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1.2 noro 1: /*
2: * Copyright (c) 1994-2000 FUJITSU LABORATORIES LIMITED
3: * All rights reserved.
4: *
5: * FUJITSU LABORATORIES LIMITED ("FLL") hereby grants you a limited,
6: * non-exclusive and royalty-free license to use, copy, modify and
7: * redistribute, solely for non-commercial and non-profit purposes, the
8: * computer program, "Risa/Asir" ("SOFTWARE"), subject to the terms and
9: * conditions of this Agreement. For the avoidance of doubt, you acquire
10: * only a limited right to use the SOFTWARE hereunder, and FLL or any
11: * third party developer retains all rights, including but not limited to
12: * copyrights, in and to the SOFTWARE.
13: *
14: * (1) FLL does not grant you a license in any way for commercial
15: * purposes. You may use the SOFTWARE only for non-commercial and
16: * non-profit purposes only, such as academic, research and internal
17: * business use.
18: * (2) The SOFTWARE is protected by the Copyright Law of Japan and
19: * international copyright treaties. If you make copies of the SOFTWARE,
20: * with or without modification, as permitted hereunder, you shall affix
21: * to all such copies of the SOFTWARE the above copyright notice.
22: * (3) An explicit reference to this SOFTWARE and its copyright owner
23: * shall be made on your publication or presentation in any form of the
24: * results obtained by use of the SOFTWARE.
25: * (4) In the event that you modify the SOFTWARE, you shall notify FLL by
1.3 noro 26: * e-mail at risa-admin@sec.flab.fujitsu.co.jp of the detailed specification
1.2 noro 27: * for such modification or the source code of the modified part of the
28: * SOFTWARE.
29: *
30: * THE SOFTWARE IS PROVIDED AS IS WITHOUT ANY WARRANTY OF ANY KIND. FLL
31: * MAKES ABSOLUTELY NO WARRANTIES, EXPRESSED, IMPLIED OR STATUTORY, AND
32: * EXPRESSLY DISCLAIMS ANY IMPLIED WARRANTY OF MERCHANTABILITY, FITNESS
33: * FOR A PARTICULAR PURPOSE OR NONINFRINGEMENT OF THIRD PARTIES'
34: * RIGHTS. NO FLL DEALER, AGENT, EMPLOYEES IS AUTHORIZED TO MAKE ANY
35: * MODIFICATIONS, EXTENSIONS, OR ADDITIONS TO THIS WARRANTY.
36: * UNDER NO CIRCUMSTANCES AND UNDER NO LEGAL THEORY, TORT, CONTRACT,
37: * OR OTHERWISE, SHALL FLL BE LIABLE TO YOU OR ANY OTHER PERSON FOR ANY
38: * DIRECT, INDIRECT, SPECIAL, INCIDENTAL, PUNITIVE OR CONSEQUENTIAL
39: * DAMAGES OF ANY CHARACTER, INCLUDING, WITHOUT LIMITATION, DAMAGES
40: * ARISING OUT OF OR RELATING TO THE SOFTWARE OR THIS AGREEMENT, DAMAGES
41: * FOR LOSS OF GOODWILL, WORK STOPPAGE, OR LOSS OF DATA, OR FOR ANY
42: * DAMAGES, EVEN IF FLL SHALL HAVE BEEN INFORMED OF THE POSSIBILITY OF
43: * SUCH DAMAGES, OR FOR ANY CLAIM BY ANY OTHER PARTY. EVEN IF A PART
44: * OF THE SOFTWARE HAS BEEN DEVELOPED BY A THIRD PARTY, THE THIRD PARTY
45: * DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE,
46: * PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE.
47: *
1.9 ! fujimoto 48: * $OpenXM: OpenXM_contrib2/asir2000/engine/H.c,v 1.8 2013/11/29 08:21:29 noro Exp $
1.2 noro 49: */
1.1 noro 50: #include "ca.h"
51: #include "inline.h"
52: #include "base.h"
53: #include <math.h>
54:
55: #if 1
56: #define Mulum mulum
57: #define Divum divum
58: #define Mulsum mulsum
59: #define Gcdum gcdum
60: #endif
61:
62: #define FCTR 0
63: #define SQFR 1
64: #define DDD 2
65: #define NEWDDD 3
66:
67: LUM LUMALLOC();
68:
1.6 noro 69: void berle(int index,int count,P f,ML *listp)
1.1 noro 70: {
71: UM wf,wf1,wf2,wfs,gcd;
72: ML flist;
73: int fn,fn1,fm,m,n,fhd;
74: register int i,j,inv,hd,*ptr,*ptr1;
75:
76: n = UDEG(f);
77: wf = W_UMALLOC(n); wf1 = W_UMALLOC(n); wf2 = W_UMALLOC(n);
78: wfs = W_UMALLOC(n); gcd = W_UMALLOC(n);
79: for ( j = 0, fn = n + 1; (j < count) && (fn > 1); ) {
80: m = sprime[index++];
81: if ( !rem(NM((Q)UCOEF(f)),m) )
82: continue;
83: ptoum(m,f,wf); cpyum(wf,wf1);
84: diffum(m,wf1,wf2); gcdum(m,wf1,wf2,gcd);
85: if ( DEG(gcd) > 0 )
86: continue;
87: hd = COEF(wf)[n]; inv = invm(hd,m);
88: for ( i = n, ptr = COEF(wf); i >= 0; i-- )
89: ptr[i] = ( ptr[i] * inv ) % m;
90: fn1 = berlecnt(m,wf);
91: if ( fn1 < fn ) {
92: fn = fn1; fm = m; fhd = hd;
93: for ( i = n, ptr = COEF(wf), ptr1 = COEF(wfs); i >= 0; i-- )
94: ptr1[i] = ptr[i];
95: }
96: j++;
97: }
98: DEG(wfs) = n;
99: *listp = flist = MLALLOC(fn); flist->n = fn; flist->mod = fm;
100: /* berlemain(fm,wfs,(UM *)flist->c); */
101: if ( fm == 2 )
102: berlemain(fm,wfs,(UM *)flist->c);
103: else
104: newddd(fm,wfs,(UM *)flist->c);
105: for ( i = DEG((UM)(flist->c[0])),
106: ptr = COEF((UM)(flist->c[0])),
107: hd = fhd, m = fm; i >= 0; i-- )
108: ptr[i] = ( ptr[i] * hd ) % m;
109: }
110:
1.6 noro 111: int berlecnt(int mod,UM f)
1.1 noro 112: {
113: register int i,j,**c;
114: int d,dr,n;
115: UM w,q;
116: int **almat();
117:
118: n = DEG(f); c = almat(n,n);
119: w = W_UMALLOC(mod + n); q = W_UMALLOC(mod + n);
120: for ( i = 1; ( d = ( mod * i ) ) < n; i++ )
121: c[d][i - 1] = 1;
