/* origin: FreeBSD /usr/src/lib/msun/src/e_atan2.c */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunSoft, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== * */ /* atan2(y,x) * Method : * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x). * 2. Reduce x to positive by (if x and y are unexceptional): * ARG (x+iy) = arctan(y/x) ... if x > 0, * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0, * * Special cases: * * ATAN2((anything), NaN ) is NaN; * ATAN2(NAN , (anything) ) is NaN; * ATAN2(+-0, +(anything but NaN)) is +-0 ; * ATAN2(+-0, -(anything but NaN)) is +-pi ; * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2; * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ; * ATAN2(+-(anything but INF and NaN), -INF) is +-pi; * ATAN2(+-INF,+INF ) is +-pi/4 ; * ATAN2(+-INF,-INF ) is +-3pi/4; * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2; * * 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. */ #include "libm.h" static const double pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */ pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */ double atan2(double y, double x) { double z; uint32_t m,lx,ly,ix,iy; if (isnan(x) || isnan(y)) return x+y; EXTRACT_WORDS(ix, lx, x); EXTRACT_WORDS(iy, ly, y); if ((ix-0x3ff00000 | lx) == 0) /* x = 1.0 */ return atan(y); m = ((iy>>31)&1) | ((ix>>30)&2); /* 2*sign(x)+sign(y) */ ix = ix & 0x7fffffff; iy = iy & 0x7fffffff; /* when y = 0 */ if ((iy|ly) == 0) { switch(m) { case 0: case 1: return y; /* atan(+-0,+anything)=+-0 */ case 2: return pi; /* atan(+0,-anything) = pi */ case 3: return -pi; /* atan(-0,-anything) =-pi */ } } /* when x = 0 */ if ((ix|lx) == 0) return m&1 ? -pi/2 : pi/2; /* when x is INF */ if (ix == 0x7ff00000) { if (iy == 0x7ff00000) { switch(m) { case 0: return pi/4; /* atan(+INF,+INF) */ case 1: return -pi/4; /* atan(-INF,+INF) */ case 2: return 3*pi/4; /* atan(+INF,-INF) */ case 3: return -3*pi/4; /* atan(-INF,-INF) */ } } else { switch(m) { case 0: return 0.0; /* atan(+...,+INF) */ case 1: return -0.0; /* atan(-...,+INF) */ case 2: return pi; /* atan(+...,-INF) */ case 3: return -pi; /* atan(-...,-INF) */ } } } /* |y/x| > 0x1p64 */ if (ix+(64<<20) < iy || iy == 0x7ff00000) return m&1 ? -pi/2 : pi/2; /* z = atan(|y/x|) without spurious underflow */ if ((m&2) && iy+(64<<20) < ix) /* |y/x| < 0x1p-64, x<0 */ z = 0; else z = atan(fabs(y/x)); switch (m) { case 0: return z; /* atan(+,+) */ case 1: return -z; /* atan(-,+) */ case 2: return pi - (z-pi_lo); /* atan(+,-) */ default: /* case 3 */ return (z-pi_lo) - pi; /* atan(-,-) */ } }