1 /* hgcd_matrix.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, 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 /* For input of size n, matrix elements are of size at most ceil(n/2)
39 - 1, but we need two limbs extra. */
40 void
41 mpn_hgcd_matrix_init (struct hgcd_matrix *M, mp_size_t n, mp_ptr p)
42 {
43 mp_size_t s = (n+1)/2 + 1;
44 M->alloc = s;
45 M->n = 1;
46 MPN_ZERO (p, 4 * s);
47 M->p[0][0] = p;
48 M->p[0][1] = p + s;
49 M->p[1][0] = p + 2 * s;
50 M->p[1][1] = p + 3 * s;
51
52 M->p[0][0][0] = M->p[1][1][0] = 1;
53 }
54
55 /* Update column COL, adding in Q * column (1-COL). Temporary storage:
56 * qn + n <= M->alloc, where n is the size of the largest element in
57 * column 1 - COL. */
58 void
59 mpn_hgcd_matrix_update_q (struct hgcd_matrix *M, mp_srcptr qp, mp_size_t qn,
60 unsigned col, mp_ptr tp)
61 {
62 ASSERT (col < 2);
63
64 if (qn == 1)
65 {
66 mp_limb_t q = qp[0];
67 mp_limb_t c0, c1;
68
69 c0 = mpn_addmul_1 (M->p[0][col], M->p[0][1-col], M->n, q);
70 c1 = mpn_addmul_1 (M->p[1][col], M->p[1][1-col], M->n, q);
71
72 M->p[0][col][M->n] = c0;
73 M->p[1][col][M->n] = c1;
74
75 M->n += (c0 | c1) != 0;
76 }
77 else
78 {
79 unsigned row;
80
81 /* Carries for the unlikely case that we get both high words
82 from the multiplication and carries from the addition. */
83 mp_limb_t c[2];
84 mp_size_t n;
85
86 /* The matrix will not necessarily grow in size by qn, so we
87 need normalization in order not to overflow M. */
88
89 for (n = M->n; n + qn > M->n; n--)
90 {
91 ASSERT (n > 0);
92 if (M->p[0][1-col][n-1] > 0 || M->p[1][1-col][n-1] > 0)
93 break;
94 }
95
96 ASSERT (qn + n <= M->alloc);
97
98 for (row = 0; row < 2; row++)
99 {
100 if (qn <= n)
101 mpn_mul (tp, M->p[row][1-col], n, qp, qn);
102 else
103 mpn_mul (tp, qp, qn, M->p[row][1-col], n);
104
105 ASSERT (n + qn >= M->n);
106 c[row] = mpn_add (M->p[row][col], tp, n + qn, M->p[row][col], M->n);
107 }
108
109 n += qn;
110
111 if (c[0] | c[1])
112 {
113 M->p[0][col][n] = c[0];
114 M->p[1][col][n] = c[1];
115 n++;
116 }
117 else
118 {
119 n -= (M->p[0][col][n-1] | M->p[1][col][n-1]) == 0;
120 ASSERT (n >= M->n);
121 }
122 M->n = n;
123 }
124
125 ASSERT (M->n < M->alloc);
126 }
127
128 /* Multiply M by M1 from the right. Since the M1 elements fit in
129 GMP_NUMB_BITS - 1 bits, M grows by at most one limb. Needs
130 temporary space M->n */
131 void
132 mpn_hgcd_matrix_mul_1 (struct hgcd_matrix *M, const struct hgcd_matrix1 *M1,
133 mp_ptr tp)
134 {
135 mp_size_t n0, n1;
136
137 /* Could avoid copy by some swapping of pointers. */
138 MPN_COPY (tp, M->p[0][0], M->n);
139 n0 = mpn_hgcd_mul_matrix1_vector (M1, M->p[0][0], tp, M->p[0][1], M->n);
140 MPN_COPY (tp, M->p[1][0], M->n);
141 n1 = mpn_hgcd_mul_matrix1_vector (M1, M->p[1][0], tp, M->p[1][1], M->n);
142
143 /* Depends on zero initialization */
144 M->n = MAX(n0, n1);
145 ASSERT (M->n < M->alloc);
146 }
147
148 /* Multiply M by M1 from the right. Needs 3*(M->n + M1->n) + 5 limbs
149 of temporary storage (see mpn_matrix22_mul_itch). */
150 void
151 mpn_hgcd_matrix_mul (struct hgcd_matrix *M, const struct hgcd_matrix *M1,
152 mp_ptr tp)
153 {
154 mp_size_t n;
155
156 /* About the new size of M:s elements. Since M1's diagonal elements
157 are > 0, no element can decrease. The new elements are of size
158 M->n + M1->n, one limb more or less. The computation of the
159 matrix product produces elements of size M->n + M1->n + 1. But
160 the true size, after normalization, may be three limbs smaller.
