154359Sroberto/* $NetBSD: n_atan.c,v 1.8 2024/06/09 13:35:38 riastradh Exp $ */ 254359Sroberto/* 354359Sroberto * Copyright (c) 1985, 1993 454359Sroberto * The Regents of the University of California. All rights reserved. 554359Sroberto * 654359Sroberto * Redistribution and use in source and binary forms, with or without 754359Sroberto * modification, are permitted provided that the following conditions 854359Sroberto * are met: 954359Sroberto * 1. Redistributions of source code must retain the above copyright 1054359Sroberto * notice, this list of conditions and the following disclaimer. 1154359Sroberto * 2. Redistributions in binary form must reproduce the above copyright 1254359Sroberto * notice, this list of conditions and the following disclaimer in the 1354359Sroberto * documentation and/or other materials provided with the distribution. 1454359Sroberto * 3. Neither the name of the University nor the names of its contributors 1554359Sroberto * may be used to endorse or promote products derived from this software 1654359Sroberto * without specific prior written permission. 1754359Sroberto * 1854359Sroberto * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 1954359Sroberto * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 2054359Sroberto * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 2154359Sroberto * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 2254359Sroberto * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 2354359Sroberto * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 2454359Sroberto * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 2554359Sroberto * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 2654359Sroberto * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 2754359Sroberto * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 2854359Sroberto * SUCH DAMAGE. 2954359Sroberto */ 3054359Sroberto 3154359Sroberto#include <sys/cdefs.h> 3254359Sroberto__RCSID("$NetBSD: n_atan.c,v 1.8 2024/06/09 13:35:38 riastradh Exp $"); 3354359Sroberto 3454359Sroberto#ifndef lint 3554359Sroberto#if 0 3654359Srobertostatic char sccsid[] = "@(#)atan.c 8.1 (Berkeley) 6/4/93"; 3754359Sroberto#endif 3854359Sroberto#endif /* not lint */ 3954359Sroberto 4054359Sroberto/* ATAN(X) 4154359Sroberto * RETURNS ARC TANGENT OF X 4254359Sroberto * DOUBLE PRECISION (IEEE DOUBLE 53 bits, VAX D FORMAT 56 bits) 4354359Sroberto * CODED IN C BY K.C. NG, 4/16/85, REVISED ON 6/10/85. 4454359Sroberto * 4554359Sroberto * Required kernel function: 4654359Sroberto * atan2(y,x) 4754359Sroberto * 4854359Sroberto * Method: 4954359Sroberto * atan(x) = atan2(x,1.0). 5054359Sroberto * 5154359Sroberto * Special case: 5254359Sroberto * if x is NaN, return x itself. 5354359Sroberto * 5454359Sroberto * Accuracy: 5554359Sroberto * 1) If atan2() uses machine PI, then 5654359Sroberto * 5754359Sroberto * atan(x) returns (PI/pi) * (the exact arc tangent of x) nearly rounded; 5854359Sroberto * and PI is the exact pi rounded to machine precision (see atan2 for 5954359Sroberto * details): 6054359Sroberto * 6154359Sroberto * in decimal: 6254359Sroberto * pi = 3.141592653589793 23846264338327 ..... 6354359Sroberto * 53 bits PI = 3.141592653589793 115997963 ..... , 6454359Sroberto * 56 bits PI = 3.141592653589793 227020265 ..... , 6554359Sroberto * 6656746Sroberto * in hexadecimal: 6754359Sroberto * pi = 3.243F6A8885A308D313198A2E.... 6854359Sroberto * 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18 error=.276ulps 6954359Sroberto * 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2 error=.206ulps 7054359Sroberto * 7154359Sroberto * In a test run with more than 200,000 random arguments on a VAX, the 7254359Sroberto * maximum observed error in ulps (units in the last place) was 7354359Sroberto * 0.86 ulps. (comparing against (PI/pi)*(exact atan(x))). 7456746Sroberto * 7556746Sroberto * 2) If atan2() uses true pi, then 7654359Sroberto * 7756746Sroberto * atan(x) returns the exact atan(x) with error below about 2 ulps. 7854359Sroberto * 7954359Sroberto * In a test run with more than 1,024,000 random arguments on a VAX, the 8054359Sroberto * maximum observed error in ulps (units in the last place) was 8154359Sroberto * 0.85 ulps. 8254359Sroberto */ 8354359Sroberto 8454359Sroberto#include "namespace.h" 8554359Sroberto 8654359Sroberto#include "mathimpl.h" 8754359Sroberto 8854359Sroberto__weak_alias(atan, _atan) 8954359Sroberto__weak_alias(atanf, _atanf) 9054359Sroberto 9154359Srobertodouble 9254359Srobertoatan(double x) 9354359Sroberto{ 9454359Sroberto double one=1.0; 9554359Sroberto return(atan2(x,one)); 9654359Sroberto} 9754359Sroberto 9854359Srobertofloat 9956746Srobertoatanf(float x) 10054359Sroberto{ 10154359Sroberto float one=1.0; 10254359Sroberto return (float)atan2(x,one); 10354359Sroberto} 10454359Sroberto 10554359Sroberto