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

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* 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)
This commit is contained in:
Szabolcs Nagy
2013-09-03 03:27:02 +00:00
parent 98be442ee8
commit d1a2ead878
15 changed files with 273 additions and 904 deletions
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84
src/math/rintl.c
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@ -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;
union ldshape u = {x};
int e = u.i.se & 0x7fff;
int s = u.i.se >> 15;
long double y;
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;
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