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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
17int mpi_tdiv_qr(MPI quot, MPI rem, MPI num, MPI den);
18
19int mpi_fdiv_r(MPI rem, MPI dividend, MPI divisor)
20{
21 int divisor_sign = divisor->sign;
22 MPI temp_divisor = NULL;
23 int err;
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 if (!temp_divisor)
32 return -ENOMEM;
33 divisor = temp_divisor;
34 }
35
36 err = mpi_tdiv_r(rem, dividend, divisor);
37 if (err)
38 goto free_temp_divisor;
39
40 if (((divisor_sign?1:0) ^ (dividend->sign?1:0)) && rem->nlimbs)
41 err = mpi_add(rem, rem, divisor);
42
43free_temp_divisor:
44 mpi_free(temp_divisor);
45
46 return err;
47}
48
49/* If den == quot, den needs temporary storage.
50 * If den == rem, den needs temporary storage.
51 * If num == quot, num needs temporary storage.
52 * If den has temporary storage, it can be normalized while being copied,
53 * i.e no extra storage should be allocated.
54 */
55
56int mpi_tdiv_r(MPI rem, MPI num, MPI den)
57{
58 return mpi_tdiv_qr(NULL, rem, num, den);
59}
60
61int mpi_tdiv_qr(MPI quot, MPI rem, MPI num, MPI den)
62{
63 mpi_ptr_t np, dp;
64 mpi_ptr_t qp, rp;
65 mpi_size_t nsize = num->nlimbs;
66 mpi_size_t dsize = den->nlimbs;
67 mpi_size_t qsize, rsize;
68 mpi_size_t sign_remainder = num->sign;
69 mpi_size_t sign_quotient = num->sign ^ den->sign;
70 unsigned int normalization_steps;
71 mpi_limb_t q_limb;
72 mpi_ptr_t marker[5];
73 int markidx = 0;
74 int err;
75
76 /* Ensure space is enough for quotient and remainder.
77 * We need space for an extra limb in the remainder, because it's
78 * up-shifted (normalized) below.
79 */
80 rsize = nsize + 1;
81 err = mpi_resize(rem, rsize);
82 if (err)
83 return err;
84
85 qsize = rsize - dsize; /* qsize cannot be bigger than this. */
86 if (qsize <= 0) {
87 if (num != rem) {
88 rem->nlimbs = num->nlimbs;
89 rem->sign = num->sign;
90 MPN_COPY(rem->d, num->d, nsize);
91 }
92 if (quot) {
93 /* This needs to follow the assignment to rem, in case the
94 * numerator and quotient are the same.
95 */
96 quot->nlimbs = 0;
97 quot->sign = 0;
98 }
99 return 0;
100 }
101
102 if (quot) {
103 err = mpi_resize(quot, qsize);
104 if (err)
105 return err;
106 }
107
108 /* Read pointers here, when reallocation is finished. */
109 np = num->d;
110 dp = den->d;
111 rp = rem->d;
112
113 /* Optimize division by a single-limb divisor. */
114 if (dsize == 1) {
115 mpi_limb_t rlimb;
116 if (quot) {
117 qp = quot->d;
118 rlimb = mpihelp_divmod_1(qp, np, nsize, dp[0]);
119 qsize -= qp[qsize - 1] == 0;
120 quot->nlimbs = qsize;
121 quot->sign = sign_quotient;
122 } else
123 rlimb = mpihelp_mod_1(np, nsize, dp[0]);
124 rp[0] = rlimb;
125 rsize = rlimb != 0?1:0;
126 rem->nlimbs = rsize;
127 rem->sign = sign_remainder;
128 return 0;
129 }
130
131 err = -ENOMEM;
132 if (quot) {
133 qp = quot->d;
134 /* Make sure QP and NP point to different objects. Otherwise the
135 * numerator would be gradually overwritten by the quotient limbs.
136 */
137 if (qp == np) { /* Copy NP object to temporary space. */
138 np = marker[markidx++] = mpi_alloc_limb_space(nsize);
139 if (!np)
140 goto out_free_marker;
141 MPN_COPY(np, qp, nsize);
142 }
143 } else /* Put quotient at top of remainder. */
144 qp = rp + dsize;
145
146 normalization_steps = count_leading_zeros(dp[dsize - 1]);
147
148 /* Normalize the denominator, i.e. make its most significant bit set by
149 * shifting it NORMALIZATION_STEPS bits to the left. Also shift the
150 * numerator the same number of steps (to keep the quotient the same!).
151 */
152 if (normalization_steps) {
153 mpi_ptr_t tp;
154 mpi_limb_t nlimb;
155
156 /* Shift up the denominator setting the most significant bit of
157 * the most significant word. Use temporary storage not to clobber
158 * the original contents of the denominator.
159 */
160 tp = marker[markidx++] = mpi_alloc_limb_space(dsize);
161 if (!tp)
162 goto out_free_marker;
163 mpihelp_lshift(tp, dp, dsize, normalization_steps);
164 dp = tp;
165
166 /* Shift up the numerator, possibly introducing a new most
167 * significant word. Move the shifted numerator in the remainder
168 * meanwhile.
169 */
170 nlimb = mpihelp_lshift(rp, np, nsize, normalization_steps);
171 if (nlimb) {
172 rp[nsize] = nlimb;
173 rsize = nsize + 1;
174 } else
175 rsize = nsize;
176 } else {
177 /* The denominator is already normalized, as required. Copy it to
178 * temporary space if it overlaps with the quotient or remainder.
179 */
180 if (dp == rp || (quot && (dp == qp))) {
181 mpi_ptr_t tp;
182
183 tp = marker[markidx++] = mpi_alloc_limb_space(dsize);
184 if (!tp)
185 goto out_free_marker;
186 MPN_COPY(tp, dp, dsize);
187 dp = tp;
188 }
189
190 /* Move the numerator to the remainder. */
191 if (rp != np)
192 MPN_COPY(rp, np, nsize);
193
194 rsize = nsize;
195 }
196
197 q_limb = mpihelp_divrem(qp, 0, rp, rsize, dp, dsize);
198
199 if (quot) {
200 qsize = rsize - dsize;
201 if (q_limb) {
202 qp[qsize] = q_limb;
203 qsize += 1;
204 }
205
206 quot->nlimbs = qsize;
207 quot->sign = sign_quotient;
208 }
209
210 rsize = dsize;
211 MPN_NORMALIZE(rp, rsize);
212
213 if (normalization_steps && rsize) {
214 mpihelp_rshift(rp, rp, rsize, normalization_steps);
215 rsize -= rp[rsize - 1] == 0?1:0;
216 }
217
218 rem->nlimbs = rsize;
219 rem->sign = sign_remainder;
220
221 err = 0;
222
223out_free_marker:
224 while (markidx) {
225 markidx--;
226 mpi_free_limb_space(marker[markidx]);
227 }
228
229 return err;
230}
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
17void mpi_tdiv_qr(MPI quot, MPI rem, MPI num, MPI den);
18void mpi_fdiv_qr(MPI quot, MPI rem, MPI dividend, MPI divisor);
19
20void 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
43void 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
50void 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
78void mpi_tdiv_r(MPI rem, MPI num, MPI den)
79{
80 mpi_tdiv_qr(NULL, rem, num, den);
81}
82
83void 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}