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];
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. */
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 */
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
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 }
235
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