134124Sbostic /* 224589Szliu * Copyright (c) 1985 Regents of the University of California. 334124Sbostic * All rights reserved. 434124Sbostic * 5*42655Sbostic * %sccs.include.redist.c% 634124Sbostic * 734124Sbostic * All recipients should regard themselves as participants in an ongoing 834124Sbostic * research project and hence should feel obligated to report their 934124Sbostic * experiences (good or bad) with these elementary function codes, using 1034124Sbostic * the sendbug(8) program, to the authors. 1124589Szliu */ 1224589Szliu 1324589Szliu #ifndef lint 14*42655Sbostic static char sccsid[] = "@(#)atan.c 5.4 (Berkeley) 06/01/90"; 1534124Sbostic #endif /* not lint */ 1624589Szliu 1724589Szliu /* ATAN(X) 1824589Szliu * RETURNS ARC TANGENT OF X 1924589Szliu * DOUBLE PRECISION (IEEE DOUBLE 53 bits, VAX D FORMAT 56 bits) 2024589Szliu * CODED IN C BY K.C. NG, 4/16/85, REVISED ON 6/10/85. 2124589Szliu * 2224589Szliu * Required kernel function: 2324589Szliu * atan2(y,x) 2424589Szliu * 2524589Szliu * Method: 2624589Szliu * atan(x) = atan2(x,1.0). 2724589Szliu * 2824589Szliu * Special case: 2924589Szliu * if x is NaN, return x itself. 3024589Szliu * 3124589Szliu * Accuracy: 3224589Szliu * 1) If atan2() uses machine PI, then 3324589Szliu * 3424589Szliu * atan(x) returns (PI/pi) * (the exact arc tangent of x) nearly rounded; 3524589Szliu * and PI is the exact pi rounded to machine precision (see atan2 for 3624589Szliu * details): 3724589Szliu * 3824589Szliu * in decimal: 3924589Szliu * pi = 3.141592653589793 23846264338327 ..... 4024589Szliu * 53 bits PI = 3.141592653589793 115997963 ..... , 4124589Szliu * 56 bits PI = 3.141592653589793 227020265 ..... , 4224589Szliu * 4324589Szliu * in hexadecimal: 4424589Szliu * pi = 3.243F6A8885A308D313198A2E.... 4524589Szliu * 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18 error=.276ulps 4624589Szliu * 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2 error=.206ulps 4724589Szliu * 4824589Szliu * In a test run with more than 200,000 random arguments on a VAX, the 4924589Szliu * maximum observed error in ulps (units in the last place) was 5024589Szliu * 0.86 ulps. (comparing against (PI/pi)*(exact atan(x))). 5124589Szliu * 5224589Szliu * 2) If atan2() uses true pi, then 5324589Szliu * 5424589Szliu * atan(x) returns the exact atan(x) with error below about 2 ulps. 5524589Szliu * 5624589Szliu * In a test run with more than 1,024,000 random arguments on a VAX, the 5724589Szliu * maximum observed error in ulps (units in the last place) was 5824589Szliu * 0.85 ulps. 5924589Szliu */ 6024589Szliu 6124589Szliu double atan(x) 6224589Szliu double x; 6324589Szliu { 6424589Szliu double atan2(),one=1.0; 6524589Szliu return(atan2(x,one)); 6624589Szliu } 67