1 /* $NetBSD: n_atan.c,v 1.6 2013/11/24 14:41:53 martin 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 #ifndef lint
32 #if 0
33 static char sccsid[] = "@(#)atan.c 8.1 (Berkeley) 6/4/93";
34 #endif
35 #endif /* not lint */
36
37 /* ATAN(X)
38 * RETURNS ARC TANGENT OF X
39 * DOUBLE PRECISION (IEEE DOUBLE 53 bits, VAX D FORMAT 56 bits)
40 * CODED IN C BY K.C. NG, 4/16/85, REVISED ON 6/10/85.
41 *
42 * Required kernel function:
43 * atan2(y,x)
44 *
45 * Method:
46 * atan(x) = atan2(x,1.0).
47 *
48 * Special case:
49 * if x is NaN, return x itself.
50 *
51 * Accuracy:
52 * 1) If atan2() uses machine PI, then
53 *
54 * atan(x) returns (PI/pi) * (the exact arc tangent of x) nearly rounded;
55 * and PI is the exact pi rounded to machine precision (see atan2 for
56 * details):
57 *
58 * in decimal:
59 * pi = 3.141592653589793 23846264338327 .....
60 * 53 bits PI = 3.141592653589793 115997963 ..... ,
61 * 56 bits PI = 3.141592653589793 227020265 ..... ,
62 *
63 * in hexadecimal:
64 * pi = 3.243F6A8885A308D313198A2E....
65 * 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18 error=.276ulps
66 * 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2 error=.206ulps
67 *
68 * In a test run with more than 200,000 random arguments on a VAX, the
69 * maximum observed error in ulps (units in the last place) was
70 * 0.86 ulps. (comparing against (PI/pi)*(exact atan(x))).
71 *
72 * 2) If atan2() uses true pi, then
73 *
74 * atan(x) returns the exact atan(x) with error below about 2 ulps.
75 *
76 * In a test run with more than 1,024,000 random arguments on a VAX, the
77 * maximum observed error in ulps (units in the last place) was
78 * 0.85 ulps.
79 */
80 #include "mathimpl.h"
81
82 double
atan(double x)83 atan(double x)
84 {
85 double one=1.0;
86 return(atan2(x,one));
87 }
88
89 float
atanf(float x)90 atanf(float x)
91 {
92 float one=1.0;
93 return (float)atan2(x,one);
94 }
95
96