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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"
#define HSqrt2 7.07106781186547524401e-01 // sqrt(2)/2
#define Ln2Hi 6.93147180369123816490e-01 // 0x3fe62e42fee00000
#define Ln2Lo 1.90821492927058770002e-10 // 0x3dea39ef35793c76
#define L1 6.666666666666735130e-01 // 0x3FE5555555555593
#define L2 3.999999999940941908e-01 // 0x3FD999999997FA04
#define L3 2.857142874366239149e-01 // 0x3FD2492494229359
#define L4 2.222219843214978396e-01 // 0x3FCC71C51D8E78AF
#define L5 1.818357216161805012e-01 // 0x3FC7466496CB03DE
#define L6 1.531383769920937332e-01 // 0x3FC39A09D078C69F
#define L7 1.479819860511658591e-01 // 0x3FC2F112DF3E5244
#define NaN 0x7FF8000000000001
#define NegInf 0xFFF0000000000000
#define PosInf 0x7FF0000000000000
// func Log(x float64) float64
TEXT ·Log(SB),NOSPLIT,$0
// test bits for special cases
MOVQ x+0(FP), BX
MOVQ $~(1<<63), AX // sign bit mask
ANDQ BX, AX
JEQ isZero
MOVQ $0, AX
CMPQ AX, BX
JGT isNegative
MOVQ $PosInf, AX
CMPQ AX, BX
JLE isInfOrNaN
// f1, ki := math.Frexp(x); k := float64(ki)
MOVQ BX, X0
MOVQ $0x000FFFFFFFFFFFFF, AX
MOVQ AX, X2
ANDPD X0, X2
MOVSD $0.5, X0 // 0x3FE0000000000000
ORPD X0, X2 // X2= f1
SHRQ $52, BX
ANDL $0x7FF, BX
SUBL $0x3FE, BX
XORPS X1, X1 // break dependency for CVTSL2SD
CVTSL2SD BX, X1 // x1= k, x2= f1
// if f1 < math.Sqrt2/2 { k -= 1; f1 *= 2 }
MOVSD $HSqrt2, X0 // x0= 0.7071, x1= k, x2= f1
CMPSD X2, X0, 5 // cmpnlt; x0= 0 or ^0, x1= k, x2 = f1
MOVSD $1.0, X3 // x0= 0 or ^0, x1= k, x2 = f1, x3= 1
ANDPD X0, X3 // x0= 0 or ^0, x1= k, x2 = f1, x3= 0 or 1
SUBSD X3, X1 // x0= 0 or ^0, x1= k, x2 = f1, x3= 0 or 1
MOVSD $1.0, X0 // x0= 1, x1= k, x2= f1, x3= 0 or 1
ADDSD X0, X3 // x0= 1, x1= k, x2= f1, x3= 1 or 2
MULSD X3, X2 // x0= 1, x1= k, x2= f1
// f := f1 - 1
SUBSD X0, X2 // x1= k, x2= f
// s := f / (2 + f)
MOVSD $2.0, X0
ADDSD X2, X0
MOVAPD X2, X3
DIVSD X0, X3 // x1=k, x2= f, x3= s
// s2 := s * s
MOVAPD X3, X4 // x1= k, x2= f, x3= s
MULSD X4, X4 // x1= k, x2= f, x3= s, x4= s2
// s4 := s2 * s2
MOVAPD X4, X5 // x1= k, x2= f, x3= s, x4= s2
MULSD X5, X5 // x1= k, x2= f, x3= s, x4= s2, x5= s4
// t1 := s2 * (L1 + s4*(L3+s4*(L5+s4*L7)))
MOVSD $L7, X6
MULSD X5, X6
ADDSD $L5, X6
MULSD X5, X6
ADDSD $L3, X6
MULSD X5, X6
ADDSD $L1, X6
MULSD X6, X4 // x1= k, x2= f, x3= s, x4= t1, x5= s4
// t2 := s4 * (L2 + s4*(L4+s4*L6))
MOVSD $L6, X6
MULSD X5, X6
ADDSD $L4, X6
MULSD X5, X6
ADDSD $L2, X6
MULSD X6, X5 // x1= k, x2= f, x3= s, x4= t1, x5= t2
// R := t1 + t2
ADDSD X5, X4 // x1= k, x2= f, x3= s, x4= R
// hfsq := 0.5 * f * f
MOVSD $0.5, X0
MULSD X2, X0
MULSD X2, X0 // x0= hfsq, x1= k, x2= f, x3= s, x4= R
// return k*Ln2Hi - ((hfsq - (s*(hfsq+R) + k*Ln2Lo)) - f)
ADDSD X0, X4 // x0= hfsq, x1= k, x2= f, x3= s, x4= hfsq+R
MULSD X4, X3 // x0= hfsq, x1= k, x2= f, x3= s*(hfsq+R)
MOVSD $Ln2Lo, X4
MULSD X1, X4 // x4= k*Ln2Lo
ADDSD X4, X3 // x0= hfsq, x1= k, x2= f, x3= s*(hfsq+R)+k*Ln2Lo
SUBSD X3, X0 // x0= hfsq-(s*(hfsq+R)+k*Ln2Lo), x1= k, x2= f
SUBSD X2, X0 // x0= (hfsq-(s*(hfsq+R)+k*Ln2Lo))-f, x1= k
MULSD $Ln2Hi, X1 // x0= (hfsq-(s*(hfsq+R)+k*Ln2Lo))-f, x1= k*Ln2Hi
SUBSD X0, X1 // x1= k*Ln2Hi-((hfsq-(s*(hfsq+R)+k*Ln2Lo))-f)
MOVSD X1, ret+8(FP)
RET
isInfOrNaN:
MOVQ BX, ret+8(FP) // +Inf or NaN, return x
RET
isNegative:
MOVQ $NaN, AX
MOVQ AX, ret+8(FP) // return NaN
RET
isZero:
MOVQ $NegInf, AX
MOVQ AX, ret+8(FP) // return -Inf
RET
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