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Contents of /trunk/js/src/fdlibm/s_atan.c

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Wed Aug 1 13:51:53 2007 UTC (12 years, 1 month 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 /* @(#)s_atan.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
53 /* atan(x)
54 * Method
55 * 1. Reduce x to positive by atan(x) = -atan(-x).
56 * 2. According to the integer k=4t+0.25 chopped, t=x, the argument
57 * is further reduced to one of the following intervals and the
58 * arctangent of t is evaluated by the corresponding formula:
59 *
60 * [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
61 * [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
62 * [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
63 * [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
64 * [39/16,INF] atan(x) = atan(INF) + atan( -1/t )
65 *
66 * Constants:
67 * The hexadecimal values are the intended ones for the following
68 * constants. The decimal values may be used, provided that the
69 * compiler will convert from decimal to binary accurately enough
70 * to produce the hexadecimal values shown.
71 */
72
73 #include "fdlibm.h"
74
75 #ifdef __STDC__
76 static const double atanhi[] = {
77 #else
78 static double atanhi[] = {
79 #endif
80 4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
81 7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
82 9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
83 1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
84 };
85
86 #ifdef __STDC__
87 static const double atanlo[] = {
88 #else
89 static double atanlo[] = {
90 #endif
91 2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
92 3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
93 1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
94 6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
95 };
96
97 #ifdef __STDC__
98 static const double aT[] = {
99 #else
100 static double aT[] = {
101 #endif
102 3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
103 -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
104 1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
105 -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
106 9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
107 -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
108 6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
109 -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
110 4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
111 -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
112 1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
113 };
114
115 #ifdef __STDC__
116 static const double
117 #else
118 static double
119 #endif
120 one = 1.0,
121 really_big = 1.0e300;
122
123 #ifdef __STDC__
124 double fd_atan(double x)
125 #else
126 double fd_atan(x)
127 double x;
128 #endif
129 {
130 fd_twoints u;
131 double w,s1,s2,z;
132 int ix,hx,id;
133
134 u.d = x;
135 hx = __HI(u);
136 ix = hx&0x7fffffff;
137 if(ix>=0x44100000) { /* if |x| >= 2^66 */
138 u.d = x;
139 if(ix>0x7ff00000||
140 (ix==0x7ff00000&&(__LO(u)!=0)))
141 return x+x; /* NaN */
142 if(hx>0) return atanhi[3]+atanlo[3];
143 else return -atanhi[3]-atanlo[3];
144 } if (ix < 0x3fdc0000) { /* |x| < 0.4375 */
145 if (ix < 0x3e200000) { /* |x| < 2^-29 */
146 if(really_big+x>one) return x; /* raise inexact */
147 }
148 id = -1;
149 } else {
150 x = fd_fabs(x);
151 if (ix < 0x3ff30000) { /* |x| < 1.1875 */
152 if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */
153 id = 0; x = (2.0*x-one)/(2.0+x);
154 } else { /* 11/16<=|x|< 19/16 */
155 id = 1; x = (x-one)/(x+one);
156 }
157 } else {
158 if (ix < 0x40038000) { /* |x| < 2.4375 */
159 id = 2; x = (x-1.5)/(one+1.5*x);
160 } else { /* 2.4375 <= |x| < 2^66 */
161 id = 3; x = -1.0/x;
162 }
163 }}
164 /* end of argument reduction */
165 z = x*x;
166 w = z*z;
167 /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
168 s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
169 s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
170 if (id<0) return x - x*(s1+s2);
171 else {
172 z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
173 return (hx<0)? -z:z;
174 }
175 }

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