122: DEG(w) = d; COEF(w)[d] = 1;
123: for ( j = d - 1; j >= 0; j-- )
124: COEF(w)[j] = 0;
125: for ( ; ( i < n ) && ( ( dr = divum(mod,w,f,q) ) != -1 ); i++ ) {
126: for ( j = dr; j >= 0; j-- )
127: COEF(w)[j + mod] = c[j][i - 1] = COEF(w)[j];
128: for ( j = mod - 1; j >= 0; j-- )
129: COEF(w)[j] = 0;
130: DEG(w) = dr + mod;
131: }
132: for ( i = 1; i < n; i++ )
133: c[i][i - 1] = ( c[i][i - 1] + mod - 1 ) % mod;
134: return berlecntmain(mod,n,n-1,c);
135: }
136:
137: /* XXX berlecntmain should not be used for large mod */
138:
1.6 noro 139: int berlecntmain(int mod,int n,int m,int **c)
1.1 noro 140: {
141: register int *p1,*p2,i,j,k,l,a;
142: int *tmp,inv;
143: int cfs;
144:
145: for ( cfs = 1, j = k = 0; j < m; j++ ) {
146: for ( i = k; ( n > i ) && ( c[i][j] == 0 ); i++ );
147: if ( i == n ) {
148: cfs++; continue;
149: }
150: if ( i != k ) {
151: tmp = c[i]; c[i] = c[k]; c[k] = tmp;
152: }
153: p1 = c[k]; inv = invm((p1[j] + mod) % mod,mod);
154: for ( l = j; l < m; l++ )
155: p1[l] = ( p1[l] * inv ) % mod;
156: for ( i = k + 1; i < n; c[i][j] = 0, i++ )
157: if ( i != k && ( a = -c[i][j] ) )
158: for ( l = j + 1, p2 = c[i]; l < m; l++ )
159: p2[l] = (a*p1[l] + p2[l]) % mod;
160: k++;
161: }
162: return ( cfs );
163: }
164:
1.6 noro 165: UM *berlemain(int mod,UM f,UM *fp)
1.1 noro 166: {
167: UM wg,ws,wf,f0,gcd,q;
168: int n;
169: register int i;
170:
171: n = DEG(f); wg = W_UMALLOC(n); mini(mod,f,wg);
172: if ( DEG(wg) <= 0 ) {
173: f0 = UMALLOC(n); cpyum(f,f0); *fp++ = f0;
174: return ( fp );
175: }
176: f0 = W_UMALLOC(n); cpyum(f,f0);
177: ws = W_UMALLOC(n); wf = W_UMALLOC(n);
178: q = W_UMALLOC(n); gcd = W_UMALLOC(n);
179: for ( i = 0; i < mod; i++ ) {
180: cpyum(f0,wf); cpyum(wg,ws);
181: COEF(ws)[0] = ( COEF(ws)[0] + mod - i ) % mod;
182: gcdum(mod,wf,ws,gcd);
183: if ( DEG(gcd) > 0 ) {
184: if ( DEG(gcd) < n ) {
185: divum(mod,f0,gcd,q); f0 = q; fp = berlemain(mod,gcd,fp);
186: }
187: break;
188: }
189: }
190: fp = berlemain(mod,f0,fp);
191: return ( fp );
192: }
193:
1.6 noro 194: void hensel(int index,int count,P f,ML *listp)
1.1 noro 195: {
196: register int i,j;
197: int q,n,bound;
198: int *p;
199: int **pp;
200: ML blist,clist,bqlist,cqlist,rlist;
201: UM *b;
202: LUM fl,tl;
203: LUM *l;
204:
205: if ( UDEG(f) == 1 ) {
206: *listp = blist = MLALLOC(1); blist->n = 1; blist->c[0] = 0;
207: return;
208: }
209: berle(index,count,f,&blist);
210: if ( blist->n == 1 ) {
211: *listp = blist = MLALLOC(1); blist->n = 1; blist->c[0] = 0;
212: return;
213: }
214: gcdgen(f,blist,&clist); henprep(f,blist,clist,&bqlist,&cqlist);
215: n = bqlist->n; q = bqlist->mod;
216: bqlist->bound = cqlist->bound = bound = mignotte(q,f);
217: if ( bound == 1 ) {
218: *listp = rlist = MLALLOC(n);
219: rlist->n = n; rlist->mod = q; rlist->bound = bound;
220: for ( i = 0, b = (UM *)bqlist->c, l = (LUM *)rlist->c; i < n; i++ ) {
221: tl = LUMALLOC(DEG(b[i]),1); l[i] = tl; p = COEF(b[i]);
222: for ( j = 0, pp = COEF(tl); j <= DEG(tl); j++ )
223: pp[j][0] = p[j];
224: }
225: } else {
226: W_LUMALLOC((int)UDEG(f),bound,fl);
227: ptolum(q,bound,f,fl); henmain(fl,bqlist,cqlist,listp);
228: }
229: }
230:
1.6 noro 231: void hensel2(int index,int count,P f,ML *listp)
1.4 noro 232: {
233: register int i,j;
234: int mod,q,n,bound,dx;
235: ML blist,clist,bqlist,cqlist,rlist;
236: UM fm,qfm,gm,qgm,hm,qhm,qam,qbm,w;
237: UM *b;
238: LUM fl,tl;
1.6 noro 239: int k;
1.4 noro 240:
241: dx = UDEG(f);
242: if ( dx == 1 ) {
243: *listp = blist = MLALLOC(1); blist->n = 1; blist->c[0] = 0;
244: return;
245: }
246: berle(index,count,f,&blist);
247: n = blist->n;
248: mod = blist->mod;
249:
250: if ( n == 1 ) {
251: *listp = blist = MLALLOC(1); blist->n = 1; blist->c[0] = 0;
252: return;
253: }
254:
255: /* find k s.t. mod^k <= 2^27 < mod^(k+1); set q = mod^k */
256: for ( k = 1, q = mod; q <= ((1<<27)/mod); q *= mod, k++ );
257:
258: /* mignotte bound */
259: bound = mignotte(q,f);
260:
261: *listp = rlist = MLALLOC(n);
262: rlist->n = n;
263: rlist->mod = q;
264: rlist->bound = bound;
265:
266: if ( bound == 1 ) {
267: gcdgen(f,blist,&clist);
268: henprep(f,blist,clist,&bqlist,&cqlist);
269:
270: for ( i = 0, b = (UM *)bqlist->c; i < n; i++ ) {
271: COEF(rlist)[i] = tl = LUMALLOC(DEG(b[i]),1);
272: for ( j = 0; j <= DEG(tl); j++ )
273: COEF(tl)[j][0] = COEF(b[i])[j];
274: COEF(rlist)[i] = tl;
275: }
276: } else {
277: /* fl = f mod q */
278: fl = LUMALLOC(dx,bound);
279: ptolum(q,bound,f,fl);
280: /* fm = f mod mod */
281: fm = W_UMALLOC(dx);
282: ptoum(mod,f,fm);
283: /* fm = f mod q */
284: qfm = W_UMALLOC(dx);
285: ptoum(q,f,qfm);
286:
287: gm = W_UMALLOC(dx); qgm = W_UMALLOC(dx);
288: hm = W_UMALLOC(dx); qhm = W_UMALLOC(dx);
289: qam = W_UMALLOC(dx); qbm = W_UMALLOC(dx);
290: w = W_UMALLOC(dx);
291: for ( i = 0; i < n-1; i++ ) {
292: cpyum(COEF(blist)[i],gm);
293: cpyum(fm,w);
294: divum(mod,w,gm,hm);
295:
296: /* find am,bm s.t. qam*qgm+qbm*qhm=1 mod q, qgm=gm mod mod, qhm=hm mod mod */
