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1 
2 /* @(#)e_acos.c 1.3 95/01/18 */
3 /*
4  * ====================================================
5  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6  *
7  * Developed at SunSoft, 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 - ieee_asin(x)
17  *	acos(-x) = pi/2 + ieee_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(ieee_sqrt((1-x)/2)))
22  *		= 2asin(ieee_sqrt((1-x)/2))
23  *		= 2s + 2s*z*R(z) 	...z=(1-x)/2, s=ieee_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 ~ ieee_sqrt(z).
27  * For x<-0.5
28  *	acos(x) = pi - 2asin(ieee_sqrt((1-|x|)/2))
29  *		= pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=ieee_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 "fdlibm.h"
39 
40 #ifdef __STDC__
41 static const double
42 #else
43 static double
44 #endif
45 one=  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
46 pi =  3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
47 pio2_hi =  1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
48 pio2_lo =  6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
49 pS0 =  1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
50 pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
51 pS2 =  2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
52 pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
53 pS4 =  7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
54 pS5 =  3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
55 qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
56 qS2 =  2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
57 qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
58 qS4 =  7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
59 
60 #ifdef __STDC__
__ieee754_acos(double x)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 hx,ix;
69 	hx = __HI(x);
70 	ix = hx&0x7fffffff;
71 	if(ix>=0x3ff00000) {	/* |x| >= 1 */
72 	    if(((ix-0x3ff00000)|__LO(x))==0) {	/* |x|==1 */
73 		if(hx>0) return 0.0;		/* ieee_acos(1) = 0  */
74 		else return pi+2.0*pio2_lo;	/* ieee_acos(-1)= pi */
75 	    }
76 	    return (x-x)/(x-x);		/* ieee_acos(|x|>1) is NaN */
77 	}
78 	if(ix<0x3fe00000) {	/* |x| < 0.5 */
79 	    if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/
80 	    z = x*x;
81 	    p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
82 	    q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
83 	    r = p/q;
84 	    return pio2_hi - (x - (pio2_lo-x*r));
85 	} else  if (hx<0) {		/* x < -0.5 */
86 	    z = (one+x)*0.5;
87 	    p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
88 	    q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
89 	    s = ieee_sqrt(z);
90 	    r = p/q;
91 	    w = r*s-pio2_lo;
92 	    return pi - 2.0*(s+w);
93 	} else {			/* x > 0.5 */
94 	    z = (one-x)*0.5;
95 	    s = ieee_sqrt(z);
96 	    df = s;
97 	    __LO(df) = 0;
98 	    c  = (z-df*df)/(s+df);
99 	    p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
100 	    q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
101 	    r = p/q;
102 	    w = r*s+c;
103 	    return 2.0*(df+w);
104 	}
105 }
106