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Diffstat (limited to 'src/math/exp_amd64.s')
| -rw-r--r-- | src/math/exp_amd64.s | 159 |
1 files changed, 159 insertions, 0 deletions
diff --git a/src/math/exp_amd64.s b/src/math/exp_amd64.s new file mode 100644 index 0000000..02b71c8 --- /dev/null +++ b/src/math/exp_amd64.s @@ -0,0 +1,159 @@ +// Copyright 2010 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +#include "textflag.h" + +// The method is based on a paper by Naoki Shibata: "Efficient evaluation +// methods of elementary functions suitable for SIMD computation", Proc. +// of International Supercomputing Conference 2010 (ISC'10), pp. 25 -- 32 +// (May 2010). The paper is available at +// https://link.springer.com/article/10.1007/s00450-010-0108-2 +// +// The original code and the constants below are from the author's +// implementation available at http://freshmeat.net/projects/sleef. +// The README file says, "The software is in public domain. +// You can use the software without any obligation." +// +// This code is a simplified version of the original. + +#define LN2 0.6931471805599453094172321214581766 // log_e(2) +#define LOG2E 1.4426950408889634073599246810018920 // 1/LN2 +#define LN2U 0.69314718055966295651160180568695068359375 // upper half LN2 +#define LN2L 0.28235290563031577122588448175013436025525412068e-12 // lower half LN2 +#define PosInf 0x7FF0000000000000 +#define NegInf 0xFFF0000000000000 +#define Overflow 7.09782712893384e+02 + +DATA exprodata<>+0(SB)/8, $0.5 +DATA exprodata<>+8(SB)/8, $1.0 +DATA exprodata<>+16(SB)/8, $2.0 +DATA exprodata<>+24(SB)/8, $1.6666666666666666667e-1 +DATA exprodata<>+32(SB)/8, $4.1666666666666666667e-2 +DATA exprodata<>+40(SB)/8, $8.3333333333333333333e-3 +DATA exprodata<>+48(SB)/8, $1.3888888888888888889e-3 +DATA exprodata<>+56(SB)/8, $1.9841269841269841270e-4 +DATA exprodata<>+64(SB)/8, $2.4801587301587301587e-5 +GLOBL exprodata<>+0(SB), RODATA, $72 + +// func Exp(x float64) float64 +TEXT ·archExp(SB),NOSPLIT,$0 + // test bits for not-finite + MOVQ x+0(FP), BX + MOVQ $~(1<<63), AX // sign bit mask + MOVQ BX, DX + ANDQ AX, DX + MOVQ $PosInf, AX + CMPQ AX, DX + JLE notFinite + // check if argument will overflow + MOVQ BX, X0 + MOVSD $Overflow, X1 + COMISD X1, X0 + JA overflow + MOVSD $LOG2E, X1 + MULSD X0, X1 + CVTSD2SL X1, BX // BX = exponent + CVTSL2SD BX, X1 + CMPB ·useFMA(SB), $1 + JE avxfma + MOVSD $LN2U, X2 + MULSD X1, X2 + SUBSD X2, X0 + MOVSD $LN2L, X2 + MULSD X1, X2 + SUBSD X2, X0 + // reduce argument + MULSD $0.0625, X0 + // Taylor series evaluation + MOVSD exprodata<>+64(SB), X1 + MULSD X0, X1 + ADDSD exprodata<>+56(SB), X1 + MULSD X0, X1 + ADDSD exprodata<>+48(SB), X1 + MULSD X0, X1 + ADDSD exprodata<>+40(SB), X1 + MULSD X0, X1 + ADDSD exprodata<>+32(SB), X1 + MULSD X0, X1 + ADDSD exprodata<>+24(SB), X1 + MULSD X0, X1 + ADDSD exprodata<>+0(SB), X1 + MULSD X0, X1 + ADDSD exprodata<>+8(SB), X1 + MULSD X1, X0 + MOVSD exprodata<>+16(SB), X1 + ADDSD X0, X1 + MULSD X1, X0 + MOVSD exprodata<>+16(SB), X1 + ADDSD X0, X1 + MULSD X1, X0 + MOVSD exprodata<>+16(SB), X1 + ADDSD X0, X1 + MULSD X1, X0 + MOVSD exprodata<>+16(SB), X1 + ADDSD X0, X1 + MULSD X1, X0 + ADDSD exprodata<>+8(SB), X0 + // return fr * 2**exponent +ldexp: + ADDL $0x3FF, BX // add bias + JLE denormal + CMPL BX, $0x7FF + JGE overflow +lastStep: + SHLQ $52, BX + MOVQ BX, X1 + MULSD X1, X0 + MOVSD X0, ret+8(FP) + RET +notFinite: + // test bits for -Inf + MOVQ $NegInf, AX + CMPQ AX, BX + JNE notNegInf + // -Inf, return 0 +underflow: // return 0 + MOVQ $0, ret+8(FP) + RET +overflow: // return +Inf + MOVQ $PosInf, BX +notNegInf: // NaN or +Inf, return x + MOVQ BX, ret+8(FP) + RET +denormal: + CMPL BX, $-52 + JL underflow + ADDL $0x3FE, BX // add bias - 1 + SHLQ $52, BX + MOVQ BX, X1 + MULSD X1, X0 + MOVQ $1, BX + JMP lastStep + +avxfma: + MOVSD $LN2U, X2 + VFNMADD231SD X2, X1, X0 + MOVSD $LN2L, X2 + VFNMADD231SD X2, X1, X0 + // reduce argument + MULSD $0.0625, X0 + // Taylor series evaluation + MOVSD exprodata<>+64(SB), X1 + VFMADD213SD exprodata<>+56(SB), X0, X1 + VFMADD213SD exprodata<>+48(SB), X0, X1 + VFMADD213SD exprodata<>+40(SB), X0, X1 + VFMADD213SD exprodata<>+32(SB), X0, X1 + VFMADD213SD exprodata<>+24(SB), X0, X1 + VFMADD213SD exprodata<>+0(SB), X0, X1 + VFMADD213SD exprodata<>+8(SB), X0, X1 + MULSD X1, X0 + VADDSD exprodata<>+16(SB), X0, X1 + MULSD X1, X0 + VADDSD exprodata<>+16(SB), X0, X1 + MULSD X1, X0 + VADDSD exprodata<>+16(SB), X0, X1 + MULSD X1, X0 + VADDSD exprodata<>+16(SB), X0, X1 + VFMADD213SD exprodata<>+8(SB), X1, X0 + JMP ldexp |