mirrored from git://gcc.gnu.org/git/gcc.git
-
Notifications
You must be signed in to change notification settings - Fork 4.4k
/
sin.go
244 lines (223 loc) · 6.37 KB
/
sin.go
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
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
// Copyright 2011 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.
package math
/*
Floating-point sine and cosine.
*/
// The original C code, the long comment, and the constants
// below were from http://netlib.sandia.gov/cephes/cmath/sin.c,
// available from http://www.netlib.org/cephes/cmath.tgz.
// The go code is a simplified version of the original C.
//
// sin.c
//
// Circular sine
//
// SYNOPSIS:
//
// double x, y, sin();
// y = sin( x );
//
// DESCRIPTION:
//
// Range reduction is into intervals of pi/4. The reduction error is nearly
// eliminated by contriving an extended precision modular arithmetic.
//
// Two polynomial approximating functions are employed.
// Between 0 and pi/4 the sine is approximated by
// x + x**3 P(x**2).
// Between pi/4 and pi/2 the cosine is represented as
// 1 - x**2 Q(x**2).
//
// ACCURACY:
//
// Relative error:
// arithmetic domain # trials peak rms
// DEC 0, 10 150000 3.0e-17 7.8e-18
// IEEE -1.07e9,+1.07e9 130000 2.1e-16 5.4e-17
//
// Partial loss of accuracy begins to occur at x = 2**30 = 1.074e9. The loss
// is not gradual, but jumps suddenly to about 1 part in 10e7. Results may
// be meaningless for x > 2**49 = 5.6e14.
//
// cos.c
//
// Circular cosine
//
// SYNOPSIS:
//
// double x, y, cos();
// y = cos( x );
//
// DESCRIPTION:
//
// Range reduction is into intervals of pi/4. The reduction error is nearly
// eliminated by contriving an extended precision modular arithmetic.
//
// Two polynomial approximating functions are employed.
// Between 0 and pi/4 the cosine is approximated by
// 1 - x**2 Q(x**2).
// Between pi/4 and pi/2 the sine is represented as
// x + x**3 P(x**2).
//
// ACCURACY:
//
// Relative error:
// arithmetic domain # trials peak rms
// IEEE -1.07e9,+1.07e9 130000 2.1e-16 5.4e-17
// DEC 0,+1.07e9 17000 3.0e-17 7.2e-18
//
// Cephes Math Library Release 2.8: June, 2000
// Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
//
// The readme file at http://netlib.sandia.gov/cephes/ says:
// Some software in this archive may be from the book _Methods and
// Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster
// International, 1989) or from the Cephes Mathematical Library, a
// commercial product. In either event, it is copyrighted by the author.
// What you see here may be used freely but it comes with no support or
// guarantee.
//
// The two known misprints in the book are repaired here in the
// source listings for the gamma function and the incomplete beta
// integral.
//
// Stephen L. Moshier
// moshier@na-net.ornl.gov
// sin coefficients
var _sin = [...]float64{
1.58962301576546568060E-10, // 0x3de5d8fd1fd19ccd
-2.50507477628578072866E-8, // 0xbe5ae5e5a9291f5d
2.75573136213857245213E-6, // 0x3ec71de3567d48a1
-1.98412698295895385996E-4, // 0xbf2a01a019bfdf03
8.33333333332211858878E-3, // 0x3f8111111110f7d0
-1.66666666666666307295E-1, // 0xbfc5555555555548
}
// cos coefficients
var _cos = [...]float64{
-1.13585365213876817300E-11, // 0xbda8fa49a0861a9b
2.08757008419747316778E-9, // 0x3e21ee9d7b4e3f05
-2.75573141792967388112E-7, // 0xbe927e4f7eac4bc6
2.48015872888517045348E-5, // 0x3efa01a019c844f5
-1.38888888888730564116E-3, // 0xbf56c16c16c14f91
4.16666666666665929218E-2, // 0x3fa555555555554b
}
// Cos returns the cosine of the radian argument x.
