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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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