1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
|
// Copyright 2017 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"
// Minimax polynomial approximation and other constants
DATA ·expm1rodataL22<> + 0(SB)/8, $-1.0
DATA ·expm1rodataL22<> + 8(SB)/8, $800.0E+00
DATA ·expm1rodataL22<> + 16(SB)/8, $1.0
DATA ·expm1rodataL22<> + 24(SB)/8, $-.231904681384629956E-16
DATA ·expm1rodataL22<> + 32(SB)/8, $0.50000000000000029671E+00
DATA ·expm1rodataL22<> + 40(SB)/8, $0.16666666666666676570E+00
DATA ·expm1rodataL22<> + 48(SB)/8, $0.83333333323590973444E-02
DATA ·expm1rodataL22<> + 56(SB)/8, $0.13889096526400683566E-02
DATA ·expm1rodataL22<> + 64(SB)/8, $0.41666666661701152924E-01
DATA ·expm1rodataL22<> + 72(SB)/8, $0.19841562053987360264E-03
DATA ·expm1rodataL22<> + 80(SB)/8, $-.693147180559945286E+00
DATA ·expm1rodataL22<> + 88(SB)/8, $0.144269504088896339E+01
DATA ·expm1rodataL22<> + 96(SB)/8, $704.0E+00
GLOBL ·expm1rodataL22<> + 0(SB), RODATA, $104
DATA ·expm1xmone<> + 0(SB)/8, $0xbff0000000000000
GLOBL ·expm1xmone<> + 0(SB), RODATA, $8
DATA ·expm1xinf<> + 0(SB)/8, $0x7ff0000000000000
GLOBL ·expm1xinf<> + 0(SB), RODATA, $8
DATA ·expm1x4ff<> + 0(SB)/8, $0x4ff0000000000000
GLOBL ·expm1x4ff<> + 0(SB), RODATA, $8
DATA ·expm1x2ff<> + 0(SB)/8, $0x2ff0000000000000
GLOBL ·expm1x2ff<> + 0(SB), RODATA, $8
DATA ·expm1xaddexp<> + 0(SB)/8, $0xc2f0000100003ff0
GLOBL ·expm1xaddexp<> + 0(SB), RODATA, $8
// Log multipliers table
DATA ·expm1tab<> + 0(SB)/8, $0.0
DATA ·expm1tab<> + 8(SB)/8, $-.171540871271399150E-01
DATA ·expm1tab<> + 16(SB)/8, $-.306597931864376363E-01
DATA ·expm1tab<> + 24(SB)/8, $-.410200970469965021E-01
DATA ·expm1tab<> + 32(SB)/8, $-.486343079978231466E-01
DATA ·expm1tab<> + 40(SB)/8, $-.538226193725835820E-01
DATA ·expm1tab<> + 48(SB)/8, $-.568439602538111520E-01
DATA ·expm1tab<> + 56(SB)/8, $-.579091847395528847E-01
DATA ·expm1tab<> + 64(SB)/8, $-.571909584179366341E-01
DATA ·expm1tab<> + 72(SB)/8, $-.548312665987204407E-01
DATA ·expm1tab<> + 80(SB)/8, $-.509471843643441085E-01
DATA ·expm1tab<> + 88(SB)/8, $-.456353588448863359E-01
DATA ·expm1tab<> + 96(SB)/8, $-.389755254243262365E-01
DATA ·expm1tab<> + 104(SB)/8, $-.310332908285244231E-01
DATA ·expm1tab<> + 112(SB)/8, $-.218623539150173528E-01
DATA ·expm1tab<> + 120(SB)/8, $-.115062908917949451E-01
GLOBL ·expm1tab<> + 0(SB), RODATA, $128
// Expm1 returns e**x - 1, the base-e exponential of x minus 1.
// It is more accurate than Exp(x) - 1 when x is near zero.
//
// Special cases are:
// Expm1(+Inf) = +Inf
// Expm1(-Inf) = -1
// Expm1(NaN) = NaN
// Very large values overflow to -1 or +Inf.
// The algorithm used is minimax polynomial approximation using a table of
// polynomial coefficients determined with a Remez exchange algorithm.
