math: clean up atan2.c

* remove volatile hacks
* don't care about inexact flag for now (removed all the +-tiny)
* fix atanl to raise underflow properly
* remove signed int arithmetics
* use pi/2 instead of pi_o_2 (gcc generates the same code, which is not
correct, but it does not matter: we mainly care about nearest rounding)

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(+,+) */