Floating Point Libra..
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1. 1 5 1 Packing and unpacking floating point to an integer container The following macros can be used to pack a floating point number into an integer and unpacking an integer representation to a floating point type when you are using the Pipelined floating point library These macros are useful in simulation when passing values from Handel C to C or C The order of the int 32 representation is Bits Description 31 Sign 30 23 Exponent 22 0 Mantissa e FloatPackInint32 Creates a 32 bit int representation of the floating point value e FloatUnpackFromint32 Creates a float from a 32 bit representation of a floating point number Macros are also provided in the pipelined floating point library for converting between integer and floating point FloatUnpackFromI nt32 macro extern macro expr FloatUnpackFromInt32 B i www celoxica com Page 8 Pipelined Floating point Library Manual Celoxica Parameters B Value of type int 32 Timing 0 clock cycles or more Description Returns a floating point value Float from an int 32 value representation The floating point value is unpacked from an int 32 type The order of the int 32 representation is from MSB bit 31 Sign bits 30 23 Exponent bits 22 0 Mantissa Example while 1 par Float Aj int 32 B A FloatUnpackFromInt32 B Macros are also provided in the pipelined floating point library for converting between integer a2. T 81 0 45 331 0218 T 1 800 570 7004 E sales emea celoxica com E sales japan celoxica com_ E sales america celoxica com i www celoxica com Pipelined Floating point Library Manual Celoxica Contents 1 PIPELINED FLOATING POINT LIBRARY vcssncccccnnccccnneccennuececnunneeununeennnanenan 4 2 NDEX rnan E E 23 A www celoxica com Page 1 Pipelined Floating point Library Manual Celoxica Assumptions amp Omissions This manual assumes that you e have used Handel C or have the Handel C Language Reference Manual e are familiar with common programming terms e g functions e are familiar with MS Windows This manual does not include e instruction in VHDL or Verilog e instruction in the use of place and route tools e tutorial example programs These are provided in the Handel C User Manual i www celoxica com Pipelined Floating point Library Manual Celoxica Conventions A number of conventions are used in this document These conventions are detailed below xX Warning Message These messages warn you that actions may damage your hardware se Handy Note These messages draw your attention to crucial pieces of information Hexadecimal numbers will appear throughout this document The convention used is that of prefixing the number with Ox in common with standard C syntax Sections of code or commands that you must type are given in typewriter font like this void main I
3. Celoxica Platform Developer s Kit ee Pipelined Floating point Library Manual Pipelined Floating point Library Manual Celoxica Celoxica the Celoxica logo and Handel C are trademarks of Celoxica Limited All other products or services mentioned herein may be trademarks of their respective owners Neither the whole nor any part of the information contained in or the product described in this document may be adapted or reproduced in any material form except with the prior written permission of the copyright holder The product described in this document is subject to continuous development and improvement All particulars of the product and its use contained in this document are given by Celoxica Limited in good faith However all warranties implied or express including but not limited to implied warranties of merchantability or fitness for purpose are excluded This document is intended only to assist the reader in the use of the product Celoxica Limited shall not be liable for any loss or damage arising from the use of any information in this document or any incorrect use of the product The information contained herein is subject to change without notice and is for general guidance only Copyright 2005 Celoxica Limited All rights reserved Authors RG Document number 1 Customer Support at http www celoxica com support Celoxica in Europe Celoxica in Japan Celoxica in the Americas T 44 0 1235 863 656
