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/* atan(x)
27 * Method
28 * 1. Reduce x to positive by atan(x) = -atan(-x).
29 * 2. According to the integer k=4t+0.25 chopped, t=x, the argument
30 * is further reduced to one of the following intervals and the
31 * arctangent of t is evaluated by the corresponding formula:
32 *
33 * [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
34 * [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
35 * [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
36 * [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
37 * [39/16,INF] atan(x) = atan(INF) + atan( -1/t )
38 *
39 * Constants:
40 * The hexadecimal values are the intended ones for the following
41 * constants. The decimal values may be used, provided that the
42 * compiler will convert from decimal to binary accurately enough
43 * to produce the hexadecimal values shown.
44 */
45
46#include "fdlibm.h"
47
48#ifdef __STDC__
49static const double atanhi[] = {
50#else
51static double atanhi[] = {
52#endif
53 4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
54 7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
55 9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
56 1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
57};
58
59#ifdef __STDC__
60static const double atanlo[] = {
61#else
62static double atanlo[] = {
63#endif
64 2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
65 3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
66 1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
67 6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
68};
69
70#ifdef __STDC__
71static const double aT[] = {
72#else
73static double aT[] = {
74#endif
75 3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
76 -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
77 1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
78 -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
79 9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
80 -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
81 6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
82 -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
83 4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
84 -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
85 1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
86};
87
88#ifdef __STDC__
89 static const double
90#else
91 static double
92#endif
93one = 1.0,
94huge = 1.0e300;
95
96#ifdef __STDC__
97 double atan(double x)
98#else
99 double atan(x)
100 double x;
101#endif
102{
103 double w,s1,s2,z;
104 int ix,hx,id;
105
106 hx = __HI(x);
107 ix = hx&0x7fffffff;
108 if(ix>=0x44100000) { /* if |x| >= 2^66 */
109 if(ix>0x7ff00000||
110 (ix==0x7ff00000&&(__LO(x)!=0)))
111 return x+x; /* NaN */
112 if(hx>0) return atanhi[3]+atanlo[3];
113 else return -atanhi[3]-atanlo[3];
114 } if (ix < 0x3fdc0000) { /* |x| < 0.4375 */
115 if (ix < 0x3e200000) { /* |x| < 2^-29 */
116 if(huge+x>one) return x; /* raise inexact */
117 }
118 id = -1;
119 } else {
120 x = fabs(x);
121 if (ix < 0x3ff30000) { /* |x| < 1.1875 */
122 if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */
123 id = 0; x = (2.0*x-one)/(2.0+x);
124 } else { /* 11/16<=|x|< 19/16 */
125 id = 1; x = (x-one)/(x+one);
126 }
127 } else {
128 if (ix < 0x40038000) { /* |x| < 2.4375 */
129 id = 2; x = (x-1.5)/(one+1.5*x);
130 } else { /* 2.4375 <= |x| < 2^66 */
131 id = 3; x = -1.0/x;
132 }
133 }}
134 /* end of argument reduction */
135 z = x*x;
136 w = z*z;
137 /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
138 s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
139 s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
140 if (id<0) return x - x*(s1+s2);
141 else {
142 z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
143 return (hx<0)? -z:z;
144 }
145}
146