Line data Source code
1 : #line 2 "../src/kernel/none/halfgcd.c"
2 : /* Copyright (C) 2019 The PARI group.
3 :
4 : This file is part of the PARI/GP package.
5 :
6 : PARI/GP is free software; you can redistribute it and/or modify it under the
7 : terms of the GNU General Public License as published by the Free Software
8 : Foundation; either version 2 of the License, or (at your option) any later
9 : version. It is distributed in the hope that it will be useful, but WITHOUT
10 : ANY WARRANTY WHATSOEVER.
11 :
12 : Check the License for details. You should have received a copy of it, along
13 : with the package; see the file 'COPYING'. If not, write to the Free Software
14 : Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. */
15 :
16 : GEN
17 2338 : ZM2_sqr(GEN A)
18 : {
19 2338 : GEN a = gcoeff(A,1,1), b = gcoeff(A,1,2), a2 = sqri(a);
20 2338 : GEN c = gcoeff(A,2,1), d = gcoeff(A,2,2), d2 = sqri(d), t = addii(a,d);
21 2338 : if (equalii(b, c)) /* symetric, 3S + 1M */
22 : {
23 322 : GEN b2 = sqri(b), M = cgetg(3, t_MAT), tb = mulii(b, t);
24 322 : gel(M,1) = mkcol2(addii(a2, b2), tb);
25 322 : gel(M,2) = mkcol2(tb, addii(b2, d2)); return M;
26 : }
27 : else
28 : { /* general, 2S + 3M */
29 2016 : GEN bc = mulii(b, c);
30 2016 : retmkmat2(mkcol2(addii(bc, a2), mulii(c, t)),
31 : mkcol2(mulii(b, t), addii(bc, d2)));
32 : }
33 : }
34 :
35 : GEN
36 7531339 : ZM2_mul(GEN A, GEN B)
37 : {
38 7531339 : const long t = ZM2_MUL_LIMIT+2;
39 7531339 : GEN A11=gcoeff(A,1,1),A12=gcoeff(A,1,2), B11=gcoeff(B,1,1),B12=gcoeff(B,1,2);
40 7531339 : GEN A21=gcoeff(A,2,1),A22=gcoeff(A,2,2), B21=gcoeff(B,2,1),B22=gcoeff(B,2,2);
41 7531339 : if (lgefint(A11) < t || lgefint(B11) < t || lgefint(A22) < t || lgefint(B22) < t
42 134653 : || lgefint(A12) < t || lgefint(B12) < t || lgefint(A21) < t || lgefint(B21) < t)
43 : { /* 8M */
44 7399364 : GEN a = mulii(A11, B11), b = mulii(A12, B21);
45 7399364 : GEN c = mulii(A11, B12), d = mulii(A12, B22);
46 7399364 : GEN e = mulii(A21, B11), f = mulii(A22, B21);
47 7399364 : GEN g = mulii(A21, B12), h = mulii(A22, B22);
48 7399364 : retmkmat2(mkcol2(addii(a,b), addii(e,f)), mkcol2(addii(c,d), addii(g,h)));
49 : } else
50 : { /* Strassen: 7M */
51 131975 : GEN M1 = mulii(addii(A11,A22), addii(B11,B22));
52 131975 : GEN M2 = mulii(addii(A21,A22), B11);
53 131975 : GEN M3 = mulii(A11, subii(B12,B22));
54 131975 : GEN M4 = mulii(A22, subii(B21,B11));
55 131975 : GEN M5 = mulii(addii(A11,A12), B22);
56 131975 : GEN M6 = mulii(subii(A21,A11), addii(B11,B12));
57 131975 : GEN M7 = mulii(subii(A12,A22), addii(B21,B22));
