/* 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 volatile double tiny = 1.0e-300; static const double zero = 0.0, pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */ pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */ pi = 3.1415926535897931160E+00; /* 0x400921FB, 0x54442D18 */ static const volatile double pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */ double atan2(double y, double x) { double z; int32_t k,m,hx,hy,ix,iy; uint32_t lx,ly; EXTRACT_WORDS(hx, lx, x); ix = hx & 0x7fffffff; EXTRACT_WORDS(hy, ly, y); iy = hy & 0x7fffffff; if ((ix|((lx|-lx)>>31)) > 0x7ff00000 || (iy|((ly|-ly)>>31)) > 0x7ff00000) /* x or y is NaN */ return x+y; if ((hx-0x3ff00000 | lx) == 0) /* x = 1.0 */ return atan(y); m = ((hy>>31)&1) | ((hx>>30)&2); /* 2*sign(x)+sign(y) */ /* when y = 0 */ if ((iy|ly) == 0) { switch(m) { case 0: case 1: return y; /* atan(+-0,+anything)=+-0 */ case 2: return pi+tiny; /* atan(+0,-anything) = pi */ case 3: return -pi-tiny; /* atan(-0,-anything) =-pi */ } } /* when x = 0 */ if ((ix|lx) == 0) return hy < 0 ? -pi_o_2-tiny : pi_o_2+tiny; /* when x is INF */ if (ix == 0x7ff00000) { if (iy == 0x7ff00000) { switch(m) { case 0: return pi_o_4+tiny; /* atan(+INF,+INF) */ case 1: return -pi_o_4-tiny; /* atan(-INF,+INF) */ case 2: return 3.0*pi_o_4+tiny; /* atan(+INF,-INF) */ case 3: return -3.0*pi_o_4-tiny; /* atan(-INF,-INF) */ } } else { switch(m) { case 0: return zero; /* atan(+...,+INF) */ case 1: return -zero; /* atan(-...,+INF) */ case 2: return pi+tiny; /* atan(+...,-INF) */ case 3: return -pi-tiny; /* atan(-...,-INF) */ } } } /* when y is INF */ if (iy == 0x7ff00000) return hy < 0 ? -pi_o_2-tiny : pi_o_2+tiny; /* compute y/x */ k = (iy-ix)>>20; if (k > 60) { /* |y/x| > 2**60 */ z = pi_o_2+0.5*pi_lo; m &= 1; } else if (hx < 0 && k < -60) /* 0 > |y|/x > -2**-60 */ z = 0.0; else /* safe to do y/x */ 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(-,-) */ } }