1 | // -*- c++ -*- |
---|
2 | //***************************************************************************** |
---|
3 | /** @file facNTLzzpEXGCD.cc |
---|
4 | * |
---|
5 | * @author Martin Lee |
---|
6 | * |
---|
7 | * @note the following code is slightly modified code out of |
---|
8 | * lzz_pEX.c from Victor Shoup's NTL. Below is NTL's copyright notice. |
---|
9 | * |
---|
10 | * Univariate GCD and extended GCD over Z/p[t]/(f)[x] for reducible f |
---|
11 | * |
---|
12 | * @par Copyright: |
---|
13 | * (c) by The SINGULAR Team, see LICENSE file |
---|
14 | * |
---|
15 | **/ |
---|
16 | //***************************************************************************** |
---|
17 | |
---|
18 | /** |
---|
19 | COPYRIGHT NOTICE |
---|
20 | for NTL 5.5 |
---|
21 | (modified for Singular 2-0-6 - 3-1) |
---|
22 | |
---|
23 | NTL -- A Library for Doing Number Theory |
---|
24 | Copyright (C) 1996-2009 Victor Shoup |
---|
25 | |
---|
26 | The most recent version of NTL is available at http://www.shoup.net |
---|
27 | |
---|
28 | This program is free software; you can redistribute it and/or |
---|
29 | modify it under the terms of the GNU General Public License |
---|
30 | as published by the Free Software Foundation; either version 2 |
---|
31 | of the License, or (at your option) any later version. |
---|
32 | |
---|
33 | This program is distributed in the hope that it will be useful, |
---|
34 | but WITHOUT ANY WARRANTY; without even the implied warranty of |
---|
35 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
---|
36 | GNU General Public License for more details. |
---|
37 | |
---|
38 | You should have received a copy of the GNU General Public License |
---|
39 | along with this program; if not, write to the Free Software |
---|
40 | Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
---|
41 | |
---|
42 | This entire copyright notice should be placed in an appropriately |
---|
43 | conspicuous place accompanying all distributions of software that |
---|
44 | make use of NTL. |
---|
45 | |
---|
46 | The above terms apply to all of the software modules distributed with NTL, |
---|
47 | i.e., all source files in either the ntl-xxx.tar.gz or WinNTL-xxx.zip |
---|
48 | distributions. In general, the individual files do not contain |
---|
49 | copyright notices. |
---|
50 | |
---|
51 | Note that the quad_float package is derived from the doubledouble package, |
---|
52 | originally developed by Keith Briggs, and also licensed unger the GNU GPL. |
---|
53 | The files quad_float.c and quad_float.h contain more detailed copyright |
---|
54 | notices. |
---|
55 | |
---|
56 | Note that the traditional long integer package used by NTL, lip.c, is derived |
---|
57 | from---and represents an extensive modification of--- |
---|
58 | a package originally developed and copyrighted by Arjen Lenstra, |
---|
59 | who has agreed to renounce any copyright claims on the particular |
---|
60 | version of the long integer package appearing in NTL, so that the |
---|
61 | this package now is covered by the GNU GPL as well. |
---|
62 | |
---|
63 | Note that the alternative long integer package used by NTL is GMP, |
---|
64 | which is written by Torbjorn Granlund <tege@swox.com>. |
---|
65 | GMP is licensed under the terms of the GNU Lesser General Public License. |
---|
66 | |
---|
67 | Note that NTL makes use of the RSA Data Security, Inc. MD5 Message |
---|
68 | Digest Algorithm. |
---|
69 | |
---|
70 | Note that prior to version 4.0, NTL was distributed under the following terms: |
---|
71 | NTL is freely available for research and educational purposes. |
---|
72 | I don't want to attach any legalistic licensing restrictions on |
---|
73 | users of NTL. |
---|
74 | However, NTL should not be linked in a commercial program |
