mirror of https://gitlab.com/rnger/amath
166 lines
5.4 KiB
C
166 lines
5.4 KiB
C
/* @(#)e_atan2.c 1.3 95/01/18 */
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/*
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* Copyright (c) 2015 Carsten Larsen
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* All rights reserved.
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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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*
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* THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
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* IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
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* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
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* IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
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* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
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* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
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* THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*
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* The origin source code can be obtained from:
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* http://www.netlib.org/fdlibm/e_atan2.c
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*
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*/
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunSoft, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*
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*/
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#include "prim.h"
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#include "math.h"
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#ifdef _WIN32
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#pragma warning( disable : 4146 )
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#endif
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/* atan2(y,x)
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* Method :
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* 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
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* 2. Reduce x to positive by (if x and y are unexceptional):
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* ARG (x+iy) = arctan(y/x) ... if x > 0,
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* ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0,
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*
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* Special cases:
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*
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* ATAN2((anything), NaN ) is NaN;
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* ATAN2(NAN , (anything) ) is NaN;
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* ATAN2(+-0, +(anything but NaN)) is +-0 ;
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* ATAN2(+-0, -(anything but NaN)) is +-pi ;
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* ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
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* ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
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* ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
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* ATAN2(+-INF,+INF ) is +-pi/4 ;
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* ATAN2(+-INF,-INF ) is +-3pi/4;
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* ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
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*
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* Constants:
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* The hexadecimal values are the intended ones for the following
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* constants. The decimal values may be used, provided that the
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* compiler will convert from decimal to binary accurately enough
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* to produce the hexadecimal values shown.
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*/
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static const double
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tiny = 1.0e-300,
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zero = 0.0,
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pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
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pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
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pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
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pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
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double atan2(double y, double x)
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{
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double z;
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sword k,m,hx,hy,ix,iy;
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uword lx,ly;
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EXTRACT_WORDS(hx,lx,x);
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ix = hx&0x7fffffff;
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EXTRACT_WORDS(hy,ly,y);
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iy = hy&0x7fffffff;
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if(((ix|((lx|-lx)>>31))>0x7ff00000)||
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((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */
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return x+y;
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if(((hx-0x3ff00000)|lx)==0) return atan(y); /* x=1.0 */
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m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */
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/* when y = 0 */
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if((iy|ly)==0) {
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switch(m) {
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case 0:
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case 1:
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return y; /* atan(+-0,+anything)=+-0 */
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case 2:
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return pi+tiny;/* atan(+0,-anything) = pi */
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case 3:
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return -pi-tiny;/* atan(-0,-anything) =-pi */
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}
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}
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/* when x = 0 */
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if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
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/* when x is INF */
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if(ix==0x7ff00000) {
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if(iy==0x7ff00000) {
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switch(m) {
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case 0:
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return pi_o_4+tiny;/* atan(+INF,+INF) */
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case 1:
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return -pi_o_4-tiny;/* atan(-INF,+INF) */
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case 2:
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return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
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case 3:
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return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
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}
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} else {
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switch(m) {
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case 0:
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return zero ; /* atan(+...,+INF) */
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case 1:
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return -zero ; /* atan(-...,+INF) */
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case 2:
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return pi+tiny ; /* atan(+...,-INF) */
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case 3:
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return -pi-tiny ; /* atan(-...,-INF) */
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}
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}
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}
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/* when y is INF */
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if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
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/* compute y/x */
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k = (iy-ix)>>20;
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if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */
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else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */
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else z=atan(fabs(y/x)); /* safe to do y/x */
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switch (m) {
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case 0:
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return z ; /* atan(+,+) */
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case 1: {
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uword zh;
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GET_HIGH_WORD(zh,z);
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SET_HIGH_WORD(z, zh ^ 0x80000000);
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}
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return z ; /* atan(-,+) */
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case 2:
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return pi-(z-pi_lo);/* atan(+,-) */
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default: /* case 3 */
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return (z-pi_lo)-pi;/* atan(-,-) */
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}
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}
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