```   1 /*
3  *
4  * The contents of this file are subject to the terms of the
6  * You may not use this file except in compliance with the License.
7  *
8  * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
9  * or http://www.opensolaris.org/os/licensing.
10  * See the License for the specific language governing permissions
11  * and limitations under the License.
12  *
13  * When distributing Covered Code, include this CDDL HEADER in each
15  * If applicable, add the following below this CDDL HEADER, with the
16  * fields enclosed by brackets "[]" replaced with your own identifying
18  *
20  */
21
22 /*
24  */
25 /*
27  * Use is subject to license terms.
28  */
29
30 #pragma weak asin = __asin
31
32 /* INDENT OFF */
33 /*
34  * asin(x)
35  * Method :
36  *      Since  asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
37  *      we approximate asin(x) on [0,0.5] by
38  *              asin(x) = x + x*x^2*R(x^2)
39  *      where
40  *              R(x^2) is a rational approximation of (asin(x)-x)/x^3
41  *      and its remez error is bounded by
42  *              |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75)
43  *
44  *      For x in [0.5,1]
45  *              asin(x) = pi/2-2*asin(sqrt((1-x)/2))
46  *      Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
47  *      then for x>0.98
48  *              asin(x) = pi/2 - 2*(s+s*z*R(z))
49  *                      = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
50  *      For x<=0.98, let pio4_hi = pio2_hi/2, then
51  *              f = hi part of s;
52  *              c = sqrt(z) - f = (z-f*f)/(s+f)         ...f+c=sqrt(z)
53  *      and
54  *              asin(x) = pi/2 - 2*(s+s*z*R(z))
55  *                      = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
56  *                      = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
57  *
58  * Special cases:
59  *      if x is NaN, return x itself;
60  *      if |x|>1, return NaN with invalid signal.
61  *
62  */
63 /* INDENT ON */
64
65 #include "libm_synonyms.h"      /* __asin, __sqrt, __isnan */
66 #include "libm_protos.h"        /* _SVID_libm_error */
67 #include "libm_macros.h"
68 #include <math.h>
69
70 /* INDENT OFF */
71 static const double xxx[] = {
72 /* one */        1.00000000000000000000e+00,    /* 3FF00000, 00000000 */
73 /* huge */       1.000e+300,
74 /* pio2_hi */    1.57079632679489655800e+00,    /* 3FF921FB, 54442D18 */
75 /* pio2_lo */    6.12323399573676603587e-17,    /* 3C91A626, 33145C07 */
76 /* pio4_hi */    7.85398163397448278999e-01,    /* 3FE921FB, 54442D18 */
77 /* coefficient for R(x^2) */
78 /* pS0 */        1.66666666666666657415e-01,    /* 3FC55555, 55555555 */
79 /* pS1 */       -3.25565818622400915405e-01,    /* BFD4D612, 03EB6F7D */
80 /* pS2 */        2.01212532134862925881e-01,    /* 3FC9C155, 0E884455 */
81 /* pS3 */       -4.00555345006794114027e-02,    /* BFA48228, B5688F3B */
82 /* pS4 */        7.91534994289814532176e-04,    /* 3F49EFE0, 7501B288 */
83 /* pS5 */        3.47933107596021167570e-05,    /* 3F023DE1, 0DFDF709 */
84 /* qS1 */       -2.40339491173441421878e+00,    /* C0033A27, 1C8A2D4B */
85 /* qS2 */        2.02094576023350569471e+00,    /* 40002AE5, 9C598AC8 */
86 /* qS3 */       -6.88283971605453293030e-01,    /* BFE6066C, 1B8D0159 */
87 /* qS4 */        7.70381505559019352791e-02     /* 3FB3B8C5, B12E9282 */
88 };
89 #define one     xxx[0]
90 #define huge    xxx[1]
91 #define pio2_hi xxx[2]
92 #define pio2_lo xxx[3]
93 #define pio4_hi xxx[4]
94 #define pS0     xxx[5]
95 #define pS1     xxx[6]
96 #define pS2     xxx[7]
97 #define pS3     xxx[8]
98 #define pS4     xxx[9]
99 #define pS5     xxx[10]
100 #define qS1     xxx[11]
101 #define qS2     xxx[12]
102 #define qS3     xxx[13]
103 #define qS4     xxx[14]
104 /* INDENT ON */
105
106 double
107 asin(double x) {
108         double t, w, p, q, c, r, s;
109         int hx, ix, i;
110
111         hx = ((int *) &x)[HIWORD];
112         ix = hx & 0x7fffffff;
113         if (ix >= 0x3ff00000) {      /* |x| >= 1 */
114                 if (((ix - 0x3ff00000) | ((int *) &x)[LOWORD]) == 0)
115                         /* asin(1)=+-pi/2 with inexact */
116                         return (x * pio2_hi + x * pio2_lo);
117                 else if (isnan(x))
119                         return (ix >= 0x7ff80000 ? x : (x - x) / (x - x));
120                         /* assumes sparc-like QNaN */
121 #else
122                         return (x - x) / (x - x);       /* asin(|x|>1) is NaN */
123 #endif
124                 else
125                         return (_SVID_libm_err(x, x, 2));
126         } else if (ix < 0x3fe00000) {        /* |x| < 0.5 */
127                 if (ix < 0x3e400000) {       /* if |x| < 2**-27 */
128                         if ((i = (int) x) == 0)
129                                 /* return x with inexact if x != 0 */
130                                 return (x);
131                 }
132                 t = x * x;
133                 p = t * (pS0 + t * (pS1 + t * (pS2 + t * (pS3 +
134                         t * (pS4 + t * pS5)))));
135                 q = one + t * (qS1 + t * (qS2 + t * (qS3 + t * qS4)));
136                 w = p / q;
137                 return (x + x * w);
138         }
139         /* 1 > |x| >= 0.5 */
140         w = one - fabs(x);
141         t = w * 0.5;
142         p = t * (pS0 + t * (pS1 + t * (pS2 + t * (pS3 + t * (pS4 + t * pS5)))));
143         q = one + t * (qS1 + t * (qS2 + t * (qS3 + t * qS4)));
144         s = sqrt(t);
145         if (ix >= 0x3FEF3333) {      /* if |x| > 0.975 */
146                 w = p / q;
147                 t = pio2_hi - (2.0 * (s + s * w) - pio2_lo);
148         } else {
149                 w = s;
150                 ((int *) &w)[LOWORD] = 0;
151                 c = (t - w * w) / (s + w);
152                 r = p / q;
153                 p = 2.0 * s * r - (pio2_lo - 2.0 * c);
154                 q = pio4_hi - 2.0 * w;
155                 t = pio4_hi - (p - q);
156         }
157         return (hx > 0 ? t : -t);
158 }
```