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cdec9cb5 DK |
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 | ||
cdec9cb5 DK |
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 | ||
57 | mpi_limb_t | |
58 | mpihelp_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.) */ | |
a6d68ecc DK |
67 | /* |
68 | * existing clients of this function have been modified | |
69 | * not to call it with dsize == 0, so this should not happen | |
70 | */ | |
cdec9cb5 DK |
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]; | |
146 | q_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 | } |