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/* mpfr_div -- divide two floating-point numbers
Copyright (C) 1999 Free Software Foundation.
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 Library General Public License as published by
the Free Software Foundation; either version 2 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 Library General Public
License for more details.
You should have received a copy of the GNU Library 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 <stdlib.h>
#include "gmp.h"
#include "gmp-impl.h"
#include "longlong.h"
#include "mpfr.h"
#include "mpfr-impl.h"
/* #define DEBUG */
void
#if __STDC__
mpfr_div (mpfr_ptr r, mpfr_srcptr u, mpfr_srcptr v, mp_rnd_t rnd_mode)
#else
mpfr_div (r, u, v, rnd_mode)
mpfr_ptr r;
mpfr_srcptr u;
mpfr_srcptr v;
mp_rnd_t rnd_mode;
#endif
{
mp_srcptr up, vp;
mp_ptr rp, tp, tp0, tmp, tmp2;
mp_size_t usize, vsize, rrsize, oldrrsize;
mp_size_t rsize;
mp_size_t sign_quotient;
mp_size_t prec, err;
mp_limb_t q_limb;
mp_exp_t rexp;
long k, mult, vn, t;
unsigned long cc = 0, rw, nw;
char can_round = 0;
TMP_DECL (marker);
if (MPFR_IS_NAN(u) || MPFR_IS_NAN(v)) { MPFR_SET_NAN(r); return; }
MPFR_CLEAR_NAN(r);
if (MPFR_IS_INF(u))
{
if (MPFR_IS_INF(v))
MPFR_SET_NAN(r);
else
{
MPFR_SET_INF(r);
if (MPFR_SIGN(r) != MPFR_SIGN(u) * MPFR_SIGN(v))
MPFR_CHANGE_SIGN(r);
}
return;
}
else
if (MPFR_IS_INF(v))
{
MPFR_CLEAR_INF(r);
MPFR_SET_ZERO(r);
if (MPFR_SIGN(r) != MPFR_SIGN(u) * MPFR_SIGN(v))
MPFR_CHANGE_SIGN(r);
return;
}
MPFR_CLEAR_INF(r); /* clear Inf flag */
usize = (MPFR_PREC(u) - 1)/BITS_PER_MP_LIMB + 1;
vsize = (MPFR_PREC(v) - 1)/BITS_PER_MP_LIMB + 1;
sign_quotient = ((MPFR_SIGN(u) * MPFR_SIGN(v) > 0) ? 1 : -1);
prec = MPFR_PREC(r);
if (!MPFR_NOTZERO(v))
{
if (!MPFR_NOTZERO(u))
{ MPFR_SET_NAN(r); return; }
else
{
MPFR_SET_INF(r);
if (MPFR_SIGN(r) != MPFR_SIGN(v) * MPFR_SIGN(u))
MPFR_CHANGE_SIGN(r);
return;
}
}
if (!MPFR_NOTZERO(u)) { MPFR_SET_ZERO(r); return; }
up = MPFR_MANT(u);
vp = MPFR_MANT(v);
#ifdef DEBUG
printf("Entering division : ");
for(k = usize - 1; k >= 0; k--) { printf("%lu ", up[k]); }
printf(" by ");
for(k = vsize - 1; k >= 0; k--) { printf("%lu ", vp[k]); }
printf(".\n");
#endif
/* Compare the mantissas */
mult = mpn_cmp(up, vp, (usize > vsize ? vsize : usize));
if (mult == 0 && vsize > usize)
{
vn = vsize - usize;
while (vn >= 0) if (vp[vn--]) { mult = 1; break; }
/* On peut diagnostiquer ici pour pas cher le cas u = v */
}
else { mult = (mult < 0 ? 1 : 0); }
rsize = (MPFR_PREC(r) + 3)/BITS_PER_MP_LIMB + 1;
rrsize = MPFR_PREC(r)/BITS_PER_MP_LIMB + 1;
/* Three extra bits are needed in order to get the quotient with enough
precision ; take one extra bit for rrsize in order to solve more
easily the problem of rounding to nearest. */
do
{
TMP_MARK (marker);
rexp = MPFR_EXP(u) - MPFR_EXP(v);
err = rsize*BITS_PER_MP_LIMB;
if (rsize < vsize) { err-=2; }
if (rsize < usize) { err--; }
if (err > rrsize * BITS_PER_MP_LIMB)
{ err = rrsize * BITS_PER_MP_LIMB; }
tp0 = (mp_ptr) TMP_ALLOC ((rsize+rrsize) * BYTES_PER_MP_LIMB);
/* fill by zero rrsize low limbs of t */
MPN_ZERO(tp0, rrsize); tp = tp0 + rrsize;
rp = (mp_ptr) TMP_ALLOC ((rrsize+1) * BYTES_PER_MP_LIMB);
if (vsize >= rsize) {
tmp = (mp_ptr) vp + vsize - rsize;
}
else {
tmp = (mp_ptr) TMP_ALLOC (rsize * BYTES_PER_MP_LIMB);
MPN_COPY (tmp + rsize - vsize, vp, vsize);
MPN_ZERO (tmp, rsize - vsize);
}
if (usize >= rsize) {
MPN_COPY (tp, up + usize - rsize, rsize);
}
else {
MPN_COPY (tp + rsize - usize, up, usize);
MPN_ZERO (tp, rsize - usize);
}
/* Do the real job */
#ifdef DEBUG
printf("Dividing : ");
for(k = rsize - 1; k >= 0; k--) { printf("%lu ", tp[k]); }
printf(" by ");
for(k = rsize - 1; k >= 0; k--) { printf("%lu ", tmp[k]); }
