diff options
Diffstat (limited to 'src/math/atan2.c')
| -rw-r--r-- | src/math/atan2.c | 68 |
1 files changed, 28 insertions, 40 deletions
diff --git a/src/math/atan2.c b/src/math/atan2.c index 825a38fe..5a1903c6 100644 --- a/src/math/atan2.c +++ b/src/math/atan2.c @@ -39,75 +39,63 @@ #include "libm.h" -// FIXME -static const volatile double -tiny = 1.0e-300; static const double -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 = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */ 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; + uint32_t m,lx,ly,ix,iy; - 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 */ + if (isnan(x) || isnan(y)) return x+y; - if ((hx-0x3ff00000 | lx) == 0) /* x = 1.0 */ + EXTRACT_WORDS(ix, lx, x); + EXTRACT_WORDS(iy, ly, y); + if ((ix-0x3ff00000 | lx) == 0) /* x = 1.0 */ return atan(y); - m = ((hy>>31)&1) | ((hx>>30)&2); /* 2*sign(x)+sign(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+tiny; /* atan(+0,-anything) = pi */ - case 3: return -pi-tiny; /* atan(-0,-anything) =-pi */ + 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 hy < 0 ? -pi_o_2-tiny : pi_o_2+tiny; + return m&1 ? -pi/2 : pi/2; /* 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) */ + 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+tiny; /* atan(+...,-INF) */ - case 3: return -pi-tiny; /* atan(-...,-INF) */ + 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) */ } } } - /* when y is INF */ - if (iy == 0x7ff00000) - return hy < 0 ? -pi_o_2-tiny : pi_o_2+tiny; + /* |y/x| > 0x1p64 */ + if (ix+(64<<20) < iy || iy == 0x7ff00000) + return m&1 ? -pi/2 : pi/2; - /* 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(|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(+,+) */ |