1/*
2 * Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
3 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
4 *
5 * This code is free software; you can redistribute it and/or modify it
6 * under the terms of the GNU General Public License version 2 only, as
7 * published by the Free Software Foundation. Oracle designates this
8 * particular file as subject to the "Classpath" exception as provided
9 * by Oracle in the LICENSE file that accompanied this code.
10 *
11 * This code is distributed in the hope that it will be useful, but WITHOUT
12 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
13 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
14 * version 2 for more details (a copy is included in the LICENSE file that
15 * accompanied this code).
16 *
17 * You should have received a copy of the GNU General Public License version
18 * 2 along with this work; if not, write to the Free Software Foundation,
19 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
20 *
21 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
22 * or visit www.oracle.com if you need additional information or have any
23 * questions.
24 */
25
26/* __ieee754_acos(x)
27 * Method :
28 * acos(x) = pi/2 - asin(x)
29 * acos(-x) = pi/2 + asin(x)
30 * For |x|<=0.5
31 * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c)
32 * For x>0.5
33 * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
34 * = 2asin(sqrt((1-x)/2))
35 * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z)
36 * = 2f + (2c + 2s*z*R(z))
37 * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
38 * for f so that f+c ~ sqrt(z).
39 * For x<-0.5
40 * acos(x) = pi - 2asin(sqrt((1-|x|)/2))
41 * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
42 *
43 * Special cases:
44 * if x is NaN, return x itself;
45 * if |x|>1, return NaN with invalid signal.
46 *
47 * Function needed: sqrt
48 */
49
50#include "fdlibm.h"
51
52#ifdef __STDC__
53static const double
54#else
55static double
56#endif
57one= 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
58pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
59pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
60pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
61pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
62pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
63pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
64pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
65pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
66pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
67qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
68qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
69qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
70qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
71
72#ifdef __STDC__
73 double __ieee754_acos(double x)
74#else
75 double __ieee754_acos(x)
76 double x;
77#endif
78{
79 double z,p,q,r,w,s,c,df;
80 int hx,ix;
81 hx = __HI(x);
82 ix = hx&0x7fffffff;
83 if(ix>=0x3ff00000) { /* |x| >= 1 */
84 if(((ix-0x3ff00000)|__LO(x))==0) { /* |x|==1 */
85 if(hx>0) return 0.0; /* acos(1) = 0 */
86 else return pi+2.0*pio2_lo; /* acos(-1)= pi */
87 }
88 return (x-x)/(x-x); /* acos(|x|>1) is NaN */
89 }
90 if(ix<0x3fe00000) { /* |x| < 0.5 */
91 if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/
92 z = x*x;
93 p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
94 q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
95 r = p/q;
96 return pio2_hi - (x - (pio2_lo-x*r));
97 } else if (hx<0) { /* x < -0.5 */
98 z = (one+x)*0.5;
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 s = sqrt(z);
102 r = p/q;
103 w = r*s-pio2_lo;
104 return pi - 2.0*(s+w);
105 } else { /* x > 0.5 */
106 z = (one-x)*0.5;
107 s = sqrt(z);
108 df = s;
109 __LO(df) = 0;
110 c = (z-df*df)/(s+df);
111 p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
112 q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
113 r = p/q;
114 w = r*s+c;
115 return 2.0*(df+w);
116 }
117}
118