4. PipeSqrt A QPtr Carry PPtr extern macro proc FloatPipeEq A B QPtr extern macro proc FloatPipeGt A B QPtr extern macro proc FloatPipeLs A B QPtr i www celoxica com Page 12 Pipelined Floating point Library Manual Celoxica Parameters A Value of type Float as parameter 1 B Value of type Float as parameter 2 ePtr Pointer of type Float or unsigned 1 for return value Carry Value indicating whether parameters need to be pipelined and returned with the result Possible values 0 no parameters 1 first parameter 2 second parameter 3 both parameters APtr Pointer of type Float for return of pipelined parameter 1 BPtr Pointer of type Float for return of pipelined parameter 2 Clock Clock signal ChipType Value identifying the chip type Set this using the FloatPipeChipTypeX macros Timing 5 clock cycles or more Description Instantiates an operator pipeline identified by the name of the procedure Each operator has a different latency which can be queried using the FloatPipeXCycles macros The Carry parameter helps to pipeline the inputs into the operation so that they can be extracted with the result If you want to perform arithmetic operations on floating point numbers within sequential code use the floating point arithmetic cores see page 16 instead Example Float A B Q Ar Br while 1 par A FloatUnpackFromInt32 Parame
5. e a second parameter Timing 0 or more clock cycles Description Sets the input parameters for the operation to which HandlePtr is connected HandlePtr is connected to an operation using FloatPipeCoreRun In addition to the inputs being set this also triggers the execution of the operation You need to run this macro in parallel with FloatPipeCoreRun Example par FloatPipeCoreRun amp MyDivider FloatPipeCoreDiv 2 Glock FloatPipeChipTypeGeneric seq FloatPipeCoreSet amp MySquareRoot A B 1 10 3 FloatPipeCoreX Floating point core arithmetic macros extern macro expr FloatPipeCoreAdd extern macro expr FloatPipeCoreSub extern macro expr FloatPipeCoreDiv F F extern macro expr FloatPipeCoreMult F F extern macro expr FloatPipeCoreSqrt i www celoxica com Page 17 Pipelined Floating point Library Manual Celoxica Parameters None Timing Compile time Description Identifier for the type of operation selected as a core These expressions are fed as the second parameter for FloatPipeCoreRun Example FloatPipeCoreRun amp MyMultiplier FloatPipeCoreMult __clock loatPipeChipTypeGeneric rj 1 10 4 FloatPipeCoreResult macro extern macro expr FloatPipeCoreResult HandlePtr Parameters HandlePtr Pointer to an operation handle created using FloatPipeCoreCreateHandle Timing 0 or more clock cycles Description An expression that returns
6. e ee eee eee 12 FloatPipeDivCycles i e 15 FloatPIDGE sesusieesitieere eddies ee 12 FloatPipeFromlInt cceeeeee eee es 11 FloatPipeFromlI ntCycles 006 15 FloatPipeGt c ce eee eee ee eects rnern 12 FloatPipeMult cceeeeee eee e eee eee 12 FloatPipeMultCycles s 15 FloatPipeSoprt cceeceee eens eee e eens 12 FloatPipeSqrtCycles s 15 Celoxica FloatPipeSub ceceeeeeeee eee nrn 12 FloatPipeSubCyclesS ceca ee 15 FloatPipeTOInt cece eee eee ee eee ees 10 FloatPipeTolntCyclesS 15 FloatPipeToUl nt 10 FloatPipeToUlntCycles 15 FloatPipeX eeri nni 12 FloatPipeXCycles iseer 15 FIOAtPOSINE vai stuns dda veweee neniani nenii 6 FloatPOSON6 cceeee cece teeta eae 6 FloatPosOneHallf cceeeeeeee eee eee 6 FloatPOSZero cece eee ee eset rere 6 FloatUnpackFroml nt32 cceeeeee ees 8 H header files 2 02 0 cece eee ee eect eee ee eed 4 P Pipelined floating point library 4 arithmetic cores 17 arithmetic operations 12 17 casting 7 changing floats to integers 7 changing integers to floats 7 Float type 4 se A www celoxica com Page 23
