source: trunk/sys/libm/e_asin.c @ 1

Last change on this file since 1 was 1, checked in by alain, 5 years ago

First import

File size: 3.5 KB
Line 
1
2/* @(#)e_asin.c 5.1 93/09/24 */
3/*
4 * ====================================================
5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 *
7 * Developed at SunPro, a Sun Microsystems, Inc. business.
8 * Permission to use, copy, modify, and distribute this
9 * software is freely granted, provided that this notice
10 * is preserved.
11 * ====================================================
12 */
13
14/* __ieee754_asin(x)
15 * Method :                 
16 *      Since  asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
17 *      we approximate asin(x) on [0,0.5] by
18 *              asin(x) = x + x*x^2*R(x^2)
19 *      where
20 *              R(x^2) is a rational approximation of (asin(x)-x)/x^3
21 *      and its remez error is bounded by
22 *              |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75)
23 *
24 *      For x in [0.5,1]
25 *              asin(x) = pi/2-2*asin(sqrt((1-x)/2))
26 *      Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
27 *      then for x>0.98
28 *              asin(x) = pi/2 - 2*(s+s*z*R(z))
29 *                      = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
30 *      For x<=0.98, let pio4_hi = pio2_hi/2, then
31 *              f = hi part of s;
32 *              c = sqrt(z) - f = (z-f*f)/(s+f)         ...f+c=sqrt(z)
33 *      and
34 *              asin(x) = pi/2 - 2*(s+s*z*R(z))
35 *                      = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
36 *                      = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
37 *
38 * Special cases:
39 *      if x is NaN, return x itself;
40 *      if |x|>1, return NaN with invalid signal.
41 *
42 */
43
44
45#include <libm/fdlibm.h>
46
47#ifdef __STDC__
48static const double 
49#else
50static double 
51#endif
52one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
53huge =  1.000e+300,
54pio2_hi =  1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
55pio2_lo =  6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
56pio4_hi =  7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
57        /* coefficient for R(x^2) */
58pS0 =  1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
59pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
60pS2 =  2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
61pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
62pS4 =  7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
63pS5 =  3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
64qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
65qS2 =  2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
66qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
67qS4 =  7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
68
69#ifdef __STDC__
70        double __ieee754_asin(double x)
71#else
72        double __ieee754_asin(x)
73        double x;
74#endif
75{
76        double t = 0.0,w,p,q,c,r,s;
77        int n0,hx,ix;
78        n0 = ((*(int*)&one)>>29)^1;
79        hx = *(n0+(int*)&x);
80        ix = hx&0x7fffffff;
81        if(ix>= 0x3ff00000) {           /* |x|>= 1 */
82            if(((ix-0x3ff00000)|*(1-n0+(int*)&x))==0)
83                    /* asin(1)=+-pi/2 with inexact */
84                return x*pio2_hi+x*pio2_lo;     
85            return (x-x)/(x-x);         /* asin(|x|>1) is NaN */   
86        } else if (ix<0x3fe00000) {     /* |x|<0.5 */
87            if(ix<0x3e400000) {         /* if |x| < 2**-27 */
88                if(huge+x>one) return x;/* return x with inexact if x!=0*/
89            } else 
90                t = x*x;
91                p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
92                q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
93                w = p/q;
94                return x+x*w;
95        }
96        /* 1> |x|>= 0.5 */
97        w = one-fabs(x);
98        t = w*0.5;
99        p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
100        q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
101        s = sqrt(t);
102        if(ix>=0x3FEF3333) {    /* if |x| > 0.975 */
103            w = p/q;
104            t = pio2_hi-(2.0*(s+s*w)-pio2_lo);
105        } else {
106            w  = s;
107            *(1-n0+(int*)&w) = 0;
108            c  = (t-w*w)/(s+w);
109            r  = p/q;
110            p  = 2.0*s*r-(pio2_lo-2.0*c);
111            q  = pio4_hi-2.0*w;
112            t  = pio4_hi-(p-q);
113        }   
114        if(hx>0) return t; else return -t;   
115}
Note: See TracBrowser for help on using the repository browser.