| /* 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(-,-) */ |
| } |
| } |
