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 113
