4.4BSD/usr/src/lib/libm/mc68881/atan2.c
/*-
* Copyright (c) 1990, 1993
* The Regents of the University of California. All rights reserved.
*
* This code is derived from software contributed to Berkeley by
* the Systems Programming Group of the University of Utah Computer
* Science Department.
*
* 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[] = "@(#)atan2.c 8.1 (Berkeley) 6/4/93";
#endif /* not lint */
/*
* ATAN2(Y,X)
* RETURN ARG (X+iY)
* DOUBLE PRECISION (IEEE DOUBLE 53 BITS)
*
* Scaled down version to weed out special cases. "Normal" cases are
* handled by calling atan2__A(), an assembly coded support routine in
* support.s.
*
* Required system supported functions :
* copysign(x,y)
* atan2__A(y,x)
*
* Method :
* 1. Deal with special cases
* 2. Call atan2__A() to do the others
*
* Special cases:
* Notations: atan2(y,x) == ARG (x+iy) == ARG(x,y).
*
* ARG( NAN , (anything) ) is NaN;
* ARG( (anything), NaN ) is NaN;
* ARG(+(anything but NaN), +-0) is +-0 ;
* ARG(-(anything but NaN), +-0) is +-PI ;
* ARG( 0, +-(anything but 0 and NaN) ) is +-PI/2;
* ARG( +INF,+-(anything but INF and NaN) ) is +-0 ;
* ARG( -INF,+-(anything but INF and NaN) ) is +-PI;
* ARG( +INF,+-INF ) is +-PI/4 ;
* ARG( -INF,+-INF ) is +-3PI/4;
* ARG( (anything but,0,NaN, and INF),+-INF ) is +-PI/2;
*
* Accuracy:
* atan2(y,x) returns (PI/pi) * the exact ARG (x+iy) nearly rounded,
* where
*
* 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 356,000 random argument on [-1,1] * [-1,1] on a
* VAX, the maximum observed error was 1.41 ulps (units of the last place)
* compared with (PI/pi)*(the exact ARG(x+iy)).
*
* Note:
* We use machine PI (the true pi rounded) in place of the actual
* value of pi for all the trig and inverse trig functions. In general,
* if trig is one of sin, cos, tan, then computed trig(y) returns the
* exact trig(y*pi/PI) nearly rounded; correspondingly, computed arctrig
* returns the exact arctrig(y)*PI/pi nearly rounded. These guarantee the
* trig functions have period PI, and trig(arctrig(x)) returns x for
* all critical values x.
*
* Constants:
* The hexadecimal values are the intended ones for the following constants.
* The decimal values may be used, provided that the compiler will convert
* from decimal to binary accurately enough to produce the hexadecimal values
* shown.
*/
static double
PIo4 = 7.8539816339744827900E-1 , /*Hex 2^ -1 * 1.921FB54442D18 */
PIo2 = 1.5707963267948965580E0 , /*Hex 2^ 0 * 1.921FB54442D18 */
PI = 3.1415926535897931160E0 ; /*Hex 2^ 1 * 1.921FB54442D18 */
double atan2(y,x)
double y,x;
{
static double zero=0, one=1;
double copysign(),atan2__A(),signy,signx;
int finite();
/* if x or y is NAN */
if(x!=x) return(x); if(y!=y) return(y);
/* copy down the sign of y and x */
signy = copysign(one,y);
signx = copysign(one,x);
/* when y = 0 */
if(y==zero) return((signx==one)?y:copysign(PI,signy));
/* when x = 0 */
if(x==zero) return(copysign(PIo2,signy));
/* when x is INF */
if(!finite(x))
if(!finite(y))
return(copysign((signx==one)?PIo4:3*PIo4,signy));
else
return(copysign((signx==one)?zero:PI,signy));
/* when y is INF */
if(!finite(y)) return(copysign(PIo2,signy));
/* else let atan2__A do the work */
return(atan2__A(y,x));
}