58 131975 : GEN T1 = addii(M1,M4), T2 = subii(M7,M5);
59 131975 : GEN T3 = subii(M1,M2), T4 = addii(M3,M6);
60 131975 : retmkmat2(mkcol2(addii(T1,T2), addii(M2,M4)),
61 : mkcol2(addii(M3,M5), addii(T3,T4)));
62 : }
63 : }
64 :
65 : static GEN
66 960 : matid2(void)
67 : {
68 960 : retmkmat2(mkcol2(gen_1,gen_0),
69 : mkcol2(gen_0,gen_1));
70 : }
71 :
72 : /* Return M*[q,1;1,0] */
73 : static GEN
74 4846415 : mulq(GEN M, GEN q)
75 : {
76 4846415 : GEN u, v, res = cgetg(3, t_MAT);
77 4846415 : u = addii(mulii(gcoeff(M,1,1), q), gcoeff(M,1,2));
78 4846415 : v = addii(mulii(gcoeff(M,2,1), q), gcoeff(M,2,2));
79 4846415 : gel(res,1) = mkcol2(u, v);
80 4846415 : gel(res,2) = gel(M,1);
81 4846415 : return res;
82 : }
83 : static GEN
84 80 : mulqab(GEN M, GEN q, GEN *ap, GEN *bp)
85 : {
86 80 : GEN b = subii(*ap, mulii(*bp, q));
87 80 : *ap = *bp; *bp = b;
88 80 : return mulq(M,q);
89 : }
90 :
91 : /* Return M*[q,1;1,0]^-1 */
92 :
93 : static GEN
94 1461 : mulqi(GEN M, GEN q, GEN *ap, GEN *bp)
95 : {
96 : GEN u, v, res, a;
97 1461 : a = addii(mulii(*ap, q), *bp);
98 1461 : *bp = *ap; *ap = a;
99 1461 : res = cgetg(3, t_MAT);
100 1461 : u = subii(gcoeff(M,1,1),mulii(gcoeff(M,1,2), q));
101 1461 : v = subii(gcoeff(M,2,1),mulii(gcoeff(M,2,2), q));
102 1461 : gel(res,1) = gel(M,2);
103 1461 : gel(res,2) = mkcol2(u,v);
104 1461 : return res;
105 : }
106 :
107 : /* test whether n is a power of 2 */
108 : static long
109 25662581 : isint2n(GEN n)
110 : {
111 25662581 : long lx = lgefint(n), i;
112 : ulong a;
113 : GEN x;
114 25662581 : if (lx == 2) return 0;
115 25662581 : x = int_MSW(n);
116 25662581 : a = (ulong)*x; if (a & (a - 1)) return 0;
117 588294 : for (i = 3; i < lx; i++)
118 : {
119 580913 : x = int_precW(x); if (*x) return 0;
120 : }
121 7381 : return 1;
122 : }
123 :
124 : static long
125 25662581 : uexpi(GEN a)
126 25662581 : { return expi(a)+!isint2n(a); }
127 :
128 : static GEN
129 135669 : FIXUP0(GEN M, GEN *a, GEN *b, long m)
130 : {
131 135669 : long cnt=0;
132 172402 : while (expi(*b) >= m)
133 : {
134 36733 : GEN r, q = dvmdii(*a, *b, &r);
135 36733 : *a = *b; *b = r;
136 36733 : M = mulq(M, q);
137 36733 : cnt++;
138 : };
139 135669 : if (cnt>6) pari_err_BUG("FIXUP0");
140 135669 : return M;
141 : }
142 :
143 : static long
144 7625886 : signdet(GEN Q)
145 : {
146 7625886 : long a = Mod4(gcoeff(Q,1,1)), b = Mod4(gcoeff(Q,1,2));
147 7625886 : long c = Mod4(gcoeff(Q,2,1)), d = Mod4(gcoeff(Q,2,2));
148 7625886 : return ((a*d-b*c)&3)==1 ? 1 : -1;
149 : }
150 :
151 : static GEN
152 7428755 : ZM_inv2(GEN M)
153 : {
154 7428755 : long e = signdet(M);
