aboutsummaryrefslogtreecommitdiff
path: root/lib/mpi/mpih-div.c
blob: c57d1d46295e39bb75c57ccd489dad15c97ed40c (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
/* mpihelp-div.c  -  MPI helper functions
 *	Copyright (C) 1994, 1996 Free Software Foundation, Inc.
 *	Copyright (C) 1998, 1999 Free Software Foundation, Inc.
 *
 * This file is part of GnuPG.
 *
 * GnuPG is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 2 of the License, or
 * (at your option) any later version.
 *
 * GnuPG 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 General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
 *
 * Note: This code is heavily based on the GNU MP Library.
 *	 Actually it's the same code with only minor changes in the
 *	 way the data is stored; this is to support the abstraction
 *	 of an optional secure memory allocation which may be used
 *	 to avoid revealing of sensitive data due to paging etc.
 *	 The GNU MP Library itself is published under the LGPL;
 *	 however I decided to publish this code under the plain GPL.
 */

#include "mpi-internal.h"
#include "longlong.h"

#ifndef UMUL_TIME
#define UMUL_TIME 1
#endif
#ifndef UDIV_TIME
#define UDIV_TIME UMUL_TIME
#endif

/* Divide num (NP/NSIZE) by den (DP/DSIZE) and write
 * the NSIZE-DSIZE least significant quotient limbs at QP
 * and the DSIZE long remainder at NP.	If QEXTRA_LIMBS is
 * non-zero, generate that many fraction bits and append them after the
 * other quotient limbs.
 * Return the most significant limb of the quotient, this is always 0 or 1.
 *
 * Preconditions:
 * 0. NSIZE >= DSIZE.
 * 1. The most significant bit of the divisor must be set.
 * 2. QP must either not overlap with the input operands at all, or
 *    QP + DSIZE >= NP must hold true.	(This means that it's
 *    possible to put the quotient in the high part of NUM, right after the
 *    remainder in NUM.
 * 3. NSIZE >= DSIZE, even if QEXTRA_LIMBS is non-zero.
 */

mpi_limb_t
mpihelp_divrem(mpi_ptr_t qp, mpi_size_t qextra_limbs,
	       mpi_ptr_t np, mpi_size_t nsize, mpi_ptr_t dp, mpi_size_t dsize)
{
	mpi_limb_t most_significant_q_limb = 0;

	switch (dsize) {
	case 0:
		/* We are asked to divide by zero, so go ahead and do it!  (To make
		   the compiler not remove this statement, return the value.)  */
		/*
		 * existing clients of this function have been modified
		 * not to call it with dsize == 0, so this should not happen
		 */
		return 1 / dsize;

	case 1:
		{
			mpi_size_t i;
			mpi_limb_t n1;
			mpi_limb_t d;

			d = dp[0];
			n1 = np[nsize - 1];

			if (n1 >= d) {
				n1 -= d;
				most_significant_q_limb = 1;
			}

			qp += qextra_limbs;
			for (i = nsize - 2; i >= 0; i--)
				udiv_qrnnd(qp[i], n1, n1, np[i], d);
			qp -= qextra_limbs;

			for (i = qextra_limbs - 1; i >= 0; i--)
				udiv_qrnnd(qp[i], n1, n1, 0, d);

			np[0] = n1;
		}
		break;

	case 2:
		{
			mpi_size_t i;
			mpi_limb_t n1, n0, n2;
			mpi_limb_t d1, d0;

			np += nsize - 2;
			d1 = dp[1];
			d0 = dp[0];
			n1 = np[1];
			n0 = np[0];

			if (n1 >= d1 && (n1 > d1 || n0 >= d0)) {
				sub_ddmmss(n1, n0, n1, n0, d1, d0);
				most_significant_q_limb = 1;
			}

			for (i = qextra_limbs + nsize - 2 - 1; i >= 0; i--) {
				mpi_limb_t q;
				mpi_limb_t r;

				if (i >= qextra_limbs)
					np--;
				else
					np[0] = 0;

				if (n1 == d1) {
					/* Q should be either 111..111 or 111..110.  Need special
					 * treatment of this rare case as normal division would
					 * give overflow.  */
					q = ~(mpi_limb_t) 0;

					r = n0 + d1;
					if (r < d1) {	/* Carry in the addition? */
						add_ssaaaa(n1, n0, r - d0,
							   np[0], 0, d0);
						qp[i] = q;
						continue;
					}
					n1 = d0 - (d0 != 0 ? 1 : 0);
					n0 = -d0;
				} else {
					udiv_qrnnd(q, r, n1, n0, d1);
					umul_ppmm(n1, n0, d0, q);
				}

				n2 = np[0];
q_test:
				if (n1 > r || (n1 == r && n0 > n2)) {
					/* The estimated Q was too large.  */
					q--;
					sub_ddmmss(n1, n0, n1, n0, 0, d0);
					r += d1;
					if (r >= d1)	/* If not carry, test Q again.  */
						goto q_test;
				}

				qp[i] = q;
				sub_ddmmss(n1, n0, r, n2, n1, n0);
			}
			np[1] = n1;
			np[0] = n0;
		}
		break;

	default:
		{
			mpi_size_t i;
			mpi_limb_t dX, d1, n0;

			np += nsize - dsize;
			dX = dp[dsize - 1];
			d1 = dp[dsize - 2];
			n0 = np[dsize - 1];

			if (n0 >= dX) {
				if (n0 > dX
				    || mpihelp_cmp(np, dp, dsize - 1) >= 0) {
					mpihelp_sub_n(np, np, dp, dsize);
					n0 = np[dsize - 1];
					most_significant_q_limb = 1;
				}
			}

			for (i = qextra_limbs + nsize - dsize - 1; i >= 0; i--) {
				mpi_limb_t q;
				mpi_limb_t n1, n2;
				mpi_limb_t cy_limb;

				if (i >= qextra_limbs) {
					np--;
					n2 = np[dsize];
				} else {
					n2 = np[dsize - 1];
					MPN_COPY_DECR(np + 1, np, dsize - 1);
					np[0] = 0;
				}

				if (n0 == dX) {
					/* This might over-estimate q, but it's probably not worth
					 * the extra code here to find out.  */
					q = ~(mpi_limb_t) 0;
				} else {
					mpi_limb_t r;

					udiv_qrnnd(q, r, n0, np[dsize - 1], dX);
					umul_ppmm(n1, n0, d1, q);

					while (n1 > r
					       || (n1 == r
						   && n0 > np[dsize - 2])) {
						q--;
						r += dX;
						if (r < dX)	/* I.e. "carry in previous addition?" */
							break;
						n1 -= n0 < d1;
						n0 -= d1;
					}
				}

				/* Possible optimization: We already have (q * n0) and (1 * n1)
				 * after the calculation of q.  Taking advantage of that, we
				 * could make this loop make two iterations less.  */
				cy_limb = mpihelp_submul_1(np, dp, dsize, q);

				if (n2 != cy_limb) {
					mpihelp_add_n(np, np, dp, dsize);
					q--;
				}

				qp[i] = q;
				n0 = np[dsize - 1];
			}
		}
	}

	return most_significant_q_limb;
}