7. ge 6 Pipelined Floating point Library Manual Celoxica Macro Description FloatNegI nf Floating point minus infinity FloatNegOne Floating point minus one 1 FloatNegOneHalf Floating point minus a half 5 FloatNegZero Floating point minus one 1 FloatPosZero Floating point zero 0 FloatPosOneHalf Floating point a half 5 FloatPosOne Floating point one 1 FloatPoslI nf Floating point infinity 1 4 FloatlsSNaN and FloatlsQNaN extern macro expr FloatIsSNaN f Invalid extern macro expr FloatIsQNaN f Indeterminate Parameters f Floating point value of type Float Timing 0 clock cycles or more Description Returns true for the check specified by the expression name Example Float A if FloatIsSNaN A 1 5 Converting between Integer and floating point numbers The following macros can be used to convert between integers and floating point numbers when you are using the Pipelined floating point library Converting recalculates the value These operations take a number of clock cycles to produce a result and are pipelined a N www celoxica com Page 7 Pipelined Floating point Library Manual Celoxica Macros are also provided in the Pipelined floating point library to pack a floating point number into an int container and unpack an int to a floating point number These macros are useful for passing values between Handel C and C C for simulation
8. have pipelined code use the floating point arithmetic macros see page 12 loatPipeCoreCreateHandle creates a Handle for the core loatPipeCoreSet Sets the input parameters for the operation loatPipeCorexX macros Set the arithmetic operation to be performed qo RY y AY loatPipeCoreResult Determines if the operation is ready to return the result e FloatPipeCoreGet Captures a pipelined result e FloatPipeCoreRun Runs the arithmetic core 1 10 1 FloatPipeCoreCreateHandle macro define FloatPipeCoreCreateHandle Name Parameters Name Name of handle for operation you want to create Timing Handle created at compile time Description Creates a handle for a core operation The name should be intuitive of the type of operation to be created There must not be any space between the name and the bracket encapsulating the name Example FloatPipeCoreCreateHandle MyMUL FloatPipeCoreCreateHandle MySUB 1 10 2 FloatPipeCoreSet macro extern macro proc FloatPipeCoreSet HandlePtr A B www celoxica com Page 16 Pipelined Floating point Library Manual Celoxica Parameters HandlePtr Pointer to an operation handle created using FloatPipeCoreCreateHandle A Float value that is the first parameter of the operation B Float value that is the second parameter of the operation You must include this parameter even if the operation does not tak
9. he single precision floating point format handled by the Pipelined floating point library You use it in a similar way to a float type in software Accessing of members is done by treating the Float type aS a struct Example Float A B C 64 if A Sign Negative par A Exponent B Exponent A Mantissa B Mantissa i www celoxica com Page 4 Pipelined Floating point Library Manual Celoxica 1 2 Floating Point I ntroduction Floating point numbers This is a single precision pipelined floating point library Each number consists of a one bit sign an eight bit exponent and a 23 bit fraction The sign bit 0 denotes a positive number and 1 denotes a negative number The exponent The exponent field needs to represent both positive and negative exponents To do this a bias is added to the actual exponent in order to get the stored exponent For single precision floats as used in this library this value is 127 For example a stored exponent value of 150 is an exponent of 200 150 50 The mantissa The mantissa or significand is the precision bit of the number is usually stored in normalized form This means there is always one digit in front of the binary point As this is always there we can Save space by assuming its presence and not representing it explicitly as a result the mantissa has effectively 24 bits of resolution Special reserved values Some exponent values are reserved to denote s
