usr/src/lib/libm/common_source/atan.c

/*
 * Copyright (c) 1985 Regents of the University of California.
 *
 * Use and reproduction of this software are granted  in  accordance  with
 * the terms and conditions specified in  the  Berkeley  Software  License
 * Agreement (in particular, this entails acknowledgement of the programs'
 * source, and inclusion of this notice) with the additional understanding
 * that  all  recipients  should regard themselves as participants  in  an
 * ongoing  research  project and hence should  feel  obligated  to report
 * their  experiences (good or bad) with these elementary function  codes,
 * using "sendbug 4bsd-bugs@BERKELEY", to the authors.
 */

#ifndef lint
static char sccsid[] =
"@(#)atan.c     1.1 (Berkeley) 8/21/85; 1.2 (ucb.elefunt) %G%";
#endif not lint

/* ATAN(X)
 * RETURNS ARC TANGENT OF X
 * DOUBLE PRECISION (IEEE DOUBLE 53 bits, VAX D FORMAT 56 bits)
 * CODED IN C BY K.C. NG, 4/16/85, REVISED ON 6/10/85.
 *
 * Required kernel function:
 *      atan2(y,x)
 *
 * Method:
 *      atan(x) = atan2(x,1.0).
 *
 * Special case:
 *      if x is NaN, return x itself.
 *
 * Accuracy:
 * 1)  If atan2() uses machine PI, then
 *
 *      atan(x) returns (PI/pi) * (the exact arc tangent of x) nearly rounded;
 *      and PI is the exact pi rounded to machine precision (see atan2 for
 *      details):
 *
 *      in decimal:
 *              pi = 3.141592653589793 23846264338327 .....
 *    53 bits   PI = 3.141592653589793 115997963 ..... ,
 *    56 bits   PI = 3.141592653589793 227020265 ..... ,
 *
 *      in hexadecimal:
 *              pi = 3.243F6A8885A308D313198A2E....
 *    53 bits   PI = 3.243F6A8885A30  =  2 * 1.921FB54442D18    error=.276ulps
 *    56 bits   PI = 3.243F6A8885A308 =  4 * .C90FDAA22168C2    error=.206ulps
 *
 *      In a test run with more than 200,000 random arguments on a VAX, the
 *      maximum observed error in ulps (units in the last place) was
 *      0.86 ulps.      (comparing against (PI/pi)*(exact atan(x))).
 *
 * 2)  If atan2() uses true pi, then
 *
 *      atan(x) returns the exact atan(x) with error below about 2 ulps.
 *
 *      In a test run with more than 1,024,000 random arguments on a VAX, the
 *      maximum observed error in ulps (units in the last place) was
 *      0.85 ulps.
 */

double atan(x)
double x;
{
        double atan2(),one=1.0;
        return(atan2(x,one));
}