1 /* $NetBSD: n_asincos.c,v 1.11 2024/06/09 13:35:38 riastradh Exp $ */
2 /*
3 * Copyright (c) 1985, 1993
4 * The Regents of the University of California. All rights reserved.
5 *
6 * Redistribution and use in source and binary forms, with or without
7 * modification, are permitted provided that the following conditions
8 * are met:
9 * 1. Redistributions of source code must retain the above copyright
10 * notice, this list of conditions and the following disclaimer.
11 * 2. Redistributions in binary form must reproduce the above copyright
12 * notice, this list of conditions and the following disclaimer in the
13 * documentation and/or other materials provided with the distribution.
14 * 3. Neither the name of the University nor the names of its contributors
15 * may be used to endorse or promote products derived from this software
16 * without specific prior written permission.
17 *
18 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
19 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
20 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
21 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
22 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
23 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
24 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
25 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
26 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
27 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
28 * SUCH DAMAGE.
29 */
30
31 #include <sys/cdefs.h>
32 __RCSID("$NetBSD: n_asincos.c,v 1.11 2024/06/09 13:35:38 riastradh Exp $");
33
34 #ifndef lint
35 #if 0
36 static char sccsid[] = "@(#)asincos.c 8.1 (Berkeley) 6/4/93";
37 #endif
38 #endif /* not lint */
39
40 /* ASIN(X)
41 * RETURNS ARC SINE OF X
42 * DOUBLE PRECISION (IEEE DOUBLE 53 bits, VAX D FORMAT 56 bits)
43 * CODED IN C BY K.C. NG, 4/16/85, REVISED ON 6/10/85.
44 *
45 * Required system supported functions:
46 * copysign(x,y)
47 * sqrt(x)
48 *
49 * Required kernel function:
50 * atan2(y,x)
51 *
52 * Method :
53 * asin(x) = atan2(x,sqrt(1-x*x)); for better accuracy, 1-x*x is
54 * computed as follows
55 * 1-x*x if x < 0.5,
56 * 2*(1-|x|)-(1-|x|)*(1-|x|) if x >= 0.5.
57 *
58 * Special cases:
59 * if x is NaN, return x itself;
60 * if |x|>1, return NaN.
61 *
62 * Accuracy:
63 * 1) If atan2() uses machine PI, then
64 *
65 * asin(x) returns (PI/pi) * (the exact arc sine of x) nearly rounded;
66 * and PI is the exact pi rounded to machine precision (see atan2 for
67 * details):
68 *
69 * in decimal:
70 * pi = 3.141592653589793 23846264338327 .....
71 * 53 bits PI = 3.141592653589793 115997963 ..... ,
72 * 56 bits PI = 3.141592653589793 227020265 ..... ,
73 *
74 * in hexadecimal:
75 * pi = 3.243F6A8885A308D313198A2E....
76 * 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18 error=.276ulps
77 * 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2 error=.206ulps
78 *
79 * In a test run with more than 200,000 random arguments on a VAX, the
80 * maximum observed error in ulps (units in the last place) was
81 * 2.06 ulps. (comparing against (PI/pi)*(exact asin(x)));
82 *
83 * 2) If atan2() uses true pi, then
84 *
85 * asin(x) returns the exact asin(x) with error below about 2 ulps.
86 *
87 * In a test run with more than 1,024,000 random arguments on a VAX, the
88 * maximum observed error in ulps (units in the last place) was
89 * 1.99 ulps.
90 */
91
92 #include "namespace.h"
93 #include "mathimpl.h"
94
__weak_alias(acos,_acos)95 __weak_alias(acos, _acos)
96 __weak_alias(acosf, _asinf)
97 __weak_alias(asin, _asin)
98 __weak_alias(asinf, _asinf)
99
100 double
101 asin(double x)
102 {
103 double s,t,one=1.0;
104 #if !defined(__vax__)&&!defined(tahoe)
105 if(x!=x) return(x); /* x is NaN */
106 #endif /* !defined(__vax__)&&!defined(tahoe) */
107 s=copysign(x,one);
108 if(s <= 0.5)
109 return(atan2(x,sqrt(one-x*x)));
110 else
111 { t=one-s; s=t+t; return(atan2(x,sqrt(s-t*t))); }
112
113 }
114
115 float
asinf(float x)116 asinf(float x)
117 {
118 return (float)asin(x);
119 }
120
121 /* ACOS(X)
122 * RETURNS ARC COS OF X
123 * DOUBLE PRECISION (IEEE DOUBLE 53 bits, VAX D FORMAT 56 bits)
124 * CODED IN C BY K.C. NG, 4/16/85, REVISED ON 6/10/85.
125 *
126 * Required system supported functions:
127 * copysign(x,y)
128 * sqrt(x)
129 *
130 * Required kernel function:
131 * atan2(y,x)
132 *
133 * Method :
134 * ________
135 * / 1 - x
136 * acos(x) = 2*atan2( / -------- , 1 ) .
137 * \/ 1 + x
138 *
139 * Special cases:
140 * if x is NaN, return x itself;
141 * if |x|>1, return NaN.
142 *
143 * Accuracy:
144 * 1) If atan2() uses machine PI, then
145 *
146 * acos(x) returns (PI/pi) * (the exact arc cosine of x) nearly rounded;
147 * and PI is the exact pi rounded to machine precision (see atan2 for
148 * details):
149 *
150 * in decimal:
151 * pi = 3.141592653589793 23846264338327 .....
152 * 53 bits PI = 3.141592653589793 115997963 ..... ,
153 * 56 bits PI = 3.141592653589793 227020265 ..... ,
154 *
155 * in hexadecimal:
156 * pi = 3.243F6A8885A308D313198A2E....
157 * 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18 error=.276ulps
158 * 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2 error=.206ulps
159 *
160 * In a test run with more than 200,000 random arguments on a VAX, the
161 * maximum observed error in ulps (units in the last place) was
162 * 2.07 ulps. (comparing against (PI/pi)*(exact acos(x)));
163 *
164 * 2) If atan2() uses true pi, then
165 *
166 * acos(x) returns the exact acos(x) with error below about 2 ulps.
167 *
168 * In a test run with more than 1,024,000 random arguments on a VAX, the
169 * maximum observed error in ulps (units in the last place) was
170 * 2.15 ulps.
171 */
172
173 double
acos(double x)174 acos(double x)
175 {
176 double t,one=1.0;
177 #if !defined(__vax__)&&!defined(tahoe)
178 if(x!=x) return(x);
179 #endif /* !defined(__vax__)&&!defined(tahoe) */
180 if( x != -1.0)
181 t=atan2(sqrt((one-x)/(one+x)),one);
182 else
183 t=atan2(one,0.0); /* t = PI/2 */
184 return(t+t);
185 }
186
187 float
acosf(float x)188 acosf(float x)
189 {
190 return (float)acos(x);
191 }
192