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math: rewrite remainder functions (remainder, remquo, fmod, modf)

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* results are exact
* modfl follows truncl (raises inexact flag spuriously now)
* modf and modff only had cosmetic cleanup
* remainder is just a wrapper around remquo now
* using iterative shift+subtract for remquo and fmod
* ld80 and ld128 are supported as well
This commit is contained in:
Szabolcs Nagy
2013-09-03 04:09:12 +00:00
parent d1a2ead878
commit ee2ee92d62
11 changed files with 481 additions and 1019 deletions
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117
src/math/modfl.c
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@ -1,40 +1,3 @@
/* origin: FreeBSD /usr/src/lib/msun/src/s_modfl.c */
/*-
* Copyright (c) 2007 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.
*
* Derived from s_modf.c, which has the following Copyright:
* ====================================================
* 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.
* ====================================================
*/
#include "libm.h"
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
@ -43,58 +6,46 @@ long double modfl(long double x, long double *iptr)
return modf(x, (double *)iptr);
}
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
#if LDBL_MANL_SIZE > 32
#define MASK ((uint64_t)-1)
#else
#define MASK ((uint32_t)-1)
#if LDBL_MANT_DIG == 64
#define TOINT 0x1p63
#elif LDBL_MANT_DIG == 113
#define TOINT 0x1p112
#endif
/* Return the last n bits of a word, representing the fractional part. */
#define GETFRAC(bits, n) ((bits) & ~(MASK << (n)))
/* The number of fraction bits in manh, not counting the integer bit */
#define HIBITS (LDBL_MANT_DIG - LDBL_MANL_SIZE)
static const long double zero[] = { 0.0, -0.0 };
long double modfl(long double x, long double *iptr)
{
union IEEEl2bits ux;
int e;
union ldshape u = {x};
uint64_t mask;
int e = (u.i.se & 0x7fff) - 0x3fff;
int s = u.i.se >> 15;
long double absx;
long double y;
ux.e = x;
e = ux.bits.exp - LDBL_MAX_EXP + 1;
if (e < HIBITS) { /* Integer part is in manh. */
if (e < 0) { /* |x|<1 */
*iptr = zero[ux.bits.sign];
return x;
}
if ((GETFRAC(ux.bits.manh, HIBITS - 1 - e)|ux.bits.manl) == 0) {
/* x is an integer. */
*iptr = x;
return zero[ux.bits.sign];
}
/* Clear all but the top e+1 bits. */
ux.bits.manh >>= HIBITS - 1 - e;
ux.bits.manh <<= HIBITS - 1 - e;
ux.bits.manl = 0;
*iptr = ux.e;
return x - ux.e;
} else if (e >= LDBL_MANT_DIG - 1) { /* x has no fraction part. */
/* no fractional part */
if (e >= LDBL_MANT_DIG-1) {
*iptr = x;
if (e == LDBL_MAX_EXP && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)) /* nan */
if (isnan(x))
return x;
return zero[ux.bits.sign];
} else { /* Fraction part is in manl. */
if (GETFRAC(ux.bits.manl, LDBL_MANT_DIG - 1 - e) == 0) {
/* x is integral. */
*iptr = x;
return zero[ux.bits.sign];
}
/* Clear all but the top e+1 bits. */
ux.bits.manl >>= LDBL_MANT_DIG - 1 - e;
ux.bits.manl <<= LDBL_MANT_DIG - 1 - e;
*iptr = ux.e;
return x - ux.e;
return s ? -0.0 : 0.0;
}
/* no integral part*/
if (e < 0) {
*iptr = s ? -0.0 : 0.0;
return x;
}
/* raises spurious inexact */
absx = s ? -x : x;
y = absx + TOINT - TOINT - absx;
if (y == 0) {
*iptr = x;
return s ? -0.0 : 0.0;
}
if (y > 0)
y -= 1;
if (s)
y = -y;
*iptr = x + y;
return -y;
}
#endif