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[] = "@(#)atan.c 1.1 (Berkeley) 08/21/85";
16 #endif not lint
17
18 /* ATAN(X)
19 * RETURNS ARC TANGENT OF X
20 * DOUBLE PRECISION (IEEE DOUBLE 53 bits, VAX D FORMAT 56 bits)
21 * CODED IN C BY K.C. NG, 4/16/85, REVISED ON 6/10/85.
22 *
23 * Required kernel function:
24 * atan2(y,x)
25 *
26 * Method:
27 * atan(x) = atan2(x,1.0).
28 *
29 * Special case:
30 * if x is NaN, return x itself.
31 *
32 * Accuracy:
33 * 1) If atan2() uses machine PI, then
34 *
35 * atan(x) returns (PI/pi) * (the exact arc tangent of x) nearly rounded;
36 * and PI is the exact pi rounded to machine precision (see atan2 for
37 * details):
38 *
39 * in decimal:
40 * pi = 3.141592653589793 23846264338327 .....
41 * 53 bits PI = 3.141592653589793 115997963 ..... ,
42 * 56 bits PI = 3.141592653589793 227020265 ..... ,
43 *
44 * in hexadecimal:
45 * pi = 3.243F6A8885A308D313198A2E....
46 * 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18 error=.276ulps
47 * 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2 error=.206ulps
48 *
49 * In a test run with more than 200,000 random arguments on a VAX, the
50 * maximum observed error in ulps (units in the last place) was
51 * 0.86 ulps. (comparing against (PI/pi)*(exact atan(x))).
52 *
53 * 2) If atan2() uses true pi, then
54 *
55 * atan(x) returns the exact atan(x) with error below about 2 ulps.
56 *
57 * In a test run with more than 1,024,000 random arguments on a VAX, the
58 * maximum observed error in ulps (units in the last place) was
59 * 0.85 ulps.
60 */
61
atan(x)62 double atan(x)
63 double x;
64 {
65 double atan2(),one=1.0;
66 return(atan2(x,one));
67 }
68