297: henprep2(mod,q,k,qfm,gm,hm,qgm,qhm,qam,qbm);
298:
299: henmain2(fl,qgm,qhm,qam,qbm,q,bound,&tl);
300: rlist->c[i] = (pointer)tl;
301: cpyum(hm,fm);
302: cpyum(qhm,qfm);
303: }
304: rlist->c[i] = fl;
305: }
306: }
307:
308: /*
309: f = g0*h0 mod m -> f = gk*hk mod m^(bound), f is replaced by hk
310: */
311:
1.6 noro 312: void henmain2(LUM f,UM g0,UM h0,UM a0,UM b0,int m,int bound,LUM *gp)
1.4 noro 313: {
314: int n,dg,dh,i,k,j,dg1,dh1;
1.6 noro 315: UM wu,wr,ws,wt,q,wh1,wg1,wc,wd,we,wz;
1.4 noro 316: LUM wb0,wb1,wb2,fk,gk,hk;
317:
318: n = DEG(f); dg = DEG(g0); dh = DEG(h0);
319:
320: W_LUMALLOC(n,bound,wb0);
321: W_LUMALLOC(n,bound,wb1);
322: W_LUMALLOC(n,bound,wb2);
323:
324: wt = W_UMALLOC(2*n); ws = W_UMALLOC(2*n);
325: wr = W_UMALLOC(2*n); wu = W_UMALLOC(2*n);
326: q = W_UMALLOC(2*n);
327: wh1 = W_UMALLOC(2*n); wg1 = W_UMALLOC(2*n);
328:
329: /* gk = g0 */
330: gk = LUMALLOC(n,bound);
331: DEG(gk) = dg;
332: for ( i = 0; i <= dg; i++ )
333: COEF(gk)[i][0] = COEF(g0)[i];
334:
335: /* hk = h0 */
336: W_LUMALLOC(n,bound,hk);
337: DEG(hk) = dh;
338: for ( i = 0; i <= dh; i++ )
339: COEF(hk)[i][0] = COEF(h0)[i];
340:
341: /* fk = gk*hk */
342: W_LUMALLOC(n,bound,fk);
343: mullum(m,bound,gk,hk,fk);
344:
345: wc = W_UMALLOC(2*n); wd = W_UMALLOC(2*n);
346: we = W_UMALLOC(2*n); wz = W_UMALLOC(2*n);
347:
348: #if 0
349: mulum(m,a0,g0,wc);
350: mulum(m,b0,h0,wd);
351: addum(m,wc,wd,wz);
352: if ( DEG(wz) != 0 || COEF(wz)[0] != 1 )
353: error("henmain2 : cannot happen(extgcd)");
354: #endif
355:
1.5 noro 356: #if 1
1.4 noro 357: fprintf(stderr,"bound=%d\n",bound);
1.5 noro 358: #endif
1.4 noro 359: for ( k = 1; k < bound; k++ ) {
1.5 noro 360: #if 1
1.4 noro 361: fprintf(stderr,".");
1.5 noro 362: #endif
1.8 noro 363:
1.9 ! fujimoto 364: #if defined(VISUAL) || defined(__MINGW32__) || defined(__MINGW64__)
1.8 noro 365: check_intr();
366: #endif
1.4 noro 367: /* at this point, f = gk*hk mod y^k */
368:
369: #if 0
370: for ( j = 0; j < k; j++ )
371: for ( i = 0; i <= n; i++ )
372: if ( COEF(f)[i][j] != COEF(f)[i][j] )
373: error("henmain2 : cannot happen(f=fk)");
374: #endif
375:
376: /* wt = (f-gk*hk)/y^k */
377: for ( i = 0; i <= n; i++ )
378: COEF(ws)[i] = COEF(f)[i][k];
379: degum(ws,n);
380: for ( i = 0; i <= n; i++ )
381: COEF(wu)[i] = COEF(fk)[i][k];
382: degum(wu,n);
383: subum(m,ws,wu,wt);
384:
385: /* compute wf1,wg1 s.t. wh1*g0+wg1*h0 = wt */
386: mulum(m,a0,wt,wh1); DEG(wh1) = divum(m,wh1,h0,q);
387: mulum(m,wh1,g0,wc); subum(m,wt,wc,wd); DEG(wd) = divum(m,wd,h0,wg1);
388:
389: /* check */
390: #if 0
391: if ( DEG(wd) >= 0 || DEG(wg1) > dg )
392: error("henmain2 : cannot happen(adj)");
393:
394: mulum(m,wg1,h0,wc); mulum(m,wh1,g0,wd); addum(m,wc,wd,we);
395: subum(m,we,wt,wz);
396: if ( DEG(wz) >= 0 )
397: error("henmain2 : cannot happen(coef)");
398: #endif
399:
400: /* fk += ((wg1*hk+wh1*gk)*y^k+wg1*wh1*y^(2*k) mod m^bound */
401:
402: /* wb0 = wh1*y^k */
403: clearlum(n,bound,wb0);
404: DEG(wb0) = dh1 = DEG(wh1);
405: for ( i = 0; i <= dh1; i++ )
406: COEF(wb0)[i][k] = COEF(wh1)[i];
407:
408: /* wb2 = gk*wb0 mod y^bound */
409: clearlum(n,bound,wb2);
410: mullum(m,bound,gk,wb0,wb2);
411:
412: /* fk += wb2 */
413: addtolum(m,bound,wb2,fk);
414:
415: /* wb1 = wg1*y^k */
416: clearlum(n,bound,wb1);
417: DEG(wb1) = dg1 = DEG(wg1);
418: for ( i = 0; i <= n; i++ )
419: COEF(wb1)[i][k] = COEF(wg1)[i];
420:
421: /* wb2 = hk*wb1 mod y^bound */
422: clearlum(n,bound,wb2);
423: mullum(m,bound,hk,wb1,wb2);
424:
425: /* fk += wb2 */
426: addtolum(m,bound,wb2,fk);
427:
428: /* fk += wg1*wh1*y^(2*k) mod y^bound) */
429: if ( 2*k < bound ) {
430: clearlum(n,bound,wb2);
431: mullum(m,bound,wb0,wb1,wb2);
432: addtolum(m,bound,wb2,fk);
433: }
434:
435: /* gk += wg1*y^k, hk += wh1*y^k */
436: for ( i = 0; i <= DEG(wg1); i++ )
437: COEF(gk)[i][k] = COEF(wg1)[i];
438: for ( i = 0; i <= DEG(wh1); i++ )
439: COEF(hk)[i][k] = COEF(wh1)[i];
440: }
1.5 noro 441: #if 1
1.4 noro 442: fprintf(stderr,"\n");
1.5 noro 443: #endif
1.4 noro 444: *gp = gk;
445: clearlum(n,bound,f);
446: DEG(f) = dh;
447: for ( i = 0; i <= dh; i++ )
448: for ( j = 0; j < bound; j++ )
449: COEF(f)[i][j] = COEF(hk)[i][j];
450: }
451:
1.6 noro 452: void clearlum(int n,int bound,LUM f)
1.4 noro 453: {
454: int i;
455:
456: for ( i = 0; i <= n; i++ )
457: bzero(COEF(f)[i],bound*sizeof(int));
458: }
459:
460: /* g += f */
461:
1.6 noro 462: void addtolum(int m,int bound,LUM f,LUM g)
1.4 noro 463: {
464: int n,i;
465:
466: n = DEG(f);
467: for ( i = 0; i <= n; i++ )
468: addpadic(m,bound,COEF(f)[i],COEF(g)[i]);
469: }
470:
1.6 noro 471: void hsq(int index,int count,P f,int *nindex,DCP *dcp)
1.1 noro 472: {
473: register int i,j,k;
474: register int **pp,**fpp;
475: register int *px,*py;
476: int **wpp;
477: int n,dr,tmp,m,b,e,np,dt;
478: LUM fpa,wb0,wb1,lcpa,tpa,tlum;
479: struct oDUM *dct;
480: UM wt,wq0,wq,wr,wm,wm0,wa,ws,wb;
481: LUM *llist,*ll;
482: UM *dlist,*l,*c;
483: ML list,fp,cfp;
484: DCP dc;
