Root/lib/mpi/mpih-div.c

1/* mpihelp-div.c - MPI helper functions
2 * Copyright (C) 1994, 1996 Free Software Foundation, Inc.
3 * Copyright (C) 1998, 1999 Free Software Foundation, Inc.
4 *
5 * This file is part of GnuPG.
6 *
7 * GnuPG is free software; you can redistribute it and/or modify
8 * it under the terms of the GNU General Public License as published by
9 * the Free Software Foundation; either version 2 of the License, or
10 * (at your option) any later version.
11 *
12 * GnuPG is distributed in the hope that it will be useful,
13 * but WITHOUT ANY WARRANTY; without even the implied warranty of
14 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
15 * GNU General Public License for more details.
16 *
17 * You should have received a copy of the GNU General Public License
18 * along with this program; if not, write to the Free Software
19 * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
20 *
21 * Note: This code is heavily based on the GNU MP Library.
22 * Actually it's the same code with only minor changes in the
23 * way the data is stored; this is to support the abstraction
24 * of an optional secure memory allocation which may be used
25 * to avoid revealing of sensitive data due to paging etc.
26 * The GNU MP Library itself is published under the LGPL;
27 * however I decided to publish this code under the plain GPL.
28 */
29
30#include "mpi-internal.h"
31#include "longlong.h"
32
33#ifndef UMUL_TIME
34#define UMUL_TIME 1
35#endif
36#ifndef UDIV_TIME
37#define UDIV_TIME UMUL_TIME
38#endif
39
40/* Divide num (NP/NSIZE) by den (DP/DSIZE) and write
41 * the NSIZE-DSIZE least significant quotient limbs at QP
42 * and the DSIZE long remainder at NP. If QEXTRA_LIMBS is
43 * non-zero, generate that many fraction bits and append them after the
44 * other quotient limbs.
45 * Return the most significant limb of the quotient, this is always 0 or 1.
46 *
47 * Preconditions:
48 * 0. NSIZE >= DSIZE.
49 * 1. The most significant bit of the divisor must be set.
50 * 2. QP must either not overlap with the input operands at all, or
51 * QP + DSIZE >= NP must hold true. (This means that it's
52 * possible to put the quotient in the high part of NUM, right after the
53 * remainder in NUM.
54 * 3. NSIZE >= DSIZE, even if QEXTRA_LIMBS is non-zero.
55 */
56
57mpi_limb_t
58mpihelp_divrem(mpi_ptr_t qp, mpi_size_t qextra_limbs,
59           mpi_ptr_t np, mpi_size_t nsize, mpi_ptr_t dp, mpi_size_t dsize)
60{
61    mpi_limb_t most_significant_q_limb = 0;
62
63    switch (dsize) {
64    case 0:
65        /* We are asked to divide by zero, so go ahead and do it! (To make
66           the compiler not remove this statement, return the value.) */
67        /*
68         * existing clients of this function have been modified
69         * not to call it with dsize == 0, so this should not happen
70         */
71        return 1 / dsize;
72
73    case 1:
74        {
75            mpi_size_t i;
76            mpi_limb_t n1;
77            mpi_limb_t d;
78
79            d = dp[0];
80            n1 = np[nsize - 1];
81
82            if (n1 >= d) {
83                n1 -= d;
84                most_significant_q_limb = 1;
85            }
86
87            qp += qextra_limbs;
88            for (i = nsize - 2; i >= 0; i--)
89                udiv_qrnnd(qp[i], n1, n1, np[i], d);
90            qp -= qextra_limbs;
91
92            for (i = qextra_limbs - 1; i >= 0; i--)
93                udiv_qrnnd(qp[i], n1, n1, 0, d);
94
95            np[0] = n1;
96        }
97        break;
98
99    case 2:
100        {
101            mpi_size_t i;
102            mpi_limb_t n1, n0, n2;
103            mpi_limb_t d1, d0;
104
105            np += nsize - 2;
106            d1 = dp[1];
107            d0 = dp[0];
108            n1 = np[1];
109            n0 = np[0];
110
111            if (n1 >= d1 && (n1 > d1 || n0 >= d0)) {
112                sub_ddmmss(n1, n0, n1, n0, d1, d0);
113                most_significant_q_limb = 1;
114            }
115
116            for (i = qextra_limbs + nsize - 2 - 1; i >= 0; i--) {
117                mpi_limb_t q;
118                mpi_limb_t r;
119