---|
75 | (although using data in a commercial |
---|
76 | product produced by a program that used NTL is fine). |
---|
77 | |
---|
78 | The hope is that the GNU GPL is actually less restrictive than these |
---|
79 | older terms; however, in any circumstances such that GNU GPL is more |
---|
80 | restrictive, then the following rule is in force: |
---|
81 | versions prior to 4.0 may continue to be used under the old terms, |
---|
82 | but users of versions 4.0 or later should adhere to the terms of the GNU GPL. |
---|
83 | **/ |
---|
84 | |
---|
85 | |
---|
86 | #include "config.h" |
---|
87 | |
---|
88 | #include "facNTLzzpEXGCD.h" |
---|
89 | |
---|
90 | #ifdef HAVE_NTL |
---|
91 | #include "NTLconvert.h" |
---|
92 | #endif |
---|
93 | |
---|
94 | #ifdef HAVE_NTL |
---|
95 | |
---|
96 | long InvModStatus (zz_pE& x, const zz_pE& a) |
---|
97 | { |
---|
98 | return InvModStatus(x._zz_pE__rep, a._zz_pE__rep, zz_pE::modulus()); |
---|
99 | } |
---|
100 | |
---|
101 | static |
---|
102 | void SetSize(vec_zz_pX& x, long n, long m) |
---|
103 | { |
---|
104 | x.SetLength(n); |
---|
105 | long i; |
---|
106 | for (i = 0; i < n; i++) |
---|
107 | x[i].rep.SetMaxLength(m); |
---|
108 | } |
---|
109 | |
---|
110 | void tryPlainRem(zz_pEX& r, const zz_pEX& a, const zz_pEX& b, vec_zz_pX& x, |
---|
111 | bool& fail) |
---|
112 | { |
---|
113 | long da, db, dq, i, j, LCIsOne; |
---|
114 | const zz_pE *bp; |
---|
115 | zz_pX *xp; |
---|
116 | |
---|
117 | |
---|
118 | zz_pE LCInv, t; |
---|
119 | zz_pX s; |
---|
120 | |
---|
121 | da = deg(a); |
---|
122 | db = deg(b); |
---|
123 | |
---|
124 | if (db < 0) Error("zz_pEX: division by zero"); |
---|
125 | |
---|
126 | if (da < db) { |
---|
127 | r = a; |
---|
128 | return; |
---|
129 | } |
---|
130 | |
---|
131 | bp = b.rep.elts(); |
---|
132 | |
---|
133 | if (IsOne(bp[db])) |
---|
134 | LCIsOne = 1; |
---|
135 | else { |
---|
136 | LCIsOne = 0; |
---|
137 | fail= InvModStatus (LCInv, bp[db]); |
---|
138 | //inv(LCInv, bp[db]); |
---|
139 | if (fail) |
---|
140 | return; |
---|
141 | } |
---|
142 | |
---|
143 | for (i = 0; i <= da; i++) |
---|
144 | x[i] = rep(a.rep[i]); |
---|
145 | |
---|
146 | xp = x.elts(); |
---|
147 | |
---|
148 | dq = da - db; |
---|
149 | |
---|
150 | for (i = dq; i >= 0; i--) { |
---|
151 | conv(t, xp[i+db]); |
---|
152 | if (!LCIsOne) |
---|
153 | mul(t, t, LCInv); |
---|
154 | NTL::negate(t, t); |
---|
155 | |
---|
156 | for (j = db-1; j >= 0; j--) { |
---|
157 | mul(s, rep(t), rep(bp[j])); |
---|
158 | add(xp[i+j], xp[i+j], s); |
---|
159 | } |
---|
160 | } |
---|
161 | |
---|
162 | r.rep.SetLength(db); |
---|
163 | for (i = 0; i < db; i++) |
---|
164 | conv(r.rep[i], xp[i]); |
---|
165 | r.normalize(); |
---|
166 | } |
---|
167 | |
---|
168 | void tryPlainDivRem(zz_pEX& q, zz_pEX& r, const zz_pEX& a, const zz_pEX& b, |
---|
169 | bool& fail) |
---|
170 | { |
---|
171 | long da, db, dq, i, j, LCIsOne; |
---|
172 | const zz_pE *bp; |
---|
173 | zz_pE *qp; |
---|
174 | zz_pX *xp; |
---|
175 | |
---|
176 | |
---|
177 | zz_pE LCInv, t; |
---|
178 | zz_pX s; |
---|
179 | |
---|
180 | da = deg(a); |
---|
181 | db = deg(b); |
---|
182 | |
---|
183 | if (db < 0) Error("zz_pEX: division by zero"); |
---|
184 | |
---|
185 | if (da < db) { |
---|
186 | r = a; |
---|
187 | clear(q); |
---|
188 | return; |
---|
189 | } |
---|
190 | |
---|
191 | zz_pEX lb; |
---|
192 | |
---|
193 | if (&q == &b) { |
---|
194 | lb = b; |
---|
195 | bp = lb.rep.elts(); |
---|
196 | } |
---|
197 | else |
---|
198 | bp = b.rep.elts(); |
---|
199 | |
---|
200 | if (IsOne(bp[db])) |
---|
201 | LCIsOne = 1; |
---|
202 | else { |
---|
203 | LCIsOne = 0; |
---|
204 | fail= InvModStatus (LCInv, bp[db]); |
---|
205 | //inv(LCInv, bp[db]); |
