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Text file src/math/log_amd64.s

Documentation: math

     1	// Copyright 2010 The Go Authors. All rights reserved.
     2	// Use of this source code is governed by a BSD-style
     3	// license that can be found in the LICENSE file.
     4	
     5	#include "textflag.h"
     6	
     7	#define HSqrt2 7.07106781186547524401e-01 // sqrt(2)/2
     8	#define Ln2Hi  6.93147180369123816490e-01 // 0x3fe62e42fee00000
     9	#define Ln2Lo  1.90821492927058770002e-10 // 0x3dea39ef35793c76
    10	#define L1     6.666666666666735130e-01   // 0x3FE5555555555593
    11	#define L2     3.999999999940941908e-01   // 0x3FD999999997FA04
    12	#define L3     2.857142874366239149e-01   // 0x3FD2492494229359
    13	#define L4     2.222219843214978396e-01   // 0x3FCC71C51D8E78AF
    14	#define L5     1.818357216161805012e-01   // 0x3FC7466496CB03DE
    15	#define L6     1.531383769920937332e-01   // 0x3FC39A09D078C69F
    16	#define L7     1.479819860511658591e-01   // 0x3FC2F112DF3E5244
    17	#define NaN    0x7FF8000000000001
    18	#define NegInf 0xFFF0000000000000
    19	#define PosInf 0x7FF0000000000000
    20	
    21	// func Log(x float64) float64
    22	TEXT ·Log(SB),NOSPLIT,$0
    23		// test bits for special cases
    24		MOVQ    x+0(FP), BX
    25		MOVQ    $~(1<<63), AX // sign bit mask
    26		ANDQ    BX, AX
    27		JEQ     isZero
    28		MOVQ    $0, AX
    29		CMPQ    AX, BX
    30		JGT     isNegative
    31		MOVQ    $PosInf, AX
    32		CMPQ    AX, BX
    33		JLE     isInfOrNaN
    34		// f1, ki := math.Frexp(x); k := float64(ki)
    35		MOVQ    BX, X0
    36		MOVQ    $0x000FFFFFFFFFFFFF, AX
    37		MOVQ    AX, X2
    38		ANDPD   X0, X2
    39		MOVSD   $0.5, X0 // 0x3FE0000000000000
    40		ORPD    X0, X2 // X2= f1
    41		SHRQ    $52, BX
    42		ANDL    $0x7FF, BX
    43		SUBL    $0x3FE, BX
    44		XORPS   X1, X1 // break dependency for CVTSL2SD
    45		CVTSL2SD BX, X1 // x1= k, x2= f1
    46		// if f1 < math.Sqrt2/2 { k -= 1; f1 *= 2 }
    47		MOVSD   $HSqrt2, X0 // x0= 0.7071, x1= k, x2= f1
    48		CMPSD   X2, X0, 5 // cmpnlt; x0= 0 or ^0, x1= k, x2 = f1
    49		MOVSD   $1.0, X3 // x0= 0 or ^0, x1= k, x2 = f1, x3= 1
    50		ANDPD   X0, X3 // x0= 0 or ^0, x1= k, x2 = f1, x3= 0 or 1
    51		SUBSD   X3, X1 // x0= 0 or ^0, x1= k, x2 = f1, x3= 0 or 1
    52		MOVSD   $1.0, X0 // x0= 1, x1= k, x2= f1, x3= 0 or 1
    53		ADDSD   X0, X3 // x0= 1, x1= k, x2= f1, x3= 1 or 2
    54		MULSD   X3, X2 // x0= 1, x1= k, x2= f1
    55		// f := f1 - 1
    56		SUBSD   X0, X2 // x1= k, x2= f
    57		// s := f / (2 + f)
    58		MOVSD   $2.0, X0
    59		ADDSD   X2, X0
    60		MOVAPD  X2, X3
    61		DIVSD   X0, X3 // x1=k, x2= f, x3= s
    62		// s2 := s * s
    63		MOVAPD  X3, X4 // x1= k, x2= f, x3= s
    64		MULSD   X4, X4 // x1= k, x2= f, x3= s, x4= s2
    65		// s4 := s2 * s2
    66		MOVAPD  X4, X5 // x1= k, x2= f, x3= s, x4= s2
    67		MULSD   X5, X5 // x1= k, x2= f, x3= s, x4= s2, x5= s4
    68		// t1 := s2 * (L1 + s4*(L3+s4*(L5+s4*L7)))
    69		MOVSD   $L7, X6
    70		MULSD   X5, X6
    71		ADDSD   $L5, X6
    72		MULSD   X5, X6
    73		ADDSD   $L3, X6
    74		MULSD   X5, X6
    75		ADDSD   $L1, X6
    76		MULSD   X6, X4 // x1= k, x2= f, x3= s, x4= t1, x5= s4
    77		// t2 := s4 * (L2 + s4*(L4+s4*L6))
    78		MOVSD   $L6, X6
    79		MULSD   X5, X6
    80		ADDSD   $L4, X6
    81		MULSD   X5, X6
    82		ADDSD   $L2, X6
    83		MULSD   X6, X5 // x1= k, x2= f, x3= s, x4= t1, x5= t2
    84		// R := t1 + t2
    85		ADDSD   X5, X4 // x1= k, x2= f, x3= s, x4= R
    86		// hfsq := 0.5 * f * f
    87		MOVSD   $0.5, X0
    88		MULSD   X2, X0
    89		MULSD   X2, X0 // x0= hfsq, x1= k, x2= f, x3= s, x4= R
    90		// return k*Ln2Hi - ((hfsq - (s*(hfsq+R) + k*Ln2Lo)) - f)
    91		ADDSD   X0, X4 // x0= hfsq, x1= k, x2= f, x3= s, x4= hfsq+R
    92		MULSD   X4, X3 // x0= hfsq, x1= k, x2= f, x3= s*(hfsq+R)
    93		MOVSD   $Ln2Lo, X4
    94		MULSD   X1, X4 // x4= k*Ln2Lo
    95		ADDSD   X4, X3 // x0= hfsq, x1= k, x2= f, x3= s*(hfsq+R)+k*Ln2Lo
    96		SUBSD   X3, X0 // x0= hfsq-(s*(hfsq+R)+k*Ln2Lo), x1= k, x2= f
    97		SUBSD   X2, X0 // x0= (hfsq-(s*(hfsq+R)+k*Ln2Lo))-f, x1= k
    98		MULSD   $Ln2Hi, X1 // x0= (hfsq-(s*(hfsq+R)+k*Ln2Lo))-f, x1= k*Ln2Hi
    99		SUBSD   X0, X1 // x1= k*Ln2Hi-((hfsq-(s*(hfsq+R)+k*Ln2Lo))-f)
   100	  	MOVSD   X1, ret+8(FP)
   101		RET
   102	isInfOrNaN:
   103		MOVQ    BX, ret+8(FP) // +Inf or NaN, return x
   104		RET
   105	isNegative:
   106		MOVQ    $NaN, AX
   107		MOVQ    AX, ret+8(FP) // return NaN
   108		RET
   109	isZero:
   110		MOVQ    $NegInf, AX
   111		MOVQ    AX, ret+8(FP) // return -Inf
   112		RET

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