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macssh/gmp/mpfr/div.c

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/* mpfr_div -- divide two floating-point numbers
Copyright (C) 1999 PolKA project, Inria Lorraine and Loria
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 <math.h>
#include <stdio.h>
#include <stdlib.h>
#include "gmp.h"
#include "gmp-impl.h"
#include "mpfr.h"
#include "longlong.h"
/* #define DEBUG */
void
mpfr_div (mpfr_ptr r, mpfr_srcptr u, mpfr_srcptr v, unsigned char rnd_mode)
{
mp_srcptr up, vp;
mp_ptr rp, tp, tp0, tmp;
mp_size_t usize, vsize, rrsize;
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;
unsigned long cc = 0, rw, nw;
char can_round = 0;
TMP_DECL (marker);
if (FLAG_NAN(u) || FLAG_NAN(v)) { SET_NAN(r); return; }
usize = (PREC(u) - 1)/BITS_PER_MP_LIMB + 1;
vsize = (PREC(v) - 1)/BITS_PER_MP_LIMB + 1;
sign_quotient = (SIGN(u) == SIGN(v) ? 1 : -1);
prec = PREC(r);
if (!NOTZERO(u)) { SET_ZERO(r); return; }
if (!NOTZERO(v))
vsize = 1 / v->_mp_d[vsize - 1]; /* Gestion des infinis ? */
if (!NOTZERO(v))
{
r->_mp_exp = 0;
MPN_ZERO(r->_mp_d, r->_mp_size);
return;
}
up = u->_mp_d;
vp = v->_mp_d;
#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 = (PREC(r) + 3)/BITS_PER_MP_LIMB + 1;
rrsize = 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. */
/* ATTENTION, USIZE DOIT RESTER > A VSIZE !!!!!!!! */
do
{
TMP_MARK (marker);
rexp = u->_mp_exp - v->_mp_exp;
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;
tmp = (mp_ptr) TMP_ALLOC (rsize * BYTES_PER_MP_LIMB);
rp = (mp_ptr) TMP_ALLOC (rrsize * BYTES_PER_MP_LIMB);
if (vsize >= rsize) {
MPN_COPY (tmp, vp + vsize - rsize, rsize);
}
else {
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
q_limb = (rsize==rrsize) /* use Burnikel-Ziegler algorithm */
? mpn_divrem_n (rp, tp0, tmp, rsize)
: mpn_divrem (rp, 0, tp0, rsize+rrsize, tmp, rsize);
tp = tp0; /* location of remainder */
#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, PREC(r))
|| (usize == rsize && vsize == rsize &&
mpfr_can_round_raw(rp, rrsize, sign_quotient, err,
GMP_RNDZ, rnd_mode, 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
printf("#");
TMP_FREE(marker);
}
}
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 */
if (can_round)
{
cc = mpfr_round_raw(rp, rp, err, (sign_quotient == -1 ? 1 : 0),
PREC(r), rnd_mode);
rrsize = (PREC(r) - 1)/BITS_PER_MP_LIMB + 1;
}
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)
cc = mpn_add_1(rp, rp, rrsize, (mp_limb_t)1 << (BITS_PER_MP_LIMB -
(PREC(r) &
(BITS_PER_MP_LIMB - 1))));
else
if (rnd_mode == GMP_RNDN) /* even rounding */
{
rw = (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 */
}
if (sign_quotient != SIGN(r)) { CHANGE_SIGN(r); }
r->_mp_exp = rexp;
if (cc) {
mpn_rshift(rp, rp, rrsize, 1);
rp[rrsize-1] |= (mp_limb_t) 1 << (BITS_PER_MP_LIMB-1);
r->_mp_exp++;
}
rsize = rrsize;
rrsize = (PREC(r) - 1)/BITS_PER_MP_LIMB + 1;
MPN_COPY(r->_mp_d, rp + rsize - rrsize, rrsize);
MANT(r) [0] &= ~(((mp_limb_t)1 << (BITS_PER_MP_LIMB -
(PREC(r) & (BITS_PER_MP_LIMB - 1)))) - 1) ;
TMP_FREE (marker);
}
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