161
162 The reason that the product has normalized size >= M->n + M1->n -
163 2 is subtle. It depends on the fact that M and M1 can be factored
164 as products of (1,1; 0,1) and (1,0; 1,1), and that we can't have
165 M ending with a large power and M1 starting with a large power of
166 the same matrix. */
167
168 /* FIXME: Strassen multiplication gives only a small speedup. In FFT
169 multiplication range, this function could be sped up quite a lot
170 using invariance. */
171 ASSERT (M->n + M1->n < M->alloc);
172
173 ASSERT ((M->p[0][0][M->n-1] | M->p[0][1][M->n-1]
174 | M->p[1][0][M->n-1] | M->p[1][1][M->n-1]) > 0);
175
176 ASSERT ((M1->p[0][0][M1->n-1] | M1->p[0][1][M1->n-1]
177 | M1->p[1][0][M1->n-1] | M1->p[1][1][M1->n-1]) > 0);
178
179 mpn_matrix22_mul (M->p[0][0], M->p[0][1],
180 M->p[1][0], M->p[1][1], M->n,
181 M1->p[0][0], M1->p[0][1],
182 M1->p[1][0], M1->p[1][1], M1->n, tp);
183
184 /* Index of last potentially non-zero limb, size is one greater. */
185 n = M->n + M1->n;
186
187 n -= ((M->p[0][0][n] | M->p[0][1][n] | M->p[1][0][n] | M->p[1][1][n]) == 0);
188 n -= ((M->p[0][0][n] | M->p[0][1][n] | M->p[1][0][n] | M->p[1][1][n]) == 0);
189 n -= ((M->p[0][0][n] | M->p[0][1][n] | M->p[1][0][n] | M->p[1][1][n]) == 0);
190
191 ASSERT ((M->p[0][0][n] | M->p[0][1][n] | M->p[1][0][n] | M->p[1][1][n]) > 0);
192
193 M->n = n + 1;
194 }
195
196 /* Multiplies the least significant p limbs of (a;b) by M^-1.
197 Temporary space needed: 2 * (p + M->n)*/
198 mp_size_t
199 mpn_hgcd_matrix_adjust (const struct hgcd_matrix *M,
200 mp_size_t n, mp_ptr ap, mp_ptr bp,
201 mp_size_t p, mp_ptr tp)
202 {
203 /* M^-1 (a;b) = (r11, -r01; -r10, r00) (a ; b)
204 = (r11 a - r01 b; - r10 a + r00 b */
205
206 mp_ptr t0 = tp;
207 mp_ptr t1 = tp + p + M->n;
208 mp_limb_t ah, bh;
209 mp_limb_t cy;
210
211 ASSERT (p + M->n < n);
212
213 /* First compute the two values depending on a, before overwriting a */
214
215 if (M->n >= p)
216 {
217 mpn_mul (t0, M->p[1][1], M->n, ap, p);
218 mpn_mul (t1, M->p[1][0], M->n, ap, p);
219 }
220 else
221 {
222 mpn_mul (t0, ap, p, M->p[1][1], M->n);
223 mpn_mul (t1, ap, p, M->p[1][0], M->n);
224 }
225
226 /* Update a */
227 MPN_COPY (ap, t0, p);
228 ah = mpn_add (ap + p, ap + p, n - p, t0 + p, M->n);
229
230 if (M->n >= p)
231 mpn_mul (t0, M->p[0][1], M->n, bp, p);
232 else
233 mpn_mul (t0, bp, p, M->p[0][1], M->n);
234
235 cy = mpn_sub (ap, ap, n, t0, p + M->n);
236 ASSERT (cy <= ah);
237 ah -= cy;
238
239 /* Update b */
240 if (M->n >= p)
241 mpn_mul (t0, M->p[0][0], M->n, bp, p);
242 else
243 mpn_mul (t0, bp, p, M->p[0][0], M->n);
244
245 MPN_COPY (bp, t0, p);
246 bh = mpn_add (bp + p, bp + p, n - p, t0 + p, M->n);
247 cy = mpn_sub (bp, bp, n, t1, p + M->n);
248 ASSERT (cy <= bh);
249 bh -= cy;
250
251 if (ah > 0 || bh > 0)
252 {
253 ap[n] = ah;
254 bp[n] = bh;
255 n++;
256 }
257 else
258 {
259 /* The subtraction can reduce the size by at most one limb. */
260 if (ap[n-1] == 0 && bp[n-1] == 0)
261 n--;
262 }
263 ASSERT (ap[n-1] > 0 || bp[n-1] > 0);
264 return n;
265 }