485:
486: sqfrum(index,count,f,nindex,&dct,&fp);
487: np = fp->n; m = fp->mod;
488: if ( ( np == 1 ) && ( dct[0].n == 1 ) ) {
489: NEWDC(dc); DEG(dc) = ONE; COEF(dc) = f; NEXT(dc) = 0; *dcp = dc;
490: return;
491: }
492: for ( i = 0, dt = 0; i < np; i++ )
493: dt = MAX(DEG(dct[i].f),dt);
494: b = mig(m,dt,f); fp->bound = b;
495: if ( np == 1 ) {
496: nthrootchk(f,dct,fp,dcp);
497: return;
498: }
499: list = W_MLALLOC(np); list->n = np; list->mod = m; list->bound = 1;
500: for ( i = 0, ll = (LUM *)list->c; i < np; i++ ) {
501: W_LUMALLOC(DEG(dct[i].f),b,ll[i]);
502: for ( j = 0, px = COEF(dct[i].f), pp = COEF(ll[i]);
503: j <= DEG(ll[i]); j++ )
504: pp[j][0] = px[j];
505: }
506: dtestsql(f,list,dct,&dc);
507: if ( dc ) {
508: *dcp = dc;
509: return;
510: }
511: n = UDEG(f);
512: W_LUMALLOC(n,b,fpa); W_LUMALLOC(0,b,lcpa);
513: W_LUMALLOC(n,b,wb0); W_LUMALLOC(n,b,wb1);
514: W_LUMALLOC(n,b,tpa);
515: wt = W_UMALLOC(n); ws = W_UMALLOC(n);
516: wr = W_UMALLOC(n);
517: wq = W_UMALLOC(2*n); wq0 = W_UMALLOC(n);
518: wm = W_UMALLOC(2*n); wm0 = W_UMALLOC(2*n);
519: wa = W_UMALLOC(2*n);
520: ptolum(m,b,f,fpa); DEG(lcpa) = 0;
521: for ( i = 0, pp = COEF(lcpa), fpp = COEF(fpa); i < b; i++ )
522: pp[0][i] = fpp[n][i];
523: gcdgen(f,fp,&cfp);
524: llist = (LUM *) ALLOCA(np*sizeof(LUM));
525: dlist = (UM *) ALLOCA(np*sizeof(UM));
526: l = (UM *)fp->c; c = (UM *)cfp->c;
527: for ( i = 0; i < np; i++ ) {
528: W_LUMALLOC(DEG(l[i]),b,llist[i]);
529: for ( j = DEG(l[i]), pp = COEF(llist[i]), px = COEF(l[i]); j >= 0; j-- )
530: pp[j][0] = px[j];
531: if ( ( e = dct[i].n ) != 1 ) {
532: wb = dct[i].f;
533: dlist[i] = W_UMALLOC(DEG(wb)*e); cpyum(l[i],dlist[i]);
534: divum(m,dlist[i],wb,wq); DEG(dlist[i])= DEG(wq);
535: for ( k = 0; k <= DEG(wq); k++ )
536: COEF(dlist[i])[k] = dmb(m,COEF(wq)[k],e,&tmp);
537: }
538: }
539: for ( i = 1; i < b; i++ ) {
540: mullum(m,i+1,lcpa,llist[0],wb0);
541: for ( j = 1; j < np; j++ ) {
542: mullum(m,i+1,llist[j],wb0,wb1);
543: tlum = wb0; wb0 = wb1; wb1 = tlum;
544: }
545: for ( j = n, px = COEF(wt), pp = COEF(fpa), wpp = COEF(wb0);
546: j >= 0; j-- )
547: px[j] = ( pp[j][i] - wpp[j][i] + m ) % m;
548: degum(wt,n);
549: for ( j = n, px = COEF(wq0); j >= 0; j-- )
550: px[j] = 0;
551: for ( j = 1; j < np; j++ ) {
552: mulum(m,wt,c[j],wm); dr = divum(m,wm,l[j],wq);
553: for ( k = DEG(wq), px = COEF(wq0), py = COEF(wq); k >= 0; k-- )
554: px[k] = ( px[k] + py[k] ) % m;
555: for ( k = dr, pp = COEF(llist[j]), px = COEF(wm); k >= 0; k-- )
556: pp[k][i] = px[k];
557: }
558: degum(wq0,n); mulum(m,wq0,l[0],wm);
559: mulum(m,wt,c[0],wm0); addum(m,wm,wm0,wa);
560: for ( j = DEG(wa), pp = COEF(llist[0]), px = COEF(wa); j >= 0; j-- )
561: pp[j][i] = px[j];
562: for ( j = n, px = COEF(wq0); j >= 0; j-- )
563: px[j] = 0;
564: for ( j = 0; j < np; j++ )
565: if ( dct[j].n == 1 )
566: for ( k = 0,
567: pp = COEF(llist[j]),
568: wpp = COEF(((LUM *)list->c)[j]);
569: k <= DEG(llist[j]); k++ )
570: wpp[k][i] = pp[k][i];
571: else {
572: pwrlum(m,i+1,((LUM *)list->c)[j],dct[j].n,tpa);
573: for ( k = 0,
574: pp = COEF(llist[j]),
575: wpp = COEF(tpa);
576: k <= DEG(l[j]); k++ )
577: COEF(wt)[k] = (pp[k][i]-wpp[k][i]+m)%m;
578: degum(wt,DEG(l[j])); dr = divum(m,wt,dlist[j],ws);
579: if ( dr >= 0 ) {
580: *dcp = 0;
581: return;
582: } else
583: for ( k = 0,
584: pp = COEF(((LUM *)list->c)[j]);
585: k <= DEG(ws); k++ )
586: pp[k][i] = COEF(ws)[k];
587: }
588: list->bound = i+1; dtestsql(f,list,dct,&dc);
589: if ( dc ) {
590: *dcp = dc;
591: return;
592: }
593: }
594: *dcp = 0;
595: }
596:
1.6 noro 597: void gcdgen(P f,ML blist,ML *clistp)
1.1 noro 598: {
599: register int i;
600: int n,d,mod,np;
601: UM wf,wm,wx,wy,wu,wv,wa,wb,wg,q,tum;
602: UM *in,*out;
603: ML clist;
604:
605: n = UDEG(f); mod = blist->mod; np = blist->n;
606: d = 2*n;
607: q = W_UMALLOC(d); wf = W_UMALLOC(d);
608: wm = W_UMALLOC(d); wx = W_UMALLOC(d);
609: wy = W_UMALLOC(d); wu = W_UMALLOC(d);
610: wv = W_UMALLOC(d); wg = W_UMALLOC(d);
611: wa = W_UMALLOC(d); wb = W_UMALLOC(d);
612: ptoum(mod,f,wf); DEG(wg) = 0; COEF(wg)[0] = 1;
613: *clistp = clist = MLALLOC(np); clist->mod = mod; clist->n = np;
614: for ( i = 0, in = (UM *)blist->c, out = (UM *)clist->c; i < np; i++ ) {
615: divum(mod,wf,in[i],q); tum = wf; wf = q; q = tum;
616: cpyum(wf,wx); cpyum(in[i],wy);
617: eucum(mod,wx,wy,wa,wb); mulum(mod,wa,wg,wm);
618: DEG(wm) = divum(mod,wm,in[i],q); out[i] = UMALLOC(DEG(wm));
619: cpyum(wm,out[i]); mulum(mod,q,wf,wu);
620: mulum(mod,wg,wb,wv); addum(mod,wu,wv,wg);
621: }
622: }
623:
1.4 noro 624: /* find a,b s.t. qa*qg+qb*qh=1 mod q, qg=g mod mod, qh=h mod mod */
625: /* q = mod^k */
626:
1.6 noro 627: void henprep2(int mod,int q,int k,UM f,UM g,UM h,UM qg,UM qh,UM qa,UM qb)
1.4 noro 628: {
629: int n;
630: UM wg,wh,wa,wb;
631: ML bl,cl,bql,cql;
632: P ff;
633:
634: n = DEG(f);
635: wg = W_UMALLOC(2*n); wh = W_UMALLOC(2*n);
636: wa = W_UMALLOC(2*n); wb = W_UMALLOC(2*n);
637: cpyum(g,wg); cpyum(h,wh);
