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AMD x86 manual Use 3DNow! Instructions for Fast Division, Optimized 14-Bit Precision Divide

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AMD Athlon™ Processor x86 Code Optimization

22007E/0 — November 1999

FEMMS instruction is supported for backward compatibility with AMD-K6 family processors, and is aliased to the EMMS instruction.

3DNow! and MMX instructions are designed to be used concurrently with no switching issues. Likewise, enhanced 3DNow! instructions can be used simultaneously with MMX instructions. However, x87 and 3DNow! instructions share the same architectural registers so there is no easy way to use them concurrently without cleaning up the register file in between using FEMMS/EMMS.

Use 3DNow!™ Instructions for Fast Division

3DNow! instructions can be used to compute a very fast, highly accurate reciprocal or quotient.

Optimized 14-Bit Precision Divide

This divide operation executes with a total latency of seven cycles, assuming that the program hides the latency of the first MOVD/MOVQ instructions within preceding code.

Example:

MOVD	MM0, [MEM]		;	0	W
PFRCP	MM0, MM0		;	1/W 1/W			(approximate)
MOVQ	MM2,	[MEM]	;	Y		X
PFMUL	MM2,	MM0	;	Y/W		X/W

Optimized Full 24-Bit Precision Divide

This divide operation executes with a total latency of 15 cycles, assuming that the program hides the latency of the first MOVD/MOVQ instructions within preceding code.

Example:

MOVD	MM0, [W]	;	0	W
PFRCP	MM1, MM0	;	1/W	1/W	(approximate)
PUNPCKLDQ	MM0, MM0	;	W	W	(MMX instr.)
PFRCPIT1	MM0, MM1	;	1/W	1/W	(refine)
MOVQ	MM2, [X_Y]	;	Y	X
PFRCPIT2	MM0, MM1	;	1/W	1/W	(final)
PFMUL	MM2, MM0	:	Y/W	X/W

108	Use 3DNow!™ Instructions for Fast Division

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AMD x86 manual Use 3DNow! Instructions for Fast Division, Optimized 14-Bit Precision Divide