155 11574811 : if (e==1) return mkmat22(gcoeff(M,2,2),negi(gcoeff(M,1,2)),
156 4146056 : negi(gcoeff(M,2,1)),gcoeff(M,1,1));
157 3282699 : else return mkmat22(negi(gcoeff(M,2,2)),gcoeff(M,1,2),
158 3282699 : gcoeff(M,2,1),negi(gcoeff(M,1,1)));
159 : }
160 :
161 : static GEN
162 1461 : lastq(GEN Q)
163 : {
164 1461 : GEN p = gcoeff(Q,1,1), q = gcoeff(Q,1,2), s = gcoeff(Q,2,2);
165 1461 : if (signe(q)==0) pari_err_BUG("halfgcd");
166 1461 : if (signe(s)==0) return p;
167 1461 : if (equali1(q)) return subiu(p,1);
168 1461 : return divii(p, q);
169 : }
170 :
171 : static GEN
172 8231 : mulT(GEN Q, GEN *ap, GEN *bp)
173 : {
174 8231 : *ap = addii(*ap, *bp);
175 8231 : *bp = negi(*bp);
176 8231 : return mkmat2(gel(Q,1),
177 8231 : mkcol2(subii(gcoeff(Q,1,1), gcoeff(Q,1,2)),
178 8231 : subii(gcoeff(Q,2,1), gcoeff(Q,2,2))));
179 : }
180 :
181 : static GEN
182 197131 : FIXUP1(GEN M, GEN a, GEN b, long m, long t, GEN *ap, GEN *bp)
183 : {
184 197131 : GEN Q = gel(M,1), a0 = gel(M,2), b0 = gel(M,3);
185 197131 : GEN q, am = remi2n(a, m), bm = remi2n(b, m);
186 197131 : if (signdet(Q)==-1)
187 : {
188 129019 : *ap = subii(mulii(bm, gcoeff(Q,1,2)),mulii(am, gcoeff(Q,2,2)));
189 129019 : *bp = subii(mulii(am, gcoeff(Q,2,1)),mulii(bm, gcoeff(Q,1,1)));
190 129019 : *ap = addii(*ap, shifti(addii(a0, gcoeff(Q,2,2)), m));
191 129019 : *bp = addii(*bp, shifti(subii(b0, gcoeff(Q,2,1)), m));
192 129019 : if (signe(*bp) >= 0)
193 120696 : return Q;
194 8323 : if (expi(addii(*ap,*bp)) >= m+t)
195 8231 : return mulT(Q, ap, bp);
196 92 : q = lastq(Q);
197 92 : Q = mulqi(Q, q, ap, bp);
198 92 : if (cmpiu(q, 2)>=0)
199 80 : return mulqab(Q, subiu(q,1), ap, bp);
200 : else
201 12 : return mulqi(Q, lastq(Q), ap, bp);
202 : }
203 : else
204 : {
205 68112 : *ap = subii(mulii(am, gcoeff(Q,2,2)),mulii(bm, gcoeff(Q,1,2)));
206 68112 : *bp = subii(mulii(bm, gcoeff(Q,1,1)),mulii(am, gcoeff(Q,2,1)));
207 68112 : *ap = addii(*ap, shifti(subii(a0, gcoeff(Q,2,2)), m));
208 68112 : *bp = addii(*bp, shifti(addii(b0, gcoeff(Q,2,1)), m));
209 68112 : if (expi(*ap) >= m+t)
210 66755 : return FIXUP0(Q, ap, bp, m+t);
211 : else
212 1357 : return signe(gcoeff(Q,1,2))==0? Q: mulqi(Q, lastq(Q), ap, bp);
213 : }
214 : }
215 :
216 : static long
217 25593688 : magic_threshold(GEN a)
218 25593688 : { return (3+uexpi(a))>>1; }
219 :
220 : static GEN
221 16867752 : HGCD_basecase(GEN y, GEN x)
222 : {
223 16867752 : pari_sp av = avma;
224 : GEN d, d1, q, r;
225 : GEN u, u1, v, v1;
226 : ulong xu, xu1, xv, xv1; /* Lehmer stage recurrence matrix */
227 : int lhmres; /* Lehmer stage return value */
228 :
229 16867752 : long m = magic_threshold(y);
