xref: /third_party/jerryscript/jerry-libm/atan.c (revision 425bb815) 
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
51static 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
59static 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
82double
83atan (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