120                if (i >= qextra_limbs)
121                    np--;
122                else
123                    np[0] = 0;
124
125                if (n1 == d1) {
126                    /* Q should be either 111..111 or 111..110. Need special
127                     * treatment of this rare case as normal division would
128                     * give overflow. */
129                    q = ~(mpi_limb_t) 0;
130
131                    r = n0 + d1;
132                    if (r < d1) { /* Carry in the addition? */
133                        add_ssaaaa(n1, n0, r - d0,
134                               np[0], 0, d0);
135                        qp[i] = q;
136                        continue;
137                    }
138                    n1 = d0 - (d0 != 0 ? 1 : 0);
139                    n0 = -d0;
140                } else {
141                    udiv_qrnnd(q, r, n1, n0, d1);
142                    umul_ppmm(n1, n0, d0, q);
143                }
144
145                n2 = np[0];
146q_test:
147                if (n1 > r || (n1 == r && n0 > n2)) {
148                    /* The estimated Q was too large. */
149                    q--;
150                    sub_ddmmss(n1, n0, n1, n0, 0, d0);
151                    r += d1;
152                    if (r >= d1) /* If not carry, test Q again. */
153                        goto q_test;
154                }
155
156                qp[i] = q;
157                sub_ddmmss(n1, n0, r, n2, n1, n0);
158            }
159            np[1] = n1;
160            np[0] = n0;
161        }
162        break;
163
164    default:
165        {
166            mpi_size_t i;
167            mpi_limb_t dX, d1, n0;
168
169            np += nsize - dsize;
170            dX = dp[dsize - 1];
171            d1 = dp[dsize - 2];
172            n0 = np[dsize - 1];
173
174            if (n0 >= dX) {
175                if (n0 > dX
176                    || mpihelp_cmp(np, dp, dsize - 1) >= 0) {
177                    mpihelp_sub_n(np, np, dp, dsize);
178                    n0 = np[dsize - 1];
179                    most_significant_q_limb = 1;
180                }
181            }
182
183            for (i = qextra_limbs + nsize - dsize - 1; i >= 0; i--) {
184                mpi_limb_t q;
185                mpi_limb_t n1, n2;
186                mpi_limb_t cy_limb;
187
188                if (i >= qextra_limbs) {
189                    np--;
190                    n2 = np[dsize];
191                } else {
192                    n2 = np[dsize - 1];
193                    MPN_COPY_DECR(np + 1, np, dsize - 1);
194                    np[0] = 0;
195                }
196
197                if (n0 == dX) {
198                    /* This might over-estimate q, but it's probably not worth
199                     * the extra code here to find out. */
200                    q = ~(mpi_limb_t) 0;
201                } else {
202                    mpi_limb_t r;
203
204                    udiv_qrnnd(q, r, n0, np[dsize - 1], dX);
205                    umul_ppmm(n1, n0, d1, q);
206
207                    while (n1 > r
208                           || (n1 == r
209                           && n0 > np[dsize - 2])) {
210                        q--;
211                        r += dX;
212                        if (r < dX) /* I.e. "carry in previous addition?" */
213                            break;
214                        n1 -= n0 < d1;
215                        n0 -= d1;
216                    }
217                }
218
219                /* Possible optimization: We already have (q * n0) and (1 * n1)
220                 * after the calculation of q. Taking advantage of that, we
221                 * could make this loop make two iterations less. */
222                cy_limb = mpihelp_submul_1(np, dp, dsize, q);
223
224                if (n2 != cy_limb) {
225                    mpihelp_add_n(np, np, dp, dsize);
226                    q--;
227                }
228
229                qp[i] = q;
230                n0 = np[dsize - 1];
231            }
232        }
233    }
234
235    return most_significant_q_limb;
236}
237

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