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log_amd64.s
// 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
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