134124Sbostic /*
2*61283Sbostic * Copyright (c) 1985, 1993
3*61283Sbostic * The Regents of the University of California. All rights reserved.
434124Sbostic *
542655Sbostic * %sccs.include.redist.c%
624589Szliu */
724589Szliu
824589Szliu #ifndef lint
9*61283Sbostic static char sccsid[] = "@(#)atan.c 8.1 (Berkeley) 06/04/93";
1034124Sbostic #endif /* not lint */
1124589Szliu
1224589Szliu /* ATAN(X)
1324589Szliu * RETURNS ARC TANGENT OF X
1424589Szliu * DOUBLE PRECISION (IEEE DOUBLE 53 bits, VAX D FORMAT 56 bits)
1524589Szliu * CODED IN C BY K.C. NG, 4/16/85, REVISED ON 6/10/85.
1624589Szliu *
1724589Szliu * Required kernel function:
1824589Szliu * atan2(y,x)
1924589Szliu *
2024589Szliu * Method:
2124589Szliu * atan(x) = atan2(x,1.0).
2224589Szliu *
2324589Szliu * Special case:
2424589Szliu * if x is NaN, return x itself.
2524589Szliu *
2624589Szliu * Accuracy:
2724589Szliu * 1) If atan2() uses machine PI, then
2824589Szliu *
2924589Szliu * atan(x) returns (PI/pi) * (the exact arc tangent of x) nearly rounded;
3024589Szliu * and PI is the exact pi rounded to machine precision (see atan2 for
3124589Szliu * details):
3224589Szliu *
3324589Szliu * in decimal:
3424589Szliu * pi = 3.141592653589793 23846264338327 .....
3524589Szliu * 53 bits PI = 3.141592653589793 115997963 ..... ,
3624589Szliu * 56 bits PI = 3.141592653589793 227020265 ..... ,
3724589Szliu *
3824589Szliu * in hexadecimal:
3924589Szliu * pi = 3.243F6A8885A308D313198A2E....
4024589Szliu * 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18 error=.276ulps
4124589Szliu * 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2 error=.206ulps
4224589Szliu *
4324589Szliu * In a test run with more than 200,000 random arguments on a VAX, the
4424589Szliu * maximum observed error in ulps (units in the last place) was
4524589Szliu * 0.86 ulps. (comparing against (PI/pi)*(exact atan(x))).
4624589Szliu *
4724589Szliu * 2) If atan2() uses true pi, then
4824589Szliu *
4924589Szliu * atan(x) returns the exact atan(x) with error below about 2 ulps.
5024589Szliu *
5124589Szliu * In a test run with more than 1,024,000 random arguments on a VAX, the
5224589Szliu * maximum observed error in ulps (units in the last place) was
5324589Szliu * 0.85 ulps.
5424589Szliu */
5524589Szliu
atan(x)5624589Szliu double atan(x)
5724589Szliu double x;
5824589Szliu {
5924589Szliu double atan2(),one=1.0;
6024589Szliu return(atan2(x,one));
6124589Szliu }
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