Contents

AMD AthlonTM Processor Trademarks Contents Instruction Decoding Optimizations Cache and Memory Optimizations Scheduling Optimizations Floating-Point Optimizations General x86 Optimization Guidelines 127 Appendix B Pipeline and Execution Unit Resources Overview Appendix E Programming the Mtrr and PAT List of Figures Xii List of Tables Xiv Revision History Xvi Introduction About this DocumentSource Level Optimizations. Describes optimizations that AMD Athlon Processor Family AMD Athlon Processor Microarchitecture Summary AMD Athlon Processor Microarchitecture Summary AMD Athlon Processor x86 Code Optimization Top Optimizations Memory Size and Alignment Issues Optimization StarGroup I Optimizations Essential Optimizations Use the 3DNow! Prefetch and Prefetchw InstructionsGroup II Optimizations-Secondary Optimizations Select DirectPath Over VectorPath InstructionsLoad-Execute Instruction Usage Use Load-Execute InstructionsUse 3DNow! Instructions Take Advantage of Write CombiningAvoid Branches Dependent on Random Data Avoid Placing Code and Data in the Same 64-Byte Cache Line 22007E/0 November Source Level Optimizations Use 32-Bit Data Types for Integer CodeExample 1 Avoid Consider the Sign of Integer OperandsExample Preferred Use Array Style Instead of Pointer Style Code Example AvoidUse unsigned types for Use signed types forVertex Example 2 Preferred Completely Unroll Small Loops Avoid Unnecessary Store-to-Load DependenciesAvoid Unnecessary Store-to-Load Dependencies Consider Expression Order in Compound Branch Conditions Optimize Switch Statements Switch Statement UsageUse Prototypes for All Functions Generic Loop Hoisting Use Const Type QualifierExample Generalization for Multiple Constant Control Code Declare Local Functions as Static Dynamic Memory Allocation Consideration Introduce Explicit Parallelism into CodeExplicitly Extract Common Subexpressions Language Structure Component Considerations ExampleAvoid PreferredOriginal ordering Avoid Sort Local Variables According to Base Type SizeNew ordering, with padding Preferred Accelerating Floating-Point Divides and Square Roots Improved ordering PreferredAccelerating Floating-Point Divides and Square Roots Avoid Unnecessary Integer Division AMD Athlon Processor x86 Code Optimization Instruction Decoding Optimizations OverviewLoad-Execute Instruction Usage Select DirectPath Over VectorPath InstructionsUse Load-Execute Integer Instructions TOP Align Branch Targets in Program Hot Spots Use Short Instruction LengthsAvoid Partial Register Reads and Writes Example 2 AvoidUse 8-Bit Sign-Extended Immediates Replace Certain Shld Instructions with Alternative CodeUse 8-Bit Sign-Extended Displacements Code Padding Using Neutral Code FillersRecommendations for the AMD Athlon Processor Code Padding Using Neutral Code Fillers AMD Athlon Processor x86 Code Optimization NOP6EDI AMD Athlon Processor x86 Code Optimization Cache and Memory Optimizations Memory Size and Alignment IssuesAvoid Memory Size Mismatches Align Data Where Possible Use the 3DNow! Prefetch and Prefetchw InstructionsExample Multiple Prefetches CodeMOV ECX, -LARGENUM Determining Prefetch Distance Prefetch Distance = 200 DS/C bytesTake Advantage of Write Combining Avoid Placing Code and Data in the Same 64-Byte Cache LineStore-to-Load Forwarding Restrictions Store-to-Load Forwarding Pitfalls -True DependenciesExample 3 Avoid Example 4 AvoidExample 6 Avoid Example 5 PreferredExample 7 Avoid Stack Alignment Considerations Summary of Store-to-Load Forwarding Pitfalls to AvoidAlign Tbyte Variables on Quadword Aligned Addresses Sort Variables According to Base Type Size Branch Optimizations Avoid Branches Dependent on Random DataAMD Athlon Processor Specific Code Blended AMD-K6and AMD Athlon Processor CodeExample 6 Increment Ring Buffer Offset Always Pair Call and ReturnExample 7 Integer Signum Function Replace Branches with Computation in 3DNow! Code Muxing ConstructsCode Sample Code Translated into 3DNow! Code3DNow! code MM5 Pfsub Psrad Avoid the Loop Instruction Avoid Far Control Transfer InstructionsAvoid Recursive Functions Scheduling Optimizations Schedule Instructions According to their LatencyUnrolling Loops Complete