of int8 and uint8. The data type of c is signed because the operand a is signed. Create a Vector of Decreasing Values If the beginning and ending operands are unsigned, the increment operand can be negative. x = fi(4,false):-1:1 x = 4 3 2 DataTypeMode: Signedness: WordLength: FractionLength: 1 Fixed-point: binary point scaling Unsigned 16 0 Use colon Operator With Floating-Point and fi operands If any of the operands is floating-point, the output has the same word length and signedness as the fi operand x = fi(1):10 x = Columns 1 through 6 1 2 3 4 Columns 7 through 10 7 8 9 10 DataTypeMode: Signedness: WordLength: FractionLength: 5 6 Fixed-point: binary point scaling Signed 16 0 x = fi(1):10 is equivalent to fi(1:10,true,16,0) so x is signed and its word length is 16 bits. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-213 colon Rewrite Code That Uses Non-Integer Operands If your code uses non-integer operands, rewrite the colon expression so that the operands are integers. The following code does not work because the colon operands are not integer values. Fs = fi(100); n = 1000; t = (0:1/Fs:(n/Fs - 1/Fs)); Rewrite the colon expression to use integer operands. Fs = fi(100); n = 1000; t = (0:(n-1))/Fs; All Colon Operands Must Be in the Range of the Data Type If the value of any of the colon operands is outside the range of the data type used in the colon expression, MATLAB generates an error. y = fi(1,true,8,0):256 MATLAB generates an error because 256 is outside the range of fi(1,true, 8,0). This behavior matches the behavior for built-in integers. For example, y = int8(1):256 generates the same error. See Also 2-214 colon | fi www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان comet Purpose Create 2-D comet plot Description Refer to the MATLAB comet reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-215 comet3 Purpose Create 3-D comet plot Description Refer to the MATLAB comet3 reference page for more information. 2-216 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان compass Purpose Plot arrows emanating from origin Description Refer to the MATLAB compass reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-217 complex Purpose Construct complex fi object from real and imaginary parts Syntax c = complex(a,b) c = complex(a) Description The complex function constructs a complex fi object from real and imaginary parts. c = complex(a,b) returns the complex result a + bi, where a and b are identically sized real N-D arrays, matrices, or scalars of the same data type. When b is all zero, c is complex with an all-zero imaginary part. This is in contrast to the addition of a + 0i, which returns a strictly real result. c = complex(a) for a real fi object a returns the complex result a + bi with real part a and an all-zero imaginary part. Even though its imaginary part is all zero, c is complex. The output fi object c has the same numerictype and fimath properties as the input fi object a. See Also 2-218 imag | real www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان coneplot Purpose Plot velocity vectors as cones in 3-D vector field Description Refer to the MATLAB coneplot reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-219 conj Purpose Complex conjugate of fi object Syntax conj(a) Description conj(a) is the complex conjugate of fi object a. When a is complex, conj(a) = real(a) − i × imag(a) The numerictype and fimath properties associated with the input a are applied to the output. See Also 2-220 complex | imag | real www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان contour Purpose Create contour graph of matrix Description Refer to the MATLAB contour reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-221 contour3 Purpose Create 3-D contour plot Description Refer to the MATLAB contour3 reference page for more information. 2-222 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان contourc Purpose Create two-level contour plot computation Description Refer to the MATLAB contourc reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-223 contourf Purpose Create filled 2-D contour plot Description Refer to the MATLAB contourf reference page for more information. 2-224 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان conv Purpose Convolution and polynomial multiplication of fi objects Syntax c = conv(a,b) c = conv(a,b,'shape') Description c = conv(a,b) outputs the convolution of input vectors a and b, at least one of which must be a fi object. c = conv(a,b,'shape') returns a subsection of the convolution, as specified by the shape parameter: • full — Returns the full convolution. This option is the default shape. • same — Returns the central part of the convolution that is the same size as input vector a. • valid — Returns only those parts of the convolution that the function computes without zero-padded edges. In this case, the length of output vector c is max(length(a)-max(0,length(b)-1), 0). The fimath properties associated with the inputs determine the numerictype properties of output fi object c: • If either a or b has a local fimath object, conv uses that fimath object to compute intermediate quantities and determine the numerictype properties of c. • If neither a nor b have an attached fimath, conv uses the default fimath to compute intermediate quantities and determine the numerictype properties of c. If either input is a built-in data type, conv casts it into a fi object using best-precision rules before the performing the convolution operation. The output fi object c always uses the default fimath. Refer to the MATLAB conv reference page for more information on the convolution algorithm. Examples The following example illustrates the convolution of a 22-sample sequence with a 16-tap FIR filter. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-225 conv • x is a 22-sample sequence of signed values with a word length of 16 bits and a fraction length of 15 bits. • h is the 16 tap FIR filter. u = (pi/4)*[1 1 1 -1 -1 -1 1 -1 -1 1 -1]; x = fi(kron(u,[1 1])); h = firls(15, [0 .1 .2 .5]*2, [1 1 0 0]); Because x is a fi object, you do not need to cast h into a fi object before performing the convolution operation. The conv function does so using best-precision scaling. Finally, use the conv function to convolve the two vectors: y = conv(x,h); The operation results in a signed fi object y with a word length of 36 bits and a fraction length of 31 bits. The default fimath properties associated with the inputs determine the numerictype of the output. The output does not have a local fimath. See Also 2-226 conv www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان convergent Purpose Round toward nearest integer with ties rounding to nearest even integer Syntax y = convergent(a) y = convergent(x) Description y = convergent(a) rounds fi object a to the nearest integer. In the case of a tie, convergent(a) rounds to the nearest even integer. y and a have the same fimath object and DataType property. When the DataType property of a is single, double, or boolean, the numerictype of y is the same as that of a. When the fraction length of a is zero or negative, a is already an integer, and the numerictype of y is the same as that of a. When the fraction length of a is positive, the fraction length of y is 0, its sign is the same as that of a, and its word length is the difference between the word length and the fraction length of a, plus one bit. If a is signed, then the minimum word length of y is 2. If a is unsigned, then the minimum word length of y is 1. For complex fi objects, the imaginary and real parts are rounded independently. convergent does not support fi objects with nontrivial slope and bias scaling. Slope and bias scaling is trivial when the slope is an integer power of 2 and the bias is 0. y = convergent(x) rounds the elements of x to the nearest integer. In the case of a tie, convergent(x) rounds to the nearest even integer. Examples Example 1 The following example demonstrates how the convergent function affects the numerictype properties of a signed fi object with a word length of 8 and a fraction length of 3. a = fi(pi, 1, 8, 3) a = www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-227 convergent 3.1250 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 8 3 y = convergent(a) y = 3 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 6 0 Example 2 The following example demonstrates how the convergent function affects the numerictype properties of a signed fi object with a word length of 8 and a fraction length of 12. a = fi(0.025,1,8,12) a = 0.0249 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 8 12 y = convergent(a) 2-228 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان convergent y = 0 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 2 0 Example 3 The functions convergent, nearest and round differ in the way they treat values whose least significant digit is 5: • The convergent function rounds ties to the nearest even integer • The nearest function rounds ties to the nearest integer toward positive infinity • The round function rounds ties to the nearest integer with greater absolute value The following table illustrates these differences for a given fi object a. a See Also convergent(a) nearest(a) round(a) –3.5 –4 –3 –4 –2.5 –2 –2 –3 –1.5 –2 –1 –2 –0.5 0 0 –1 0.5 0 1 1 1.5 2 2 2 2.5 2 3 3 3.5 4 4 4 ceil | fix | floor | nearest | round www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-229 copyobj Purpose Make independent copy of quantizer object Syntax q1 = copyobj(q) [q1,q2,...] = copyobj(obja,objb,...) Description q1 = copyobj(q) makes a copy of quantizer object q and returns it in q1. [q1,q2,...] = copyobj(obja,objb,...)copies obja into q1, objb into q2, and so on. Using copyobj to copy a quantizer object is not the same as using the command syntax q1 = q to copy a quantizer object. quantizer objects have memory (their read-only properties). When you use copyobj, the resulting copy is independent of the original item; it does not share the original object’s memory, such as the values of the properties min, max, noverflows, or noperations. Using q1 = q creates a new object that is an alias for the original and shares the original object’s memory, and thus its property values. Examples q = quantizer([8 7]); q1 = copyobj(q) See Also quantizer | get | set 2-230 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان cordicabs Purpose CORDIC-based absolute value Syntax r r r r Description r = cordicabs(c) returns the magnitude of the complex elements of C. = = = = cordicabs(c) cordicabs(c,niters) cordicabs(c,niters,'ScaleOutput',b) cordicabs(c,'ScaleOutput',b) r = cordicabs(c,niters) performs niters iterations of the algorithm. r = cordicabs(c,niters,'ScaleOutput',b) specifies both the number of iterations and, depending on the Boolean value of b, whether to scale the output by the inverse CORDIC gain value. r = cordicabs(c,'ScaleOutput',b) scales the output depending on the Boolean value of b. Input Arguments c c is a vector of complex values. niters niters is the number of iterations the CORDIC algorithm performs. This argument is optional. When specified, niters must be a positive, integer-valued scalar. If you do not specify niters, or if you specify a value that is too large, the algorithm uses a maximum value. For fixed-point operation, the maximum number of iterations is the word length of r or one less than the word length of theta, whichever is smaller. For floating-point operation, the maximum value is 52 for double or 23 for single. Increasing the number of iterations can produce more accurate results but also increases the expense of the computation and adds latency. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-231 cordicabs Name-Value Pair Arguments Optional comma-separated pairs of Name,Value arguments, where Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (''). ’ScaleOutput’ ScaleOutput is a Boolean value that specifies whether to scale the output by the inverse CORDIC gain factor. This argument is optional. If you set ScaleOutput to true or 1, the output values are multiplied by a constant, which incurs extra computations. If you set ScaleOutput to false or 0, the output is not scaled. Default: true Output Arguments r Definitions CORDIC r contains the magnitude values of the complex input values. If the inputs are fixed-point values, r is also fixed point (and is always signed, with binary point scaling). All input values must have the same data type. If the inputs are signed, then the word length of r is the input word length + 2. If the inputs are unsigned, then the word length of r is the input word length + 3. The fraction length of r is always the same as the fraction length of the inputs. CORDIC is an acronym for COordinate Rotation DIgital Computer. The Givens rotation-based CORDIC algorithm is among one of the most hardware-efficient algorithms available because it requires only iterative shift-add operations (see [1], [2]). The CORDIC algorithm eliminates the need for explicit multipliers. Using CORDIC, you can calculate various functions, such as sine, cosine, arc sine, arc cosine, arc tangent, and vector magnitude. You can also use this algorithm for divide, square root, hyperbolic, and logarithmic functions. 2-232 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان cordicabs Increasing the number of CORDIC iterations can produce more accurate results, but doing so also increases the expense of the computation and adds latency. Examples Compare cordicabs and abs of double values. dblValues = complex(rand(5,4),rand(5,4)); r_dbl_ref = abs(dblValues) r_dbl_cdc = cordicabs(dblValues) Compute absolute values of fixed-point inputs. fxpValues = fi(dblValues); r_fxp_cdc = cordicabs(fxpValues) References [1] Volder, JE. “The CORDIC Trigonometric Computing Technique.” IRE Transactions on Electronic Computers. Vol. EC-8, September 1959, pp. 330–334. [2] Andraka, R. “A survey of CORDIC algorithm for FPGA based computers.” Proceedings of the 1998 ACM/SIGDA sixth international symposium on Field programmable gate arrays. Feb. 22–24, 1998, pp. 191–200. See Also cordiccart2pol | cordicangle | abs www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-233 cordicangle Purpose CORDIC-based phase angle Syntax theta = cordicangle(c) theta = cordicangle(c,niters) Description theta = cordicangle(c) returns the phase angles, in radians, of matrix c, which contains complex elements. theta = cordicangle(c,niters) performs niters iterations of the algorithm. Input Arguments c Matrix of complex numbers niters niters is the number of iterations the CORDIC algorithm performs. This argument is optional. When specified, niters must be a positive, integer-valued scalar. If you do not specify niters, or if you specify a value that is too large, the algorithm uses a maximum value. For fixed-point operation, the maximum number of iterations is the word length of r or one less than the word length of theta, whichever is smaller. For floating-point operation, the maximum value is 52 for double or 23 for single. Increasing the number of iterations can produce more accurate results but also increases the expense of the computation and adds latency. Output Arguments 2-234 theta theta contains the polar coordinates angle values, which are in the range [–pi, pi] radians. If x and y are floating-point, then theta has the same data type as x and y. Otherwise, theta is a fixed-point data type with the same word length as x and y and with a best-precision fraction length for the [-pi, pi] range. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان cordicangle Definitions CORDIC CORDIC is an acronym for COordinate Rotation DIgital Computer. The Givens rotation-based CORDIC algorithm is among one of the most hardware-efficient algorithms available because it requires only iterative shift-add operations (see [1], [2]). The CORDIC algorithm eliminates the need for explicit multipliers. Using CORDIC, you can calculate various functions, such as sine, cosine, arc sine, arc cosine, arc tangent, and vector magnitude. You can also use this algorithm for divide, square root, hyperbolic, and logarithmic functions. Increasing the number of CORDIC iterations can produce more accurate results, but doing so also increases the expense of the computation and adds latency. Examples Phase angle for double-valued input and for fixed-point-valued input. dblRandomVals theta_dbl_ref theta_dbl_cdc fxpRandomVals theta_fxp_cdc = = = = = complex(rand(5,4), rand(5,4)); angle(dblRandomVals); cordicangle(dblRandomVals) fi(dblRandomVals); cordicangle(fxpRandomVals) theta_dbl_cdc = 1.0422 0.5893 0.5840 0.7212 1.3640 1.0987 0.8874 0.2113 0.2074 0.3288 1.2536 0.3580 0.8933 0.9820 1.4434 0.6122 0.2020 0.6355 0.8110 1.1291 1.2534 0.3579 0.8931 0.9819 1.4434 0.6123 0.2019 0.6357 0.8110 1.1289 theta_fxp_cdc = 1.0422 0.5894 0.5840 0.7212 1.3640 1.0989 0.8872 0.2112 0.2075 0.3289 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-235 cordicangle DataTypeMode: Signedness: WordLength: FractionLength: References Fixed-point: binary point scaling Signed 16 13 [1] Volder, JE. “The CORDIC Trigonometric Computing Technique.” IRE Transactions on Electronic Computers. Vol. EC-8, September 1959, pp. 330–334. [2] Andraka, R. “A survey of CORDIC algorithm for FPGA based computers.” Proceedings of the 1998 ACM/SIGDA sixth international symposium on Field programmable gate arrays. Feb. 22–24, 1998, pp. 191–200. See Also 2-236 cordicatan2 | cordiccart2pol | cordicabs | angle www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان cordicatan2 Purpose CORDIC-based four quadrant inverse tangent Syntax theta = cordicatan2(y,x) theta = cordicatan2(y,x,niters) Description theta = cordicatan2(y,x) computes the four quadrant arctangent of y and x using a “CORDIC” on page 2-266 algorithm approximation. theta = cordicatan2(y,x,niters) performs niters iterations of the algorithm. Input Arguments y,x y,x are Cartesian coordinates. y and x must be the same size. If they are not the same size, at least one value must be a scalar value. Both y and x must have the same data type. niters niters is the number of iterations the CORDIC algorithm performs. This is an optional argument. When specified, niters must be a positive, integer-valued scalar. If you do not specify niters or if you specify a value that is too large, the algorithm uses a maximum value. For fixed-point operation, the maximum number of iterations is one less than the word length of y or x. For floating-point operation, the maximum value is 52 for double or 23 for single. Increasing the number of iterations can produce more accurate results but also increases the expense of the computation and adds latency. Output Arguments theta theta is the arctangent value, which is in the range [-pi, pi] radians. If y and x are floating-point numbers, then theta has the same data type as y and x. Otherwise, theta is a fixed-point data type with the same word length as y and x and with a best-precision fraction length for the [-pi, pi] range. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-237 cordicatan2 Definitions CORDIC CORDIC is an acronym for COordinate Rotation DIgital Computer. The Givens rotation-based CORDIC algorithm is among one of the most hardware-efficient algorithms available because it requires only iterative shift-add operations (see [1], [2]). The CORDIC algorithm eliminates the need for explicit multipliers. Using CORDIC, you can calculate various functions, such as sine, cosine, arc sine, arc cosine, arc tangent, and vector magnitude. You can also use this algorithm for divide, square root, hyperbolic, and logarithmic functions. Increasing the number of CORDIC iterations can produce more accurate results, but doing so also increases the expense of the computation and adds latency. Examples Floating-point CORDIC arctangent calculation. theta_cdat2_float = cordicatan2(0.5,-0.5) theta_cdat2_float = 2.3562 Fixed- point CORDIC arctangent calculation. theta_cdat2_fixpt = cordicatan2(fi(0.5,1,16,15),fi(-0.5,1,16,15)); theta_cdat2_fixpt = 2.3562 DataTypeMode: Signedness: WordLength: FractionLength: References 2-238 Fixed-point: binary point scaling Signed 16 13 [1] Volder, JE. “The CORDIC Trigonometric Computing Technique.” IRE Transactions on Electronic Computers. Vol. EC-8, September 1959, pp. 330–334. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان cordicatan2 [2] Andraka, R. “A survey of CORDIC algorithm for FPGA based computers.” Proceedings of the 1998 ACM/SIGDA sixth international symposium on Field programmable gate arrays. Feb. 22–24, 1998, pp. 191–200. See Also atan2 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-239 cordiccart2pol Purpose CORDIC-based approximation of Cartesian-to-polar conversion Syntax [theta,r] [theta,r] [theta,r] [theta,r] Description [theta,r] = cordiccart2pol(x,y) using a CORDIC algorithm approximation, returns the polar coordinates, angle theta and radius r, of the Cartesian coordinates, x and y. = = = = cordiccart2pol(x,y) cordiccart2pol(x,y, niters) cordiccart2pol(x,y, niters,'ScaleOutput',b) cordiccart2pol(x,y, 'ScaleOutput',b) [theta,r] = cordiccart2pol(x,y, niters) performs niters iterations of the algorithm. [theta,r] = cordiccart2pol(x,y, niters,'ScaleOutput',b) specifies both the number of iterations and, depending on the Boolean value of b, whether to scale the r output by the inverse CORDIC gain value. [theta,r] = cordiccart2pol(x,y, 'ScaleOutput',b) scales the r output by the inverse CORDIC gain value, depending on the Boolean value of b. Input Arguments x,y x,y are Cartesian coordinates. x and y must be the same size. If they are not the same size, at least one value must be a scalar value. Both x and y must have the same data type. niters niters is the number of iterations the CORDIC algorithm performs. This argument is optional. When specified, niters must be a positive, integer-valued scalar. If you do not specify niters, or if you specify a value that is too large, the algorithm uses a maximum value. For fixed-point operation, the maximum number of iterations is the word length of r or one less than the word length of theta, whichever is smaller. For floating-point operation, the maximum value is 52 for double or 23 for single. Increasing the number of iterations can produce 2-240 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان cordiccart2pol more accurate results but also increases the expense of the computation and adds latency. Name-Value Pair Arguments Optional comma-separated pairs of Name,Value arguments, where Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (''). ’ScaleOutput’ ScaleOutput is a Boolean value that specifies whether to scale the output by the inverse CORDIC gain factor. This argument is optional. If you set ScaleOutput to true or 1, the output values are multiplied by a constant, which incurs extra computations. If you set ScaleOutput to false or 0, the output is not scaled. Default: true Output Arguments theta theta contains the polar coordinates angle values, which are in the range [–pi, pi] radians. If x and y are floating-point, then theta has the same data type as x and y. Otherwise, theta is a fixed-point data type with the same word length as x and y and with a best-precision fraction length for the [-pi, pi] range. r r contains the polar coordinates radius magnitude values. r is real-valued and can be a scalar value or have the same dimensions as theta If the inputs x,y are fixed-point values, r is also fixed point (and is always signed, with binary point scaling). Both x,y input values must have the same data type. If the inputs are signed, then the word length of r is the input word length + 2. If the inputs are unsigned, then the word length of r is the input word length + 3. The fraction length of r is always the same as the fraction length of the x,y inputs. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-241 cordiccart2pol Definitions CORDIC CORDIC is an acronym for COordinate Rotation DIgital Computer. The Givens rotation-based CORDIC algorithm is among one of the most hardware-efficient algorithms available because it requires only iterative shift-add operations (see [1], [2]). The CORDIC algorithm eliminates the need for explicit multipliers. Using CORDIC, you can calculate various functions, such as sine, cosine, arc sine, arc cosine, arc tangent, and vector magnitude. You can also use this algorithm for divide, square root, hyperbolic, and logarithmic functions. Increasing the number of CORDIC iterations can produce more accurate results, but doing so also increases the expense of the computation and adds latency. Examples Convert fixed-point Cartesian coordinates to polar coordinates. [thPos,r]=cordiccart2pol(sfi([0.75:-0.25:-1.0],16,15),sfi(0.5,16,15)) thPos = 0.5881 0.7854 1.1072 DataTypeMode: Signedness: WordLength: FractionLength: 1.5708 2.0344 2.3562 2.5535 2.6780 Fixed-point: binary point scaling Signed 16 13 r = 0.9014 0.7071 0.5591 DataTypeMode: Signedness: WordLength: FractionLength: 0.5000 0.5591 0.9014 Fixed-point: binary point scaling Signed 18 15 [thNeg,r]=... 2-242 0.7071 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 1.1180 cordiccart2pol cordiccart2pol(sfi([0.75:-0.25:-1.0],16,15),sfi(-0.5,16,15)) thNeg = -0.5881 -0.7854 -1.1072 -1.5708 -2.0344 -2.3562 -2.5535 -2.6780 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 16 13 r = 0.9014 0.7071 0.5591 DataTypeMode: Signedness: WordLength: FractionLength: References 0.5000 0.5591 0.7071 0.9014 1.1180 Fixed-point: binary point scaling Signed 18 15 [1] Volder, JE. “The CORDIC Trigonometric Computing Technique.” IRE Transactions on Electronic Computers. Vol. EC-8, September 1959, pp. 330–334. [2] Andraka, R. “A survey of CORDIC algorithm for FPGA based computers.” Proceedings of the 1998 ACM/SIGDA sixth international symposium on Field programmable gate arrays. Feb. 22–24, 1998, pp. 191–200. See Also cordicatan2 | cordicpol2cart | cart2pol www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-243 cordiccexp Purpose CORDIC-based approximation of complex exponential Syntax y = cordiccexp(theta,niters) Description y = cordiccexp(theta,niters) computes cos(theta) + j*sin(theta) using a “CORDIC” on page 2-266 algorithm approximation. y contains the approximated complex result. Input Arguments theta theta can be a signed or unsigned scalar, vector, matrix, or N-dimensional array containing the angle values in radians. All values of theta must be real and in the range [–2π 2π). niters niters is the number of iterations the CORDIC algorithm performs. This is an optional argument. When specified, niters must be a positive, integer-valued scalar. If you do not specify niters or if you specify a value that is too large, the algorithm uses a maximum value. For fixed-point operation, the maximum number of iterations is one less than the word length of theta. For floating-point operation, the maximum value is 52 for double or 23 for single. Increasing the number of iterations can produce more accurate results, but it also increases the expense of the computation and adds latency. Output Arguments y Definitions CORDIC y is the approximated complex result of the cordiccexp function. When the input to the function is floating point, the output data type is the same as the input data type. When the input is fixed point, the output has the same word length as the input, and a fraction length equal to the WordLength – 2. CORDIC is an acronym for COordinate Rotation DIgital Computer. The Givens rotation-based CORDIC algorithm is among one of the 2-244 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان cordiccexp most hardware-efficient algorithms available because it requires only iterative shift-add operations (see [1], [2]). The CORDIC algorithm eliminates the need for explicit multipliers. Using CORDIC, you can calculate various functions, such as sine, cosine, arc sine, arc cosine, arc tangent, and vector magnitude. You can also use this algorithm for divide, square root, hyperbolic, and logarithmic functions. Increasing the number of CORDIC iterations can produce more accurate results, but doing so also increases the expense of the computation and adds latency. Examples The following example illustrates the effect of the number of iterations on the result of the cordiccexp approximation. wrdLn = 8; theta = fi(pi/2, 1, wrdLn); fprintf('\n\nNITERS\t\tY (SIN)\t ERROR\t LSBs\t\tX (COS)\t ERROR\t LSBs\n'); fprintf('------\t\t-------\t ------\t ----\t\t-------\t ------\t ----\n'); for niters = 1:(wrdLn - 1) cis = cordiccexp(theta, niters); fl = cis.FractionLength; x = real(cis); y = imag(cis); x_dbl = double(x); x_err = abs(x_dbl - cos(double(theta))); y_dbl = double(y); y_err = abs(y_dbl - sin(double(theta))); fprintf('%d\t\t%1.4f\t%1.4f\t%1.1f\t\t%1.4f\t%1.4f\t%1.1f\n',... niters,y_dbl,y_err,(y_err*pow2(fl)),x_dbl,x_err,(x_err*pow2(fl))); end fprintf('\n'); The output table appears as follows: NITERS ------ Y (SIN) ERROR LSBs ------- ------ ---- X (COS) ------- www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان ERROR ------ LSBs ---- 2-245 cordiccexp 1 2 3 4 5 6 7 References 0.7031 0.9375 0.9844 0.9844 1.0000 1.0000 1.0000 0.2968 0.0625 0.0156 0.0156 0.0000 0.0000 0.0000 19.0 4.0 1.0 1.0 0.0 0.0 0.0 0.7031 0.3125 0.0938 -0.0156 0.0312 0.0000 0.0156 0.7105 0.3198 0.1011 0.0083 0.0386 0.0073 0.0230 45.5 20.5 6.5 0.5 2.5 0.5 1.5 [1] Volder, JE. “The CORDIC Trigonometric Computing Technique.” IRE Transactions on Electronic Computers. Vol. EC-8, September 1959, pp. 330–334. [2] Andraka, R. “A survey of CORDIC algorithm for FPGA based computers.” Proceedings of the 1998 ACM/SIGDA sixth international symposium on Field programmable gate arrays. Feb. 22–24, 1998, pp. 191–200. See Also cordiccos | cordicsin | cordicsincos Tutorials • Demo: Fixed-Point Sine and Cosine Calculation • Demo: Fixed-Point Arctangent Calculation 2-246 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان cordiccos Purpose CORDIC-based approximation of cosine Syntax y = cordiccos(theta, niters) Description y = cordiccos(theta, niters) computes the cosine of theta using a Input Arguments theta “CORDIC” on page 2-266 algorithm approximation. theta can be a signed or unsigned scalar, vector, matrix, or N-dimensional array containing the angle values in radians. All values of theta must be real and in the range [–2π 2π). niters niters is the number of iterations the CORDIC algorithm performs. This is an optional argument. When specified, niters must be a positive, integer-valued scalar. If you do not specify niters or if you specify a value that is too large, the algorithm uses a maximum value. For fixed-point operation, the maximum number of iterations is one less than the word length of theta. For floating-point operation, the maximum value is 52 for double or 23 for single. Increasing the number of iterations can produce more accurate results, but it also increases the expense of the computation and adds latency. Output Arguments Definitions y y is the CORDIC-based approximation of the cosine of theta. When the input to the function is floating point, the output data type is the same as the input data type. When the input is fixed point, the output has the same word length as the input, and a fraction length equal to the WordLength – 2. CORDIC CORDIC is an acronym for COordinate Rotation DIgital Computer. The Givens rotation-based CORDIC algorithm is among one of the most hardware-efficient algorithms available because it requires only www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-247 cordiccos iterative shift-add operations (see [1], [2]). The CORDIC algorithm eliminates the need for explicit multipliers. Using CORDIC, you can calculate various functions, such as sine, cosine, arc sine, arc cosine, arc tangent, and vector magnitude. You can also use this algorithm for divide, square root, hyperbolic, and logarithmic functions. Increasing the number of CORDIC iterations can produce more accurate results, but doing so also increases the expense of the computation and adds latency. Examples Compare the results produced by various iterations of the cordiccos algorithm to the results of the double-precision cos function: % Create stepSize thRadDbl thRadFxp cosThRef 1024 points between [0, 2*pi) = pi/512; = 0:stepSize:(2*pi - stepSize); % signed, 12-bit fixed-point = sfi(thRadDbl, 12); % reference results = cos(double(thRadFxp)); % Use 12-bit quantized inputs and vary the number % of iterations from 2 to 10. % Compare the fixed-point CORDIC results to the % double-precision trig function results. for niters = 2:2:10 cdcCosTh = cordiccos(thRadFxp, niters); errCdcRef = cosThRef - double(cdcCosTh); figure; hold on; axis([0 2*pi -1.25 1.25]); plot(thRadFxp, cosThRef, 'b'); plot(thRadFxp, cdcCosTh, 'g'); plot(thRadFxp, errCdcRef, 'r'); ylabel('cos(\Theta)'); set(gca,'XTick',0:pi/2:2*pi); set(gca,'XTickLabel',{'0','pi/2','pi','3*pi/2','2*pi'}); set(gca,'YTick',-1:0.5:1); set(gca,'YTickLabel',{'-1.0','-0.5','0','0.5','1.0'}); ref_str = 'Reference: cos(double(\Theta))'; cdc_str = sprintf('12-bit CORDIC cosine; N = %d', niters); 2-248 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان cordiccos err_str = sprintf('Error (max = %f)', max(abs(errCdcRef))); legend(ref_str, cdc_str, err_str); end After 10 iterations, the CORDIC algorithm has approximated the cosine of theta to within 0.005187 of the double-precision cosine result. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-249 cordiccos References 2-250 [1] Volder, JE. “The CORDIC Trigonometric Computing Technique.” IRE Transactions on Electronic Computers. Vol. EC-8, September 1959, pp. 330–334. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان cordiccos [2] Andraka, R. “A survey of CORDIC algorithm for FPGA based computers.” Proceedings of the 1998 ACM/SIGDA sixth international symposium on Field programmable gate arrays. Feb. 22–24, 1998, pp. 191–200. See Also cordiccexp | cordicsin | cordicsincos Tutorials • Demo: Fixed-Point Sine and Cosine Calculation • Demo: Fixed-Point Arctangent Calculation www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-251 cordicpol2cart Purpose CORDIC-based approximation of polar-to-Cartesian conversion Syntax [x,y] [x,y] [x,y] [x,y] Description [x,y] = cordicpol2cart(theta,r) returns the Cartesian = = = = cordicpol2cart(theta,r) cordicpol2cart(theta,r,niters) cordicpol2cart(theta,r,Name,Value) cordicpol2cart(theta,r,niters,Name,Value) xy coordinates of r* e^(j*theta) using a CORDIC algorithm approximation. [x,y] = cordicpol2cart(theta,r,niters) performs niters iterations of the algorithm. [x,y] = cordicpol2cart(theta,r,Name,Value) scales the output depending on the Boolean value of b. [x,y] = cordicpol2cart(theta,r,niters,Name,Value) specifies both the number of iterations and Name,Value pair for whether to scale the output. Input Arguments theta theta can be a signed or unsigned scalar, vector, matrix, or N-dimensional array containing the angle values in radians. All values of theta must be in the range [–2π 2π). r r contains the input magnitude values and can be a scalar or have the same dimensions as theta. r must be real valued. niters niters is the number of iterations the CORDIC algorithm performs. This argument is optional. When specified, niters must be a positive, integer-valued scalar. If you do not specify niters, or if you specify a value that is too large, the algorithm uses a maximum value. For fixed-point operation, the maximum number of iterations is the word 2-252 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان cordicpol2cart length of r or one less than the word length of theta, whichever is smaller. For floating-point operation, the maximum value is 52 for double or 23 for single. Increasing the number of iterations can produce more accurate results but also increases the expense of the computation and adds latency. Name-Value Pair Arguments Optional comma-separated pairs of Name,Value arguments, where Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (''). ’ScaleOutput’ ScaleOutput is a Boolean value that specifies whether to scale the output by the inverse CORDIC gain factor. This argument is optional. If you set ScaleOutput to true or 1, the output values are multiplied by a constant, which incurs extra computations. If you set ScaleOutput to false or 0, the output is not scaled. Default: true Output Arguments [x,y] [x,y] contains the approximated Cartesian coordinates. When the input r is floating point, the output [x,y] has the same data type as the input. When the input r is a signed integer or fixed point data type, the outputs [x,y] are signed fi objects. These fi objects have word lengths that are two bits larger than that of r. Their fraction lengths are the same as the fraction length of r. When the input r is an unsigned integer or fixed point, the outputs [x,y] are signed fi objects. These fi objects have word lengths are three bits larger than that of r. Their fraction lengths are the same as the fraction length of r. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-253 cordicpol2cart Definitions CORDIC CORDIC is an acronym for COordinate Rotation DIgital Computer. The Givens rotation-based CORDIC algorithm is among one of the most hardware-efficient algorithms available because it requires only iterative shift-add operations (see [1], [2]). The CORDIC algorithm eliminates the need for explicit multipliers. Using CORDIC, you can calculate various functions, such as sine, cosine, arc sine, arc cosine, arc tangent, and vector magnitude. You can also use this algorithm for divide, square root, hyperbolic, and logarithmic functions. Increasing the number of CORDIC iterations can produce more accurate results, but doing so also increases the expense of the computation and adds latency. Examples Run the following code, and evaluate the accuracy of the CORDIC-based Polar-to-Cartesian conversion. wrdLn = 16; theta = fi(pi/3, 1, wrdLn); u = fi( 2.0, 1, wrdLn); fprintf('\n\nNITERS\tX\t\t ERROR\t LSBs\t\tY\t\t ERROR\t LSBs\n'); fprintf('------\t-------\t ------\t ----\t\t-------\t ------\t ----\n'); for niters = 1:(wrdLn - 1) [x_ref, y_ref] = pol2cart(double(theta),double(u)); [x_fi, y_fi] = cordicpol2cart(theta, u, niters); x_dbl = double(x_fi); y_dbl = double(y_fi); x_err = abs(x_dbl - x_ref); y_err = abs(y_dbl - y_ref); fprintf('%d\t%1.4f\t %1.4f\t %1.1f\t\t%1.4f\t %1.4f\t %1.1f\n',... niters,x_dbl,x_err,(x_err * pow2(x_fi.FractionLength)),... y_dbl,y_err,(y_err * pow2(y_fi.FractionLength))); end fprintf('\n'); 2-254 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان cordicpol2cart NITERS X ------ ------1 1.4142 2 0.6324 3 1.0737 4 0.8561 5 0.9672 6 1.0214 7 0.9944 8 1.0079 9 1.0011 10 0.9978 11 0.9994 12 1.0002 13 0.9999 14 0.9996 15 0.9998 References ERROR LSBs Y ERROR LSBs ------ ---- ------- ------ ---0.4142 3392.8 1.4142 0.3178 2603.8 0.3676 3011.2 1.8973 0.1653 1354.2 0.0737 603.8 1.6873 0.0448 366.8 0.1440 1179.2 1.8074 0.0753 617.2 0.0329 269.2 1.7505 0.0185 151.2 0.0213 174.8 1.7195 0.0126 102.8 0.0056 46.2 1.7351 0.0031 25.2 0.0079 64.8 1.7274 0.0046 37.8 0.0011 8.8 1.7313 0.0007 5.8 0.0022 18.2 1.7333 0.0012 10.2 0.0006 5.2 1.7323 0.0003 2.2 0.0002 1.8 1.7318 0.0002 1.8 0.0002 1.2 1.7321 0.0000 0.2 0.0004 3.2 1.7321 0.0000 0.2 0.0003 2.2 1.7321 0.0000 0.2 [1] Volder, JE. “The CORDIC Trigonometric Computing Technique.” IRE Transactions on Electronic Computers. Vol. EC-8, September 1959, pp. 330–334. [2] Andraka, R. “A survey of CORDIC algorithm for FPGA based computers.” Proceedings of the 1998 ACM/SIGDA sixth international symposium on Field programmable gate arrays. Feb. 22–24, 1998, pp. 191–200. See Also cordicrotate | cordicsincos | pol2cart www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-255 cordicrotate Purpose Rotate input using CORDIC-based approximation Syntax v v v v Description v = cordicrotate(theta,u) rotates the input u by theta using a = = = = cordicrotate(theta,u) cordicrotate(theta,u,niters) cordicrotate(theta,u,Name,Value) cordicrotate(theta,u,niters,Name,Value) CORDIC algorithm approximation. The function returns the result of u .* e^(j*theta). v = cordicrotate(theta,u,niters) performs niters iterations of the algorithm. v = cordicrotate(theta,u,Name,Value) scales the output depending on the Boolean value, b. v = cordicrotate(theta,u,niters,Name,Value) specifies both the number of iterations and the Name,Value pair for whether to scale the output. Input Arguments theta theta can be a signed or unsigned scalar, vector, matrix, or N-dimensional array containing the angle values in radians. All values of theta must be in the range [–2π 2π). u u can be a signed or unsigned scalar value or have the same dimensions as theta. u can be real or complex valued. niters niters is the number of iterations the CORDIC algorithm performs. This argument is optional. When specified, niters must be a positive, integer-valued scalar. If you do not specify niters, or if you specify a value that is too large, the algorithm uses a maximum value. For fixed-point operation, the maximum number of iterations is the word 2-256 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان cordicrotate length of u or one less than the word length of theta, whichever is smaller. For floating-point operation, the maximum value is 52 for double or 23 for single. Increasing the number of iterations can produce more accurate results, but it also increases the expense of the computation and adds latency. Name-Value Pair Arguments Optional comma-separated pairs of Name,Value arguments, where Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (''). ’ScaleOutput’ ScaleOutput is a Boolean value that specifies whether to scale the output by the inverse CORDIC gain factor. This argument is optional. If you set ScaleOutput to true or 1, the output values are multiplied by a constant, which incurs extra computations. If you set ScaleOutput to false or 0, the output is not scaled. Default: true Output Arguments v v contains the approximated result of the CORDIC rotation algorithm. When the input u is floating point, the output v has the same data type as the input. When the input u is a signed integer or fixed point data type, the output v is a signed fi object. This fi object has a word length that is two bits larger than that of u. Its fraction length is the same as the fraction length of u. When the input u is an unsigned integer or fixed point, the output v is a signed fi object. This fi object has a word length that is three bits larger than that of u. Its fraction length is the same as the fraction length of u. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-257 cordicrotate Definitions CORDIC CORDIC is an acronym for COordinate Rotation DIgital Computer. The Givens rotation-based CORDIC algorithm is among one of the most hardware-efficient algorithms available because it requires only iterative shift-add operations (see [1], [2]). The CORDIC algorithm eliminates the need for explicit multipliers. Using CORDIC, you can calculate various functions, such as sine, cosine, arc sine, arc cosine, arc tangent, and vector magnitude. You can also use this algorithm for divide, square root, hyperbolic, and logarithmic functions. Increasing the number of CORDIC iterations can produce more accurate results, but doing so also increases the expense of the computation and adds latency. Examples Run the following code, and evaluate the accuracy of the CORDIC-based complex rotation. wrdLn theta u uTeTh = = = = 16; fi(-pi/3, 1, wrdLn); fi(0.25 - 7.1i, 1, wrdLn); double(u) .* exp(1i * double(theta)); fprintf('\n\nNITERS\tReal\t ERROR\t LSBs\t\tImag\tERROR\tLSBs\n'); fprintf('------\t-------\t ------\t ----\t\t-------\t------\t----\n'); for niters = 1:(wrdLn - 1) v_fi = cordicrotate(theta, u, niters); v_dbl = double(v_fi); x_err = abs(real(v_dbl) - real(uTeTh)); y_err = abs(imag(v_dbl) - imag(uTeTh)); fprintf('%d\t%1.4f\t %1.4f\t %1.1f\t\t%1.4f\t %1.4f\t %1.1f\n',... niters, real(v_dbl),x_err,(x_err * pow2(v_fi.FractionLength)), ... imag(v_dbl),y_err, (y_err * pow2(v_fi.FractionLength))); end fprintf('\n'); The output table appears as follows: 2-258 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان cordicrotate NITERS -----1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 References Real -------4.8438 -6.6567 -5.8560 -6.3098 -6.0935 -5.9766 -6.0359 -6.0061 -6.0210 -6.0286 -6.0247 -6.0227 -6.0237 -6.0242 -6.0239 ERROR LSBs Imag ERROR LSBs ------ ---- ------- ------ -----1.1800 4833.5 -5.1973 1.4306 5859.8 0.6329 2592.5 -2.4824 1.2842 5260.2 0.1678 687.5 -4.0227 0.2560 1048.8 0.2860 1171.5 -3.2649 0.5018 2055.2 0.0697 285.5 -3.6528 0.1138 466.2 0.0472 193.5 -3.8413 0.0746 305.8 0.0121 49.5 -3.7476 0.0191 78.2 0.0177 72.5 -3.7947 0.0280 114.8 0.0028 11.5 -3.7710 0.0043 17.8 0.0048 19.5 -3.7590 0.0076 31.2 0.0009 3.5 -3.7651 0.0015 6.2 0.0011 4.5 -3.7683 0.0017 6.8 0.0001 0.5 -3.7666 0.0001 0.2 0.0004 1.5 -3.7656 0.0010 4.2 0.0001 0.5 -3.7661 0.0005 2.2 [1] Volder, JE. “The CORDIC Trigonometric Computing Technique.” IRE Transactions on Electronic Computers. Vol. EC-8, September 1959, pp. 330–334. [2] Andraka, R. “A survey of CORDIC algorithm for FPGA based computers.” Proceedings of the 1998 ACM/SIGDA sixth international symposium on Field programmable gate arrays. Feb. 22–24, 1998, pp. 191–200. See Also cordicpol2cart | cordiccexp www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-259 cordicsin Purpose CORDIC-based approximation of sine Syntax y = cordicsin(theta,niters) Description y = cordicsin(theta,niters) computes the sine of theta using a Input Arguments theta “CORDIC” on page 2-266 algorithm approximation. theta can be a signed or unsigned scalar, vector, matrix, or N-dimensional array containing the angle values in radians. All values of theta must be real and in the range [–2π 2π). niters niters is the number of iterations the CORDIC algorithm performs. This is an optional argument. When specified, niters must be a positive, integer-valued scalar. If you do not specify niters or if you specify a value that is too large, the algorithm uses a maximum value. For fixed-point operation, the maximum number of iterations is one less than the word length of theta. For floating-point operation, the maximum value is 52 for double or 23 for single. Increasing the number of iterations can produce more accurate results, but it also increases the expense of the computation and adds latency. Output Arguments y y is the CORDIC-based approximation of the sine of theta. When the input to the function is floating point, the output data type is the same as the input data type. When the input is fixed point, the output has the same word length as the input, and a fraction length equal to the WordLength – 2. Definitions CORDIC CORDIC is an acronym for COordinate Rotation DIgital Computer. The Givens rotation-based CORDIC algorithm is among one of the most hardware-efficient algorithms available because it requires only 2-260 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان cordicsin iterative shift-add operations (see [1], [2]). The CORDIC algorithm eliminates the need for explicit multipliers. Using CORDIC, you can calculate various functions, such as sine, cosine, arc sine, arc cosine, arc tangent, and vector magnitude. You can also use this algorithm for divide, square root, hyperbolic, and logarithmic functions. Increasing the number of CORDIC iterations can produce more accurate results, but doing so also increases the expense of the computation and adds latency. Examples Compare the results produced by various iterations of the cordicsin algorithm to the results of the double-precision sin function: % Create stepSize thRadDbl thRadFxp sinThRef 1024 points between [0, 2*pi) = pi/512; = 0:stepSize:(2*pi - stepSize); = sfi(thRadDbl, 12); % signed, 12-bit fixed point = sin(double(thRadFxp)); % reference results % Use 12-bit quantized inputs and vary the number of iterations % from 2 to 10. % Compare the fixed-point cordicsin function results to the % results of the double-precision sin function. for niters = 2:2:10 cdcSinTh = cordicsin(thRadFxp, niters); errCdcRef = sinThRef - double(cdcSinTh); figure; hold on; axis([0 2*pi -1.25 1.25]); plot(thRadFxp, sinThRef, 'b'); plot(thRadFxp, cdcSinTh, 'g'); plot(thRadFxp, errCdcRef, 'r'); ylabel('sin(\Theta)'); set(gca,'XTick',0:pi/2:2*pi); set(gca,'XTickLabel',{'0','pi/2','pi','3*pi/2','2*pi'}); set(gca,'YTick',-1:0.5:1); set(gca,'YTickLabel',{'-1.0','-0.5','0','0.5','1.0'}); ref_str = 'Reference: sin(double(\Theta))'; cdc_str = sprintf('12-bit CORDIC sine; N = %d', niters); www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-261 cordicsin err_str = sprintf('Error (max = %f)', max(abs(errCdcRef))); legend(ref_str, cdc_str, err_str); end After 10 iterations, the CORDIC algorithm has approximated the sine of theta to within 0.005492 of the double-precision sine result. 