/[jscoverage]/trunk/js/src/fdlibm/e_acos.c
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Contents of /trunk/js/src/fdlibm/e_acos.c

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Revision 2 - (show annotations)
Wed Aug 1 13:51:53 2007 UTC (14 years, 9 months ago) by siliconforks
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Initial import.

1 /* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
2 *
3 * ***** BEGIN LICENSE BLOCK *****
4 * Version: MPL 1.1/GPL 2.0/LGPL 2.1
5 *
6 * The contents of this file are subject to the Mozilla Public License Version
7 * 1.1 (the "License"); you may not use this file except in compliance with
8 * the License. You may obtain a copy of the License at
9 * http://www.mozilla.org/MPL/
10 *
11 * Software distributed under the License is distributed on an "AS IS" basis,
12 * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
13 * for the specific language governing rights and limitations under the
14 * License.
15 *
16 * The Original Code is Mozilla Communicator client code, released
17 * March 31, 1998.
18 *
19 * The Initial Developer of the Original Code is
20 * Sun Microsystems, Inc.
21 * Portions created by the Initial Developer are Copyright (C) 1998
22 * the Initial Developer. All Rights Reserved.
23 *
24 * Contributor(s):
25 *
26 * Alternatively, the contents of this file may be used under the terms of
27 * either of the GNU General Public License Version 2 or later (the "GPL"),
28 * or the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
29 * in which case the provisions of the GPL or the LGPL are applicable instead
30 * of those above. If you wish to allow use of your version of this file only
31 * under the terms of either the GPL or the LGPL, and not to allow others to
32 * use your version of this file under the terms of the MPL, indicate your
33 * decision by deleting the provisions above and replace them with the notice
34 * and other provisions required by the GPL or the LGPL. If you do not delete
35 * the provisions above, a recipient may use your version of this file under
36 * the terms of any one of the MPL, the GPL or the LGPL.
37 *
38 * ***** END LICENSE BLOCK ***** */
39
40 /* @(#)e_acos.c 1.3 95/01/18 */
41 /*
42 * ====================================================
43 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
44 *
45 * Developed at SunSoft, a Sun Microsystems, Inc. business.
46 * Permission to use, copy, modify, and distribute this
47 * software is freely granted, provided that this notice
48 * is preserved.
49 * ====================================================
50 */
51
52 /* __ieee754_acos(x)
53 * Method :
54 * acos(x) = pi/2 - asin(x)
55 * acos(-x) = pi/2 + asin(x)
56 * For |x|<=0.5
57 * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c)
58 * For x>0.5
59 * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
60 * = 2asin(sqrt((1-x)/2))
61 * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z)
62 * = 2f + (2c + 2s*z*R(z))
63 * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
64 * for f so that f+c ~ sqrt(z).
65 * For x<-0.5
66 * acos(x) = pi - 2asin(sqrt((1-|x|)/2))
67 * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
68 *
69 * Special cases:
70 * if x is NaN, return x itself;
71 * if |x|>1, return NaN with invalid signal.
72 *
73 * Function needed: sqrt
74 */
75
76 #include "fdlibm.h"
77
78 #ifdef __STDC__
79 static const double
80 #else
81 static double
82 #endif
83 one= 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
84 pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
85 pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
86 pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
87 pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
88 pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
89 pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
90 pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
91 pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
92 pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
93 qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
94 qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
95 qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
96 qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
97
98 #ifdef __STDC__
99 double __ieee754_acos(double x)
100 #else
101 double __ieee754_acos(x)
102 double x;
103 #endif
104 {
105 fd_twoints u;
106 double df;
107 double z,p,q,r,w,s,c;
108 int hx,ix;
109 u.d = x;
110 hx = __HI(u);
111 ix = hx&0x7fffffff;
112 if(ix>=0x3ff00000) { /* |x| >= 1 */
113 if(((ix-0x3ff00000)|__LO(u))==0) { /* |x|==1 */
114 if(hx>0) return 0.0; /* acos(1) = 0 */
115 else return pi+2.0*pio2_lo; /* acos(-1)= pi */
116 }
117 return (x-x)/(x-x); /* acos(|x|>1) is NaN */
118 }
119 if(ix<0x3fe00000) { /* |x| < 0.5 */
120 if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/
121 z = x*x;
122 p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
123 q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
124 r = p/q;
125 return pio2_hi - (x - (pio2_lo-x*r));
126 } else if (hx<0) { /* x < -0.5 */
127 z = (one+x)*0.5;
128 p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
129 q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
130 s = fd_sqrt(z);
131 r = p/q;
132 w = r*s-pio2_lo;
133 return pi - 2.0*(s+w);
134 } else { /* x > 0.5 */
135 z = (one-x)*0.5;
136 s = fd_sqrt(z);
137 u.d = s;
138 __LO(u) = 0;
139 df = u.d;
140 c = (z-df*df)/(s+df);
141 p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
142 q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
143 r = p/q;
144 w = r*s+c;
145 return 2.0*(df+w);
146 }
147 }

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