88 lines
3.3 KiB
C
88 lines
3.3 KiB
C
/*
|
|
* Copyright (c) 1985 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. All advertising materials mentioning features or use of this software
|
|
* must display the following acknowledgement:
|
|
* This product includes software developed by the University of
|
|
* California, Berkeley and its contributors.
|
|
* 4. 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.
|
|
*/
|
|
|
|
#ifndef lint
|
|
static char sccsid[] = "@(#)atan.c 5.5 (Berkeley) 10/9/90";
|
|
#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));
|
|
}
|