10. mbedded features primitives available on the FPGA Set using the FloatPipeChipTypeX macros Use FloatPipeChipTypeGeneric for simulation Timing Does not terminate in normal use Description Runs the arithmetic operation selected with the selected parameters and links the handle to the operation There is no check done for matching the name of the handle to that of the operation You should run this macro in parallel with the rest of your code Example FloatPipeCoreCreateHandle MySquareRoot par FloatPipeCoreRun amp MySquareRoot FloatPipeCoreSaqrt Clock FloatPipeChipTypeGeneric seq Float In Result FloatPipeCoreSet amp MySquareRoot In FloatPosZero while FloatPipeCoreResult amp MySquareRoot delay FloatPipeCoreGet amp MySquareRoot amp Result i www celoxica com Page 20 Pipelined Floating point Library Manual Celoxica 1 11 FloatPipeChipTypeX macros extern macro expr FloatPipeChipTypeVirtex2 extern macro expr FloatPipeChipTypeGeneric Parameters None Timing Compile time Description Identifier for the type of chip chosen Some chip types contain embedded hardware cores that can be used by floating point operations The identifiers available indicate which chips are currently supported For simulation you must manually set the parameter to FloatPipeChipTypeGeneric This expression is fed as the last parameter of FloatPipeMult and Fl
11. nd floating point FloatPacklI ni nt32 macro extern macro expr FloatPackInInt32 A i www celoxica com Page 9 Pipelined Floating point Library Manual Parameters Timing Description Example Float A int 32 B Celoxica A Value of type Float 0 clock cycles or more Creates a 32 bit int representation of the floating point value The floating point value is packed into a int 32 type The order of the int representation is from MSB bit 31 Sign bits 30 23 Exponent bits 22 0 Mantissa B FloatPackInInt32 A Macros are also provided in the pipelined floating point library for converting between integer and floating point 1 5 2 FloatPipeTol nt and FloatPipeToUI nt extern macro proc FloatPipeToInt A QPtr IsInt64 extern macro proc FloatPipeToUInt A QPtr IsUInt64 i www celoxica com Page 10 Pipelined Floating point Library Manual Celoxica Parameters A Floating point value of type Float QPtr Integer of type int 32 or int 64 for FloatPipeToInt and unsigned 32 or unsigned 64 for FloatPipeToUInt IsInt64 Compile time constant If IsInt64 is 1 this indicates that parameter QPtr is of type int 64 Or unsigned 64 Timing 10 clock cycles or more for FloatPipeToInt 9 clock cycles or more for FloatPipeToUInt Description FloatPipeToInt converts a floating point value of type Float to int 32 or int 64 FloatPipeToUInt conve
12. nformation about a type of object you must specify is given in italics like this copy SourceFileName DestinationFileName Optional elements are enclosed in square brackets like this struct type_Name Curly brackets around an element show that it is optional but it may be repeated any number of times string character i www celoxica com Pipelined Floating point Library Manual Celoxica 1 Pipelined floating point library The pipelined floating point library is a platform independent core It allows you to perform floating point operations in a pipelined manner on single precision floating point numbers The library contains e The Float type type for a single precision floating point number e Macro procedures to perform arithmetic operations on floating point numbers These are useful if you want to use the operations within pipelined code e Macros to create cores which perform arithmetic operations on floating point numbers These are useful if you want to use operations within sequential code e Macros for casting and converting between integers and floating point numbers e FloatPipeChipTypeX macros optimize code by allowing embedded cores to be used for floating point operations To use the library you need to include float_pipe hch in your code and link to float_pipe hcl and stdlib hcl The libraries are in Instal1Dir PDK Hardware Lib 1 1 Float type Float Description The Float type is t
