forked from bonzini/smalltalk
/
asinl.c
218 lines (194 loc) · 6.38 KB
/
asinl.c
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
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#include "mathl.h"
/*
Long double expansions contributed by
Stephen L. Moshier <moshier@na-net.ornl.gov>
*/
/* asin(x)
* Method :
* Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
* we approximate asin(x) on [0,0.5] by
* asin(x) = x + x*x^2*R(x^2)
* Between .5 and .625 the approximation is
* asin(0.5625 + x) = asin(0.5625) + x rS(x) / sS(x)
* For x in [0.625,1]
* asin(x) = pi/2-2*asin(sqrt((1-x)/2))
*
* Special cases:
* if x is NaN, return x itself;
* if |x|>1, return NaN with invalid signal.
*
*/
#include <math.h>
static const long double
one = 1.0L,
huge = 1.0e+4932L,
pio2_hi = 1.5707963267948966192313216916397514420986L,
pio2_lo = 4.3359050650618905123985220130216759843812E-35L,
pio4_hi = 7.8539816339744830961566084581987569936977E-1L,
/* coefficient for R(x^2) */
/* asin(x) = x + x^3 pS(x^2) / qS(x^2)
0 <= x <= 0.5
peak relative error 1.9e-35 */
pS0 = -8.358099012470680544198472400254596543711E2L,
pS1 = 3.674973957689619490312782828051860366493E3L,
pS2 = -6.730729094812979665807581609853656623219E3L,
pS3 = 6.643843795209060298375552684423454077633E3L,
pS4 = -3.817341990928606692235481812252049415993E3L,
pS5 = 1.284635388402653715636722822195716476156E3L,
pS6 = -2.410736125231549204856567737329112037867E2L,
pS7 = 2.219191969382402856557594215833622156220E1L,
pS8 = -7.249056260830627156600112195061001036533E-1L,
pS9 = 1.055923570937755300061509030361395604448E-3L,
qS0 = -5.014859407482408326519083440151745519205E3L,
qS1 = 2.430653047950480068881028451580393430537E4L,
qS2 = -4.997904737193653607449250593976069726962E4L,
qS3 = 5.675712336110456923807959930107347511086E4L,
qS4 = -3.881523118339661268482937768522572588022E4L,
qS5 = 1.634202194895541569749717032234510811216E4L,
qS6 = -4.151452662440709301601820849901296953752E3L,
qS7 = 5.956050864057192019085175976175695342168E2L,
qS8 = -4.175375777334867025769346564600396877176E1L,
/* 1.000000000000000000000000000000000000000E0 */
/* asin(0.5625 + x) = asin(0.5625) + x rS(x) / sS(x)
-0.0625 <= x <= 0.0625
peak relative error 3.3e-35 */
rS0 = -5.619049346208901520945464704848780243887E0L,
rS1 = 4.460504162777731472539175700169871920352E1L,
rS2 = -1.317669505315409261479577040530751477488E2L,
rS3 = 1.626532582423661989632442410808596009227E2L,
rS4 = -3.144806644195158614904369445440583873264E1L,
rS5 = -9.806674443470740708765165604769099559553E1L,
rS6 = 5.708468492052010816555762842394927806920E1L,
rS7 = 1.396540499232262112248553357962639431922E1L,
rS8 = -1.126243289311910363001762058295832610344E1L,
rS9 = -4.956179821329901954211277873774472383512E-1L,
rS10 = 3.313227657082367169241333738391762525780E-1L,
sS0 = -4.645814742084009935700221277307007679325E0L,
sS1 = 3.879074822457694323970438316317961918430E1L,
sS2 = -1.221986588013474694623973554726201001066E2L,
sS3 = 1.658821150347718105012079876756201905822E2L,
sS4 = -4.804379630977558197953176474426239748977E1L,
sS5 = -1.004296417397316948114344573811562952793E2L,
sS6 = 7.530281592861320234941101403870010111138E1L,
sS7 = 1.270735595411673647119592092304357226607E1L,
sS8 = -1.815144839646376500705105967064792930282E1L,
sS9 = -7.821597334910963922204235247786840828217E-2L,
/* 1.000000000000000000000000000000000000000E0 */
asinr5625 = 5.9740641664535021430381036628424864397707E-1L;
long double
asinl (long double x)
{
long double y, t, p, q;
int sign;
sign = 1;
y = x;
if (x < 0.0L)
{
sign = -1;
y = -x;
}
if (y >= 1.0L) /* |x|>= 1 */
{
if (y == 1.0L)
/* asin(1)=+-pi/2 with inexact */
return x * pio2_hi + x * pio2_lo;
return (x - x) / (x - x); /* asin(|x|>1) is NaN */
}
else if (y < 0.5L) /* |x| < 0.5 */
{
if (y < 0.000000000000000006938893903907228377647697925567626953125L) /* |x| < 2**-57 */
if (huge + y > one)
return y; /* return x with inexact if x!=0 */
t = x * x;
p = (((((((((pS9 * t
+ pS8) * t
+ pS7) * t
+ pS6) * t
+ pS5) * t
+ pS4) * t
+ pS3) * t
+ pS2) * t
+ pS1) * t
+ pS0) * t;
q = (((((((( t
+ qS8) * t
+ qS7) * t
+ qS6) * t
+ qS5) * t
+ qS4) * t
+ qS3) * t
+ qS2) * t
+ qS1) * t
+ qS0;
return x + x * (p / q);
}
else if (y < 0.625) /* 0.625 */
{
t = y - 0.5625;
p = ((((((((((rS10 * t
+ rS9) * t
+ rS8) * t
+ rS7) * t
+ rS6) * t
+ rS5) * t
+ rS4) * t
+ rS3) * t
+ rS2) * t
+ rS1) * t
+ rS0) * t;
q = ((((((((( t
+ sS9) * t
+ sS8) * t
+ sS7) * t
+ sS6) * t
+ sS5) * t
+ sS4) * t
+ sS3) * t
+ sS2) * t
+ sS1) * t
+ sS0;
t = asinr5625 + p / q;
}
else
t = pio2_hi + pio2_lo - 2 * asinl(sqrtl((1-y)/2));
return t * sign;
}
#if 0
main()
{
printf ("%.18Lg %.18Lg\n",
asinl(1.0L),
1.5707963267948966192313216916397514420984L);
printf ("%.18Lg %.18Lg\n",
asinl(0.7071067811865475244008443621048490392848L),
0.7853981633974483096156608458198757210492L);
printf ("%.18Lg %.18Lg\n",
asinl(0.5L),
0.5235987755982988730771072305465838140328L);
printf ("%.18Lg %.18Lg\n",
asinl(0.3090169943749474241022934171828190588600L),
0.3141592653589793238462643383279502884196L);
printf ("%.18Lg %.18Lg\n",
asinl(-1.0L),
-1.5707963267948966192313216916397514420984L);
printf ("%.18Lg %.18Lg\n",
asinl(-0.7071067811865475244008443621048490392848L),
-0.7853981633974483096156608458198757210492L);
printf ("%.18Lg %.18Lg\n",
asinl(-0.5L),
-0.5235987755982988730771072305465838140328L);
printf ("%.18Lg %.18Lg\n",
asinl(-0.3090169943749474241022934171828190588600L),
-0.3141592653589793238462643383279502884196L);
}
#endif