638:
639: /* wa*g+wb*h = 1 mod mod */
640: eucum(mod,wg,wh,wa,wb);
641:
642: #if 0
643: /* check */
644: wt = W_UMALLOC(2*n); ws = W_UMALLOC(2*n); wu = W_UMALLOC(2*n);
645: mulum(mod,wa,g,wt);
646: mulum(mod,wb,h,ws);
647: addum(mod,wt,ws,wu);
648: if ( DEG(wu) != 0 || COEF(wu)[0] != 1 )
649: error("henprep 1");
650: #endif
651:
652: bl = MLALLOC(2); bl->n = 2; bl->mod = mod; bl->c[0] = g; bl->c[1] = h;
653: cl = MLALLOC(2); cl->n = 2; cl->mod = mod; cl->c[0] = wb; cl->c[1] = wa;
654: umtop(CO->v,f,&ff); /* XXX */
655: henprep(ff,bl,cl,&bql,&cql); /* XXX */
656:
657: cpyum(bql->c[0],qg); cpyum(bql->c[1],qh);
658: cpyum(cql->c[0],qb); cpyum(cql->c[1],qa);
659:
660: #if 0
661: /* check */
662: mulum(q,qa,qg,wt);
663: mulum(q,qb,qh,ws);
664: addum(q,wt,ws,wu);
665: if ( DEG(wu) != 0 || COEF(wu)[0] != 1 )
666: error("henprep 2");
667: #endif
668: }
669:
1.1 noro 670: /*
1.4 noro 671: henprep(f,blist,clist,&bqlist,&cqlist);
1.1 noro 672: */
673:
1.6 noro 674: void henprep(P f,ML blist,ML clist,ML *bqlistp,ML *cqlistp)
1.1 noro 675: {
676: register int i,j,k,*px,*py,*pz;
677: int n,pmax,dr,tmp,p,p1,mod,np,b,q;
678: UM w,wm,wn,wa,wt,wq,wf,quot,tum,*in,*inc,*out,*outc;
679: ML bqlist,cqlist;
680:
681: n = UDEG(f); p = mod = blist->mod; np = blist->n;
682: /* for ( b = 1, q = mod; q <= (unsigned int)(LBASE / (L)mod); q *= mod, b++ ); */
683: for ( b = 1, q = mod; q <= ((1<<27) / mod); q *= mod, b++ );
684: w = W_UMALLOC(n); ptoum(q,f,w);
685: wm = W_UMALLOC(2*n); wn = W_UMALLOC(2*n);
686: wa = W_UMALLOC(2*n); wt = W_UMALLOC(2*n);
687: wq = W_UMALLOC(2*n); wf = W_UMALLOC(2*n);
688: quot = W_UMALLOC(2*n);
689: *bqlistp = bqlist = MLALLOC(np); *cqlistp = cqlist = MLALLOC(np);
690: for ( i = 0; i < n+2; i++ )
691: COEF(wq)[i] = 0;
692: for ( i = 0,
693: in = (UM *)blist->c, inc = (UM *)clist->c,
694: out = (UM *)bqlist->c, outc = (UM *)cqlist->c;
695: i < np; i++ ) {
696: out[i] = C_UMALLOC(n+1); cpyum(in[i],out[i]);
697: outc[i] = C_UMALLOC(n+1); cpyum(inc[i],outc[i]);
698: }
699: for ( pmax = 1, i = b; i > 0; i-- )
700: pmax *= mod;
701: for ( i = 1; i < b; i++, p = p1 ) {
702: cpyum(out[0],wm);
703: for ( j = 1; j < np; j++ ) {
704: mulum(pmax,wm,out[j],wn);
705: tum = wm; wm = wn; wn = tum;
706: }
707: for ( j = n, px = COEF(w), py = COEF(wm), pz = COEF(wt); j >= 0; j-- ) {
708: tmp = ( ( px[j] - py[j] ) / p ) % mod;
709: pz[j] = ( tmp >= 0? tmp : tmp + mod );
710: }
711: degum(wt,n);
712: for ( j = 1; j < np; j++ ) {
713: mulum(mod,wt,inc[j],wm); dr = divum(mod,wm,in[j],quot);
714: for ( k = DEG(quot); k >= 0; k-- )
715: COEF(wq)[k] = ( COEF(wq)[k] + COEF(quot)[k] ) % mod;
716: for ( k = dr, px = COEF(out[j]), py = COEF(wm); k >= 0; k-- )
717: px[k] += p * py[k];
718: }
719: degum(wq,n); mulum(mod,wq,in[0],wm);
720: mulum(mod,wt,inc[0],wn); addum(mod,wm,wn,wa);
721: for ( j = DEG(wa), px = COEF(out[0]), py = COEF(wa); j >= 0; j-- )
722: px[j] += p * py[j];
723: for ( j = n, px = COEF(wq); j >= 0; j-- )
724: px[j] = 0;
725: p1 = p * mod;
726: for ( j = n, px = COEF(wt); j >= 1; j-- )
727: px[j] = 0;
728: px[0] = 1;
729: for ( j = 0; j < np; j++ ) {
730: cpyum(w,wf);
731: for ( k = DEG(wf), px = COEF(wf); k >= 0; k-- )
732: px[k] %= p1;
733: divum(p1,wf,out[j],quot); mulum(p1,outc[j],quot,wm);
734: for ( k = DEG(wm), px = COEF(wt), py = COEF(wm); k >= 0; k-- )
735: px[k] = ( px[k] - py[k] ) % p1;
736: }
737: degum(wt,n);
738: for ( j = DEG(wt), px = COEF(wt); j >= 0; j-- )
739: px[j] = ((tmp=(px[j]/p)%mod)>= 0?tmp:tmp + mod);
740: for ( j = 0; j < np; j++ ) {
741: mulum(mod,wt,outc[j],wm); dr = divum(mod,wm,in[j],quot);
742: for ( k = dr, px = COEF(outc[j]), py = COEF(wm); k >= 0; k-- )
743: px[k] += p * py[k];
744: degum(outc[j],MAX(DEG(outc[j]),dr));
745: }
746: }
747: bqlist->n = cqlist->n = np;
748: bqlist->mod = cqlist->mod = q;
749: }
750:
751: /*
752: henmain(fl,bqlist,cqlist,listp)
753: */
754:
1.6 noro 755: void henmain(LUM f,ML bqlist,ML cqlist,ML *listp)
1.1 noro 756: {
757: register int i,j,k;
758: int *px,*py;
759: int **pp,**pp1;
760: int n,np,mod,bound,dr,tmp;
761: UM wt,wq0,wq,wr,wm,wm0,wa,q;
762: LUM wb0,wb1,tlum;
763: UM *b,*c;
764: LUM *l;
765: ML list;
766:
767: n = DEG(f); np = bqlist->n; mod = bqlist->mod; bound = bqlist->bound;
768: *listp = list = MLALLOC(n);
769: list->n = np; list->mod = mod; list->bound = bound;
770: W_LUMALLOC(n,bound,wb0); W_LUMALLOC(n,bound,wb1);
771: wt = W_UMALLOC(n); wq0 = W_UMALLOC(n); wq = W_UMALLOC(n);
772: wr = W_UMALLOC(n); wm = W_UMALLOC(2*n); wm0 = W_UMALLOC(2*n);
773: wa = W_UMALLOC(2*n); q = W_UMALLOC(2*n);
774: b = (UM *)bqlist->c; c = (UM *)cqlist->c; l = (LUM *)list->c;
775: for ( i = 0; i < np; i++ ) {
776: l[i] = LUMALLOC(DEG(b[i]),bound);
777: for ( j = DEG(b[i]), pp = COEF(l[i]), px = COEF(b[i]); j >= 0; j-- )
778: pp[j][0] = px[j];
779: }
1.5 noro 780: #if 0
1.4 noro 781: fprintf(stderr,"bound=%d\n",bound);
1.5 noro 782: #endif
1.1 noro 783: for ( i = 1; i < bound; i++ ) {
1.5 noro 784: #if 0