//
// Special cases are:
// Cos(±Inf) = NaN
// Cos(NaN) = NaN
//extern cos
func libc_cos(float64) float64
func Cos(x float64) float64 {
return libc_cos(x)
}
func cos(x float64) float64 {
const (
PI4A = 7.85398125648498535156E-1 // 0x3fe921fb40000000, Pi/4 split into three parts
PI4B = 3.77489470793079817668E-8 // 0x3e64442d00000000,
PI4C = 2.69515142907905952645E-15 // 0x3ce8469898cc5170,
)
// special cases
switch {
case IsNaN(x) || IsInf(x, 0):
return NaN()
}
// make argument positive
sign := false
x = Abs(x)
var j uint64
var y, z float64
if x >= reduceThreshold {
j, z = trigReduce(x)
} else {
j = uint64(x * (4 / Pi)) // integer part of x/(Pi/4), as integer for tests on the phase angle
y = float64(j) // integer part of x/(Pi/4), as float
// map zeros to origin
if j&1 == 1 {
j++
y++
}
j &= 7 // octant modulo 2Pi radians (360 degrees)
z = ((x - y*PI4A) - y*PI4B) - y*PI4C // Extended precision modular arithmetic
}
if j > 3 {
j -= 4
sign = !sign
}
if j > 1 {
sign = !sign
}
zz := z * z
if j == 1 || j == 2 {
y = z + z*zz*((((((_sin[0]*zz)+_sin[1])*zz+_sin[2])*zz+_sin[3])*zz+_sin[4])*zz+_sin[5])
} else {
y = 1.0 - 0.5*zz + zz*zz*((((((_cos[0]*zz)+_cos[1])*zz+_cos[2])*zz+_cos[3])*zz+_cos[4])*zz+_cos[5])
}
if sign {
y = -y
}
return y
}
// Sin returns the sine of the radian argument x.
//
// Special cases are:
// Sin(±0) = ±0
// Sin(±Inf) = NaN
// Sin(NaN) = NaN
//extern sin
func libc_sin(float64) float64
func Sin(x float64) float64 {
return libc_sin(x)
}
func sin(x float64) float64 {
const (
PI4A = 7.85398125648498535156E-1 // 0x3fe921fb40000000, Pi/4 split into three parts
PI4B = 3.77489470793079817668E-8 // 0x3e64442d00000000,
PI4C = 2.69515142907905952645E-15 // 0x3ce8469898cc5170,
)
// special cases
switch {
case x == 0 || IsNaN(x):
return x // return ±0 || NaN()
case IsInf(x, 0):
return NaN()
}
// make argument positive but save the sign
sign := false
if x < 0 {
x = -x
sign = true
}
var j uint64
var y, z float64
if x >= reduceThreshold {
j, z = trigReduce(x)
} else {
j = uint64(x * (4 / Pi)) // integer part of x/(Pi/4), as integer for tests on the phase angle
y = float64(j) // integer part of x/(Pi/4), as float
// map zeros to origin
if j&1 == 1 {
j++
y++
}
j &= 7 // octant modulo 2Pi radians (360 degrees)
z = ((x - y*PI4A) - y*PI4B) - y*PI4C // Extended precision modular arithmetic
}
// reflect in x axis
if j > 3 {
sign = !sign
j -= 4
}
zz := z * z
if j == 1 || j == 2 {
y = 1.0 - 0.5*zz + zz*zz*((((((_cos[0]*zz)+_cos[1])*zz+_cos[2])*zz+_cos[3])*zz+_cos[4])*zz+_cos[5])
} else {
y = z + z*zz*((((((_sin[0]*zz)+_sin[1])*zz+_sin[2])*zz+_sin[3])*zz+_sin[4])*zz+_sin[5])
}
if sign {
y = -y
}
return y
}