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

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

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1
2/* @(#)e_acos.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_acos(x)
15 * Method :                 
16 *      acos(x)  = pi/2 - asin(x)
17 *      acos(-x) = pi/2 + asin(x)
18 * For |x|<=0.5
19 *      acos(x) = pi/2 - (x + x*x^2*R(x^2))     (see asin.c)
20 * For x>0.5
21 *      acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
22 *              = 2asin(sqrt((1-x)/2)) 
23 *              = 2s + 2s*z*R(z)        ...z=(1-x)/2, s=sqrt(z)
24 *              = 2f + (2c + 2s*z*R(z))
25 *     where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
26 *     for f so that f+c ~ sqrt(z).
27 * For x<-0.5
28 *      acos(x) = pi - 2asin(sqrt((1-|x|)/2))
29 *              = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
30 *
31 * Special cases:
32 *      if x is NaN, return x itself;
33 *      if |x|>1, return NaN with invalid signal.
34 *
35 * Function needed: sqrt
36 */
37
38#include <libm/fdlibm.h>
39
40#ifdef __STDC__
41static const double 
42#else
43static double 
44#endif
45one=  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
46pi =  3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
47pio2_hi =  1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
48pio2_lo =  6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
49pS0 =  1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
50pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
51pS2 =  2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
52pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
53pS4 =  7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
54pS5 =  3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
55qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
56qS2 =  2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
57qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
58qS4 =  7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
59
60#ifdef __STDC__
61        double __ieee754_acos(double x)
62#else
63        double __ieee754_acos(x)
64        double x;
65#endif
66{
67        double z,p,q,r,w,s,c,df;
68        int n0,hx,ix;
69        n0 = ((*(int*)&one)>>29)^1;
70        hx = *(n0+(int*)&x);
71        ix = hx&0x7fffffff;
72        if(ix>=0x3ff00000) {    /* |x| >= 1 */
73            if(((ix-0x3ff00000)|*(1-n0+(int*)&x))==0) { /* |x|==1 */
74                if(hx>0) return 0.0;            /* acos(1) = 0  */
75                else return pi+2.0*pio2_lo;     /* acos(-1)= pi */
76            }
77            return (x-x)/(x-x);         /* acos(|x|>1) is NaN */
78        }
79        if(ix<0x3fe00000) {     /* |x| < 0.5 */
80            if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/
81            z = x*x;
82            p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
83            q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
84            r = p/q;
85            return pio2_hi - (x - (pio2_lo-x*r));
86        } else  if (hx<0) {             /* x < -0.5 */
87            z = (one+x)*0.5;
88            p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
89            q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
90            s = sqrt(z);
91            r = p/q;
92            w = r*s-pio2_lo;
93            return pi - 2.0*(s+w);
94        } else {                        /* x > 0.5 */
95            z = (one-x)*0.5;
96            s = sqrt(z);
97            df = s;
98            *(1-n0+(int*)&df) = 0;
99            c  = (z-df*df)/(s+df);
100            p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
101            q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
102            r = p/q;
103            w = r*s+c;
104            return 2.0*(df+w);
105        }
106}
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