1.4 noro 785: fprintf(stderr,".");
1.5 noro 786: #endif
1.9 ! fujimoto 787: #if defined(VISUAL) || defined(__MINGW32__) || defined(__MINGW64__)
1.8 noro 788: check_intr();
789: #endif
1.1 noro 790: mullum(mod,i+1,l[0],l[1],wb0);
791: for ( j = 2; j < np; j++ ) {
792: mullum(mod,i+1,l[j],wb0,wb1);
793: tlum = wb0; wb0 = wb1; wb1 = tlum;
794: }
795: for ( j = n, px = COEF(wt); j >= 0; j-- )
796: px[j] = 0;
797: for ( j = n, pp = COEF(f), pp1 = COEF(wb0); j >= 0; j-- ) {
798: tmp = ( pp[j][i] - pp1[j][i] ) % mod;
799: COEF(wt)[j] = ( tmp < 0 ? tmp + mod : tmp );
800: }
801: degum(wt,n);
802: for ( j = n, px = COEF(wq0); j >= 0; j-- )
803: px[j] = 0;
804: for ( j = 1; j < np; j++ ) {
805: mulum(mod,wt,c[j],wm); dr = divum(mod,wm,b[j],q);
806: for ( k = DEG(q), px = COEF(wq0), py = COEF(q); k >= 0; k-- )
807: px[k] = ( px[k] + py[k] ) % mod;
808: for ( k = dr, pp = COEF(l[j]), px = COEF(wm); k >= 0; k-- )
809: pp[k][i] = px[k];
810: }
811: degum(wq0,n); mulum(mod,wq0,b[0],wm);
812: mulum(mod,wt,c[0],wm0); addum(mod,wm,wm0,wa);
813: for ( j = DEG(wa), pp = COEF(l[0]), px = COEF(wa); j >= 0; j-- )
814: pp[j][i] = px[j];
815: for ( j = n, px = COEF(wq0); j >= 0; j-- )
816: px[j] = 0;
817: }
1.5 noro 818: #if 0
1.4 noro 819: fprintf(stderr,"\n");
1.5 noro 820: #endif
1.1 noro 821: }
822:
1.7 noro 823: /*
824: henmain_incremental(fl,bqlist,cqlist,start)
825: fl = bqlist[0]*... mod q^start
826: */
827:
828: void henmain_incremental(LUM f,LUM *bqlist,ML cqlist,
829: int np, int mod, int start, int bound)
830: {
831: register int i,j,k;
832: int *px,*py;
833: int **pp,**pp1;
834: int n,dr,tmp;
835: UM wt,wq0,wq,wr,wm,wm0,wa,q;
836: LUM wb0,wb1,tlum;
837: UM *b,*c;
838: LUM *l;
839: ML list;
840:
841: n = DEG(f);
842: W_LUMALLOC(n,bound,wb0); W_LUMALLOC(n,bound,wb1);
843: wt = W_UMALLOC(n); wq0 = W_UMALLOC(n); wq = W_UMALLOC(n);
844: wr = W_UMALLOC(n); wm = W_UMALLOC(2*n); wm0 = W_UMALLOC(2*n);
845: wa = W_UMALLOC(2*n); q = W_UMALLOC(2*n);
846: c = (UM *)cqlist->c; l = bqlist;
847: b = (UM *)ALLOCA(n*sizeof(UM));
848: for ( i = 0; i < np; i++ ) {
849: j = DEG(l[i]);
850: b[i] = W_UMALLOC(j);
851: DEG(b[i]) = j;
852: for ( pp = COEF(l[i]), px = COEF(b[i]); j >= 0; j-- )
853: px[j] = pp[j][0];
854: }
855: #if 0
856: fprintf(stderr,"bound=%d\n",bound);
857: #endif
858: for ( i = start; i < bound; i++ ) {
859: #if 0
860: fprintf(stderr,".");
861: #endif
862: mullum(mod,i+1,l[0],l[1],wb0);
863: for ( j = 2; j < np; j++ ) {
864: mullum(mod,i+1,l[j],wb0,wb1);
865: tlum = wb0; wb0 = wb1; wb1 = tlum;
866: }
867: for ( j = n, px = COEF(wt); j >= 0; j-- )
868: px[j] = 0;
869: for ( j = n, pp = COEF(f), pp1 = COEF(wb0); j >= 0; j-- ) {
870: tmp = ( pp[j][i] - pp1[j][i] ) % mod;
871: COEF(wt)[j] = ( tmp < 0 ? tmp + mod : tmp );
872: }
873: degum(wt,n);
874: for ( j = n, px = COEF(wq0); j >= 0; j-- )
875: px[j] = 0;
876: for ( j = 1; j < np; j++ ) {
877: mulum(mod,wt,c[j],wm); dr = divum(mod,wm,b[j],q);
878: for ( k = DEG(q), px = COEF(wq0), py = COEF(q); k >= 0; k-- )
879: px[k] = ( px[k] + py[k] ) % mod;
880: for ( k = dr, pp = COEF(l[j]), px = COEF(wm); k >= 0; k-- )
881: pp[k][i] = px[k];
882: }
883: degum(wq0,n); mulum(mod,wq0,b[0],wm);
884: mulum(mod,wt,c[0],wm0); addum(mod,wm,wm0,wa);
885: for ( j = DEG(wa), pp = COEF(l[0]), px = COEF(wa); j >= 0; j-- )
886: pp[j][i] = px[j];
887: for ( j = n, px = COEF(wq0); j >= 0; j-- )
888: px[j] = 0;
889: }
890: #if 0
891: fprintf(stderr,"\n");
892: #endif
893: }
894:
1.1 noro 895: static double M;
896: static int E;
897:
1.6 noro 898: int mignotte(int q,P f)
1.1 noro 899: {
900: int p;
901: unsigned int *b;
902: N c;
903: DCP dc;
904:
905: for ( dc = DC(f), M = 0, E = 0; dc; dc = NEXT(dc) ) {
906: c = NM((Q)COEF(dc)); p = PL(c); b = BD(c);
907: sqad(b[p-1],(p-1)*BSH);
908: }
909: if (E % 2) M *= 2; M = ceil(sqrt(M)); E /= 2;
910: c = NM((Q)COEF(DC(f))); p = PL(c); M *= ((double)BD(c)[p-1]+1.0); E += (p-1) * BSH;
911: return (int)ceil( (0.31*(E+UDEG(f)+1)+log10((double)M)) / log10((double)q) );
912: }
913:
1.6 noro 914: int mig(int q,int d,P f)
1.1 noro 915: {
916: int p;
917: unsigned int *b;
918: N c;
919: DCP dc;
920:
921: for ( dc = DC(f), M = 0, E = 0; dc; dc = NEXT(dc) ) {
922: c = NM((Q)COEF(dc)); p = PL(c); b = BD(c);
923: sqad(b[p-1],(p-1)*BSH);
924: }
925: if (E % 2) M *= 2; M = ceil(sqrt(M)); E /= 2;
926: c = NM((Q)COEF(DC(f))); p = PL(c);
927: M *= (BD(c)[p-1]+1); E += (p-1) * BSH;
928: return (int)ceil( (0.31*(E+d+1)+log10((double)M)) / log10((double)q) );
929: }
930:
1.6 noro 931: void sqad(unsigned int man,int exp)
1.1 noro 932: {
933: int e,sqe;
934: unsigned int t;
935: double man1,d,sqm;
936: int diff;
937:
938: if ( man == BMASK ) {
939: e = BSH; man1 = 1.0;
940: } else {
941: man += 1;
942: for ( e = 0, t = man; t; e++, t >>= 1 );
943: e--; d = (double)(1<<e);
944: man1 = ((double)man)/d;
945: }
946: exp += e; sqm = man1 * man1; sqe = 2 * exp;
947: if ( sqm >= 2.0 ) {
948: sqm /= 2.0; sqe++;
949: }