TEXT ·expm1Asm(SB), NOSPLIT, $0-16
FMOVD x+0(FP), F0
MOVD $·expm1rodataL22<>+0(SB), R5
LTDBR F0, F0
BLTU L20
FMOVD F0, F2
L2:
WORD $0xED205060 //cdb %f2,.L23-.L22(%r5)
BYTE $0x00
BYTE $0x19
BGE L16
BVS L16
WFCEDBS V2, V2, V2
BVS LEXITTAGexpm1
MOVD $·expm1xaddexp<>+0(SB), R1
FMOVD 88(R5), F1
FMOVD 0(R1), F2
WFMSDB V0, V1, V2, V1
FMOVD 80(R5), F6
WFADB V1, V2, V4
FMOVD 72(R5), F2
FMADD F6, F4, F0
FMOVD 64(R5), F3
FMOVD 56(R5), F6
FMOVD 48(R5), F5
FMADD F2, F0, F6
WFMADB V0, V5, V3, V5
WFMDB V0, V0, V2
LGDR F1, R1
WFMADB V6, V2, V5, V6
FMOVD 40(R5), F3
FMOVD 32(R5), F5
WFMADB V0, V3, V5, V3
FMOVD 24(R5), F5
WFMADB V2, V6, V3, V2
FMADD F5, F4, F0
FMOVD 16(R5), F6
WFMADB V0, V2, V6, V2
RISBGZ $57, $60, $3, R1, R3
WORD $0xB3130022 //lcdbr %f2,%f2
MOVD $·expm1tab<>+0(SB), R2
WORD $0x68432000 //ld %f4,0(%r3,%r2)
FMADD F4, F0, F0
SLD $48, R1, R2
WFMSDB V2, V0, V4, V0
LDGR R2, F4
WORD $0xB3130000 //lcdbr %f0,%f0
FSUB F4, F6
WFMSDB V0, V4, V6, V0
FMOVD F0, ret+8(FP)
RET
L16:
WFCEDBS V2, V2, V4
BVS LEXITTAGexpm1
WORD $0xED205008 //cdb %f2,.L34-.L22(%r5)
BYTE $0x00
BYTE $0x19
BLT L6
WFCEDBS V2, V0, V0
BVS L7
MOVD $·expm1xinf<>+0(SB), R1
FMOVD 0(R1), F0
FMOVD F0, ret+8(FP)
RET
L20:
WORD $0xB3130020 //lcdbr %f2,%f0
BR L2
L6:
MOVD $·expm1xaddexp<>+0(SB), R1
FMOVD 88(R5), F5
FMOVD 0(R1), F4
WFMSDB V0, V5, V4, V5
FMOVD 80(R5), F3
WFADB V5, V4, V1
VLEG $0, 48(R5), V16
WFMADB V1, V3, V0, V3
FMOVD 56(R5), F4
FMOVD 64(R5), F7
FMOVD 72(R5), F6
WFMADB V3, V16, V7, V16
WFMADB V3, V6, V4, V6
WFMDB V3, V3, V4
MOVD $·expm1tab<>+0(SB), R2
WFMADB V6, V4, V16, V6
VLEG $0, 32(R5), V16
FMOVD 40(R5), F7
WFMADB V3, V7, V16, V7
VLEG $0, 24(R5), V16
WFMADB V4, V6, V7, V4
WFMADB V1, V16, V3, V1
FMOVD 16(R5), F6
FMADD F4, F1, F6
LGDR F5, R1
WORD $0xB3130066 //lcdbr %f6,%f6
RISBGZ $57, $60, $3, R1, R3
WORD $0x68432000 //ld %f4,0(%r3,%r2)
FMADD F4, F1, F1
MOVD $0x4086000000000000, R2
FMSUB F1, F6, F4
WORD $0xB3130044 //lcdbr %f4,%f4
WFCHDBS V2, V0, V0
BEQ L21
ADDW $0xF000, R1
RISBGN $0, $15, $48, R1, R2
LDGR R2, F0
FMADD F0, F4, F0
MOVD $·expm1x4ff<>+0(SB), R3
FMOVD 0(R5), F4
FMOVD 0(R3), F2
WFMADB V2, V0, V4, V0
FMOVD F0, ret+8(FP)
RET
L7:
MOVD $·expm1xmone<>+0(SB), R1
FMOVD 0(R1), F0
FMOVD F0, ret+8(FP)
RET
L21:
ADDW $0x1000, R1
RISBGN $0, $15, $48, R1, R2
LDGR R2, F0
FMADD F0, F4, F0
MOVD $·expm1x2ff<>+0(SB), R3
FMOVD 0(R5), F4
FMOVD 0(R3), F2
WFMADB V2, V0, V4, V0
FMOVD F0, ret+8(FP)
RET
LEXITTAGexpm1:
FMOVD F0, ret+8(FP)
RET
|
