/*
* 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";
#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));
}