13. oatPipeCoreRun Example FloatPipeCoreRun amp MyMultiplier FloatPipeCoreMult clock loatPipeChipTypeVirtex2 fj i www celoxica com Page 21 Pipelined Floating point Library Manual 2 Index F Float type ceeeee eee eee ee ene eee eeee nena 4 floating point library cece ee 4 Floatl SQNAN ceceee cece eee eee e eee 7 FloathSSNAN i cecctee cert ive devaneeeeeaeteans 7 FloatNegInf c ce ceeee eee eee ates teens 6 FloatNegOne ccceeeeee eee nent teens 6 FloatNegOneHalf ccceeeee scene es 6 FloatNeQZero ccccececeeeeeeeeeeeeeeeeees 6 FloatPackI nINt32 cceeee cece e eee es 9 FloatPipeAdd ccceeeee eee e neta eae 12 FloatPipeAddCycles cceeeeeee ees 15 FloatPipeChipTypeGeneric 21 FloatPipeChipTypeVirtex2 21 FloatPipeChipTypex ceeeeeeee es 21 FloatPipeCoreAdd ccceeeeeeeeeeees 17 FloatPipeCoreCreateHandle 16 FloatPipeCoreDiv cceeeeee eee 17 FloatPipeCoreGet ccceeeeeeeeeaees 18 FloatPipeCoreMult cece eeee eee 17 FloatPipeCoreResult cceeeeeeees 18 FloatPipeCoreRUun ceseeeeeeeeeeeees 19 FloatPipeCoreSet ccccceeeeeeeeenees 16 FloatPipeCoreSapft eceeeeee eee eee 17 FloatPipeCoreSub cccceeee eee eenees 17 FloatPipeDIV cceeeeee ee
14. pecial values in floating point These can all be represented using the floating point library See FloatNegX and FloatPosX common floating point values and FloatlsSNAN and Floatl SQNAN i www celoxica com Page 5 Pipelined Floating point Library Manual Celoxica Zero Zero is denoted by an exponent field of zero and a fraction field of zero The sign bit denotes 0 and 0 these are equivalent Infinity An exponent of all 1 s and a fraction of all O s The sign bit denotes infinity and infinity Not a Number represented as an exponent of all ones and a NAN non zero fraction There are two types of NaN QNaN Quiet NaN and SNaN Signalling NaN QNaN s denote indeterminate operations while SNaN s denote invalid operations A QNaN is a NaN with the most significant fractional bit set An SNaN is a NaN with the most significant fractional bit clear 1 3 FloatNegX and FloatPosX common floating point values extern macro expr FloatNegInf extern macro expr FloatNegOne extern macro expr FloatNegOneHalf extern macro expr FloatNegZero extern macro expr FloatPosZero extern macro expr FloatPosOneHalf extern macro expr FloatPosOne extern macro expr FloatPosInf Parameters None Timing Compile time Description Float values representing the associated numbers The Neg or Pos indicates the sign bit value Example Float A A FloatPosOne i www celoxica com Pa
15. rn macro expr FloatPipeSubCycles extern macro expr FloatPipeDivCycles extern macro expr FloatPipeMultCycles extern macro expr FloatPipeSgqrtCycles extern macro expr FloatPipeEgqCycles extern macro expr FloatPipeGtCycles extern macro expr FloatPipeLsCycles Parameters None Timing Compile time Description Constant Value representing the number of clock cycles needed for the result to be registered for the operation described by the routine name FloatPipeXCycles macro Corresponding floating point operation FloatPipeFromIntCycles FloatPipeFromInt FloatPipeToIntCycles FloatPipeToInt FloatPipeToUIntCycles FloatPipeToUInt FloatPipeAddCycles FloatPipeAdd FloatPipeSubCycles FloatPipeSub FloatPipeDivCycles FloatPipeDiv FloatPipeMultCycles FloatPipeMult FloatPipeSqrtCycles FloatPipeSqrt FloatPipeEqCycles FloatPipeEq FloatPipeGtCycles FloatPipeGt FloatPipeLsCycles FloatPipeLs Example int x x 0 Float A B C while x FloatPipeAddCycles i www celoxica com Page 15 Pipelined Floating point Library Manual Celoxica par FloatPipeAdd A B amp C pa ae 1 10 Floating point arithmetic cores The Pipelined floating point library contains macros which allow you set up cores to perform arithmetic operations on floating point numbers The cores are best used in sequential code If you
