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 the above copyright notice and this paragraph are 7 * duplicated in all such forms and that any documentation, 8 * advertising materials, and other materials related to such 9 * distribution and use acknowledge that the software was developed 10 * by the University of California, Berkeley. The name of the 11 * University may not be used to endorse or promote products derived 12 * from this software without specific prior written permission. 13 * THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR 14 * IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED 15 * WARRANTIES OF MERCHANTIBILITY AND FITNESS FOR A PARTICULAR PURPOSE. 16 * 17 * All recipients should regard themselves as participants in an ongoing 18 * research project and hence should feel obligated to report their 19 * experiences (good or bad) with these elementary function codes, using 20 * the sendbug(8) program, to the authors. 21 */ 22 23 #ifndef lint 24 static char sccsid[] = "@(#)atan.c 5.3 (Berkeley) 06/30/88"; 25 #endif /* not lint */ 26 27 /* ATAN(X) 28 * RETURNS ARC TANGENT OF X 29 * DOUBLE PRECISION (IEEE DOUBLE 53 bits, VAX D FORMAT 56 bits) 30 * CODED IN C BY K.C. NG, 4/16/85, REVISED ON 6/10/85. 31 * 32 * Required kernel function: 33 * atan2(y,x) 34 * 35 * Method: 36 * atan(x) = atan2(x,1.0). 37 * 38 * Special case: 39 * if x is NaN, return x itself. 40 * 41 * Accuracy: 42 * 1) If atan2() uses machine PI, then 43 * 44 * atan(x) returns (PI/pi) * (the exact arc tangent of x) nearly rounded; 45 * and PI is the exact pi rounded to machine precision (see atan2 for 46 * details): 47 * 48 * in decimal: 49 * pi = 3.141592653589793 23846264338327 ..... 50 * 53 bits PI = 3.141592653589793 115997963 ..... , 51 * 56 bits PI = 3.141592653589793 227020265 ..... , 52 * 53 * in hexadecimal: 54 * pi = 3.243F6A8885A308D313198A2E.... 55 * 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18 error=.276ulps 56 * 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2 error=.206ulps 57 * 58 * In a test run with more than 200,000 random arguments on a VAX, the 59 * maximum observed error in ulps (units in the last place) was 60 * 0.86 ulps. (comparing against (PI/pi)*(exact atan(x))). 61 * 62 * 2) If atan2() uses true pi, then 63 * 64 * atan(x) returns the exact atan(x) with error below about 2 ulps. 65 * 66 * In a test run with more than 1,024,000 random arguments on a VAX, the 67 * maximum observed error in ulps (units in the last place) was 68 * 0.85 ulps. 69 */ 70 71 double atan(x) 72 double x; 73 { 74 double atan2(),one=1.0; 75 return(atan2(x,one)); 76 } 77