// 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 ·archLog(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