1 /* 2 * Copyright (c) 1985, 1993 3 * The Regents of the University of California. All rights reserved. 4 * 5 * %sccs.include.redist.c% 6 */ 7 8 #ifndef lint 9 static char sccsid[] = "@(#)atan.c 8.1 (Berkeley) 06/04/93"; 10 #endif /* not lint */ 11 12 /* ATAN(X) 13 * RETURNS ARC TANGENT OF X 14 * DOUBLE PRECISION (IEEE DOUBLE 53 bits, VAX D FORMAT 56 bits) 15 * CODED IN C BY K.C. NG, 4/16/85, REVISED ON 6/10/85. 16 * 17 * Required kernel function: 18 * atan2(y,x) 19 * 20 * Method: 21 * atan(x) = atan2(x,1.0). 22 * 23 * Special case: 24 * if x is NaN, return x itself. 25 * 26 * Accuracy: 27 * 1) If atan2() uses machine PI, then 28 * 29 * atan(x) returns (PI/pi) * (the exact arc tangent of x) nearly rounded; 30 * and PI is the exact pi rounded to machine precision (see atan2 for 31 * details): 32 * 33 * in decimal: 34 * pi = 3.141592653589793 23846264338327 ..... 35 * 53 bits PI = 3.141592653589793 115997963 ..... , 36 * 56 bits PI = 3.141592653589793 227020265 ..... , 37 * 38 * in hexadecimal: 39 * pi = 3.243F6A8885A308D313198A2E.... 40 * 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18 error=.276ulps 41 * 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2 error=.206ulps 42 * 43 * In a test run with more than 200,000 random arguments on a VAX, the 44 * maximum observed error in ulps (units in the last place) was 45 * 0.86 ulps. (comparing against (PI/pi)*(exact atan(x))). 46 * 47 * 2) If atan2() uses true pi, then 48 * 49 * atan(x) returns the exact atan(x) with error below about 2 ulps. 50 * 51 * In a test run with more than 1,024,000 random arguments on a VAX, the 52 * maximum observed error in ulps (units in the last place) was 53 * 0.85 ulps. 54 */ 55 56 double atan(x) 57 double x; 58 { 59 double atan2(),one=1.0; 60 return(atan2(x,one)); 61 } 62