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1 | /* mpi-div.c - MPI functions |
2 | * Copyright (C) 1994, 1996, 1998, 2001, 2002, | |
3 | * 2003 Free Software Foundation, Inc. | |
4 | * | |
5 | * This file is part of Libgcrypt. | |
6 | * | |
7 | * Note: This code is heavily based on the GNU MP Library. | |
8 | * Actually it's the same code with only minor changes in the | |
9 | * way the data is stored; this is to support the abstraction | |
10 | * of an optional secure memory allocation which may be used | |
11 | * to avoid revealing of sensitive data due to paging etc. | |
12 | */ | |
13 | ||
14 | #include "mpi-internal.h" | |
15 | #include "longlong.h" | |
16 | ||
17 | void mpi_tdiv_qr(MPI quot, MPI rem, MPI num, MPI den); | |
18 | void mpi_fdiv_qr(MPI quot, MPI rem, MPI dividend, MPI divisor); | |
19 | ||
20 | void mpi_fdiv_r(MPI rem, MPI dividend, MPI divisor) | |
21 | { | |
22 | int divisor_sign = divisor->sign; | |
23 | MPI temp_divisor = NULL; | |
24 | ||
25 | /* We need the original value of the divisor after the remainder has been | |
26 | * preliminary calculated. We have to copy it to temporary space if it's | |
27 | * the same variable as REM. | |
28 | */ | |
29 | if (rem == divisor) { | |
30 | temp_divisor = mpi_copy(divisor); | |
31 | divisor = temp_divisor; | |
32 | } | |
33 | ||
34 | mpi_tdiv_r(rem, dividend, divisor); | |
35 | ||
36 | if (((divisor_sign?1:0) ^ (dividend->sign?1:0)) && rem->nlimbs) | |
37 | mpi_add(rem, rem, divisor); | |
38 | ||
39 | if (temp_divisor) | |
40 | mpi_free(temp_divisor); | |
41 | } | |
42 | ||
43 | void mpi_fdiv_q(MPI quot, MPI dividend, MPI divisor) | |
44 | { | |
45 | MPI tmp = mpi_alloc(mpi_get_nlimbs(quot)); | |
46 | mpi_fdiv_qr(quot, tmp, dividend, divisor); | |
47 | mpi_free(tmp); | |
48 | } | |
49 | ||
50 | void mpi_fdiv_qr(MPI quot, MPI rem, MPI dividend, MPI divisor) | |
51 | { | |
52 | int divisor_sign = divisor->sign; | |
53 | MPI temp_divisor = NULL; | |
54 | ||
55 | if (quot == divisor || rem == divisor) { | |
56 | temp_divisor = mpi_copy(divisor); | |
57 | divisor = temp_divisor; | |
58 | } | |
59 | ||
60 | mpi_tdiv_qr(quot, rem, dividend, divisor); | |
61 | ||
62 | if ((divisor_sign ^ dividend->sign) && rem->nlimbs) { | |
63 | mpi_sub_ui(quot, quot, 1); | |
64 | mpi_add(rem, rem, divisor); | |
65 | } | |
66 | ||
67 | if (temp_divisor) | |
68 | mpi_free(temp_divisor); | |
69 | } | |
70 | ||
71 | /* If den == quot, den needs temporary storage. | |
72 | * If den == rem, den needs temporary storage. | |
73 | * If num == quot, num needs temporary storage. | |
74 | * If den has temporary storage, it can be normalized while being copied, | |
75 | * i.e no extra storage should be allocated. | |
76 | */ | |
77 | ||
78 | void mpi_tdiv_r(MPI rem, MPI num, MPI den) | |
79 | { | |
80 | mpi_tdiv_qr(NULL, rem, num, den); | |
81 | } | |
82 | ||
83 | void mpi_tdiv_qr(MPI quot, MPI rem, MPI num, MPI den) | |
84 | { | |
85 | mpi_ptr_t np, dp; | |
86 | mpi_ptr_t qp, rp; | |
87 | mpi_size_t nsize = num->nlimbs; | |
88 | mpi_size_t dsize = den->nlimbs; | |
89 | mpi_size_t qsize, rsize; | |
90 | mpi_size_t sign_remainder = num->sign; | |
91 | mpi_size_t sign_quotient = num->sign ^ den->sign; | |
92 | unsigned int normalization_steps; | |
93 | mpi_limb_t q_limb; | |
94 | mpi_ptr_t marker[5]; | |
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95 | int markidx = 0; |
96 | ||
97 | /* Ensure space is enough for quotient and remainder. | |
98 | * We need space for an extra limb in the remainder, because it's | |
99 | * up-shifted (normalized) below. | |
100 | */ | |
101 | rsize = nsize + 1; | |
102 | mpi_resize(rem, rsize); | |
103 | ||
104 | qsize = rsize - dsize; /* qsize cannot be bigger than this. */ | |
105 | if (qsize <= 0) { | |
106 | if (num != rem) { | |
107 | rem->nlimbs = num->nlimbs; | |
108 | rem->sign = num->sign; | |
109 | MPN_COPY(rem->d, num->d, nsize); | |
110 | } | |
111 | if (quot) { | |
112 | /* This needs to follow the assignment to rem, in case the | |
