Chapter X87 Floating-Point Optimizations 237 | AMD 250 specification

25112 Rev. 3.06 September 2005

Software Optimization Guide for AMD64 Processors

9.11Using SIMD Instructions for Fast Square Roots and Fast

Reciprocal Square Roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .211

9.12Use XOR Operations to Negate Operands of SSE, SSE2, and

3DNow!™ Instructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .215

9.13 Clearing MMX™ and XMM Registers with XOR Instructions . . . . . . . . . . . . . . . .216

9.14Finding the Floating-Point Absolute Value of Operands of SSE, SSE2, and

3DNow!™ Instructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .217

9.15Accumulating Single-PrecisionFloating-Point Numbers Using SSE, SSE2,

and 3DNow!™ Instructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .218

9.16	Complex-Number Arithmetic Using SSE, SSE2, and 3DNow!™ Instructions . .	. .221
9.17	Optimized 4 ⋅ 4 Matrix Multiplication on 4 ⋅ 1 Column Vector Routines	. .230
Chapter 10	x87 Floating-Point Optimizations	. .237
10.1	Using Multiplication Rather Than Division	. .238
10.2	Achieving Two Floating-Point Operations per Clock Cycle	. .239
10.3	Floating-Point Compare Instructions	. .244
10.4	Using the FXCH Instruction Rather Than FST/FLD Pairs	. .245
10.5	Floating-Point Subexpression Elimination	. .246
10.6	Accumulating Precision-Sensitive Quantities in x87 Registers	. .247
10.7	Avoiding Extended-Precision Data	. .248
Appendix A	Microarchitecture for AMD Athlon™ 64 and AMD Opteron™ Processors	. .249
A.1	Key Microarchitecture Features	. .250
A.2	Microarchitecture for AMD Athlon™ 64 and AMD Opteron™ Processors . . . .	. .251
A.3	Superscalar Processor	. .251
A.4	Processor Block Diagram	. .251
A.5	L1 Instruction Cache	. .252
A.6	Branch-Prediction Table	. .253
A.7	Fetch-Decode Unit	. .254
A.8	Instruction Control Unit	. .254
A.9	Translation-Lookaside Buffer	. .254
A.10	L1 Data Cache	. .255
A.11	Integer Scheduler	. .256

Contents

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AMD 250 manual Chapter X87 Floating-Point Optimizations 237