Loop UnrollingPartial Loop Unrolling Without Loop Unrolling With Partial Loop UnrollingDeriving Loop Control For PartiallyUnrolled Loops Example 1 rolled loopUse Function Inlining OverviewAvoid Address Generation Interlocks Always Inline Functions if Called from One SiteUse Movzx and Movsx Minimize Pointer Arithmetic in LoopsMOV ECX, Maxsize Push Memory Data Carefully Example 3 PreferredPush Memory Data Carefully Replace Divides with Multiplies Integer OptimizationsMultiplication by Reciprocal Division Utility Unsigned Division by Multiplication of Constant Simpler Code for Signed Division by Multiplication of ConstantRestricted Dividend Signed Division By Signed Division By 2nRemainder of Signed Integer 2 orUse Alternative Code When Multiplying by a Constant Integer 2n or -2nADD REG1, REG1 REG1, REG2 SHL Use MMX Instructions for Integer-Only Work Latency of Repeated String Instructions Repeated String Instruction UsageGuidelines for Repeated String Instructions Using Movq Ensure DF=0 UPAlign Source Destination withUse XOR Instruction to Clear Integer Registers Efficient 64-Bit Integer ArithmeticExample 5 Right shift Example 4 Left shiftExample 6 Multiplication Example 7 Division EBX, ESP+12 DividendloExample 8 Remainder SHR EDX Efficient Implementation of Population Count Function StepBit field. Thus the following computation is performed MOV EDX, EDX SHR Derivation of Multiplier Used for Integer Division by Utility sdiv.exe was compiled using the following code MOV ECX EDX Imul ADD SHR SAR Ensure All FPU Data is Aligned Floating-Point OptimizationsUse Multiplies Rather than Divides Floating-Point Compare Instructions Use Ffreep Macro to Pop One Register from the FPU StackAvoid Using Extended-Precision Data Use the Fxch Instruction Rather than FST/FLD PairsMinimize Floating-Point-to-Integer Conversions Example 1 FastExample 2 Potentially faster Example 3 Potentially faster Example 4 FastestFloating-Point Subexpression Elimination 104 Take Advantage of the Fsincos Instruction 106 Use 3DNow! Instructions 3DNow! and MMX OptimizationsUse Femms Instruction Optimized 14-Bit Precision Divide Use 3DNow! Instructions for Fast DivisionOptimized Full 24-Bit Precision Divide Pipelined Pair of 24-Bit Precision Divides Newton-Raphson ReciprocalOptimized 15-Bit Precision Square Root Optimized 24-Bit Precision Square RootNewton-Raphson Reciprocal Square Root 3DNow! and MMX Intra-Operand Swapping AMD AthlonSpecific Code Blended CodeFast Conversion of Signed Words to Floating-Point Use MMX Pxor to Negate 3DNow! DataUse MMX Pcmp Instead of 3DNow! Pfcmp Both NumbersPositive One Negative, One PositiveUse MMX Instructions for Block Copies and Block Fills AMD-K6and AMD Athlon Processor Blended Code116 Processor Specific Use MMX Pxor to Clear All Bits in an MMX Register Optimized Matrix Multiplication Use MMX Pcmpeqd to Set All Bits in an MMX RegisterMOV EBX, RES Optimized Matrix Multiplication 121 Data Use 3DNow! Pavgusb for MPEG-2 Motion Compensation MM0=QWORD1 Stream of Packed Unsigned Bytes Complex Number Arithmetic General x86 Optimization Guidelines Short FormsRegister Operands DependenciesStack Allocation AMD Athlon Processor Microarchitecture IntroductionAMD Athlon Processor Microarchitecture Superscalar ProcessorAMD Athlon Processor Microarchitecture 131 Predecode Branch PredictionEarly Decoding Instruction Control Unit Data CacheInteger Scheduler Integer Execution UnitFloating-Point Scheduler Floating-Point Execution Unit 12 toLoad-Store Unit LSU Load/Store UnitWrite Combining L2 Cache ControllerAMD Athlon System Bus 140 AMD Athlon Processor Microarchitecture Pipeline and Execution Unit Resources Overview Fetch and Decode Pipeline StagesC T L R O M Cycle 1-FETCH Cycle 2-SCANCycle 3 DirectPath Cycle 3 VectorPathInteger Pipeline Stages Integer Pipeline StagesCycle 7-SCHED Cycle 8-EXECCycle 9-ADDGEN Cycle 10 -DCACCFloating-Point Pipeline Stages Floating-Point Pipeline StagesCycle 7-STKREN Cycle 8-REGRENCycle 9-SCHEDW Cycle 10 -SCHEDExecution Unit Resources TerminologyOperands ResultsInteger Pipeline Operation Types Integer Pipeline OperationsInteger Decode Types Floating-Point Pipeline Operation Types Floating-Point Pipeline OperationsFloating-Point