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
44 mpi_limb_t
45 mpihelp_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];
133 q_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 }