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, 16 insertions, 70 deletions

diff --git a/src/math/rintl.c b/src/math/rintl.c
index b13cfeb3..26725073 100644
--- a/src/math/rintl.c
+++ b/src/math/rintl.c
@@ -1,30 +1,3 @@
-/* origin: FreeBSD /usr/src/lib/msun/src/s_rintl.c */
-/*-
- * Copyright (c) 2008 David Schultz <das@FreeBSD.ORG>
- * All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- * 1. Redistributions of source code must retain the above copyright
- *    notice, this list of conditions and the following disclaimer.
- * 2. Redistributions in binary form must reproduce the above copyright
- *    notice, this list of conditions and the following disclaimer in the
- *    documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
- * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
- * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
- * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
- * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
- * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
- * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
- * SUCH DAMAGE.
- */
-
 #include "libm.h"
 
 #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
@@ -33,53 +6,26 @@ long double rintl(long double x)
 	return rint(x);
 }
 #elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
-
-#define BIAS    (LDBL_MAX_EXP - 1)
-
-static const float
-shift[2] = {
 #if LDBL_MANT_DIG == 64
-	0x1.0p63, -0x1.0p63
+#define TOINT 0x1p63
 #elif LDBL_MANT_DIG == 113
-	0x1.0p112, -0x1.0p112
+#define TOINT 0x1p112
 #endif
-};
-static const float zero[2] = { 0.0, -0.0 };
-
 long double rintl(long double x)
 {
-	union IEEEl2bits u;
-	uint32_t expsign;
-	int ex, sign;
-
-	u.e = x;
-	expsign = u.xbits.expsign;
-	ex = expsign & 0x7fff;
-
-	if (ex >= BIAS + LDBL_MANT_DIG - 1) {
-		if (ex == BIAS + LDBL_MAX_EXP)
-			return x + x; /* Inf, NaN, or unsupported format */
-		return x;             /* finite and already an integer */
-	}
-	sign = expsign >> 15;
-
-	/*
-	 * The following code assumes that intermediate results are
-	 * evaluated in long double precision. If they are evaluated in
-	 * greater precision, double rounding may occur, and if they are
-	 * evaluated in less precision (as on i386), results will be
-	 * wildly incorrect.
-	 */
-	x += shift[sign];
-	x -= shift[sign];
-
-	/*
-	 * If the result is +-0, then it must have the same sign as x, but
-	 * the above calculation doesn't always give this.  Fix up the sign.
-	 */
-	if (ex < BIAS && x == 0.0)
-		return zero[sign];
-
-	return x;
+	union ldshape u = {x};
+	int e = u.i.se & 0x7fff;
+	int s = u.i.se >> 15;
+	long double y;
+
+	if (e >= 0x3fff+LDBL_MANT_DIG-1)
+		return x;
+	if (s)
+		y = x - TOINT + TOINT;
+	else
+		y = x + TOINT - TOINT;
+	if (y == 0)
+		return 0*x;
+	return y;
 }
 #endif