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1 Vol. 44 No. 6 June 2003 Java IA-32 IEEE 754 IA-32 Java Just-in-Time 40% Efficient Implementation of Strict Floating-point Semantics Kazuyuki Shudo, Satoshi Sekiguchi and Yoichi Muraoka IA-32 processors yield different results of floating-point operations from other processors, even though they are all compliant with IEEE 754. The Java specifications need runtime systems to implement the FP-strict semantics, which other IEEE 754 compliant processors naturally fulfill. We implemented the semantics on a Java Just-in-Time compiler for IA-32. This study reveals that single-precision operations can be performed with precision control bits of the processor staying as double-precision. Performance evaluation demonstrates that our implementation method reduced the performance decline by the semantics down to 40%. 1. IEEE 754 1) SPARCAlphaPowerPCMIPSIA-32 x86 IEEE 754 IA-32 IA-32 Java Java National Institute of Advanced Industrial Science and Technology School of Science & Engineering, Waseda University 2) IA-32 Java 3) SPARC IA-32 IA-32 Java Intel IBM Java 2 strictfp 4) strictfp strictfp IA-32 strictfp strictfp Java JIT 5),6) JIT 1234

2 Vol. 44 No. 6 Java 1235 Java IA-32 Java strictfp 7 Java 2. IA-32 IEEE 754 normalized number ( 1) s 2 E (1.b 1b 2 b p 1) 2 10 s : 0 1 b i : 1 0 1) p : [bit] E : IA-32 IEEE IEEE 754 IA-32 x87 Table 1 1 The properties of each precision of IA-32. [bit] p [bit] E [bit] E E IA () 32 bit bit x86 80 bit x (not 11) bit 1 IA-32 Fig. 1 Floating-point value formats of IA x87 SPARC fmuls fmuld MIPS mul.s mul.d 1 1 x87 IA IA reg + IA-32 x (1) reg (2) reg (3) reg strictfp IA-32 IA-32 Intel AMD K6 AthlonTransmeta Crusoe 3. Golliver IA-32 strictfp FP-strict 4) Golliver 7) Java Grande Numerics Working Group FP-strict

3 1236 June : (b) xx...xx xx( 0 1 )xx... (c) (b) xx( 0 1 )xx... (c) 0 : xx...xx xx( 0 1 )xx (a) (: x 0 1.) Fig Binary expression of double-precision values that suffers double rounding Golliver 2 4 7) Golliver store-reload scaling FP-strict FP-strict denormalized number 15 normalized number 2 0 IEEE ( 1) s 2 E (0.b 1b 2 b p 1) gradual IEEE

4 Vol. 44 No. 6 Java 1237 (1) (2) (3) (4) (5) (6) 2...x 1 1xx( 0 1 )xx......x x 1 0xx x 0 1xx( 0 1 )xx......x x 0 0xx... Fig (3)(2) 1 (4)(5) (: 2. x 0 1.) 3 2 The mechanism of double rounding problem. 2 2 FP-strict a bc 4 15 IA IEEE IEEE (b) 1...xx (4)...xx xx( 0 1 )xx... (c) 1...xx 0 1 (5) 2...xx (a) 1...xx 1...xx xx( 0 1 )xx... (3) 1...xx xx 0 (2)...xx 1 0 : (a)(c) 0 (b) Fig. 4 The bit patterns of significand that suffers double rounding problem a 1 b c a 1 bc 0 3 4abc 0

5 1238 June abc ac b ac 0 b ac 0 b 1 2 IEEE (0x x3FF ) (0x000FFFFFFFFFFFFF 0x3FEFFFFFFFFFFFFF) ( 1022) gradual IEEE JIT 3 Golliver Java JIT shujit 5),6) Java bytecode dmul shujit internal instruction flush_cache dld dmul dst IA-32 machine language addl $8,%esp fmull (%esp) 5 shujit Fig. 5 Code generation method of shujit. JIT 4.1 JIT shujit IA-32 JIT OS Linux FreeBSDNetBSD 5 Java 1 5 5) 1 Golliver 4.3 FP-strict 1 frcstrictfp FP-strict strictfp 1 ignstrictfp strictfp frcstrictfp FP-strict

6 Vol. 44 No. 6 Java IA-32 x87 2 FP-strict FP-strict IA (1) 53 (2) : : xx...xx xx...xx xx( 0 1 )xx... (a) xx...xx xx( 0 1 )xx (b) xx( 0 1 )xx... (c) xx...xx (a) 1 2 (b) xx( 0 1 )xx... (c) (b) xx( 0 1 )xx... (c) 6 2 Fig. 6 The significands that suffers double rounding to double and single precision

7 1240 June xx...xx xx( 0 1 )xx xx( 0 1 )xx xx...xx xx( 0 1 )xx (: ) xx( 0 1 )xx Fig. 7 The bit patterns that suffers double rounding to double and single precision xxx xxx xxxx xx xx( 0 1 ) 6 8 Fig. 8 Addition and subtraction of single precision numbers A GHz Pentium FP-strict 4.3 JIT 2 3 IA-32 x n fscale 2 strictfp JIT JIT fscale MHz Pentium II

