/* $OpenBSD: n_atan.c,v 1.5 2008/06/21 08:26:19 martynas Exp $ */ /* $NetBSD: n_atan.c,v 1.1 1995/10/10 23:36:36 ragge Exp $ */ /* * Copyright (c) 1985, 1993 * The Regents of the University of California. All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * 1. Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * 3. Neither the name of the University nor the names of its contributors * may be used to endorse or promote products derived from this software * without specific prior written permission. * * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF * SUCH DAMAGE. */ #ifndef lint static char sccsid[] = "@(#)atan.c 8.1 (Berkeley) 6/4/93"; #endif /* not lint */ /* ATAN(X) * RETURNS ARC TANGENT OF X * DOUBLE PRECISION (IEEE DOUBLE 53 bits, VAX D FORMAT 56 bits) * CODED IN C BY K.C. NG, 4/16/85, REVISED ON 6/10/85. * * Required kernel function: * atan2(y,x) * * Method: * atan(x) = atan2(x,1.0). * * Special case: * if x is NaN, return x itself. * * Accuracy: * 1) If atan2() uses machine PI, then * * atan(x) returns (PI/pi) * (the exact arc tangent of x) nearly rounded; * and PI is the exact pi rounded to machine precision (see atan2 for * details): * * in decimal: * pi = 3.141592653589793 23846264338327 ..... * 53 bits PI = 3.141592653589793 115997963 ..... , * 56 bits PI = 3.141592653589793 227020265 ..... , * * in hexadecimal: * pi = 3.243F6A8885A308D313198A2E.... * 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18 error=.276ulps * 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2 error=.206ulps * * In a test run with more than 200,000 random arguments on a VAX, the * maximum observed error in ulps (units in the last place) was * 0.86 ulps. (comparing against (PI/pi)*(exact atan(x))). * * 2) If atan2() uses true pi, then * * atan(x) returns the exact atan(x) with error below about 2 ulps. * * In a test run with more than 1,024,000 random arguments on a VAX, the * maximum observed error in ulps (units in the last place) was * 0.85 ulps. */ #include "math.h" double atan(double x) { double one=1.0; return(atan2(x,one)); }