2-262 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان cordicsin References [1] Volder, JE. “The CORDIC Trigonometric Computing Technique.” IRE Transactions on Electronic Computers. Vol. EC-8, September 1959, pp. 330–334. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-263 cordicsin [2] Andraka, R. “A survey of CORDIC algorithm for FPGA based computers.” Proceedings of the 1998 ACM/SIGDA sixth international symposium on Field programmable gate arrays. Feb. 22–24, 1998, pp. 191–200. See Also cordiccexp | cordiccos | cordicsincos Tutorials • Demo: Fixed-Point Sine and Cosine Calculation • Demo: Fixed-Point Arctangent Calculation 2-264 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان cordicsincos Purpose CORDIC-based approximation of sine and cosine Syntax [y, x] = cordicsincos(theta,niters) Description [y, x] = cordicsincos(theta,niters) computes the sine and cosine of theta using a “CORDIC” on page 2-266 algorithm approximation. y contains the approximated sine result, and x contains the approximated cosine result. Input Arguments theta theta can be a signed or unsigned scalar, vector, matrix, or N-dimensional array containing the angle values in radians. All values of theta must be real and in the range [–2π 2π). When theta has a fixed-point data type, it must be signed. niters niters is the number of iterations the CORDIC algorithm performs. This is an optional argument. When specified, niters must be a positive, integer-valued scalar. If you do not specify niters or if you specify a value that is too large, the algorithm uses a maximum value. For fixed-point operation, the maximum number of iterations is one less than the word length of theta. For floating-point operation, the maximum value is 52 for double or 23 for single. Increasing the number of iterations can produce more accurate results, but it also increases the expense of the computation and adds latency. Output Arguments y CORDIC-based approximated sine of theta. When the input to the function is floating point, the output data type is the same as the input data type. When the input is fixed point, the output has the same word length as the input, and a fraction length equal to the WordLength – 2. x www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-265 cordicsincos CORDIC-based approximated cosine of theta. When the input to the function is floating point, the output data type is the same as the input data type. When the input is fixed point, the output has the same word length as the input, and a fraction length equal to the WordLength – 2. Definitions CORDIC CORDIC is an acronym for COordinate Rotation DIgital Computer. The Givens rotation-based CORDIC algorithm is among one of the most hardware-efficient algorithms available because it requires only iterative shift-add operations (see [1], [2]). The CORDIC algorithm eliminates the need for explicit multipliers. Using CORDIC, you can calculate various functions, such as sine, cosine, arc sine, arc cosine, arc tangent, and vector magnitude. You can also use this algorithm for divide, square root, hyperbolic, and logarithmic functions. Increasing the number of CORDIC iterations can produce more accurate results, but doing so also increases the expense of the computation and adds latency. Examples The following example illustrates the effect of the number of iterations on the result of the cordicsincos approximation. wrdLn = 8; theta = fi(pi/2, 1, wrdLn); fprintf('\n\nNITERS\t\tY (SIN)\t ERROR\t LSBs\t\tX (COS)\t ERROR\t LSBs\n'); fprintf('------\t\t-------\t ------\t ----\t\t-------\t ------\t ----\n'); for niters = 1:(wrdLn - 1) [y, x] = cordicsincos(theta, niters); y_FL = y.FractionLength; y_dbl = double(y); x_dbl = double(x); y_err = abs(y_dbl - sin(double(theta))); x_err = abs(x_dbl - cos(double(theta))); fprintf(' %d\t\t%1.4f\t %1.4f\t %1.1f\t\t%1.4f\t %1.4f\t %1.1f\n', ... niters, y_dbl,y_err, (y_err * pow2(y_FL)), x_dbl,x_err, ... (x_err * pow2(y_FL))); 2-266 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان cordicsincos end fprintf('\n'); The output table appears as follows: NITERS -----1 2 3 4 5 6 7 References Y (SIN) ------0.7031 0.9375 0.9844 0.9844 1.0000 1.0000 1.0000 ERROR -----0.2968 0.0625 0.0156 0.0156 0.0000 0.0000 0.0000 LSBs ---19.0 4.0 1.0 1.0 0.0 0.0 0.0 X (COS) ------0.7031 0.3125 0.0938 -0.0156 0.0312 0.0000 0.0156 ERROR -----0.7105 0.3198 0.1011 0.0083 0.0386 0.0073 0.0230 LSBs ---45.5 20.5 6.5 0.5 2.5 0.5 1.5 [1] Volder, JE. “The CORDIC Trigonometric Computing Technique.” IRE Transactions on Electronic Computers. Vol. EC-8, September 1959, pp. 330–334. [2] Andraka, R. “A survey of CORDIC algorithm for FPGA based computers.” Proceedings of the 1998 ACM/SIGDA sixth international symposium on Field programmable gate arrays. Feb. 22–24, 1998, pp. 191–200. See Also cordiccexp | cordiccos | cordicsin Tutorials • Demo: Fixed-Point Sine and Cosine Calculation • Demo: Fixed-Point Arctangent Calculation www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-267 cos Purpose Cosine of fi object Syntax y = cos(theta) Description y = cos(theta) returns the cosine of fi input theta using a Input Arguments theta table-lookup algorithm. theta can be a real-valued, signed or unsigned scalar, vector, matrix, or N-dimensional array containing the fixed-point angle values in radians. Valid data types of theta are: • fi single • fi double • fi fixed-point with binary point scaling • fi scaled double with binary point scaling Output Arguments Definitions y y is the cosine of theta. y is a signed, fixed-point number in the range [-1,1]. It has a 16-bit word length and 15-bit fraction length (numerictype(1,16,15)). This cosine calculation is accurate only to within the top 16 most-significant bits of the input. Cosine The cosine of angle Θ is defined as cos( ) Examples ei ei 2 Calculate the cosine of fixed-point input values. theta = fi([0,pi/4,pi/3,pi/2,(2*pi)/3,(3*pi)/4,pi]) 2-268 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان cos theta = 0 0.7854 1.0472 DataTypeMode: Signedness: WordLength: FractionLength: 1.5708 2.0944 2.3562 3.1416 Fixed-point: binary point scaling Signed 16 13 y = cos(theta) y = 1.0000 0.7072 0.4999 DataTypeMode: Signedness: WordLength: FractionLength: Algorithms 0.0001 -0.4999 -0.7070 -1.0000 Fixed-point: binary point scaling Signed 16 15 The cos function computes the cosine of fixed-point input using an 8-bit lookup table as follows: 1 Cast the input to a 16-bit stored integer value, using the 16 most-significant bits. 2 Perform a modulo 2π, so the input is in the range [0,2π) radians. 3 Compute the table index, based on the 16-bit stored integer value, normalized to the full uint16 range. 4 Use the 8 most-significant bits to obtain the first value from the table. 5 Use the next-greater table value as the second value. 6 Use the 8 least-significant bits to interpolate between the first and second values, using nearest-neighbor linear interpolation. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-269 cos See Also 2-270 cos | angle | sin | atan2 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان ctranspose Purpose Complex conjugate transpose of fi object Syntax ctranspose(a) Description ctranspose(a) returns the complex conjugate transpose of fi object a. It is also called for the syntax a'. See Also transpose www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-271 dec Purpose Unsigned decimal representation of stored integer of fi object Syntax dec(a) Description dec(a) returns the stored integer of fi object a in unsigned decimal format as a string. dec(a) is equivalent to a.dec. . Fixed-point numbers can be represented as real-world value = 2− fraction length × stored integer or, equivalently as real-world value = (slope × stored integer) + bias The stored integer is the raw binary number, in which the binary point is assumed to be at the far right of the word. Examples The code a = fi([-1 1],1,8,7); y = dec(a) z = a.dec returns y = 128 127 z = 128 See Also 2-272 127 bin | hex | storedInteger | oct | sdec www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان denormalmax Purpose Largest denormalized quantized number for quantizer object Syntax x = denormalmax(q) Description x = denormalmax(q) is the largest positive denormalized quantized number where q is a quantizer object. Anything larger than x is a normalized number. Denormalized numbers apply only to floating-point format. When q represents fixed-point numbers, this function returns eps(q). Examples q = quantizer('float',[6 3]); x = denormalmax(q) x = 0.1875 Algorithms When q is a floating-point quantizer object, denormalmax(q) = realmin(q) - denormalmin(q) When q is a fixed-point quantizer object, denormalmax(q) = eps(q) See Also denormalmin | eps | quantizer www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-273 denormalmin Purpose Smallest denormalized quantized number for quantizer object Syntax x = denormalmin(q) Description x = denormalmin(q) is the smallest positive denormalized quantized number where q is a quantizer object. Anything smaller than x underflows to zero with respect to the quantizer object q. Denormalized numbers apply only to floating-point format. When q represents a fixed-point number, denormalmin returns eps(q). Examples q = quantizer('float',[6 3]); x = denormalmin(q) x = 0.0625 Algorithms When q is a floating-point quantizer object, x = 2 Emin − f where Emin is equal to exponentmin(q). When q is a fixed-point quantizer object, x = eps(q) = 2− f where f is equal to fractionlength(q). See Also 2-274 denormalmax | eps | quantizer www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان diag Purpose Diagonal matrices or diagonals of matrix Description Refer to the MATLAB diag reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-275 disp Purpose Display object Description Refer to the MATLAB disp reference page for more information. 2-276 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان divide Purpose Divide two objects Syntax c = divide(T,a,b) c = T.divide(a,b) Description c = divide(T,a,b) and c = T.divide(a,b) perform division on the elements of a by the elements of b. The result c has the numerictype object T. If a and b are both fi objects, c has the same fimath object as a. If c has a fi Fixed data type, and any one of the inputs have fi floating point data types, then the fi floating point is converted into a fixed-point value. Intermediate quantities are calculated using the fimath object of a. See “Data Type Propagation Rules” on page 2-277. a and b must have the same dimensions unless one is a scalar. If either a or b is scalar, then c has the dimensions of the nonscalar object. If either a or b is a fi object, and the other is a MATLAB built-in numeric type, then the built-in object is cast to the word length of the fi object, preserving best-precision fraction length. Intermediate quantities are calculated using the fimath object of the input fi object. See “Data Type Propagation Rules” on page 2-277. If a and b are both MATLAB built-in doubles, then c is the floating-point quotient a./b, and numerictype T is ignored. Note The divide function is not currently supported for [Slope Bias] signals. Data Type Propagation Rules For syntaxes for which Fixed-Point Designer software uses the numerictype object T, the divide function follows the data type propagation rules listed in the following table. In general, these rules can be summarized as “floating-point data types are propagated.” This allows you to write code that can be used with both fixed-point and floating-point inputs. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-277 divide Data Type of Input fi Objects a and b Data Type of numerictype object T Data Type of Output c Built-in double Built-in double Any Built-in double fi Fixed fi Fixed fi Fixed Data type of numerictype object T fi Fixed fi Fixed fi double fi double fi Fixed fi Fixed fi single fi single fi Fixed fi Fixed fi ScaledDouble fi ScaledDouble with properties of numerictype object T fi double fi double fi Fixed fi double fi double fi double fi double fi double fi double fi double fi single fi single fi double fi double fi ScaledDouble fi double fi single fi single fi Fixed fi single fi single fi single fi double fi double fi single fi single fi single fi single fi single fi single fi ScaledDouble fi single fi ScaledDouble fi ScaledDouble fi Fixed fi ScaledDouble with properties of numerictype object T 2-278 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان divide Data Type of Input fi Objects a and b Data Type of numerictype object T Data Type of Output c fi ScaledDouble fi ScaledDouble fi double fi double fi ScaledDouble fi ScaledDouble fi single fi single fi ScaledDouble fi ScaledDouble fi ScaledDouble fi ScaledDouble with properties of numerictype object T Examples This example highlights the precision of the fi divide function. First, create an unsigned fi object with an 80-bit word length and 2^-83 scaling, which puts the leading 1 of the representation into the most significant bit. Initialize the object with double-precision floating-point value 0.1, and examine the binary representation: P = ... fipref('NumberDisplay','bin',... 'NumericTypeDisplay','short',... 'FimathDisplay','none'); a = fi(0.1, false, 80, 83) a = 11001100110011001100110011001100110011001100110011010000 000000000000000000000000 u80,83 Notice that the infinite repeating representation is truncated after 52 bits, because the mantissa of an IEEE standard double-precision floating-point number has 52 bits. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-279 divide Contrast the above to calculating 1/10 in fixed-point arithmetic with the quotient set to the same numeric type as before: T = numerictype('Signed',false,'WordLength',80,... 'FractionLength',83); a = fi(1); b = fi(10); c = T.divide(a,b); c.bin ans = 11001100110011001100110011001100110011001100110011001100 110011001100110011001100 Notice that when you use the divide function, the quotient is calculated to the full 80 bits, regardless of the precision of a and b. Thus, the fi object c represents 1/10 more precisely than IEEE standard double-precision floating-point number can. With 1000 bits of precision, T = numerictype('Signed',false,'WordLength',1000,... 'FractionLength',1003); a = fi(1); b = fi(10); c = T.divide(a,b); 2-280 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان divide c.bin ans = 11001100110011001100110011001100110011001100110011001100 11001100110011001100110011001100110011001100110011001100 11001100110011001100110011001100110011001100110011001100 11001100110011001100110011001100110011001100110011001100 11001100110011001100110011001100110011001100110011001100 11001100110011001100110011001100110011001100110011001100 11001100110011001100110011001100110011001100110011001100 11001100110011001100110011001100110011001100110011001100 11001100110011001100110011001100110011001100110011001100 11001100110011001100110011001100110011001100110011001100 11001100110011001100110011001100110011001100110011001100 11001100110011001100110011001100110011001100110011001100 11001100110011001100110011001100110011001100110011001100 11001100110011001100110011001100110011001100110011001100 11001100110011001100110011001100110011001100110011001100 11001100110011001100110011001100110011001100110011001100 11001100110011001100110011001100110011001100110011001100 110011001100110011001100110011001100110011001100 See Also add | fi | fimath | mpy | mrdivide | numerictype | rdivide | sub | sum www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-281 double Purpose Double-precision floating-point real-world value of fi object Syntax double(a) Description double(a) returns the real-world value of a fi object in double-precision floating point. double(a) is equivalent to a.double. Fixed-point numbers can be represented as real-world value = 2− fraction length × stored integer or, equivalently as real-world value = (slope × stored integer) + bias Examples The code a = fi([-1 1],1,8,7); y = double(a) z = a.double returns y = -1 0.9922 -1 0.9922 z = See Also 2-282 single www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان end Purpose Last index of array Description Refer to the MATLAB end reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-283 eps Purpose Quantized relative accuracy for fi or quantizer objects Syntax eps(obj) Description eps(obj) returns the value of the least significant bit of the value of the fi object or quantizer object obj. The result of this function is equivalent to that given by the Fixed-Point Designer function lsb. See Also intmax | intmin | lowerbound | lsb | range | realmax | realmin | upperbound 2-284 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان eq Purpose Determine whether real-world values of two fi objects are equal Syntax c = eq(a,b) a == b Description c = eq(a,b) is called for the syntax a == b when a or b is a fi object. a and b must have the same dimensions unless one is a scalar. A scalar can be compared with another object of any size. a == b does an element-by-element comparison between a and b and returns a matrix of the same size with elements set to 1 where the relation is true, and 0 where the relation is false. See Also ge | gt | isequal | le | lt | ne www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-285 errmean Purpose Mean of quantization error Syntax m = errmean(q) Description m = errmean(q) returns the mean of a uniformly distributed random quantization error that arises from quantizing a signal by quantizer object q. Note The results are not exact when the signal precision is close to the precision of the quantizer. Examples Find m, the mean of the quantization error for quantizer q: q = quantizer; m = errmean(q) m = -1.525878906250000e-005 Now compare m to m_est, the sample mean from a Monte Carlo experiment: r = realmax(q); u = 2*r*rand(1000,1)-r; y = quantize(q,u); e = y - u; m_est = mean(e) % % % % Original signal Quantized signal Error Estimate of the error mean m_est = -1.519507450175317e-005 See Also 2-286 errpdf | errvar | quantize www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان errorbar Purpose Plot error bars along curve Description Refer to the MATLAB errorbar reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-287 errpdf Purpose Probability density function of quantization error Syntax [f,x] = errpdf(q) f = errpdf(q,x) Description [f,x] = errpdf(q) returns the probability density function f evaluated at the values in x. The vector x contains the uniformly distributed random quantization errors that arise from quantizing a signal by quantizer object q. f = errpdf(q,x) returns the probability density function f evaluated at the values in vector x. Note The results are not exact when the signal precision is close to the precision of the quantizer. Examples q = quantizer('nearest',[4 3]); [f,x] = errpdf(q); subplot(211) plot(x,f) title('Computed PDF of the quantization error.') The output plot shows the probability density function of the quantization error. 2-288 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان errpdf Compare this result to a plot of the sample probability density function from a Monte Carlo experiment: r = realmax(q); u = 2*r*rand(10000,1)-r; % Original signal y = quantize(q,u); % Quantized signal e = y - u; % Error subplot(212) hist(e,20);set(gca,'xlim',[min(x) max(x)]) title('Estimate of the PDF of the quantization error.') www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-289 errpdf See Also 2-290 errmean | errvar | quantize www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان errvar Purpose Variance of quantization error Syntax v = errvar(q) Description v = errvar(q) returns the variance of a uniformly distributed random quantization error that arises from quantizing a signal by quantizer object q. Note The results are not exact when the signal precision is close to the precision of the quantizer. Examples Find v, the variance of the quantization error for quantizer object q: q = quantizer; v = errvar(q) v = 7.761021455128987e-011 Now compare v to v_est, the sample variance from a Monte Carlo experiment: r = realmax(q); u = 2*r*rand(1000,1)-r; % Original signal y = quantize(q,u); % Quantized signal e = y - u; % Error v_est = var(e) % Estimate of the error variance v_est = 7.520208858166330e-011 See Also errmean | errpdf | quantize www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-291 etreeplot Purpose Plot elimination tree Description Refer to the MATLAB etreeplot reference page for more information. 2-292 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان exponentbias Purpose Exponent bias for quantizer object Syntax b = exponentbias(q) Description b = exponentbias(q) returns the exponent bias of the quantizer object q. For fixed-point quantizer objects, exponentbias(q) returns 0. Examples q = quantizer('double'); b = exponentbias(q) b = 1023 Algorithms For floating-point quantizer objects, b = 2e−1 − 1 where e = eps(q), and exponentbias is the same as the exponent maximum. For fixed-point quantizer objects, b = 0 by definition. See Also eps | exponentlength | exponentmax | exponentmin www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-293 exponentlength Purpose Exponent length of quantizer object Syntax e = exponentlength(q) Description e = exponentlength(q) returns the exponent length of quantizer object q. When q is a fixed-point quantizer object, exponentlength(q) returns 0. This is useful because exponent length is valid whether the quantizer object mode is floating point or fixed point. Examples q = quantizer('double'); e = exponentlength(q) e = 11 Algorithms The exponent length is part of the format of a floating-point quantizer object [w e]. For fixed-point quantizer objects, e = 0 by definition. See Also eps | exponentbias | exponentmax | exponentmin 2-294 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان exponentmax Purpose Maximum exponent for quantizer object Syntax exponentmax(q) Description exponentmax(q) returns the maximum exponent for quantizer object q. When q is a fixed-point quantizer object, it returns 0. Examples q = quantizer('double'); emax = exponentmax(q) emax = 1023 Algorithms For floating-point quantizer objects, Emax = 2e−1 − 1 For fixed-point quantizer objects, See Also Emax = 0 by definition. eps | exponentbias | exponentlength | exponentmin www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-295 exponentmin Purpose Minimum exponent for quantizer object Syntax emin = exponentmin(q) Description emin = exponentmin(q) returns the minimum exponent for quantizer object q. If q is a fixed-point quantizer object, exponentmin returns 0. Examples q = quantizer('double'); emin = exponentmin(q) emin = -1022 Algorithms For floating-point quantizer objects, Emin = −2e−1 + 2 For fixed-point quantizer objects, See Also 2-296 Emin = 0 . eps | exponentbias | exponentlength | exponentmax www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان ezcontour Purpose Easy-to-use contour plotter Description Refer to the MATLAB ezcontour reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-297 ezcontourf Purpose Easy-to-use filled contour plotter Description Refer to the MATLAB ezcontourf reference page for more information. 2-298 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان ezmesh Purpose Easy-to-use 3-D mesh plotter Description Refer to the MATLAB ezmesh reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-299 ezplot Purpose Easy-to-use function plotter Description Refer to the MATLAB ezplot reference page for more information. 2-300 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان ezplot3 Purpose Easy-to-use 3-D parametric curve plotter Description Refer to the MATLAB ezplot3 reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-301 ezpolar Purpose Easy-to-use polar coordinate plotter Description Refer to the MATLAB ezpolar reference page for more information. 2-302 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان ezsurf Purpose Easy-to-use 3-D colored surface plotter Description Refer to the MATLAB ezsurf reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-303 ezsurfc Purpose Easy-to-use combination surface/contour plotter Description Refer to the MATLAB ezsurfc reference page for more information. 2-304 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان feather Purpose Plot velocity vectors Description Refer to the MATLAB feather reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-305 fi Purpose Construct fixed-point numeric object Syntax a a a a a a a a a b a a a a a a a a Description You can use the fi constructor function in the following ways: = = = = = = = = = = = = = = = = = = fi fi(v) fi(v,s) fi(v,s,w) fi(v,s,w,f) fi(v,s,w,slope,bias) fi(v,s,w,slopeadjustmentfactor,fixedexponent,bias) fi(v,T) fi(v,F) fi(a,F) fi(v,T,F) fi(v,s,F) fi(v,s,w,F) fi(v,s,w,f,F) fi(v,s,w,slope,bias,F) fi(v,s,w,slopeadjustmentfactor,fixedexponent,bias,F) fi(...'PropertyName',PropertyValue...) fi('PropertyName',PropertyValue...) • a = fi is the default constructor and returns a fi object with no value, 16-bit word length, and 15-bit fraction length. • a = fi(v) returns a signed fixed-point object with value v, 16-bit word length, and best-precision fraction length. • a = fi(v,s) returns a fixed-point object with value v, Signed property value s, 16-bit word length, and best-precision fraction length. s can be 0 (false) for unsigned or 1 (true) for signed. • a = fi(v,s,w) returns a fixed-point object with value v, Signed property value s, word length w, and best-precision fraction length. • a = fi(v,s,w,f) returns a fixed-point object with value v, Signed property value s, word length w, and fraction length f. Fraction length can be greater than word length or negative, see “Create a fi 2-306 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان fi Object With Fraction Length Greater Than Word Length” on page 2-313 and “Create a fi Object With Negative Fraction Length” on page 2-315. • a = fi(v,s,w,slope,bias) returns a fixed-point object with value v, Signed property value s, word length w, slope, and bias. • a = fi(v,s,w,slopeadjustmentfactor,fixedexponent,bias) returns a fixed-point object with value v, Signed property value s, word length w, slopeadjustmentfactor, fixedexponent, and bias. • a = fi(v,T) returns a fixed-point object with value v and embedded.numerictype T. Refer to “numerictype Object Construction” for more information on numerictype objects. • a = fi(v,F) returns a fixed-point object with value v, embedded.fimath F, 16-bit word length, and best-precision fraction length. Refer to “fimath Object Construction” for more information on fimath objects. • b = fi(a,F) allows you to maintain the value and numerictype object of fi object a, while changing its fimath object to F. • a = fi(v,T,F) returns a fixed-point object with value v, embedded.numerictype T, and embedded.fimath F. The syntax a = fi(v,T,F) is equivalent to a = fi(v,F,T). • a = fi(v,s,F) returns a fixed-point object with value v, Signed property value s, 16-bit word length, best-precision fraction length, and embedded.fimath F. • a = fi(v,s,w,F) returns a fixed-point object with value v, Signed property value s, word length w, best-precision fraction length, and embedded.fimath F. • a = fi(v,s,w,f,F) returns a fixed-point object with value v, Signed property value s, word length w, fraction length f, and embedded.fimath F. • a = fi(v,s,w,slope,bias,F) returns a fixed-point object with value v, Signed property value s, word length w, slope, bias, and embedded.fimath F. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-307 fi • a = fi(v,s,w,slopeadjustmentfactor,fixedexponent,bias,F) returns a fixed-point object with value v, Signed property value s, word length w, slopeadjustmentfactor, fixedexponent, bias, and embedded.fimath F. • a = fi(...'PropertyName',PropertyValue...) and a = fi('PropertyName',PropertyValue...) allow you to set fixed-point objects for a fi object by property name/property value pairs. The fi object has the following three general types of properties: • “Data Properties” on page 2-308 • “fimath Properties” on page 2-309 • “numerictype Properties” on page 2-310 Note These properties are described in detail in “fi Object Properties” on page 1-2 in the Properties Reference. Data Properties The data properties of a fi object are always writable. • bin — Stored integer value of a fi object in binary • data — Numerical real-world value of a fi object • dec — Stored integer value of a fi object in decimal • double — Real-world value of a fi object, stored as a MATLAB double • hex — Stored integer value of a fi object in hexadecimal • int — Stored integer value of a fi object, stored in a built-in MATLAB integer data type. You can also use int8, int16, int32, int64, uint8, uint16, uint32, and uint64 to get the stored integer value of a fi object in these formats • oct — Stored integer value of a fi object in octal 2-308 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان fi These properties are described in detail in “fi Object Properties” on page 1-2. fimath Properties When you create a fi object and specify fimath object properties in the fi constructor, a fimath object is created as a property of the fi object. If you do not specify any fimath properties in the fi constructor, the resulting fi has no attached fimath object. • fimath — fimath properties associated with a fi object The following fimath properties are, by transitivity, also properties of a fi object. The properties of the fimath object listed below are always writable. • CastBeforeSum — Whether both operands are cast to the sum data type before addition Note This property is hidden when the SumMode is set to FullPrecision. • MaxProductWordLength — Maximum allowable word length for the product data type • MaxSumWordLength — Maximum allowable word length for the sum data type • OverflowMode — Overflow mode • ProductBias — Bias of the product data type • ProductFixedExponent — Fixed exponent of the product data type • ProductFractionLength — Fraction length, in bits, of the product data type • ProductMode — Defines how the product data type is determined • ProductSlope — Slope of the product data type www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-309 fi • ProductSlopeAdjustmentFactor — Slope adjustment factor of the product data type • ProductWordLength — Word length, in bits, of the product data type • RoundingMethod — Rounding mode • SumBias — Bias of the sum data type • SumFixedExponent — Fixed exponent of the sum data type • SumFractionLength — Fraction length, in bits, of the sum data type • SumMode — Defines how the sum data type is determined • SumSlope — Slope of the sum data type • SumSlopeAdjustmentFactor — Slope adjustment factor of the sum data type • SumWordLength — The word length, in bits, of the sum data type These properties are described in detail in “fimath Object Properties” on page 1-4. numerictype Properties When you create a fi object, a numerictype object is also automatically created as a property of the fi object. numerictype — Object containing all the data type information of a fi object, Simulink signal or model parameter The following numerictype properties are, by transitivity, also properties of a fi object. The properties of the numerictype object become read only after you create the fi object. However, you can create a copy of a fi object with new values specified for the numerictype properties. • Bias — Bias of a fi object • DataType — Data type category associated with a fi object • DataTypeMode — Data type and scaling mode of a fi object 2-310 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان fi • DataTypeOverride — Data type override for applying fipref data type override settings to fi objects. This property provides a convenient way to ignore a global fipref data type override setting. Note that this property is not visible when its value is the default, Inherit. When this property is set to Off, the fi object uses the numerictype data type settings and ignores fipref settings. • FixedExponent — Fixed-point exponent associated with a fi object • SlopeAdjustmentFactor — Slope adjustment associated with a fi object • FractionLength — Fraction length of the stored integer value of a fi object in bits • Scaling — Fixed-point scaling mode of a fi object • Signed — Whether a fi object is signed or unsigned • Signedness — Whether a fi object is signed or unsigned Note numerictype objects can have a Signedness of Auto, but all fi objects must be Signed or Unsigned. If a numerictype object with Auto Signedness is used to create a fi object, the Signedness property of the fi object automatically defaults to Signed. • Slope — Slope associated with a fi object • WordLength — Word length of the stored integer value of a fi object in bits For further details on these properties, see “numerictype Object Properties” on page 1-15. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-311 fi Examples Note For information about the display format of fi objects, refer to “View Fixed-Point Data”. For examples of casting, see “Cast fi Objects”. Create a fi Object Create a signed fi object with a value of pi, a word length of 8 bits, and a fraction length of 3 bits. a = fi(pi, 1, 8, 3) a = 3.1250 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 8 3 Create an Array of fi Objects a = fi((magic(3)/10), 1, 16, 12) a = 0.8000 0.3000 0.3999 0.1001 0.5000 0.8999 DataTypeMode: Signedness: WordLength: FractionLength: 2-312 0.6001 0.7000 0.2000 Fixed-point: binary point scaling Signed 16 12 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان fi Create a fi Object With Default Precision If you omit the argument f, the fraction length is set automatically to achieve the best precision possible. a = fi(pi, 1, 8) a = 3.1563 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 8 5 Create a fi Object With Default Word Length and Precision If you omit w and f, the word length is set automatically to 16 bits and the fraction length is set to achieve the best precision possible. a = fi(pi, 1) a = 3.1416 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 16 13 Create a fi Object With Fraction Length Greater Than Word Length When you use binary-point representation for a fixed-point number, the fraction length can be greater than the word length. In this case, there www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-313 fi are implicit leading zeros (for positive numbers) or ones (for negative numbers) between the binary point and the first significant binary digit. Consider a signed value with a word length of 8, fraction length of 10 and a stored integer value of 5. We can calculate the real-world value. RealWorldValue = StoredInteger * 2 ^ -FractionLength RealWorldValue = 5 * 2 ^ -10 = 0.0048828125. Create a signed fi object with a value of 0.0048828125, a word length of 8 bits, and a fraction length of 10 bits. a = fi(0.0048828125, true, 8, 10) a = 0.004882812500000 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 8 10 Get the stored integer value of a. a.int ans = 5 Get the binary value of the stored integer. a.bin ans = 00000101 2-314 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان fi Because the fraction length is 2 bits longer than the word length, the binary value of the stored integer is x.xx00000101 , where x is a placeholder for implicit zeros. 0.0000000101 (binary) is equivalent to 0.0048828125 (decimal). Create a fi Object With Negative Fraction Length When you use binary-point representation for a fixed-point number, the fraction length can be negative. In this case, there are implicit trailing zeros (for positive numbers) or ones (for negative numbers) between the binary point and the first significant binary digit. Consider a signed value with a word length of 8, fraction length of –2 and a stored integer value of 5. We can calculate the real-world value. RealWorldValue = StoredInteger * 2 ^ -FractionLength RealWorldValue = 5 * 2 ^ 2 = 20. Create a signed fi object with a value of 20, a word length of 8 bits, and a fraction length of –2 bits. a = fi(20, true, 8, -2) a = 20 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 8 10 Get the stored integer value of a. a.int ans = 5 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-315 fi Get the binary value of the stored integer. a.bin ans = 00000101 Because the fraction length is negative, the binary value of the stored integer is 00000101xx , where x is a placeholder for implicit zeros. 000000010100 (binary) is equivalent to 20 (decimal). Create a fi Object Specifying Rounding and Overflow You can use property name/property value pairs to set fi properties, such as rounding method and overflow action, when you create the object. a = fi(pi, 'RoundingMethod', 'Floor', 'OverflowAction', 'Wrap') a = 3.1415 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 16 13 RoundingMethod: OverflowAction: ProductMode: SumMode: Floor Wrap FullPrecision FullPrecision Remove Local fimath You can remove a local fimath object from a fi object at any time using the removefimath function. a = fi(pi, 'RoundingMethod', 'Floor', 'OverflowAction', 'Wrap') 2-316 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان fi a = removefimath(a) a = 3.1415 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 16 13 RoundingMethod: OverflowAction: ProductMode: SumMode: Floor Wrap FullPrecision FullPrecision a = 3.1415 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 16 13 fi object a now has no local fimath. To reassign it a local fimath object, use the setfimath function. a = setfimath(a, fimath('ProductMode', 'KeepLSB')) a = 3.1415 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 16 13 RoundingMethod: Nearest OverflowAction: Saturate www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-317 fi ProductMode: KeepLSB ProductWordLength: 32 SumMode: FullPrecision fi object a now has a local fimath object with a ProductMode of KeepLSB. The values of the remaining fimath object properties are default fimath values. Use fi as an Indexing Argument Set up an array to be indexed. x = 10:-1:1 x = 10 9 8 7 6 5 4 3 2 1 Create a fi object and use it to index into x. k = fi(3); y = x(k) y = 8 Use fi in a Switch Statement You can use a fi object as the switch condition and as one or more of the cases in the switch expression. function y = test_switch(u, v) cExpr = fi(u + v, 0, 2, 0); t = 1; switch cExpr % condition expression type: ufix2 case 0 y = t * 2; case fi(1,0,2,0) y = t * 3; 2-318 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان fi case 2 y = t * 4; case 3 y = t * 3; otherwise y = 0; end end y = test_switch(1,2.0) y = 3 Use fi as a Colon Operator Use a fi object as a colon operator. When you use fi as a colon operator, all colon operands must have integer values. a b c x = = = = fi(1,0,3,0); fi(2,0,8,0); fi(12,0,8,0); a:b:c x = 1 3 5 DataTypeMode: Signedness: WordLength: FractionLength: 7 9 11 Fixed-point: binary point scaling Unsigned 8 0 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-319 fi Create Fixed-point Vector With Non-integer Spacing To create a fixed-point vector with non-integer spacing, first create the vector, then cast the vector to fixed-point. x = fi(0:0.1:10); Alternatively, use the linspace function. x = fi(linspace(0,10, 101)); The following code, where one of the colon operands is not an integer, generates an error. a b c z = = = = fi(0); fi(0.1); fi(10); a:b:c Set Data Type Override on a fi Object Set the DataTypeOverride property of a fi object so that the fi object does not use the data type override settings of the fipref object. Set up fipref with data type override set to 'TrueDoubles' for all numeric types. fipref('DataTypeOverride', 'TrueDoubles') ans = NumberDisplay: NumericTypeDisplay: FimathDisplay: LoggingMode: DataTypeOverride: DataTypeOverrideAppliesTo: 2-320 'RealWorldValue' 'full' 'full' 'Off' 'TrueDoubles' 'AllNumericTypes' www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان fi Create a new fi object without specifying its DataTypeOverride property so that it uses the data type override settings specified using fipref. x = fi(pi, 1, 16, 13) x = 3.1416 DataTypeMode: Double Now create a fi object and set its DataTypeOverride property to 'Off' so that it ignores the data type override settings specified using fipref. y = fi(pi, 1, 16, 13, 'DataTypeOverride','Off') y = 3.1416 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 16 13 See Also fimath | fipref | isfimathlocal | numerictype | quantizer | sfi | ufi Concepts • “fi Object Functions” • “Binary Point Interpretation” • www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-321 fiaccel Purpose Accelerate fixed-point code Syntax fiaccel -options fcn Description fiaccel -options fcn translates the MATLAB file fcn.m to a MEX function, which accelerates fixed-point code. To use fiaccel, your code must meet one of these requirements: • The top-level function has no inputs or outputs, and the code uses fi • The top-level function has an output or a non-constant input, and at least one output or input is a fi. • The top-level function has at least one input or output containing a built-in integer class (int8, uint8, int16, uint16, int32, uint32, int64, or uint64), and the code uses fi. Note If your top-level file is on a path that contains Unicode characters, code generation might not be able to find the file. Input Arguments fcn MATLAB function from which to generate a MEX function. fcn must be suitable for code generation. For information on code generation, see “Code Acceleration and Code Generation from MATLAB” options Choice of compiler options. fiaccel gives precedence to individual command-line options over options specified using a configuration object. If command-line options conflict, the rightmost option prevails. 2-322 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان fiaccel -args example_inputs Define the size, class, and complexity of all MATLAB function inputs. Use the values in example_inputs to define these properties. example_inputs must be a cell array that specifies the same number and order of inputs as the MATLAB function. -config config_object Specify MEX generation parameters, based on config_object, defined as a MATLAB variable using coder.mexconfig. For example: cfg = coder.mexconfig; -d out_folder Store generated files in the absolute or relative path specified by out_folder. If the folder specified by out_folder does not exist, fiaccel creates it for you. If you do not specify the folder location, fiaccel generates files in the default folder: fiaccel/mex/fcn. fcn is the name of the MATLAB function specified at the command line. The function does not support the following characters in folder names: asterisk (*), question-mark (?), dollar ($), and pound (#). www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-323 fiaccel -g Compiles the MEX function in debug mode, with optimization turned off. If not specified, fiaccel generates the MEX function in optimized mode. -global global_values Specify initial values for global variables in MATLAB file. Use the values in cell array global_values to initialize global variables in the function you compile. The cell array should provide the name and initial value of each global variable. You must initialize global variables before compiling with fiaccel. If you do not provide initial values for global variables using the -global option, fiaccel checks for the variable in the MATLAB global workspace. If you do not supply an initial value, fiaccel generates an error. The generated MEX code and MATLAB each have their own copies of global data. To ensure consistency, you must synchronize their global data whenever the two interact. If you do not synchronize the data, their global variables might differ. 2-324 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان fiaccel -histogram Compute the log2 histogram for all named, intermediate and expression values. A histogram column appears in the code generation report table. -I include_path Add include_path to the beginning of the code generation path. fiaccel searches the code generation path first when converting MATLAB code to MEX code. -launchreport Generate and open a code generation report. If you do not specify this option, fiaccel generates a report only if error or warning messages occur or you specify the -report option. -o output_file_name Generate the MEX function with the base name output_file_name plus a platform-specific extension. output_file_name can be a file name or include an existing path. If you do not specify an output file name, the base name is fcn_mex, which allows you to run the original MATLAB function and the MEX function and compare the results. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-325 fiaccel -O optimization_option Optimize generated MEX code, based on the value of optimization_option: • enable:inline — Enable function inlining • disable:inline — Disable function inlining If not specified, fiaccel uses inlining for optimization. Examples -report Generate a code generation report. If you do not specify this option, fiaccel generates a report only if error or warning messages occur or you specify the -launchreport option. -? Display help for fiaccel command. Create a test file and compute the moving average. Then, use fiaccel to accelerate the code and compare. function avg = test_moving_average(x) %#codegen if nargin < 1, x = fi(rand(100,1),1,16,15); end z = fi(zeros(10,1),1,16,15); avg = x; for k = 1:length(x) [avg(k),z] = moving_average(x(k),z); end function [avg,z] = moving_average(x,z) %#codegen 2-326 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان fiaccel if nargin < 2, z = fi(zeros(10,1),1,16,15); end z(2:end) = z(1:end-1); % Update buffer z(1) = x; % Add new value avg = mean(z); % Compute moving average % Use fiaccel to create a MEX function and % accelerate the code x = fi(rand(100,1),1,16,15); fiaccel test_moving_average -args {x} -report % Compare the non-accelerated and accelerated code. x = fi(rand(100,1),1,16,15); % Non-compiled version tic,avg = test_moving_average(x);toc % Compiled version tic,avg = test_moving_average_mex(x);toc See Also coder.ArrayType | coder.Constant | coder.EnumType | coder.FiType | coder.newtype | coder.PrimitiveType | coder.resize | coder.StructType | coder.Type | coder.typeof www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-327 filter Purpose One-dimensional digital filter of fi objects Syntax y = filter(b,1,x) [y,zf] = filter(b,1,x,zi) y = filter(b,1,x,zi,dim) Description y = filter(b,1,x) filters the data in the fixed-point vector x using the filter described by the fixed-point vector b. The function returns the filtered data in the output fi object y. Inputs b and x must be fi objects. filter always operates along the first non-singleton dimension. Thus, the filter operates along the first dimension for column vectors and nontrivial matrices, and along the second dimension for row vectors. [y,zf] = filter(b,1,x,zi) gives access to initial and final conditions of the delays, zi and zf. zi is a vector of length length(b)-1, or an array with the leading dimension of size length(b)-1 and with remaining dimensions matching those of x. zi must be a fi object with the same data type as y and zf. If you do not specify a value for zi, it defaults to a fixed-point array with a value of 0 and the appropriate numerictype and size. y = filter(b,1,x,zi,dim) performs the filtering operation along the specified dimension. If you do not want to specify the vector of initial conditions, use [] for the input argument zi. Tips • The filter function only supports FIR filters. In the general filter representation, b/a, the denominator, a, of an FIR filter is the scalar 1, which is the second input of this function. • The numerictype of b can be different than the numerictype of x. • If you want to specify initial conditions, but do not know what numerictype to use, first try filtering your data without initial conditions. You can do so by specifying [] for the input zi. After performing the filtering operation, you have the numerictype of y and zf (if requested). Because the numerictype of zi must match that of y and zf, you now know the numerictype to use for the initial conditions. 2-328 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان filter Input Arguments b Fixed-point vector of the filter coefficients. x Fixed-point vector containing the data for the function to filter. zi Fixed-point vector containing the initial conditions of the delays. If the initial conditions of the delays are zero, you can specify zero, or, if you do not know the appropriate size and numerictype for zi, use []. If you do not specify a value for zi, the parameter defaults to a fixed-point vector with a value of zero and the same numerictype and size as the output zf (default). dim Dimension along which to perform the filtering operation. Output Arguments y Output vector containing the filtered fixed-point data. zf Fixed-point output vector containing the final conditions of the delays. Definitions Filter length (L) The filter length is length(b), or the number of filter coefficients specified in the fixed-point vector b. Filter order (N) The filter order is the number of states (delays) of the filter, and is equal to L-1. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-329 filter Examples The following example filters a high-frequency fixed-point sinusoid from a signal that contains both a low- and high-frequency fixed-point sinusoid. w1 w2 n xd x b gd y = = = = = = = = .1*pi; .6*pi; 0:999; sin(w1*n) + sin(w2*n); sfi(xd,12); ufi([.1:.1:1,1-.1:-.1:.1]/4,10); (length(b)-1)/2; filter(b,1,x); %% Plot results, accomodate for group-delay of filter plot(n(1:end-gd),x(1:end-gd)) hold on plot(n(1:end-gd),y(gd+1:end),'r--') axis([0 50 -2 2]) legend('Unfiltered signal','Filtered signal') xlabel('Sample index (n)') ylabel('Signal value') The resulting plot shows both the unfiltered and filtered signals. 2-330 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان filter Algorithms The filter function uses a Direct-Form Transposed FIR implementation of the following difference equation: y(n) = b1 * xn + b2 * xn−1 + ... + bL * xn− N www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-331 filter where L is the filter length and N is the filter order. The following diagram shows the direct-form transposed FIR filter structure used by the filter function: 1 Section input b1 + + 1 Section output z-1 b2 + + z-1 bL-1 bL See Also 2-332 + + z-1 conv | filter www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان fimath Purpose Set fixed-point math settings Syntax F = fimath F = fimath(...'PropertyName',PropertyValue...) Description You can use the fimath constructor function in the following ways: • F = fimath creates a fimath object with default fimath property settings: RoundingMethod: OverflowAction: ProductMode: SumMode: Nearest Saturate FullPrecision FullPrecision • F = fimath(...'PropertyName',PropertyValue...) allows you to set the attributes of a fimath object using property name/property value pairs. All property names that you do not specify in the constructor use default values. The properties of the fimath object are listed below. These properties are described in detail in “fimath Object Properties” on page 1-4 in the Properties Reference. • CastBeforeSum — Whether both operands are cast to the sum data type before addition Note This property is hidden when the SumMode is set to FullPrecision. • OverflowAction — Action to take on overflow • ProductBias — Bias of the product data type • ProductFixedExponent — Fixed exponent of the product data type • ProductFractionLength — Fraction length, in bits, of the product data type www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-333 fimath • ProductMode — Defines how the product data type is determined • ProductSlope — Slope of the product data type • ProductSlopeAdjustmentFactor — Slope adjustment factor of the product data type • ProductWordLength — Word length, in bits, of the product data type • RoundingMethod — Rounding method • SumBias — Bias of the sum data type • SumFixedExponent — Fixed exponent of the sum data type • SumFractionLength — Fraction length, in bits, of the sum data type • SumMode — Defines how the sum data type is determined • SumSlope — Slope of the sum data type • SumSlopeAdjustmentFactor — Slope adjustment factor of the sum data type • SumWordLength — Word length, in bits, of the sum data type Examples Example 1 Type F = fimath to create a default fimath object. It has these settings: F = RoundingMethod: OverflowAction: ProductMode: SumMode: 2-334 Nearest Saturate FullPrecision FullPrecision www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان fimath Example 2 You can set properties of fimath objects at the time of object creation by including properties after the arguments of the fimath constructor function. For example, to set the overflow action to Saturate and the rounding method to Convergent, F = fimath('OverflowAction','Saturate',... 'RoundingMethod','Convergent') F = RoundingMethod: OverflowAction: ProductMode: SumMode: Convergent Saturate FullPrecision FullPrecision See Also fi | fipref | numerictype | quantizer Related Examples • “fimath Object Construction” Concepts • “fimath Object Properties” • “fimath Properties Usage for Fixed-Point Arithmetic” www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-335 fipref Purpose Set fixed-point preferences Syntax P = fipref P = fipref(...'PropertyName',PropertyValue...) Description You can use the fipref constructor function in the following ways: • P = fipref creates a default fipref object. • P = fipref(...'PropertyName',PropertyValue...) allows you to set the attributes of a object using property name/property value pairs. The properties of the fipref object are listed below. These properties are described in detail in “fipref Object Properties” on page 1-12. • FimathDisplay — Display options for the local fimath attributes of fi objects. When fi objects to not have a local fimath, their fimath attributes are never displayed. • DataTypeOverride — Data type override options. • DataTypeOverrideAppliesTo— Data type override setting applicability. • LoggingMode — Logging options for operations performed on fi objects. • NumericTypeDisplay — Display options for the numeric type attributes of a fi object. • NumberDisplay — Display options for the value of a fi object. Your fipref settings persist throughout your MATLAB session. Use reset(fipref) to return to the default settings during your session. Use savefipref to save your display preferences for subsequent MATLAB sessions. See “View Fixed-Point Data” for more information on the display preferences used for most code examples in the documentation. 2-336 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان fipref Examples Example 1 Type P = fipref to create a default fipref object. P = NumberDisplay: NumericTypeDisplay: FimathDisplay: LoggingMode: DataTypeOverride: 'RealWorldValue' 'full' 'full' 'Off' 'ForceOff' Example 2 You can set properties of fipref objects at the time of object creation by including properties after the arguments of the fipref constructor function. For example, to set NumberDisplay to bin and NumericTypeDisplay to short, P = fipref('NumberDisplay','bin',... 'NumericTypeDisplay', 'short') P = NumberDisplay: NumericTypeDisplay: FimathDisplay: LoggingMode: DataTypeOverride: 'bin' 'short' 'full' 'Off' 'ForceOff' See Also fi | fimath | numerictype | quantizer | savefipref Related Examples • “fipref Object Construction” www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-337 fipref Concepts 2-338 • “fipref Object Properties” www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان fix Purpose Round toward zero Syntax y = fix(a) Description y = fix(a) rounds fi object a to the nearest integer in the direction of zero and returns the result in fi object y. y and a have the same fimath object and DataType property. When the DataType property of a is single, double, or boolean, the numerictype of y is the same as that of a. When the fraction length of a is zero or negative, a is already an integer, and the numerictype of y is the same as that of a. When the fraction length of a is positive, the fraction length of y is 0, its sign is the same as that of a, and its word length is the difference between the word length and the fraction length of a. If a is signed, then the minimum word length of y is 2. If a is unsigned, then the minimum word length of y is 1. For complex fi objects, the imaginary and real parts are rounded independently. fix does not support fi objects with nontrivial slope and bias scaling. Slope and bias scaling is trivial when the slope is an integer power of 2 and the bias is 0. Examples Example 1 The following example demonstrates how the fix function affects the numerictype properties of a signed fi object with a word length of 8 and a fraction length of 3. a = fi(pi, 1, 8, 3) a = 3.1250 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-339 fix DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 8 3 y = fix(a) y = 3 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 5 0 Example 2 The following example demonstrates how the fix function affects the numerictype properties of a signed fi object with a word length of 8 and a fraction length of 12. a = fi(0.025,1,8,12) a = 0.0249 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 8 12 y = fix(a) y = 2-340 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان fix 0 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 2 0 Example 3 The functions ceil, fix, and floor differ in the way they round fi objects: • The ceil function rounds values to the nearest integer toward positive infinity • The fix function rounds values toward zero • The floor function rounds values to the nearest integer toward negative infinity The following table illustrates these differences for a given fi object a. a See Also ceil(a) fix(a) floor(a) – 2.5 –2 –2 –3 –1.75 –1 –1 –2 –1.25 –1 –1 –2 –0.5 0 0 –1 0.5 1 0 0 1.25 2 1 1 1.75 2 1 1 2.5 3 2 2 ceil | convergent | floor | nearest | round www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-341 fixed.aggregateType Purpose Compute aggregate numerictype Syntax aggNT = fixed.aggregateType(A,B) Description aggNT = fixed.aggregateType(A,B) computes the smallest binary Input Arguments A point scaled numerictype that is able to represent both the full range and precision of inputs A and B. An integer, binary point scaled fixed-point fi object, or numerictype object. B An integer, binary point scaled fixed-point fi object, or numerictype object. Output Arguments aggNT Examples Compute the aggregate numerictype of two numerictype objects. A numerictype object. % can represent range [-4,4) and precision 2^-13 a_nt = numerictype(true,16,13); % can represent range [-2,2) and precision 2^-16 b_nt = numerictype(true,18,16); % can represent range [-4,4) and precision 2^-16 aggNT = fixed.aggregateType(a_nt,b_nt) aggNT = DataTypeMode: Signedness: WordLength: FractionLength: 2-342 Fixed-point: binary point scaling Signed 19 16 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان fixed.aggregateType Compute the aggregate numerictype of two fi objects. % Unsigned, WordLength: 16, FractionLength: 14 a_fi = ufi(pi,16); % Signed, WordLength: 24, FractionLength: 21 b_fi = sfi(-pi,24); % Signed, WordLength: 24, FractionLength: 21 aggNT = fixed.aggregateType(a_fi,b_fi) aggNT = DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 24 21 Compute the aggregate numerictype of a fi object and an integer. % Unsigned, WordLength: 16, FractionLength: 14 % can represent range [0,3] and precision 2^-14 a_fi = ufi(pi,16); % Unsigned, WordLength: 8, FractionLength: 0 % can represent range [0,255] and precision 2^0 cInt = uint8(0); % Unsigned with WordLength: 14+8, FractionLength: 14 % can represent range [0,255] and precision 2^-14 aggNT = fixed.aggregateType(a_fi,cInt) aggNT = DataTypeMode: Fixed-point: binary point scaling Signedness: Unsigned WordLength: 22 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-343 fixed.aggregateType FractionLength: 14 See Also 2-344 numerictype | fi www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان fixed.Quantizer Purpose Quantize fixed-point numbers Syntax q q q q Description = = = = fixed.Quantizer fixed.Quantizer(nt,rm,oa) fixed.Quantizer(s,wl,fl,rm,oa) fixed.Quantizer(Name,Value) q = fixed.Quantizer creates a quantizer q that quantizes fixed-point (fi) numbers using default fixed-point settings. q = fixed.Quantizer(nt,rm,oa) uses the numerictype (nt) object information and the RoundingMethod (rm) and OverflowAction (oa) properties. The numerictype, rounding method, and overflow action apply only during the quantization. The resulting, quantized q does not have any fimath attached to it. q = fixed.Quantizer(s,wl,fl,rm,oa) uses the Signed (s), WordLength (wl), FractionLength (fl), RoundingMethod (rm), and OverflowAction (oa) properties. q = fixed.Quantizer(Name,Value) creates a quantizer with the property options specified by one or more Name,Value pair arguments. You separate pairs of Name,Value arguments with commas. Name is the argument name, and Value is the corresponding value. Name must appear inside single quotes (''). You can specify several name-value pair arguments in any order as Name1,Value1, ,NameN,ValueN. Tips • Use y = quantize(q,x) to quantize input array x using the fixed-point settings of quantizer q. x can be any fixed-point number fi, except a Boolean value. If x is a scaled double, the x and y data will be the same, but y will have fixed-point settings. If x is a double or single then y = x. This functionality lets you share the same code for both floating-point data types and fi objects when quantizers are present. • Use n = numerictype(q) to get a numerictype for the current settings of quantizer q. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-345 fixed.Quantizer • Use clone(q) to create a quantizer object with the same property values as q. • If you use a fixed.quantizer in code generation, note that it is a handle object and must be declared as persistent. Input Arguments nt Binary-point, scaled numerictype object or slope-bias scaled, fixed-point numerictype object. If your fixed.Quantizer uses a numerictype object that has either a Signedness of Auto or unspecified Scaling, an error occurs. rm Rounding method to apply to the output data. Valid rounding methods are: Ceiling, Convergent, Floor, Nearest, Round, and Zero. The associated property name is RoundingMethod. Default: Floor oa Overflow action to take in case of data overflow. Valid overflow actions are Saturate and Wrap. The associated property name is OverflowAction. Default: Wrap s Logical value, true or false, indicating whether the output is signed or unsigned, respectively. The associated property name is Signed. Default: true wl Word length (number of bits) of the output data. The associated property name is WordLength. 2-346 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان fixed.Quantizer Default: 16 fl Fraction length of the output data. The associated property name is FractionLength. Default: 15 Name-Value Pair Arguments Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN. Bias The bias is part of the numerical representation used to interpret a fixed-point number. Along with the slope, the bias forms the scaling of the number. Default: 0 FixedExponent Fixed-point exponent associated with the object. The exponent is part of the numerical representation used to express a fixed-point number. The exponent of a fixed-point number is equal to the negative of the fraction length. FixedExponent must be an integer. Default: -15 FractionLength Fraction length of the stored integer value of the object, in bits. The fraction length can be any integer value. This property automatically defaults to the best precision possible based on the value of the word length and the real-world value of the fi object. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-347 fixed.Quantizer Default: 15 OverflowAction Action to take in case of data overflow. Valid overflow actions are Saturate and Wrap. . Default: Wrap RoundingMethod Rounding method to apply to the output data. Valid rounding methods are: Ceiling, Convergent, Floor, Nearest, Round, and Zero. Default: Floor Scaling Scaling mode of the object. The possible values of this property are: • BinaryPoint — Scaling for the fi object is defined by the fraction length. • SlopeBias — Scaling for the fi object is defined by the slope and bias. • Unspecified — A temporary setting that is only allowed at fi object creation, to allow for the automatic assignment of a binary point best-precision scaling. Default: BinaryPoint Signed Whether the object is signed. The possible values of this property are: • 1 — signed • 0 — unsigned • true — signed • false — unsigned 2-348 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان fixed.Quantizer Note Although the Signed property is still supported, the Signedness property always appears in the numerictype object display. If you choose to change or set the signedness of your numerictype object using the Signed property, MATLAB updates the corresponding value of the Signedness property. Default: true Signedness Whether the object is signed, unsigned, or has an unspecified sign. The possible values of this property are: • Signed — signed • Unsigned — unsigned Default: Signed Slope Slope associated with the object. The slope is part of the numerical representation used to express a fixed-point number. Along with the bias, the slope forms the scaling of a fixed-point number. Default: 2^-15 SlopeAdjustmentFactor Slope adjustment associated with the object. The slope adjustment is equivalent to the fractional slope of a fixed-point number. The fractional slope is part of the numerical representation used to express a fixed-point number. SlopeAdjustmentFactor must be greater than or equal to 1 and less than 2. Default: 1 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-349 fixed.Quantizer WordLength Word length of the stored integer value of the object, in bits. The word length can be any positive integer value. Default: 16 Output Arguments q Definitions Fixed-point numbers Quantizer that quantizes fi input numbers Fixed-point numbers can be represented as real-world value = (slope × stored integer) + bias where the slope can be expressed as slope = fractional slope × 2 fixed exponent Examples Use fixed.Quantizer to reduce the word length that results from adding two fixed-point numbers. q = fixed.Quantizer; x1 = fi(0.1,1,16,15); x2 = fi(0.8,1,16,15); y = quantize(q,x1+x2); Use fixed.Quantizer object to change a binary point scaled fixed-point fi to a slope-bias scaled fixed-point fi qsb = fixed.Quantizer(numerictype(1,7,1.6,0.2),... 'Round','Saturate'); ysb = quantize(qsb,fi(pi,1,16,13)); 2-350 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان fixed.Quantizer See Also fi | numerictype | quantizer How To • “Set numerictype Object Properties” www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-351 fixpt_instrument_purge Purpose Remove corrupt fixed-point instrumentation from model Note fixpt_instrument_purge will be removed in a future release. Syntax fixpt_instrument_purge fixpt_instrument_purge(modelName, interactive) Description The fixpt_instrument_purge script finds and removes fixed-point instrumentation from a model left by the Fixed-Point Tool and the fixed-point autoscaling script. The Fixed-Point Tool and the fixed-point autoscaling script each add callbacks to a model. For example, the Fixed-Point Tool appends commands to model-level callbacks. These callbacks make the Fixed-Point Tool respond to simulation events. Similarly, the autoscaling script adds instrumentation to some parameter values that gathers information required by the script. Normally, these types of instrumentation are automatically removed from a model. The Fixed-Point Tool removes its instrumentation when the model is closed. The autoscaling script removes its instrumentation shortly after it is added. However, there are cases where abnormal termination of a model leaves fixed-point instrumentation behind. The purpose of fixpt_instrument_purge is to find and remove fixed-point instrumentation left over from abnormal termination. fixpt_instrument_purge(modelName, interactive) removes instrumentation from model modelName. interactive is true by default, which prompts you to make each change. When interactive is set to false, all found instrumentation is automatically removed from the model. See Also 2-352 autofixexp | fxptdlg www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان flipdim Purpose Flip array along specified dimension Description Refer to the MATLAB flipdim reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-353 fliplr Purpose Flip matrix left to right Description Refer to the MATLAB fliplr reference page for more information. 2-354 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان flipud Purpose Flip matrix up to down Description Refer to the MATLAB flipud reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-355 floor Purpose Round toward negative infinity Syntax y = floor(a) Description y = floor(a) rounds fi object a to the nearest integer in the direction of negative infinity and returns the result in fi object y. y and a have the same fimath object and DataType property. When the DataType property of a is single, double, or boolean, the numerictype of y is the same as that of a. When the fraction length of a is zero or negative, a is already an integer, and the numerictype of y is the same as that of a. When the fraction length of a is positive, the fraction length of y is 0, its sign is the same as that of a, and its word length is the difference between the word length and the fraction length of a. If a is signed, then the minimum word length of y is 2. If a is unsigned, then the minimum word length of y is 1. For complex fi objects, the imaginary and real parts are rounded independently. floor does not support fi objects with nontrivial slope and bias scaling. Slope and bias scaling is trivial when the slope is an integer power of 2 and the bias is 0. Examples Example 1 The following example demonstrates how the floor function affects the numerictype properties of a signed fi object with a word length of 8 and a fraction length of 3. a = fi(pi, 1, 8, 3) a = 3.1250 2-356 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان floor DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 8 3 y = floor(a) y = 3 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 5 0 Example 2 The following example demonstrates how the floor function affects the numerictype properties of a signed fi object with a word length of 8 and a fraction length of 12. a = fi(0.025,1,8,12) a = 0.0249 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 8 12 y = floor(a) y = 0 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-357 floor DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 2 0 Example 3 The functions ceil, fix, and floor differ in the way they round fi objects: • The ceil function rounds values to the nearest integer toward positive infinity • The fix function rounds values toward zero • The floor function rounds values to the nearest integer toward negative infinity The following table illustrates these differences for a given fi object a. a See Also 2-358 ceil(a) fix(a) floor(a) – 2.5 –2 –2 –3 –1.75 –1 –1 –2 –1.25 –1 –1 –2 –0.5 0 0 –1 0.5 1 0 0 1.25 2 1 1 1.75 2 1 1 2.5 3 2 2 ceil | convergent | fix | nearest | round www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان fplot Purpose Plot function between specified limits Description Refer to the MATLAB fplot reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-359 fractionlength Purpose Fraction length of quantizer object Syntax fractionlength(q) Description fractionlength(q) returns the fraction length of quantizer object q. Algorithms For floating-point quantizer objects, f = w - e - 1, where w is the word length and e is the exponent length. For fixed-point quantizer objects, f is part of the format [w f]. See Also 2-360 fi | numerictype | quantizer | wordlength www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان ge Purpose Determine whether real-world value of one fi object is greater than or equal to another Syntax c = ge(a,b) a >= b Description c = ge(a,b) is called for the syntax a >= b when a or b is a fi object. a and b must have the same dimensions unless one is a scalar. A scalar can be compared with another object of any size. a >= b does an element-by-element comparison between a and b and returns a matrix of the same size with elements set to 1 where the relation is true, and 0 where the relation is false. See Also eq | gt | le | lt | ne www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-361 get Purpose Property values of object Syntax value = get(o,'propertyname') structure = get(o) Description value = get(o,'propertyname') returns the property value of the property 'propertyname' for the object o. If you replace the string 'propertyname' by a cell array of a vector of strings containing property names, get returns a cell array of a vector of corresponding values. structure = get(o) returns a structure containing the properties and states of object o. o can be a fi, fimath, fipref, numerictype, or quantizer object. See Also 2-362 set www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان getlsb Purpose Least significant bit Syntax c = getlsb(a) Description c = getlsb(a) returns the value of the least significant bit in a as a u1,0. a can be a scalar fi object or a vector fi object. getlsb only supports fi objects with fixed-point data types. Examples The following example uses getlsb to find the least significant bit in the fi object a. a = fi(-26, 1, 6, 0); c = getlsb(a) c = 0 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Unsigned 1 0 You can verify that the least significant bit in the fi object a is 0 by looking at the binary representation of a. disp(bin(a)) 100110 See Also bitand | bitandreduce | bitconcat | bitget | bitor | bitorreduce | bitset | bitxor | bitxorreduce | getmsb www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-363 getmsb Purpose Most significant bit Syntax c = getmsb(a) Description c = getmsb(a) returns the value of the most significant bit in a as a u1,0. a can be a scalar fi object or a vector fi object. getmsb only supports fi objects with fixed-point data types. Examples The following example uses getmsb to find the most significant bit in the fi object a. a = fi(-26, 1, 6, 0); c = getmsb(a) c = 1 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Unsigned 1 0 >> You can verify that the most significant bit in the fi object a is 1 by looking at the binary representation of a. disp(bin(a)) 100110 See Also 2-364 bitand | bitandreduce | bitconcat | bitget | bitor | bitorreduce | bitset | bitxor | bitxorreduce | getlsb www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان globalfimath Purpose Configure global fimath and return handle object Syntax G = globalfimath G = globalfimath(f) G = globalfimath('PropertyName1',PropertyValue1,...) Description G = globalfimath returns a handle object to the global fimath. G = globalfimath(f) sets the properties of the global fimath to match those of the input fimath object f, and returns a handle object to it. sets the global fimath using the named properties and their corresponding values. Properties that you do not specify in this syntax are automatically set to that of the current global fimath. G = globalfimath('PropertyName1',PropertyValue1,...) Examples This example shows you how to use the globalfimath function to set, change and reset the global fimath. F = fimath('RoundMode','Floor','OverflowMode','Wrap'); globalfimath(F); F1 = fimath; % Will be the same as F A = fi(pi); % A associates with the global fimath % % % G Now set the "SumMode" property of the global fimath to "KeepMSB" and retain all the other property values of the current global fimath. = globalfimath('SumMode','KeepMSB'); % It is also possible to change the global fimath by % directly interacting with the handle object G. G.ProductMode = 'SpecifyPrecision'; % The global fimath may also be reset to the factory % default by calling the reset method on G. This is % equivalent to using the resetglobalfimath function. reset(G); www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-365 globalfimath See Also 2-366 fimath | removeglobalfimathpref | resetglobalfimath www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان gplot Purpose Plot set of nodes using adjacency matrix Description Refer to the MATLAB gplot reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-367 gt Purpose Determine whether real-world value of one fi object is greater than another Syntax c = gt(a,b) a > b Description c = gt(a,b) is called for the syntax a > b when a or b is a fi object. a and b must have the same dimensions unless one is a scalar. A scalar can be compared with another object of any size. a > b does an element-by-element comparison between a and b and returns a matrix of the same size with elements set to 1 where the relation is true, and 0 where the relation is false. See Also 2-368 eq | ge | le | lt | ne www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان hankel Purpose Hankel matrix Description Refer to the MATLAB hankel reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-369 hdlram Purpose Single, simple dual, or dual-port RAM for memory read/write access Description hdlram reads from and writes to memory locations for a single, simple dual, or dual-port RAM. The output data is delayed one step. The RAM size, or number of locations, is inferred from the data type of the address variable as shown in the following table. Data type of address variable RAM address size (bits) single or double 16 uintN N embedded.fi WordLength The maximum RAM address size is 32 bits. Construction H = hdlram creates a single port RAM System object. This object allows you to read from or write to a memory location in the RAM. The output data port corresponds to the read/write address passed in with the step method. H = hdlram(Name,Value) creates a single, simple dual, or dual port hdlram System object, H, with each specified property Name set to the specified Value. You can specify additional name-value pair arguments in any order as (Name1,Value1,...,NameN,ValueN). See “Properties” on page 2-370 for the list of available property names. Properties RAMType Type of RAM to be created Default: Single port Specify the type of RAM to be created. Values of this property are: 2-370 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان hdlram Single Port Create a single port RAM, with 3 inputs and 1 output. Inputs: • Write Data • Write address • Write enable Outputs: Read/Write Data Simple dual port Create a simple dual-port RAM, with 4 inputs and 1 output. Inputs: • Write Data • Write address • Write enable • Read address Outputs: Read Data Dual port Create a dual-port RAM, with 4 inputs and 2 outputs. Inputs: • Write Data • Read/Write address • Write enable • Read address Outputs: www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-371 hdlram • Write Data • Read Data WriteOutputValue Behavior for Write output Default: New data Specify the behavior for Write output for single-port and dual-port RAMs. Values of this property are: Methods Examples New data Send out new data at the address to the output. Old data Send out old data at the address to the output. clone Construct hdlram System object with same property values isLocked Locked status for input attributes and nontunable properties release Allow changes to property values and input characteristics step Read or write input value to memory location Create Single-Port RAM System Object Construct System object to read from or write to a memory location in RAM. The output data port corresponds to the read/write address passed in. During a write operation, the old data at the write address is sent out as the output. 2-372 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان hdlram H = hdlram('RAMType','Single port','WriteOutputValue','Old data') H = System: hdlram Properties: RAMType: 'Single port' WriteOutputValue: 'Old data' Create Simple Dual-Port RAM System Object Construct System object to read from and write to different memory locations in RAM. The output data port corresponds to the read address. If a read operation is performed at the same address as the write operation, old data at that address is read out as the output. H = hdlram('RAMType','Simple dual port') H = System: hdlram Properties: RAMType: 'Simple dual port' Create Dual-Port RAM System Object Construct System object to read from and write to different memory locations in RAM. There are two output ports, a write output data port and a read output data port. The write output data port sends out the new data at the write address. The read output data port sends out the old data at the read address. H = hdlram('RAMType','Dual port','WriteOutputValue','New data') www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-373 hdlram H = System: hdlram Properties: RAMType: 'Dual port' WriteOutputValue: 'New data' Read/Write Single-Port RAM Create System object that can write to a single port RAM, and read the newly written value out. Construct single-port RAM System object. hRAM = hdlram('RAMType','Single port','WriteOutputValue','New data'); Preallocate memory. dataLength = 100; [dataIn dataOut] = deal(zeros(1,dataLength)); Write randomly generated data to the System object, and then read data back out again. for ii = 1:dataLength dataIn(ii) = randi([0 63],1,1,'uint8'); addressIn = uint8(ii-1); writeEnable = true; dataOut(ii) = step(hRAM,dataIn(ii),addressIn,writeEnable); end ; Related Examples 2-374 • • • • • “Create System Objects” “Set Up System Objects” “Process Data Using System Objects” “Tuning System object™ Properties in MATLAB” “Find Help and Examples for System Objects” www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان hdlram.clone Purpose Construct hdlram System object with same property values Syntax C = clone(H) Description C = clone(H) creates another instance of the System object, H, with Input Arguments H Output Arguments C See Also hdlram | hdlram.isLocked | hdlram.release | hdlram.step | the same property values. The clone method creates a new, unlocked object with uninitialized states. Instance of hdlram New hdlram System object with the same property values as the original System object. The clone method creates a new, unlocked object with uninitialized states. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-375 hdlram.IsLocked Purpose Locked status for input attributes and nontunable properties Syntax L = isLocked(OBJ) Description L = isLocked(OBJ) returns a logical value, L, which indicates whether input attributes and nontunable properties are locked for the System object, OBJ. The object performs an internal initialization the first time the step method is executed. This initialization locks nontunable properties and input specifications, such as dimensions, complexity, and data type of the input data. After the System object is locked, the isLocked method returns a true value. Input Arguments OBJ Output Arguments L See Also hdlram | hdlram.clone | hdlram.release | hdlram.step | 2-376 Instance of hdlram Logical value. Either 1 (true) or 0 (false). www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان hdlram.release Purpose Allow changes to property values and input characteristics Syntax release(OBJ) Description release(OBJ) releases system resources (such as memory, file handles, and hardware connections) of System object, OBJ. Releasing these resources allows all of the System object properties and input characteristics to be changed. After you call the release method on a System object, any subsequent calls to step or release that you make are not supported for code generation. Input Arguments OBJ See Also hdlram | hdlram.clone | hdlram.isLocked | hdlram.step | Instance of hdlram www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-377 hdlram.step Purpose Read or write input value to memory location Syntax DATAOUT = step(H,WRITEDATA,READWRITEADDRESS,WRITEENABLE) READDATAOUT = step(H,WRITEDATA,WRITEADDRESS,WRITEENABLE, READADDRESS) [WRITEDATAOUT,READDATAOUT] = step(H,WRITEDATA,WRITEADDRESS, WRITEENABLE,READADDRESS) Description DATAOUT = step(H,WRITEDATA,READWRITEADDRESS,WRITEENABLE) allows you to read the value in memory location READWRITEADDRESS when WRITEENABLE is false. It also allows you to write the value WRITEDATA into the memory location READWRITEADDRESS when WRITEENABLE is true. DATAOUT is the new or old data at READWRITEADDRESS when WRITEENABLE is true, or the data at READWRITEADDRESS when WRITEENABLE is false. This step syntax is appropriate for a single-port RAM System object. READDATAOUT = step(H,WRITEDATA,WRITEADDRESS,WRITEENABLE, READADDRESS) allows you to write the value WRITEDATA into memory location WRITEADDRESS when WRITEENABLE is true. READDATAOUT is the old data at the address location READADDRESS. This step syntax is appropriate for a simple dual-port RAM System object. [WRITEDATAOUT,READDATAOUT] = step(H,WRITEDATA,WRITEADDRESS, WRITEENABLE,READADDRESS) allows you to write the value WRITEDATA into the memory location WRITEADDRESS when WRITEENABLE is true. WRITEDATAOUT is the new or old data at memory location WRITEADDRESS. READDATAOUT is the old data at the address location READADDRES. This step syntax is appropriate for a dual-port RAM System object. 2-378 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان hdlram.step hdlram Input Requirements Examples Input Requirement WRITEDATA Must be scalar. This value can be double, single, integer, or a fixed-point (fi) object, and can be real or complex. WRITEENABLE Must be a scalar, logical value. WRITEADDRESS and READADDRESS Must be real and unsigned. This value can be either fixed-point (fi) objects or integers. Read/Write Single-Port RAM Create System object that can write to a single port RAM and read the newly written value out. Construct single-port RAM System object. hRAM = hdlram('RAMType','Single port','WriteOutputValue','New data'); Preallocate memory. dataLength = 100; [dataIn dataOut] = deal(zeros(1,dataLength)); Write randomly generated data to the System object, and then read data back out again. for ii = 1:dataLength dataIn(ii) = randi([0 63],1,1,'uint8'); addressIn = uint8(ii-1); writeEnable = true; dataOut(ii) = step(hRAM,dataIn(ii),addressIn,writeEnable); end ; See Also hdlram | hdlram.clone | hdlram.isLocked | hdlram.release | www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-379 hex Purpose Hexadecimal representation of stored integer of fi object Syntax hex(a) Description hex(a) returns the stored integer of fi object a in hexadecimal format as a string. hex(a) is equivalent to a.hex. Fixed-point numbers can be represented as real-world value = 2− fraction length × stored integer or, equivalently as real-world value = (slope × stored integer) + bias The stored integer is the raw binary number, in which the binary point is assumed to be at the far right of the word. Examples Viewing fi Objects in Hexadecimal Format The following code a = fi([-1 1],1,8,7); y = hex(a) z = a.hex returns y = 80 7f z = 80 2-380 7f www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان hex Writing Hex Data to a File The following example shows how to write hex data from the MATLAB workspace into a text file. First, define your data and create a writable text file called hexdata.txt: x = (0:15)'/16; a = fi(x,0,16,16); h = fopen('hexdata.txt','w'); Use the fprintf function to write your data to the hexdata.txt file: for k=1:length(a) fprintf(h,'%s\n',hex(a(k))); end fclose(h); To see the contents of the file you created, use the type function: type hexdata.txt MATLAB returns: 0000 1000 2000 3000 4000 5000 6000 7000 8000 9000 a000 b000 c000 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-381 hex d000 e000 f000 Reading Hex Data from a File The following example shows how to read hex data from a text file back into the MATLAB workspace. Open hexdata.txt for reading and read its contents into a workspace variable: h = fopen('hexdata.txt','r'); nextline = ''; str=''; while ischar(nextline) nextline = fgetl(h); if ischar(nextline) str = [str;nextline]; end end Create a fi object with the correct scaling and assign it the hex values stored in the str variable: b = fi([],0,16,16); b.hex = str b = 0 0.0625 0.1250 0.1875 0.2500 0.3125 0.3750 0.4375 2-382 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان hex 0.5000 0.5625 0.6250 0.6875 0.7500 0.8125 0.8750 0.9375 DataTypeMode: Signedness: WordLength: FractionLength: See Also Fixed-point: binary point scaling Unsigned 16 16 bin | dec | storedInteger | oct www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-383 hex2num Purpose Convert hexadecimal string to number using quantizer object Syntax x = hex2num(q,h) [x1,x2,...] = hex2num(q,h1,h2,...) Description x = hex2num(q,h) converts hexadecimal string h to numeric matrix x. The attributes of the numbers in x are specified by quantizer object q. When h is a cell array containing hexadecimal strings, hex2num returns x as a cell array of the same dimension containing numbers. For fixed-point hexadecimal strings, hex2num uses two’s complement representation. For floating-point strings, the representation is IEEE Standard 754 style. When there are fewer hexadecimal digits than needed to represent the number, the fixed-point conversion zero-fills on the left. Floating-point conversion zero-fills on the right. [x1,x2,...] = hex2num(q,h1,h2,...) converts hexadecimal strings h1, h2,... to numeric matrices x1, x2,.... hex2num and num2hex are inverses of one another, with the distinction that num2hex returns the hexadecimal strings in a column. Examples To create all the 4-bit fixed-point two’s complement numbers in fractional form, use the following code. q = quantizer([4 3]); h = ['7 3 F B';'6 2 E A';'5 1 D 9';'4 0 C 8']; x = hex2num(q,h) x = 0.8750 0.7500 0.6250 0.5000 See Also 2-384 0.3750 0.2500 0.1250 0 -0.1250 -0.2500 -0.3750 -0.5000 -0.6250 -0.7500 -0.8750 -1.0000 bin2num | num2bin | num2hex | num2int www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان hist Purpose Create histogram plot Description Refer to the MATLAB hist reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-385 histc Purpose Histogram count Description Refer to the MATLAB histc reference page for more information. 2-386 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان horzcat Purpose Horizontally concatenate multiple fi objects Syntax c = horzcat(a,b,...) [a, b, ...] Description c = horzcat(a,b,...) is called for the syntax [a, b, ...] when any of a, b, ... , is a fi object. [a b, ...] or [a,b, ...] is the horizontal concatenation of matrices a and b. a and b must have the same number of rows. Any number of matrices can be concatenated within one pair of brackets. N-D arrays are horizontally concatenated along the second dimension. The first and remaining dimensions must match. Horizontal and vertical concatenation can be combined together as in [1 2;3 4]. [a b; c] is allowed if the number of rows of a equals the number of rows of b, and if the number of columns of a plus the number of columns of b equals the number of columns of c. The matrices in a concatenation expression can themselves be formed via a concatenation as in [a b;[c d]]. Note The fimath and numerictype properties of a concatenated matrix of fi objects c are taken from the leftmost fi object in the list (a,b,...). See Also vertcat www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-387 imag Purpose Imaginary part of complex number Description Refer to the MATLAB imag reference page for more information. 2-388 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان innerprodintbits Purpose Number of integer bits needed for fixed-point inner product Syntax innerprodintbits(a,b) Description innerprodintbits(a,b) computes the minimum number of integer bits necessary in the inner product of a'*b to guarantee that no overflows occur and to preserve best precision. • a and b are fi vectors. • The values of a are known. • Only the numeric type of b is relevant. The values of b are ignored. Examples The primary use of this function is to determine the number of integer bits necessary in the output Y of an FIR filter that computes the inner product between constant coefficient row vector B and state column vector Z. For example, for k=1:length(X); Z = [X(k);Z(1:end-1)]; Y(k) = B * Z; end Algorithms In general, an inner product grows log2(n) bits for vectors of length n. However, in the case of this function the vector a is known and its values do not change. This knowledge is used to compute the smallest number of integer bits that are necessary in the output to guarantee that no overflow will occur. The largest gain occurs when the vector b has the same sign as the constant vector a. Therefore, the largest gain due to the vector a is a*sign(a'), which is equal to sum(abs(a)). The overall number of integer bits necessary to guarantee that no overflow occurs in the inner product is computed by: n = ceil(log2(sum(abs(a)))) + number of integer bits in b + 1 sign bit www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-389 innerprodintbits The extra sign bit is only added if both a and b are signed and b attains its minimum. This prevents overflow in the event of (-1)*(-1). 2-390 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان int8 Purpose Convert fi object to signed 8-bit integer Syntax c = int8(a) Description c = int8(a) returns the built-in int8 value of fi object a, based on Examples This example shows the int8 values of a fi object. its real world value. If necessary, the data is rounded-to-nearest and saturated to fit into an int8. a = fi([-pi 0.1 pi],1,8); c = int8(a) c = -3 See Also 0 3 storedInteger | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-391 int16 Purpose Convert fi object to signed 16-bit integer Syntax c = int16(a) Description c = int16(a) returns the built-in int16 value of fi object a, based on its real world value. If necessary, the data is rounded-to-nearest and saturated to fit into an int16. Examples This example shows the int16 values of a fi object. a = fi([-pi 0.1 pi],1,16); c = int16(a) c = -3 See Also 2-392 0 3 storedInteger | int8 | int32 | int64 | uint8 | uint16 | uint32 | uint64 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان int32 Purpose Convert fi object to signed 32-bit integer Syntax c = int32(a) Description c = int32(a) returns the built-in int32 value of fi object a, based on its real world value. If necessary, the data is rounded-to-nearest and saturated to fit into an int32. Examples This example shows the int32 values of a fi object. a = fi([-pi 0.1 pi],1,32); c = int32(a) c = -3 See Also 0 3 storedInteger | int8 | int16 | int64 | uint8 | uint16 | uint32 | uint64 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-393 int64 Purpose Convert fi object to signed 64-bit integer Syntax c = int64(a) Description c = int64(a) returns the built-in int64 value of fi object a, based on its real world value. If necessary, the data is rounded-to-nearest and saturated to fit into an int64. Examples This example shows the int64 values of a fi object. a = fi([-pi 0.1 pi],1,64); c = int64(a) c = -3 See Also 2-394 0 3 storedInteger | int8 | int16 | int32 | uint8 | uint16 | uint32 | uint64 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان intmax Purpose Largest positive stored integer value representable by numerictype of fi object Syntax x = intmax(a) Description x = intmax(a) returns the largest positive stored integer value representable by the numerictype of a. See Also eps | intmin | lowerbound | lsb | range | realmax | realmin | stripscaling | upperbound www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-395 intmin Purpose Smallest stored integer value representable by numerictype of fi object Syntax x = intmin(a) Description x = intmin(a) returns the smallest stored integer value representable by the numerictype of a. Examples a = fi(pi, true, 16, 12); x = intmin(a) x = -32768 DataTypeMode: Signedness: WordLength: FractionLength: See Also 2-396 Fixed-point: binary point scaling Signed 16 0 eps | intmax | lowerbound | lsb | range | realmax | realmin | stripscaling | upperbound www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان ipermute Purpose Inverse permute dimensions of multidimensional array Description Refer to the MATLAB ipermute reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-397 isboolean Purpose Determine whether input is Boolean Syntax y = isboolean(a) y = isboolean(T) Description y = isboolean(a) returns 1 when the DataType property of fi object a is boolean, and 0 otherwise. y = isboolean(T) returns 1 when the DataType property of numerictype object T is boolean, and 0 otherwise. See Also 2-398 isdouble | isfixed | isfloat | isscaleddouble | isscalingbinarypoint | isscalingslopebias | isscalingunspecified | issingle www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان iscolumn Purpose Determine whether fi object is column vector Syntax y = iscolumn(a) Description y = iscolumn(a) returns 1 if the fi object a is a column vector, and 0 otherwise. See Also isrow www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-399 isdouble Purpose Determine whether input is double-precision data type Syntax y = isdouble(a) y = isdouble(T) Description y = isdouble(a) returns 1 when the DataType property of fi object a is double, and 0 otherwise. y = isdouble(T) returns 1 when the DataType property of numerictype object T is double, and 0 otherwise. See Also 2-400 isboolean | isfixed | isfloat | isscaleddouble | isscaledtype | isscalingbinarypoint | isscalingslopebias | isscalingunspecified | issingle www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان isempty Purpose Determine whether array is empty Description Refer to the MATLAB isempty reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-401 isequal Purpose Determine whether real-world values of two fi objects are equal, or determine whether properties of two fimath, numerictype, or quantizer objects are equal Syntax y y y y Description y = isequal(a,b,...) returns 1 if all the fi object inputs have the same real-world value. Otherwise, the function returns 0. = = = = isequal(a,b,...) isequal(F,G,...) isequal(T,U,...) isequal(q,r,...) y = isequal(F,G,...) returns 1 if all the fimath object inputs have the same properties. Otherwise, the function returns 0. y = isequal(T,U,...) returns 1 if all the numerictype object inputs have the same properties. Otherwise, the function returns 0. y = isequal(q,r,...) returns 1 if all the quantizer object inputs have the same properties. Otherwise, the function returns 0. See Also 2-402 eq | ispropequal www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان isfi Purpose Determine whether variable is fi object Syntax y = isfi(a) Description y = isfi(a) returns 1 if a is a fi object, and 0 otherwise. See Also fi | isfimath | isfipref | isnumerictype | isquantizer www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-403 isfimath Purpose Determine whether variable is fimath object Syntax y = isfimath(F) Description y = isfimath(F) returns 1 if F is a fimath object, and 0 otherwise. See Also fimath | isfi | isfipref | isnumerictype | isquantizer 2-404 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان isfimathlocal Purpose Determine whether fi object has local fimath Syntax y = isfimathlocal(a) Description y = isfimathlocal(a) returns 1 if the fi object a has a local fimath object, and 0 if a does not have a local fimath. See Also fimath | isfi | isfipref | isnumerictype | isquantizer | sfi | ufi www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-405 isfinite Purpose Determine whether array elements are finite Description Refer to the MATLAB isfinite reference page for more information. 