146 lines
5.4 KiB
C
146 lines
5.4 KiB
C
/*-
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* Copyright (c) 1990 The Regents of the University of California.
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* All rights reserved.
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*
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* This code is derived from software contributed to Berkeley by
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* the Systems Programming Group of the University of Utah Computer
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* Science Department.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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* 3. All advertising materials mentioning features or use of this software
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* must display the following acknowledgement:
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* This product includes software developed by the University of
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* California, Berkeley and its contributors.
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* 4. Neither the name of the University nor the names of its contributors
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* may be used to endorse or promote products derived from this software
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* without specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*/
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#ifndef lint
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/*static char sccsid[] = "from: @(#)atan2.c 5.1 (Berkeley) 5/17/90";*/
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static char rcsid[] = "$Id: atan2.c,v 1.1 1993/08/14 13:43:32 mycroft Exp $";
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#endif /* not lint */
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/*
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* ATAN2(Y,X)
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* RETURN ARG (X+iY)
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* DOUBLE PRECISION (IEEE DOUBLE 53 BITS)
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*
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* Scaled down version to weed out special cases. "Normal" cases are
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* handled by calling atan2__A(), an assembly coded support routine in
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* support.s.
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*
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* Required system supported functions :
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* copysign(x,y)
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* atan2__A(y,x)
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*
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* Method :
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* 1. Deal with special cases
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* 2. Call atan2__A() to do the others
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*
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* Special cases:
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* Notations: atan2(y,x) == ARG (x+iy) == ARG(x,y).
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*
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* ARG( NAN , (anything) ) is NaN;
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* ARG( (anything), NaN ) is NaN;
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* ARG(+(anything but NaN), +-0) is +-0 ;
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* ARG(-(anything but NaN), +-0) is +-PI ;
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* ARG( 0, +-(anything but 0 and NaN) ) is +-PI/2;
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* ARG( +INF,+-(anything but INF and NaN) ) is +-0 ;
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* ARG( -INF,+-(anything but INF and NaN) ) is +-PI;
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* ARG( +INF,+-INF ) is +-PI/4 ;
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* ARG( -INF,+-INF ) is +-3PI/4;
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* ARG( (anything but,0,NaN, and INF),+-INF ) is +-PI/2;
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*
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* Accuracy:
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* atan2(y,x) returns (PI/pi) * the exact ARG (x+iy) nearly rounded,
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* where
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*
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* in decimal:
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* pi = 3.141592653589793 23846264338327 .....
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* 53 bits PI = 3.141592653589793 115997963 ..... ,
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* 56 bits PI = 3.141592653589793 227020265 ..... ,
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*
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* in hexadecimal:
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* pi = 3.243F6A8885A308D313198A2E....
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* 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18 error=.276ulps
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* 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2 error=.206ulps
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*
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* In a test run with 356,000 random argument on [-1,1] * [-1,1] on a
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* VAX, the maximum observed error was 1.41 ulps (units of the last place)
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* compared with (PI/pi)*(the exact ARG(x+iy)).
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*
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* Note:
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* We use machine PI (the true pi rounded) in place of the actual
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* value of pi for all the trig and inverse trig functions. In general,
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* if trig is one of sin, cos, tan, then computed trig(y) returns the
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* exact trig(y*pi/PI) nearly rounded; correspondingly, computed arctrig
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* returns the exact arctrig(y)*PI/pi nearly rounded. These guarantee the
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* trig functions have period PI, and trig(arctrig(x)) returns x for
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* all critical values x.
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*
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* Constants:
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* The hexadecimal values are the intended ones for the following constants.
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* The decimal values may be used, provided that the compiler will convert
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* from decimal to binary accurately enough to produce the hexadecimal values
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* shown.
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*/
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static double
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PIo4 = 7.8539816339744827900E-1 , /*Hex 2^ -1 * 1.921FB54442D18 */
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PIo2 = 1.5707963267948965580E0 , /*Hex 2^ 0 * 1.921FB54442D18 */
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PI = 3.1415926535897931160E0 ; /*Hex 2^ 1 * 1.921FB54442D18 */
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double atan2(y,x)
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double y,x;
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{
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static double zero=0, one=1;
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double copysign(),atan2__A(),signy,signx;
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int finite();
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/* if x or y is NAN */
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if(x!=x) return(x); if(y!=y) return(y);
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/* copy down the sign of y and x */
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signy = copysign(one,y);
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signx = copysign(one,x);
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/* when y = 0 */
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if(y==zero) return((signx==one)?y:copysign(PI,signy));
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/* when x = 0 */
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if(x==zero) return(copysign(PIo2,signy));
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/* when x is INF */
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if(!finite(x))
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if(!finite(y))
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return(copysign((signx==one)?PIo4:3*PIo4,signy));
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else
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return(copysign((signx==one)?zero:PI,signy));
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/* when y is INF */
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if(!finite(y)) return(copysign(PIo2,signy));
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/* else let atan2__A do the work */
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return(atan2__A(y,x));
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}
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