1*34124Sbostic /* 224589Szliu * Copyright (c) 1985 Regents of the University of California. 3*34124Sbostic * All rights reserved. 4*34124Sbostic * 5*34124Sbostic * Redistribution and use in source and binary forms are permitted 6*34124Sbostic * provided that this notice is preserved and that due credit is given 7*34124Sbostic * to the University of California at Berkeley. The name of the University 8*34124Sbostic * may not be used to endorse or promote products derived from this 9*34124Sbostic * software without specific prior written permission. This software 10*34124Sbostic * is provided ``as is'' without express or implied warranty. 11*34124Sbostic * 12*34124Sbostic * All recipients should regard themselves as participants in an ongoing 13*34124Sbostic * research project and hence should feel obligated to report their 14*34124Sbostic * experiences (good or bad) with these elementary function codes, using 15*34124Sbostic * the sendbug(8) program, to the authors. 1624589Szliu */ 1724589Szliu 1824589Szliu #ifndef lint 19*34124Sbostic static char sccsid[] = "@(#)atan.c 5.2 (Berkeley) 04/29/88"; 20*34124Sbostic #endif /* not lint */ 2124589Szliu 2224589Szliu /* ATAN(X) 2324589Szliu * RETURNS ARC TANGENT OF X 2424589Szliu * DOUBLE PRECISION (IEEE DOUBLE 53 bits, VAX D FORMAT 56 bits) 2524589Szliu * CODED IN C BY K.C. NG, 4/16/85, REVISED ON 6/10/85. 2624589Szliu * 2724589Szliu * Required kernel function: 2824589Szliu * atan2(y,x) 2924589Szliu * 3024589Szliu * Method: 3124589Szliu * atan(x) = atan2(x,1.0). 3224589Szliu * 3324589Szliu * Special case: 3424589Szliu * if x is NaN, return x itself. 3524589Szliu * 3624589Szliu * Accuracy: 3724589Szliu * 1) If atan2() uses machine PI, then 3824589Szliu * 3924589Szliu * atan(x) returns (PI/pi) * (the exact arc tangent of x) nearly rounded; 4024589Szliu * and PI is the exact pi rounded to machine precision (see atan2 for 4124589Szliu * details): 4224589Szliu * 4324589Szliu * in decimal: 4424589Szliu * pi = 3.141592653589793 23846264338327 ..... 4524589Szliu * 53 bits PI = 3.141592653589793 115997963 ..... , 4624589Szliu * 56 bits PI = 3.141592653589793 227020265 ..... , 4724589Szliu * 4824589Szliu * in hexadecimal: 4924589Szliu * pi = 3.243F6A8885A308D313198A2E.... 5024589Szliu * 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18 error=.276ulps 5124589Szliu * 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2 error=.206ulps 5224589Szliu * 5324589Szliu * In a test run with more than 200,000 random arguments on a VAX, the 5424589Szliu * maximum observed error in ulps (units in the last place) was 5524589Szliu * 0.86 ulps. (comparing against (PI/pi)*(exact atan(x))). 5624589Szliu * 5724589Szliu * 2) If atan2() uses true pi, then 5824589Szliu * 5924589Szliu * atan(x) returns the exact atan(x) with error below about 2 ulps. 6024589Szliu * 6124589Szliu * In a test run with more than 1,024,000 random arguments on a VAX, the 6224589Szliu * maximum observed error in ulps (units in the last place) was 6324589Szliu * 0.85 ulps. 6424589Szliu */ 6524589Szliu 6624589Szliu double atan(x) 6724589Szliu double x; 6824589Szliu { 6924589Szliu double atan2(),one=1.0; 7024589Szliu return(atan2(x,one)); 7124589Szliu } 72