2-406 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان isfipref Purpose Determine whether input is fipref object Syntax y = isfipref(P) Description y = isfipref(P) returns 1 if P is a fipref object, and 0 otherwise. See Also fipref | isfi | isfimath | isnumerictype | isquantizer www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-407 isfixed Purpose Determine whether input is fixed-point data type Syntax y = isfixed(a) y = isfixed(T) y = isfixed(q) Description y = isfixed(a) returns 1 when the DataType property of fi object a is Fixed, and 0 otherwise. y = isfixed(T) returns 1 when the DataType property of numerictype object T is Fixed, and 0 otherwise. y = isfixed(q) returns 1 when q is a fixed-point quantizer, and 0 otherwise. See Also 2-408 isboolean | isdouble | isfloat | isscaleddouble | isscaledtype | isscalingbinarypoint | isscalingslopebias | isscalingunspecified | issingle www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان isfloat Purpose Determine whether input is floating-point data type Syntax y = isfloat(a) y = isfloat(T) y = isfloat(q) Description y = isfloat(a) returns 1 when the DataType property of fi object a is single or double, and 0 otherwise. y = isfloat(T) returns 1 when the DataType property of numerictype object T is single or double, and 0 otherwise. y = isfloat(q) returns 1 when q is a floating-point quantizer, and 0 otherwise. See Also isboolean | isdouble | isfixed | isscaleddouble | isscaledtype | isscalingbinarypoint | isscalingslopebias | isscalingunspecified | issingle www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-409 isinf Purpose Determine whether array elements are infinite Description Refer to the MATLAB isinf reference page for more information. 2-410 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان isnan Purpose Determine whether array elements are NaN Description Refer to the MATLAB isnan reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-411 isnumeric Purpose Determine whether input is numeric array Description Refer to the MATLAB isnumeric reference page for more information. 2-412 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان isnumerictype Purpose Determine whether input is numerictype object Syntax y = isnumerictype(T) Description y = isnumerictype(T) returns 1 if T is a numerictype object, and 0 otherwise. See Also isfi | isfimath | isfipref | isquantizer | numerictype www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-413 isobject Purpose Determine whether input is MATLAB object Description Refer to the MATLAB isobject reference page for more information. 2-414 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان ispropequal Purpose Determine whether properties of two fi objects are equal Syntax y = ispropequal(a,b,...) Description y = ispropequal(a,b,...) returns 1 if all the inputs are fi objects and all the inputs have the same properties. Otherwise, the function returns 0. To compare the real-world values of two fi objects a and b, use a == b or isequal(a,b). See Also fi | isequal www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-415 isquantizer Purpose Determine whether input is quantizer object Syntax y = isquantizer(q) Description y = isquantizer(q) returns 1 when q is a quantizer object, and 0 otherwise. See Also quantizer | isfi | isfimath | isfipref | isnumerictype 2-416 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان isreal Purpose Determine whether array elements are real Description Refer to the MATLAB isreal reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-417 isrow Purpose Determine whether fi object is row vector Syntax y = isrow(a) Description y = isrow(a) returns 1 if the fi object a is a row vector, and 0 See Also iscolumn 2-418 otherwise. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان isscalar Purpose Determine whether input is scalar Description Refer to the MATLAB isscalar reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-419 isscaleddouble Purpose Determine whether input is scaled double data type Syntax y = isscaleddouble(a) y = isscaleddouble(T) Description y = isscaleddouble(a) returns 1 when the DataType property of fi object a is ScaledDouble, and 0 otherwise. y = isscaleddouble(T) returns 1 when the DataType property of numerictype object T is ScaledDouble, and 0 otherwise. See Also 2-420 isboolean | isdouble | isfixed | isfloat | isscaledtype | isscalingbinarypoint | isscalingslopebias | isscalingunspecified | issingle www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان isscaledtype Purpose Determine whether input is fixed-point or scaled double data type Syntax y = isscaledtype(a) y = isscaledtype(T) Description y = isscaledtype(a) returns 1 when the DataType property of fi object a is Fixed or ScaledDouble, and 0 otherwise. y = isscaledtype(T) returns 1 when the DataType property of numerictype object T is Fixed or ScaledDouble, and 0 otherwise. See Also isboolean | isdouble | isfixed | isfloat | numerictype | isscaleddouble | isscalingbinarypoint | isscalingslopebias | isscalingunspecified | issingle www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-421 isscalingbinarypoint Purpose Determine whether input has binary point scaling Syntax y = isscalingbinarypoint(a) y = isscalingbinarypoint(T) Description y = isscalingbinarypoint(a) returns 1 when the fi object a has binary point scaling or trivial slope and bias scaling. Otherwise, the function returns 0. Slope and bias scaling is trivial when the slope is an integer power of two and the bias is zero. y = isscalingbinarypoint(T) returns 1 when the numerictype object T has binary point scaling or trivial slope and bias scaling. Otherwise, the function returns 0. Slope and bias scaling is trivial when the slope is an integer power of two and the bias is zero. See Also 2-422 isboolean | isdouble | isfixed | isfloat | isscaleddouble | isscaledtype | isscalingslopebias | isscalingunspecified | issingle www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان isscalingslopebias Purpose Determine whether input has nontrivial slope and bias scaling Syntax y = isscalingslopebias(a) y = isscalingslopebias(T) Description y = isscalingslopebias(a) returns 1 when the fi object a has nontrivial slope and bias scaling, and 0 otherwise. Slope and bias scaling is trivial when the slope is an integer power of two and the bias is zero. y = isscalingslopebias(T) returns 1 when the numerictype object T has nontrivial slope and bias scaling, and 0 otherwise. Slope and bias scaling is trivial when the slope is an integer power of two and the bias is zero. See Also isboolean | isdouble | isfixed | isfloat | isscaleddouble | isscaledtype | isscalingbinarypoint | isscalingunspecified | issingle www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-423 isscalingunspecified Purpose Determine whether input has unspecified scaling Syntax y = isscalingunspecified(a) y = isscalingunspecified(T) Description y = isscalingunspecified(a) returns 1 if fi object a has a fixed-point or scaled double data type and its scaling has not been specified. y = isscalingunspecified(T) returns 1 if numerictype object T has a fixed-point or scaled double data type and its scaling has not been specified. See Also 2-424 isboolean | isdouble | isfixed | isfloat | isscaleddouble | isscaledtype | isscalingbinarypoint | isscalingslopebias | issingle www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان issigned Purpose Determine whether fi object is signed Syntax y = issigned(a) Description y = issigned(a) returns 1 if the fi object a is signed, and 0 if it is unsigned. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-425 issingle Purpose Determine whether input is single-precision data type Syntax y = issingle(a) y = issingle(T) Description y = issingle(a) returns 1 when the DataType property of fi object a is single, and 0 otherwise. y = issingle(T) returns 1 when the DataType property of numerictype object T is single, and 0 otherwise. See Also 2-426 isboolean | isdouble | isfixed | isfloat | isscaleddouble | isscaledtype | isscalingbinarypoint | isscalingslopebias | isscalingunspecified www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان isslopebiasscaled Purpose Determine whether numerictype object has nontrivial slope and bias Syntax y = isslopebiasscaled(T) Description y = isslopebiasscaled(T) returns 1 when numerictype object T has nontrivial slope and bias scaling, and 0 otherwise. Slope and bias scaling is trivial when the slope is an integer power of 2, and the bias is 0. See Also isboolean | isdouble | isfixed | isfloat | isscaleddouble | isscaledtype | issingle | numerictype www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-427 isvector Purpose Determine whether input is vector Description Refer to the MATLAB isvector reference page for more information. 2-428 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان le Purpose Determine whether real-world value of fi object is less than or equal to another Syntax c = le(a,b) a <= b Description c = le(a,b) is called for the syntax a <= b when a or b is a fi object. a and b must have the same dimensions unless one is a scalar. A scalar can be compared with another object of any size. a <= b does an element-by-element comparison between a and b and returns a matrix of the same size with elements set to 1 where the relation is true, and 0 where the relation is false. See Also eq | ge | gt | lt | ne www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-429 length Purpose Vector length Description Refer to the MATLAB length reference page for more information. 2-430 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان line Purpose Create line object Description Refer to the MATLAB line reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-431 logical Purpose Convert numeric values to logical Description Refer to the MATLAB logical reference page for more information. 2-432 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان loglog Purpose Create log-log scale plot Description Refer to the MATLAB loglog reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-433 logreport Purpose Quantization report Syntax logreport(a) logreport(a, b, ...) Description logreport(a) displays the minlog, maxlog, lowerbound, upperbound, noverflows, and nunderflows for the fi object a. logreport(a, b, ...) displays the report for each fi object a, b, ... . Examples The following example produces a logreport for fi objects a and b: fipref('LoggingMode','On'); a = fi(pi); b = fi(randn(10),1,8,7); Warning: 27 overflows occurred in the fi assignment operation. Warning: 1 underflow occurred in the fi assignment operation. logreport(a,b) See Also 2-434 minlog maxlog lowerbound upperbound noverflows a 3.141602 3.141602 -4 3.999878 0 0 b -1 0.9921875 -1 0.9921875 27 1 fipref | quantize | quantizer www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان nunderflows lowerbound Purpose Lower bound of range of fi object Syntax lowerbound(a) Description lowerbound(a) returns the lower bound of the range of fi object a. If L=lowerbound(a) and U=upperbound(a), then [L,U]=range(a). See Also eps | intmax | intmin | lsb | range | realmax | realmin | upperbound www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-435 lsb Purpose Scaling of least significant bit of fi object, or value of least significant bit of quantizer object Syntax b = lsb(a) p = lsb(q) Description b = lsb(a) returns the scaling of the least significant bit of fi object a. The result is equivalent to the result given by the eps function. p = lsb(q) returns the quantization level of quantizer object q, or the distance from 1.0 to the next largest floating-point number if q is a floating-point quantizer object. Examples This example uses the lsb function to find the value of the least significant bit of the quantizer object q. q = quantizer('fixed',[8 7]); p = lsb(q) p = 0.0078 See Also 2-436 eps | intmax | intmin | lowerbound | quantize | range | realmax | realmin | upperbound www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان lt Purpose Determine whether real-world value of one fi object is less than another Syntax c = lt(a,b) a < b Description c = lt(a,b) is called for the syntax a < b when a or b is a fi object. a and b must have the same dimensions unless one is a scalar. A scalar can be compared with another object of any size. a < b does an element-by-element comparison between a and b and returns a matrix of the same size with elements set to 1 where the relation is true, and 0 where the relation is false. See Also eq | ge | gt | le | ne www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-437 max Purpose Largest element in array of fi objects Syntax max(a) max(a,b) [y,v] = max(a) [y,v] = max(a,[],dim) Description • For vectors, max(a) is the largest element in a. • For matrices, max(a) is a row vector containing the maximum element from each column. • For N-D arrays, max(a) operates along the first nonsingleton dimension. max(a,b) returns an array the same size as a and b with the largest elements taken from a or b. Either one can be a scalar. [y,v] = max(a) returns the indices of the maximum values in vector v. If the values along the first nonsingleton dimension contain more than one maximal element, the index of the first one is returned. [y,v] = max(a,[],dim) operates along the dimension dim. When complex, the magnitude max(abs(a)) is used, and the angle angle(a) is ignored. NaNs are ignored when computing the maximum. See Also 2-438 mean | median | min | sort www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان maxlog Purpose Log maximums Syntax y = maxlog(a) y = maxlog(q) Description y = maxlog(a) returns the largest real-world value of fi object a since logging was turned on or since the last time the log was reset for the object. Turn on logging by setting the fipref object LoggingMode property to on. Reset logging for a fi object using the resetlog function. y = maxlog(q) is the maximum value after quantization during a call to quantize(q,...) for quantizer object q. This value is the maximum value encountered over successive calls to quantize since logging was turned on, and is reset with resetlog(q). maxlog(q) is equivalent to get(q,'maxlog') and q.maxlog. Examples Example 1: Using maxlog with fi objects P = fipref('LoggingMode','on'); format long g a = fi([-1.5 eps 0.5], true, 16, 15); a(1) = 3.0; maxlog(a) Warning: 1 overflow occurred in the fi assignment operation. > In embedded.fi.fi at 510 In fi at 220 Warning: 1 underflow occurred in the fi assignment operation. > In embedded.fi.fi at 510 In fi at 220 Warning: 1 overflow occurred in the fi assignment operation. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-439 maxlog ans = 0.999969482421875 The largest value maxlog can return is the maximum representable value of its input. In this example, a is a signed fi object with word length 16, fraction length 15 and range: -1 ≤ x ≤ 1 – 2-15 You can obtain the numerical range of any fi object a using the range function: format long g r = range(a) r = -1 0.999969482421875 Example 2: Using maxlog with quantizer objects q = quantizer; warning on format long g x = [-20:10]; y = quantize(q,x); maxlog(q) Warning: 29 overflows. > In embedded.quantizer.quantize at 74 ans = .999969482421875 2-440 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان maxlog The largest value maxlog can return is the maximum representable value of its input. You can obtain the range of x after quantization using the range function: format long g r = range(q) r = -1 See Also 0.999969482421875 fipref | minlog | noverflows | nunderflows | reset | resetlog www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-441 mean Purpose Average or mean value of fixed-point array Syntax c = mean(a) c = mean(a,dim) Description c = mean(a) computes the mean value of the fixed-point array a along its first nonsingleton dimension. c = mean(a,dim) computes the mean value of the fixed-point array a along dimension dim. dim must be a positive, real-valued integer with a power-of-two slope and a bias of 0. The input to the mean function must be a real-valued fixed-point array. The fixed-point output array c has the same numerictype properties as the fixed-point input array a and has no local fimath. When a is an empty fixed-point array (value = []), the value of the output array is zero. Examples Compute the mean value along the first dimension (rows) of a fixed-point array. x = fi([0 1 2; 3 4 5], 1, 32); % x is a signed FI object with a 32-bit word length % and a best-precision fraction length of 28-bits mx1 = mean(x,1) Compute the mean value along the second dimension (columns) of a fixed-point array. x = fi([0 1 2; 3 4 5], 1, 32); % x is a signed FI object with a 32-bit word length % and a best-precision fraction length of 28 bits mx2 = mean(x,2) 2-442 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان mean Algorithms The general equation for computing the mean of an array a, across dimension dim is: sum(a,dim)/size(a,dim) Because size(a,dim) is always a positive integer, the algorithm casts size(a,dim) to an unsigned 32-bit fi object with a fraction length of zero (SizeA). The algorithm then computes the mean of a according to the following equation, where Tx represents the numerictype properties of the fixed-point input array a: c = Tx.divide(sum(a,dim), SizeA) See Also max | median | min www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-443 median Purpose Median value of fixed-point array Syntax c = median(a) c = median(a,dim) Description c = median(a) computes the median value of the fixed-point array a along its first nonsingleton dimension. c = median(a,dim) computes the median value of the fixed-point array a along dimension dim. dim must be a positive, real-valued integer with a power-of-two slope and a bias of 0. The input to the median function must be a real-valued fixed-point array. The fixed-point output array c has the same numerictype properties as the fixed-point input array a and has no local fimath. When a is an empty fixed-point array (value = []), the value of the output array is zero. Examples Compute the median value along the first dimension of a fixed-point array. x = fi([0 1 2; 3 4 5; 7 2 2; 6 4 9], 1, 32) % x is a signed FI object with a 32-bit word length % and a best-precision fraction length of 27 bits mx1 = median(x,1) Compute the median value along the second dimension (columns) of a fixed-point array. x = fi([0 1 2; 3 4 5; 7 2 2; 6 4 9], 1, 32) % x is a signed FI object with a 32-bit word length % and a best-precision fraction length of 27 bits mx2 = median(x, 2) 2-444 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان median See Also max | mean | min www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-445 mesh Purpose Create mesh plot Description Refer to the MATLAB mesh reference page for more information. 2-446 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان meshc Purpose Create mesh plot with contour plot Description Refer to the MATLAB meshc reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-447 meshz Purpose Create mesh plot with curtain plot Description Refer to the MATLAB meshz reference page for more information. 2-448 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان min Purpose Smallest element in array of fi objects Syntax min(a) min(a,b) [y,v] = min(a) [y,v] = min(a,[],dim) Description • For vectors, min(a) is the smallest element in a. • For matrices, min(a) is a row vector containing the minimum element from each column. • For N-D arrays, min(a) operates along the first nonsingleton dimension. min(a,b) returns an array the same size as a and b with the smallest elements taken from a or b. Either one can be a scalar. [y,v] = min(a) returns the indices of the minimum values in vector v. If the values along the first nonsingleton dimension contain more than one minimal element, the index of the first one is returned. [y,v] = min(a,[],dim) operates along the dimension dim. When complex, the magnitude min(abs(a)) is used, and the angle angle(a) is ignored. NaNs are ignored when computing the minimum. See Also max | mean | median | sort www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-449 minlog Purpose Log minimums Syntax y = minlog(a) y = minlog(q) Description y = minlog(a) returns the smallest real-world value of fi object a since logging was turned on or since the last time the log was reset for the object. Turn on logging by setting the fipref object LoggingMode property to on. Reset logging for a fi object using the resetlog function. y = minlog(q) is the minimum value after quantization during a call to quantize(q,...) for quantizer object q. This value is the minimum value encountered over successive calls to quantize since logging was turned on, and is reset with resetlog(q). minlog(q) is equivalent to get(q,'minlog') and q.minlog. Examples Example 1: Using minlog with fi objects P = fipref('LoggingMode','on'); a = fi([-1.5 eps 0.5], true, 16, 15); a(1) = 3.0; minlog(a) ans = -1 The smallest value minlog can return is the minimum representable value of its input. In this example, a is a signed fi object with word length 16, fraction length 15 and range: -1 ≤ x ≤ 1 – 2-15 You can obtain the numerical range of any fi object a using the range function: 2-450 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان minlog format long g r = range(a) r = -1 0.999969482421875 Example 2: Using minlog with quantizer objects q = quantizer; warning on x = [-20:10]; y = quantize(q,x); minlog(q) Warning: 29 overflows. > In embedded.quantizer.quantize at 74 ans = -1 The smallest value minlog can return is the minimum representable value of its input. You can obtain the range of x after quantization using the range function: format long g r = range(q) r = -1 See Also 0.999969482421875 fipref | maxlog | noverflows | nunderflows | reset | resetlog www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-451 minus Purpose Matrix difference between fi objects Syntax minus(a,b) Description minus(a,b) is called for the syntax a - b when a or b is an object. a - b subtracts matrix b from matrix a. a and b must have the same dimensions unless one is a scalar value (a 1-by-1 matrix). A scalar value can be subtracted from any other value. minus does not support fi objects of data type Boolean. Note For information about the fimath properties involved in Fixed-Point Designer calculations, see “fimath Properties Usage for Fixed-Point Arithmetic” and “fimath ProductMode and SumMode” in the Fixed-Point Designer User’s Guide. For information about calculations using Fixed-Point Designer software, see the Fixed-Point Designer documentation. See Also 2-452 mtimes | plus | times | uminus www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان mod Purpose Modulus after division for fi objects Syntax M = mod(X,Y) Description M = mod(X,Y) if Y ~= 0, returns X-n.*Y, where n = floor(X./Y). The inputs X and Y must be real arrays of the same size, or either can be a real scalar. For fixed-point or integer input arguments, the output data type is the aggregate type of both input signedness, word lengths, and fraction lengths. For fixed-point inputs, the word length of the internally computed aggregate fixed-point output data type cannot exceed 32 bits. For floating-point input arguments, the output data type is the same as the inputs. Note The combination of fixed-point and floating-point inputs is not currently supported. Input Arguments X Integer, fixed-point, or floating-point array, or real scalar. Y Array of the same size as X, or real scalar. Output Arguments Examples M Result of modulus operation. If both inputs X and Y are floating-point, then the data type of M is the same as the inputs. If either input X or Y is fixed-point, then the data type of M is the aggregate numerictype. This value equals that of fixed.aggregateType(X,Y). Calculate the mod of two fi objects. % 7-bit signed fixed-point object x = fi(-3,1,7,0); % 15-bit signed fixed-point object www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-453 mod y = fi(2,1,15,0); M1 = mod(x,y) M1 = 1 DataTypeMode: Signedness: WordLength: FractionLength: M2 = mod(y,x) M2 = Fixed-point: binary point scaling Signed 15 0 -1 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 15 0 Convert the fi inputs in the previous example to double type, and calculate the mod. Mf1 = mod(double(x),double(y)) Mf1 = 1 Mf2 = mod(double(y),double(x)) Mf2 = -1 See Also 2-454 fixed.aggregateType | mod www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان mpower Purpose Fixed-point matrix power (^) Syntax c = mpower(a,k) c = a^k Description c = mpower(a,k) and c = a^k compute matrix power. The exponent k requires a positive, real-valued integer value. The fixed-point output array c has the same local fimath as the input a. If a has no local fimath, the output c also has no local fimath. The matrix power operation is performed using default fimath settings. Tips For more information about the mpower function, see the MATLAB mpower reference page. Examples Compute the power of a 2-dimensional square matrix for exponent values 0, 1, 2, and 3. x = fi([0 1; 2 4], 1, 32); px0 px1 px2 px3 See Also = = = = x^0 x^1 x^2 x^3 mpower | power www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-455 mpy Purpose Multiply two objects using fimath object Syntax c = F.mpy(a,b) Description c = F.mpy(a,b) performs elementwise multiplication on a and b using fimath object F. This is helpful in cases when you want to override the fimath objects of a and b, or if the fimath properties associated with a and b are different. The output fi object c has no local fimath. a and b can both be fi objects with the same dimensions unless one is a scalar. If either a or b is scalar, then c has the dimensions of the nonscalar object. a and b can also be doubles, singles, or integers. Examples In this example, c is the 40-bit product of a and b with fraction length 30. a = fi(pi); b = fi(exp(1)); F = fimath('ProductMode','SpecifyPrecision',... 'ProductWordLength',40,'ProductFractionLength',30); c = F.mpy(a, b) c = 8.5397 DataTypeMode: Signedness: WordLength: FractionLength: Algorithms Fixed-point: binary point scaling Signed 40 30 c = F.mpy(a,b) is similar to a.fimath = F; b.fimath = F; c = a .* b 2-456 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان mpy c = 8.5397 DataTypeMode: Signedness: WordLength: FractionLength: RoundingMethod: OverflowAction: ProductMode: ProductWordLength: ProductFractionLength: SumMode: Fixed-point: binary point scaling Signed 40 30 nearest saturate SpecifyPrecision 40 30 FullPrecision but not identical. When you use mpy, the fimath properties of a and b are not modified, and the output fi object c has no local fimath. When you use the syntax c = a .* b, where a and b have their own fimath objects, the output fi object c gets assigned the same fimath object as inputs a and b. See “fimath Rules for Fixed-Point Arithmetic” in the Fixed-Point Designer User’s Guide for more information. See Also add | divide | fi | fimath | mrdivide | numerictype | rdivide | sub | sum www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-457 mrdivide Purpose Forward slash (/) or right-matrix division Syntax c = mrdivide(a,b) c = a/b Description c = mrdivide(a,b) and c = a/b perform right-matrix division. When one or both of the inputs is a fi object, the denominator input, b, must be a scalar and the output fi object c is equivalent to c = rdivide(a,b) or c = a./b (right-array division). The numerator input a can be complex, but the denominator input b must always be real-valued. When the numerator input a is complex, the real and imaginary parts of a are independently divided by b. For information on the data type rules used by the mrdivide function, see the rdivide reference page. Examples In this example, you use the forward slash (/) to perform right matrix division on a 3-by-3 magic square of fi objects. Because the numerator input is a fi object, the denominator input b must be a scalar: a = fi(magic(3)) b = fi(3, 1, 12, 8) c = a/b The mrdivide function outputs a signed 3-by-3 array of fi objects, each of which has a word length of 16 bits and a fraction length of 3 bits. a = 8 3 4 1 5 9 6 7 2 DataTypeMode: Signedness: WordLength: FractionLength: 2-458 Fixed-point: binary point scaling Signed 16 11 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان mrdivide b = 3 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 12 8 c = 2.6250 1.0000 1.3750 0.3750 1.6250 3.0000 DataTypeMode: Signedness: WordLength: FractionLength: See Also 2.0000 2.3750 0.6250 Fixed-point: binary point scaling Signed 16 3 add | divide | fi | fimath | numerictype | rdivide | sub | sum www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-459 mtimes Purpose Matrix product of fi objects Syntax mtimes(a,b) Description mtimes(a,b) is called for the syntax a * b when a or b is an object. a * b is the matrix product of a and b. A scalar value (a 1-by-1 matrix) can multiply any other value. Otherwise, the number of columns of a must equal the number of rows of b. mtimes does not support fi objects of data type Boolean. Note For information about the fimath properties involved in Fixed-Point Designer calculations, see “fimath Properties Usage for Fixed-Point Arithmetic” and “fimath ProductMode and SumMode” in the Fixed-Point Designer documentation. For information about calculations using Fixed-Point Designer software, see the Fixed-Point Designer documentation. See Also 2-460 plus | minus | times | uminus www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان ndgrid Purpose Generate arrays for N-D functions and interpolation Description Refer to the MATLAB ndgrid reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-461 ndims Purpose Number of array dimensions Description Refer to the MATLAB ndims reference page for more information. 2-462 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان ne Purpose Determine whether real-world values of two fi objects are not equal Syntax c = ne(a,b) a ~= b Description c = ne(a,b) is called for the syntax a ~= b when a or b is a fi object. a and b must have the same dimensions unless one is a scalar. A scalar can be compared with another object of any size. a ~= b does an element-by-element comparison between a and b and returns a matrix of the same size with elements set to 1 where the relation is true, and 0 where the relation is false. See Also eq | ge | gt | le | lt www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-463 nearest Purpose Round toward nearest integer with ties rounding toward positive infinity Syntax y = nearest(a) Description y = nearest(a) rounds fi object a to the nearest integer or, in case of a tie, to the nearest integer in the direction of positive infinity, and returns the result in fi object y. y and a have the same fimath object and DataType property. When the DataType property of a is single, double, or boolean, the numerictype of y is the same as that of a. When the fraction length of a is zero or negative, a is already an integer, and the numerictype of y is the same as that of a. When the fraction length of a is positive, the fraction length of y is 0, its sign is the same as that of a, and its word length is the difference between the word length and the fraction length of a, plus one bit. If a is signed, then the minimum word length of y is 2. If a is unsigned, then the minimum word length of y is 1. For complex fi objects, the imaginary and real parts are rounded independently. nearest does not support fi objects with nontrivial slope and bias scaling. Slope and bias scaling is trivial when the slope is an integer power of 2 and the bias is 0. Examples Example 1 The following example demonstrates how the nearest function affects the numerictype properties of a signed fi object with a word length of 8 and a fraction length of 3. a = fi(pi, 1, 8, 3) a = 2-464 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان nearest 3.1250 DataTypeMode: Signedness: WordLength: FractionLength: y = nearest(a) Fixed-point: binary point scaling Signed 8 3 y = 3 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 6 0 Example 2 The following example demonstrates how the nearest function affects the numerictype properties of a signed fi object with a word length of 8 and a fraction length of 12. a = fi(0.025,1,8,12) a = 0.0249 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 8 12 y = nearest(a) y = www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-465 nearest 0 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 2 0 Example 3 The functions convergent, nearest and round differ in the way they treat values whose least significant digit is 5: • The convergent function rounds ties to the nearest even integer • The nearest function rounds ties to the nearest integer toward positive infinity • The round function rounds ties to the nearest integer with greater absolute value The following table illustrates these differences for a given fi object a. a See Also 2-466 convergent(a) nearest(a) round(a) –3.5 –4 –3 –4 –2.5 –2 –2 –3 –1.5 –2 –1 –2 –0.5 0 0 –1 0.5 0 1 1 1.5 2 2 2 2.5 2 3 3 3.5 4 4 4 ceil | convergent | fix | floor | round www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان noperations Purpose Number of operations Syntax noperations(q) Description noperations(q) is the number of quantization operations during a call to quantize(q,...) for quantizer object q. This value accumulates over successive calls to quantize. You reset the value of noperations to zero by issuing the command resetlog(q). Each time any data element is quantized, noperations is incremented by one. The real and complex parts are counted separately. For example, (complex * complex) counts four quantization operations for products and two for sum, because(a+bi)*(c+di) = (a*c - b*d) + (a*d + b*c). In contrast, (real*real) counts one quantization operation. In addition, the real and complex parts of the inputs are quantized individually. As a result, for a complex input of length 204 elements, noperations counts 408 quantizations: 204 for the real part of the input and 204 for the complex part. If any inputs, states, or coefficients are complex-valued, they are all expanded from real values to complex values, with a corresponding increase in the number of quantization operations recorded by noperations. In concrete terms, (real*real) requires fewer quantizations than (real*complex) and (complex*complex). Changing all the values to complex because one is complex, such as the coefficient, makes the (real*real) into (real*complex), raising noperations count. See Also maxlog | minlog www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-467 not Purpose Find logical NOT of array or scalar input Description Refer to the MATLAB not reference page for more information. 2-468 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان noverflows Purpose Number of overflows Syntax y = noverflows(a) y = noverflows(q) Description y = noverflows(a) returns the number of overflows of fi object a since logging was turned on or since the last time the log was reset for the object. Turn on logging by setting the fipref property LoggingMode to on. Reset logging for a fi object using the resetlog function. y = noverflows(q) returns the accumulated number of overflows resulting from quantization operations performed by a quantizer object q. See Also maxlog | minlog | nunderflows | resetlog www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-469 nts Purpose Determine fixed-point data type Syntax nts nts({'block',PORT}) nts({line-handle}) nts({gsl}) Description nts opens the NumericTypeScope window. To connect to a signal in a Simulink model, select the signal and then, in the NumericTypeScope window, select File > Connect to Simulink Signal. The NumericTypeScope suggests a fixed-point data type in the form of a numerictype object based on the dynamic range of the input data and the criteria that you specify in the Bit Allocation Panel on page 478. The scope allows you to visualize the dynamic range of data in the form of a log2 histogram. It displays the data values on the X-axis and the number or percentage of occurrences on the Y-axis. Each bin in the histogram corresponds to a bit in a word. For example, 20 corresponds to the first integer bit in the binary word, 2-1 corresponds to the first fractional bit in the binary word. nts({'block',PORT}) opens the NumericTypeScope window and connects the scope to the signal output from block on output port with index PORT. If the block has more than one output port, you must specify the port index. The scope cannot connect to more than one output port. nts({line-handle}) opens the NumericTypeScope window and connects the scope to the Simulink signal which has the line handle specified in line-handle. nts({gsl}) opens the NumericTypeScope window and connects the scope to the currently selected Simulink signal. You must select a signal in a Simulink model first, otherwise the scope opens with no signal selected. Tips 2-470 • Use the NumericTypeScope to help you identify any values that are outside range or below precision based on the current data type. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان nts When the information is available, the scope indicates values that are outside range, below precision, and in range of the data type by color-coding the histogram bars as follows: - Blue — Histogram bin contains values that are in range of the current data type. - Red — Histogram bin contains values that are outside range in the current data type. - Yellow — Histogram bin contains values that are below precision in the current data type. • Select View > Vertical Units to select whether to display values as a percentage or as an actual count. • Use the View > Bring All NumericTypeScope Windows Forward menu option to manage your NumericTypeScope windows. Selecting this option or pressing Ctrl+F brings all NumericTypeScope windows into view. Input Arguments block Full path to the specified block. line-handle Handle of the Simulink signal that you want to view with the scope. To get the handle of the currently selected signal, at the MATLAB command line, enter nts({gsl}). PORT Index of the output port that you want to view with the scope. If the block has more than one output port, you must specify the index. The scope cannot connect to more than one output port. The The NumericTypeScope opens with the default toolbars displayed at the top NumericTypeScopeof the window and the dialog panels to the right. Window www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-471 nts ﻣﺘﻠﺐ ﺳﺎﯾﺖ | www.MatlabSite.com ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-472 nts Toolbars By default the scope displays a toolbar that provides these options: Button Action New NumericTypeScope. Connect to Simulink signal. The scope connects to the currently selected signal. If a block with only one output port is selected and the Connect scope on selection of is set to Signal lines or blocks, connects to the output port of the selected block. For more information, see Sources Pane on page 477. After connecting the scope to a signal in a Simulink model, the scope displays an additional toolbar with the following options: Button Action Stop simulation Start simulation Simulate one step Snapshot. Freezes the display so that you can examine the results. To reenable display refreshing, click the button again. Highlight Simulink signal. Persistent. By default, the scope makes a persistent connection to the selected signal. If you want to view different signals during the simulation, click this button to make a floating connection. You can then select any signal in the model and the scope displays it. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-473 nts Dialog Boxes and Panels • “Configuration Dialog Box” on page 2-474 • “Dialog Panels” on page 2-478 Configuration Dialog Box Use the NumericTypeScope configuration dialog box to control the behavior and appearance of the scope window. To open the Configuration dialog box, from the scope main menu, select File > Configuration > Edit, or, with the scope as your active window, press the N key. For information about each pane, see Core Pane on page 475 and Sources Pane on page 477. To save configuration settings for future use, select File > Configuration > Save as. The configuration settings you save become the default configuration settings for the NumericTypeScope. 2-474 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان nts Caution Before saving your own set of configuration settings in the matlab/toolbox/fixpoint folder, save a backup copy of the default configuration settings in another location. If you do not save a backup copy of the default configuration settings, you cannot restore these settings at a later time. To save your configuration settings for future use, save them in the matlab/toolbox/fixpoint folder with the file name NumericTypeScopeSL.cfg. You can re-save your configuration settings at anytime, but you must save them in this folder with this filename. Core Pane The Core pane controls the general settings of the scope. To open the Core:General UI Options dialog box, select General UI and then click Options. • Display the full source path in the title bar—Select this check box to display the full path to the selected block in the model. Otherwise, the scope displays only the block name. • Open message log—Control when the Message Log window opens. The Message log window helps you debug issues with the scope. Choose to open the Message Log window for any of these conditions: www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-475 nts - for any new messages for warn/fail messages only for fail messages manually The option defaults to for warn/fail messages. You can open the Message Log at any time by selecting Help > Message Log or by pressing Ctrl+M. The Message Log dialog box provides a system level record of loaded configuration settings and registered extensions. The Message Log displays summaries and details of each message, and you can filter the display of messages by Type and Category. - Type—Select the type of messages to display in the Message Log. You can select All, Info, Warn, or Fail. Type defaults to All. - Category—Select the category of messages to display in the Message Log. You can select All, Configuration, or Extension. The scope uses Configuration messages to indicate when new configuration files are loaded, and Extension messages to indicate when components are registered. Category defaults to All. To open the Core:Source UI Options dialog box, select General UI and then click Options. 2-476 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان nts • Keyboard commands respect source playback modes—Has no effect. The following table shows the keyboard shortcut mapping. You cannot disable this mapping. Action Keyboard Shortcut Open new NumericTypeScope Insert Change configuration N Display keyboard help K Play simulation P Pause simulation Space Stop simulation S Step forward Right arrow, Page down • Recently used sources list—Sets the maximum number of recently used sources displayed under the Files menu option. Sources Pane The Sources pane controls how the scope connects to Simulink. You cannot disable the Simulink source. To open the Sources:Simulink Options dialog box, select the Sources tab and then click Options. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-477 nts • Load Simulink model if not open—When selected, if you specify a signal in a Simulink model that is not currently open, the scope opens the model. • Connect scope on selection of—Connects the scope only when you select signal lines or when you select signal lines or blocks. If you select Signal lines or blocks, the scope cannot connect to blocks that have more than one output port. Dialog Panels Bit Allocation Panel The scope Bit Allocation panel provides options for specifying data type criteria. Adjust these criteria to observe the effect on suggested numerictype. For streaming data, the suggested numerictype adjusts over time in order to continue to satisfy the specified criteria. You can: • Specify a known word length and signedness and, using Specify constraint, add additional constraints such as the maximum number of occurrences outside range or the smallest value that the suggested data type must represent. 2-478 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان nts • Specify Integer length and Fraction length constraints so that the scope suggests an appropriate word length. • Set the Signedness and Word length to Auto so that the scope suggests values for these parameters. • Enable Graphical control and use the cursors on either side of the binary point to adjust the fraction length and observe the effect on the suggested numerictype on the input data. For example, you can see the number of values that are outside range, below precision, or both. You can also view representable minimum and maximum values of the changed suggested data type. • Specify extra bits for either the fraction length or the integer length. The extra bits act as a safety margin to minimize the risk of overflow and precision loss. Legend The scope Legend panel informs you which colors the scope uses to indicate values. These colors represent values that are outside range, in range, or below precision when displayed in the scope. Resulting Type The Resulting Type panel describes the fixed-point data type as defined by scope settings. By manipulating the visual display (via the Bit Allocation panel or with the cursors), you can change the data type specification. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-479 nts The Data Details section displays the percentage of values that fall outside range or below precision with the numerictype object located at the top of this panel. SQNR (Signal Quantization Noise Ratio) varies depending on the signal. If the parameter has no value, then there is not enough data to calculate the SQNR. When scope information or the numerictype changes, the SQNR resets. The Type Details section provides details about the fixed-point data type. You can copy the numerictype specification by right-clicking the Resulting Type pane and then selecting Copy numerictype. Input Data The Input Data panel provides statistical information about the values currently displayed in the NumericScopeType. 