1 /* $NetBSD: n_atan.c,v 1.6 2013/11/24 14:41:53 martin 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 33 static 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 82 double 83 atan(double x) 84 { 85 double one=1.0; 86 return(atan2(x,one)); 87 } 88 89 float 90 atanf(float x) 91 { 92 float one=1.0; 93 return (float)atan2(x,one); 94 } 95 96