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/* mpfr_div_ui -- divide a floating-point number by a machine integer
Copyright (C) 1999, 2000, 2001 Free Software Foundation, Inc.
This file is part of the MPFR Library.
The MPFR Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 2.1 of the License, or (at your
option) any later version.
The MPFR Library is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
License for more details.
You should have received a copy of the GNU Lesser General Public License
along with the MPFR Library; see the file COPYING.LIB. If not, write to
the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
MA 02111-1307, USA. */
#include <stdio.h>
#include "gmp.h"
#include "gmp-impl.h"
#include "longlong.h"
#include "mpfr.h"
#include "mpfr-impl.h"
/* returns 0 if result exact, non-zero otherwise */
int
mpfr_div_ui (mpfr_ptr y, mpfr_srcptr x, unsigned long int u, mp_rnd_t rnd_mode)
{
long int xn, yn, dif, sh, i;
mp_limb_t *xp, *yp, *tmp, c, d;
int inexact, middle = 1;
TMP_DECL(marker);
if (MPFR_IS_NAN(x))
{
MPFR_SET_NAN(y);
MPFR_RET_NAN;
}
MPFR_CLEAR_NAN(y); /* clear NaN flag */
if (MPFR_IS_INF(x))
{
MPFR_SET_INF(y);
if (MPFR_SIGN(y) * MPFR_SIGN(x) < 0) /* consider u=0 as +0 */
MPFR_CHANGE_SIGN(y);
return 0;
}
if (u == 0)
{
if (MPFR_IS_ZERO(x)) /* 0/0 is NaN */
{
MPFR_SET_NAN(y);
MPFR_RET_NAN;
}
else /* x/0 is Inf */
{
MPFR_SET_INF(y);
MPFR_SET_SAME_SIGN(y, x);
return 0;
}
}
MPFR_CLEAR_INF(y);
if (MPFR_IS_ZERO(x))
{
MPFR_SET_ZERO(y);
return 0;
}
TMP_MARK(marker);
xn = (MPFR_PREC(x) - 1)/BITS_PER_MP_LIMB + 1;
yn = (MPFR_PREC(y) - 1)/BITS_PER_MP_LIMB + 1;
xp = MPFR_MANT(x);
yp = MPFR_MANT(y);
MPFR_EXP(y) = MPFR_EXP(x);
if (MPFR_SIGN(x) * MPFR_SIGN(y) < 0)
MPFR_CHANGE_SIGN(y);
dif = yn + 1 - xn;
/* we need to store yn+1 = xn + dif limbs of the quotient */
/* don't use tmp=yp since the mpn_lshift call below requires yp >= tmp+1 */
tmp = TMP_ALLOC((yn + 1) * BYTES_PER_MP_LIMB);
c = (mp_limb_t) u;
if (dif >= 0)
c = mpn_divrem_1 (tmp, dif, xp, xn, c); /* used all the dividend */
else /* dif < 0 i.e. xn > yn, don't use the (-dif) low limbs from x */
c = mpn_divrem_1 (tmp, 0, xp - dif, yn + 1, c);
inexact = (c != 0);
if (rnd_mode == GMP_RNDN)
{
if (2 * c < (mp_limb_t) u)
middle = -1;
else if (2 * c > (mp_limb_t) u)
middle = 1;
else
middle = 0; /* exactly in the middle */
}
for (i=0; ((inexact == 0) || (middle == 0)) && (i < -dif); i++)
if (xp[i])
inexact = middle = 1; /* larger than middle */
if (tmp[yn] == 0) /* high limb is zero */
{
tmp--;
sh = 0;
MPFR_EXP(y) -= BITS_PER_MP_LIMB;
}
/* now we have yn limbs starting from tmp[1], with tmp[yn]<>0 */
/* shift left to normalize */
count_leading_zeros(sh, tmp[yn]);
if (sh)
{
mpn_lshift (yp, tmp + 1, yn, sh);
yp[0] += tmp[0] >> (BITS_PER_MP_LIMB - sh);
middle = middle || ((tmp[0] << sh) != 0);
inexact = inexact || ((tmp[0] << sh) != 0);
MPFR_EXP(y) -= sh;
}
else
MPN_COPY(yp, tmp + 1, yn);
sh = yn * BITS_PER_MP_LIMB - MPFR_PREC(y);
/* it remains sh bits in less significant limb of y */
d = *yp & ((MP_LIMB_T_ONE << sh) - MP_LIMB_T_ONE);
*yp ^= d; /* set to zero lowest sh bits */
TMP_FREE(marker);
if ((d == 0) && (inexact == 0))
return 0; /* result is exact */
switch (rnd_mode)
{
case GMP_RNDZ:
MPFR_RET(-MPFR_SIGN(x)); /* result is inexact */
case GMP_RNDU:
if (MPFR_SIGN(y) > 0)
mpfr_add_one_ulp (y, rnd_mode);
MPFR_RET(1); /* result is inexact */
case GMP_RNDD:
if (MPFR_SIGN(y) < 0)
mpfr_add_one_ulp (y, rnd_mode);
MPFR_RET(-1); /* result is inexact */
case GMP_RNDN:
if (sh && d < (MP_LIMB_T_ONE << (sh - 1)))
MPFR_RET(-MPFR_SIGN(x));
else if (sh && d > (MP_LIMB_T_ONE << (sh - 1)))
{
mpfr_add_one_ulp (y, rnd_mode);
MPFR_RET(MPFR_SIGN(x));
}
else /* sh = 0 or d = 1 << (sh-1) */
{
/* we are in the middle if:
(a) sh > 0 and inexact == 0
(b) sh=0 and middle=1
*/
if ((sh && inexact) || (!sh && (middle > 0)) || (*yp & (MP_LIMB_T_ONE << sh)))
{
mpfr_add_one_ulp (y, rnd_mode);
MPFR_RET(MPFR_SIGN(x));
}
else
MPFR_RET(-MPFR_SIGN(x));
}
}
MPFR_RET(inexact); /* should never go here */
}
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