2-480 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان nts Examples Connect a NumericTypeScope to a signal in a Simulink model Open a NumericTypeScope window and connect to a signal. Open the model. fxpdemo_approx Open a NumericTypeScope. nts In the fxpdemo_approx model, select the yEven signal. In the NumericTypeScope window, select File > Connect to Simulink Signal. Run the simulation to view the dynamic range of the output. The NumericTypeScope suggests a data type for the output. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-481 nts ﻣﺘﻠﺐ ﺳﺎﯾﺖ | www.MatlabSite.com ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-482 nts Specify the block path and name and the output port number. blk='fxpdemo_approx/Even'; nts({blk,1}) Run the simulation to view the dynamic range of the output. The NumericTypeScope suggests a data type for the output. Specify a Simulink signal to display Connect a NumericTypeScope to a signal selected in a model. Open the model. fxpdemo_approx In the fxpdemo_approx model, select the yEven signal. Open a NumericTypeScope, specifying the line handle of the selected signal. nts({gsl}) See Also hist | log2 | numerictypescope www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-483 num2bin Purpose Convert number to binary string using quantizer object Syntax y = num2bin(q,x) Description y = num2bin(q,x) converts numeric array x into binary strings returned in y. When x is a cell array, each numeric element of x is converted to binary. If x is a structure, each numeric field of x is converted to binary. num2bin and bin2num are inverses of one another, differing in that num2bin returns the binary strings in a column. Examples x = magic(3)/9; q = quantizer([4,3]); y = num2bin(q,x) Warning: 1 overflow. y = 0111 0010 0011 0000 0100 0111 0101 0110 0001 See Also 2-484 bin2num | hex2num | num2hex | num2int www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان num2hex Purpose Convert number to hexadecimal equivalent using quantizer object Syntax y = num2hex(q,x) Description y = num2hex(q,x) converts numeric array x into hexadecimal strings returned in y. When x is a cell array, each numeric element of x is converted to hexadecimal. If x is a structure, each numeric field of x is converted to hexadecimal. For fixed-point quantizer objects, the representation is two’s complement. For floating-point quantizer objects, the representation is IEEE Standard 754 style. For example, for q = quantizer('double') num2hex(q,nan) ans = fff8000000000000 The leading fraction bit is 1, all other fraction bits are 0. Sign bit is 1, exponent bits are all 1. num2hex(q,inf) ans = 7ff0000000000000 Sign bit is 0, exponent bits are all 1, all fraction bits are 0. num2hex(q,-inf) ans = fff0000000000000 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-485 num2hex Sign bit is 1, exponent bits are all 1, all fraction bits are 0. num2hex and hex2num are inverses of each other, except that num2hex returns the hexadecimal strings in a column. Examples This is a floating-point example using a quantizer object q that has 6-bit word length and 3-bit exponent length. x = magic(3); q = quantizer('float',[6 3]); y = num2hex(q,x) y = 18 12 14 0c 15 18 16 17 10 See Also 2-486 bin2num | hex2num | num2bin | num2int www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان num2int Purpose Convert number to signed integer Syntax y = num2int(q,x) [y1,y,...] = num2int(q,x1,x,...) Description y = num2int(q,x) uses q.format to convert numeric x to an integer. = num2int(q,x1,x,...) uses q.format to convert numeric values x1, x2,... to integers y1,y2,... [y1,y,...] Examples All the two’s complement 4-bit numbers in fractional form are given by x = [0.875 0.750 0.625 0.500 0.375 0.250 0.125 0.000 -0.125 -0.250 -0.375 -0.500 -0.625 -0.750 -0.875 -1.000]; q=quantizer([4 3]); y = num2int(q,x) y = 7 6 5 4 Algorithms 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 When q is a fixed-point quantizer object, f is equal to fractionlength(q), and x is numeric y = x × 2f When q is a floating-point quantizer object, y = x. num2int is meaningful only for fixed-point quantizer objects. See Also bin2num | hex2num | num2bin | num2hex www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-487 numberofelements Purpose Number of data elements in an array Note numberofelements will be removed in a future release. Use numel instead. Syntax numberofelements(a) Description numberofelements(a) returns the number of data elements in an array. Using numberofelements in your MATLAB code returns the same result for built-in types and fi objects. Use numberofelements to write data-type independent MATLAB code for array handling. See Also 2-488 numel | nargin | nargout | prod | size | subsref | subsasgn www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان numel Purpose Number of data elements in fi array Syntax n = numel(A) Description n = numel(A) returns the number of elements, n, in fi array A. Using numel in your MATLAB code returns the same result for built-in types and fi objects. Use numel to write data-type independent MATLAB code for array handling. Input Arguments A - Input array scalar | vector | matrix | multidimensional array Input array, specified as a scalar, vector, matrix, or multidimensional array of fi objects. Complex Number Support: Yes Examples Number of Elements in 2-D fi Array Create a 2-by-3- array of fi objects. X = fi(ones(2,3),1,24,12) X = 1 1 1 1 1 1 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 24 12 numel counts 6 elements in the matrix. n = numel(X) www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-489 numel n = 6 Number of Elements in Multidimensional fi Array Create a 2-by-3-by-4 array of fi objects. X = fi(ones(2,3,4),1,24,12) X = (:,:,1) 1 1 (:,:,2) 1 1 (:,:,3) 1 1 (:,:,4) 1 1 = 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 = = = DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 24 12 numel counts 24 elements in the matrix. n = numel(X) n = 2-490 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان numel 24 numel 2-491 ﻣﺘﻠﺐ ﺳﺎﯾﺖ | www.MatlabSite.com ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان See Also numerictype Purpose Construct numerictype object Syntax T T T T T T T T T T T Description You can use the numerictype constructor function in the following ways: = = = = = = = = = = = numerictype numerictype(s) numerictype(s,w) numerictype(s,w,f) numerictype(s,w,slope,bias) numerictype(s,w,slopeadjustmentfactor,fixedexponent,bias) numerictype(property1,value1, ...) numerictype(T1, property1, value1, ...) numerictype('double') numerictype('single') numerictype('boolean') • T = numerictype creates a default numerictype object. • T = numerictype(s) creates a numerictype object with Fixed-point: unspecified scaling, Signed property value s, and 16-bit word length. • T = numerictype(s,w) creates a numerictype object with Fixed-point: unspecified scaling, Signed property value s, and word length w. • T = numerictype(s,w,f) creates a numerictype object with Fixed-point: binary point scaling, Signed property value s, word length w and fraction length f. • T = numerictype(s,w,slope,bias) creates a numerictype object with Fixed-point: slope and bias scaling, Signed property value s, word length w, slope, and bias. • T = numerictype(s,w,slopeadjustmentfactor,fixedexponent,bias) creates a numerictype object with Fixed-point: slope and bias scaling, Signed property value s, word length w, slopeadjustmentfactor, fixedexponent, and bias. 2-492 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان numerictype • T = numerictype(property1,value1, ...) allows you to set properties for a numerictype object using property name/property value pairs. All properties for which you do not specify a value get assigned their default value. • T = numerictype(T1, property1, value1, ...) allows you to make a copy of an existing numerictype object, while modifying any or all of the property values. • T = numerictype('double') creates a double numerictype. • T = numerictype('single') creates a single numerictype. • T = numerictype('boolean') creates a Boolean numerictype. The properties of the numerictype object are listed below. These properties are described in detail in “numerictype Object Properties” on page 1-15. • Bias — Bias • DataType — Data type category • DataTypeOverride — Data type override settings. Note that this property is not visible when its value is the default, Inherit. • DataTypeMode — Data type and scaling mode • FixedExponent — Fixed-point exponent • SlopeAdjustmentFactor — Slope adjustment • FractionLength — Fraction length of the stored integer value, in bits • Scaling — Fixed-point scaling mode • Signed — Signed or unsigned • Signedness — Signed, unsigned, or auto • Slope — Slope • WordLength — Word length of the stored integer value, in bits www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-493 numerictype Examples Create a default numerictype object Type T = numerictype to create a default numerictype object. T = DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 16 15 Create a numerictype object with specified word and fraction lengths The following code creates a signed numerictype object with a 32-bit word length and 30-bit fraction length. T = numerictype(1, 32, 30) T = DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 32 30 Create a numerictype object with unspecified scaling If you omit the argument f, the scaling is unspecified. T = numerictype(1, 32) T = 2-494 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان numerictype DataTypeMode: Fixed-point: unspecified scaling Signedness: Signed WordLength: 32 Create a numerictype object with default word length and scaling If you omit the arguments w and f, the word length is automatically set to 16 bits and the scaling is unspecified. T = numerictype(1) T = DataTypeMode: Fixed-point: unspecified scaling Signedness: Signed WordLength: 16 Create a numerictype object with specified property values You can use property name/property value pairs to set numerictype properties when you create the object. T = numerictype('Signed', true, 'DataTypeMode', 'Fixed-point: slope an T = DataTypeMode: Signedness: WordLength: Slope: Bias: Fixed-point: slope and bias scaling Signed 32 0.25 4 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-495 numerictype Note When you create a numerictype object using property name/property value pairs, Fixed-Point Designer software first creates a default numerictype object, and then, for each property name you specify in the constructor, assigns the corresponding value. This behavior differs from the behavior that occurs when you use a syntax such as T = numerictype(s,w). See “Example: Construct a numerictype Object with Property Name and Property Value Pairs” in the Fixed-Point Designer User’s Guide for more information. Create a numerictype object with unspecified sign You can create a numerictype object with an unspecified sign by using property name/property values pairs to set the Signedness property to Auto. T = numerictype('Signedness', 'Auto') T = DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Auto 16 15 Note Although you can create numerictype objects with an unspecified sign (Signedness: Auto), all fi objects must have a Signedness of Signed or Unsigned. If you use a numerictype object with Signedness: Auto to construct a fi object, the Signedness property of the fi object automatically defaults to Signed. 2-496 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان numerictype Create a numerictype object with specified data type You can create a numerictype object with a specific data type by including the property name/property value pair in the numerictype constructor. T = numerictype(false, 24, 12, 'DataType', 'ScaledDouble') T = DataTypeMode: Signedness: WordLength: FractionLength: Scaled double: binary point scaling Unsigned 24 12 MATLAB returns an unsigned numerictype object, T, with the specified WordLength of 24, FractionLength of 12, and with DataType set to ScaledDouble. See Also fi | fimath | fipref | quantizer Related Examples • “numerictype Objects Usage to Share Data Type and Scaling Settings of fi objects” Concepts • “numerictype Object Properties” • “numerictype Structure of Fixed-Point Objects” www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-497 NumericTypeScope Purpose Determine fixed-point data type Syntax H = NumericTypeScope show(H) step(H, data) reset(H) Description The NumericTypeScope is an object that provides information about the dynamic range of your data. The scope provides a visual representation of the dynamic range of your data in the form of a log2 histogram. In this histogram, the bit weights appear along the X-axis, and the percentage of occurrences along the Y-axis. Each bin of the histogram corresponds to a bit in the binary word. For example, 20 corresponds to the first integer bit in the binary word, 2-1 corresponds to the first fractional bit in the binary word. The scope suggests a data type in the form of a numerictype object that satisfies the specified criteria. See the section on Bit Allocation in “Dialog Panels” on page 2-505. H = NumericTypeScope returns a NumericTypeScope object that you can use to view the dynamic range of data in MATLAB. To view the NumericTypeScope window after creating H, use the show method. show(H) opens the NumericTypeScope object H and brings it into view. Closing the scope window does not delete the object from your workspace. If the scope object still exists in your workspace, you can open it and bring it back into view using the show method. step(H, data) processes your data and allows you to visualize the dynamic range. The object H retains previously collected information about the variable between each call to step. reset(H) clears all stored information from the NumericTypeScope object H. Resetting the object clears the information displayed in the scope window. 2-498 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان NumericTypeScope Identifying Values Outside Range and Below Precision The NumericTypeScope can also help you identify any values that are outside range or below precision based on the current data type. To prepare the NumericTypeScope to identify them, provide an input variable that is a fi object and verify that one of the following conditions is true: • The DataTypeMode of the fi object is set to Scaled doubles: binary point scaling. • The DataTypeOverride property of the Fixed-Point Designer fipref object is set to ScaledDoubles. When the information is available, the scope indicates values that are outside range, below precision, and in range of the data type by color-coding the histogram bars as follows: • Blue — Histogram bin contains values that are in range of the current data type. • Red — Histogram bin contains values that are outside range in the current data type. • Yellow — Histogram bin contains values that are below precision in the current data type. For an example of the scope color coding, see the figures in “Vertical Units” on page 2-508. See also Legend in “Dialog Panels” on page 2-505. See the “Examples” on page 2-512 section to learn more about using the NumericTypeScope to select data types. Dialog Boxes and Toolbar • “The NumericTypeScope Window” on page 2-500 • “Configuration Dialog Box” on page 2-502 • “Dialog Panels” on page 2-505 • “Vertical Units” on page 2-508 • “Bring All NumericType Scope Windows Forward” on page 2-510 • “Toolbar (Mac Only)” on page 2-511 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-499 NumericTypeScope The NumericTypeScope Window The NumericTypeScope opens with the default toolbars displayed at the top of the window and the dialog panels to the right. 2-500 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان NumericTypeScope 2-501 ﻣﺘﻠﺐ ﺳﺎﯾﺖ | www.MatlabSite.com ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان NumericTypeScope Configuration Dialog Box The NumericTypeScope configuration allows you to control the behavior and appearance of the scope window. To open the Configuration dialog box, select File > Configuration > Edit, or, with the scope as your active window, press the N key. The Configuration Dialog box contains a series of panes each containing a table of configuration options. See the reference section for each pane for instructions on setting the options on each one. This dialog box has one pane, the Core pane, with only one option, for General UI settings for the scope user interface. To save configuration settings for future use, select File > Configuration > Save as. The configuration settings you save become the default configuration settings for the NumericTypeScope object. 2-502 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان NumericTypeScope Caution Before saving your own set of configuration settings in the matlab/toolbox/fixedpoint/fixedpoint folder, save a backup copy of the default configuration settings in another location. If you do not save a backup copy of the default configuration settings, you cannot restore these settings at a later time. To save your configuration settings for future use, save them in the matlab/toolbox/fixedpoint/fixedpoint folder with the file name NumericTypeScopeComponent.cfg. You can re-save your configuration settings at anytime, but remember to do so in the specified folder using the specified file name. Core Pane The Core pane in the Configuration dialog box controls the general settings of the scope. Click General UI and then click Options to open the Core:General UI Options dialog box. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-503 NumericTypeScope • Display the full source path in the title bar—Select this check box to display the file name and variable name in the scope title bar. If the scope is not from a file, or if you clear this check box, the scope displays only the variable name in the title bar. • Open message log—Control when the Message Log window opens. The Message log window helps you debug issues with the scope. Choose to open the Message Log window for any of these conditions: - for any new messages for warn/fail messages only for fail messages manually The option defaults to for warn/fail messages. You can open the Message Log at any time by selecting Help > Message Log or by pressing Ctrl+M. The Message Log dialog box provides a system level record of loaded configuration settings and registered extensions. The Message Log displays summaries and details of each message, and you can filter the display of messages by Type and Category. 2-504 - Type—Select the type of messages to display in the Message Log. You can select All, Info, Warn, or Fail. Type defaults to All. - Category—Select the category of messages to display in the Message Log. You can select All, Configuration, or Extension. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان NumericTypeScope The scope uses Configuration messages to indicate when new configuration files are loaded, and Extension messages to indicate when components are registered. Category defaults to All. Dialog Panels • Bit Allocation on page 505 • Legend on page 507 • Resulting Type on page 507 • Input Data on page 508 Bit Allocation The scope Bit Allocation dialog panel, as shown in the following figure, offers you several options for specifying data type criteria. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-505 NumericTypeScope You can use this panel to specify a known word length and the desired maximum occurrences outside range. You can also use the panel to specify the desired number of occurrences outside range and the smallest value to be represented by the suggested data type. For streaming data, the suggested numerictype object adjusts over time in order to continue to satisfy the specified criteria. The scope also allows you to interact with the histogram plot. When you select Graphical control on the Bit Allocation dialog panel, you enable cursors on either side of the binary point. You can interact with these cursors and observe the effect of the suggested numerictype on the input data. For example, you can see the number of values that are outside range, below precision, or both. You can also view representable minimum and maximum values of the data type. 2-506 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان NumericTypeScope Legend The scope Legend panel informs you which colors the scope uses to indicate values. These colors represent values that are outside range, in range, or below precision when displayed in the scope. Resulting Type The Resulting Type panel describes the fixed-point data type as defined by scope settings. By manipulating the visual display (via the Bit Allocation panel or with the cursors) you can change the value of the data type. The Data Details section displays the percentage of values that fall outside range or below precision with the numerictype object located at the top of this panel. SQNR (Signal Quantization Noise Ratio) varies depending on the signal. If the parameter has no value, then there is not enough data to calculate the SQNR. When scope information or the numerictype changes, the SQNR resets. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-507 NumericTypeScope Type Details section provides details about the fixed-point data type. Input Data The Input Data panel provides statistical information about the values currently displayed in the NumericScopeType object. Vertical Units Use the Vertical Units selection to display values that are outside range or below precision as a percentage or as an actual count. For example, the following image shows the values that are outside range or below precision as a percentage of the total values. 2-508 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان NumericTypeScope This next example shows the values that are outside range or below precision as an actual count. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-509 NumericTypeScope Bring All NumericType Scope Windows Forward The NumericScopeType GUI offers a View > Bring All NumericType Scopes Forward menu option to help you manage your NumericTypeScope windows. Selecting this option or pressing 2-510 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان NumericTypeScope Ctrl+F brings all NumericTypeScope windows into view. If a NumericTypeScope window is not currently open, this menu option opens the window and brings it into view. Toolbar (Mac Only) Activate the Toolbar by selecting View > Toolbar. When this tool is active, you can dock or undock the scope from the GUI. The toolbar feature is for the Mac only. Selecting Toolbar on Windows® and UNIX® versions displays only an empty toolbar. The docking icon always appears in the GUI in the upper-right corner for these versions. Methods reset Use this method to clear the information stored in the object H. Doing so allows you to reuse H to process data from a different variable. Example: >>reset(H) show Use this method to open the scope window and bring it into view. Example: >>show(H) step Use this method to process your data and visualize the dynamic range in the scope window. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-511 NumericTypeScope Example: >>step(H, data) Examples Set the DataTypeOverride to Scaled Doubles, and view the dynamic range of a fi object. fp = fipref; initialDTOSetting = fp.DataTypeOverride; fp.DataTypeOverride = 'ScaledDoubles'; a = fi(magic(10),1,8,2); b = fi([a; 2.^(-5:4)],1,8,3); h = NumericTypeScope; step(h,b); fp.DataTypeOverride = initialDTOSetting; The log2 histogram display shows that the values appear both outside range and below precision in the variable. In this case, b has a data type of numerictype(1,8,3). The numerictype(1,8,3) data type provides 5 integer bits (including the signed bit), and 3 fractional bits. Thus, this data type can represent only values between –24 and 24– 2–3 (from 16 to 15.8750). Given the range and precision of this data type, values greater than 24 fall outside the range and values less than 2–3 fall below the precision of the data type. When you examine the NumericTypeScope display, you can see that values requiring bits 5, 6, and 7 are outside range and values requiring fractional bits 4 and 5 are below precision. Given this information, you can prevent values that are outside range and below precision by changing the data type of the variable b to numerictype(0,13,5). View the dynamic range, and determine an appropriate numeric type for a fi object with a DataTypeMode of Scaled double: binary point scaling. Create a numerictype object with a DataTypeMode of Scaled double: binary point scaling. You can then use that numerictype object to construct your fi objects. Because you set the DataTypeMode to Scaled 2-512 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان NumericTypeScope double: binary point scaling, the NumericTypeScope can now identify overflows in your data. T = numerictype; T.DataTypeMode = 'Scaled double: binary point scaling'; T.WordLength = 8; T.FractionLength = 6; a = fi(sin(0:100)*3.5, T); b = fi(cos(0:100)*1.75,T); acc = fi(0,T); h = NumericTypeScope; for i = 1:length(a) acc(:) = a(i)*0.7+b(i); step(h,acc); end This dynamic range analysis shows that you can represent the entire range of data in the accumulator with 5 bits; three to the left of the binary point (integer bits) and two to the right of it (fractional bits). You can verify that this data type is able to represent all the values by changing the WordLength and FractionLength properties of the numerictype object T. Then, use T to redefine the accumulator. To view the dynamic range analysis based on this new data type, reset the NumericTypeScope object h, and rerun the loop: T.WordLength = 5; T.FractionLength = 2; acc = fi(0,T); reset(h); for i = 1:length(a) acc(:) = a(i)*0.7 + b(i); step(h,acc); end See Also hist | log2 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-513 nunderflows Purpose Number of underflows Syntax y = nunderflows(a) y = nunderflows(q) Description y = nunderflows(a) returns the number of underflows of fi object a since logging was turned on or since the last time the log was reset for the object. Turn on logging by setting the fipref property LoggingMode to on. Reset logging for a fi object using the resetlog function. y = nunderflows(q) returns the accumulated number of underflows resulting from quantization operations performed by a quantizer object q. See Also 2-514 maxlog | minlog | noverflows | resetlog www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان oct Purpose Octal representation of stored integer of fi object Syntax oct(a) Description oct(a) returns the stored integer of fi object a in octal format as a string. oct(a) is equivalent to a.oct. Fixed-point numbers can be represented as real-world value = 2− fraction length × stored integer or, equivalently as real-world value = (slope × stored integer) + bias The stored integer is the raw binary number, in which the binary point is assumed to be at the far right of the word. Examples The following code a = fi([-1 1],1,8,7); y = oct(a) z = a.oct returns y = 200 177 z = 200 See Also 177 bin | dec | hex | storedInteger www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-515 ones Purpose Create array of all ones with fixed-point properties Syntax X X X X Description X = ones('like',p) returns a scalar 1 with the same numerictype, complexity (real or complex), and fimath as p. = = = = ones('like',p) ones(n,'like',p) ones(sz1,...,szN,'like',p) ones(sz,'like',p) X = ones(n,'like',p) returns an n-by-n array of ones like p. X = ones(sz1,...,szN,'like',p) returns an sz1-by-...-by-szN array of ones like p. X = ones(sz,'like',p) returns an array of ones like p. The size vector, sz, defines size(X). Input Arguments n - Size of square matrix integer value Size of square matrix, specified as an integer value, defines the output as a square, n-by-n matrix of ones. • If n is zero, X is an empty matrix. • If n is negative, it is treated as zero. Data Types double | single | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 sz1,...,szN - Size of each dimension two or more integer values Size of each dimension, specified as two or more integer values, defines X as a sz1-by...-by-szN array. 2-516 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان ones • If the size of any dimension is zero, X is an empty array. • If the size of any dimension is negative, it is treated as zero. • If any trailing dimensions greater than two have a size of one, the output, X, does not include those dimensions. Data Types double | single | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 sz - Output size row vector of integer values Output size, specified as a row vector of integer values. Each element of this vector indicates the size of the corresponding dimension. • If the size of any dimension is zero, X is an empty array. • If the size of any dimension is negative, it is treated as zero. • If any trailing dimensions greater than two have a size of one, the output, X, does not include those dimensions. Example: sz = [2,3,4] defines X as a 2-by-3-by-4 array. Data Types double | single | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 p - Prototype fi object | numeric variable Prototype, specified as a fi object or numeric variable. To use the prototype to specify a complex object, you must specify a value for the prototype. Otherwise, you do not need to specify a value. Complex Number Support: Yes Tips Using the b = cast(a,'like',p) syntax to specify data types separately from algorithm code allows you to: www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-517 ones • Reuse your algorithm code with different data types. • Keep your algorithm uncluttered with data type specifications and switch statements for different data types. • Improve readability of your algorithm code. • Switch between fixed-point and floating-point data types to compare baselines. • Switch between variations of fixed-point settings without changing the algorithm code. Examples 2-D Array of Ones With Fixed-Point Attributes Create a 2-by-3 array of ones with specified numerictype and fimath properties. Create a signed fi object with word length of 24 and fraction length of 12. p = fi([],1,24,12); Create a 2-by-3- array of ones that has the same numerictype properties as p. X = ones(2,3,'like',p) X = 1 1 1 1 1 1 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 24 12 Size Defined by Existing Array Define a 3-by-2 array A. 2-518 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان ones A = [1 4 ; 2 5 ; 3 6]; sz = size(A) sz = 3 2 Create a signed fi object with word length of 24 and fraction length of 12. p = fi([],1,24,12); Create an array of ones that is the same size as A and has the same numerictype properties as p. X = ones(sz,'like',p) X = 1 1 1 1 1 1 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 24 12 Square Array of Ones With Fixed-Point Attributes Create a 4-by-4 array of ones with specified numerictype and fimath properties. Create a signed fi object with word length of 24 and fraction length of 12. p = fi([],1,24,12); www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-519 ones Create a 4-by-4 array of ones that has the same numerictype properties as p. X = ones(4, 'like', p) X = 1 1 1 1 1 1 1 1 1 1 1 1 DataTypeMode: Signedness: WordLength: FractionLength: 1 1 1 1 Fixed-point: binary point scaling Signed 24 12 Complex Fixed-Point One Create a scalar fixed-point 1 that is not real valued, but instead is complex like an existing array. Define a complex fi object. p = fi( [1+2i 3i],1,24,12); Create a scalar 1 that is complex like p. X = ones('like',p) X = 1.0000 + 0.0000i DataTypeMode: Signedness: WordLength: FractionLength: 2-520 Fixed-point: binary point scaling Signed 24 12 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان ones Write MATLAB Code That Is Independent of Data Types Write a MATLAB algorithm that you can run with different data types without changing the algorithm itself. To reuse the algorithm, define the data types separately from the algorithm. This approach allows you to define a baseline by running the algorithm with floating-point data types. You can then test the algorithm with different fixed-point data types and compare the fixed-point behavior to the baseline without making any modifications to the original MATLAB code. Write a MATLAB function, my_filter, that takes an input parameter, T, which is a structure that defines the data types of the coefficients and the input and output data. function [y,z] = my_filter(b,a,x,z,T) % Cast the coefficients to the coefficient type b = cast(b,'like',T.coeffs); a = cast(a,'like',T.coeffs); % Create the output using zeros with the data type y = zeros(size(x),'like',T.data); for i=1:length(x) y(i) = b(1)*x(i) + z(1); z(1) = b(2)*x(i) + z(2) - a(2) * y(i); z(2) = b(3)*x(i) - a(3) * y(i); end end Write a MATLAB function, zeros_ones_cast_example, that calls my_filter with a floating-point step input and a fixed-point step input, and then compares the results. function zeros_ones_cast_example % Define coefficients for a filter with specification % [b,a] = butter(2,0.25) b = [0.097631072937818 0.195262145875635 0.097631072937818]; www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-521 ones a = [1.000000000000000 -0.942809041582063 0.333333333333333]; % Define floating-point types T_float.coeffs = double([]); T_float.data = double([]); % Create a step input using ones with the % floating-point data type t = 0:20; x_float = ones(size(t),'like',T_float.data); % Initialize the states using zeros with the % floating-point data type z_float = zeros(1,2,'like',T_float.data); % Run the floating-point algorithm y_float = my_filter(b,a,x_float,z_float,T_float); % Define fixed-point types T_fixed.coeffs = fi([],true,8,6); T_fixed.data = fi([],true,8,6); % Create a step input using ones with the % fixed-point data type x_fixed = ones(size(t),'like',T_fixed.data); % Initialize the states using zeros with the % fixed-point data type z_fixed = zeros(1,2,'like',T_fixed.data); % Run the fixed-point algorithm y_fixed = my_filter(b,a,x_fixed,z_fixed,T_fixed); % Compare the results coder.extrinsic('clf','subplot','plot','legend'); clf subplot(211) 2-522 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان ones plot(t,y_float,'co-',t,y_fixed,'kx-') legend('Floating-point output','Fixed-point output'); title('Step response'); subplot(212) plot(t,y_float - double(y_fixed),'rs-') legend('Error') figure(gcf) end See Also zeros | cast | ones Related Examples • “Implement FIR Filter Algorithm for Floating-Point and Fixed-Point Types using cast and zeros” Concepts • “Command-Line Fixed-Point Conversion Workflow” • “Command-Line Fixed-Point Conversion Best Practices” www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-523 or Purpose Find logical OR of array or scalar inputs Description Refer to the MATLAB or reference page for more information. 2-524 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان patch Purpose Create patch graphics object Description Refer to the MATLAB patch reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-525 pcolor Purpose Create pseudocolor plot Description Refer to the MATLAB pcolor reference page for more information. 2-526 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان permute Purpose Rearrange dimensions of multidimensional array Description Refer to the MATLAB permute reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-527 plot Purpose Create linear 2-D plot Description Refer to the MATLAB plot reference page for more information. 2-528 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان plot3 Purpose Create 3-D line plot Description Refer to the MATLAB plot3 reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-529 plotmatrix Purpose Draw scatter plots Description Refer to the MATLAB plotmatrix reference page for more information. 2-530 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان plotyy Purpose Create graph with y-axes on right and left sides Description Refer to the MATLAB plotyy reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-531 plus Purpose Matrix sum of fi objects Syntax plus(a,b) Description plus(a,b) is called for the syntax a + b when a or b is an object. a + b adds matrices a and b. a and b must have the same dimensions unless one is a scalar value (a 1-by-1 matrix). A scalar value can be added to any other value. plus does not support fi objects of data type Boolean. Note For information about the fimath properties involved in Fixed-Point Designer calculations, see “fimath Properties Usage for Fixed-Point Arithmetic” and “fimath ProductMode and SumMode” in the Fixed-Point Designer documentation. For information about calculations using Fixed-Point Designer software, see the Fixed-Point Designer documentation. See Also 2-532 minus | mtimes | times | uminus www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان polar Purpose Plot polar coordinates Description Refer to the MATLAB polar reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-533 pow2 Purpose Efficient fixed-point multiplication by 2K Syntax b = pow2(a,K) Description b = pow2(a,K) returns the value of a shifted by K bits where K is an integer and a and b are fi objects. The output b always has the same word length and fraction length as the input a. Note In fixed-point arithmetic, shifting by K bits is equivalent to, and more efficient than, computing b = a*2k. If K is a non-integer, the pow2 function will round it to floor before performing the calculation. The scaling of a must be equivalent to binary point-only scaling; in other words, it must have a power of 2 slope and a bias of 0. a can be real or complex. If a is complex, pow2 operates on both the real and complex portions of a. The pow2 function obeys the OverflowAction and RoundingMethod properties associated with a. If obeying the RoundMode property associated with a is not important, try using the bitshift function. The pow2 function does not support fi objects of data type Boolean. The function also does not support the syntax b = pow2(a) when a is a fi object. Examples Example 1 In the following example, a is a real-valued fi object, and K is a positive integer. The pow2 function shifts the bits of a 3 places to the left, effectively multiplying a by 23. a = fi(pi,1,16,8) 2-534 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان pow2 b = pow2(a,3) binary_a = bin(a) binary_b = bin(b) MATLAB returns: a = 3.1406 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 16 8 b = 25.1250 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 16 8 binary_a = 0000001100100100 binary_b = 0001100100100000 Example 2 In the following example, a is a real-valued fi object, and K is a negative integer. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-535 pow2 The pow2 function shifts the bits of a 4 places to the right, effectively multiplying a by 2–4. a = fi(pi,1,16,8) b = pow2(a,-4) binary_a = bin(a) binary_b = bin(b) MATLAB returns: a = 3.1406 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 16 8 b = 0.1953 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 16 8 binary_a = 0000001100100100 binary_b = 0000000000110010 2-536 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان pow2 Example 3 The following example shows the use of pow2 with a complex fi object: format long g P = fipref('NumericTypeDisplay', 'short'); a = fi(57 - 2i, 1, 16, 8) a = 57 - 2i s16,8 pow2(a, 2) ans = 127.99609375 - 8i s16,8 See Also bitshift | bitsll | bitsra | bitsrl www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-537 power Purpose Fixed-point array power (.^) Syntax c = power(a,k) c = a.^k Description c = power(a,k) and c = a.^k compute element-by-element power. The exponent k requires a positive, real-valued integer value. The fixed-point output array c has the same local fimath as the input a. If a has no local fimath, the output c also has no local fimath. The array power operation is performed using default fimath settings. Tips For more information about the power function, see the MATLAB power reference page. Examples Compute the power of a 2-dimensional array for exponent values 0, 1, 2, and 3. x = fi([0 1 2; 3 4 5], 1, 32); px0 px1 px2 px3 See Also 2-538 = = = = x.^0 x.^1 x.^2 x.^3 power | mpower www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان quantize Purpose Quantize fixed-point numbers Syntax y y y y = = = = yBP yBP yBP yBP yBP Description quantize(x) quantize(x,nt) quantize(x,nt,rm) quantize(x,nt,rm,oa) = = = = = quantize(x,s) quantize(x,s,wl) quantize(x,s,wl,fl) quantize(x,s,wl,fl,rm) quantize(x,s,wl,fl,rm,oa) y = quantize(x) quantizes x using these default values: • numerictype (true,16,15) • Floor rounding method • Wrap overflow action The numerictype, rounding method, and overflow action apply only during the quantization. The resulting value, quantized y, does not have any fimath attached to it. y = quantize(x,nt) quantizes x to the specified numerictype nt. The rounding method and overflow action use default values. y = quantize(x,nt,rm) quantizes x to the specified numerictype, nt and rounding method, rm. The overflow action uses the default value. y = quantize(x,nt,rm,oa) quantizes x to the specified numerictype, nt, rounding method, rm, and overflow action, oa. yBP = quantize(x,s) quantizes x to a binary-point, scaled fixed-point number. The s input specifies the sign to be used in numerictype (s,16,15). Unspecified properties use these default values: www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-539 quantize • WordLength 16 • FractionLength 15 • RoundingMethod Floor • OverflowAction Wrap yBP = quantize(x,s,wl) uses the specified word length, wl. The fraction length defaults to wl–1. Unspecified properties use default values. yBP = quantize(x,s,wl,fl) uses the specified fraction length, fl. Unspecified properties use default values. yBP = quantize(x,s,wl,fl,rm) uses the specified rounding method, rm. Unspecified properties use default values. yBP = quantize(x,s,wl,fl,rm,oa) uses the specified overflow action, oa. Input Arguments x - Input data fi objects or built-in integers Input data to quantize. Valid inputs are: • Built-in signed or unsigned integers (int8, int16, int32, int64, uint8, uint16, uint32, uint64) • Binary point scaled fixed-point fi • Slope-bias scaled fixed-point fi Although fi doubles and fi singles are allowed as inputs, they pass through the quantize function without being quantized. nt - Numerictype (true,16,15) (default) 2-540 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان quantize Numerictype object that defines the sign, word length, and fraction length of a fixed-point number. rm - Rounding method Floor (default) | Ceiling | Convergent | Nearest | Round | Zero Rounding method to use oa - Overflow action Wrap (default) | Saturate Action to take when a data overflow occurs s - Signedness true (default) | false Whether the fixed-point number is signed (true) or unsigned (false) wl - Word length 16 (default) Word length of the fixed-point number fl - Fraction length 15 (default) Fraction length of the fixed-point number Output Arguments y - Quantized output fi object Quantized value of the input yBP - Quantized output fi object Input quantized to binary-point scaled value www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-541 quantize Examples Quantize Binary-Point Scaled to Binary-Point Scaled Data Create numerictype object, ntBP, which specifies a signed, 8-bit word length, 4-bit fraction length data type. ntBP = numerictype(1,8,4); Define the input. x_BP = fi(pi) x_BP = 3.1416 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 16 13 Use the defined numerictype, ntBP, to quantize the input, x_BP, to a binary-point scaled data type. yBP1 = quantize(x_BP,ntBP) yBP1 = 3.1250 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 8 4 Quantize Binary-Point Scaled to Slope-Bias Data Create a numerictype object, ntSB, which specifies a slope-bias data type. 2-542 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان quantize ntSB = numerictype('Scaling','SlopeBias', ... 'SlopeAdjustmentFactor',1.8,'Bias',... 1,'FixedExponent',-12); Define the input. x_BP = fi(pi) x_BP = 3.1416 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 16 13 Use the defined numerictype, ntSB, to quantize the input, x_BP, to a slope-bias data type. ySB1 = quantize(x_BP, ntSB) ySB1 = 3.1410 DataTypeMode: Signedness: WordLength: Slope: Bias: Fixed-point: slope and bias scaling Signed 16 0.000439453125 1 Quantize Slope-Bias Scaled to Binary-Point Scaled Data Create a numerictype object, ntBP, which specifies a signed, 8-bit word length, 4-bit fraction length data type. ntBP = numerictype(1,8,4); www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-543 quantize Define the input. x_SB = fi(rand(5,3),numerictype('Scaling','SlopeBias','Bias',-0.125)) x_SB = 0.8147 0.8750 0.1270 0.8750 0.6324 0.0975 0.2785 0.5469 0.8750 0.8750 DataTypeMode: Signedness: WordLength: Slope: Bias: 0.1576 0.8750 0.8750 0.4854 0.8003 Fixed-point: slope and bias scaling Signed 16 3.0517578125e-5 -0.125 Use the defined numerictype, ntBP, to quantize the input, x_SB, to a binary point scaled data type. yBP2 = quantize(x_SB,ntBP,'Nearest','Saturate') yBP2 = 0.8125 0.8750 0.1250 0.8750 0.6250 0.1250 0.2500 0.5625 0.8750 0.8750 DataTypeMode: Signedness: WordLength: FractionLength: 2-544 0.1875 0.8750 0.8750 0.5000 0.8125 Fixed-point: binary point scaling Signed 8 4 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان quantize Quantize Slope-Bias Scaled to Slope-Bias Scaled Data Create a numerictype object, ntSB, which specifies a slope-bias data type. ntSB = numerictype('Scaling','SlopeBias', ... 'SlopeAdjustmentFactor',1.8,'Bias',... 1,'FixedExponent',-12); Define the input. x_SB = fi(rand(5,3),numerictype('Scaling','SlopeBias','Bias',-0.125)) x_SB = 0.8147 0.8750 0.1270 0.8750 0.6324 0.0975 0.2785 0.5469 0.8750 0.8750 DataTypeMode: Signedness: WordLength: Slope: Bias: 0.1576 0.8750 0.8750 0.4854 0.8003 Fixed-point: slope and bias scaling Signed 16 3.0517578125e-5 -0.125 Use the defined numerictype, ntSB, to quantize the input, x_SB, to a slope-bias data type. ySB2 = quantize(x_SB,ntSB,'Ceiling','Wrap') ySB2 = 0.8150 0.8752 0.1272 0.8752 0.0978 0.2789 0.5469 0.8752 0.1580 0.8752 0.8752 0.4854 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-545 quantize 0.6326 0.8752 0.8005 DataTypeMode: Signedness: WordLength: Slope: Bias: Fixed-point: slope and bias scaling Signed 16 0.000439453125 1 Quantize Built-in Integer to Binary-Point Scaled Data Create a numerictype object, ntBP, which specifies a signed, 8-bit word length, 4-bit fraction length data type. ntBP = numerictype(1,8,4); Define the input. xInt = int8(-16:4:16) xInt = -16 -12 -8 -4 0 4 8 12 16 Use the defined numerictype, ntBP, to quantize the inputxInt to a binary point scaled data type. yBP3 = quantize(xInt,ntBP,'Zero') yBP3 = 0 4 -8 -4 0 DataTypeMode: Signedness: WordLength: FractionLength: 4 -8 -4 Fixed-point: binary point scaling Signed 8 4 Show the range of the quantized output. 2-546 0 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان quantize range(yBP3) ans = -8.0000 7.9375 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 8 4 The first two and last three values are wrapped because they are outside the representable range of the output type. Quantize Built-in Integer to Slope-Bias Data Create a numerictype object ntSB, which specifies a slope-bias data type. ntSB = numerictype('Scaling','SlopeBias', ... 'SlopeAdjustmentFactor',1.8,'Bias',... 