Contents

Software Optimization Guide For AMD64 Processors 2001 2005 Advanced Micro Devices, Inc. All rights reserved Contents General 64-Bit Optimizations Chapter Cache and Memory Optimizations Chapter Integer Optimizations 159 Chapter X87 Floating-Point Optimizations 237 Viii Appendix B Implementation of Write-Combining Index Software Optimization Guide for AMD64 Processors Tables Tables Xii Tables Figures Xiv Revision History Xvi Revision History Getting Started Quickly Intended Audience Using This Guide Providing Feedback Special InformationNumbering Systems Typographic Notation Primitive Operations Important New TermsInternal Instruction Formats Instructions, Macro-ops and Micro-ops Types of InstructionsMrom Optimizations by Rank Key OptimizationsGuideline Key Optimizations by Rank C++ Source-Level Optimizations C++ Source-Level Optimizations Rationale Declarations of Floating-Point ValuesOptimization Application Using Arrays and Pointers Matrix Example Instead, use the equivalent array notation Additional Considerations Related Information Unrolling Small Loops Expression Order in Compound Branch Conditions Chapter C++ Source-Level Optimizations Long Logical Expressions in If Statements Arrange Boolean Operands for Quick Expression Evaluation If *p == y && strlenp Dynamic Memory Allocation Consideration Listing 3. Avoid Unnecessary Store-to-Load Dependencies Application Examples Matching Store and Load Size Listing 6. Preferred C++ Source-Level Optimizations Switch and Noncontiguous Case Expressions Example Related Information Arranging Cases by Probability of Occurrence Use of Function Prototypes Use of const Type Qualifier Rationale and Examples Generic Loop Hoisting Listing Chapter C++ Source-Level Optimizations Local Static Functions Explicit Parallelism in Code Listing 11. Preferred Extracting Common Subexpressions Listing 15. Example 2 Preferred Sorting and Padding C and C++ Structures Sorting and Padding C and C++ Structures C++ Source-Level Optimizations Sorting Local Variables Related Information Replacing Integer Division with Multiplication Listing 16. Avoid Frequently Dereferenced Pointer Arguments Listing 17. Preferred Array Indices Rational 23 32-Bit Integral Data Types Sign of Integer Operands Listing 20. Example 2 Avoid Accelerating Floating-Point Division and Square Root Examples Fast Floating-Point-to-Integer Conversion Listing 23. Slow Branches Dependent on Integer Comparisons Are Fast Speeding Up Branches Based on Comparisons Between Floats Comparisons against Positive Constant Comparisons among Two Floats Improving Performance in Linux Libraries Software Optimization Guide for AMD64 Processors General 64-Bit Optimizations 64-Bit Registers and Integer Arithmetic This code performs 64-bit addition using 32-bit registers ESP+8ESP+4 = multiplicand Background 64-Bit Arithmetic and Large-Integer Multiplication G1 = c3 E1 + f1 + g0 = c2 D1 + e0 + f0 = c1 D0 = c0 XMM END Text Segment 128-Bit Media Instructions and Floating-Point Operations 32-Bit Legacy GPRs and Small Unsigned Integers Chapter General 64-Bit Optimizations General 64-Bit Optimizations Instruction-Decoding Optimizations DirectPath Instructions Load-Execute Integer Instructions Optimization Load-Execute Instructions Movss xmm0, floatvar1 mulss xmm0, floatvar2 Application Branch Targets in Program Hot Spots 32/64-Bit vs -Bit Forms of the LEA Instruction Take Advantage of x86 and AMD64 Complex Addressing Modes Cmpb %al,0x68e35%r10,%r13 Short Instruction Encodings Partial-Register Reads and Writes Avoid Functions That Allocate Local Variables Using Leave for Function EpiloguesFunctions That Do not Allocate Local Variables Traditional function epilogue looks like this Alternatives to Shld Instruction Lea reg1, reg1*8+reg2 10 8-Bit Sign-Extended Immediate Values 11 8-Bit Sign-Extended Displacements NOP Code Padding with Operand-Size Override Instruction-Decoding Optimizations Cache and Memory Optimizations Avoid Memory-Size MismatchesExamples-Store-to-Load-Forwarding Stalls Bit Avoid Examples-Large-to-small Mismatches Preferred If the Contents of MM0 are No Longer NeededPreferred If Stores Are Close to the Load Preferred If the Stores and Loads are Close Together, Option Natural Alignment of Data Objects Cache-Coherent Nonuniform Memory Access ccNUMA CPU0 OS Implications