Text file src/pkg/math/exp_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 // The method is based on a paper by Naoki Shibata: "Efficient evaluation
8 // methods of elementary functions suitable for SIMD computation", Proc.
9 // of International Supercomputing Conference 2010 (ISC'10), pp. 25 -- 32
10 // (May 2010). The paper is available at
11 // https://www.springerlink.com/content/340228x165742104/
12 //
13 // The original code and the constants below are from the author's
14 // implementation available at http://freshmeat.net/projects/sleef.
15 // The README file says, "The software is in public domain.
16 // You can use the software without any obligation."
17 //
18 // This code is a simplified version of the original.
19
20 #define LN2 0.6931471805599453094172321214581766 // log_e(2)
21 #define LOG2E 1.4426950408889634073599246810018920 // 1/LN2
22 #define LN2U 0.69314718055966295651160180568695068359375 // upper half LN2
23 #define LN2L 0.28235290563031577122588448175013436025525412068e-12 // lower half LN2
24 #define PosInf 0x7FF0000000000000
25 #define NegInf 0xFFF0000000000000
26 #define Overflow 7.09782712893384e+02
27
28 DATA exprodata<>+0(SB)/8, $0.5
29 DATA exprodata<>+8(SB)/8, $1.0
30 DATA exprodata<>+16(SB)/8, $2.0
31 DATA exprodata<>+24(SB)/8, $1.6666666666666666667e-1
32 DATA exprodata<>+32(SB)/8, $4.1666666666666666667e-2
33 DATA exprodata<>+40(SB)/8, $8.3333333333333333333e-3
34 DATA exprodata<>+48(SB)/8, $1.3888888888888888889e-3
35 DATA exprodata<>+56(SB)/8, $1.9841269841269841270e-4
36 DATA exprodata<>+64(SB)/8, $2.4801587301587301587e-5
37 GLOBL exprodata<>+0(SB), RODATA, $72
38
39 // func Exp(x float64) float64
40 TEXT ·Exp(SB),NOSPLIT,$0
41 // test bits for not-finite
42 MOVQ x+0(FP), BX
43 MOVQ $~(1<<63), AX // sign bit mask
44 MOVQ BX, DX
45 ANDQ AX, DX
46 MOVQ $PosInf, AX
47 CMPQ AX, DX
48 JLE notFinite
49 // check if argument will overflow
50 MOVQ BX, X0
51 MOVSD $Overflow, X1
52 COMISD X1, X0
53 JA overflow
54 MOVSD $LOG2E, X1
55 MULSD X0, X1
56 CVTSD2SL X1, BX // BX = exponent
57 CVTSL2SD BX, X1
58 CMPB ·useFMA(SB), $1
59 JE avxfma
60 MOVSD $LN2U, X2
61 MULSD X1, X2
62 SUBSD X2, X0
63 MOVSD $LN2L, X2
64 MULSD X1, X2
65 SUBSD X2, X0
66 // reduce argument
67 MULSD $0.0625, X0
68 // Taylor series evaluation
69 MOVSD exprodata<>+64(SB), X1
70 MULSD X0, X1
71 ADDSD exprodata<>+56(SB), X1
72 MULSD X0, X1
73 ADDSD exprodata<>+48(SB), X1
74 MULSD X0, X1
75 ADDSD exprodata<>+40(SB), X1
76 MULSD X0, X1
77 ADDSD exprodata<>+32(SB), X1
78 MULSD X0, X1
79 ADDSD exprodata<>+24(SB), X1
80 MULSD X0, X1
81 ADDSD exprodata<>+0(SB), X1
82 MULSD X0, X1
83 ADDSD exprodata<>+8(SB), X1
84 MULSD X1, X0
85 MOVSD exprodata<>+16(SB), X1
86 ADDSD X0, X1
87 MULSD X1, X0
88 MOVSD exprodata<>+16(SB), X1
89 ADDSD X0, X1
90 MULSD X1, X0
91 MOVSD exprodata<>+16(SB), X1
92 ADDSD X0, X1
93 MULSD X1, X0
94 MOVSD exprodata<>+16(SB), X1
95 ADDSD X0, X1
96 MULSD X1, X0
97 ADDSD exprodata<>+8(SB), X0
98 // return fr * 2**exponent
99 ldexp:
100 ADDL $0x3FF, BX // add bias
101 JLE denormal
102 CMPL BX, $0x7FF
103 JGE overflow
104 lastStep:
105 SHLQ $52, BX
106 MOVQ BX, X1
107 MULSD X1, X0
108 MOVSD X0, ret+8(FP)
109 RET
110 notFinite:
111 // test bits for -Inf
112 MOVQ $NegInf, AX
113 CMPQ AX, BX
114 JNE notNegInf
115 // -Inf, return 0
116 underflow: // return 0
117 MOVQ $0, ret+8(FP)
118 RET
119 overflow: // return +Inf
120 MOVQ $PosInf, BX
121 notNegInf: // NaN or +Inf, return x
122 MOVQ BX, ret+8(FP)
123 RET
124 denormal:
125 CMPL BX, $-52
126 JL underflow
127 ADDL $0x3FE, BX // add bias - 1
128 SHLQ $52, BX
129 MOVQ BX, X1
130 MULSD X1, X0
131 MOVQ $1, BX
132 JMP lastStep
133
134 avxfma:
135 MOVSD $LN2U, X2
136 VFNMADD231SD X2, X1, X0
137 MOVSD $LN2L, X2
138 VFNMADD231SD X2, X1, X0
139 // reduce argument
140 MULSD $0.0625, X0
141 // Taylor series evaluation
142 MOVSD exprodata<>+64(SB), X1
143 VFMADD213SD exprodata<>+56(SB), X0, X1
144 VFMADD213SD exprodata<>+48(SB), X0, X1
145 VFMADD213SD exprodata<>+40(SB), X0, X1
146 VFMADD213SD exprodata<>+32(SB), X0, X1
147 VFMADD213SD exprodata<>+24(SB), X0, X1
148 VFMADD213SD exprodata<>+0(SB), X0, X1
149 VFMADD213SD exprodata<>+8(SB), X0, X1
150 MULSD X1, X0
151 VADDSD exprodata<>+16(SB), X0, X1
152 MULSD X1, X0
153 VADDSD exprodata<>+16(SB), X0, X1
154 MULSD X1, X0
155 VADDSD exprodata<>+16(SB), X0, X1
156 MULSD X1, X0
157 VADDSD exprodata<>+16(SB), X0, X1
158 VFMADD213SD exprodata<>+8(SB), X1, X0
159 JMP ldexp
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