Decode Types Load/Store Unit Stages Load/Store Pipeline OperationsStage 1 Cycle Stage 2 Cycle Stage 3 Cycle Code Sample Analysis ADD EDI, EBX SHL Imul EAX, ECX INC ESI MOVINC EBX ADD ESI, EDX DEC EDX MOV EDI, ECX SUB Sample 2 Integer Register and Memory Load OperationsSAR Appendix C Implementation Write CombiningWrite-Combining Definitions and Abbreviations What is Write Combining?Programming Details Write-Combining Operations Write Combining Completion Events INIT, HaltAMD Athlon System Bus Commands Generation Rules Sending Write-Buffer Data to the System160 Write-Combining Operations Performance-Monitoring Counters Performance Counter UsagePerfEvtSel30 MSRs MSR Addresses C0010000h-C0010003h PerfEvtSel30 RegistersPerformance Counter Usage 163 Performance-Monitoring Counters 65h 73hSnoop hits 74hEvent Source Event Description Waited to use the L2Instruction cache fetches Instruction cache missesPerfCtr30 MSRs MSR Addresses C0010004h-C0010007h Event and Time-Stamp Monitoring Software Starting and Stopping the Performance-Monitoring CountersMonitoring Counter Overflow 170 Monitoring Counter Overflow Programming the Mtrr Memory Type Range Register Mtrr Mechanism172 Memory Type Range Register Mtrr Mechanism FFFFFFFFh Fixed Ranges100000h Kbytes each Fixed Ranges C0000h 80000h Memory Types Memory Type EncodingsMtrr Capability Register FormatMemory Type Range Register Mtrr Mechanism 175 Standard Mtrr Types and Properties Attribute Table PAT Attribute Table MSR 277hPAT Entry Reset Value PATi 3-Bit EncodingsMTRRs and PAT PATiEffective Memory Type Based on PAT and MTRRs PAT Memory Type Mtrr Memory TypeFinal Output Memory Types Input Memory TypeAttribute Table PAT 181 7FFFF 6FFFF 5FFFF 4FFFF 3FFFF 2FFFF 1FFFF 0FFFF 9FFFF 9BFFF 97FFF 93FFF 8FFFF 8BFFF 87FFF 83FFFBffff Bbfff B7FFF B3FFF Affff Abfff A7FFF A3FFF C7FFF C6FFF C5FFF C4FFF C3FFF C2FFF C1FFF C0FFFAttribute Table PAT 183 MTRRphysMaskn Register Format MTRR-Related Model-Specific Register MSR Map 186 Appendix F Instruction Dispatch Execution ResourcesInteger Instructions AAAAAD AAMModR/M Decode Byte ADC mreg8, reg8ADC mem8, reg8 ADC mreg16/32, reg16/32Bound Bswap EAXBswap ECX Bswap EDXCBW/CWDE CLCCLD CLICMOVE/CMOVZ reg16/32, reg16/32 0Fh CMOVE/CMOVZ reg16/32, mem16/32 0FhCMOVG/CMOVNLE reg16/32, reg16/32 0Fh CMOVG/CMOVNLE reg16/32, mem16/32 0FhCpuid CWD/CDQDAA DASEnter AL, DXAX, DX EAX, DXInvd InvlpgLahf LeaveLOOPE/LOOPZ disp8 E1h LOOPNE/LOOPNZ disp8 E0hLSL reg16/32, mreg16/32 0Fh 03h LSL reg16/32, mem16/32 0Fh 03hNOP Xchg EAX, EAX OUT DX, AL OUT DX, AXOUT DX, EAX POP ESPOP EBX POP ESPPOP EBP POP ESIRdpmc RdmsrRdtsc Sahf SBB mreg16/32, reg16/32 SBB mem16/32, reg16/32SBB reg8, mreg8 SBB reg8, mem8Sets mreg8 Sets mem8Setns mreg8 Setns mem8STD STCSTI Syscall SysenterSysexit SysretXchg EAX, EAX Xchg EAX, ECXXchg EAX, EDX Xchg EAX, EBXMMX Instructions EmmsPandn mmreg1, mmreg2 DFhPandn mmreg, mem64 Pcmpeqb mmreg1, mmreg2FADD/FMUL MMX Extensions FPUFloating-Point Instructions Fcos FcomppFdecstp Finit FincstpFLD1 FLDL2E FLDL2TFLDLG2 FLDLN2Fstsw AX FtstFucom FucompDNow! Instructions FemmsDNow! Extensions DirectPath versus VectorPath Instructions DirectPath InstructionsBT mreg16/32, reg16/32 BT mreg16/32, imm8 BT mem16/32, imm8 DirectPath Integer InstructionsCBW/CWDE CLC CMC DEC mreg8 DEC mem8 DEC mreg16/32 DEC mem16/32 INC mreg8 INC mem8 INC mreg16/32 INC mem16/32 JO short disp8222 DirectPath Instructions DirectPath Instructions 223 224 DirectPath Instructions Wait Xchg EAX, EAX 226 DirectPath Instructions DirectPath MMX Instructions DirectPath MMX Extensions DirectPath Floating-Point Instructions Fcompp FdecstpFist mem16int FLD1 FLDL2E FLDL2T FLDLG2 FLDLN2 Fldpi FldzFtst Fucom Fucomp Fucompp Fwait Fxch VectorPath Instructions VectorPath Integer InstructionsAAA AAD AAM AAS CLD CLI CltsInstruction Mnemonic DIV EAX, mem16/32 AL, DX AX, DX EAX, DX Invd InvlpgPOP mreg 16/32 POP mem 16/32 Push mreg16/32 Push mem16/32PUSHA/PUSHAD PUSHF/PUSHFD Rdmsr Rdpmc RdtscVectorPath MMX Instructions VectorPath MMX ExtensionsSyscall Sysenter Sysexit Sysret Wbinvd WrmsrVectorPath Floating-Point Instructions Fptan Fpatan FrndintFscale Fsin Fsincos Fxam Fxtract FYL2X FYL2XP1236 Index 238 Index Index 239 240 Index