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// 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 PosOne 0x3FF0000000000000
#define PosInf 0x7FF0000000000000
#define NaN 0x7FF8000000000001
#define PI4A 0.7853981554508209228515625 // pi/4 split into three parts
#define PI4B 0.794662735614792836713604629039764404296875e-8
#define PI4C 0.306161699786838294306516483068750264552437361480769e-16
#define M4PI 1.273239544735162542821171882678754627704620361328125 // 4/pi
#define T0 1.0
#define T1 -8.33333333333333333333333e-02 // (-1.0/12)
#define T2 2.77777777777777777777778e-03 // (+1.0/360)
#define T3 -4.96031746031746031746032e-05 // (-1.0/20160)
#define T4 5.51146384479717813051146e-07 // (+1.0/1814400)
// func Sincos(d float64) (sin, cos float64)
TEXT ┬ĚSincos(SB),NOSPLIT,$0
// test for special cases
MOVQ $~(1<<63), DX // sign bit mask
MOVQ x+0(FP), BX
ANDQ BX, DX
JEQ isZero
MOVQ $PosInf, AX
CMPQ AX, DX
JLE isInfOrNaN
// Reduce argument
MOVQ BX, X7 // x7= d
MOVQ DX, X0 // x0= |d|
MOVSD $M4PI, X2
MULSD X0, X2
CVTTSD2SQ X2, BX // bx= q
MOVQ $1, AX
ANDQ BX, AX
ADDQ BX, AX
CVTSQ2SD AX, X2
MOVSD $PI4A, X3
MULSD X2, X3
SUBSD X3, X0
MOVSD $PI4B, X3
MULSD X2, X3
SUBSD X3, X0
MOVSD $PI4C, X3
MULSD X2, X3
SUBSD X3, X0
MULSD $0.125, X0 // x0= x, x7= d, bx= q
// Evaluate Taylor series
MULSD X0, X0
MOVSD $T4, X2
MULSD X0, X2
ADDSD $T3, X2
MULSD X0, X2
ADDSD $T2, X2
MULSD X0, X2
ADDSD $T1, X2
MULSD X0, X2
ADDSD $T0, X2
MULSD X2, X0 // x0= x, x7= d, bx= q
// Apply double angle formula
MOVSD $4.0, X2
SUBSD X0, X2
MULSD X2, X0
MOVSD $4.0, X2
SUBSD X0, X2
MULSD X2, X0
MOVSD $4.0, X2
SUBSD X0, X2
MULSD X2, X0
MULSD $0.5, X0 // x0= x, x7= d, bx= q
// sin = sqrt((2 - x) * x)
MOVSD $2.0, X2
SUBSD X0, X2
MULSD X0, X2
SQRTSD X2, X2 // x0= x, x2= z, x7= d, bx= q
// cos = 1 - x
MOVSD $1.0, X1
SUBSD X0, X1 // x1= x, x2= z, x7= d, bx= q
// if ((q + 1) & 2) != 0 { sin, cos = cos, sin }
MOVQ $1, DX
ADDQ BX, DX
ANDQ $2, DX
SHRQ $1, DX
SUBQ $1, DX
MOVQ DX, X3
// sin = (y & z) | (^y & x)
MOVAPD X2, X0
ANDPD X3, X0 // x0= sin
MOVAPD X3, X4
ANDNPD X1, X4
ORPD X4, X0 // x0= sin, x1= x, x2= z, x3= y, x7= d, bx= q
// cos = (y & x) | (^y & z)
ANDPD X3, X1 // x1= cos
ANDNPD X2, X3
ORPD X3, X1 // x0= sin, x1= cos, x7= d, bx= q
// if ((q & 4) != 0) != (d < 0) { sin = -sin }
MOVQ BX, AX
MOVQ $61, CX
SHLQ CX, AX
MOVQ AX, X3
XORPD X7, X3
MOVQ $(1<<63), AX
MOVQ AX, X2 // x2= -0.0
ANDPD X2, X3
ORPD X3, X0 // x0= sin, x1= cos, x2= -0.0, bx= q
// if ((q + 2) & 4) != 0 { cos = -cos }
MOVQ $2, AX
ADDQ AX, BX
MOVQ $61, CX
SHLQ CX, BX
MOVQ BX, X3
ANDPD X2, X3
ORPD X3, X1 // x0= sin, x1= cos
// return (sin, cos)
MOVSD X0, sin+8(FP)
MOVSD X1, cos+16(FP)
RET
isZero: // return (┬▒0.0, 1.0)
MOVQ BX, sin+8(FP)
MOVQ $PosOne, AX
MOVQ AX, cos+16(FP)
RET
isInfOrNaN: // return (NaN, NaN)
MOVQ $NaN, AX
MOVQ AX, sin+8(FP)
MOVQ AX, cos+16(FP)
RET