1 /* Copyright JS Foundation and other contributors, http://js.foundation
2 *
3 * Licensed under the Apache License, Version 2.0 (the "License");
4 * you may not use this file except in compliance with the License.
5 * You may obtain a copy of the License at
6 *
7 * http://www.apache.org/licenses/LICENSE-2.0
8 *
9 * Unless required by applicable law or agreed to in writing, software
10 * distributed under the License is distributed on an "AS IS" BASIS
11 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
12 * See the License for the specific language governing permissions and
13 * limitations under the License.
14 *
15 * This file is based on work under the following copyright and permission
16 * notice:
17 *
18 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
19 *
20 * Developed at SunSoft, a Sun Microsystems, Inc. business.
21 * Permission to use, copy, modify, and distribute this
22 * software is freely granted, provided that this notice
23 * is preserved.
24 *
25 * @(#)s_atan.c 1.3 95/01/18
26 */
27
28 #include "jerry-libm-internal.h"
29
30 /* atan(x)
31 *
32 * Method:
33 * 1. Reduce x to positive by atan(x) = -atan(-x).
34 * 2. According to the integer k=4t+0.25 chopped, t=x, the argument
35 * is further reduced to one of the following intervals and the
36 * arctangent of t is evaluated by the corresponding formula:
37 *
38 * [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
39 * [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
40 * [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
41 * [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
42 * [39/16,INF] atan(x) = atan(INF) + atan( -1/t )
43 *
44 * Constants:
45 * The hexadecimal values are the intended ones for the following
46 * constants. The decimal values may be used, provided that the
47 * compiler will convert from decimal to binary accurately enough
48 * to produce the hexadecimal values shown.
49 */
50
51 static const double atanhi[] =
52 {
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 static const double atanlo[] =
60 {
61 2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
62 3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
63 1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
64 6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
65 };
66
67 #define aT0 3.33333333333329318027e-01 /* 0x3FD55555, 0x5555550D */
68 #define aT1 -1.99999999998764832476e-01 /* 0xBFC99999, 0x9998EBC4 */
69 #define aT2 1.42857142725034663711e-01 /* 0x3FC24924, 0x920083FF */
70 #define aT3 -1.11111104054623557880e-01 /* 0xBFBC71C6, 0xFE231671 */
71 #define aT4 9.09088713343650656196e-02 /* 0x3FB745CD, 0xC54C206E */
72 #define aT5 -7.69187620504482999495e-02 /* 0xBFB3B0F2, 0xAF749A6D */
73 #define aT6 6.66107313738753120669e-02 /* 0x3FB10D66, 0xA0D03D51 */
74 #define aT7 -5.83357013379057348645e-02 /* 0xBFADDE2D, 0x52DEFD9A */
75 #define aT8 4.97687799461593236017e-02 /* 0x3FA97B4B, 0x24760DEB */
76 #define aT9 -3.65315727442169155270e-02 /* 0xBFA2B444, 0x2C6A6C2F */
77 #define aT10 1.62858201153657823623e-02 /* 0x3F90AD3A, 0xE322DA11 */
78
79 #define one 1.0
80 #define huge 1.0e300
81
82 double
atan(double x)83 atan (double x)
84 {
85 double w, s1, s2, z;
86 int ix, hx, id;
87
88 hx = __HI (x);
89 ix = hx & 0x7fffffff;
90 if (ix >= 0x44100000) /* if |x| >= 2^66 */
91 {
92 if (ix > 0x7ff00000 || (ix == 0x7ff00000 && (__LO (x) != 0)))
93 {
94 return x + x; /* NaN */
95 }
96 if (hx > 0)
97 {
98 return atanhi[3] + atanlo[3];
99 }
100 else
101 {
102 return -atanhi[3] - atanlo[3];
103 }
104 }
105 if (ix < 0x3fdc0000) /* |x| < 0.4375 */
106 {
107 if (ix < 0x3e200000) /* |x| < 2^-29 */
108 {
109 if (huge + x > one) /* raise inexact */
110 {
111 return x;
112 }
113 }
114 id = -1;
115 }
116 else
117 {
118 x = fabs (x);
119 if (ix < 0x3ff30000) /* |x| < 1.1875 */
120 {
121 if (ix < 0x3fe60000) /* 7/16 <= |x| < 11/16 */
122 {
123 id = 0;
124 x = (2.0 * x - one) / (2.0 + x);
125 }
126 else /* 11/16 <= |x| < 19/16 */
127 {
128 id = 1;
129 x = (x - one) / (x + one);
130 }
131 }
132 else
133 {
134 if (ix < 0x40038000) /* |x| < 2.4375 */
135 {
136 id = 2;
137 x = (x - 1.5) / (one + 1.5 * x);
138 }
139 else /* 2.4375 <= |x| < 2^66 */
140 {
141 id = 3;
142 x = -1.0 / x;
143 }
144 }
145 }
146 /* end of argument reduction */
147 z = x * x;
148 w = z * z;
149 /* break sum from i=0 to 10 aT[i] z**(i+1) into odd and even poly */
150 s1 = z * (aT0 + w * (aT2 + w * (aT4 + w * (aT6 + w * (aT8 + w * aT10)))));
151 s2 = w * (aT1 + w * (aT3 + w * (aT5 + w * (aT7 + w * aT9))));
152 if (id < 0)
153 {
154 return x - x * (s1 + s2);
155 }
156 else
157 {
158 z = atanhi[id] - ((x * (s1 + s2) - atanlo[id]) - x);
159 return (hx < 0) ? -z : z;
160 }
161 } /* atan */
162
163 #undef aT0
164 #undef aT1
165 #undef aT2
166 #undef aT3
167 #undef aT4
168 #undef aT5
169 #undef aT6
170 #undef aT7
171 #undef aT8
172 #undef aT9
173 #undef aT10
174 #undef one
175 #undef huge
176