1 /* hgcd_jacobi.c.
2
3 THE FUNCTIONS IN THIS FILE ARE INTERNAL WITH MUTABLE INTERFACES. IT IS ONLY
4 SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST
5 GUARANTEED THAT THEY'LL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.
6
7 Copyright 2003-2005, 2008, 2011, 2012 Free Software Foundation, Inc.
8
9 This file is part of the GNU MP Library.
10
11 The GNU MP Library is free software; you can redistribute it and/or modify
12 it under the terms of either:
13
14 * the GNU Lesser General Public License as published by the Free
15 Software Foundation; either version 3 of the License, or (at your
16 option) any later version.
17
18 or
19
20 * the GNU General Public License as published by the Free Software
21 Foundation; either version 2 of the License, or (at your option) any
22 later version.
23
24 or both in parallel, as here.
25
26 The GNU MP Library is distributed in the hope that it will be useful, but
27 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
28 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
29 for more details.
30
31 You should have received copies of the GNU General Public License and the
32 GNU Lesser General Public License along with the GNU MP Library. If not,
33 see https://www.gnu.org/licenses/. */
34
35 #include "gmp-impl.h"
36 #include "longlong.h"
37
38 /* This file is almost a copy of hgcd.c, with some added calls to
39 mpn_jacobi_update */
40
41 struct hgcd_jacobi_ctx
42 {
43 struct hgcd_matrix *M;
44 unsigned *bitsp;
45 };
46
47 static void
48 hgcd_jacobi_hook (void *p, mp_srcptr gp, mp_size_t gn,
49 mp_srcptr qp, mp_size_t qn, int d)
50 {
51 ASSERT (!gp);
52 ASSERT (d >= 0);
53
54 MPN_NORMALIZE (qp, qn);
55 if (qn > 0)
56 {
57 struct hgcd_jacobi_ctx *ctx = (struct hgcd_jacobi_ctx *) p;
58 /* NOTES: This is a bit ugly. A tp area is passed to
59 gcd_subdiv_step, which stores q at the start of that area. We
60 now use the rest. */
61 mp_ptr tp = (mp_ptr) qp + qn;
62
63 mpn_hgcd_matrix_update_q (ctx->M, qp, qn, d, tp);
64 *ctx->bitsp = mpn_jacobi_update (*ctx->bitsp, d, qp[0] & 3);
65 }
66 }
67
68 /* Perform a few steps, using some of mpn_hgcd2, subtraction and
69 division. Reduces the size by almost one limb or more, but never
70 below the given size s. Return new size for a and b, or 0 if no
71 more steps are possible.
72
73 If hgcd2 succeeds, needs temporary space for hgcd_matrix_mul_1, M->n
74 limbs, and hgcd_mul_matrix1_inverse_vector, n limbs. If hgcd2
75 fails, needs space for the quotient, qn <= n - s + 1 limbs, for and
76 hgcd_matrix_update_q, qn + (size of the appropriate column of M) <=
77 resulting size of M.
78
79 If N is the input size to the calling hgcd, then s = floor(N/2) +
80 1, M->n < N, qn + matrix size <= n - s + 1 + n - s = 2 (n - s) + 1
81 < N, so N is sufficient.
82 */
83
84 static mp_size_t
85 hgcd_jacobi_step (mp_size_t n, mp_ptr ap, mp_ptr bp, mp_size_t s,
86 struct hgcd_matrix *M, unsigned *bitsp, mp_ptr tp)
87 {
88 struct hgcd_matrix1 M1;
89 mp_limb_t mask;
90 mp_limb_t ah, al, bh, bl;
91
92 ASSERT (n > s);
93
94 mask = ap[n-1] | bp[n-1];
95 ASSERT (mask > 0);
96
97 if (n == s + 1)
98 {
99 if (mask < 4)
100 goto subtract;
101
102 ah = ap[n-1]; al = ap[n-2];
103 bh = bp[n-1]; bl = bp[n-2];
104 }
105 else if (mask & GMP_NUMB_HIGHBIT)
106 {
107 ah = ap[n-1]; al = ap[n-2];
108 bh = bp[n-1]; bl = bp[n-2];
109 }
110 else
111 {
112 int shift;
113
114 count_leading_zeros (shift, mask);
115 ah = MPN_EXTRACT_NUMB (shift, ap[n-1], ap[n-2]);
