1/* mpn_sbpi1_bdiv_q -- schoolbook Hensel division with precomputed inverse,
2   returning quotient only.
3
4   Contributed to the GNU project by Niels M�ller.
5
6   THE FUNCTIONS IN THIS FILE ARE INTERNAL FUNCTIONS WITH MUTABLE INTERFACES.
7   IT IS ONLY SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES.  IN FACT, IT IS
8   ALMOST GUARANTEED THAT THEY'LL CHANGE OR DISAPPEAR IN A FUTURE GMP RELEASE.
9
10Copyright 2005, 2006, 2009 Free Software Foundation, Inc.
11
12This file is part of the GNU MP Library.
13
14The GNU MP Library is free software; you can redistribute it and/or modify
15it under the terms of the GNU Lesser General Public License as published by
16the Free Software Foundation; either version 3 of the License, or (at your
17option) any later version.
18
19The GNU MP Library is distributed in the hope that it will be useful, but
20WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
21or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
22License for more details.
23
24You should have received a copy of the GNU Lesser General Public License
25along with the GNU MP Library.  If not, see http://www.gnu.org/licenses/.  */
26
27#include "gmp.h"
28#include "gmp-impl.h"
29
30
31/* Computes Q = N / D mod B^nn, destroys N.
32
33   D must be odd. dinv is (-D)^-1 mod B.
34
35
36   The straightforward way to compute Q is to cancel one limb at a time, using
37
38     qp[i] = D^{-1} * np[i] (mod B)
39     N -= B^i * qp[i] * D
40
41   But we prefer addition to subtraction, since mpn_addmul_1 is often faster
42   than mpn_submul_1.  Q = - N / D can be computed by iterating
43
44     qp[i] = (-D)^{-1} * np[i] (mod B)
45     N += B^i * qp[i] * D
46
47   And then we flip the sign, -Q = (not Q) + 1. */
48
49void
50mpn_sbpi1_bdiv_q (mp_ptr qp,
51		  mp_ptr np, mp_size_t nn,
52		  mp_srcptr dp, mp_size_t dn,
53		  mp_limb_t dinv)
54{
55  mp_size_t i;
56  mp_limb_t cy, q;
57
58  ASSERT (dn > 0);
59  ASSERT (nn >= dn);
60  ASSERT ((dp[0] & 1) != 0);
61
62  for (i = nn - dn; i > 0; i--)
63    {
64      q = dinv * np[0];
65      qp[0] = ~q;
66      qp++;
67      cy = mpn_addmul_1 (np, dp, dn, q);
68      mpn_add_1 (np + dn, np + dn, i, cy);
69      ASSERT (np[0] == 0);
70      np++;
71    }
72
73  for (i = dn; i > 1; i--)
74    {
75      q = dinv * np[0];
76      qp[0] = ~q;
77      qp++;
78      mpn_addmul_1 (np, dp, i, q);
79      ASSERT (np[0] == 0);
80      np++;
81    }
82
83  /* Final limb */
84  q = dinv * np[0];
85  qp[0] = ~q;
86  mpn_add_1 (qp - nn + 1, qp - nn + 1, nn, 1);
87}
88