230 :
231 : /* There is no special case for single-word numbers since this is
232 : * mainly meant to be used with large moduli. */
233 16867752 : if (cmpii(y,x) <= 0)
234 : {
235 107070 : d = x; d1 = y;
236 107070 : u = gen_1; u1 = gen_0;
237 107070 : v = gen_0; v1 = gen_1;
238 : } else
239 : {
240 16760682 : d = y; d1 = x;
241 16760682 : u = gen_0; u1 = gen_1;
242 16760682 : v = gen_1; v1 = gen_0;
243 : }
244 36879060 : while (lgefint(d) > 3 && expi(d1) >= m + BITS_IN_LONG + 1)
245 : {
246 : /* do a Lehmer-Jebelean round */
247 20343912 : lhmres = lgcdii((ulong *)d, (ulong *)d1, &xu, &xu1, &xv, &xv1, 0);
248 :
249 20343912 : if (lhmres)
250 : {
251 19277224 : if (lhmres == 1 || lhmres == -1)
252 : {
253 462233 : if (xv1 == 1)
254 : {
255 395738 : r = subii(d,d1); d = d1; d1 = r;
256 395738 : r = addii(u,u1); u = u1; u1 = r;
257 395738 : r = addii(v,v1); v = v1; v1 = r;
258 : }
259 : else
260 : {
261 66495 : r = subii(d, mului(xv1,d1)); d = d1; d1 = r;
262 66495 : r = addii(u, mului(xv1,u1)); u = u1; u1 = r;
263 66495 : r = addii(v, mului(xv1,v1)); v = v1; v1 = r;
264 : }
265 : }
266 : else
267 : {
268 18814991 : r = subii(muliu(d,xu), muliu(d1,xv));
269 18814991 : d1 = subii(muliu(d,xu1), muliu(d1,xv1)); d = r;
270 18814991 : r = addii(muliu(u,xu), muliu(u1,xv));
271 18814991 : u1 = addii(muliu(u,xu1), muliu(u1,xv1)); u = r;
272 18814991 : r = addii(muliu(v,xu), muliu(v1,xv));
273 18814991 : v1 = addii(muliu(v,xu1), muliu(v1,xv1)); v = r;
274 18814991 : if (lhmres&1) togglesign(d); else togglesign(d1);
275 : }
276 : } /* lhmres != 0 */
277 20343912 : if (expi(d1) < m) break;
278 :
279 20011308 : if (lhmres <= 0 && signe(d1))
280 : {
281 1121162 : q = dvmdii(d,d1,&r);
282 1121162 : d = d1; d1 = r;
283 1121162 : r = addii(u, mulii(q,u1)); u = u1; u1 = r;
284 1121162 : r = addii(v, mulii(q,v1)); v = v1; v1 = r;
285 : }
286 20011308 : if (gc_needed(av,1))
287 : {
288 0 : if(DEBUGMEM>1) pari_warn(warnmem,"ratlift");
289 0 : (void)gc_all(av, 6, &d, &d1, &u, &u1, &v, &v1);
290 : }
291 : }
292 93781621 : while (expi(d1) >= m)
293 : {
294 76913869 : GEN r, q = dvmdii(d,d1, &r);
295 76913869 : d = d1; d1 = r; swap(u,u1); swap(v,v1);
296 76913869 : u1 = addii(mulii(u, q), u1);
297 76913869 : v1 = addii(mulii(v, q), v1);
298 : }
299 16867752 : return gc_GEN(av, mkvec3(mkmat22(u1,u,v1,v), d, d1));
300 : }
301 :
302 : static GEN HGCD(GEN x, GEN y);
303 :
304 : /*
305 : Based on
306 : Klaus Thull and Chee K. Yap,
307 : A unified approach to HGCD algorithms for polynomials andintegers,
308 : 1990, Manuscript.
309 : URL: http://cs.nyu.edu/cs/faculty/yap/papers.
