// 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 // http://www.springerlink.com/content/340228x165742104/ // // 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 T0 1.0 #define T1 0.5 #define T2 1.6666666666666666667e-1 #define T3 4.1666666666666666667e-2 #define T4 8.3333333333333333333e-3 #define T5 1.3888888888888888889e-3 #define T6 1.9841269841269841270e-4 #define T7 2.4801587301587301587e-5 #define PosInf 0x7FF0000000000000 #define NegInf 0xFFF0000000000000 // func Exp(x float64) float64 TEXT ·Exp(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 MOVQ BX, X0 MOVSD $LOG2E, X1 MULSD X0, X1 CVTSD2SL X1, BX // BX = exponent CVTSL2SD BX, X1 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 $T7, X1 MULSD X0, X1 ADDSD $T6, X1 MULSD X0, X1 ADDSD $T5, X1 MULSD X0, X1 ADDSD $T4, X1 MULSD X0, X1 ADDSD $T3, X1 MULSD X0, X1 ADDSD $T2, X1 MULSD X0, X1 ADDSD $T1, X1 MULSD X0, X1 ADDSD $T0, X1 MULSD X1, X0 MOVSD $2.0, X1 ADDSD X0, X1 MULSD X1, X0 MOVSD $2.0, X1 ADDSD X0, X1 MULSD X1, X0 MOVSD $2.0, X1 ADDSD X0, X1 MULSD X1, X0 MOVSD $2.0, X1 ADDSD X0, X1 MULSD X1, X0 ADDSD $1.0, X0 // return fr * 2**exponent MOVL $0x3FF, AX // bias ADDL AX, BX JLE underflow CMPL BX, $0x7FF JGE overflow MOVL $52, CX SHLQ CX, 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, AX MOVQ AX, ret+8(FP) RET overflow: // return +Inf MOVQ $PosInf, BX notNegInf: // NaN or +Inf, return x MOVQ BX, ret+8(FP) RET