16. rts a floating point value of type Float to unsigned 32 or unsigned 64 storage IsInt64 determines whether the storage created for the int or unsigned number is 32 or 64 bit Example int 64 Q1 unsigned 32 Q2 Float A 2 while 1 par A 0O FloatUnpackFromInt32 ABus in A 1 FloatUnpackFromInt32 BBus in FloatPipeToInt A 0 amp Q1 1 FloatPipeToUInt A 1 amp Q2 0 1 6 FloatPipeFromI nt macro extern macro proc FloatPipeFromInt A QPtr IsInt64 i www celoxica com Page 11 Pipelined Floating point Library Manual Celoxica Parameters A Integer of type int 32 Or int 64 ePtr Value of type Float to store the conversion IsInt64 Compile time constant If IsInt64 is 1 this indicates that parameter A is of type int 64 Timing 8 clock cycles or more Description Converts a signed integer of type int 32 or int 64 to a single precision floating point value of type Float IsInt64 should be set to 1 for integers of type int 64 Example int 64 A Float Q while 1 par A ABus in FloatPipeFromiInt A amp Q 1 1 7 FloatPipeX Floating point arithmetic macros extern macro proc FloatPipeAdd A B QPtr Carry APtr BPtr extern macro proc FloatPipeSub A B QPtr Carry APtr BPtr extern macro proc FloatPipeMult A B QPtr Carry APtr BPtr Clock ChipType extern macro proc FloatPipeDiv A B QPtr Carry APtr BPtr extern macro proc Float
17. terABus in B FloatUnpackFromInt32 ParameterBBus in FloatPipeSub A B amp Q 3 amp Ar amp Br i www celoxica com Page 13 Pipelined Floating point Library Manual Macro FloatPipeAdd FloatPipeSub FloatPipeMult FloatPipeDiv FloatPipeSqrt FloatPipeEq FloatPipeGt FloatPipeLs Celoxica Description Pipelined floating point adder Pipelined floating point subtracter Pipelined floating point multiplier Pipelined floating point divider Pipelined floating point square rooter Pipelined floating point comparator if A is equal to B result is 1 Pipelined floating point comparator if A is greater than B result is 1 Pipelined floating point comparator if A is less than B result is 1 1 8 Floating point constants The following constants are provided in the pipelined floating point library extern macro expr FloatPi extern macro expr FloatE Constant Pi E Parameters Timing Description Example Float A A FloatPi Description 3 14159265 2 71828183 None Compile time Float values representing the associated numbers a A www celoxica com Page 14 Pipelined Floating point Library Manual Celoxica 1 9 FloatPipeXCycles clock cycles for floating point operations extern macro expr FloatPipeFromIntCycles extern macro expr FloatPipeToIntCycles extern macro expr FloatPipeToUIntCycles extern macro expr FloatPipeAddCycles exte
18. true if the operation selected is ready to return the result in the current clock cycle Example seq FloatPipeCoreSet amp MyDivider A B while FloatPipeCoreResult amp MyDivider 0 delay 1 10 5 FloatPipeCoreGet macro extern macro proc FloatPipeCoreGet HandlePtr ResultPtr i www celoxica com Page 18 Pipelined Floating point Library Manual Celoxica Parameters HandlePtr Pointer to an operation handle created using FloatPipeCoreCreateHandle ResultPtr Pointer of type Float for the core to latch the result Timing 0 or more clock cycles Description A procedure that can be used to latch the result from the core result register This procedure is used in conjunction with FloatPipeCoreResult to capture the pipelined result Example while FloatPipeCoreResult amp MyDivider 0 delay FloatPipeCoreGet amp MyDivider amp Result 1 10 6 FloatPipeCoreRun macro extern macro proc FloatPipeCoreRun HandlePtr Operation Clock ChipType i www celoxica com Page 19 Pipelined Floating point Library Manual Celoxica Parameters HandlePtr Pointer to an operation handle created using FloatPipeCoreCreateHandle Operation Type of arithmetic operation the core will perform Set this using the FloatPipeCoreX macros Clock Interface expression or signal returning the clock pulse ChipType dentifier for the FPGA PLD target Enables the core to use e
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