| // 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. |
| |
| // 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),7,$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, r+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, r+8(FP) |
| RET |
| overflow: // return +Inf |
| MOVQ $PosInf, BX |
| notNegInf: // NaN or +Inf, return x |
| MOVQ BX, r+8(FP) |
| RET |
