1 /* $NetBSD: n_atan.c,v 1.1 1995/10/10 23:36:36 ragge 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 static char sccsid[] = "@(#)atan.c 8.1 (Berkeley) 6/4/93"; 37 #endif /* not lint */ 38 39 /* ATAN(X) 40 * RETURNS ARC TANGENT OF X 41 * DOUBLE PRECISION (IEEE DOUBLE 53 bits, VAX D FORMAT 56 bits) 42 * CODED IN C BY K.C. NG, 4/16/85, REVISED ON 6/10/85. 43 * 44 * Required kernel function: 45 * atan2(y,x) 46 * 47 * Method: 48 * atan(x) = atan2(x,1.0). 49 * 50 * Special case: 51 * if x is NaN, return x itself. 52 * 53 * Accuracy: 54 * 1) If atan2() uses machine PI, then 55 * 56 * atan(x) returns (PI/pi) * (the exact arc tangent of x) nearly rounded; 57 * and PI is the exact pi rounded to machine precision (see atan2 for 58 * details): 59 * 60 * in decimal: 61 * pi = 3.141592653589793 23846264338327 ..... 62 * 53 bits PI = 3.141592653589793 115997963 ..... , 63 * 56 bits PI = 3.141592653589793 227020265 ..... , 64 * 65 * in hexadecimal: 66 * pi = 3.243F6A8885A308D313198A2E.... 67 * 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18 error=.276ulps 68 * 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2 error=.206ulps 69 * 70 * In a test run with more than 200,000 random arguments on a VAX, the 71 * maximum observed error in ulps (units in the last place) was 72 * 0.86 ulps. (comparing against (PI/pi)*(exact atan(x))). 73 * 74 * 2) If atan2() uses true pi, then 75 * 76 * atan(x) returns the exact atan(x) with error below about 2 ulps. 77 * 78 * In a test run with more than 1,024,000 random arguments on a VAX, the 79 * maximum observed error in ulps (units in the last place) was 80 * 0.85 ulps. 81 */ 82 83 double atan(x) 84 double x; 85 { 86 double atan2(),one=1.0; 87 return(atan2(x,one)); 88 } 89