math: rewrite rounding functions (ceil, floor, trunc, round, rint)

* faster, smaller, cleaner implementation than the bit hacks of fdlibm
* use arithmetics like y=(double)(x+0x1p52)-0x1p52, which is an integer
neighbor of x in all rounding modes (0<=x<0x1p52) and only use bithacks
when that's faster and smaller (for float it usually is)
* the code assumes standard excess precision handling for casts
* long double code supports both ld80 and ld128
* nearbyint is not changed (it is a wrapper around rint)

1 files changed, 15 insertions, 85 deletions

diff --git a/src/math/rint.c b/src/math/rint.c
index 775c7b8d..81f4e622 100644
--- a/src/math/rint.c
+++ b/src/math/rint.c
@@ -1,90 +1,20 @@
-/* origin: FreeBSD /usr/src/lib/msun/src/s_rint.c */
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-/*
- * rint(x)
- * Return x rounded to integral value according to the prevailing
- * rounding mode.
- * Method:
- *      Using floating addition.
- * Exception:
- *      Inexact flag raised if x not equal to rint(x).
- */
-
-#include "libm.h"
-
-static const double
-TWO52[2] = {
-  4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */
- -4.50359962737049600000e+15, /* 0xC3300000, 0x00000000 */
-};
+#include <math.h>
+#include <stdint.h>
 
 double rint(double x)
 {
-	int32_t i0,j0,sx;
-	uint32_t i,i1;
-	double w,t;
+	union {double f; uint64_t i;} u = {x};
+	int e = u.i>>52 & 0x7ff;
+	int s = u.i>>63;
+	double_t y;
 
-	EXTRACT_WORDS(i0, i1, x);
-	// FIXME: signed shift
-	sx = (i0>>31) & 1;
-	j0 = ((i0>>20)&0x7ff) - 0x3ff;
-	if (j0 < 20) {
-		if (j0 < 0) {
-			if (((i0&0x7fffffff)|i1) == 0)
-				return x;
-			i1 |= i0 & 0x0fffff;
-			i0 &= 0xfffe0000;
-			i0 |= ((i1|-i1)>>12) & 0x80000;
-			SET_HIGH_WORD(x, i0);
-			STRICT_ASSIGN(double, w, TWO52[sx] + x);
-			t = w - TWO52[sx];
-			GET_HIGH_WORD(i0, t);
-			SET_HIGH_WORD(t, (i0&0x7fffffff)|(sx<<31));
-			return t;
-		} else {
-			i = 0x000fffff>>j0;
-			if (((i0&i)|i1) == 0)
-				return x; /* x is integral */
-			i >>= 1;
-			if (((i0&i)|i1) != 0) {
-				/*
-				 * Some bit is set after the 0.5 bit.  To avoid the
-				 * possibility of errors from double rounding in
-				 * w = TWO52[sx]+x, adjust the 0.25 bit to a lower
-				 * guard bit.  We do this for all j0<=51.  The
-				 * adjustment is trickiest for j0==18 and j0==19
-				 * since then it spans the word boundary.
-				 */
-				if (j0 == 19)
-					i1 = 0x40000000;
-				else if (j0 == 18)
-					i1 = 0x80000000;
-				else
-					i0 = (i0 & ~i)|(0x20000>>j0);
-			}
-		}
-	} else if (j0 > 51) {
-		if (j0 == 0x400)
-			return x+x;  /* inf or NaN */
-		return x;            /* x is integral */
-	} else {
-		i = (uint32_t)0xffffffff>>(j0-20);
-		if ((i1&i) == 0)
-			return x;    /* x is integral */
-		i >>= 1;
-		if ((i1&i) != 0)
-			i1 = (i1 & ~i)|(0x40000000>>(j0-20));
-	}
-	INSERT_WORDS(x, i0, i1);
-	STRICT_ASSIGN(double, w, TWO52[sx] + x);
-	return w - TWO52[sx];
+	if (e >= 0x3ff+52)
+		return x;
+	if (s)
+		y = (double)(x - 0x1p52) + 0x1p52;
+	else
+		y = (double)(x + 0x1p52) - 0x1p52;
+	if (y == 0)
+		return s ? -0.0 : 0;
+	return y;
 }