1 /* $NetBSD: n_atan.c,v 1.4 2002/06/15 00:10:17 matt 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. All advertising materials mentioning features or use of this software 15 * must display the following acknowledgement: 16 * This product includes software developed by the University of 17 * California, Berkeley and its contributors. 18 * 4. Neither the name of the University nor the names of its contributors 19 * may be used to endorse or promote products derived from this software 20 * without specific prior written permission. 21 * 22 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 23 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 24 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 25 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 26 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 27 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 28 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 29 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 30 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 31 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 32 * SUCH DAMAGE. 33 */ 34 35 #ifndef lint 36 #if 0 37 static char sccsid[] = "@(#)atan.c 8.1 (Berkeley) 6/4/93"; 38 #endif 39 #endif /* not lint */ 40 41 /* ATAN(X) 42 * RETURNS ARC TANGENT OF X 43 * DOUBLE PRECISION (IEEE DOUBLE 53 bits, VAX D FORMAT 56 bits) 44 * CODED IN C BY K.C. NG, 4/16/85, REVISED ON 6/10/85. 45 * 46 * Required kernel function: 47 * atan2(y,x) 48 * 49 * Method: 50 * atan(x) = atan2(x,1.0). 51 * 52 * Special case: 53 * if x is NaN, return x itself. 54 * 55 * Accuracy: 56 * 1) If atan2() uses machine PI, then 57 * 58 * atan(x) returns (PI/pi) * (the exact arc tangent of x) nearly rounded; 59 * and PI is the exact pi rounded to machine precision (see atan2 for 60 * details): 61 * 62 * in decimal: 63 * pi = 3.141592653589793 23846264338327 ..... 64 * 53 bits PI = 3.141592653589793 115997963 ..... , 65 * 56 bits PI = 3.141592653589793 227020265 ..... , 66 * 67 * in hexadecimal: 68 * pi = 3.243F6A8885A308D313198A2E.... 69 * 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18 error=.276ulps 70 * 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2 error=.206ulps 71 * 72 * In a test run with more than 200,000 random arguments on a VAX, the 73 * maximum observed error in ulps (units in the last place) was 74 * 0.86 ulps. (comparing against (PI/pi)*(exact atan(x))). 75 * 76 * 2) If atan2() uses true pi, then 77 * 78 * atan(x) returns the exact atan(x) with error below about 2 ulps. 79 * 80 * In a test run with more than 1,024,000 random arguments on a VAX, the 81 * maximum observed error in ulps (units in the last place) was 82 * 0.85 ulps. 83 */ 84 #include "mathimpl.h" 85 86 double 87 atan(double x) 88 { 89 double one=1.0; 90 return(atan2(x,one)); 91 } 92