Dual-Core AMD Opteron Processor Configuration Multiprocessor Considerations 100 Store-to-Load Forwarding RestrictionsStore-to-Load Forwarding Pitfalls-True Dependencies Narrow-to-Wide Store-Buffer Data-Forwarding Restriction Misaligned Store-Buffer Data-Forwarding Restriction Wide-to-Narrow Store-Buffer Data-Forwarding Restriction101 102 High-Byte Store-Buffer Data-Forwarding RestrictionOne Supported Store-to-Load Forwarding Case Store-to-Load Forwarding-False Dependencies 103 Summary of Store-to-Load-Forwarding Pitfalls to Avoid Prefetching versus Preloading Prefetch Instructions104 105 Unit-Stride AccessHardware Prefetching PREFETCH/W versus PREFETCHNTA/T0/T1/T2 Write-Combining Usage Prefetchw versus Prefetch106 107 Multiple Prefetches 108 Determining Prefetch Distance Processor-Limited Code Memory-Limited Code Cache and Memory Optimizations Definitions 111 Prefetch at Least 64 Bytes Away from Surrounding Stores Streaming-Store/Non-Temporal Instructions 113 Write-combining L1 Data Cache Bank Conflicts How to Know If a Bank Conflict ExistsFields Used to Address the Multibank L1 Data Cache 115 Placing Code and Data in the Same 64-Byte Cache Line 117 Sorting and Padding C and C++ Structures 118 119 Copying Small Data Structures Memory Copy120 121 122 Stack ConsiderationsExtend Arguments to 32 Bits Before Pushing onto Stack Optimized Stack Usage 123 Cache Issues when Writing Instruction Bytes to Memory 124 Interleave Loads and Stores 125 This Chapter 126 Density of Branches Align 127 128 Two-Byte Near-Return RET Instruction 129 130 Branches That Depend on Random DataSigned Integer ABS Function x = labsx Unsigned Integer min Function z = x y ? x y 131 Conditional Write 132 Pairing Call and Return 133 Recursive Functions 134 135 Nonzero Code-Segment Base Values Muxing Constructs Replacing Branches with Computation136 MMX Solution Avoid SSE Solution Preferred137 Example 2 C Code Sample Code Translated into AMD64 CodeExample 1 C Code Example 1 3DNow! Code Example 4 3DNow! Code Example 3 C CodeExample 3 3DNow! Code Example 4 C Code Example 5 3DNow! Code Example 5 C Code140 141 Loop Instruction 142 Far Control-Transfer Instructions 143 Chapter Scheduling Optimizations 144 Instruction Scheduling by Latency Loop Unrolling Loop Unrolling145 Example Partial Loop Unrolling Complete Loop UnrollingExample Complete Loop Unrolling Partial Loop Unrolling 147 Fadd 148 Deriving the Loop Control for Partially Unrolled Loops 149 Inline Functions 150 Additional Recommendations Address-Generation Interlocks Address-Generation Interlocks151 152 153 Movzx and Movsx 154 Pointer Arithmetic in Loops 155 156 157 Pushing Memory Data Directly onto the Stack 158 159 Chapter Integer Optimizations Unsigned Division Utility Replacing Division with MultiplicationMultiplication by Reciprocal Division Utility Signed Division Utility 161 Unsigned Division by Multiplication of ConstantAlgorithm Divisors 1 = d 231, Odd d Algorithm Divisors 231 = d Signed Division by Signed Division by Multiplication of ConstantSimpler Code for Restricted Dividend Algorithm Divisors 2 = d Remainder of Signed Division by 2n or -2n Signed Division by 2nSigned Division by -2n Remainder of Signed Division by 2 or 164 Alternative Code for Multiplying by a Constant 165 166 167 Repeated String InstructionsLatency of Repeated String Instructions Guidelines for Repeated String Instructions 168 Use the Largest Possible Operand Size Acceptable Using XOR to Clear Integer Registers169 Bit Negation Efficient 64-Bit Integer Arithmetic in 32-Bit ModeBit Addition Bit Subtraction 171 Bit Right ShiftBit Multiplication Bit Unsigned Division 172 173 Bit Signed Division 174 Bit Unsigned Remainder Computation 175 176 Bit Signed Remainder Computation 177 178 179 180 Integer Version Binary-to-ASCII Decimal Conversion Retaining Leading Zeros Efficient Binary-to-ASCII Decimal Conversion181 182 183 Binary-to-ASCII Decimal Conversion Suppressing Leading Zeros 184 185 186 Unsigned Integer Division 187 188 Example Code Signed Integer Division189 190 191 192 Optimizing Integer Division 193 Optimizing with Simd Instructions 194 195 Ensure All Packed Floating-Point Data are Aligned 196 Rationale-Single Precision 197 Rational-Double Precision 198 Use MOVLPx/MOVHPx Instructions for Unaligned Data Access 199 Use Movapd and Movaps Instead of