1,'FixedExponent',-12); Define the input. xInt = int8(-16:4:16) xInt = -16 -12 -8 -4 0 4 8 12 16 Use the defined numerictype, ntSB, to quantize the input, xInt, to a slope-bias data type. ySB3 = quantize(xInt,ntSB,'Round','Saturate') ySB3 = Columns 1 through 6 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-547 quantize -13.4000 -11.9999 Columns 7 through 9 8.0000 12.0000 DataTypeMode: Signedness: WordLength: Slope: Bias: -8.0000 -4.0001 -0.0002 4.0001 15.3996 Fixed-point: slope and bias scaling Signed 16 0.000439453125 1 Show the range of the quantized output. range(ySB3) ans = -13.4000 15.3996 DataTypeMode: Signedness: WordLength: Slope: Bias: Fixed-point: slope and bias scaling Signed 16 0.000439453125 1 The first and last values saturate because they are at the limits of he representable range of the output type. See Also fi | fimath | fixed.Quantizer | numerictype Related Examples • “Compute Quantization Error” 2-548 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان quantize method Purpose Apply quantizer object to data Syntax y = quantize(q, x) [y1,y2,...] = quantize(q,x1,x2,...) Description y = quantize(q, x) uses the quantizer object q to quantize x. When x is a numeric array, each element of x is quantized. When x is a cell array, each numeric element of the cell array is quantized. When x is a structure, each numeric field of x is quantized. Quantize does not change nonnumeric elements or fields of x, nor does it issue warnings for nonnumeric values. The output y is a built-in double. When the input x is a structure or cell array, the fields of y are built-in doubles. [y1,y2,...] = quantize(q,x1,x2,...) is equivalent to y1 = quantize(q,x1), y2 = quantize(q,x2),... The quantizer object states • max — Maximum value before quantizing • min — Minimum value before quantizing • noverflows — Number of overflows • nunderflows — Number of underflows • noperations — Number of quantization operations are updated during the call to quantize, and running totals are kept until a call to resetlog is made. Examples The following examples demonstrate using quantize to quantize data. Example 1 - Custom Precision Floating-Point The code listed here produces the plot shown in the following figure. u=linspace(-15,15,1000); q=quantizer([6 3],'float'); range(q) www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-549 quantize method ans = -14 14 y=quantize(q,u); plot(u,y);title(tostring(q)) Warning: 68 overflows. quantizer(’float’, ’floor’, [6 3]) 15 10 5 0 −5 −10 −15 −15 −10 −5 0 5 10 Example 2 - Fixed-Point The code listed here produces the plot shown in the following figure. u=linspace(-15,15,1000); 2-550 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 15 quantize method q=quantizer([6 2],'wrap'); range(q) ans = -8.0000 7.7500 y=quantize(q,u); plot(u,y);title(tostring(q)) Warning: 468 overflows. quantizer(’fixed’, ’floor’, ’wrap’, [6 2]) 8 6 4 2 0 −2 −4 −6 −8 −15 See Also −10 −5 0 5 10 15 assignmentquantizer | quantizer | set | unitquantize | unitquantizer www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-551 quantizer Purpose Construct quantizer object Syntax q q q q q Description q = quantizer creates a quantizer object with properties set to their default values. To use this object to quantize values, use the quantize method. = = = = = quantizer quantizer('PropertyName1',PropertyValue1,...) quantizer(PropertyValue1,PropertyValue2,...) quantizer(struct) quantizer(pn,pv) q = quantizer('PropertyName1',PropertyValue1,...) uses property name/ property value pairs. q = quantizer(PropertyValue1,PropertyValue2,...) creates a quantizer object with the listed property values. When two values conflict, quantizer sets the last property value in the list. Property values are unique; you can set the property names by specifying just the property values in the command. q = quantizer(struct), where struct is a structure whose field names are property names, sets the properties named in each field name with the values contained in the structure. q = quantizer(pn,pv) sets the named properties specified in the cell array of strings pn to the corresponding values in the cell array pv. The quantizer object property values are listed below. These properties are described in detail in “quantizer Object Properties” on page 1-20. 2-552 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان quantizer Property Name Property Value Description mode 'double' Double-precision mode. Override all other parameters. 'float' Custom-precision floating-point mode. 'fixed' Signed fixed-point mode. 'single' Single-precision mode. Override all other parameters. 'ufixed' Unsigned fixed-point mode. 'ceil' Round toward positive infinity. 'convergent' Round to nearest integer with ties rounding to nearest even integer. 'fix' Round toward zero. 'floor' Round toward negative infinity. 'Nearest' Round to nearest integer with ties rounding toward positive infinity. 'Round' Round to nearest integer with ties rounding to nearest integer with greater absolute value. roundmode www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-553 quantizer Property Name Property Value Description overflowmode (fixed-point only) 'saturate' Saturate on overflow. 'wrap' Wrap on overflow. [wordlength fractionlength] Format for fixed or ufixed mode. [wordlength exponentlength] Format for float mode. format The default property values for a quantizer object are mode = 'fixed'; roundmode = 'floor'; overflowmode = 'saturate'; format = [16 15]; Along with the preceding properties, quantizer objects have read-only states: max, min, noverflows, nunderflows, and noperations. They can be accessed through quantizer/get or q.maxlog, q.minlog, q.noverflows, q.nunderflows, and q.noperations, but they cannot be set. They are updated during the quantizer/quantize method, and are reset by the resetlog function. The following table lists the read-only quantizer object states: 2-554 Property Name Description max Maximum value before quantizing min Minimum value before quantizing noverflows Number of overflows nunderflows Number of underflows noperations Number of data points quantized www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان quantizer Examples The following example operations are equivalent. Setting quantizer object properties by listing property values only in the command, q = quantizer('fixed', 'Ceiling', 'Saturate', [5 4]) Using a structure struct to set quantizer object properties, struct.mode = 'fixed'; struct.roundmode = 'ceil'; struct.overflowmode = 'saturate'; struct.format = [5 4]; q = quantizer(struct); www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-555 quantizer Using property name and property value cell arrays pn and pv to set quantizer object properties, pn = {'mode', 'roundmode', 'overflowmode', 'format'}; pv = {'fixed', 'ceil', 'saturate', [5 4]}; q = quantizer(pn, pv) Using property name/property value pairs to configure a quantizer object, q = quantizer( 'mode', 'fixed','roundingmode','ceil',... 'overflowmode', 'saturate', 'format', [5 4]); See Also 2-556 assignmentquantizer | fi | fimath | fipref | numerictype | quantize | set | unitquantize | unitquantizer www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان quiver Purpose Create quiver or velocity plot Description Refer to the MATLAB quiver reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-557 quiver3 Purpose Create 3-D quiver or velocity plot Description Refer to the MATLAB quiver3 reference page for more information. 2-558 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان randquant Purpose Generate uniformly distributed, quantized random number using quantizer object Syntax randquant(q,n) randquant(q,m,n) randquant(q,m,n,p,...) randquant(q,[m,n]) randquant(q,[m,n,p,...]) Description randquant(q,n) uses quantizer object q to generate an n-by-n matrix with random entries whose values cover the range of q when q is a fixed-point quantizer object. When q is a floating-point quantizer object, randquant populates the n-by-n array with values covering the range -[square root of realmax(q)] to [square root of realmax(q)] randquant(q,m,n) uses quantizer object q to generate an m-by-n matrix with random entries whose values cover the range of q when q is a fixed-point quantizer object. When q is a floating-point quantizer object, randquant populates the m-by-n array with values covering the range -[square root of realmax(q)] to [square root of realmax(q)] randquant(q,m,n,p,...) uses quantizer object q to generate an m-by-n-by-p-by ... matrix with random entries whose values cover the range of q when q is fixed-point quantizer object. When q is a floating-point quantizer object, randquant populates the matrix with values covering the range -[square root of realmax(q)] to [square root of realmax(q)] randquant(q,[m,n]) uses quantizer object q to generate an m-by-n matrix with random entries whose values cover the range of q when q is a fixed-point quantizer object. When q is a floating-point quantizer object, randquant populates the m-by-n array with values covering the range www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-559 randquant -[square root of realmax(q)] to [square root of realmax(q)] randquant(q,[m,n,p,...]) uses quantizer object q to generate p m-by-n matrices containing random entries whose values cover the range of q when q is a fixed-point quantizer object. When q is a floating-point quantizer object, randquant populates the m-by-n arrays with values covering the range -[square root of realmax(q)] to [square root of realmax(q)] randquant produces pseudorandom numbers. The number sequence randquant generates during each call is determined by the state of the generator. Because MATLAB resets the random number generator state at startup, the sequence of random numbers generated by the function remains the same unless you change the state. randquant works like rng in most respects. Examples q=quantizer([4 3]); rng('default') randquant(q,3) ans = 0.5000 0.6250 -0.8750 See Also 2-560 0.6250 0.1250 -0.8750 -0.5000 0 0.7500 quantizer | rand | range | realmax www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان range Purpose Numerical range of fi or quantizer object Syntax range(a) [min, max]= range(a) r = range(q) [min, max] = range(q) Description range(a) returns a fi object with the minimum and maximum possible values of fi object a. All possible quantized real-world values of a are in the range returned. If a is a complex number, then all possible values of real(a) and imag(a) are in the range returned. [min, max]= range(a) returns the minimum and maximum values of fi object a in separate output variables. r = range(q) returns the two-element row vector r = [a b] such that for all real x, y = quantize(q,x) returns y in the range a ≤ y ≤ b. [min, max] = range(q) returns the minimum and maximum values of the range in separate output variables. Examples q = quantizer('float',[6 3]); r = range(q) r = -14 14 q = quantizer('fixed',[4 2],'floor'); [min,max] = range(q) min = -2 max = 1.7500 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-561 range Algorithms If q is a floating-point quantizer object, a = -realmax(q), b = realmax(q). If q is a signed fixed-point quantizer object (datamode = 'fixed'), a = − realmax(q) − eps(q) = b = realmax(q) = −2w−1 2f 2w−1 − 1 2f If q is an unsigned fixed-point quantizer object (datamode = 'ufixed'), a=0 b = realmax(q) = 2w − 1 2f See realmax for more information. See Also 2-562 eps | exponentmax | exponentmin | fractionlength | intmax | intmin | lowerbound | lsb | max | min | realmax | realmin | upperbound www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان rdivide Purpose Right-array division (./) Syntax c = rdivide(a,b) c = a./b Description c = rdivide(a,b) and c = a./b perform right-array division by dividing each element of a by the corresponding element of b. If inputs a and b are not the same size, one of them must be a scalar value. The numerator input a can be complex, but the denominator b requires a real-valued input. If a is complex, the real and imaginary parts of a are independently divided by b. The following table shows the rules used to assign property values to the output of the rdivide function. Output Property Rule Signedness If either input is Signed, the output is Signed. If both inputs are Unsigned, the output is Unsigned. WordLength The output word length equals the maximum of the input word lengths. FractionLength For c = a./b, the fraction length of output c equals the fraction length of a minus the fraction length of b. The following table shows the rules the rdivide function uses to handle inputs with different data types. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-563 rdivide Case Rule Interoperation of fi objects and built-in integers Built-in integers are treated as fixed-point objects. For example, B = int8(2) is treated as an s8,0 fi object. Interoperation of fi objects and constants MATLAB for code generation treats constant integers as fixed-point objects with the same word length as the fi object and a fraction length of 0. Interoperation of mixed data types Similar to all other fi object functions, when inputs a and b have different data types, the data type with the higher precedence determines the output data type. The order of precedence is as follows: 1 ScaledDouble 2 Fixed-point 3 Built-in double 4 Built-in single When both inputs are fi objects, the only data types that are allowed to mix are ScaledDouble and Fixed-point. Examples In this example, you perform right-array division on a 3-by-3 magic square of fi objects. Each element of the 3-by-3 magic square is divided by the corresponding element in the 3-by-3 input array b. a = fi(magic(3)) b = int8([3 3 4; 1 2 4 ; 3 1 2 ]) c = a./b 2-564 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان rdivide The mrdivide function outputs a 3-by-3 array of signed fi objects, each of which has a word length of 16 bits and fraction length of 11 bits. a = 8 3 4 1 5 9 6 7 2 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 16 11 b = 3 1 3 3 2 1 4 4 2 c = 2.6665 3.0000 1.3335 0.3335 2.5000 9.0000 DataTypeMode: Signedness: WordLength: FractionLength: See Also 1.5000 1.7500 1.0000 Fixed-point: binary point scaling Signed 16 11 add | divide | fi | fimath | mrdivide | numerictype | sub | sum www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-565 real Purpose Real part of complex number Description Refer to the MATLAB real reference page for more information. 2-566 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان realmax Purpose Largest positive fixed-point value or quantized number Syntax realmax(a) realmax(q) Description realmax(a) is the largest real-world value that can be represented in the data type of fi object a. Anything larger overflows. realmax(q) is the largest quantized number that can be represented where q is a quantizer object. Anything larger overflows. Examples q = quantizer('float',[6 3]); x = realmax(q) x = 14 Algorithms If q is a floating-point quantizer object, the largest positive number, x, is x = 2 Emax ⋅ (2 − eps(q)) If q is a signed fixed-point quantizer object, the largest positive number, x, is x= 2w−1 − 1 2f If q is an unsigned fixed-point quantizer object (datamode = 'ufixed'), the largest positive number, x, is x= 2w − 1 2f www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-567 realmax See Also 2-568 eps | exponentmax | exponentmin | fractionlength | intmax | intmin | lowerbound | lsb | quantizer | range | realmin | upperbound www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان realmin Purpose Smallest positive normalized fixed-point value or quantized number Syntax realmin(a) realmin(q) Description realmin(a) is the smallest positive real-world value that can be represented in the data type of fi object a. Anything smaller underflows. realmin(q) is the smallest positive normal quantized number where q is a quantizer object. Anything smaller than x underflows or is an IEEE “denormal” number. Examples q = quantizer('float',[6 3]); x = realmin(q) x = 0.2500 Algorithms If q is a floating-point quantizer object, x = 2 Emin where Emin = exponentmin(q) is the minimum exponent. If q is a signed or unsigned fixed-point quantizer object, x = 2− f = where f is the fraction length. See Also eps | exponentmax | exponentmin | fractionlength | intmax | intmin | lowerbound | lsb | range | realmax | upperbound www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-569 reinterpretcast Purpose Convert fixed-point data types without changing underlying data Syntax c = reinterpretcast(a, T) Description c = reinterpretcast(a, T) converts the input a to the data type specified by numerictype object T without changing the underlying data. The result is returned in fi object c. The input a must be a built-in integer or a fi object with a fixed-point data type. T must be a numerictype object with a fully specified fixed-point data type. The word length of inputs a and T must be the same. The reinterpretcast function differs from the MATLAB typecast and cast functions in that it only operates on fi objects and built-in integers, and it does not allow the word length of the input to change. Examples In the following example, a is a signed fi object with a word length of 8 bits and a fraction length of 7 bits. The reinterpretcast function converts a into an unsigned fi object c with a word length of 8 bits and a fraction length of 0 bits. The real-world values of a and c are different, but their binary representations are the same. a = fi([-1 pi/4], true, 8, 7) T = numerictype(false, 8, 0); c = reinterpretcast(a, T) a = -1.0000 0.7891 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 8 7 c = 128 2-570 101 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان reinterpretcast DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Unsigned 8 0 To verify that the underlying data has not changed, compare the binary representations of a and c: binary_a = bin(a) binary_c = bin(c) binary_a = 10000000 01100101 binary_c = 10000000 See Also 01100101 cast | fi | numerictype | typecast www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-571 removefimath Purpose Remove fimath object from fi object Syntax y = removefimath(x) Description y = removefimath(x) returns a fi object y with x’s numerictype Input Arguments and value, and no fimath object attached. You can use this function as y = removefimath(y), which gives you localized control over the fimath settings. This function also is useful for preventing errors about embedded.fimath of both operands needing to be equal. x - Input data fi object | built-in integer | double | single Input data, specified as a fi object or built-in integer, from which to copy the data type and value to the output. x must be a fi object or an integer data type (int8, int16, int32, int64, uint8, uint16, uint32, or uint64). If x is not a fi object or integer data type, then y = x. Output Arguments y - Output fi object fi object | built-in integer | double | single Output fi object, returned as a fi object with no fimath object attached. The data type and value of the output match the input. If the input, x, is not a fi object y = x. Examples Remove fimath Object from fi Object This example shows how to define a fi object, define a fimath object, attach the fimath object to the fi object and then, remove the attached fimath object. a f a b = = = = fi(pi) fimath('RoundingMethod','Floor','OverflowAction','Wrap'); setfimath(a,f) removefimath(a) a = 2-572 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان removefimath 3.1416 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 16 13 a = 3.1416 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 16 13 RoundingMethod: OverflowAction: ProductMode: SumMode: Floor Wrap FullPrecision FullPrecision b = 3.1416 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 16 13 Set and Remove fimath for Code Generation Use the pattern x = setfimath(x,f) and y = removefimath(y) to insulate variables from fimath settings outside the function. This pattern does not create copies of the data in generated code. function y = fixed_point_32bit_KeepLSB_plus_example(a,b) f = fimath('OverflowAction','Wrap',... www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-573 removefimath a b y y 'RoundingMethod','Floor',... 'SumMode','KeepLSB',... 'SumWordLength',32); = setfimath(a,f); = setfimath(b,f); = a + b; = removefimath(y); end If you have the MATLAB Coder product, you can generate C code. This example generates C code on a computer with 32-bit, native integer type. a = fi(0,1,16,15); b = fi(0,1,16,15); codegen fixed_point_32bit_KeepLSB_plus_example... -args {a,b} -launchreport int32_T fixed_point_32bit_KeepLSB_plus_example(int16_T a, int16_T b) { return a + b; } See Also 2-574 fi | fimath | setfimath www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان repmat Purpose Replicate and tile array Description Refer to the MATLAB repmat reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-575 rescale Purpose Change scaling of fi object Syntax b = rescale(a, fractionlength) b = rescale(a, slope, bias) b = rescale(a, slopeadjustmentfactor, fixedexponent, bias) b = rescale(a, ..., PropertyName, PropertyValue, ...) Description The rescale function acts similarly to the fi copy function with the following exceptions: • The fi copy constructor preserves the real-world value, while rescale preserves the stored integer value. • rescale does not allow the Signed and WordLength properties to be changed. Examples In the following example, fi object a is rescaled to create fi object b. The real-world values of a and b are different, while their stored integer values are the same: p = fipref('FimathDisplay','none',... 'NumericTypeDisplay','short'); a = fi(10,1,8,3) a = 10 s8,3 b = rescale(a,1) b = 40 s8,1 stored_integer_a = storedInteger(a); 2-576 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان rescale stored_integer_b = storedInteger(b); isequal(stored_integer_a, stored_integer_b) ans = 1 See Also fi www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-577 reset Purpose Reset objects to initial conditions Syntax reset(P) reset(q) Description reset(P) resets the fipref object P to its initial conditions. reset(q) resets the following quantizer object properties to their initial conditions: • minlog • maxlog • noverflows • nunderflows • noperations See Also 2-578 resetlog www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان resetglobalfimath Purpose Set global fimath to MATLAB factory default Syntax resetglobalfimath Description resetglobalfimath sets the global fimath to the MATLAB factory default in your current MATLAB session. The MATLAB factory default has the following properties: RoundMode: OverflowMode: ProductMode: MaxProductWordLength: SumMode: MaxSumWordLength: Examples nearest saturate FullPrecision 128 FullPrecision 128 In this example, you create your own fimath object F and set it as the global fimath. Then, using the resetglobalfimath command, reset the global fimath to the MATLAB factory default setting. F = fimath('RoundMode','Floor','OverflowMode','Wrap'); globalfimath(F); F1 = fimath a = fi(pi) F1 = RoundMode: OverflowMode: ProductMode: MaxProductWordLength: SumMode: MaxSumWordLength: floor wrap FullPrecision 128 FullPrecision 128 a = 3.1416 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-579 resetglobalfimath DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 16 13 Now, set the global fimath back to the factory default setting using resetglobalfimath: resetglobalfimath; F2 = fimath a = fi(pi) F2 = RoundMode: OverflowMode: ProductMode: MaxProductWordLength: SumMode: MaxSumWordLength: nearest saturate FullPrecision 128 FullPrecision 128 a = 3.1416 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 16 13 You’ve now set the global fimath in your current MATLAB session back to the factory default setting. To use the factory default setting 2-580 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان resetglobalfimath of the global fimath in future MATLAB sessions, you must use the removeglobalfimathpref command. Alternatives reset(G) — If G is a handle to the global fimath, reset(G) is equivalent to using the resetglobalfimath command. See Also fimath | globalfimath | removeglobalfimathpref www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-581 removeglobalfimathpref Purpose Remove global fimath preference Syntax removeglobalfimathpref Description removeglobalfimathpref removes your global fimath from the MATLAB preferences. Doing so forces MATLAB to use the MATLAB factory default setting of the global fimath in future MATLAB sessions. The removeglobalfimathpref function does not change the global fimath for your current MATLAB session. To revert back to the factory default setting of the global fimath in your current MATLAB session, use the resetglobalfimath command. Examples Removing Your Global fimath from the MATLAB Preferences Typing removeglobalfimathpref; at the MATLAB command line removes your global fimath from the MATLAB preferences. Using the removeglobalfimathpref function allows you to: • Continue using your global fimath in the current MATLAB session • Use the MATLAB factory default setting of the global fimath in all future MATLAB sessions To revert back to the MATLAB factory default setting of the global fimath in both your current and future MATLAB sessions, use both the resetglobalfimath and the removeglobalfimathpref commands: resetglobalfimath; removeglobalfimath; See Also 2-582 fimath | globalfimath | resetglobalfimath www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان resetlog Purpose Clear log for fi or quantizer object Syntax resetlog(a) resetlog(q) Description resetlog(a) clears the log for fi object a. resetlog(q) clears the log for quantizer object q. Turn logging on or off by setting the fipref property LoggingMode. See Also fipref | maxlog | minlog | noperations | noverflows | nunderflows | reset www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-583 reshape Purpose Reshape array Description Refer to the MATLAB reshape reference page for more information. 2-584 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان rgbplot Purpose Plot colormap Description Refer to the MATLAB rgbplot reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-585 ribbon Purpose Create ribbon plot Description Refer to the MATLAB ribbon reference page for more information. 2-586 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان rose Purpose Create angle histogram Description Refer to the MATLAB rose reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-587 round Purpose Round fi object toward nearest integer or round input data using quantizer object Syntax y = round(a) y = round(q,x) Description y = round(a) rounds fi object a to the nearest integer. In the case of a tie, round rounds values to the nearest integer with greater absolute value. The rounded value is returned in fi object y. y and a have the same fimath object and DataType property. When the DataType of a is single, double, or boolean, the numerictype of y is the same as that of a. When the fraction length of a is zero or negative, a is already an integer, and the numerictype of y is the same as that of a. When the fraction length of a is positive, the fraction length of y is 0, its sign is the same as that of a, and its word length is the difference between the word length and the fraction length of a, plus one bit. If a is signed, then the minimum word length of y is 2. If a is unsigned, then the minimum word length of y is 1. For complex fi objects, the imaginary and real parts are rounded independently. round does not support fi objects with nontrivial slope and bias scaling. Slope and bias scaling is trivial when the slope is an integer power of 2 and the bias is 0. y = round(q,x) uses the RoundingMethod and FractionLength settings of q to round the numeric data x, but does not check for overflows during the operation. Compare to quantize. Examples Example 1 The following example demonstrates how the round function affects the numerictype properties of a signed fi object with a word length of 8 and a fraction length of 3. 2-588 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان round a = fi(pi, 1, 8, 3) a = 3.1250 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 8 3 y = round(a) y = 3 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 6 0 Example 2 The following example demonstrates how the round function affects the numerictype properties of a signed fi object with a word length of 8 and a fraction length of 12. a = fi(0.025,1,8,12) a = 0.0249 DataTypeMode: Fixed-point: binary point scaling Signedness: Signed www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-589 round WordLength: 8 FractionLength: 12 y = round(a) y = 0 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 2 0 Example 3 The functions convergent, nearest and round differ in the way they treat values whose least significant digit is 5: • The convergent function rounds ties to the nearest even integer • The nearest function rounds ties to the nearest integer toward positive infinity • The round function rounds ties to the nearest integer with greater absolute value The following table illustrates these differences for a given fi object a. a 2-590 convergent(a) nearest(a) round(a) –3.5 –4 –3 –4 –2.5 –2 –2 –3 –1.5 –2 –1 –2 –0.5 0 0 –1 0.5 0 1 1 1.5 2 2 2 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان round a convergent(a) nearest(a) round(a) 2.5 2 3 3 3.5 4 4 4 Example 4 Create a quantizer object, and use it to quantize input data. The quantizer object applies its properties to the input data to return quantized output. q = quantizer('fixed', 'convergent', 'wrap', [3 2]); x = (-2:eps(q)/4:2)'; y = round(q,x); plot(x,[x,y],'.-'); axis square; Applying quantizer object q to the data results in the staircase-shape output plot shown in the following figure. Linear data input results in output where y shows distinct quantization levels. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-591 round 2 1.5 1 0.5 0 −0.5 −1 −1.5 Input data x Output data y −2 −2 See Also 2-592 −1.5 −1 −0.5 0 0.5 1 1.5 2 ceil | convergent | fix | floor | nearest | quantize | quantizer www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان savefipref Purpose Save fi preferences for next MATLAB session Syntax savefipref Description savefipref saves the settings of the current fipref object for the next See Also fipref MATLAB session. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-593 scatter Purpose Create scatter or bubble plot Description Refer to the MATLAB scatter reference page for more information. 2-594 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان scatter3 Purpose Create 3-D scatter or bubble plot Description Refer to the MATLAB scatter3 reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-595 sdec Purpose Signed decimal representation of stored integer of fi object Syntax sdec(a) Description Fixed-point numbers can be represented as real-world value = 2− fraction length × stored integer or, equivalently as real-world value = (slope × stored integer) + bias The stored integer is the raw binary number, in which the binary point is assumed to be at the far right of the word. sdec(a) returns the stored integer of fi object a in signed decimal format as a string. Examples The code a = fi([-1 1],1,8,7); sdec(a) returns -128 See Also 2-596 127 bin | dec | hex | storedInteger | oct www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان semilogx Purpose Create semilogarithmic plot with logarithmic x-axis Description Refer to the MATLAB semilogx reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-597 semilogy Purpose Create semilogarithmic plot with logarithmic y-axis Description Refer to the MATLAB semilogy reference page for more information. 2-598 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان set Purpose Set or display property values for quantizer objects Syntax set(q, PropertyValue1, PropertyValue2,...) set(q,s) set(q,pn,pv) set(q,'PropertyName1',PropertyValue1,'PropertyName2', PropertyValue2,...) q.PropertyName = Value s = set(q) Description set(q, PropertyValue1, PropertyValue2,...) sets the properties of quantizer object q. If two property values conflict, the last value in the list is the one that is set. set(q,s), where s is a structure whose field names are object property names, sets the properties named in each field name with the values contained in the structure. set(q,pn,pv) sets the named properties specified in the cell array of strings pn to the corresponding values in the cell array pv. set(q,'PropertyName1',PropertyValue1,'PropertyName2', PropertyValue2,...) sets multiple property values with a single statement. Note You can use property name/property value string pairs, structures, and property name/property value cell array pairs in the same call to set. q.PropertyName = Value uses dot notation to set property PropertyName to Value. set(q) displays the possible values for all properties of quantizer object q. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-599 set s = set(q) returns a structure containing the possible values for the properties of quantizer object q. Note The set function operates on quantizer objects. To learn about setting the properties of other objects, see properties of fi, fimath, fipref, and numerictype objects. See Also 2-600 get www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان setfimath Purpose Attach fimath object to fi object Syntax y = setfimath(x,f) Description y = setfimath(x,f) returns a fi object, y, with x’s numerictype and value, and attached fimath object, f. This function and the related removefimath function are useful for preventing errors about embedded.fimath of both operands needing to be equal. The y = setfimath(x,f) syntax does not modify the input, x. To modify x, use x = setfimath(x,f). If you use setfimath in an expression, such as, a*setfimath(b,f), the fimath object is used in the temporary variable, but b is not modified. Input Arguments x - Input data fi object | built-in integer | double | single Input data, specified as a fi object or built-in integer value, from which to copy the data type and value to the output. x must be a fi object or an integer data type (int8, int16, int32, int64, uint8, uint16, uint32, or uint64). Otherwise, the fimath object is not applied. If x is not a fi object or integer data type, y = x. f - Input fimath object fimath object Input fimath object, specified as an existing fimath object to attach to the output. An error occurs if f is not a fimath object. Output Arguments y - Output fi object fi object Output fi object, returned as a fi object with the same data type and value as the x input. y also has attached fimath object, f. If the input, x, is not a fi object or integer data type, then y = x. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-601 setfimath Examples Add fimath object to fi Object This example shows how to define a fi object, define a fimath object, and use setfimath to attach the fimath object to the fi object. Create a fi object without a fimath object. a = fi(pi) a = 3.1416 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 16 13 Create a fimath object and attach it to the fi object. f = fimath('OverflowAction','Wrap','RoundingMethod','Floor'); b = setfimath(a,f) b = 3.1416 2-602 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 16 13 RoundingMethod: OverflowAction: ProductMode: SumMode: Floor Wrap FullPrecision FullPrecision www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان setfimath Set and Remove fimath for Code Generation Use the pattern x = setfimath(x,f) and y = removefimath(y) to insulate variables from fimath settings outside the function. This pattern does not create copies of the data in generated code. function y = fixed_point_32bit_KeepLSB_plus_example(a,b) f = fimath('OverflowAction','Wrap',... 'RoundingMethod','Floor',... 'SumMode','KeepLSB',... 'SumWordLength',32); a = setfimath(a,f); b = setfimath(b,f); y = a + b; y = removefimath(y); end If you have the MATLAB Coder product, you can generate C code. This example generates C code on a computer with 32-bit, native integer type. a = fi(0,1,16,15); b = fi(0,1,16,15); codegen fixed_point_32bit_KeepLSB_plus_example... -args {a,b} -launchreport int32_T fixed_point_32bit_KeepLSB_plus_example(int16_T a, int16_T b) { return a + b; } See Also fi | fimath | removefimath www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-603 sfi Purpose Construct signed fixed-point numeric object Syntax a a a a a a Description You can use the sfi constructor function in the following ways: = = = = = = sfi sfi(v) sfi(v,w) sfi(v,w,f) sfi(v,w,slope,bias) sfi(v,w,slopeadjustmentfactor,fixedexponent,bias) • a = sfi is the default constructor and returns a signed fi object with no value, 16-bit word length, and 15-bit fraction length. • a = sfi(v) returns a signed fixed-point object with value v, 16-bit word length, and best-precision fraction length. • a = sfi(v,w) returns a signed fixed-point object with value v, word length w, and best-precision fraction length. • a = sfi(v,w,f) returns a signed fixed-point object with value v, word length w, and fraction length f. • a = sfi(v,w,slope,bias) returns a signed fixed-point object with value v, word length w, slope, and bias. • a = sfi(v,w,slopeadjustmentfactor,fixedexponent,bias) returns a signed fixed-point object with value v, word length w, slopeadjustmentfactor, fixedexponent, and bias. fi objects created by the sfi constructor function have the following general types of properties: • “Data Properties” on page 2-308 • “fimath Properties” on page 2-605 • “numerictype Properties” on page 2-310 These properties are described in detail in “fi Object Properties” on page 1-2 in the Properties Reference. 2-604 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان sfi Note fi objects created by the sfi constructor function have no local fimath. Data Properties The data properties of a fi object are always writable. • bin — Stored integer value of a fi object in binary • data — Numerical real-world value of a fi object • dec — Stored integer value of a fi object in decimal • double — Real-world value of a fi object, stored as a MATLAB double • hex — Stored integer value of a fi object in hexadecimal • int — Stored integer value of a fi object, stored in a built-in MATLAB integer data type. You can also use int8, int16, int32, int64, uint8, uint16, uint32, and uint64 to get the stored integer value of a fi object in these formats • oct — Stored integer value of a fi object in octal These properties are described in detail in “fi Object Properties” on page 1-2. fimath Properties When you create a fi object with the sfi constructor function, that fi object does not have a local fimath object. You can attach a fimath object to that fi object if you do not want to use the default fimath settings. For more information, see “fimath Object Construction” in the Fixed-Point Designer documentation. • fimath — fixed-point math object The following fimath properties are always writable and, by transitivity, are also properties of a fi object. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-605 sfi • CastBeforeSum — Whether both operands are cast to the sum data type before addition Note This property is hidden when the SumMode is set to FullPrecision. • OverflowAction — Action to take on overflow • ProductBias — Bias of the product data type • ProductFixedExponent — Fixed exponent of the product data type • ProductFractionLength — Fraction length, in bits, of the product data type • ProductMode — Defines how the product data type is determined • ProductSlope — Slope of the product data type • ProductSlopeAdjustmentFactor — Slope adjustment factor of the product data type • ProductWordLength — Word length, in bits, of the product data type • RoundingMethod — Rounding method • SumBias — Bias of the sum data type • SumFixedExponent — Fixed exponent of the sum data type • SumFractionLength — Fraction length, in bits, of the sum data type • SumMode — Defines how the sum data type is determined • SumSlope — Slope of the sum data type • SumSlopeAdjustmentFactor — Slope adjustment factor of the sum data type • SumWordLength — The word length, in bits, of the sum data type These properties are described in detail in “fimath Object Properties” on page 1-4. 2-606 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان sfi numerictype Properties When you create a fi object, a numerictype object is also automatically created as a property of the fi object. numerictype — Object containing all the data type information of a fi object, Simulink signal or model parameter The following numerictype properties are, by transitivity, also properties of a fi object. The properties of the numerictype object become read only after you create the fi object. However, you can create a copy of a fi object with new values specified for the numerictype properties. • Bias — Bias of a fi object • DataType — Data type category associated with a fi object • DataTypeMode — Data type and scaling mode of a fi object • FixedExponent — Fixed-point exponent associated with a fi object • SlopeAdjustmentFactor — Slope adjustment associated with a fi object • FractionLength — Fraction length of the stored integer value of a fi object in bits • Scaling — Fixed-point scaling mode of a fi object • Signed — Whether a fi object is signed or unsigned • Signedness — Whether a fi object is signed or unsigned Note numerictype objects can have a Signedness of Auto, but all fi objects must be Signed or Unsigned. If a numerictype object with Auto Signedness is used to create a fi object, the Signedness property of the fi object automatically defaults to Signed. • Slope — Slope associated with a fi object www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-607 sfi • WordLength — Word length of the stored integer value of a fi object in bits For further details on these properties, see “numerictype Object Properties” on page 1-15. Examples Note For information about the display format of fi objects, refer to Display Settings. For examples of casting, see “Cast fi Objects”. Example 1 For example, the following creates a signed fi object with a value of pi, a word length of 8 bits, and a fraction length of 3 bits: a = sfi(pi,8,3) a = 3.1250 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 8 3 Default fimath properties are associated with a. When a fi object does not have a local fimath object, no fimath object properties are displayed in its output. To determine whether a fi object has a local fimath object, use the isfimathlocal function. isfimathlocal(a) ans = 0 2-608 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان sfi A returned value of 0 means the fi object does not have a local fimath object. When the isfimathlocal function returns a 1, the fi object has a local fimath object. Example 2 The value v can also be an array: a = sfi((magic(3)/10),16,12) a = 0.8000 0.3000 0.3999 0.1001 0.5000 0.8999 DataTypeMode: Signedness: WordLength: FractionLength: 0.6001 0.7000 0.2000 Fixed-point: binary point scaling Signed 16 12 Example 3 If you omit the argument f, it is set automatically to the best precision possible: a = sfi(pi,8) a = 3.1563 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 8 5 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-609 sfi Example 4 If you omit w and f, they are set automatically to 16 bits and the best precision possible, respectively: a = sfi(pi) a = 3.1416 DataTypeMode: Signedness: WordLength: FractionLength: See Also 2-610 Fixed-point: binary point scaling Signed 16 13 fi | fimath | fipref | isfimathlocal | numerictype | quantizer | ufi www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان shiftdata Purpose Shift data to operate on specified dimension Syntax [x,perm,nshifts] = shiftdata(x,dim) Description [x,perm,nshifts] = shiftdata(x,dim) shifts data x to permute dimension dim to the first column using the same permutation as the built-in filter function. The vector perm returns the permutation vector that is used. If dim is missing or empty, then the first non-singleton dimension is shifted to the first column, and the number of shifts is returned in nshifts. shiftdata is meant to be used in tandem with unshiftdata, which shifts the data back to its original shape. These functions are useful for creating functions that work along a certain dimension, like filter, goertzel, sgolayfilt, and sosfilt. Examples Example 1 This example shifts x, a 3-x-3 magic square, permuting dimension 2 to the first column. unshiftdata shifts x back to its original shape. 1. Create a 3-x-3 magic square: x = fi(magic(3)) x = 8 3 4 1 5 9 6 7 2 2. Shift the matrix x to work along the second dimension: [x,perm,nshifts] = shiftdata(x,2) www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-611 shiftdata The permutation vector, perm, and the number of shifts, nshifts, are returned along with the shifted matrix, x: x = 8 1 6 3 5 7 4 9 2 perm = 2 1 nshifts = [] 3. Shift the matrix back to its original shape: y = unshiftdata(x,perm,nshifts) y = 8 3 4 1 5 9 6 7 2 Example 2 This example shows how shiftdata and unshiftdata work when you define dim as empty. 1. Define x as a row vector: x = 1:5 2-612 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان shiftdata x = 1 2 3 4 5 2. Define dim as empty to shift the first non-singleton dimension of x to the first column: [x,perm,nshifts] = shiftdata(x,[]) x is returned as a column vector, along with perm, the permutation vector, and nshifts, the number of shifts: x = 1 2 3 4 5 perm = [] nshifts = 1 3. Using unshiftdata, restore x to its original shape: y = unshiftdata(x,perm,nshifts) www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-613 shiftdata y = 1 See Also 2-614 2 3 4 5 permute | shiftdim | unshiftdata www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان shiftdim Purpose Shift dimensions Description Refer to the MATLAB shiftdim reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-615 showfixptsimerrors Purpose Show overflows from most recent fixed-point simulation Note showfixptsimerrors will be removed in a future release. Use fxptdlg instead. Syntax showfixptsimerrors Description The showfixptsimerrors script displays any overflows from the most recent fixed-point simulation. This information is also visible in the Fixed-Point Tool. See Also autofixexp | fxptdlg 2-616 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان showfixptsimranges Purpose Show logged maximum values, minimum values, and overflow data from fixed-point simulation Note showfixptsimranges will be removed in a future release. Use fxptdlg instead. Syntax showfixptsimranges showfixptsimranges(action) Description showfixptsimranges displays the logged maximum values, minimum values, and overflow data from the most recent fixed-point simulation in the MATLAB Command Window. showfixptsimranges(action) stores the logged maximum values, minimum values, and overflow data from the most recent fixed-point simulation in the workspace variable FixPtSimRanges. If action is 'verbose', the logged data also appears in the MATLAB Command Window. If action is 'quiet', no data appears. See Also autofixexp | fxptdlg www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-617 showInstrumentationResults Purpose Results logged by instrumented, compiled C code function Syntax showInstrumentationResults('mex_fcn') showInstrumentationResults ('mex_fcn' '-options') showInstrumentationResults mex_fcn showInstrumentationResults mex_fcn -options Description showInstrumentationResults('mex_fcn') opens the Code Generation Report, showing results from calling the instrumented MEX function mex_fcn. Hovering over variables and expressions in the report displays the logged information. The logged information includes minimum and maximum values, proposed fraction or word lengths, percent of current range, and whether the value is always a whole number, depending on which options you specify. If you specify to include them in the buildInstrumentedMex function, histograms are also included. The same information is displayed in a summary table in the Variables tab. showInstrumentationResults ('mex_fcn' '-options') specifies options for the instrumentation results section of the Code Generation Report. showInstrumentationResults mex_fcn and showInstrumentationResults mex_fcn -options are alternative syntaxes for opening the Code Generation Report. When you call showInstrumentationResults, a file named instrumentation/mex_fcn/html/index.html is created. mex_fcn is the name of the corresponding instrumented MEX function. Selecting this file opens a web-based version of the Code Generation Report. To open this file from within MATLAB, right-click on the file and select Open Outside MATLAB. showInstrumentationResults returns an error if the instrumented mex_fcn has not yet been called. Input Arguments mex_fcn Instrumented MEX function created using buildInstrumentedMex. options 2-618 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان showInstrumentationResults Instrumentation results options. -defaultDT T Default data type to propose for double or single data type inputs, where T is either a numerictype object or one of these strings: remainFloat, double, single, int8, int16, int32, int64, uint8, uint16, uint32, or uint64. If you specify an int or uint, the signedness and word length are that int or uint value and a fraction length is proposed. The default is remainFloat, which does not propose any data types. -nocode Do not display MATLAB code in the printable report. Display only the tables of logged variables. This option only has effect in combination with the -printable option. -optimizeWholeNumbers Optimize the word length of variables whose simulation min/max logs indicate that they are always whole numbers. -percentSafetyMargin N Safety margin for simulation min/max, where N is a percent value. -printable Create and open a printable HTML report. The report opens in the system browser. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-619 showInstrumentationResults Examples -proposeFL Propose fraction lengths for specified word lengths. -proposeWL Propose word lengths for specified fraction lengths. Generate an instrumented MEX function, then run a test bench. Call showInstrumentationResults to open the Code Generation Report. Note The logged results from showInstrumentationResults are an accumulation of all previous calls to the instrumented MEX function. To clear the log, see clearInstrumentationResults. 1 Create a temporary directory, then import an example function from Fixed-Point Designer. tempdirObj=fidemo.fiTempdir('showInstrumentationResults') copyfile(fullfile(matlabroot,'toolbox','fixedpoint',... 'fidemos','fi_m_radix2fft_withscaling.m'),... 'testfft.m','f') 2 Define prototype input arguments. T = numerictype('DataType','ScaledDouble','Scaling',... 'Unspecified'); n = 128; x = complex(fi(zeros(n,1),T)); W = coder.Constant(fi(fidemo.fi_radix2twiddles(n),T)); 3 Generate an instrumented MEX function. Use the -o option to specify the MEX function name. buildInstrumentedMex testfft -o testfft_instrumented... 2-620 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان showInstrumentationResults -args {x,W} -histogram 4 Run a test bench to record instrumentation results. Call showInstrumentationResults to open the Code Generation Report. View the simulation minimum and maximum values, proposed fraction length, percent of current range, and whole number status by hovering over a variable in the report. for i=1:20 x(:) = 2*rand(size(x))-1; y = testfft_instrumented(x); end showInstrumentationResults testfft_instrumented... -proposeFL -percentSafetyMargin 10 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-621 showInstrumentationResults 2-622 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان showInstrumentationResults 5 View the histogram for a variable by clicking in the Variables tab. For information on the figure, refer to the NumericTypeScope reference page. 6 Close the histogram display and then, clear the results log. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-623 showInstrumentationResults clearInstrumentationResults testfft_instrumented 7 Clear the MEX function, then delete temporary files. clear testfft_instrumented; tempdirObj.cleanUp; See Also 2-624 fiaccel | clearInstrumentationResults | buildInstrumentedMex | NumericTypeScope | codegen | mex www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان sin Purpose Sine of fixed-point values Syntax y = sin(theta) Description y = sin(theta) returns the sine of fi input theta using a table-lookup Input Arguments theta algorithm. theta can be a real-valued, signed or unsigned scalar, vector, matrix, or N-dimensional array containing the fixed-point angle values in radians. Valid data types of theta are: • fi single • fi double • fi fixed-point with binary point scaling • fi scaled double with binary point scaling Output Arguments Definitions y y is the sine of theta. y is a signed, fixed-point number in the range [-1,1]. It has a 16-bit word length and 15-bit fraction length (numerictype(1,16,15)) This sine calculation is accurate only to within the top 16 most-significant bits of the input. Sine The sine of angle Θ is defined as sin( ) Examples ei ei 2i Calculate the sine of fixed-point input values. theta = fi([-pi/2,-pi/3,-pi/4 0, pi/4,pi/3,pi/2]) www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-625 sin theta = theta = -1.5708 -1.0472 -0.7854 DataTypeMode: Signedness: WordLength: FractionLength: 0 0.7854 1.0472 1.5708 Fixed-point: binary point scaling Signed 16 14 y = sin(theta) y = -1.0000 -0.8661 -0.7072 DataTypeMode: Signedness: WordLength: FractionLength: Algorithms 0 0.7070 0.8659 0.9999 Fixed-point: binary point scaling Signed 16 15 The sin function computes the sine of fixed-point input using an 8-bit lookup table as follows: 1 Cast the input to a 16-bit stored integer value, using the 16 most-significant bits. 2 Perform a modulo 2π, so the input is in the range [0,2π) radians. 3 Compute the table index, based on the 16-bit stored integer value, normalized to the full uint16 range. 4 Use the 8 most-significant bits to obtain the first value from the table. 5 Use the next-greater table value as the second value. 2-626 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان sin 6 Use the 8 least-significant bits to interpolate between the first and second values, using nearest-neighbor linear interpolation. See Also sin | angle | cos | atan2 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-627 sign Purpose Perform signum function on array Syntax c = sign(a) Description c = sign(a) returns an array c the same size as a, where each element of c is • 1 if the corresponding element of a is greater than zero • 0 if the corresponding element of a is zero • -1 if the corresponding element of a is less than zero The elements of c are of data type int8. sign does not support complex fi inputs. 2-628 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان single Purpose Single-precision floating-point real-world value of fi object Syntax single(a) Description Fixed-point numbers can be represented as real-world value = 2− fraction length × stored integer or, equivalently as real-world value = (slope × stored integer) + bias single(a) returns the real-world value of a fi object in single-precision floating point. See Also double www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-629 size Purpose Array dimensions Description Refer to the MATLAB size reference page for more information. 2-630 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان slice Purpose Create volumetric slice plot Description Refer to the MATLAB slice reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-631 sort Purpose Sort elements of real-valued fi object in ascending or descending order Description Refer to the MATLAB sort reference page for more information. 2-632 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان spy Purpose Visualize sparsity pattern Description Refer to the MATLAB spy reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-633 sqrt Purpose Square root of fi object Syntax c c c c Description This function computes the square root of a fi object using a bisection algorithm. = = = = sqrt(a) sqrt(a,T) sqrt(a,F) sqrt(a,T,F) c = sqrt(a) returns the square root of fi object a. Intermediate quantities are calculated using the fimath associated with a. The numerictype object of c is determined automatically for you using an internal rule. c = sqrt(a,T) returns the square root of fi object a with numerictype object T. Intermediate quantities are calculated using the fimath associated with a. See “Data Type Propagation Rules” on page 2-635. c = sqrt(a,F) returns the square root of fi object a. Intermediate quantities are calculated using the fimath object F. The numerictype object of c is determined automatically for you using an internal rule. When a is a built-in double or single data type, this syntax is equivalent to c = sqrt(a) and the fimath object F is ignored. c = sqrt(a,T,F) returns the square root fi object a with numerictype object T. Intermediate quantities are also calculated using the fimath object F. See “Data Type Propagation Rules” on page 2-635. sqrt does not support complex, negative-valued, or [Slope Bias] inputs. Internal Rule For syntaxes where the numerictype object of the output is not specified as an input to the sqrt function, it is automatically calculated according to the following internal rule: signc = signa 2-634 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان sqrt WLc = ceil( WLa ) 2 FLc = WLc − ceil( WLa − FLa ) 2 Data Type Propagation Rules For syntaxes for which you specify a numerictype object T, the sqrt function follows the data type propagation rules listed in the following table. In general, these rules can be summarized as “floating-point data types are propagated.” This allows you to write code that can be used with both fixed-point and floating-point inputs. Data Type of Input fi Object a Data Type of numerictype object T Data Type of Output c Built-in double Any Built-in double Built-in single Any Built-in single fi Fixed fi Fixed Data type of numerictype object T fi ScaledDouble fi Fixed ScaledDouble with properties of numerictype object T fi double fi Fixed fi double fi single fi Fixed fi single Any fi data type fi double fi double Any fi data type fi single fi single www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-635 squeeze Purpose Remove singleton dimensions Description Refer to the MATLAB squeeze reference page for more information. 2-636 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان stairs Purpose Create stairstep graph Description Refer to the MATLAB stairs reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-637 stem Purpose Plot discrete sequence data Description Refer to the MATLAB stem reference page for more information. 2-638 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان stem3 Purpose Plot 3-D discrete sequence data Description Refer to the MATLAB stem3 reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-639 storedInteger Purpose Stored integer value of fi object Syntax st_int = storedInteger(f) Description st_int = storedInteger(f) returns the stored integer value of fi object f. Fixed-point numbers can be represented as real-world value = 2− fraction length × stored integer or, equivalently as real-world value = (slope × stored integer) + bias The stored integer is the raw binary number, in which the binary point is assumed to be at the far right of the word. Input Arguments f - Fixed-point numeric object fi object Fixed-point numeric object from which you want to get the stored integer value. Output Arguments st_int - Stored integer value of fi object integer Data Types int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 The returned stored integer value is the smallest built-in integer data type in which the stored integer value f fits. Signed fi values return stored integers of type int8, int16, int32, or int64. Unsigned fi values return stored integers of type uint8, uint16, uint32, or uint64. The return type is determined based on the stored integer word length (WL): 2-640 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان storedInteger • WL ≤ 8 bits, the return type is int8 or uint8. • 8 bits < WL ≤ 16 bits, the return type is int16 or uint16. • 16 bits < WL ≤ 32 bits, the return type is int32 or uint32. • 32 bits < WL ≤ 64 bits, the return type is int64 or uint64. Note When the word length is greater than 64 bits, the storedInteger function errors. For bit-true integer representation of very large word lengths, use bin, oct, dec, hex, or sdec. Examples Stored Integer Value of fi Objects Find the stored integer values for two fi objects. Use the class function to display the stored integer data types. x = fi([0.2 0.3 0.5 0.3 0.2]); in_x = storedInteger(x); c1 = class(in_x) numtp = numerictype('WordLength',17); x_n = fi([0.2 0.3 0.5 0.3 0.2],'numerictype',numtp); in_xn = storedInteger(x_n); c2 = class(in_xn) See Also int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | storedIntegerToDouble www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-641 storedIntegerToDouble Purpose Convert stored integer value of fi object to built-in double value Syntax d = storedIntegerToDouble(f) Description d = storedIntegerToDouble(f) converts the stored integer value of fi object, f, to a double-precision floating-point value, d. If the input word length is greater than 52 bits, a quantization error may occur. INF is returned if the stored integer value of the input fi object is outside the representable range of built-in double values. Input Arguments f Examples Convert Stored Integer Value of fi Object to Double-Precision Value fi object Convert the stored integer of a fi value to a double-precision value. Use the class function to verify that the stored integer is a double-precision value. f = fi(pi,1,16,12); d = storedIntegerToDouble(f); dtype = class(d) See Also 2-642 storedInteger | fi | class www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان streamribbon Purpose Create 3-D stream ribbon plot Description Refer to the MATLAB streamribbon reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-643 streamslice Purpose Draw streamlines in slice planes Description Refer to the MATLAB streamslice reference page for more information. 2-644 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان streamtube Purpose Create 3-D stream tube plot Description Refer to the MATLAB streamtube reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-645 stripscaling Purpose Stored integer of fi object Syntax I = stripscaling(a) Description I = stripscaling(a) returns the stored integer of a as a fi object with binary-point scaling, zero fraction length and the same word length and sign as a. Examples Stripscaling is useful for converting the value of a fi object to its stored integer value. fipref('NumericTypeDisplay','short', ... 'FimathDisplay','none'); format long g a = fi(0.1,true,48,47) a = 0.100000000000001 s48,47 b = stripscaling(a) b = 14073748835533 s48,0 bin(a) ans = 000011001100110011001100110011001100110011001101 bin(b) ans = 000011001100110011001100110011001100110011001101 2-646 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان stripscaling Notice that the stored integer values of a and b are identical, while their real-world values are different. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-647 sub Purpose Subtract two objects using fimath object Syntax c = F.sub(a,b) Description c = F.sub(a,b) subtracts objects a and b using fimath object F. This is helpful in cases when you want to override the fimath objects of a and b, or if the fimath properties associated with a and b are different. The output fi object c has no local fimath. a and b must both be fi objects and must have the same dimensions unless one is a scalar. If either a or b is scalar, then c has the dimensions of the nonscalar object. Examples In this example, c is the 32-bit difference of a and b with fraction length 16. a = fi(pi); b = fi(exp(1)); F = fimath('SumMode','SpecifyPrecision',... 'SumWordLength',32,'SumFractionLength',16); c = F.sub(a, b) c = 0.4233 DataTypeMode: Signedness: WordLength: FractionLength: Algorithms Fixed-point: binary point scaling Signed 32 16 c = F.sub(a,b) is similar to a.fimath = F; b.fimath = F; c = a - b 2-648 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان sub c = 0.4233 DataTypeMode: Signedness: WordLength: FractionLength: RoundingMethod: OverflowAction: ProductMode: SumMode: SumWordLength: SumFractionLength: CastBeforeSum: Fixed-point: binary point scaling Signed 32 16 Nearest Saturate FullPrecision SpecifyPrecision 32 16 true but not identical. When you use sub, the fimath properties of a and b are not modified, and the output fi object c has no local fimath. When you use the syntax c = a - b, where a and b have their own fimath objects, the output fi object c gets assigned the same fimath object as inputs a and b. See “fimath Rules for Fixed-Point Arithmetic” in the Fixed-Point Designer User’s Guide for more information. See Also add | divide | fi | fimath | mpy | mrdivide | numerictype | rdivide www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-649 subsasgn Purpose Subscripted assignment Syntax a(I) = b a(I,J) = b a(I,:) = b a(:,I) = b a(I,J,K,...) = b a = subsasgn(a,S,b) Description a(I) = b assigns the values of b into the elements of a specified by the subscript vector I. b must have the same number of elements as I or be a scalar value. a(I,J) = b assigns the values of b into the elements of the rectangular submatrix of a specified by the subscript vectors I and J. b must have LENGTH(I) rows and LENGTH(J) columns. A colon used as a subscript, as in a(I,:) the entire column or row. = b or a(:,I) = b indicates For multidimensional arrays, a(I,J,K,...) = b assigns b to the specified elements of a. b must be length(I)-by-length(J)-by-length(K)-... or be shiftable to that size by adding or removing singleton dimensions. a = subsasgn(a,S,b) is called for the syntax a(i)=b, a{i}=b, or a.i=b when a is an object. S is a structure array with the following fields: • type — String containing '()', '{}', or '.' specifying the subscript type • subs — Cell array or string containing the actual subscripts For instance, the syntax a(1:2,:) = b calls a=subsasgn(a,S,b) where S is a 1-by-1 structure with S.type='()' and S.subs = {1:2,':'}. A colon used as a subscript is passed as the string ':'. You can use fixed-point assignment, for example a(:) = b, to cast a value with one numerictype object into another numerictype object. This subscripted assignment statement assigns the value of b into a 2-650 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان subsasgn while keeping the numerictype object of a. Subscripted assignment works the same way for integer data types. Examples Example 1 For fi objects a and b, there is a difference between a = b and a(:) = b In the first case, a = b replaces a with b while a assumes the value, numerictype object and fimath object associated with b. In the second case, a(:) = b assigns the value of b into a while keeping the numerictype object of a. You can use this to cast a value with one numerictype object into another numerictype object. For example, cast a 16-bit number into an 8-bit number: a = fi(0, 1, 8, 7) a = 0 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 8 7 b = fi(pi/4, 1, 16, 15) b = 0.7854 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-651 subsasgn DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 16 15 a(:) = b a = 0.7891 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 8 7 Example 2 This example defines a variable acc to emulate a 40–bit accumulator of a DSP. The products and sums in this example are assigned into the accumulator using the syntax acc(1) = .... Assigning values into the accumulator is like storing a value in a register. To begin, turn the logging mode on and define the variables. In this example, n is the number of points in the input data x and output data y, and t represents time. The remaining variables are all defined as fi objects. The input data x is a high-frequency sinusoid added to a low-frequency sinusoid. fipref('LoggingMode','on'); n = 100; t = (0:n-1)/n; x = fi(sin(2*pi*t) + 0.2*cos(2*pi*50*t)); b = fi([.5 .5]); y = fi(zeros(size(x)), numerictype(x)); acc = fi(0.0, true, 40, 30); The following loop takes a running average of the input x using the coefficients in b. Notice that acc is assigned into acc(1) = ... versus 2-652 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان subsasgn using acc = ..., which would overwrite and change the data type of acc. for k = 2:n acc(1) = b(1)*x(k); acc(1) = acc + b(2)*x(k-1); y(k) = acc; end By averaging every other sample, the loop shown above passes the low-frequency sinusoid through and attenuates the high-frequency sinusoid. plot(t,x,'x-',t,y,'o-') legend('input data x','output data y') www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-653 subsasgn The log report shows the minimum and maximum logged values and ranges of the variables used. Because acc is assigned into, rather than over written, these logs reflect the accumulated minimum and maximum values. logreport(x,y,b,acc) The table below shows selected output from the log report: 2-654 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان subsasgn Value minlog maxlog lowerbound upperbound x –1.200012 1.197998 –2 1.999939 y –0.9990234 0.9990234 –2 1.999939 b 0.5 0.5 –1 0.9999695 acc –0.9990234 0.9989929 –512 512 Display acc to verify that its data type did not change: acc acc = -0.0941 DataTypeMode: Signedness: WordLength: FractionLength: See Also subsref Related Examples • “Cast fi Objects” Fixed-point: binary point scaling Signed 40 30 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-655 subsref Purpose Subscripted reference Description Refer to the MATLAB subsref reference page for more information. 2-656 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان sum Purpose Sum of array elements Syntax S= sum (A) S= sum ( A, dim) S = sum ( ___ , type ) Description S= sum (A) returns the sum along different dimensions of the fi array A. If A is a vector, sum(A) returns the sum of the elements. If A is a matrix, sum(A) treats the columns of A as vectors, returning a row vector of the sums of each column. If A is a multidimensional array, sum(A) treats the values along the first non-singleton dimension as vectors, returning an array of row vectors. S= sum ( A, dim) sums along the dimension dim of A. S = sum ( ___ , type ) returns an array in the class specified by type, using any of the input arguments in the previous syntaxes. type can be 'double' or 'native'. • If type is 'double', then sum returns a double-precision array, regardless of the input data type. • If type is 'native', then sum returns an array with the same class of input array A. The fimath object is used in the calculation of the sum. If SumMode is FullPrecision, KeepLSB, or KeepMSB, then the number of integer bits of growth for sum(A) is ceil(log2(size(A,dim))). sum does not support fi objects of data type Boolean. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-657 sum Input Arguments A - Input fi array fi object | numeric variable fi input array, specified as a scalar, vector, matrix, or multidimensional array. Data Types: fi|single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 Complex Number Support: Yes dim - Dimension to operate along positive integer scalar Dimension to operate along, specified as a positive integer scalar. dim can also be a fi object. If no value is specified, the default is the first array dimension whose size does not equal 1. Data Types: fi|single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 type - Output class 'double' | 'native' Output class, specified as 'double' or 'native', defines the data type that the operation is performed in and returned in. Data Types char Output Arguments S - Sum array scalar | vector | matrix | multidimensional array Sum array, returned as a scalar, vector, matrix, or multidimensional array. Examples Sum of Vector Elements Create a fi vector, and specify fimath properties in the constructor. A=fi([1 2 5 8 5], 'SumMode', 'KeepLSB', 'SumWordLength', 32) 2-658 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان sum A = 1 2 5 8 5 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 16 11 RoundingMethod: OverflowAction: ProductMode: SumMode: SumWordLength: CastBeforeSum: Nearest Saturate FullPrecision KeepLSB 32 true Compute the sum of the elements of A. S=sum(A) S = 21 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 32 11 RoundingMethod: OverflowAction: ProductMode: SumMode: SumWordLength: CastBeforeSum: Nearest Saturate FullPrecision KeepLSB 32 true The output S is a scalar with the specified SumWordLength of 32. The FractionLength of S is 11 because SumMode was set to KeepLSB. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-659 sum Sum of Elements in Each Column Create a fi array, and compute the sum of the elements in each column. A=fi([1 2 8;3 7 0;1 2 2]) A = 1 3 1 2 7 2 8 0 2 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 16 11 S=sum(A) S = 5 11 10 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 18 11 MATLAB returns a row vector with the sums of each column of A. The WordLength of S has increased by two bits because ceil(log2(size(A,1)))=2. The FractionLength remains the same because the default setting of SumMode is FullPrecision. Sum of Elements in Each Row Compute the sum along the second dimension (dim=2) of 3-by-3 matrix A. 2-660 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان sum A=fi([1 2 8;3 7 0;1 2 2]) A = 1 3 1 2 7 2 8 0 2 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 16 11 S=sum(A, 2) S = 11 10 5 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 18 11 MATLAB returns a column vector of the sums of the elements in each row. The WordLength of S is 18 because ceil(log2(size(A,2)))=2. Sum of Elements Preserving Data Type Compute the sums of the columns of A so that the output array, S, has the same data type. A=fi([1 2 8;3 7 0;1 2 2]), class(A) A = www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-661 sum 1 3 1 2 7 2 8 0 2 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 16 11 ans = embedded.fi S=sum(A, 'native'), class(S) S = 5 11 10 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 18 11 ans = embedded.fi MATLAB preserves the data type of A and returns a row vector S of type embedded.fi. See Also 2-662 sum | add | divide | fi | fimath | mpy | mrdivide | numerictype | rdivide | sub www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان surf Purpose Create 3-D shaded surface plot Description Refer to the MATLAB surf reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-663 surfc Purpose Create 3-D shaded surface plot with contour plot Description Refer to the MATLAB surfc reference page for more information. 2-664 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان surfl Purpose Create surface plot with colormap-based lighting Description Refer to the MATLAB surfl reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-665 surfnorm Purpose Compute and display 3-D surface normals Description Refer to the MATLAB surfnorm reference page for more information. 2-666 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان text Purpose Create text object in current axes Description Refer to the MATLAB text reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-667 times Purpose Element-by-element multiplication of fi objects Syntax C= times(A,B) C= A.* B Description C= times(A,B) is called for the syntax C= A.* B when A or B is an object. A.*B denotes element-by-element multiplication. A and B must have the same dimensions unless one is a scalar value. A scalar value can be multiplied by any other value. times does not support fi objects of data type Boolean. Note For information about the fimath properties involved in Fixed-Point Designer calculations, see “fimath Properties Usage for Fixed-Point Arithmetic” and “fimath ProductMode and SumMode” in the Fixed-Point Designer documentation. For information about calculations using Fixed-Point Designer software, see the Fixed-Point Designer documentation. Examples Multiply a fi Object by a Scalar Use the times function to perform element-by-element multiplication of a fi object and a scalar. a=4; b=fi([2 4 7; 9 0 2]) b = 2 9 4 0 7 2 DataTypeMode: Fixed-point: binary point scaling 2-668 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان times Signedness: Signed WordLength: 16 FractionLength: 11 c=a.*b c = 8 36 16 0 28 8 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 32 23 Multiply Two fi Objects Use the times function to perform element-by-element multiplication of two fi objects. a=fi([5 9 9; 1 2 -3], 1, 16, 3) a = 5 1 9 2 9 -3 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 16 3 b=fi([2 4 7; 9 0 2], 1, 16, 3) b = 2 9 4 0 7 2 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-669 times DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 16 3 c=a.*b c = 10 9 36 0 63 -6 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 32 6 The word length and fraction length of c are equal to the sums of the word lengths and fraction lengths of a and b. This is because the default setting of ProductMode in fimath is FullPrecision. See Also 2-670 plus | minus | mtimes | uminus www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان toeplitz Purpose Create Toeplitz matrix Syntax t = toeplitz(a,b) t = toeplitz(b) Description t = toeplitz(a,b) returns a nonsymmetric Toeplitz matrix having a as its first column and b as its first row. b is cast to the numerictype of a. t = toeplitz(b) returns the symmetric or Hermitian Toeplitz matrix formed from vector b, where b is the first row of the matrix. The output fi object t has the same numerictype properties as the leftmost fi object input. If the leftmost fi object input has a local fimath, the output fi object t is assigned the same local fimath. Otherwise, the output fi object t has no local fimath. Examples toeplitz(a,b) casts b into the data type of a. In this example, overflow occurs: fipref('NumericTypeDisplay','short'); format short g a = fi([1 2 3],true,8,5) a = 1 2 3 s8,5 b = fi([1 4 8],true,16,10) b = 1 4 s16,10 8 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-671 toeplitz toeplitz(a,b) ans = 1 2 3 3.9688 1 2 3.9688 3.9688 1 s8,5 toeplitz(b,a) casts a into the data type of b. In this example, overflow does not occur: toeplitz(b,a) ans = 1 4 8 2 1 4 s16,10 3 2 1 If one of the arguments of toeplitz is a built-in data type, it is cast to the data type of the fi object. x = [1 exp(1) pi] x = 1 2.7183 3.1416 2.7188 1 2 3.1563 2.7188 1 toeplitz(a,x) ans = 1 2 3 s8,5 2-672 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان toeplitz )toeplitz(x,a = ans 3 2 1 2-673 2 1 2.7188 1 2.7188 3.1563 s8,5 ﻣﺘﻠﺐ ﺳﺎﯾﺖ | www.MatlabSite.com ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان tostring Purpose Convert numerictype or quantizer object to string Syntax s = tostring(T) s = tostring(q) Description s = tostring(T) converts numerictype object T to a string s such that eval(s) would create a numerictype object with the same properties as T. s = tostring(q) converts quantizer object q to a string s. After converting q to a string, the function eval(s) can use s to create a quantizer object with the same properties as q. Examples This example uses the tostring function to convert a numerictype object T to a string s T = numerictype(true,16,15); s = tostring(T); T1 = eval(s); isequal(T,T1) ans = 1 See Also 2-674 eval | numerictype | quantizer www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان transpose Purpose Transpose operation Description Refer to the MATLAB transpose reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-675 treeplot Purpose Plot picture of tree Description Refer to the MATLAB treeplot reference page for more information. 2-676 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان tril Purpose Lower triangular part of matrix Description Refer to the MATLAB tril reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-677 trimesh Purpose Create triangular mesh plot Description Refer to the MATLAB trimesh reference page for more information. 2-678 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان triplot Purpose Create 2-D triangular plot Description Refer to the MATLAB triplot reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-679 trisurf Purpose Create triangular surface plot Description Refer to the MATLAB trisurf reference page for more information. 2-680 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان triu Purpose Upper triangular part of matrix Description Refer to the MATLAB triu reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-681 ufi Purpose Construct unsigned fixed-point numeric object Syntax a a a a a a Description You can use the ufi constructor function in the following ways: = = = = = = ufi ufi(v) ufi(v,w) ufi(v,w,f) ufi(v,w,slope,bias) ufi(v,w,slopeadjustmentfactor,fixedexponent,bias) • a = ufi is the default constructor and returns an unsigned fi object with no value, 16-bit word length, and 15-bit fraction length. • a = ufi(v) returns an unsigned fixed-point object with value v, 16-bit word length, and best-precision fraction length. • a = ufi(v,w) returns an unsigned fixed-point object with value v, word length w, and best-precision fraction length. • a = ufi(v,w,f) returns an unsigned fixed-point object with value v, word length w, and fraction length f. • a = ufi(v,w,slope,bias) returns an unsigned fixed-point object with value v, word length w, slope, and bias. • a = ufi(v,w,slopeadjustmentfactor,fixedexponent,bias) returns an unsigned fixed-point object with value v, word length w, slopeadjustmentfactor, fixedexponent, and bias. fi objects created by the ufi constructor function have the following general types of properties: • “Data Properties” on page 2-308 • “fimath Properties” on page 2-683 • “numerictype Properties” on page 2-310 These properties are described in detail in “fi Object Properties” on page 1-2 in the Properties Reference. 2-682 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان ufi Note fi objects created by the ufi constructor function have no local fimath. Data Properties The data properties of a fi object are always writable. • bin — Stored integer value of a fi object in binary • data — Numerical real-world value of a fi object • dec — Stored integer value of a fi object in decimal • double — Real-world value of a fi object, stored as a MATLAB double • hex — Stored integer value of a fi object in hexadecimal • int — Stored integer value of a fi object, stored in a built-in MATLAB integer data type. You can also use int8, int16, int32, int64, uint8, uint16, uint32, and uint64 to get the stored integer value of a fi object in these formats • oct — Stored integer value of a fi object in octal These properties are described in detail in “fi Object Properties” on page 1-2. fimath Properties When you create a fi object with the ufi constructor function, that fi object does not have a local fimath object. You can attach a fimath object to that fi object if you do not want to use the default fimath settings. For more information, see “fimath Object Construction” in the Fixed-Point Designer documentation. • fimath — fixed-point math object The following fimath properties are always writable and, by transitivity, are also properties of a fi object. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-683 ufi • CastBeforeSum — Whether both operands are cast to the sum data type before addition Note This property is hidden when the SumMode is set to FullPrecision. • OverflowAction — Action to take on overflow • ProductBias — Bias of the product data type • ProductFixedExponent — Fixed exponent of the product data type • ProductFractionLength — Fraction length, in bits, of the product data type • ProductMode — Defines how the product data type is determined • ProductSlope — Slope of the product data type • ProductSlopeAdjustmentFactor — Slope adjustment factor of the product data type • ProductWordLength — Word length, in bits, of the product data type • RoundingMethod — Rounding method • SumBias — Bias of the sum data type • SumFixedExponent — Fixed exponent of the sum data type • SumFractionLength — Fraction length, in bits, of the sum data type • SumMode — Defines how the sum data type is determined • SumSlope — Slope of the sum data type • SumSlopeAdjustmentFactor — Slope adjustment factor of the sum data type • SumWordLength — The word length, in bits, of the sum data type These properties are described in detail in “fimath Object Properties” on page 1-4. 2-684 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان ufi numerictype Properties When you create a fi object, a numerictype object is also automatically created as a property of the fi object. numerictype — Object containing all the data type information of a fi object, Simulink signal or model parameter The following numerictype properties are, by transitivity, also properties of a fi object. The properties of the numerictype object become read only after you create the fi object. However, you can create a copy of a fi object with new values specified for the numerictype properties. • Bias — Bias of a fi object • DataType — Data type category associated with a fi object • DataTypeMode — Data type and scaling mode of a fi object • FixedExponent — Fixed-point exponent associated with a fi object • SlopeAdjustmentFactor — Slope adjustment associated with a fi object • FractionLength — Fraction length of the stored integer value of a fi object in bits • Scaling — Fixed-point scaling mode of a fi object • Signed — Whether a fi object is signed or unsigned • Signedness — Whether a fi object is signed or unsigned Note numerictype objects can have a Signedness of Auto, but all fi objects must be Signed or Unsigned. If a numerictype object with Auto Signedness is used to create a fi object, the Signedness property of the fi object automatically defaults to Signed. • Slope — Slope associated with a fi object www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-685 ufi • WordLength — Word length of the stored integer value of a fi object in bits For further details on these properties, see “numerictype Object Properties” on page 1-15. Examples Note For information about the display format of fi objects, refer to “View Fixed-Point Data”. For examples of casting, see “Cast fi Objects”. Example 1 For example, the following creates an unsigned fi object with a value of pi, a word length of 8 bits, and a fraction length of 3 bits: a = ufi(pi,8,3) a = 3.1250 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Unsigned 8 3 Default fimath properties are associated with a. When a fi object does not have a local fimath object, no fimath object properties are displayed in its output. To determine whether a fi object has a local fimath object, use the isfimathlocal function. isfimathlocal(a) ans = 0 2-686 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان ufi A returned value of 0 means the fi object does not have a local fimath object. When the isfimathlocal function returns a 1, the fi object has a local fimath object. Example 2 The value v can also be an array: a = ufi((magic(3)/10),16,12) a = 0.8000 0.3000 0.3999 0.1001 0.5000 0.8999 DataTypeMode: Signedness: WordLength: FractionLength: 0.6001 0.7000 0.2000 Fixed-point: binary point scaling Unsigned 16 12 >> Example 3 If you omit the argument f, it is set automatically to the best precision possible: a = ufi(pi,8) a = 3.1406 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Unsigned 8 6 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-687 ufi Example 4 If you omit w and f, they are set automatically to 16 bits and the best precision possible, respectively: a = ufi(pi) a = 3.1416 DataTypeMode: Signedness: WordLength: FractionLength: See Also 2-688 Fixed-point: binary point scaling Unsigned 16 14 fi | fimath | fipref | isfimathlocal | numerictype | quantizer | sfi www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان uint8 Purpose Convert fi object to unsigned 8-bit integer Syntax c = uint8(a) Description c = uint8(a) returns the built-in uint8 value of fi object a, based on its real world value. If necessary, the data is rounded-to-nearest and saturated to fit into an uint8. Examples This example shows the uint8 values of a fi object. a = fi([-pi 0.5 pi],0,8); c = uint8(a) c = 0 See Also 1 3 storedInteger | int8 | int16 | int32 | int64 | uint16 | uint32 | uint64 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-689 uint16 Purpose Convert fi object to unsigned 16-bit integer Syntax c = uint16(a) Description c = uint16(a) returns the built-in uint16 value of fi object a, based Examples This example shows the uint16 values of a fi object. on its real world value. If necessary, the data is rounded-to-nearest and saturated to fit into an uint16. a = fi([-pi 0.5 pi],0,16); c = uint16(a) c = 0 See Also 2-690 1 3 storedInteger | int8 | int16 | int32 | int64 | uint8 | uint32 | uint64 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان uint32 Purpose Stored integer value of fi object as built-in uint32 Syntax c = uint32(a) Description c = uint32(a) returns the built-in uint32 value of fi object a, based Examples This example shows the uint32 values of a fi object. on its real world value. If necessary, the data is rounded-to-nearest and saturated to fit into an uint32. a = fi([-pi 0.5 pi],0,32); c = uint32(a) c = 0 See Also 1 3 storedInteger | int8 | int16 | int32 | int64 | uint8 | uint16 | uint64 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-691 uint64 Purpose Convert fi object to unsigned 64-bit integer Syntax c = uint64(a) Description c = uint64(a) returns the built-in uint64 value of fi object a, based Examples This example shows the uint64 values of a fi object. on its real world value. If necessary, the data is rounded-to-nearest and saturated to fit into an uint64. a = fi([-pi 0.5 pi],0,64); c = uint64(a) c = 0 See Also 2-692 1 3 storedInteger | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان uminus Purpose Negate elements of fi object array Syntax uminus(a) Description uminus(a) is called for the syntax -a when a is an object. -a negates the elements of a. uminus does not support fi objects of data type Boolean. Examples When wrap occurs, -(-1) = -1 : fipref('NumericTypeDisplay','short', ... 'fimathDisplay','none'); format short g a = fi(-1,true,8,7,'OverflowMode','wrap') a = -1 s8,7 -a ans = -1 s8,7 b = fi([-1-i -1-i],true,8,7,'OverflowMode','wrap') b = -1 - 1i -1 - 1i -1 - 1i -1 - 1i s8,7 -b ans = www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-693 uminus s8,7 b' ans = -1 -1 - 1i 1i s8,7 When saturation occurs, -(-1) = 0.99... : c = fi(-1,true,8,7,'OverflowMode','saturate') c = -1 s8,7 -c ans = 0.99219 s8,7 d = fi([-1-i -1-i],true,8,7,'OverflowMode','saturate') d = -1 - 1i -1 - 1i 0.99219 + s8,7 0.99219i 0.99219 + 0.99219i s8,7 -d ans = d' 2-694 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان uminus ans = -1 + -1 + 0.99219i 0.99219i s8,7 See Also plus | minus | mtimes | times www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-695 unitquantize Purpose Quantize except numbers within eps of +1 Syntax y = unitquantize(q, x) [y1,y2,...] = unitquantize(q,x1,x2,...) Description y = unitquantize(q, x) works the same as quantize except that numbers within eps(q) of +1 are made exactly equal to +1 . [y1,y2,...] = unitquantize(q,x1,x2,...) is equivalent to y1 = unitquantize(q,x1), y2 = unitquantize(q,x2),... Examples This example demonstrates the use of unitquantize with a quantizer object q and a vector x. q x y z e = = = = = quantizer('fixed','floor','saturate',[4 3]); (0.8:.1:1.2)'; unitquantize(q,x); [x y] eps(q) This quantization outputs an array containing the original values of x and the quantized values of x, followed by the value of eps(q): z = 0.8000 0.9000 1.0000 1.1000 1.2000 0.7500 1.0000 1.0000 1.0000 1.0000 e = 0.1250 2-696 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان unitquantize See Also eps | quantize | quantizer | unitquantizer www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-697 unitquantizer Purpose Constructor for unitquantizer object Syntax q = unitquantizer(...) Description q = unitquantizer(...) constructs a unitquantizer object, which is the same as a quantizer object in all respects except that its quantize method quantizes numbers within eps(q) of +1 to exactly +1. See quantizer for parameters. Examples In this example, a vector x is quantized by a unitquantizer object u . u x y z e = = = = = unitquantizer([4 3]); (0.8:.1:1.2)'; quantize(u,x); [x y] eps(u) This quantization outputs an array containing the original values of x and the values of x that were quantized by the unitquantizer object u. The output also includes e, the value of eps(u). z = 0.8000 0.9000 1.0000 1.1000 1.2000 0.7500 1.0000 1.0000 1.0000 1.0000 e = 0.1250 See Also 2-698 quantize | quantizer | unitquantize www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان unshiftdata Purpose Inverse of shiftdata Syntax y = unshiftdata(x,perm,nshifts) Description y = unshiftdata(x,perm,nshifts) restores the orientation of the data that was shifted with shiftdata. The permutation vector is given by perm, and nshifts is the number of shifts that was returned from shiftdata. unshiftdata is meant to be used in tandem with shiftdata. These functions are useful for creating functions that work along a certain dimension, like filter, goertzel, sgolayfilt, and sosfilt. Examples Example 1 This example shifts x, a 3-by-3 magic square, permuting dimension 2 to the first column. unshiftdata shifts x back to its original shape. 1. Create a 3-by-3 magic square: x = fi(magic(3)) x = 8 3 4 1 5 9 6 7 2 2. Shift the matrix x to work along the second dimension: [x,perm,nshifts] = shiftdata(x,2) This command returns the permutation vector, perm, and the number of shifts, nshifts, are returned along with the shifted matrix, x: x = www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-699 unshiftdata 8 1 6 3 5 7 4 9 2 perm = 2 1 nshifts = [] 3. Shift the matrix back to its original shape: y = unshiftdata(x,perm,nshifts) y = 8 3 4 1 5 9 6 7 2 Example 2 This example shows how shiftdata and unshiftdata work when you define dim as empty. 1. Define x as a row vector: x = 1:5 x = 1 2-700 2 3 4 5 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان unshiftdata 2. Define dim as empty to shift the first non-singleton dimension of x to the first column: [x,perm,nshifts] = shiftdata(x,[]) This command returns x as a column vector, along with perm, the permutation vector, and nshifts, the number of shifts: x = 1 2 3 4 5 perm = [] nshifts = 1 3. Using unshiftdata, restore x to its original shape: y = unshiftdata(x,perm,nshifts) y = 1 See Also 2 3 4 5 ipermute | shiftdata | shiftdim www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-701 uplus Purpose Unary plus Description Refer to the MATLAB uplus reference page for more information. 2-702 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان upperbound Purpose Upper bound of range of fi object Syntax upperbound(a) Description upperbound(a) returns the upper bound of the range of fi object a. If L = lowerbound(a) and U = upperbound(a), then [L,U] = range(a). See Also eps | intmax | intmin | lowerbound | lsb | range | realmax | realmin www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-703 vertcat Purpose Vertically concatenate multiple fi objects Syntax c = vertcat(a,b,...) [a; b; ...] [a;b] Description c = vertcat(a,b,...) is called for the syntax [a; b; ...] when any of a, b, ... , is a fi object. [a;b] is the vertical concatenation of matrices a and b. a and b must have the same number of columns. Any number of matrices can be concatenated within one pair of brackets. N-D arrays are vertically concatenated along the first dimension. The remaining dimensions must match. Horizontal and vertical concatenation can be combined, as in [1 2;3 4]. [a b; c] is allowed if the number of rows of a equals the number of rows of b, and if the number of columns of a plus the number of columns of b equals the number of columns of c. The matrices in a concatenation expression can themselves be formed via a concatenation, as in [a b;[c d]]. Note The fimath and numerictype objects of a concatenated matrix of fi objects c are taken from the leftmost fi object in the list (a,b,...). See Also 2-704 horzcat www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان voronoi Purpose Create Voronoi diagram Description Refer to the MATLAB voronoi reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-705 voronoin Purpose Create n-D Voronoi diagram Description Refer to the MATLAB voronoin reference page for more information. 2-706 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان waterfall Purpose Create waterfall plot Description Refer to the MATLAB waterfall reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-707 wordlength Purpose Word length of quantizer object Syntax wordlength(q) Description wordlength(q) returns the word length of the quantizer object q. Examples q = quantizer([16 15]); wordlength(q) ans = 16 See Also 2-708 fi | fractionlength | exponentlength | numerictype | quantizer www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان xlim Purpose Set or query x-axis limits Description Refer to the MATLAB xlim reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-709 xor Purpose Logical exclusive-OR Description Refer to the MATLAB xor reference page for more information. 2-710 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان ylim Purpose Set or query y-axis limits Description Refer to the MATLAB ylim reference page for more information. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-711 zeros Purpose Create array of all zeros with fixed-point properties Syntax X X X X Description X = zeros('like',p) returns a scalar 0 with the same numerictype, complexity (real or complex), and fimath as p. = = = = zeros('like',p) zeros(n,'like',p) zeros(sz1,...,szN,'like',p) zeros(sz,'like',p) X = zeros(n,'like',p) returns an n-by-n array of zeros like p. X = zeros(sz1,...,szN,'like',p) returns an sz1-by-...-by-szN array of zeros like p. X = zeros(sz,'like',p) returns an array of zeros like p. The size vector, sz, defines size(X). Input Arguments n - Size of square matrix integer value Size of square matrix, specified as an integer value, defines the output as a square, n-by-n matrix of ones. • If n is zero, X is an empty matrix. • If n is negative, it is treated as zero. Data Types double | single | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 sz1,...,szN - Size of each dimension two or more integer values Size of each dimension, specified as two or more integer values, defines X as a sz1-by...