950: diff = E - sqe;
951: if ( diff > 18 )
952: return;
953: if ( diff < -18 ) {
954: M = sqm; E = sqe;
955: return;
956: }
957: if ( diff >= 0 )
958: M += (sqm / (double)(1<<diff));
959: else {
960: M = ( ( M / (double)(1<<-diff)) + sqm ); E = sqe;
961: }
962: if ( M >= 2.0 ) {
963: M /= 2.0; E++;
964: }
965: }
966:
1.6 noro 967: void ptolum(int q,int bound,P f,LUM fl)
1.1 noro 968: {
969: DCP dc;
970: int i,j;
971: int **pp;
972: int d,br,s;
973: unsigned int r;
974: int *c;
975: unsigned int *m,*w;
976:
977: for ( dc = DC(f), pp = COEF(fl); dc; dc = NEXT(dc) ) {
978: d = PL(NM((Q)COEF(dc))); m = BD(NM((Q)COEF(dc)));
979: c = pp[QTOS(DEG(dc))]; w = (unsigned int *)W_ALLOC(d);
980: for ( i = 0; i < d; i++ )
981: w[i] = m[i];
1.7 noro 982: for ( i = 0; i < bound && d >= 1; ) {
1.1 noro 983: for ( j = d - 1, r = 0; j >= 0; j-- ) {
984: DSAB(q,r,w[j],w[j],r)
985: }
986: c[i++] = (int)r;
987: if ( !w[d-1] )
988: d--;
989: }
990: if ( SGN((Q)COEF(dc)) < 0 )
991: for (i = 0, br = 0; i < bound; i++ )
992: if ( ( s = -(c[i] + br) ) < 0 ) {
993: c[i] = s + q; br = 1;
994: } else {
995: c[i] = 0; br = 0;
996: }
997: }
998: }
999:
1.6 noro 1000: void modfctrp(P p,int mod,int flag,DCP *dcp)
1.1 noro 1001: {
1002: int cm,n,i,j,k;
1003: DCP dc,dc0;
1004: P zp;
1005: Q c,q;
1006: UM mp;
1007: UM *tl;
1008: struct oDUM *udc,*udc1;
1009:
1010: if ( !p ) {
1011: *dcp = 0; return;
1012: }
1013: ptozp(p,1,&c,&zp);
1014: if ( DN(c) || !(cm = rem(NM(c),mod)) ) {
1015: *dcp = 0; return;
1016: }
1017: mp = W_UMALLOC(UDEG(p));
1018: ptoum(mod,zp,mp);
1019: if ( (n = DEG(mp)) < 0 ) {
1020: *dcp = 0; return;
1021: } else if ( n == 0 ) {
1022: cm = dmar(cm,COEF(mp)[0],0,mod); STOQ(cm,q);
1023: NEWDC(dc); COEF(dc) = (P)q; DEG(dc) = ONE;
1024: NEXT(dc) = 0; *dcp = dc;
1025: return;
1026: }
1027: if ( COEF(mp)[n] != 1 ) {
1028: cm = dmar(cm,COEF(mp)[n],0,mod);
1029: i = invm(COEF(mp)[n],mod);
1030: for ( j = 0; j <= n; j++ )
1031: COEF(mp)[j] = dmar(COEF(mp)[j],i,0,mod);
1032: }
1033: W_CALLOC(n+1,struct oDUM,udc);
1034: gensqfrum(mod,mp,udc);
1035: switch ( flag ) {
1036: case FCTR:
1037: tl = (UM *)ALLOCA((n+1)*sizeof(UM));
1038: W_CALLOC(DEG(mp)+1,struct oDUM,udc1);
1039: for ( i = 0,j = 0; udc[i].f; i++ )
1040: if ( DEG(udc[i].f) == 1 ) {
1041: udc1[j].f = udc[i].f; udc1[j].n = udc[i].n; j++;
1042: } else {
1043: bzero((char *)tl,(n+1)*sizeof(UM));
1044: berlemain(mod,udc[i].f,tl);
1045: for ( k = 0; tl[k]; k++, j++ ) {
1046: udc1[j].f = tl[k]; udc1[j].n = udc[i].n;
1047: }
1048: }
1049: udc = udc1; break;
1050: case SQFR:
1051: break;
1052: case DDD:
1053: tl = (UM *)ALLOCA((n+1)*sizeof(UM));
1054: W_CALLOC(DEG(mp)+1,struct oDUM,udc1);
1055: for ( i = 0,j = 0; udc[i].f; i++ )
1056: if ( DEG(udc[i].f) == 1 ) {
1057: udc1[j].f = udc[i].f; udc1[j].n = udc[i].n; j++;
1058: } else {
1059: bzero((char *)tl,(n+1)*sizeof(UM));
1060: ddd(mod,udc[i].f,tl);
1061: for ( k = 0; tl[k]; k++, j++ ) {
1062: udc1[j].f = tl[k]; udc1[j].n = udc[i].n;
1063: }
1064: }
1065: udc = udc1; break;
1066: case NEWDDD:
1067: tl = (UM *)ALLOCA((n+1)*sizeof(UM));
1068: W_CALLOC(DEG(mp)+1,struct oDUM,udc1);
1069: for ( i = 0,j = 0; udc[i].f; i++ )
1070: if ( DEG(udc[i].f) == 1 ) {
1071: udc1[j].f = udc[i].f; udc1[j].n = udc[i].n; j++;
1072: } else {
1073: bzero((char *)tl,(n+1)*sizeof(UM));
1074: if ( mod == 2 )
1075: berlemain(mod,udc[i].f,tl);
1076: else
1077: newddd(mod,udc[i].f,tl);
1078: for ( k = 0; tl[k]; k++, j++ ) {
1079: udc1[j].f = tl[k]; udc1[j].n = udc[i].n;
1080: }
1081: }
1082: udc = udc1; break;
1083: }
1084: NEWDC(dc0); STOQ(cm,q); COEF(dc0) = (P)q; DEG(dc0) = ONE; dc = dc0;
1085: for ( n = 0; udc[n].f; n++ ) {
1086: NEWDC(NEXT(dc)); dc = NEXT(dc);
1087: STOQ(udc[n].n,DEG(dc)); umtop(VR(p),udc[n].f,&COEF(dc));
1088: }
1089: NEXT(dc) = 0; *dcp = dc0;
1090: }
1091:
1.6 noro 1092: void gensqfrum(int mod,UM p,struct oDUM *dc)
1.1 noro 1093: {
1094: int n,i,j,d;
1095: UM t,s,g,f,f1,b;
1096:
1097: if ( (n = DEG(p)) == 1 ) {
1098: dc[0].f = UMALLOC(DEG(p)); cpyum(p,dc[0].f); dc[0].n = 1;
1099: return;
1100: }
1101: t = W_UMALLOC(n); s = W_UMALLOC(n); g = W_UMALLOC(n);
1102: f = W_UMALLOC(n); f1 = W_UMALLOC(n); b = W_UMALLOC(n);
1103: diffum(mod,p,t); cpyum(p,s); Gcdum(mod,t,s,g);
1104: if ( !DEG(g) ) {
1105: dc[0].f = UMALLOC(DEG(p)); cpyum(p,dc[0].f); dc[0].n = 1;
1106: return;
1107: }
1108: cpyum(p,b); cpyum(p,t); Divum(mod,t,g,f);
1109: for ( i = 0, d = 0; DEG(f); i++ ) {
1110: while ( 1 ) {
1111: cpyum(b,t);
1112: if ( Divum(mod,t,f,s) >= 0 )
1113: break;
1114: else {
1115: cpyum(s,b); d++;
1116: }
1117: }
1118: cpyum(b,t); cpyum(f,s); Gcdum(mod,t,s,f1);
1119: Divum(mod,f,f1,s); cpyum(f1,f);
1120: dc[i].f = UMALLOC(DEG(s)); cpyum(s,dc[i].f); dc[i].n = d;
1121: }
1122: if ( DEG(b) > 0 ) {
1123: d = 1;
1124: while ( 1 ) {
1125: cpyum(b,t);
1126: for ( j = DEG(t); j >= 0; j-- )
1127: if ( COEF(t)[j] && (j % mod) )
1128: break;
1129: if ( j >= 0 )
1130: break;
1131: else {
1132: DEG(s) = DEG(t)/mod;
