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, 17 insertions, 75 deletions

diff --git a/src/math/floor.c b/src/math/floor.c
index ecb9dde8..ebc9fabe 100644
--- a/src/math/floor.c
+++ b/src/math/floor.c
@@ -1,82 +1,24 @@
-/* origin: FreeBSD /usr/src/lib/msun/src/s_floor.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.
- * ====================================================
- */
-/*
- * floor(x)
- * Return x rounded toward -inf to integral value
- * Method:
- *      Bit twiddling.
- * Exception:
- *      Inexact flag raised if x not equal to floor(x).
- */
-
 #include "libm.h"
 
-static const double huge = 1.0e300;
-
 double floor(double x)
 {
-	int32_t i0,i1,j0;
-	uint32_t i,j;
+	union {double f; uint64_t i;} u = {x};
+	int e = u.i >> 52 & 0x7ff;
+	double_t y;
 
-	EXTRACT_WORDS(i0, i1, x);
-	// FIXME: signed shift
-	j0 = ((i0>>20)&0x7ff) - 0x3ff;
-	if (j0 < 20) {
-		if (j0 < 0) {  /* |x| < 1 */
-			/* raise inexact if x != 0 */
-			if (huge+x > 0.0) {
-				if (i0 >= 0) {  /* x >= 0 */
-					i0 = i1 = 0;
-				} else if (((i0&0x7fffffff)|i1) != 0) {
-					i0 = 0xbff00000;
-					i1 = 0;
-				}
-			}
-		} else {
-			i = 0x000fffff>>j0;
-			if (((i0&i)|i1) == 0)
-				return x; /* x is integral */
-			 /* raise inexact flag */
-			if (huge+x > 0.0) {
-				if (i0 < 0)
-					i0 += 0x00100000>>j0;
-				i0 &= ~i;
-				i1 = 0;
-			}
-		}
-	} else if (j0 > 51) {
-		if (j0 == 0x400)
-			return x+x; /* inf or NaN */
-		else
-			return x;   /* x is integral */
-	} else {
-		i = (uint32_t)0xffffffff>>(j0-20);
-		if ((i1&i) == 0)
-			return x;   /* x is integral */
-		/* raise inexact flag */
-		if (huge+x > 0.0) {
-			if (i0 < 0) {
-				if (j0 == 20)
-					i0++;
-				else {
-					j = i1+(1<<(52-j0));
-					if (j < i1)
-						i0++; /* got a carry */
-					i1 = j;
-				}
-			}
-			i1 &= ~i;
-		}
+	if (e >= 0x3ff+52 || x == 0)
+		return x;
+	/* y = int(x) - x, where int(x) is an integer neighbor of x */
+	if (u.i >> 63)
+		y = (double)(x - 0x1p52) + 0x1p52 - x;
+	else
+		y = (double)(x + 0x1p52) - 0x1p52 - x;
+	/* special case because of non-nearest rounding modes */
+	if (e <= 0x3ff-1) {
+		FORCE_EVAL(y);
+		return u.i >> 63 ? -1 : 0;
 	}
-	INSERT_WORDS(x, i0, i1);
-	return x;
+	if (y > 0)
+		return x + y - 1;
+	return x + y;
 }