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/* $OpenBSD: n_atan.c,v 1.13 2013/07/15 04:09:44 espie Exp $ */
/* $NetBSD: n_atan.c,v 1.1 1995/10/10 23:36:36 ragge Exp $ */
/*
* Copyright (c) 1985, 1993
* The Regents of the University of California. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* 3. Neither the name of the University nor the names of its contributors
* may be used to endorse or promote products derived from this software
* without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*/
/* 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.
*/
#include <math.h>
double
atan(double x)
{
double one=1.0;
return(atan2(x,one));
}
__strong_alias(atanl, atan);
float
atanf(float x)
{
float one=1.0f;
return(atan2f(x,one));
}
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