Movupd and Movups Loop type Description 200 201 202 Double-Precision 32 ⋅ 32 Matrix Multiplication 203 204 205 206 207 208 Passing Data between MMX and 3DNow! Instructions 209 Storing Floating-Point Data in MMX Registers 210 Emms and Femms Usage XMM Text Segment 211 212 213 214 Double Precision Single Precision215 216 Clearing MMX and XMM Registers with XOR Instructions 217 218 219 220 221 Code below Puts the Floating Point Sign Mask 222 223 224 225 226 Pfpnacc 227 228 229 230 Listing 27 ⋅ 4 Matrix Multiplication SSE 231 XMM3 232 Listing 28 ⋅ 4 Matrix Multiplication 3DNow! Technology 233 234 235 236 237 X87 Floating-Point Optimizations 238 Using Multiplication Rather Than Division 239 Achieving Two Floating-Point Operations per Clock Cycle 240 241 242 Align and Pack DirectPath x87 Instructions 243 244 Floating-Point Compare Instructions 245 Using the Fxch Instruction Rather Than FST/FLD Pairs 246 Floating-Point Subexpression Elimination 247 Accumulating Precision-Sensitive Quantities in x87 Registers 248 Avoiding Extended-Precision Data 249 Key Microarchitecture Features Superscalar Processor Processor Block Diagram251 L1 Instruction Cache AMD Athlon 64 and AMD Opteron Processors Block Diagram Branch-Prediction Table L1 Instruction Cache Specifications by Processor253 Translation-Lookaside Buffer L1 Instruction TLB SpecificationsFetch-Decode Unit Instruction Control Unit L2 TLB Specifications L1 Data TLB Specifications10 L1 Data Cache Integer Scheduler L1 Data Cache Specifications by ProcessorInteger Execution Unit 257 Floating-Point Scheduler Load-Store Unit Floating-Point Execution UnitFloating-Point Unit 259 16 L2 Cache Integrated Memory Controller Buses for AMD Athlon 64 and AMD Opteron ProcessorHyperTransport Technology Interface 261 HyperTransport Technology Software Optimization Guide for AMD64 Processors 263 Write-Combining Definitions and Abbreviations Write-combining Operations Programming Details264 265 Write-Combining Completion Events 266 Sending Write-Buffer Data to the System 267 Optimizations 268 269 Appendix C Instruction Latencies 270 Understanding Instruction EntriesExample Instruction Entry Parts of the Instruction Entry 271 Interpreting Placeholders 272 Interpreting Latencies AAA Integer InstructionsInteger Instructions 273 ADD reg16/32/64, mem16/32/64 274 Bswap EAX/RAX/R8 275 276 277 Mem16/32/64 CMOVNP/CMOVPO reg16/32/64, reg16/32/64 278 CMP reg16/32/64, mreg16/32/64 279 280 281 282 283 JA/JNBE disp16/32 284 Lahf 285 286 Mfence 287 288 NOP Xchg EAX, EAX 289 290 291 292 Rdtsc 293Rdmsr Rdpmc Sahf 294 SBB reg16/32/64, mem16/32/64 295 296 297 298 STI 299STC STD Sysexit 300Syscall Sysenter 301 Xchg AX/EAX/RAX, SI/ESI/RSI/R14 302Xchg AX/EAX/RAX, DI/EDI/RDI/R15 MMX Technology Instructions MMX Technology Instructions303 Fmul 304 305 306 X87 Floating-Point Instructions X87 Floating-Point Instructions307 Fdecstp 308Fadd Fcompp Fadd Fcos Fincstp 309FADD/FMUL Fstore Finit 310 311 312 FYL2X 313Fxch Fxtract Femms 3DNow! Technology Instructions3DNow! Technology Instructions 314 315 DNow! Technology Instructions 3DNow! Technology Extensions 3DNow! Technology Extensions316 SSE Instructions SSE Instructions317 318 319 320 321 Mem64 Prefetchnta mem8 0Fh 18h Mm-000-xxx DirectPath 322 Sfence 323 324 325 SSE2 Instructions SSE2 Instructions326 0FH 327Fmul Fstore 328 Maskmovdqu 329 Fadd Fmul Fstore 330 331 332 Fadd Fmul 333 334 335 336 337 338 Fmul Punpckhbw 339Fmul Punpckhdq 340 341 SSE3 Instructions SSE3 Instructions342 343 344 345 Fast-Write Optimizations 346 Fast-Write Optimizations for Graphics-Engine Programming 347 Cacheable-Memory Command Structure 348 349 Fast-Write Optimizations for Video-Memory Copies 350 351 Memory Optimizations 352 Northbridge Command Flow Optimizations for Vertex-Geometry Copies to AGP Memory Optimizations for Texture-Map Copies to AGP Memory353 354 Types of SSE and SSE2 Instructions Types of XMM-Register Data355 356 Half-Register Operations Clearing XMM Registers Zeroing Out an XMM Register357 358 359 Reuse of Dead Registers 360 Moving Data Between XMM Registers and GPRs 361 Saving and Restoring Registers of Unknown Format 362 SSE and SSE2 Copy Loops 363 Explicit Load Instructions Converting Scalar Values Data Conversion364 INT GPR FPS Converting Vector ValuesConverting Directly from Memory 365 366 367 Numerics 368 Index