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/* mpn/bdivmod.c: mpn_bdivmod for computing U/V mod 2^d.
Copyright (C) 1991, 1993, 1994, 1995, 1996 Free Software Foundation, Inc.
This file is part of the GNU MP Library.
The GNU MP 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 GNU MP 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 GNU MP 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. */
/* q_high = mpn_bdivmod (qp, up, usize, vp, vsize, d).
Puts the low d/BITS_PER_MP_LIMB limbs of Q = U / V mod 2^d at qp, and
returns the high d%BITS_PER_MP_LIMB bits of Q as the result.
Also, U - Q * V mod 2^(usize*BITS_PER_MP_LIMB) is placed at up. Since the
low d/BITS_PER_MP_LIMB limbs of this difference are zero, the code allows
the limb vectors at qp to overwrite the low limbs at up, provided qp <= up.
Preconditions:
1. V is odd.
2. usize * BITS_PER_MP_LIMB >= d.
3. If Q and U overlap, qp <= up.
Ken Weber (kweber@mat.ufrgs.br, kweber@mcs.kent.edu)
Funding for this work has been partially provided by Conselho Nacional
de Desenvolvimento Cienti'fico e Tecnolo'gico (CNPq) do Brazil, Grant
301314194-2, and was done while I was a visiting reseacher in the Instituto
de Matema'tica at Universidade Federal do Rio Grande do Sul (UFRGS).
References:
T. Jebelean, An algorithm for exact division, Journal of Symbolic
Computation, v. 15, 1993, pp. 169-180.
K. Weber, The accelerated integer GCD algorithm, ACM Transactions on
Mathematical Software, v. 21 (March), 1995, pp. 111-122. */
#include "gmp.h"
#include "gmp-impl.h"
#include "longlong.h"
mp_limb_t
#if __STDC__
mpn_bdivmod (mp_ptr qp, mp_ptr up, mp_size_t usize,
mp_srcptr vp, mp_size_t vsize, unsigned long int d)
#else
mpn_bdivmod (qp, up, usize, vp, vsize, d)
mp_ptr qp;
mp_ptr up;
mp_size_t usize;
mp_srcptr vp;
mp_size_t vsize;
unsigned long int d;
#endif
{
/* Cache for v_inv is used to make mpn_accelgcd faster. */
static mp_limb_t previous_low_vlimb = 0;
static mp_limb_t v_inv; /* 1/V mod 2^BITS_PER_MP_LIMB. */
if (vp[0] != previous_low_vlimb) /* Cache miss; compute v_inv. */
{
mp_limb_t v = previous_low_vlimb = vp[0];
mp_limb_t make_zero = 1;
mp_limb_t two_i = 1;
v_inv = 0;
do
{
while ((two_i & make_zero) == 0)
two_i <<= 1, v <<= 1;
v_inv += two_i;
make_zero -= v;
}
while (make_zero);
}
/* Need faster computation for some common cases in mpn_accelgcd. */
if (usize == 2 && vsize == 2 &&
(d == BITS_PER_MP_LIMB || d == 2*BITS_PER_MP_LIMB))
{
mp_limb_t hi, lo;
mp_limb_t q = up[0] * v_inv;
umul_ppmm (hi, lo, q, vp[0]);
up[0] = 0, up[1] -= hi + q*vp[1], qp[0] = q;
if (d == 2*BITS_PER_MP_LIMB)
q = up[1] * v_inv, up[1] = 0, qp[1] = q;
return 0;
}
/* Main loop. */
while (d >= BITS_PER_MP_LIMB)
{
mp_limb_t q = up[0] * v_inv;
mp_limb_t b = mpn_submul_1 (up, vp, MIN (usize, vsize), q);
if (usize > vsize)
mpn_sub_1 (up + vsize, up + vsize, usize - vsize, b);
d -= BITS_PER_MP_LIMB;
up += 1, usize -= 1;
*qp++ = q;
}
if (d)
{
mp_limb_t b;
mp_limb_t q = (up[0] * v_inv) & (((mp_limb_t)1<<d) - 1);
switch (q)
{
case 0: return 0;
case 1: b = mpn_sub_n (up, up, vp, MIN (usize, vsize)); break;
default: b = mpn_submul_1 (up, vp, MIN (usize, vsize), q); break;
}
if (usize > vsize)
mpn_sub_1 (up + vsize, up + vsize, usize - vsize, b);
return q;
}
return 0;
}
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