127 lines
3.9 KiB
C
127 lines
3.9 KiB
C
/* mpn/bdivmod.c: mpn_bdivmod for computing U/V mod 2^d.
|
|
|
|
Copyright 1991, 1993, 1994, 1995, 1996, 1999, 2000, 2001, 2002 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 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 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 Lesser General Public
|
|
License for more details.
|
|
|
|
You should have received a copy of the GNU Lesser General Public License
|
|
along with the GNU MP Library; see the file COPYING.LIB. If not, write to
|
|
the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
|
|
MA 02110-1301, 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 "mpir.h"
|
|
#include "gmp-impl.h"
|
|
#include "longlong.h"
|
|
|
|
|
|
mp_limb_t
|
|
mpn_bdivmod (mp_ptr qp, mp_ptr up, mp_size_t usize,
|
|
mp_srcptr vp, mp_size_t vsize, gmp_ui d)
|
|
{
|
|
mp_limb_t v_inv;
|
|
|
|
ASSERT (usize >= 1);
|
|
ASSERT (vsize >= 1);
|
|
ASSERT (usize * GMP_NUMB_BITS >= d);
|
|
ASSERT (! MPN_OVERLAP_P (up, usize, vp, vsize));
|
|
ASSERT (! MPN_OVERLAP_P (qp, d/GMP_NUMB_BITS, vp, vsize));
|
|
ASSERT (MPN_SAME_OR_INCR2_P (qp, d/GMP_NUMB_BITS, up, usize));
|
|
ASSERT_MPN (up, usize);
|
|
ASSERT_MPN (vp, vsize);
|
|
|
|
/* 1/V mod 2^GMP_NUMB_BITS. */
|
|
modlimb_invert (v_inv, vp[0]);
|
|
|
|
/* Fast code for two cases previously used by the accel part of mpn_gcd.
|
|
(Could probably remove this now it's inlined there.) */
|
|
if (usize == 2 && vsize == 2 &&
|
|
(d == GMP_NUMB_BITS || d == 2*GMP_NUMB_BITS))
|
|
{
|
|
mp_limb_t hi, lo;
|
|
mp_limb_t q = (up[0] * v_inv) & GMP_NUMB_MASK;
|
|
umul_ppmm (hi, lo, q, vp[0] << GMP_NAIL_BITS);
|
|
up[0] = 0;
|
|
up[1] -= hi + q*vp[1];
|
|
qp[0] = q;
|
|
if (d == 2*GMP_NUMB_BITS)
|
|
{
|
|
q = (up[1] * v_inv) & GMP_NUMB_MASK;
|
|
up[1] = 0;
|
|
qp[1] = q;
|
|
}
|
|
return 0;
|
|
}
|
|
|
|
/* Main loop. */
|
|
while (d >= GMP_NUMB_BITS)
|
|
{
|
|
mp_limb_t q = (up[0] * v_inv) & GMP_NUMB_MASK;
|
|
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 -= GMP_NUMB_BITS;
|
|
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);
|
|
if (q <= 1)
|
|
{
|
|
if (q == 0)
|
|
return 0;
|
|
else
|
|
b = mpn_sub_n (up, up, vp, MIN (usize, vsize));
|
|
}
|
|
else
|
|
b = mpn_submul_1 (up, vp, MIN (usize, vsize), q);
|
|
|
|
if (usize > vsize)
|
|
mpn_sub_1 (up + vsize, up + vsize, usize - vsize, b);
|
|
return q;
|
|
}
|
|
|
|
return 0;
|
|
}
|