e_acos.c revision 97407 
1/* @(#)e_acos.c 5.1 93/09/24 */
2/*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunPro, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
9 * is preserved.
10 * ====================================================
11 */
12
13#ifndef lint
14static char rcsid[] = "$FreeBSD: head/lib/msun/src/e_acos.c 97407 2002-05-28 17:03:12Z alfred $";
15#endif
16
17/* __ieee754_acos(x)
18 * Method :
19 *	acos(x)  = pi/2 - asin(x)
20 *	acos(-x) = pi/2 + asin(x)
21 * For |x|<=0.5
22 *	acos(x) = pi/2 - (x + x*x^2*R(x^2))	(see asin.c)
23 * For x>0.5
24 * 	acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
25 *		= 2asin(sqrt((1-x)/2))
26 *		= 2s + 2s*z*R(z) 	...z=(1-x)/2, s=sqrt(z)
27 *		= 2f + (2c + 2s*z*R(z))
28 *     where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
29 *     for f so that f+c ~ sqrt(z).
30 * For x<-0.5
31 *	acos(x) = pi - 2asin(sqrt((1-|x|)/2))
32 *		= pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
33 *
34 * Special cases:
35 *	if x is NaN, return x itself;
36 *	if |x|>1, return NaN with invalid signal.
37 *
38 * Function needed: __ieee754_sqrt
39 */
40
41#include "math.h"
42#include "math_private.h"
43
44static const double
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
60double
61__generic___ieee754_acos(double x)
62{
63	double z,p,q,r,w,s,c,df;
64	int32_t hx,ix;
65	GET_HIGH_WORD(hx,x);
66	ix = hx&0x7fffffff;
67	if(ix>=0x3ff00000) {	/* |x| >= 1 */
68	    u_int32_t lx;
69	    GET_LOW_WORD(lx,x);
70	    if(((ix-0x3ff00000)|lx)==0) {	/* |x|==1 */
71		if(hx>0) return 0.0;		/* acos(1) = 0  */
72		else return pi+2.0*pio2_lo;	/* acos(-1)= pi */
73	    }
74	    return (x-x)/(x-x);		/* acos(|x|>1) is NaN */
75	}
76	if(ix<0x3fe00000) {	/* |x| < 0.5 */
77	    if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/
78	    z = x*x;
79	    p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
80	    q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
81	    r = p/q;
82	    return pio2_hi - (x - (pio2_lo-x*r));
83	} else  if (hx<0) {		/* x < -0.5 */
84	    z = (one+x)*0.5;
85	    p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
86	    q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
87	    s = __ieee754_sqrt(z);
88	    r = p/q;
89	    w = r*s-pio2_lo;
90	    return pi - 2.0*(s+w);
91	} else {			/* x > 0.5 */
92	    z = (one-x)*0.5;
93	    s = __ieee754_sqrt(z);
94	    df = s;
95	    SET_LOW_WORD(df,0);
96	    c  = (z-df*df)/(s+df);
97	    p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
98	    q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
99	    r = p/q;
100	    w = r*s+c;
101	    return 2.0*(df+w);
102	}
103}
104