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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}
1// SPDX-License-Identifier: GPL-2.0-or-later
2/* mpihelp-div.c - MPI helper functions
3 * Copyright (C) 1994, 1996 Free Software Foundation, Inc.
4 * Copyright (C) 1998, 1999 Free Software Foundation, Inc.
5 *
6 * This file is part of GnuPG.
7 *
8 * Note: This code is heavily based on the GNU MP Library.
9 * Actually it's the same code with only minor changes in the
10 * way the data is stored; this is to support the abstraction
11 * of an optional secure memory allocation which may be used
12 * to avoid revealing of sensitive data due to paging etc.
13 * The GNU MP Library itself is published under the LGPL;
14 * however I decided to publish this code under the plain GPL.
15 */
16
17#include "mpi-internal.h"
18#include "longlong.h"
19
20#ifndef UMUL_TIME
21#define UMUL_TIME 1
22#endif
23#ifndef UDIV_TIME
24#define UDIV_TIME UMUL_TIME
25#endif
26
27/* Divide num (NP/NSIZE) by den (DP/DSIZE) and write
28 * the NSIZE-DSIZE least significant quotient limbs at QP
29 * and the DSIZE long remainder at NP. If QEXTRA_LIMBS is
30 * non-zero, generate that many fraction bits and append them after the
31 * other quotient limbs.
32 * Return the most significant limb of the quotient, this is always 0 or 1.
33 *
34 * Preconditions:
35 * 0. NSIZE >= DSIZE.
36 * 1. The most significant bit of the divisor must be set.
37 * 2. QP must either not overlap with the input operands at all, or
38 * QP + DSIZE >= NP must hold true. (This means that it's
39 * possible to put the quotient in the high part of NUM, right after the
40 * remainder in NUM.
41 * 3. NSIZE >= DSIZE, even if QEXTRA_LIMBS is non-zero.
42 */
43
44mpi_limb_t
45mpihelp_divrem(mpi_ptr_t qp, mpi_size_t qextra_limbs,
46 mpi_ptr_t np, mpi_size_t nsize, mpi_ptr_t dp, mpi_size_t dsize)
47{
48 mpi_limb_t most_significant_q_limb = 0;
49
50 switch (dsize) {
51 case 0:
52 /* We are asked to divide by zero, so go ahead and do it! (To make
53 the compiler not remove this statement, return the value.) */
54 /*
55 * existing clients of this function have been modified
56 * not to call it with dsize == 0, so this should not happen
57 */
58 return 1 / dsize;
59
60 case 1:
61 {
62 mpi_size_t i;
63 mpi_limb_t n1;
64 mpi_limb_t d;
65
66 d = dp[0];
67 n1 = np[nsize - 1];
68
69 if (n1 >= d) {
70 n1 -= d;
71 most_significant_q_limb = 1;
72 }
73
74 qp += qextra_limbs;
75 for (i = nsize - 2; i >= 0; i--)
76 udiv_qrnnd(qp[i], n1, n1, np[i], d);
77 qp -= qextra_limbs;
78
79 for (i = qextra_limbs - 1; i >= 0; i--)
80 udiv_qrnnd(qp[i], n1, n1, 0, d);
81
82 np[0] = n1;
83 }
84 break;
85
86 case 2:
87 {
88 mpi_size_t i;
89 mpi_limb_t n1, n0, n2;
90 mpi_limb_t d1, d0;
91
92 np += nsize - 2;
93 d1 = dp[1];
94 d0 = dp[0];
95 n1 = np[1];
96 n0 = np[0];
97
98 if (n1 >= d1 && (n1 > d1 || n0 >= d0)) {
99 sub_ddmmss(n1, n0, n1, n0, d1, d0);
100 most_significant_q_limb = 1;
101 }
102
103 for (i = qextra_limbs + nsize - 2 - 1; i >= 0; i--) {
104 mpi_limb_t q;
105 mpi_limb_t r;
106
107 if (i >= qextra_limbs)
108 np--;
109 else
110 np[0] = 0;
111
112 if (n1 == d1) {
113 /* Q should be either 111..111 or 111..110. Need special
114 * treatment of this rare case as normal division would
115 * give overflow. */
116 q = ~(mpi_limb_t) 0;
117
118 r = n0 + d1;
119 if (r < d1) { /* Carry in the addition? */
120 add_ssaaaa(n1, n0, r - d0,
121 np[0], 0, d0);
122 qp[i] = q;
123 continue;
124 }
125 n1 = d0 - (d0 != 0 ? 1 : 0);
126 n0 = -d0;
127 } else {
128 udiv_qrnnd(q, r, n1, n0, d1);
129 umul_ppmm(n1, n0, d0, q);
130 }
131
132 n2 = np[0];
133q_test:
134 if (n1 > r || (n1 == r && n0 > n2)) {
135 /* The estimated Q was too large. */
136 q--;
137 sub_ddmmss(n1, n0, n1, n0, 0, d0);
138 r += d1;
139 if (r >= d1) /* If not carry, test Q again. */
140 goto q_test;
141 }
142
143 qp[i] = q;
144 sub_ddmmss(n1, n0, r, n2, n1, n0);
145 }
146 np[1] = n1;
147 np[0] = n0;
148 }
149 break;
150
151 default:
152 {
153 mpi_size_t i;
154 mpi_limb_t dX, d1, n0;
155
156 np += nsize - dsize;
157 dX = dp[dsize - 1];
158 d1 = dp[dsize - 2];
159 n0 = np[dsize - 1];
160
161 if (n0 >= dX) {
162 if (n0 > dX
163 || mpihelp_cmp(np, dp, dsize - 1) >= 0) {
164 mpihelp_sub_n(np, np, dp, dsize);
165 n0 = np[dsize - 1];
166 most_significant_q_limb = 1;
167 }
168 }
169
170 for (i = qextra_limbs + nsize - dsize - 1; i >= 0; i--) {
171 mpi_limb_t q;
172 mpi_limb_t n1, n2;
173 mpi_limb_t cy_limb;
174
175 if (i >= qextra_limbs) {
176 np--;
177 n2 = np[dsize];
178 } else {
179 n2 = np[dsize - 1];
180 MPN_COPY_DECR(np + 1, np, dsize - 1);
181 np[0] = 0;
182 }
183
184 if (n0 == dX) {
185 /* This might over-estimate q, but it's probably not worth
186 * the extra code here to find out. */
187 q = ~(mpi_limb_t) 0;
188 } else {
189 mpi_limb_t r;
190
191 udiv_qrnnd(q, r, n0, np[dsize - 1], dX);
192 umul_ppmm(n1, n0, d1, q);
193
194 while (n1 > r
195 || (n1 == r
196 && n0 > np[dsize - 2])) {
197 q--;
198 r += dX;
199 if (r < dX) /* I.e. "carry in previous addition?" */
200 break;
201 n1 -= n0 < d1;
202 n0 -= d1;
203 }
204 }
205
206 /* Possible optimization: We already have (q * n0) and (1 * n1)
207 * after the calculation of q. Taking advantage of that, we
208 * could make this loop make two iterations less. */
209 cy_limb = mpihelp_submul_1(np, dp, dsize, q);
210
211 if (n2 != cy_limb) {
212 mpihelp_add_n(np, np, dp, dsize);
213 q--;
214 }
215
216 qp[i] = q;
217 n0 = np[dsize - 1];
218 }
219 }
220 }
221
222 return most_significant_q_limb;
223}