310 : */
311 :
312 : static GEN
313 128790 : HGCD_split(GEN a, GEN b)
314 : {
315 128790 : pari_sp av = avma;
316 128790 : long m = magic_threshold(a), t, l, k, tp;
317 : GEN a0, b0, ap, bp, c, d, c0, d0, cp, dp, R, S, T, q, r;
318 128790 : if (signe(b) < 0 || cmpii(a,b)<0) pari_err_BUG("HGCD_split");
319 128790 : if (expi(b) < m)
320 552 : return gc_GEN(av, mkvec3(matid2(), a, b));
321 128238 : a0 = addiu(shifti(a, -m), 1);
322 128238 : if (cmpiu(a0,7) <= 0)
323 : {
324 0 : R = FIXUP0(matid2(), &a, &b, m);
325 0 : return gc_GEN(av, mkvec3(R, a, b));
326 : }
327 128238 : b0 = shifti(b,-m);
328 128238 : t = magic_threshold(a0);
329 128238 : R = FIXUP1(HGCD(a0,b0),a, b, m, t, &ap, &bp);
330 128238 : if (expi(bp) < m)
331 59324 : return gc_GEN(av, mkvec3(R, ap, bp));
332 68914 : q = dvmdii(ap, bp, &r);
333 68914 : c = bp; d = r;
334 68914 : if (cmpiu(shifti(c,-m),6) <= 0)
335 : {
336 21 : R = FIXUP0(mulq(R, q), &c, &d, m);
337 21 : return gc_GEN(av, mkvec3(R, c, d));
338 : }
339 68893 : l = uexpi(c);
340 68893 : k = 2*m-l-1; if (k<0) pari_err_BUG("halfgcd");
341 68893 : c0 = addiu(shifti(c, -k), 1); if (cmpiu(c0,8)<0) pari_err_BUG("halfgcd");
342 68893 : d0 = shifti(d, -k);
343 68893 : tp = magic_threshold(c0);
344 68893 : S = FIXUP1(HGCD(c0,d0), c, d, k, tp, &cp, &dp);
345 68893 : if (!(expi(cp)>=m+1 && m+1 > expi(dp))) pari_err_BUG("halfgcd");
346 68893 : T = FIXUP0(ZM2_mul(mulq(R, q), S), &cp, &dp, m);
347 68893 : return gc_GEN(av, mkvec3(T, cp, dp));
348 : }
349 :
350 : static GEN
351 16996542 : HGCD(GEN x, GEN y)
352 : {
353 16996542 : if (lgefint(y)-2 < HALFGCD_LIMIT)
354 16867752 : return HGCD_basecase(x, y);
355 : else
356 128790 : return HGCD_split(x, y);
357 : }
358 :
359 : static GEN
360 32144388 : HGCD0(GEN x, GEN y)
361 : {
362 32144388 : if (signe(y) >= 0 && cmpii(x, y) >= 0)
363 16792957 : return HGCD(x, y);
364 15351431 : if (cmpii(x, y) < 0)
365 : {
366 12651449 : GEN M = HGCD0(y, x), Q = gel(M,1);
367 12651449 : return mkvec3(mkmat22(gcoeff(Q,2,1),gcoeff(Q,2,2),gcoeff(Q,1,1),gcoeff(Q,1,2)),
368 12651449 : gel(M,2),gel(M,3));
369 : } /* Now y <= x*/
370 2699982 : if (signe(x) <= 0)
371 : { /* y <= x <=0 */
372 6454 : GEN M = HGCD(negi(y), negi(x)), Q = gel(M,1);
373 6454 : return mkvec3(mkmat22(negi(gcoeff(Q,2,1)),negi(gcoeff(Q,2,2)),
374 6454 : negi(gcoeff(Q,1,1)),negi(gcoeff(Q,1,2))),
375 6454 : gel(M,2),gel(M,3));
376 : }
377 : else /* y <= 0 <=x */
378 : {
379 2693528 : GEN M = HGCD0(x, negi(y)), Q = gel(M,1);
380 2693528 : return mkvec3(mkmat22(gcoeff(Q,1,1),gcoeff(Q,1,2),negi(gcoeff(Q,2,1)),negi(gcoeff(Q,2,2))),
381 2693528 : gel(M,2),gel(M,3));
382 : }
383 : }
384 :
385 : GEN
386 7428347 : halfgcdii(GEN A, GEN B)
387 : {
388 7428347 : pari_sp av = avma;
389 7428347 : GEN M, Q, a, b, m = abscmpii(A, B)>0 ? A: B;
390 7428347 : M = HGCD0(A,B); Q = gel(M,1); a = gel(M,2); b = gel(M,3);
391 12168738 : while (signe(b) && abscmpii(sqri(b), m) >= 0)
392 : {
393 4740391 : GEN r, q = dvmdii(a, b, &r);
394 4740391 : a = b; b = r;
395 4740391 : Q = mulq(Q, q);
396 : }
397 7428347 : return gc_GEN(av, mkvec2(ZM_inv2(Q),mkcol2(a,b)));
398 : }
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