-by-szN array. 2-712 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان zeros • If the size of any dimension is zero, X is an empty array. • If the size of any dimension is negative, it is treated as zero. • If any trailing dimensions greater than two have a size of one, the output, X, does not include those dimensions. Data Types double | single | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 sz - Output size row vector of integer values Output size, specified as a row vector of integer values. Each element of this vector indicates the size of the corresponding dimension. • If the size of any dimension is zero, X is an empty array. • If the size of any dimension is negative, it is treated as zero. • If any trailing dimensions greater than two have a size of one, the output, X, does not include those dimensions. Example: sz = [2,3,4] defines X as a 2-by-3-by-4 array. Data Types double | single | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 p - Prototype fi object | numeric variable Prototype, specified as a fi object or numeric variable. To use the prototype to specify a complex object, you must specify a value for the prototype. Otherwise, you do not need to specify a value. Complex Number Support: Yes Tips Using the b = cast(a,'like',p) syntax to specify data types separately from algorithm code allows you to: www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-713 zeros • Reuse your algorithm code with different data types. • Keep your algorithm uncluttered with data type specifications and switch statements for different data types. • Improve readability of your algorithm code. • Switch between fixed-point and floating-point data types to compare baselines. • Switch between variations of fixed-point settings without changing the algorithm code. Examples 2-D Array of Zeros With Fixed-Point Attributes Create a 2-by-3 array of zeros with specified numerictype and fimath properties. Create a signed fi object with word length of 24 and fraction length of 12. p = fi([],1,24,12); Create a 2-by-3 array of zeros that has the same numerictype properties as p. X = zeros(2,3,'like',p) X = 0 0 0 0 0 0 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 16 8 Size Defined by Existing Array Define a 3-by-2 array A. 2-714 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان zeros A = [1 4 ; 2 5 ; 3 6]; sz = size(A) sz = 3 2 Create a signed fi object with word length of 24 and fraction length of 12. p = fi([],1,24,12); Create an array of zeros that is the same size as A and has the same numerictype properties as p. X = zeros(sz,'like',p) X = 0 0 0 0 0 0 DataTypeMode: Signedness: WordLength: FractionLength: Fixed-point: binary point scaling Signed 24 12 Square Array of Zeros With Fixed-Point Attributes Create a 4-by-4 array of zeros with specified numerictype and fimath properties. Create a signed fi object with word length of 24 and fraction length of 12. p = fi([],1,24,12); www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-715 zeros Create a 4-by-4 array of zeros that has the same numerictype properties as p. X = zeros(4, 'like', p) X = 0 0 0 0 0 0 0 0 0 0 0 0 DataTypeMode: Signedness: WordLength: FractionLength: 0 0 0 0 Fixed-point: binary point scaling Signed 24 12 Complex Fixed-Point Zero Create a scalar fixed-point 0 that is not real valued, but instead is complex like an existing array. Define a complex fi object. p = fi( [1+2i 3i],1,24,12); Create a scalar 1 that is complex like p. X = zeros('like',p) X = 0.0000 + 0.0000i DataTypeMode: Signedness: WordLength: FractionLength: 2-716 Fixed-point: binary point scaling Signed 24 12 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان zeros Write MATLAB Code That Is Independent of Data Types Write a MATLAB algorithm that you can run with different data types without changing the algorithm itself. To reuse the algorithm, define the data types separately from the algorithm. This approach allows you to define a baseline by running the algorithm with floating-point data types. You can then test the algorithm with different fixed-point data types and compare the fixed-point behavior to the baseline without making any modifications to the original MATLAB code. Write a MATLAB function, my_filter, that takes an input parameter, T, which is a structure that defines the data types of the coefficients and the input and output data. function [y,z] = my_filter(b,a,x,z,T) % Cast the coefficients to the coefficient type b = cast(b,'like',T.coeffs); a = cast(a,'like',T.coeffs); % Create the output using zeros with the data type y = zeros(size(x),'like',T.data); for i=1:length(x) y(i) = b(1)*x(i) + z(1); z(1) = b(2)*x(i) + z(2) - a(2) * y(i); z(2) = b(3)*x(i) - a(3) * y(i); end end Write a MATLAB function, zeros_ones_cast_example, that calls my_filter with a floating-point step input and a fixed-point step input, and then compares the results. function zeros_ones_cast_example % Define coefficients for a filter with specification % [b,a] = butter(2,0.25) b = [0.097631072937818 0.195262145875635 0.097631072937818]; www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-717 zeros a = [1.000000000000000 -0.942809041582063 0.333333333333333]; % Define floating-point types T_float.coeffs = double([]); T_float.data = double([]); % Create a step input using ones with the % floating-point data type t = 0:20; x_float = ones(size(t),'like',T_float.data); % Initialize the states using zeros with the % floating-point data type z_float = zeros(1,2,'like',T_float.data); % Run the floating-point algorithm y_float = my_filter(b,a,x_float,z_float,T_float); % Define fixed-point types T_fixed.coeffs = fi([],true,8,6); T_fixed.data = fi([],true,8,6); % Create a step input using ones with the % fixed-point data type x_fixed = ones(size(t),'like',T_fixed.data); % Initialize the states using zeros with the % fixed-point data type z_fixed = zeros(1,2,'like',T_fixed.data); % Run the fixed-point algorithm y_fixed = my_filter(b,a,x_fixed,z_fixed,T_fixed); % Compare the results coder.extrinsic('clf','subplot','plot','legend'); clf subplot(211) 2-718 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان zeros plot(t,y_float,'co-',t,y_fixed,'kx-') legend('Floating-point output','Fixed-point output'); title('Step response'); subplot(212) plot(t,y_float - double(y_fixed),'rs-') legend('Error') figure(gcf) end See Also cast | ones | zeros Related Examples • “Implement FIR Filter Algorithm for Floating-Point and Fixed-Point Types using cast and zeros” Concepts • “Command-Line Fixed-Point Conversion Workflow” • “Command-Line Fixed-Point Conversion Best Practices” www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان 2-719 zlim Purpose Set or query z-axis limits Description Refer to the MATLAB zlim reference page for more information. 2-720 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان Glossary Glossary This glossary defines terms related to fixed-point data types and numbers. These terms may appear in some or all of the documents that describe MathWorks products that have fixed-point support. arithmetic shift Shift of the bits of a binary word for which the sign bit is recycled for each bit shift to the right. A zero is incorporated into the least significant bit of the word for each bit shift to the left. In the absence of overflows, each arithmetic shift to the right is equivalent to a division by 2, and each arithmetic shift to the left is equivalent to a multiplication by 2. See also binary point, binary word, bit, logical shift, most significant bit bias Part of the numerical representation used to interpret a fixed-point number. Along with the slope, the bias forms the scaling of the number. Fixed-point numbers can be represented as real-world value = (slope × stored integer) + bias where the slope can be expressed as slope = fractional slope × 2exponent See also fixed-point representation, fractional slope, integer, scaling, slope, [Slope Bias] binary number Value represented in a system of numbers that has two as its base and that uses 1’s and 0’s (bits) for its notation. See also bit www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان Glossary-1 Glossary binary point Symbol in the shape of a period that separates the integer and fractional parts of a binary number. Bits to the left of the binary point are integer bits and/or sign bits, and bits to the right of the binary point are fractional bits. See also binary number, bit, fraction, integer, radix point binary point-only scaling Scaling of a binary number that results from shifting the binary point of the number right or left, and which therefore can only occur by powers of two. See also binary number, binary point, scaling binary word Fixed-length sequence of bits (1’s and 0’s). In digital hardware, numbers are stored in binary words. The way in which hardware components or software functions interpret this sequence of 1’s and 0’s is described by a data type. See also bit, data type, word bit Smallest unit of information in computer software or hardware. A bit can have the value 0 or 1. ceiling (round toward) Rounding mode that rounds to the closest representable number in the direction of positive infinity. This is equivalent to the ceil mode in Fixed-Point Designer software. See also convergent rounding, floor (round toward), nearest (round toward), rounding, truncation, zero (round toward) Glossary-2 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان Glossary contiguous binary point Binary point that occurs within the word length of a data type. For example, if a data type has four bits, its contiguous binary point must be understood to occur at one of the following five positions: .0000 0.000 00.00 000.0 0000. See also data type, noncontiguous binary point, word length convergent rounding Rounding mode that rounds to the nearest allowable quantized value. Numbers that are exactly halfway between the two nearest allowable quantized values are rounded up only if the least significant bit (after rounding) would be set to 0. See also ceiling (round toward), floor (round toward), nearest (round toward), rounding, truncation, zero (round toward) data type Set of characteristics that define a group of values. A fixed-point data type is defined by its word length, its fraction length, and whether it is signed or unsigned. A floating-point data type is defined by its word length and whether it is signed or unsigned. See also fixed-point representation, floating-point representation, fraction length, signedness, word length data type override Parameter in the Fixed-Point Tool that allows you to set the output data type and scaling of fixed-point blocks on a system or subsystem level. See also data type, scaling exponent Part of the numerical representation used to express a floating-point or fixed-point number. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان Glossary-3 Glossary 1. Floating-point numbers are typically represented as real - world value = mantissa × 2exponent 2. Fixed-point numbers can be represented as real-world value = (slope × stored integer) + bias where the slope can be expressed as slope = fractional slope × 2exponent The exponent of a fixed-point number is equal to the negative of the fraction length: exponent = −1 × fraction length See also bias, fixed-point representation, floating-point representation, fraction length, fractional slope, integer, mantissa, slope fixed-point representation Method for representing numerical values and data types that have a set range and precision. 1. Fixed-point numbers can be represented as real-world value = (slope × stored integer) + bias where the slope can be expressed as slope = fractional slope × 2exponent The slope and the bias together represent the scaling of the fixed-point number. 2. Fixed-point data types can be defined by their word length, their fraction length, and whether they are signed or unsigned. See also bias, data type, exponent, fraction length, fractional slope, integer, precision, range, scaling, slope, word length Glossary-4 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان Glossary floating-point representation Method for representing numerical values and data types that can have changing range and precision. 1. Floating-point numbers can be represented as real - world value = mantissa × 2exponent 2. Floating-point data types are defined by their word length. See also data type, exponent, mantissa, precision, range, word length floor (round toward) Rounding mode that rounds to the closest representable number in the direction of negative infinity. See also ceiling (round toward), convergent rounding, nearest (round toward), rounding, truncation, zero (round toward) fraction Part of a fixed-point number represented by the bits to the right of the binary point. The fraction represents numbers that are less than one. See also binary point, bit, fixed-point representation fraction length Number of bits to the right of the binary point in a fixed-point representation of a number. See also binary point, bit, fixed-point representation, fraction www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان Glossary-5 Glossary fractional slope Part of the numerical representation used to express a fixed-point number. Fixed-point numbers can be represented as real-world value = (slope × stored integer) + bias where the slope can be expressed as slope = fractional slope × 2exponent The term slope adjustment is sometimes used as a synonym for fractional slope. See also bias, exponent, fixed-point representation, integer, slope full range The broadest range available for a data type. From –∞ to ∞ for floating-point types. For integer types, the representable range is the range from the smallest to largest integer value (finite) the type can represent. For example, from -128 to 127 for a signed 8–bit integer. Also known as representable range. guard bits Extra bits in either a hardware register or software simulation that are added to the high end of a binary word to ensure that no information is lost in case of overflow. See also binary word, bit, overflow incorrect range A range that is too restrictive and does not include values that can actually occur in the model element. A range that is too broad is not considered incorrect because it will not lead to overflow. See also range analysis integer 1. Part of a fixed-point number represented by the bits to the left of the binary point. The integer represents numbers that are greater than or equal to one. Glossary-6 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان Glossary 2. Also called the "stored integer." The raw binary number, in which the binary point is assumed to be at the far right of the word. The integer is part of the numerical representation used to express a fixed-point number. Fixed-point numbers can be represented as real - world value = 2− fraction length × stored integer or real-world value = (slope × stored integer) + bias where the slope can be expressed as slope = fractional slope × 2exponent See also bias, fixed-point representation, fractional slope, integer, real-world value, slope integer length Number of bits to the left of the binary point in a fixed-point representation of a number. See also binary point, bit, fixed-point representation, fraction length, integer least significant bit (LSB) Bit in a binary word that can represent the smallest value. The LSB is the rightmost bit in a big-endian-ordered binary word. The weight of the LSB is related to the fraction length according to weight of LSB = 2− fraction length See also big-endian, binary word, bit, most significant bit www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان Glossary-7 Glossary logical shift Shift of the bits of a binary word, for which a zero is incorporated into the most significant bit for each bit shift to the right and into the least significant bit for each bit shift to the left. See also arithmetic shift, binary point, binary word, bit, most significant bit mantissa Part of the numerical representation used to express a floating-point number. Floating-point numbers are typically represented as real - world value = mantissa × 2exponent See also exponent, floating-point representation model element Entities in a model that range analysis software tracks, for example, blocks, signals, parameters, block internal data (such as accumulators, products). See also range analysis most significant bit (MSB) Bit in a binary word that can represent the largest value. The MSB is the leftmost bit in a big-endian-ordered binary word. See also binary word, bit, least significant bit nearest (round toward) Rounding mode that rounds to the closest representable number, with the exact midpoint rounded to the closest representable number in the direction of positive infinity. This is equivalent to the nearest mode in Fixed-Point Designer software. See also ceiling (round toward), convergent rounding, floor (round toward), rounding, truncation, zero (round toward) Glossary-8 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان Glossary noncontiguous binary point Binary point that is understood to fall outside the word length of a data type. For example, the binary point for the following 4-bit word is understood to occur two bits to the right of the word length, 0000 . thereby giving the bits of the word the following potential values: 25 24 23 22 . See also binary point, data type, word length one’s complement representation Representation of signed fixed-point numbers. Negating a binary number in one’s complement requires a bitwise complement. That is, all 0’s are flipped to 1’s and all 1’s are flipped to 0’s. In one’s complement notation there are two ways to represent zero. A binary word of all 0’s represents "positive" zero, while a binary word of all 1’s represents "negative" zero. See also binary number, binary word, sign/magnitude representation, signed fixed-point, two’s complement representation overflow Situation that occurs when the magnitude of a calculation result is too large for the range of the data type being used. In many cases you can choose to either saturate or wrap overflows. See also saturation, wrapping padding Extending the least significant bit of a binary word with one or more zeros. See also least significant bit precision 1. Measure of the smallest numerical interval that a fixed-point data type and scaling can represent, determined by the value of the number’s least significant bit. The precision is given by the slope, or the number www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان Glossary-9 Glossary of fractional bits. The term resolution is sometimes used as a synonym for this definition. 2. Measure of the difference between a real-world numerical value and the value of its quantized representation. This is sometimes called quantization error or quantization noise. See also data type, fraction, least significant bit, quantization, quantization error, range, slope Q format Representation used by Texas Instruments™ to encode signed two’s complement fixed-point data types. This fixed-point notation takes the form Qm.n where • Q indicates that the number is in Q format. • m is the number of bits used to designate the two’s complement integer part of the number. • n is the number of bits used to designate the two’s complement fractional part of the number, or the number of bits to the right of the binary point. In Q format notation, the most significant bit is assumed to be the sign bit. See also binary point, bit, data type, fixed-point representation, fraction, integer, two’s complement quantization Representation of a value by a data type that has too few bits to represent it exactly. See also bit, data type, quantization error quantization error Error introduced when a value is represented by a data type that has too few bits to represent it exactly, or when a value is converted from Glossary-10 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان Glossary one data type to a shorter data type. Quantization error is also called quantization noise. See also bit, data type, quantization radix point Symbol in the shape of a period that separates the integer and fractional parts of a number in any base system. Bits to the left of the radix point are integer and/or sign bits, and bits to the right of the radix point are fraction bits. See also binary point, bit, fraction, integer, sign bit range Span of numbers that a certain data type can represent. See also data type, full range, precision, representable range www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان Glossary-11 Glossary range analysis Static analysis of model to derive minimum and maximum range values for elements in the model. The software statically analyzes the ranges of the individual computations in the model based on specified design ranges, inputs, and the semantics of the calculation. real-world value Stored integer value with fixed-point scaling applied. Fixed-point numbers can be represented as real - world value = 2− fraction length × stored integer or real-world value = (slope × stored integer) + bias where the slope can be expressed as slope = fractional slope × 2exponent See also integer representable range The broadest range available for a data type. From –∞ to ∞ for floating-point types. For integer types, the representable range is the range from the smallest to largest integer value (finite) the type can represent. For example, from -128 to 127 for a signed 8–bit integer. Also known as full range. resolution See precision rounding Limiting the number of bits required to express a number. One or more least significant bits are dropped, resulting in a loss of precision. Rounding is necessary when a value cannot be expressed exactly by the number of bits designated to represent it. Glossary-12 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان Glossary See also bit, ceiling (round toward), convergent rounding, floor (round toward), least significant bit, nearest (round toward), precision, truncation, zero (round toward) saturation Method of handling numeric overflow that represents positive overflows as the largest positive number in the range of the data type being used, and negative overflows as the largest negative number in the range. See also overflow, wrapping scaled double A double data type that retains fixed-point scaling information. For example, in Simulink and Fixed-Point Designer software you can use data type override to convert your fixed-point data types to scaled doubles. You can then simulate to determine the ideal floating-point behavior of your system. After you gather that information you can turn data type override off to return to fixed-point data types, and your quantities still have their original scaling information because it was held in the scaled double data types. scaling 1. Format used for a fixed-point number of a given word length and signedness. The slope and bias together form the scaling of a fixed-point number. 2. Changing the slope and/or bias of a fixed-point number without changing the stored integer. See also bias, fixed-point representation, integer, slope shift Movement of the bits of a binary word either toward the most significant bit ("to the left") or toward the least significant bit ("to the right"). Shifts to the right can be either logical, where the spaces emptied at the front of the word with each shift are filled in with zeros, or arithmetic, where the word is sign extended as it is shifted to the right. See also arithmetic shift, logical shift, sign extension www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان Glossary-13 Glossary sign bit Bit (or bits) in a signed binary number that indicates whether the number is positive or negative. See also binary number, bit sign extension Addition of bits that have the value of the most significant bit to the high end of a two’s complement number. Sign extension does not change the value of the binary number. See also binary number, guard bits, most significant bit, two’s complement representation, word Glossary-14 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان Glossary sign/magnitude representation Representation of signed fixed-point or floating-point numbers. In sign/magnitude representation, one bit of a binary word is always the dedicated sign bit, while the remaining bits of the word encode the magnitude of the number. Negation using sign/magnitude representation consists of flipping the sign bit from 0 (positive) to 1 (negative), or from 1 to 0. See also binary word, bit, fixed-point representation, floating-point representation, one’s complement representation, sign bit, signed fixed-point, signedness, two’s complement representation signed fixed-point Fixed-point number or data type that can represent both positive and negative numbers. See also data type, fixed-point representation, signedness, unsigned fixed-point signedness The signedness of a number or data type can be signed or unsigned. Signed numbers and data types can represent both positive and negative values, whereas unsigned numbers and data types can only represent values that are greater than or equal to zero. See also data type, sign bit, sign/magnitude representation, signed fixed-point, unsigned fixed-point slope Part of the numerical representation used to express a fixed-point number. Along with the bias, the slope forms the scaling of a fixed-point number. Fixed-point numbers can be represented as real-world value = (slope × stored integer) + bias where the slope can be expressed as slope = fractional slope × 2exponent www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان Glossary-15 Glossary See also bias, fixed-point representation, fractional slope, integer, scaling, [Slope Bias] slope adjustment See fractional slope [Slope Bias] Representation used to define the scaling of a fixed-point number. See also bias, scaling, slope stored integer See integer trivial scaling Scaling that results in the real-world value of a number being simply equal to its stored integer value: real - world value = stored integer In [Slope Bias] representation, fixed-point numbers can be represented as real-world value = (slope × stored integer) + bias In the trivial case, slope = 1 and bias = 0. In terms of binary point-only scaling, the binary point is to the right of the least significant bit for trivial scaling, meaning that the fraction length is zero: real - world value = stored integer × 2− fraction length = stored integer × 20 Scaling is always trivial for pure integers, such as int8, and also for the true floating-point types single and double. See also bias, binary point, binary point-only scaling, fixed-point representation, fraction length, integer, least significant bit, scaling, slope, [Slope Bias] Glossary-16 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان Glossary truncation Rounding mode that drops one or more least significant bits from a number. See also ceiling (round toward), convergent rounding, floor (round toward), nearest (round toward), rounding, zero (round toward) two’s complement representation Common representation of signed fixed-point numbers. Negation using signed two’s complement representation consists of a translation into one’s complement followed by the binary addition of a one. See also binary word, one’s complement representation, sign/magnitude representation, signed fixed-point unsigned fixed-point Fixed-point number or data type that can only represent numbers greater than or equal to zero. See also data type, fixed-point representation, signed fixed-point, signedness word Fixed-length sequence of binary digits (1’s and 0’s). In digital hardware, numbers are stored in words. The way hardware components or software functions interpret this sequence of 1’s and 0’s is described by a data type. See also binary word, data type word length Number of bits in a binary word or data type. See also binary word, bit, data type wrapping Method of handling overflow. Wrapping uses modulo arithmetic to cast a number that falls outside of the representable range the data type being used back into the representable range. See also data type, overflow, range, saturation www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان Glossary-17 Glossary zero (round toward) Rounding mode that rounds to the closest representable number in the direction of zero. This is equivalent to the fix mode in Fixed-Point Designer software. See also ceiling (round toward), convergent rounding, floor (round toward), nearest (round toward), rounding, truncation Glossary-18 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان A Selected Bibliography [1] Burrus, C.S., J.H. McClellan, A.V. Oppenheim, T.W. Parks, R.W. Schafer, and H.W. Schuessler, Computer-Based Exercises for Signal Processing Using MATLAB, Prentice Hall, Englewood Cliffs, New Jersey, 1994. [2] Franklin, G.F., J.D. Powell, and M.L. Workman, Digital Control of Dynamic Systems, Second Edition, Addison-Wesley Publishing Company, Reading, Massachusetts, 1990. [3] Handbook For Digital Signal Processing, edited by S.K. Mitra and J.F. Kaiser, John Wiley & Sons, Inc., New York, 1993. [4] Hanselmann, H., “Implementation of Digital Controllers — A Survey,” Automatica, Vol. 23, No. 1, pp. 7-32, 1987. [5] Jackson, L.B., Digital Filters and Signal Processing, Second Edition, Kluwer Academic Publishers, Seventh Printing, Norwell, Massachusetts, 1993. [6] Middleton, R. and G. Goodwin, Digital Control and Estimation — A Unified Approach, Prentice Hall, Englewood Cliffs, New Jersey. 1990. [7] Moler, C., “Floating points: IEEE Standard unifies arithmetic model,” Cleve’s Corner, The MathWorks, Inc., 1996. You can find this article at http://www.mathworks.com/company/newsletters/news_notes/clevescorner/index.html. [8] Ogata, K., Discrete-Time Control Systems, Second Edition, Prentice Hall, Englewood Cliffs, New Jersey, 1995. [9] Roberts, R.A. and C.T. Mullis, Digital Signal Processing, Addison-Wesley Publishing Company, Reading, Massachusetts, 1987. www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان Selected Bibliography ﻣﺘﻠﺐ ﺳﺎﯾﺖ | www.MatlabSite.com ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان A A-2 Index A Index abs function 2-2 accelerating fixed-point code 2-322 add function 2-17 all function 2-19 and function 2-20 any function 2-21 area function 2-22 assignmentquantizer function 2-23 autofixexp function 2-29 automatic scaling autofixexp 2-29 fixpt_instrument_purge 2-352 script 2-29 autoscaling autofixexp 2-29 fixpt_instrument_purge 2-352 script 2-29 B bar function 2-31 barh function 2-32 Bias property 1-15 bin function 2-33 bin property 1-2 bin2num function 2-34 bitand function 2-36 bitcmp function 2-41 bitor function 2-53 bitreplicate function 2-59 bitshift function 2-70 bitxor function 2-85 buffer function 2-91 C CastBeforeSum property 1-4 ceil function 2-108 clabel function 2-111 code generation from MATLAB resolving extrinsic function calls in generated code 2-140 coder.inline function 2-146 coder.nullcopy function 2-167 comet function 2-215 comet3 function 2-216 compass function 2-217 complex function 2-218 coneplot function 2-219 conj function 2-220 contour function 2-221 contour3 function 2-222 contourc function 2-223 contourf function 2-224 Controlling inlining in generated code 2-146 conv function 2-225 convergent function 2-227 copyobj function 2-230 cordicabs function 2-231 cordicangle function 2-234 cordicatan2 function 2-237 cordiccart2pol function 2-240 cordiccexp function 2-244 cordiccos function 2-247 cordicpol2cart function 2-252 cordicrotate function 2-256 cordicsin function 2-260 cordicsincos function 2-265 ctranspose function 2-271 D data property 1-2 DataType property 1-15 DataTypeMode property 1-15 DataTypeOverride property 1-12 1-16 DataTypeOverrideAppliesTo property 1-12 dec function 2-272 dec property 1-2 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان Index-1 Index Declaring uninitialized variables 2-167 denormalmax function 2-273 denormalmin function 2-274 diag function 2-275 disp function 2-276 div function 2-277 double function 2-282 double property 1-2 E end function 2-283 eps function 2-284 eq function 2-285 errmean function 2-286 errorbar function 2-287 errpdf function 2-288 errvar function 2-291 etreeplot function 2-292 exponentbias function 2-293 exponentlength function 2-294 exponentmax function 2-295 exponentmin function 2-296 ezcontour function 2-297 ezcontourf function 2-298 ezmesh function 2-299 ezplot function 2-300 ezplot3 function 2-301 ezpolar function 2-302 ezsurf function 2-303 ezsurfc function 2-304 F feather function 2-305 fi function 2-306 fi objects properties bin 1-2 data 1-2 Index-2 dec 1-2 double 1-2 fimath 1-2 hex 1-3 NumericType 1-3 oct 1-3 fiaccel function 2-322 filter function 2-328 fimath function 2-333 fimath objects properties CastBeforeSum 1-4 MaxProductWordLength 1-4 MaxSumWordLength 1-4 OverflowMode 1-4 ProductBias 1-5 ProductFixedExponent 1-5 ProductFractionLength 1-5 ProductMode 1-5 ProductSlope 1-7 ProductSlopeAdjustmentFactor 1-7 ProductWordLength 1-7 RoundMode 1-8 SumBias 1-8 SumFixedExponent 1-8 SumFractionLength 1-9 SumMode 1-9 SumSlope 1-11 SumSlopeAdjustmentFactor 1-11 SumWordLength 1-11 fimath property 1-2 FimathDisplay property 1-12 fipref function 2-336 fipref objects properties DataTypeOverride 1-12 DataTypeOverrideAppliesTo 1-12 FimathDisplay 1-12 LoggingMode 1-13 NumberDisplay 1-14 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان Index NumericTypeDisplay 1-13 fix function 2-339 FixedExponent property 1-16 fixpt_instrument_purge function 2-352 flipdim function 2-353 fliplr function 2-354 flipud function 2-355 floor function 2-356 format rat 1-14 Format property 1-20 fplot function 2-359 fractionlength function 2-360 FractionLength property 1-17 function line 2-431 functions abs 2-2 add 2-17 all 2-19 and 2-20 any 2-21 area 2-22 assignmentquantizer 2-23 autofixexp 2-29 bar 2-31 barh 2-32 bin 2-33 bin2num 2-34 bitand 2-36 bitcmp 2-41 bitor 2-53 bitreplicate 2-59 bitshift 2-70 bitxor 2-85 buffer 2-91 ceil 2-108 clabel 2-111 comet 2-215 comet3 2-216 compass 2-217 complex 2-218 coneplot 2-219 conj 2-220 contour 2-221 contour3 2-222 contourc 2-223 contourf 2-224 conv 2-225 convergent 2-227 copyobj 2-230 cordicabs 2-231 cordicangle 2-234 cordicatan2 2-237 cordiccart2pol 2-240 cordiccexp 2-244 cordiccos 2-247 cordicpol2cart 2-252 cordicrotate 2-256 cordicsin 2-260 cordicsincos 2-265 ctranspose 2-271 dec 2-272 denormalmax 2-273 denormalmin 2-274 diag 2-275 disp 2-276 div 2-277 double 2-282 end 2-283 eps 2-284 eq 2-285 errmean 2-286 errorbar 2-287 errpdf 2-288 errvar 2-291 etreeplot 2-292 exponentbias 2-293 exponentlength 2-294 exponentmax 2-295 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان Index-3 Index exponentmin 2-296 ezcontour 2-297 ezcontourf 2-298 ezmesh 2-299 ezplot 2-300 ezplot3 2-301 ezpolar 2-302 ezsurf 2-303 ezsurfc 2-304 feather 2-305 fi 2-306 filter 2-328 fimath 2-333 fipref 2-336 fix 2-339 fixpt_instrument_purge 2-352 flipdim 2-353 fliplr 2-354 flipud 2-355 floor 2-356 fplot 2-359 fractionlength 2-360 ge 2-361 get 2-362 getlsb 2-363 getmsb 2-364 gplot 2-367 gt 2-368 hankel 2-369 hex 2-380 hex2num 2-384 hist 2-385 histc 2-386 horzcat 2-387 imag 2-388 int16 2-392 int32 2-393 int64 2-394 int8 2-391 intmax 2-395 Index-4 intmin 2-396 ipermute 2-397 isboolean 2-398 iscolumn 2-399 isdouble 2-400 isempty 2-401 isequal 2-402 isfi 2-403 isfimath 2-404 isfimathlocal 2-405 isfinite 2-406 isfipref 2-407 isfixed 2-408 isfloat 2-409 isinf 2-410 isnan 2-411 isnumeric 2-412 isnumerictype 2-413 isobject 2-414 isquantizer 2-416 isreal 2-417 isrow 2-418 isscalar 2-419 isscaleddouble 2-420 isscaledtype 2-421 isscalingbinarypoint 2-422 isscalingslopebias 2-423 isscalingunspecified 2-424 issigned 2-425 issingle 2-426 isslopebiasscaled 2-427 isvector 2-428 le 2-429 length 2-430 logical 2-432 loglog 2-433 logreport 2-434 lowerbound 2-435 lsb 2-436 lt 2-437 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان Index max 2-438 maxlog 2-439 mean 2-442 median 2-444 mesh 2-446 meshc 2-447 meshz 2-448 min 2-449 minlog 2-450 minus 2-452 mpower 2-455 mpy 2-456 mrdivide 2-458 mtimes 2-460 ndgrid 2-461 ndims 2-462 ne 2-463 nearest 2-464 noperations 2-467 not 2-468 noverflows 2-469 num2bin 2-484 num2hex 2-485 num2int 2-487 numberofelements 2-488 numerictype 2-492 nunderflows 2-514 oct 2-515 or 2-524 patch 2-525 pcolor 2-526 permute 2-527 plot 2-528 plot3 2-529 plotmatrix 2-530 plotyy 2-531 plus 2-532 polar 2-533 pow2 2-534 power 2-538 quantize 2-549 quantizer 2-552 quiver 2-557 quiver3 2-558 randquant 2-559 range 2-561 rdivide 2-563 real 2-566 realmax 2-567 realmin 2-569 reinterpretcast 2-570 removeglobalfimathpref 2-582 repmat 2-575 rescale 2-576 reset 2-578 resetglobalfimath 2-579 resetlog 2-583 reshape 2-584 rgbplot 2-585 ribbon 2-586 rose 2-587 round 2-588 savefipref 2-593 scatter 2-594 scatter3 2-595 sdec 2-596 semilogx 2-597 semilogy 2-598 set 2-599 sfi 2-604 shiftdata 2-611 shiftdim 2-615 showfixptsimerrors 2-616 showfixptsimranges 2-617 sign 2-628 single 2-629 size 2-630 slice 2-631 sort 2-632 spy 2-633 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان Index-5 Index sqrt 2-634 squeeze 2-636 stairs 2-637 stem 2-638 stem3 2-639 storedInteger 2-640 streamribbon 2-643 streamslice 2-644 streamtube 2-645 stripscaling 2-646 sub 2-648 subsasgn 2-650 subsref 2-656 surf 2-663 surfc 2-664 surfl 2-665 surfnorm 2-666 text 2-667 times 2-668 toeplitz 2-671 tostring 2-674 transpose 2-675 treeplot 2-676 tril 2-677 trimesh 2-678 triplot 2-679 trisurf 2-680 triu 2-681 ufi 2-682 uint16 2-690 uint32 2-691 uint64 2-692 uint8 2-689 uminus 2-693 unitquantize 2-696 unitquantizer 2-698 unshiftdata 2-699 uplus 2-702 upperbound 2-703 vertcat 2-704 Index-6 voronoi 2-705 voronoin 2-706 waterfall 2-707 wordlength 2-708 xlim 2-709 xor 2-710 ylim 2-711 zlim 2-720 G ge function 2-361 get function 2-362 getlsb function 2-363 getmsb function 2-364 gplot function 2-367 gt function 2-368 H hankel function 2-369 hex function 2-380 hex property 1-3 hex2num function 2-384 hist function 2-385 histc function 2-386 horzcat function 2-387 I imag function 2-388 int16 function 2-392 int32 function 2-393 int64 function 2-394 int8 function 2-391 intmax function 2-395 intmin function 2-396 ipermute function 2-397 isboolean function 2-398 iscolumn function 2-399 isdouble function 2-400 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان Index isempty function 2-401 isequal function 2-402 isfi function 2-403 isfimath function 2-404 isfimathlocal function 2-405 isfinite function 2-406 isfipref function 2-407 isfixed function 2-408 isfloat function 2-409 isinf function 2-410 isnan function 2-411 isnumeric function 2-412 isnumerictype function 2-413 isobject function 2-414 isquantizer function 2-416 isreal function 2-417 isrow function 2-418 isscalar function 2-419 isscaleddouble function 2-420 isscaledtype function 2-421 isscalingbinarypoint function 2-422 isscalingslopebias function 2-423 isscalingunspecified function 2-424 issigned function 2-425 issingle function 2-426 isslopebiasscaled function 2-427 isvector function 2-428 L le function 2-429 length function 2-430 line function 2-431 LoggingMode property 1-13 logical function 2-432 loglog function 2-433 logreport function 2-434 lowerbound function 2-435 lsb function 2-436 lt function 2-437 M max function 2-438 maxlog function 2-439 MaxProductWordLength property 1-4 MaxSumWordLength property 1-4 mean function 2-442 median function 2-444 mesh function 2-446 meshc function 2-447 meshz function 2-448 min function 2-449 minlog function 2-450 minus function 2-452 Mode property 1-20 mpower function 2-455 mpy function 2-456 mrdivide function 2-458 mtimes function 2-460 N ndgrid function 2-461 ndims function 2-462 ne function 2-463 nearest function 2-464 nopnerations function 2-467 not function 2-468 noverflows function 2-469 num2bin function 2-484 num2hex function 2-485 num2int function 2-487 NumberDisplay property 1-14 numberofelements function 2-488 numerictype function 2-492 numerictype objects properties Bias 1-15 DataType 1-15 DataTypeMode 1-15 DataTypeOverride 1-16 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان Index-7 Index FixedExponent 1-16 FractionLength 1-17 Scaling 1-17 Signed 1-17 Signedness 1-18 Slope 1-18 SlopeAdjustmentFactor 1-19 WordLength 1-19 NumericType property 1-3 NumericTypeDisplay property 1-13 nunderflows function 2-514 O oct function 2-515 oct property 1-3 or function 2-524 OverflowAction property fimath objects 1-4 quantizers 1-21 P patch function 2-525 pcolor function 2-526 permute function 2-527 plot function 2-528 plot3 function 2-529 plotmatrix function 2-530 plotyy function 2-531 plus function 2-532 polar function 2-533 pow2 function 2-534 power function 2-538 ProductBias property 1-5 ProductFixedExponent property 1-5 ProductFractionLength property 1-5 ProductMode property 1-5 ProductSlope property 1-7 ProductSlopeAdjustmentFactor property 1-7 Index-8 ProductWordLength property 1-7 properties Bias, numerictype objects 1-15 bin, fi objects 1-2 CastBeforeSum, fimath objects 1-4 data, fi objects 1-2 DataType, numerictype objects 1-15 DataTypeMode, numerictype objects 1-15 DataTypeOverride, fipref objects 1-12 DataTypeOverride, numerictype objects 1-16 DataTypeOverrideAppliesTo, fipref objects 1-12 dec, fi objects 1-2 double, fi objects 1-2 fimath, fi objects 1-2 FimathDisplay, fipref objects 1-12 FixedExponent, numerictype objects 1-16 Format, quantizers 1-20 FractionLength, numerictype objects 1-17 hex, fi objects 1-3 LoggingMode, fipref objects 1-13 MaxProductWordLength, fimath objects 1-4 MaxSumWordLength, fimath objects 1-4 Mode, quantizers 1-20 NumberDisplay, fipref objects 1-14 NumericType, fi objects 1-3 NumericTypeDisplay, fipref objects 1-13 oct, fi objects 1-3 OverflowAction, quantizers 1-21 OverflowMode, fimath objects 1-4 ProductBias, fimath objects 1-5 ProductFixedExponent, fimath objects 1-5 ProductFractionLength, fimath objects 1-5 ProductMode, fimath objects 1-5 ProductSlope, fimath objects 1-7 ProductSlopeAdjustmentFactor, fimath objects 1-7 ProductWordLength, fimath objects 1-7 RoundingMethod, quantizers 1-22 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان Index RoundMode, fimath objects 1-8 Scaling, numerictype objects 1-17 Signed, numerictype objects 1-17 Signedness, numerictype objects 1-18 Slope, numerictype objects 1-18 SlopeAdjustmentFactor, numerictype objects 1-19 SumBias, fimath objects 1-8 SumFixedExponent, fimath objects 1-8 SumFractionLength, fimath objects 1-9 SumMode, fimath objects 1-9 SumSlope, fimath objects 1-11 SumSlopeAdjustmentFactor, fimath objects 1-11 SumWordLength, fimath objects 1-11 WordLength, numerictype objects 1-19 removeglobalfimathpref function 2-582 repmat function 2-575 rescale function 2-576 reset function 2-578 resetglobalfimath function 2-579 resetlog function 2-583 reshape function 2-584 rgbplot function 2-585 ribbon function 2-586 rose function 2-587 round function 2-588 RoundingMethod property quantizers 1-22 RoundMode property fimath objects 1-8 S Q quantize function 2-549 quantizer function 2-552 quantizers properties Format 1-20 Mode 1-20 OverflowAction 1-21 RoundingMethod 1-22 quiver function 2-557 quiver3 function 2-558 R randquant function 2-559 range function 2-561 rat format 1-14 rdivide function 2-563 real function 2-566 realmax function 2-567 realmin function 2-569 reinterpretcast function 2-570 savefipref function 2-593 Scaling property 1-17 scatter function 2-594 scatter3 function 2-595 sdec function 2-596 semilogx function 2-597 semilogy function 2-598 set function 2-599 sfi function 2-604 shiftdata function 2-611 shiftdim function 2-615 showfixptsimerrors function 2-616 showfixptsimranges function 2-617 sign function 2-628 Signed property 1-17 Signedness property 1-18 single function 2-629 size function 2-630 slice function 2-631 Slope property 1-18 SlopeAdjustmentFactor property 1-19 sort function 2-632 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان Index-9 Index spy function 2-633 sqrt function 2-634 squeeze function 2-636 stairs function 2-637 stem function 2-638 stem3 function 2-639 storedInteger function 2-640 streamribbon function 2-643 streamslice function 2-644 streamtube function 2-645 stripscaling function 2-646 sub function 2-648 subsasgn function 2-650 subsref function 2-656 SumBias property 1-8 SumFixedExponent property 1-8 SumFractionLength property 1-9 SumMode property 1-9 SumSlope property 1-11 SumSlopeAdjustmentFactor property 1-11 SumWordLength property 1-11 surf function 2-663 surfc function 2-664 surfl function 2-665 surfnorm function 2-666 U ufi function 2-682 uint16 function 2-690 uint32 function 2-691 uint64 function 2-692 uint8 function 2-689 uminus function 2-693 unitquantize function 2-696 unitquantizer function 2-698 unshiftdata function 2-699 uplus function 2-702 upperbound function 2-703 V vertcat function 2-704 voronoi function 2-705 voronoin function 2-706 W waterfall function 2-707 wordlength function 2-708 WordLength property 1-19 X T text function 2-667 times function 2-668 toeplitz function 2-671 tostring function 2-674 transpose function 2-675 treeplot function 2-676 tril function 2-677 trimesh function 2-678 triplot function 2-679 trisurf function 2-680 triu function 2-681 Index-10 xlim function 2-709 xor function 2-710 Y ylim function 2-711 Z zlim function 2-720 www.MatlabSite.com | ﻣﺘﻠﺐ ﺳﺎﯾﺖ ﻣﺮﺟﻊ آﻣﻮزش ﺑﺮﻧﺎﻣﻪﻧﻮﯾﺴﯽ ﻣﺘﻠﺐ در اﯾﺮان معرفی چند منبع در زمینه آموزش برنامه نویسی MATLABیا متلب کتاب های به زبان انگلیسی عنوانMatlab, Third Edition: A Practical Introduction to : Programming and Problem Solving ترجمه عنوان :متلب :مقدمه ای عملی بر برنامه نويسی و حل مساله ،چاپ سوم مولفینStormy Attaway : سال چاپ2013 : انتشاراتButterworth-Heinemann : کتاب های به زبان فارسی عنوان :اصول و مبانی متلب برای علوم مهندسی مولفین :برايان هان ،دانیل تی ،والنتین مترجمین :رامین موالنا پور ،سارا موالناپور ،نینا اسدی پور انتشارات :سها دانش لینک دسترسی :لینک لینک دسترسی :لینک عنوانMATLAB For Dummies : ترجمه عنوان :تلب به زبان ساده مولفینJim Sizemore, John Paul Mueller : سال چاپ2014 : انتشاراتFor Dummies : عنوان :کاربرد MATLABدر علوم مهندسی مولفین :حیدرعلی شايانفر ،حسین شايقی انتشارات :ياوريان لینک دسترسی :لینک لینک دسترسی :لینک عنوانEssential MATLAB for Engineers and Scientists : عنوان :برنامه نويسی MATLABبرای مهندسان ترجمه عنوان :آنچه بايد مهندسین و دانشمندان از متلب بدانند مولفین :محمود کشاورز مهر ،بهزاد عبدی مولفینBrian Hahn, Daniel Valentine: سال چاپ2013 : انتشاراتAcademic Press : انتشارات :نوپردازان لینک دسترسی :لینک لینک دسترسی :لینک عنوانMATLAB: An Introduction with Applications : عنوان :آموزش کاربردی مباحث پیشرفته با MATLAB ترجمه عنوان :مقدمه ای بر متلب و کاربردهای آن مولفین :نیما جمشیدی ،علی ابويی مهريزی ،رسول مواليی مولفAmos Gilat : انتشارات :عابد سال چاپ2014 : انتشاراتWiley : لینک دسترسی :لینک لینک دسترسی :لینک عنوانMATLAB For Beginners: A Gentle Approach: عنوان :کاملترين مرجع آموزشی و کاربردی MATLAB ترجمه عنوان :متلب برای افراد مبتدی با يک رويکرد تدريجی مولفین :علی اکبر علمداری ،نسرين علمداری مولفPeter I. Kattan: انتشارات :نگارنده دانش سال چاپ2008 : انتشاراتCreateSpace Independent Publishing Platform : لینک دسترسی :لینک لینک دسترسی :لینک عنوانMATLAB for Engineers : عنوان :برنامه نويسی MATLABبرای مهندسین ترجمه عنوان :متلب برای مهندسین مولف :استفن چاپمن مولفHolly Moore : سال چاپ2011 : انتشاراتPrentice Hall : لینک دسترسی :لینک عنوانMastering MATLAB : ترجمه عنوان :تسلط بر متلب مولفینDuane C. Hanselman, Bruce L. Littlefield : سال چاپ2011 : انتشاراتPrentice Hall : لینک دسترسی :لینک مترجم :سعدان زکائی انتشارات :دانشگاه صنعتی خواجه نصیرالدين طوسی لینک دسترسی :لینک عنوان :آموزش گام به گام محاسبات عددی با متلب مولف :کلیو مولر مترجم :رسول نصیری انتشارات :نشر گستر لینک دسترسی :لینک منابع آموزشی آنالین عنوان :مجموعه فرادرسهای برنامهنويسی متلب مدرس :دکتر سید مصطفی کالمی هريس مدت زمان ۹ :ساعت و ۳دقیقه زبان :فارسی ارائه دهنده :فرادرس لینک دسترسی :لینک عنوان :مجموعه فرادرسهای متلب برای علوم و مهندسی مدرس :دکتر سید مصطفی کالمی هريس مدت زمان 14 :ساعت و 2۲دقیقه زبان :فارسی ارائه دهنده :فرادرس لینک دسترسی :لینک عنوان :مجموعه فرادرسهای برنامه نويسی متلب پیشرفته مدرس :دکتر سید مصطفی کالمی هريس مدت زمان ۲ :ساعت و 12دقیقه زبان :فارسی ارائه دهنده :فرادرس لینک دسترسی :لینک عنوانIntroduction to Programming with MATLAB : ترجمه عنوان :آشنايی با برنامهنويسی متلب مدرسینAkos Ledeczi, Michael Fitzpatrick, Robert Tairas : زبان :انگلیسی ارائه دهندهVanderbilt University : لینک دسترسی :لینک عنوانIntroduction to MATLAB : ترجمه عنوان :مقدمهای بر متلب مدرسDanilo Šćepanović : زبان :انگلیسی ارائه دهندهMIT OCW : لینک دسترسی :لینک عنوانUp and Running with MATLAB : ترجمه عنوان :شروع سريع کار با متلب مدرسPatrick Royal : زبان :انگلیسی ارائه دهندهlynda.com : لینک دسترسی :لینک عنوانModelling and Simulation using MATLAB : ترجمه عنوان :مدلسازی و شبیهسازی با استفاده از متلب مدرسین Prof. Dr.-Ing. Georg Fries :و دیگران زبان :انگلیسی ارائه دهندهiversity.org : لینک دسترسی :لینک
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