Implementation of binary floating-point arithmetic on embedded

120 Pages·2010·1.21 MB·English

Implementation of binary floating-point arithmetic
on embedded integer processors
Polynomialevaluation-basedalgorithms
and
certifiedcodegeneration
GuillaumeRevy
Advisors: Claude-PierreJeannerodandGillesVillard
Are´naireINRIAproject-team(LIP,EnsLyon) Universite´deLyon CNRS
Ph.D.Defense–December1st,2009
GuillaumeRevy–December1st,2009. Implementationofbinaryfloating-pointarithmeticonembeddedintegerprocessors 1/45
SomeembeddedsystemsdonothaveanyFPU(floating-pointunit)
Highlyusedinaudioandvideoapplications
(cid:73) demandingonfloating-pointcomputations
Motivation
Embeddedsystemsareubiquitous
(cid:73) microprocessorsdedicatedtooneorafewspecifictasks
(cid:73) satisfyconstraints: area,energyconsumption,conceptioncost
GuillaumeRevy–December1st,2009. Implementationofbinaryfloating-pointarithmeticonembeddedintegerprocessors 2/45
Highlyusedinaudioandvideoapplications
(cid:73) demandingonfloating-pointcomputations
Motivation
Embeddedsystemsareubiquitous
(cid:73) microprocessorsdedicatedtooneorafewspecifictasks
(cid:73) satisfyconstraints: area,energyconsumption,conceptioncost
SomeembeddedsystemsdonothaveanyFPU(floating-pointunit)
Embeddedsystems
NoFPU
GuillaumeRevy–December1st,2009. Implementationofbinaryfloating-pointarithmeticonembeddedintegerprocessors 2/45
Motivation
Embeddedsystemsareubiquitous
(cid:73) microprocessorsdedicatedtooneorafewspecifictasks
(cid:73) satisfyconstraints: area,energyconsumption,conceptioncost
SomeembeddedsystemsdonothaveanyFPU(floating-pointunit)
Applications
FPcomputations
Embeddedsystems
NoFPU
Highlyusedinaudioandvideoapplications
(cid:73) demandingonfloating-pointcomputations
GuillaumeRevy–December1st,2009. Implementationofbinaryfloating-pointarithmeticonembeddedintegerprocessors 2/45
Motivation
Embeddedsystemsareubiquitous
(cid:73) microprocessorsdedicatedtooneorafewspecifictasks
(cid:73) satisfyconstraints: area,energyconsumption,conceptioncost
SomeembeddedsystemsdonothaveanyFPU(floating-pointunit)
Applications
FPcomputations
Embeddedsystems
Softwareimplementing
NoFPU floating-pointarithmetic
Highlyusedinaudioandvideoapplications
(cid:73) demandingonfloating-pointcomputations
GuillaumeRevy–December1st,2009. Implementationofbinaryfloating-pointarithmeticonembeddedintegerprocessors 2/45
Motivation
Embeddedsystemsareubiquitous
(cid:73) microprocessorsdedicatedtooneorafewspecifictasks
(cid:73) satisfyconstraints: area,energyconsumption,conceptioncost
SomeembeddedsystemsdonothaveanyFPU(floating-pointunit)
ST2Ims-3IusC1ebimdascPTceyooeihsrm3rreteyiexpemrhseraccIonlosntnTettrrIrranrooupPbsllblItlpCrueuerTatrunrsfLnaufcineBcttprhDidopenobrrBurtRe4efir8gugegawfilingrenislesriietc(statie6htetdree4rS3)rs2T-BbIMUuitsulIUIMUulIUD(LSULtToSonaLUridetB)UTLBDmsPrSDC4uebbDWr-CegoebuuxsImifnirasffsedSipffyctttoteeDreehosecrrorrthreIyelstmsCSCMUCS64T-Bbuits AFpPpcolimcpauttiaotinonss
61interruptsDebuglink Embeddedsystems
Softwareimplementing
NoFPU floating-pointarithmetic
Highlyusedinaudioandvideoapplications
(cid:73) demandingonfloating-pointcomputations
GuillaumeRevy–December1st,2009. Implementationofbinaryfloating-pointarithmeticonembeddedintegerprocessors 2/45
VLIW(VeryLongInstructionWord)
→ instructionsgroupedintobundles
→ Instruction-LevelParallelism(ILP)explicitlyexposedbythecompiler
uint32_t R1 = A0 + C; Issue1 Issue2 Issue3 Issue4
