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Diffstat (limited to 'src/math/atan2.c')
| -rw-r--r-- | src/math/atan2.c | 119 |
1 files changed, 119 insertions, 0 deletions
diff --git a/src/math/atan2.c b/src/math/atan2.c new file mode 100644 index 00000000..3c35fbf0 --- /dev/null +++ b/src/math/atan2.c @@ -0,0 +1,119 @@ +/* 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 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 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(-,-) */ + } +} |