1 /* @(#)e_acos.c 5.1 93/09/24 */
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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
10 * ====================================================
14 static char rcsid[] = "$FreeBSD$";
19 * acos(x) = pi/2 - asin(x)
20 * acos(-x) = pi/2 + asin(x)
22 * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c)
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).
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)
35 * if x is NaN, return x itself;
36 * if |x|>1, return NaN with invalid signal.
38 * Function needed: __ieee754_sqrt
42 #include "math_private.h"
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 */
61 __ieee754_acos(double x)
63 double z,p,q,r,w,s,c,df;
67 if(ix>=0x3ff00000) { /* |x| >= 1 */
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 */
74 return (x-x)/(x-x); /* acos(|x|>1) is NaN */
76 if(ix<0x3fe00000) { /* |x| < 0.5 */
77 if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/
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)));
82 return pio2_hi - (x - (pio2_lo-x*r));
83 } else if (hx<0) { /* 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);
90 return pi - 2.0*(s+w);
91 } else { /* x > 0.5 */
93 s = __ieee754_sqrt(z);
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)));