uint32_t R2 = A3 * X;
uint32_t R3 = A1 * X; 0 R1 R2 R3
uint32_t R4 = X * X; 1 R4
Overview of the ST231 architecture
ST231core SDIports 4-issueVLIW32-bitintegerprocessor
ICache InsbIturTufLfceBtrion rR4efi8egwlgreiesri(sati6tetdee4r)rs Mul Mul D(LSULtToSonaLUridetB) UTLB DrC4ebWCgouxinrafsSifcttteDrheeroreIls SCUSTBus Pa→ralnleolFePxeUcutionunit
CMC64-bit
Ims-usebimdseyosrtyem conTtrraopllPbeCrruannaincthd rBergafiinsltecehr IU IU IU IU DmsuP-ebbsrmiseudyffoeefsrtetycerhm (cid:73)(cid:73) 42ipnitpeeglienreAdLmUultipliers32×32→32
PeTrimi3pxehresralscIonntetrrroullpetrsupDpeobrutgunit S32T-Bbuits Latencies: ALU→1cycle,Mul→3
61interrupts Debuglink cycles
GuillaumeRevy–December1st,2009. Implementationofbinaryfloating-pointarithmeticonembeddedintegerprocessors 3/45
uint32_t R1 = A0 + C; Issue1 Issue2 Issue3 Issue4
uint32_t R2 = A3 * X;
uint32_t R3 = A1 * X; 0 R1 R2 R3
uint32_t R4 = X * X; 1 R4
Overview of the ST231 architecture
ST231core SDIports 4-issueVLIW32-bitintegerprocessor
ICache InsbIturTufLfceBtrion rR4efi8egwlgreiesri(sati6tetdee4r)rs Mul Mul D(LSULtToSonaLUridetB) UTLB DrC4ebWCgouxinrafsSifcttteDrheeroreIls SCUSTBus Pa→ralnleolFePxeUcutionunit
CMC64-bit
Ims-usebimdseyosrtyem conTtrraopllPbeCrruannaincthd rBergafiinsltecehr IU IU IU IU DmsuP-ebbsrmiseudyffoeefsrtetycerhm (cid:73)(cid:73) 42ipnitpeeglienreAdLmUultipliers32×32→32
PeTrimi3pxehresralscIonntetrrroullpetrsupDpeobrutgunit S32T-Bbuits Latencies: ALU→1cycle,Mul→3
61interrupts Debuglink cycles
VLIW(VeryLongInstructionWord)
→ instructionsgroupedintobundles
→ Instruction-LevelParallelism(ILP)explicitlyexposedbythecompiler
GuillaumeRevy–December1st,2009. Implementationofbinaryfloating-pointarithmeticonembeddedintegerprocessors 3/45
Overview of the ST231 architecture
ST231core SDIports 4-issueVLIW32-bitintegerprocessor
ICache InsbIturTufLfceBtrion rR4efi8egwlgreiesri(sati6tetdee4r)rs Mul Mul D(LSULtToSonaLUridetB) UTLB DrC4ebWCgouxinrafsSifcttteDrheeroreIls SCUSTBus Pa→ralnleolFePxeUcutionunit
CMC64-bit
Ims-usebimdseyosrtyem conTtrraopllPbeCrruannaincthd rBergafiinsltecehr IU IU IU IU DmsuP-ebbsrmiseudyffoeefsrtetycerhm (cid:73)(cid:73) 42ipnitpeeglienreAdLmUultipliers32×32→32
PeTrimi3pxehresralscIonntetrrroullpetrsupDpeobrutgunit S32T-Bbuits Latencies: ALU→1cycle,Mul→3
61interrupts Debuglink cycles
VLIW(VeryLongInstructionWord)
→ instructionsgroupedintobundles
→ Instruction-LevelParallelism(ILP)explicitlyexposedbythecompiler
uint32_t R1 = A0 + C; Issue1 Issue2 Issue3 Issue4
uint32_t R2 = A3 * X;
uint32_t R3 = A1 * X; 0 R1 R2 R3
uint32_t R4 = X * X; 1 R4
GuillaumeRevy–December1st,2009. Implementationofbinaryfloating-pointarithmeticonembeddedintegerprocessors 3/45
How to emulate floating-point arithmetic in software?
Designandimplementationofefficientsoftwaresupportfor
IEEE754floating-pointarithmeticonintegerprocessors
ExistingsoftwareforIEEE754floating-pointarithmetic:
(cid:73) Softwarefloating-pointsupportofGCC,GlibcandµClibc,GoFast
Floating-PointLibrary
(cid:73) SoftFloat(→STlib)
(cid:73) FLIP(Floating-pointLibraryforIntegerProcessors)
• softwaresupportforbinary32floating-pointarithmeticonintegerprocessors
• correctly-roundedaddition,subtraction,multiplication,division,squareroot,
reciprocal,...
• handlingsubnormals,andhandlingspecialinputs
GuillaumeRevy–December1st,2009. Implementationofbinaryfloating-pointarithmeticonembeddedintegerprocessors 4/45