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/* acos(x)
14 * Method :
15 *	acos(x)  = pi/2 - asin(x)
16 *	acos(-x) = pi/2 + asin(x)
17 * For |x|<=0.5
18 *	acos(x) = pi/2 - (x + x*x^2*R(x^2))	(see asin.c)
19 * For x>0.5
20 * 	acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
21 *		= 2asin(sqrt((1-x)/2))
22 *		= 2s + 2s*z*R(z) 	...z=(1-x)/2, s=sqrt(z)
23 *		= 2f + (2c + 2s*z*R(z))
24 *     where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
25 *     for f so that f+c ~ sqrt(z).
26 * For x<-0.5
27 *	acos(x) = pi - 2asin(sqrt((1-|x|)/2))
28 *		= pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
29 *
30 * Special cases:
31 *	if x is NaN, return x itself;
32 *	if |x|>1, return NaN with invalid signal.
33 *
34 * Function needed: sqrt
35 */
36
37#include <float.h>
38#include <math.h>
39
40#include "math_private.h"
41
42static const double
43one=  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
44pi =  3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
45pio2_hi =  1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
46pio2_lo =  6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
47pS0 =  1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
48pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
49pS2 =  2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
50pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
51pS4 =  7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
52pS5 =  3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
53qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
54qS2 =  2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
55qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
56qS4 =  7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
57
58double
59acos(double x)
60{
61	double z,p,q,r,w,s,c,df;
62	int32_t hx,ix;
63	GET_HIGH_WORD(hx,x);
64	ix = hx&0x7fffffff;
65	if(ix>=0x3ff00000) {	/* |x| >= 1 */
66	    u_int32_t lx;
67	    GET_LOW_WORD(lx,x);
68	    if(((ix-0x3ff00000)|lx)==0) {	/* |x|==1 */
69		if(hx>0) return 0.0;		/* acos(1) = 0  */
70		else return pi+2.0*pio2_lo;	/* acos(-1)= pi */
71	    }
72	    return (x-x)/(x-x);		/* acos(|x|>1) is NaN */
73	}
74	if(ix<0x3fe00000) {	/* |x| < 0.5 */
75	    if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/
76	    z = x*x;
77	    p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
78	    q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
79	    r = p/q;
80	    return pio2_hi - (x - (pio2_lo-x*r));
81	} else  if (hx<0) {		/* x < -0.5 */
82	    z = (one+x)*0.5;
83	    p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
84	    q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
85	    s = sqrt(z);
86	    r = p/q;
87	    w = r*s-pio2_lo;
88	    return pi - 2.0*(s+w);
89	} else {			/* x > 0.5 */
90	    z = (one-x)*0.5;
91	    s = sqrt(z);
92	    df = s;
93	    SET_LOW_WORD(df,0);
94	    c  = (z-df*df)/(s+df);
95	    p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
96	    q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
97	    r = p/q;
98	    w = r*s+c;
99	    return 2.0*(df+w);
100	}
101}
102DEF_STD(acos);
103LDBL_MAYBE_UNUSED_CLONE(acos);
104