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 * @(#)e_acos.c 1.3 95/01/18
26 */
27
28 #include "jerry-libm-internal.h"
29
30 /* acos(x)
31 *
32 * Method:
33 * acos(x) = pi/2 - asin(x)
34 * acos(-x) = pi/2 + asin(x)
35 * For |x|<=0.5
36 * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c)
37 * For x>0.5
38 * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
39 * = 2asin(sqrt((1-x)/2))
40 * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z)
41 * = 2f + (2c + 2s*z*R(z))
42 * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
43 * for f so that f+c ~ sqrt(z).
44 * For x<-0.5
45 * acos(x) = pi - 2asin(sqrt((1-|x|)/2))
46 * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
47 *
48 * Special cases:
49 * if x is NaN, return x itself;
50 * if |x|>1, return NaN with invalid signal.
51 *
52 * Function needed: sqrt
53 */
54
55 #define one 1.00000000000000000000e+00 /* 0x3FF00000, 0x00000000 */
56 #define pi 3.14159265358979311600e+00 /* 0x400921FB, 0x54442D18 */
57 #define pio2_hi 1.57079632679489655800e+00 /* 0x3FF921FB, 0x54442D18 */
58 #define pio2_lo 6.12323399573676603587e-17 /* 0x3C91A626, 0x33145C07 */
59 #define pS0 1.66666666666666657415e-01 /* 0x3FC55555, 0x55555555 */
60 #define pS1 -3.25565818622400915405e-01 /* 0xBFD4D612, 0x03EB6F7D */
61 #define pS2 2.01212532134862925881e-01 /* 0x3FC9C155, 0x0E884455 */
62 #define pS3 -4.00555345006794114027e-02 /* 0xBFA48228, 0xB5688F3B */
63 #define pS4 7.91534994289814532176e-04 /* 0x3F49EFE0, 0x7501B288 */
64 #define pS5 3.47933107596021167570e-05 /* 0x3F023DE1, 0x0DFDF709 */
65 #define qS1 -2.40339491173441421878e+00 /* 0xC0033A27, 0x1C8A2D4B */
66 #define qS2 2.02094576023350569471e+00 /* 0x40002AE5, 0x9C598AC8 */
67 #define qS3 -6.88283971605453293030e-01 /* 0xBFE6066C, 0x1B8D0159 */
68 #define qS4 7.70381505559019352791e-02 /* 0x3FB3B8C5, 0xB12E9282 */
69
70 double
acos(double x)71 acos (double x)
72 {
73 double z, p, q, r, w, s, c;
74 int hx, ix;
75
76 hx = __HI (x);
77 ix = hx & 0x7fffffff;
78 if (ix >= 0x3ff00000) /* |x| >= 1 */
79 {
80 if (((ix - 0x3ff00000) | __LO (x)) == 0) /* |x| == 1 */
81 {
82 if (hx > 0) /* acos(1) = 0 */
83 {
84 return 0.0;
85 }
86 else /* acos(-1) = pi */
87 {
88 return pi + 2.0 * pio2_lo;
89 }
90 }
91 return NAN; /* acos(|x|>1) is NaN */
92 }
93 if (ix < 0x3fe00000) /* |x| < 0.5 */
94 {
95 if (ix <= 0x3c600000) /* if |x| < 2**-57 */
96 {
97 return pio2_hi + pio2_lo;
98 }
99 z = x * x;
100 p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5)))));
101 q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));
102 r = p / q;
103 return pio2_hi - (x - (pio2_lo - x * r));
104 }
105 else if (hx < 0) /* x < -0.5 */
106 {
107 z = (one + x) * 0.5;
108 p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5)))));
109 q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));
110 s = sqrt (z);
111 r = p / q;
112 w = r * s - pio2_lo;
113 return pi - 2.0 * (s + w);
114 }
115 else /* x > 0.5 */
116 {
117 double_accessor df;
118 z = (one - x) * 0.5;
119 s = sqrt (z);
120 df.dbl = s;
121 df.as_int.lo = 0;
122 c = (z - df.dbl * df.dbl) / (s + df.dbl);
123 p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5)))));
124 q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));
125 r = p / q;
126 w = r * s + c;
127 return 2.0 * (df.dbl + w);
128 }
129 } /* acos */
130
131 #undef one
132 #undef pi
133 #undef pio2_hi
134 #undef pio2_lo
135 #undef pS0
136 #undef pS1
137 #undef pS2
138 #undef pS3
139 #undef pS4
140 #undef pS5
141 #undef qS1
142 #undef qS2
143 #undef qS3
144 #undef qS4
145