113 | * numerator and quotient are the same. | |
114 | */ | |
115 | quot->nlimbs = 0; | |
116 | quot->sign = 0; | |
117 | } | |
118 | return; | |
119 | } | |
120 | ||
121 | if (quot) | |
122 | mpi_resize(quot, qsize); | |
123 | ||
124 | /* Read pointers here, when reallocation is finished. */ | |
125 | np = num->d; | |
126 | dp = den->d; | |
127 | rp = rem->d; | |
128 | ||
129 | /* Optimize division by a single-limb divisor. */ | |
130 | if (dsize == 1) { | |
131 | mpi_limb_t rlimb; | |
132 | if (quot) { | |
133 | qp = quot->d; | |
134 | rlimb = mpihelp_divmod_1(qp, np, nsize, dp[0]); | |
135 | qsize -= qp[qsize - 1] == 0; | |
136 | quot->nlimbs = qsize; | |
137 | quot->sign = sign_quotient; | |
138 | } else | |
139 | rlimb = mpihelp_mod_1(np, nsize, dp[0]); | |
140 | rp[0] = rlimb; | |
141 | rsize = rlimb != 0?1:0; | |
142 | rem->nlimbs = rsize; | |
143 | rem->sign = sign_remainder; | |
144 | return; | |
145 | } | |
146 | ||
147 | ||
148 | if (quot) { | |
149 | qp = quot->d; | |
150 | /* Make sure QP and NP point to different objects. Otherwise the | |
151 | * numerator would be gradually overwritten by the quotient limbs. | |
152 | */ | |
153 | if (qp == np) { /* Copy NP object to temporary space. */ | |
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154 | np = marker[markidx++] = mpi_alloc_limb_space(nsize); |
155 | MPN_COPY(np, qp, nsize); | |
156 | } | |
157 | } else /* Put quotient at top of remainder. */ | |
158 | qp = rp + dsize; | |
159 | ||
160 | normalization_steps = count_leading_zeros(dp[dsize - 1]); | |
161 | ||
162 | /* Normalize the denominator, i.e. make its most significant bit set by | |
163 | * shifting it NORMALIZATION_STEPS bits to the left. Also shift the | |
164 | * numerator the same number of steps (to keep the quotient the same!). | |
165 | */ | |
166 | if (normalization_steps) { | |
167 | mpi_ptr_t tp; | |
168 | mpi_limb_t nlimb; | |
169 | ||
170 | /* Shift up the denominator setting the most significant bit of | |
171 | * the most significant word. Use temporary storage not to clobber | |
172 | * the original contents of the denominator. | |
173 | */ | |
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174 | tp = marker[markidx++] = mpi_alloc_limb_space(dsize); |
175 | mpihelp_lshift(tp, dp, dsize, normalization_steps); | |
176 | dp = tp; | |
177 | ||
178 | /* Shift up the numerator, possibly introducing a new most | |
179 | * significant word. Move the shifted numerator in the remainder | |
180 | * meanwhile. | |
181 | */ | |
182 | nlimb = mpihelp_lshift(rp, np, nsize, normalization_steps); | |
183 | if (nlimb) { | |
184 | rp[nsize] = nlimb; | |
185 | rsize = nsize + 1; | |
186 | } else | |
187 | rsize = nsize; | |
188 | } else { | |
189 | /* The denominator is already normalized, as required. Copy it to | |
190 | * temporary space if it overlaps with the quotient or remainder. | |
191 | */ | |
192 | if (dp == rp || (quot && (dp == qp))) { | |
193 | mpi_ptr_t tp; | |
194 | ||
a8ea8bdd TZ |
195 | tp = marker[markidx++] = mpi_alloc_limb_space(dsize); |
196 | MPN_COPY(tp, dp, dsize); | |
197 | dp = tp; | |
198 | } | |
199 | ||
200 | /* Move the numerator to the remainder. */ | |
201 | if (rp != np) | |
202 | MPN_COPY(rp, np, nsize); | |
203 | ||
204 | rsize = nsize; | |
205 | } | |
206 | ||
207 | q_limb = mpihelp_divrem(qp, 0, rp, rsize, dp, dsize); | |
208 | ||
209 | if (quot) { | |
210 | qsize = rsize - dsize; | |
211 | if (q_limb) { | |
212 | qp[qsize] = q_limb; | |
213 | qsize += 1; | |
214 | } | |
215 | ||
216 | quot->nlimbs = qsize; | |
217 | quot->sign = sign_quotient; | |
218 | } | |
219 | ||
220 | rsize = dsize; | |
221 | MPN_NORMALIZE(rp, rsize); | |
222 | ||
223 | if (normalization_steps && rsize) { | |
224 | mpihelp_rshift(rp, rp, rsize, normalization_steps); | |
225 | rsize -= rp[rsize - 1] == 0?1:0; | |
226 | } | |
227 | ||
228 | rem->nlimbs = rsize; | |
229 | rem->sign = sign_remainder; | |
230 | while (markidx) { | |
231 | markidx--; | |
232 | mpi_free_limb_space(marker[markidx]); | |
233 | } | |
234 | } |