printf(".\n");
#endif
#if (__GNU_MP_VERSION < 3)
q_limb = mpn_divrem (rp, 0, tp0, rsize+rrsize, tmp, rsize);
tp = tp0; /* location of remainder */
#else /* mpn_tdiv_qr is the preferred division interface in GMP 3 */
tmp2 = (mp_ptr) TMP_ALLOC (rsize * BYTES_PER_MP_LIMB);
mpn_tdiv_qr(rp, tmp2, 0, tp0, rsize+rrsize, tmp, rsize);
q_limb = rp[rrsize];
tp = tmp2; /* location of remainder */
#endif
#ifdef DEBUG
printf("The result is : \n");
printf("Quotient : ");
for(k = rrsize - 1; k >= 0; k--) { printf("%lu ", rp[k]); }
printf("Remainder : ");
for(k = rsize - 1; k >= 0; k--) { printf("%lu ", tp[k]); }
printf("(q_limb = %lu)\n", q_limb);
#endif
/* msb-normalize the result */
if (q_limb)
{
count_leading_zeros(k, q_limb);
mpn_rshift(rp, rp, rrsize, BITS_PER_MP_LIMB - k);
rp[rrsize - 1] |= (q_limb << k);
rexp += BITS_PER_MP_LIMB - k;
}
else
{
count_leading_zeros(k, rp[rrsize - 1]);
if (k) { mpn_lshift(rp, rp, rrsize, k); }
rexp -= k;
}
can_round = (mpfr_can_round_raw(rp, rrsize, sign_quotient, err,
GMP_RNDN, rnd_mode, MPFR_PREC(r))
|| (usize == rsize && vsize == rsize &&
mpfr_can_round_raw(rp, rrsize, sign_quotient, err,
GMP_RNDZ, rnd_mode, MPFR_PREC(r))));
/* If we used all the limbs of both the dividend and the divisor,
then we have the correct RNDZ rounding */
if (!can_round && (rsize < usize || rsize < vsize))
{
#ifdef DEBUG
printf("Increasing the precision.\n");
#endif
TMP_FREE(marker);
/* in case we can't round at the first iteration,
jump right away to the maximum precision of both
operands, to avoid multiple iterations when for
example the divisor is 1.0.
*/
if (rsize < usize) rsize = usize - 1;
if (rsize < vsize) rsize = vsize - 1;
}
}
while (!can_round && (rsize < usize || rsize < vsize)
&& (rsize++) && (rrsize++));
/* ON PEUT PROBABLEMENT SE DEBROUILLER DES QUE rsize >= vsize */
/* MAIS IL FAUT AJOUTER LE BOUT QUI MANQUE DE usize A rsize */
oldrrsize = rrsize;
rrsize = (MPFR_PREC(r) - 1)/BITS_PER_MP_LIMB + 1;
if (can_round)
{
cc = mpfr_round_raw(rp, rp, err, (sign_quotient == -1 ? 1 : 0),
MPFR_PREC(r), rnd_mode);
}
else {
/* Use the remainder to find out the correct rounding */
/* Note that at this point the division has been done */
/* EXACTLY. */
if ((rnd_mode == GMP_RNDD && sign_quotient == -1)
|| (rnd_mode == GMP_RNDU && sign_quotient == 1)
|| (rnd_mode == GMP_RNDN))
{
/* We cannot round, so that the last bits of the quotient
have to be zero; just look if the remainder is nonzero */
k = rsize - 1;
while (k >= 0) { if (tp[k]) break; k--; }
if (k >= 0)
{
t = MPFR_PREC(r) & (BITS_PER_MP_LIMB - 1);
if (t)
{
cc = mpn_add_1(rp, rp, rrsize,
(mp_limb_t)1 << (BITS_PER_MP_LIMB - t));
}
else
{
cc = mpn_add_1(rp, rp, rrsize, 1);
}
}
else
if (rnd_mode == GMP_RNDN) /* even rounding */
{
rw = (MPFR_PREC(r) + 1) & (BITS_PER_MP_LIMB - 1);
if (rw) { rw = BITS_PER_MP_LIMB - rw; nw = 0; } else nw = 1;
if ((rw ? (rp[nw] >> (rw + 1)) & 1 :
(rp[nw] >> (BITS_PER_MP_LIMB - 1)) & 1))
{
cc = mpn_add_1(rp + nw, rp + nw, rrsize,
((mp_limb_t)1) << rw);
}
}
/* cas 0111111 */
}
/* Warning: we computed the result on oldrrsize limbs, but we want it
on rrsize limbs only. Both can differ, especially when the target
precision is a multiple of the number of bits per limb, since we've
taken an extra bit to make rounding to nearest easier. */
rp += oldrrsize-rrsize;
}
if (sign_quotient * MPFR_SIGN(r) < 0) { MPFR_CHANGE_SIGN(r); }
MPFR_EXP(r) = rexp;
if (cc) {
mpn_rshift(rp, rp, rrsize, 1);
rp[rrsize-1] |= (mp_limb_t) 1 << (BITS_PER_MP_LIMB-1);
MPFR_EXP(r)++;
}
rw = rrsize * BITS_PER_MP_LIMB - MPFR_PREC(r);
MPN_COPY(MPFR_MANT(r), rp, rrsize);
MPFR_MANT(r)[0] &= ~(((mp_limb_t)1 << rw) - 1);
TMP_FREE (marker);
}
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