1 /* 2 * Copyright (c) 1985 Regents of the University of California. 3 * 4 * Use and reproduction of this software are granted in accordance with 5 * the terms and conditions specified in the Berkeley Software License 6 * Agreement (in particular, this entails acknowledgement of the programs' 7 * source, and inclusion of this notice) with the additional understanding 8 * that all recipients should regard themselves as participants in an 9 * ongoing research project and hence should feel obligated to report 10 * their experiences (good or bad) with these elementary function codes, 11 * using "sendbug 4bsd-bugs@BERKELEY", to the authors. 12 */ 13 14 #ifndef lint 15 static char sccsid[] = 16 "@(#)atan.c 1.1 (Berkeley) 8/21/85; 1.2 (ucb.elefunt) 09/11/85"; 17 #endif not lint 18 19 /* ATAN(X) 20 * RETURNS ARC TANGENT OF X 21 * DOUBLE PRECISION (IEEE DOUBLE 53 bits, VAX D FORMAT 56 bits) 22 * CODED IN C BY K.C. NG, 4/16/85, REVISED ON 6/10/85. 23 * 24 * Required kernel function: 25 * atan2(y,x) 26 * 27 * Method: 28 * atan(x) = atan2(x,1.0). 29 * 30 * Special case: 31 * if x is NaN, return x itself. 32 * 33 * Accuracy: 34 * 1) If atan2() uses machine PI, then 35 * 36 * atan(x) returns (PI/pi) * (the exact arc tangent of x) nearly rounded; 37 * and PI is the exact pi rounded to machine precision (see atan2 for 38 * details): 39 * 40 * in decimal: 41 * pi = 3.141592653589793 23846264338327 ..... 42 * 53 bits PI = 3.141592653589793 115997963 ..... , 43 * 56 bits PI = 3.141592653589793 227020265 ..... , 44 * 45 * in hexadecimal: 46 * pi = 3.243F6A8885A308D313198A2E.... 47 * 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18 error=.276ulps 48 * 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2 error=.206ulps 49 * 50 * In a test run with more than 200,000 random arguments on a VAX, the 51 * maximum observed error in ulps (units in the last place) was 52 * 0.86 ulps. (comparing against (PI/pi)*(exact atan(x))). 53 * 54 * 2) If atan2() uses true pi, then 55 * 56 * atan(x) returns the exact atan(x) with error below about 2 ulps. 57 * 58 * In a test run with more than 1,024,000 random arguments on a VAX, the 59 * maximum observed error in ulps (units in the last place) was 60 * 0.85 ulps. 61 */ 62 63 double atan(x) 64 double x; 65 { 66 double atan2(),one=1.0; 67 return(atan2(x,one)); 68 } 69