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465ae836 | 1 | // SPDX-License-Identifier: GPL-2.0-or-later |
cdec9cb5 DK |
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 | * | |
cdec9cb5 DK |
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 | ||
cdec9cb5 DK |
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.) */ | |
a6d68ecc DK |
54 | /* |
55 | * existing clients of this function have been modified | |
56 | * not to call it with dsize == 0, so this should not happen | |
57 | */ | |
cdec9cb5 DK |
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 | } |