Text file src/math/log_amd64.s

     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 ¬∑archLog(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
   113  

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