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/* mpfr_div_{ui,si} -- divide a floating-point number by a machine integer
Copyright 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009 Free Software Foundation, Inc.
Contributed by the Arenaire and Cacao projects, INRIA.
This file is part of the GNU MPFR Library.
The GNU 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 GNU 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 GNU MPFR Library; see the file COPYING.LIB. If not, write to
the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston,
MA 02110-1301, USA. */
#define MPFR_NEED_LONGLONG_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 i;
int sh;
mp_size_t xn, yn, dif;
mp_limb_t *xp, *yp, *tmp, c, d;
mp_exp_t exp;
int inexact, middle = 1, nexttoinf;
MPFR_TMP_DECL(marker);
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
{
if (MPFR_IS_NAN (x))
{
MPFR_SET_NAN (y);
MPFR_RET_NAN;
}
else if (MPFR_IS_INF (x))
{
MPFR_SET_INF (y);
MPFR_SET_SAME_SIGN (y, x);
MPFR_RET (0);
}
else
{
MPFR_ASSERTD (MPFR_IS_ZERO(x));
if (u == 0) /* 0/0 is NaN */
{
MPFR_SET_NAN(y);
MPFR_RET_NAN;
}
else
{
MPFR_SET_ZERO(y);
MPFR_SET_SAME_SIGN (y, x);
MPFR_RET(0);
}
}
}
else if (MPFR_UNLIKELY (u <= 1))
{
if (u < 1)
{
/* x/0 is Inf since x != 0*/
MPFR_SET_INF (y);
MPFR_SET_SAME_SIGN (y, x);
MPFR_RET (0);
}
else /* y = x/1 = x */
return mpfr_set (y, x, rnd_mode);
}
else if (MPFR_UNLIKELY (IS_POW2 (u)))
return mpfr_div_2si (y, x, MPFR_INT_CEIL_LOG2 (u), rnd_mode);
MPFR_CLEAR_FLAGS (y);
MPFR_SET_SAME_SIGN (y, x);
MPFR_TMP_MARK (marker);
xn = MPFR_LIMB_SIZE (x);
yn = MPFR_LIMB_SIZE (y);
xp = MPFR_MANT (x);
yp = MPFR_MANT (y);
exp = MPFR_GET_EXP (x);
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 = (mp_limb_t*) MPFR_TMP_ALLOC ((yn + 1) * BYTES_PER_MP_LIMB);
c = (mp_limb_t) u;
MPFR_ASSERTN (u == c);
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);
/* First pass in estimating next bit of the quotient, in case of RNDN *
* In case we just have the right number of bits (postpone this ?), *
* we need to check whether the remainder is more or less than half *
* the divisor. The test must be performed with a subtraction, so as *
* to prevent carries. */
if (MPFR_LIKELY (rnd_mode == GMP_RNDN))
{
if (c < (mp_limb_t) u - c) /* We have u > c */
middle = -1;
else if (c > (mp_limb_t) u - c)
middle = 1;
else
middle = 0; /* exactly in the middle */
}
/* If we believe that we are right in the middle or exact, we should check
that we did not neglect any word of x (division large / 1 -> small). */
for (i=0; ((inexact == 0) || (middle == 0)) && (i < -dif); i++)
if (xp[i])
inexact = middle = 1; /* larger than middle */
/*
If the high limb of the result is 0 (xp[xn-1] < u), remove it.
Otherwise, compute the left shift to be performed to normalize.
In the latter case, we discard some low bits computed. They
contain information useful for the rounding, hence the updating
of middle and inexact.
*/
if (tmp[yn] == 0)
{
MPN_COPY(yp, tmp, yn);
exp -= BITS_PER_MP_LIMB;
}
else
{
int shlz;
count_leading_zeros (shlz, tmp[yn]);
/* shift left to normalize */
if (MPFR_LIKELY (shlz != 0))
{
mp_limb_t w = tmp[0] << shlz;
mpn_lshift (yp, tmp + 1, yn, shlz);
yp[0] += tmp[0] >> (BITS_PER_MP_LIMB - shlz);
if (w > (MPFR_LIMB_ONE << (BITS_PER_MP_LIMB - 1)))
{ middle = 1; }
else if (w < (MPFR_LIMB_ONE << (BITS_PER_MP_LIMB - 1)))
{ middle = -1; }
else
{ middle = (c != 0); }
inexact = inexact || (w != 0);
exp -= shlz;
}
else
{ /* this happens only if u == 1 and xp[xn-1] >=
1<<(BITS_PER_MP_LIMB-1). It might be better to handle the
u == 1 case seperately ?
*/
MPN_COPY (yp, tmp + 1, yn);
}
}
MPFR_UNSIGNED_MINUS_MODULO (sh, MPFR_PREC (y));
/* it remains sh bits in less significant limb of y */
d = *yp & MPFR_LIMB_MASK (sh);
*yp ^= d; /* set to zero lowest sh bits */
MPFR_TMP_FREE (marker);
if (exp < __gmpfr_emin - 1)
return mpfr_underflow (y, rnd_mode == GMP_RNDN ? GMP_RNDZ : rnd_mode,
MPFR_SIGN (y));
if (MPFR_UNLIKELY (d == 0 && inexact == 0))
nexttoinf = 0; /* result is exact */
else
switch (rnd_mode)
{
case GMP_RNDZ:
inexact = - MPFR_INT_SIGN (y); /* result is inexact */
nexttoinf = 0;
break;
case GMP_RNDU:
inexact = 1;
nexttoinf = MPFR_IS_POS (y);
break;
case GMP_RNDD:
inexact = -1;
nexttoinf = MPFR_IS_NEG (y);
break;
default:
MPFR_ASSERTD (rnd_mode == GMP_RNDN);
/* We have one more significant bit in yn. */
if (sh && d < (MPFR_LIMB_ONE << (sh - 1)))
{
inexact = - MPFR_INT_SIGN (y);
nexttoinf = 0;
}
else if (sh && d > (MPFR_LIMB_ONE << (sh - 1)))
{
inexact = MPFR_INT_SIGN (y);
nexttoinf = 1;
}
else /* sh = 0 or d = 1 << (sh-1) */
{
/* The first case is "false" even rounding (significant bits
indicate even rounding, but the result is inexact, so up) ;
The second case is the case where middle should be used to
decide the direction of rounding (no further bit computed) ;
The third is the true even rounding.
*/
if ((sh && inexact) || (!sh && middle > 0) ||
(!inexact && *yp & (MPFR_LIMB_ONE << sh)))
{
inexact = MPFR_INT_SIGN (y);
nexttoinf = 1;
}
else
{
inexact = - MPFR_INT_SIGN (y);
nexttoinf = 0;
}
}
}
if (nexttoinf &&
MPFR_UNLIKELY (mpn_add_1 (yp, yp, yn, MPFR_LIMB_ONE << sh)))
{
exp++;
yp[yn-1] = MPFR_LIMB_HIGHBIT;
}
/* Set the exponent. Warning! One may still have an underflow. */
MPFR_EXP (y) = exp;
return mpfr_check_range (y, inexact, rnd_mode);
}
int mpfr_div_si (mpfr_ptr y, mpfr_srcptr x, long int u, mp_rnd_t rnd_mode)
{
int res;
if (u >= 0)
res = mpfr_div_ui (y, x, u, rnd_mode);
else
{
res = -mpfr_div_ui (y, x, -u, MPFR_INVERT_RND (rnd_mode));
MPFR_CHANGE_SIGN (y);
}
return res;
}