116 al = MPN_EXTRACT_NUMB (shift, ap[n-2], ap[n-3]);
117 bh = MPN_EXTRACT_NUMB (shift, bp[n-1], bp[n-2]);
118 bl = MPN_EXTRACT_NUMB (shift, bp[n-2], bp[n-3]);
119 }
120
121 /* Try an mpn_hgcd2 step */
122 if (mpn_hgcd2_jacobi (ah, al, bh, bl, &M1, bitsp))
123 {
124 /* Multiply M <- M * M1 */
125 mpn_hgcd_matrix_mul_1 (M, &M1, tp);
126
127 /* Can't swap inputs, so we need to copy. */
128 MPN_COPY (tp, ap, n);
129 /* Multiply M1^{-1} (a;b) */
130 return mpn_matrix22_mul1_inverse_vector (&M1, ap, tp, bp, n);
131 }
132
133 subtract:
134 {
135 struct hgcd_jacobi_ctx ctx;
136 ctx.M = M;
137 ctx.bitsp = bitsp;
138
139 return mpn_gcd_subdiv_step (ap, bp, n, s, hgcd_jacobi_hook, &ctx, tp);
140 }
141 }
142
143 /* Reduces a,b until |a-b| fits in n/2 + 1 limbs. Constructs matrix M
144 with elements of size at most (n+1)/2 - 1. Returns new size of a,
145 b, or zero if no reduction is possible. */
146
147 /* Same scratch requirements as for mpn_hgcd. */
148 mp_size_t
149 mpn_hgcd_jacobi (mp_ptr ap, mp_ptr bp, mp_size_t n,
150 struct hgcd_matrix *M, unsigned *bitsp, mp_ptr tp)
151 {
152 mp_size_t s = n/2 + 1;
153
154 mp_size_t nn;
155 int success = 0;
156
157 if (n <= s)
158 /* Happens when n <= 2, a fairly uninteresting case but exercised
159 by the random inputs of the testsuite. */
160 return 0;
161
162 ASSERT ((ap[n-1] | bp[n-1]) > 0);
163
164 ASSERT ((n+1)/2 - 1 < M->alloc);
165
166 if (ABOVE_THRESHOLD (n, HGCD_THRESHOLD))
167 {
168 mp_size_t n2 = (3*n)/4 + 1;
169 mp_size_t p = n/2;
170
171 nn = mpn_hgcd_jacobi (ap + p, bp + p, n - p, M, bitsp, tp);
172 if (nn > 0)
173 {
174 /* Needs 2*(p + M->n) <= 2*(floor(n/2) + ceil(n/2) - 1)
175 = 2 (n - 1) */
176 n = mpn_hgcd_matrix_adjust (M, p + nn, ap, bp, p, tp);
177 success = 1;
178 }
179 while (n > n2)
180 {
181 /* Needs n + 1 storage */
182 nn = hgcd_jacobi_step (n, ap, bp, s, M, bitsp, tp);
183 if (!nn)
184 return success ? n : 0;
185 n = nn;
186 success = 1;
187 }
188
189 if (n > s + 2)
190 {
191 struct hgcd_matrix M1;
192 mp_size_t scratch;
193
194 p = 2*s - n + 1;
195 scratch = MPN_HGCD_MATRIX_INIT_ITCH (n-p);
196
197 mpn_hgcd_matrix_init(&M1, n - p, tp);
198 nn = mpn_hgcd_jacobi (ap + p, bp + p, n - p, &M1, bitsp, tp + scratch);
199 if (nn > 0)
200 {
201 /* We always have max(M) > 2^{-(GMP_NUMB_BITS + 1)} max(M1) */
202 ASSERT (M->n + 2 >= M1.n);
203
204 /* Furthermore, assume M ends with a quotient (1, q; 0, 1),
205 then either q or q + 1 is a correct quotient, and M1 will
206 start with either (1, 0; 1, 1) or (2, 1; 1, 1). This
207 rules out the case that the size of M * M1 is much
208 smaller than the expected M->n + M1->n. */
209
210 ASSERT (M->n + M1.n < M->alloc);
211
212 /* Needs 2 (p + M->n) <= 2 (2*s - n2 + 1 + n2 - s - 1)
213 = 2*s <= 2*(floor(n/2) + 1) <= n + 2. */
214 n = mpn_hgcd_matrix_adjust (&M1, p + nn, ap, bp, p, tp + scratch);
215
216 /* We need a bound for of M->n + M1.n. Let n be the original
217 input size. Then
218
219 ceil(n/2) - 1 >= size of product >= M.n + M1.n - 2
220
221 and it follows that
222
223 M.n + M1.n <= ceil(n/2) + 1
224
225 Then 3*(M.n + M1.n) + 5 <= 3 * ceil(n/2) + 8 is the
226 amount of needed scratch space. */
227 mpn_hgcd_matrix_mul (M, &M1, tp + scratch);
228 success = 1;
229 }
230 }
231 }
232
233 for (;;)
234 {
235 /* Needs s+3 < n */
236 nn = hgcd_jacobi_step (n, ap, bp, s, M, bitsp, tp);
237 if (!nn)
238 return success ? n : 0;
239
240 n = nn;
241 success = 1;
242 }
243 }