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
atan(x)56 double atan(x)
57 double x;
58 {
59 double atan2(),one=1.0;
60 return(atan2(x,one));
61 }
62