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exp_amd64.s
// 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
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