108 lines
3.2 KiB
C
108 lines
3.2 KiB
C
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/* origin: FreeBSD /usr/src/lib/msun/src/e_atan2.c */
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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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/* 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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#include "libm.h"
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static const double
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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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uint32_t m,lx,ly,ix,iy;
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if (isnan(x) || isnan(y))
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return x+y;
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EXTRACT_WORDS(ix, lx, x);
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EXTRACT_WORDS(iy, ly, y);
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if (((ix-0x3ff00000) | lx) == 0) /* x = 1.0 */
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return atan(y);
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m = ((iy>>31)&1) | ((ix>>30)&2); /* 2*sign(x)+sign(y) */
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ix = ix & 0x7fffffff;
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iy = iy & 0x7fffffff;
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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: return y; /* atan(+-0,+anything)=+-0 */
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case 2: return pi; /* atan(+0,-anything) = pi */
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case 3: return -pi; /* 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)
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return m&1 ? -pi/2 : pi/2;
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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: return pi/4; /* atan(+INF,+INF) */
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case 1: return -pi/4; /* atan(-INF,+INF) */
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case 2: return 3*pi/4; /* atan(+INF,-INF) */
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case 3: return -3*pi/4; /* atan(-INF,-INF) */
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}
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} else {
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switch(m) {
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case 0: return 0.0; /* atan(+...,+INF) */
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case 1: return -0.0; /* atan(-...,+INF) */
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case 2: return pi; /* atan(+...,-INF) */
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case 3: return -pi; /* atan(-...,-INF) */
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}
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}
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}
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/* |y/x| > 0x1p64 */
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if (ix+(64<<20) < iy || iy == 0x7ff00000)
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return m&1 ? -pi/2 : pi/2;
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/* z = atan(|y/x|) without spurious underflow */
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if ((m&2) && iy+(64<<20) < ix) /* |y/x| < 0x1p-64, x<0 */
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z = 0;
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else
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z = atan(fabs(y/x));
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switch (m) {
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case 0: return z; /* atan(+,+) */
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case 1: return -z; /* atan(-,+) */
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case 2: 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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