1 /* 2 * Copyright (c) 1985 Regents of the University of California. 3 * All rights reserved. 4 * 5 * Redistribution and use in source and binary forms are permitted 6 * provided that this notice is preserved and that due credit is given 7 * to the University of California at Berkeley. The name of the University 8 * may not be used to endorse or promote products derived from this 9 * software without specific prior written permission. This software 10 * is provided ``as is'' without express or implied warranty. 11 * 12 * All recipients should regard themselves as participants in an ongoing 13 * research project and hence should feel obligated to report their 14 * experiences (good or bad) with these elementary function codes, using 15 * the sendbug(8) program, to the authors. 16 */ 17 18 #ifndef lint 19 static char sccsid[] = "@(#)atan.c 5.2 (Berkeley) 04/29/88"; 20 #endif /* not lint */ 21 22 /* ATAN(X) 23 * RETURNS ARC TANGENT OF X 24 * DOUBLE PRECISION (IEEE DOUBLE 53 bits, VAX D FORMAT 56 bits) 25 * CODED IN C BY K.C. NG, 4/16/85, REVISED ON 6/10/85. 26 * 27 * Required kernel function: 28 * atan2(y,x) 29 * 30 * Method: 31 * atan(x) = atan2(x,1.0). 32 * 33 * Special case: 34 * if x is NaN, return x itself. 35 * 36 * Accuracy: 37 * 1) If atan2() uses machine PI, then 38 * 39 * atan(x) returns (PI/pi) * (the exact arc tangent of x) nearly rounded; 40 * and PI is the exact pi rounded to machine precision (see atan2 for 41 * details): 42 * 43 * in decimal: 44 * pi = 3.141592653589793 23846264338327 ..... 45 * 53 bits PI = 3.141592653589793 115997963 ..... , 46 * 56 bits PI = 3.141592653589793 227020265 ..... , 47 * 48 * in hexadecimal: 49 * pi = 3.243F6A8885A308D313198A2E.... 50 * 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18 error=.276ulps 51 * 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2 error=.206ulps 52 * 53 * In a test run with more than 200,000 random arguments on a VAX, the 54 * maximum observed error in ulps (units in the last place) was 55 * 0.86 ulps. (comparing against (PI/pi)*(exact atan(x))). 56 * 57 * 2) If atan2() uses true pi, then 58 * 59 * atan(x) returns the exact atan(x) with error below about 2 ulps. 60 * 61 * In a test run with more than 1,024,000 random arguments on a VAX, the 62 * maximum observed error in ulps (units in the last place) was 63 * 0.85 ulps. 64 */ 65 66 double atan(x) 67 double x; 68 { 69 double atan2(),one=1.0; 70 return(atan2(x,one)); 71 } 72