/[jscoverage]/trunk/js/src/fdlibm/s_atan.c
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Annotation of /trunk/js/src/fdlibm/s_atan.c

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Wed Aug 1 13:51:53 2007 UTC (14 years, 11 months ago) by siliconforks
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1 siliconforks 2 /* -*- 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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