n_atan.c revision 1.5 
1/*	$NetBSD: n_atan.c,v 1.5 2003/08/07 16:44:50 agc 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
33static 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
82double
83atan(double x)
84{
85	double one=1.0;
86	return(atan2(x,one));
87}
88