---|
206 | if (fail) |
---|
207 | return; |
---|
208 | } |
---|
209 | |
---|
210 | vec_zz_pX x; |
---|
211 | |
---|
212 | SetSize(x, da+1, 2*zz_pE::degree()); |
---|
213 | |
---|
214 | for (i = 0; i <= da; i++) |
---|
215 | x[i] = rep(a.rep[i]); |
---|
216 | |
---|
217 | xp = x.elts(); |
---|
218 | |
---|
219 | dq = da - db; |
---|
220 | q.rep.SetLength(dq+1); |
---|
221 | qp = q.rep.elts(); |
---|
222 | |
---|
223 | for (i = dq; i >= 0; i--) { |
---|
224 | conv(t, xp[i+db]); |
---|
225 | if (!LCIsOne) |
---|
226 | mul(t, t, LCInv); |
---|
227 | qp[i] = t; |
---|
228 | NTL::negate(t, t); |
---|
229 | |
---|
230 | for (j = db-1; j >= 0; j--) { |
---|
231 | mul(s, rep(t), rep(bp[j])); |
---|
232 | add(xp[i+j], xp[i+j], s); |
---|
233 | } |
---|
234 | } |
---|
235 | |
---|
236 | r.rep.SetLength(db); |
---|
237 | for (i = 0; i < db; i++) |
---|
238 | conv(r.rep[i], xp[i]); |
---|
239 | r.normalize(); |
---|
240 | } |
---|
241 | |
---|
242 | |
---|
243 | void tryNTLGCD(zz_pEX& x, const zz_pEX& a, const zz_pEX& b, bool& fail) |
---|
244 | { |
---|
245 | zz_pE t; |
---|
246 | |
---|
247 | if (IsZero(b)) |
---|
248 | x = a; |
---|
249 | else if (IsZero(a)) |
---|
250 | x = b; |
---|
251 | else { |
---|
252 | long n = max(deg(a),deg(b)) + 1; |
---|
253 | zz_pEX u(INIT_SIZE, n), v(INIT_SIZE, n); |
---|
254 | |
---|
255 | vec_zz_pX tmp; |
---|
256 | SetSize(tmp, n, 2*zz_pE::degree()); |
---|
257 | |
---|
258 | u = a; |
---|
259 | v = b; |
---|
260 | do { |
---|
261 | tryPlainRem(u, u, v, tmp, fail); |
---|
262 | if (fail) |
---|
263 | return; |
---|
264 | swap(u, v); |
---|
265 | } while (!IsZero(v)); |
---|
266 | |
---|
267 | x = u; |
---|
268 | } |
---|
269 | |
---|
270 | if (IsZero(x)) return; |
---|
271 | if (IsOne(LeadCoeff(x))) return; |
---|
272 | |
---|
273 | /* make gcd monic */ |
---|
274 | |
---|
275 | |
---|
276 | fail= InvModStatus (t, LeadCoeff(x)); |
---|
277 | if (fail) |
---|
278 | return; |
---|
279 | mul(x, x, t); |
---|
280 | } |
---|
281 | |
---|
282 | void tryNTLXGCD(zz_pEX& d, zz_pEX& s, zz_pEX& t, const zz_pEX& a, |
---|
283 | const zz_pEX& b, bool& fail) |
---|
284 | { |
---|
285 | zz_pE z; |
---|
286 | |
---|
287 | |
---|
288 | if (IsZero(b)) { |
---|
289 | set(s); |
---|
290 | clear(t); |
---|
291 | d = a; |
---|
292 | } |
---|
293 | else if (IsZero(a)) { |
---|
294 | clear(s); |
---|
295 | set(t); |
---|
296 | d = b; |
---|
297 | } |
---|
298 | else { |
---|
299 | long e = max(deg(a), deg(b)) + 1; |
---|
300 | |
---|
301 | zz_pEX temp(INIT_SIZE, e), u(INIT_SIZE, e), v(INIT_SIZE, e), |
---|
302 | u0(INIT_SIZE, e), v0(INIT_SIZE, e), |
---|
303 | u1(INIT_SIZE, e), v1(INIT_SIZE, e), |
---|
304 | u2(INIT_SIZE, e), v2(INIT_SIZE, e), q(INIT_SIZE, e); |
---|
305 | |
---|
306 | |
---|
307 | set(u1); clear(v1); |
---|
308 | clear(u2); set(v2); |
---|
309 | u = a; v = b; |
---|
310 | |
---|
311 | do { |
---|
312 | fail= InvModStatus (z, LeadCoeff(v)); |
---|
313 | if (fail) |
---|
314 | return; |
---|
315 | DivRem(q, u, u, v); |
---|
316 | swap(u, v); |
---|
317 | u0 = u2; |
---|
318 | v0 = v2; |
---|
319 | mul(temp, q, u2); |
---|
320 | sub(u2, u1, temp); |
---|
321 | mul(temp, q, v2); |
---|
322 | sub(v2, v1, temp); |
---|
323 | u1 = u0; |
---|
324 | v1 = v0; |
---|
325 | } while (!IsZero(v)); |
---|
326 | |
---|
327 | d = u; |
---|
328 | s = u1; |
---|
329 | t = v1; |
---|
330 | } |
---|
331 | |
---|
332 | if (IsZero(d)) return; |
---|
333 | if (IsOne(LeadCoeff(d))) return; |
---|
334 | |
---|
335 | /* make gcd monic */ |
---|
336 | |
---|
337 | fail= InvModStatus (z, LeadCoeff(d)); |
---|
338 | if (fail) |
---|
339 | return; |
---|
340 | mul(d, d, z); |
---|
341 | mul(s, s, z); |
---|
342 | mul(t, t, z); |
---|
343 | } |
---|
344 | #endif |
---|
345 | |
---|