8 Vol. 44 No. 6 Java BulletTrain 8) 2.0.0b15 BulletTrain Ahead-of-Time strictfp 2 IA GHz Pentium MHz Mobile Pentium III OS BulletTrain Windows 2000 SP2 Linux shujit Java Blackdown Java 2 SE FCS Pentium 4 shujit SSE2 x87 SSE2 SSE C FP-strict C Java C 4.3 C GCC Pentium 4 Pentium 4 Pentium III ªªªªª ªªªªª ªªªªª ªªªªª ªªªªªªª s ªª 9 Pentium 4 Fig. 9 Multiplication on Pentium 4 processor. ªªªªª ªªªªª ªªªªª ªªªªª ªªªªªªª s ªª 10 Pentium 4 Fig. 10 Division on Pentium 4 processor. ªªªªª ªªªªª ªªªªª ªªªªª ªªªªªªª s ªª 11 Pentium III Fig. 11 Multiplication on Pentium III processor. ªªªªª ªªªªª ªªªªª ªªªªª ªªªªªªª s ªª 12 Pentium III Fig. 12 Division on Pentium III processor. Pentium III 4 raw

9 1242 June 2003 Table 2 2 C Penalty for FP-strictness in C language., raw Pentium 4, Pentium 4, Pentium III, Pentium III, ªªªªª ˆ 13 Pentium 4 SPEC JVM98 Fig. 13 SPEC JVM98 on Pentium 4 processor. ˆ ªªªªª 14 Pentium 4 Linpack Benchmark Fig. 14 Linpack benchmark on Pentium 4 processor. 2 FP-strict shujit fscale 23 BulletTrain fscale Pentium 4 Pentium III 2 C FP-strict raw Java Grande Numerics WG FP-strict 2 4 7) 2 6 C 5.2 SPEC JVM98 Linpack Benchmark Pentium 4 SPEC JVM98Pentium 4 Linpack Pentium III SPEC JVM98Pentium III Linpack FP-strict ªªªªª ˆ 15 Pentium III SPEC JVM98 Fig. 15 SPEC JVM98 on Pentium III processor. ˆ ªªªªª 16 Pentium III Linpack Benchmark Fig. 16 Linpack benchmark on Pentium III processor.

10 Vol. 44 No. 6 Java shujit FP-strict Table 3 Performance ratio of FP-strict operation to normal operation with shujit. fscale Pentium 4, mpegaudio 58.2% 36.8% Pentium 4, Linpack 62.5% 36.6% Pentium III, mpegaudio 74.3% 46.3% Pentium III, Linpack 59.6% 40.6% shujit % 74.3% 60% 40% fscale 36.6% 46.3% 5.1 fscale 6. SSE2 IA-32 Pentium 4 Streaming SIMD Extensions 2SSE2SSE2 Single Instruction Multiple DataSIMD IEEE 754 IEEE 754 9) SIMD Single Instruction Single DataSISD 1 IA-32 x87 x87 sin x87 SSE2 Golliver 3 FP-strict x87 15 FP-strict SSE SSE2 x87 SSE2 x87 FP-strict 5.1 SPEC JVM98 jess SSE2 1% 3% x87 SSE2 SSE2 FP-strict SSE Pentium 4 IA IA-32 SSE2 SSE2 Pentium III IA-32 PC Java Pentium 4 IA-32 x87 FP-strict 7. strictfp Java strictfp 1 IA-32 strictfp Java IEEE ) strictfp IEEE IEEE

11 1244 June 2003 IA-32 Streaming SIMD ExtensionsSSE SSE SSE2 6 SSE2 128 XMM SSE 4 SSE FP-strict SSE Pentium III Transmeta Crusoe TM5600 Pentium II IA IA-32 IEEE 754 Java JIT fscale 40% Java strictfp IA-32 Java Java IA ) : IEEE Standard for Binary Floating-point Arithmetic (1985). 2) Lindholm, T. and Yellin, F.: The Java Virtual Machine Specification, Addison Wesley (1997). 3) Gosling, J., Joy, B., Steele, G. and Bracha, G.: Java Language Specification, Second Edition, Addison Wesley (2000). 4) Sun Microsystems, Inc.: Updates to the Java Language Specification for JDK Release 1.2 Floating Point (1999). docs/books/jls/strictfp-changes.pdf. 5),, : Java Just-in- Time,, Vol. J86-DI, No. 4, pp (2003). 6) Shudo, K.: shujit Java Just-in-Time Compiler for x86 processors (1998). shudo.net/jit/. 7) Java Grande Forum Numerics Working Group: Improving Java for Numerical Computation (1998). javanumerics/. 8) NaturalBridge, Inc.: BulletTrain optimizing bytecode compiler (1998). naturalbridge.com/bullettrain.html. 9) Intel Corporation: IA 32 Intel Architecture Software Developer s Manual Volume 1: Basic Architecture (2001). A GHz Pentium

12 Vol. 44 No. 6 Java m n m n f mf n mn 23 f m f n f m +2 0 (1.m) f m f n e m e n mn g mg n mn 2 em en 127 g m g n 2 Golliver FP-strict Fig. 17 Algorithm to search pairs of dividend and divisor which suffer doublerounding in single-precision division. 4 e n Table 4 Quotients corresponding to exponent of divisor e n. e n (0 21 ) (0 22 ) (0 22 ) e n e n f mg m f n g n ( ) ( ) 2 e n e n m n e n 4 e n e n e n IEEE CSACM

13 1246 June SIGMA-1 Ninf SIAMIEEE Ph.D Illiac-IV NTT 1985

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