1133: for ( j = 0; j <= DEG(t); j++ )
1134: COEF(s)[j] = COEF(t)[j*mod];
1135: cpyum(s,b); d *= mod;
1136: }
1137: }
1138: gensqfrum(mod,b,dc+i);
1139: for ( j = i; dc[j].f; j++ )
1140: dc[j].n *= d;
1141: }
1142: }
1143:
1144: #if 0
1.6 noro 1145: void srchum(int mod,UM p1,UM p2,UM gr)
1.1 noro 1146: {
1147: UM m,m1,m2,q,r,t,g1,g2;
1148: int lc,d,d1,d2,i,j,k,l,l1,l2,l3,tmp,adj;
1149: V v;
1150:
1151: d = MAX(DEG(p1),DEG(p2));
1152: g1 = W_UMALLOC(d); g2 = W_UMALLOC(d);
1153: bzero((char *)g1,(d+2)*sizeof(int)); bzero((char *)g2,(d+2)*sizeof(int));
1154: if ( d == DEG(p1) ) {
1155: cpyum(p1,g1); cpyum(p2,g2);
1156: } else {
1157: cpyum(p1,g2); cpyum(p2,g1);
1158: }
1159: if ( ( d1 = DEG(g1) ) > ( d2 = DEG(g2) ) ) {
1160: j = d1 - 1; adj = 1;
1161: } else
1162: j = d2;
1163: lc = 1;
1164: r = W_UMALLOC(d1+d2); q = W_UMALLOC(d1+d2);
1165: m1 = W_UMALLOC(d1+d2); t = W_UMALLOC(d1+d2);
1166: bzero((char *)r,(d1+d2+2)*sizeof(int)); bzero((char *)q,(d1+d2+2)*sizeof(int));
1167: bzero((char *)m1,(d1+d2+2)*sizeof(int)); bzero((char *)t,(d1+d2+2)*sizeof(int));
1168: m = W_UMALLOC(0); bzero((char *)m,2*sizeof(int));
1169: adj = pwrm(mod,COEF(g2)[DEG(g2)],DEG(g1));
1170: DEG(m) = 0; COEF(m)[0] = invm(COEF(g2)[DEG(g2)],mod);
1171: Mulum(mod,g2,m,r); cpyum(r,g2);
1172: while ( 1 ) {
1173: if ( ( k = DEG(g2) ) < 0 ) {
1174: DEG(gr) = -1;
1175: return;
1176: }
1177: if ( k == j ) {
1178: if ( k == 0 ) {
1179: DEG(m) = 0; COEF(m)[0] = adj;
1180: Mulum(mod,g2,m,gr);
1181: return;
1182: } else {
1183: DEG(m) = 0;
1184: COEF(m)[0] = pwrm(mod,COEF(g2)[k],DEG(g1)-k+1);
1185: Mulum(mod,g1,m,r); DEG(r) = Divum(mod,r,g2,t);
1186: DEG(m) = 0; COEF(m)[0] = dmb(mod,lc,lc,&tmp);
1187: Divum(mod,r,m,q); cpyum(g2,g1); cpyum(q,g2);
1188: lc = COEF(g1)[DEG(g1)]; j = k - 1;
1189: }
1190: } else {
1191: d = j - k;
1192: DEG(m) = 0; COEF(m)[0] = pwrm(mod,COEF(g2)[DEG(g2)],d);
1193: Mulum(mod,g2,m,m1); l = pwrm(mod,lc,d);
1194: DEG(m) = 0; COEF(m)[0] = l; Divum(mod,m1,m,t);
1195: if ( k == 0 ) {
1196: DEG(m) = 0; COEF(m)[0] = adj;
1197: Mulum(mod,t,m,gr);
1198: return;
1199: } else {
1200: DEG(m) = 0;
1201: COEF(m)[0] = pwrm(mod,COEF(g2)[k],DEG(g1)-k+1);
1202: Mulum(mod,g1,m,r); DEG(r) = Divum(mod,r,g2,q);
1203: l1 = dmb(mod,lc,lc,&tmp); l2 = dmb(mod,l,l1,&tmp);
1204: DEG(m) = 0; COEF(m)[0] = l2;
1205: Divum(mod,r,m,q); cpyum(t,g1); cpyum(q,g2);
1206: if ( d % 2 )
1207: for ( i = DEG(g2); i >= 0; i-- )
1208: COEF(g2)[i] = ( mod - COEF(g2)[i] ) % mod;
1209: lc = COEF(g1)[DEG(g1)]; j = k - 1;
1210: }
1211: }
1212: }
1213: }
1214:
1.6 noro 1215: UM *resberle(int mod,UM f,UM *fp)
1.1 noro 1216: {
1217: UM w,wg,ws,wf,f0,gcd,q,res;
1218: int n;
1219: register int i;
1220:
1221: n = DEG(f); wg = W_UMALLOC(n); mini(mod,f,wg);
1222: if ( DEG(wg) <= 0 ) {
1223: f0 = UMALLOC(n); cpyum(f,f0); *fp++ = f0;
1224: return ( fp );
1225: }
1226: f0 = W_UMALLOC(n); cpyum(f,f0);
1227: ws = W_UMALLOC(n); wf = W_UMALLOC(n);
1228: q = W_UMALLOC(n); gcd = W_UMALLOC(n);
1229: res = W_UMALLOC(2*n);
1230: srchum(mod,f,wg,res);
1231: for ( i = 0; i < mod; i++ ) {
1232: if ( substum(mod,res,i) )
1233: continue;
1234: cpyum(f0,wf); cpyum(wg,ws);
1235: COEF(ws)[0] = ( COEF(ws)[0] + mod - i ) % mod;
1236: Gcdum(mod,wf,ws,gcd);
1237: if ( DEG(gcd) > 0 ) {
1238: if ( DEG(gcd) < n ) {
1239: Divum(mod,f0,gcd,q); f0 = q; fp = resberle(mod,gcd,fp);
1240: }
1241: break;
1242: }
1243: }
1244: fp = resberle(mod,f0,fp);
1245: return ( fp );
1246: }
1247:
1.6 noro 1248: int substum(int mod,UM p,int a)
1.1 noro 1249: {
1250: int i,j,s;
1251: int *c;
1252:
1253: if ( DEG(p) < 0 )
1254: return 0;
1255: if ( DEG(p) == 0 )
1256: return COEF(p)[0];
1257: for ( i = DEG(p), c = COEF(p), s = c[i]; i >= 0; ) {
1258: for ( j = i--; (i>=0) && !c[i]; i-- );
1259: if ( i >= 0 )
1260: s = (s*pwrm(mod,a,j-i)%mod+c[i])%mod;
1261: else
1262: s = s*pwrm(mod,a,j)%mod;
1263: }
1264: return s;
1265: }
1266: #endif
1267:
1.6 noro 1268: void ddd(int mod,UM f,UM *r)
1.1 noro 1269: {
1270: register int i,j;
1271: int d,n;
1272: UM q,s,t,u,v,w,g,x,m;
1273: UM *base;
1274:
1275: n = DEG(f);
1276: if ( n == 1 ) {
1277: r[0] = UMALLOC(1); cpyum(f,r[0]); r[1] = 0; return;
1278: }
1279: base = (UM *)ALLOCA(n*sizeof(UM)); bzero((char *)base,n*sizeof(UM));
1280: w = W_UMALLOC(2*n); q = W_UMALLOC(2*n); m = W_UMALLOC(2*n);
1281: base[0] = W_UMALLOC(0); DEG(base[0]) = 0; COEF(base[0])[0] = 1;
1282: t = W_UMALLOC(1); DEG(t) = 1; COEF(t)[0] = 0; COEF(t)[1] = 1;
1283: pwrmodum(mod,t,mod,f,w); base[1] = W_UMALLOC(DEG(w)); cpyum(w,base[1]);
1284: for ( i = 2; i < n; i++ ) {
1285: mulum(mod,base[i-1],base[1],m); DEG(m) = divum(mod,m,f,q);
1286: base[i] = W_UMALLOC(DEG(m)); cpyum(m,base[i]);
1287: }
1288: v = W_UMALLOC(n); cpyum(f,v);
1289: DEG(w) = 1; COEF(w)[0] = 0; COEF(w)[1] = 1;
1290: x = W_UMALLOC(1); DEG(x) = 1; COEF(x)[0] = 0; COEF(x)[1] = 1;
1291: t = W_UMALLOC(n); s = W_UMALLOC(n); u = W_UMALLOC(n); g = W_UMALLOC(n);
1292: for ( j = 0, d = 1; 2*d <= DEG(v); d++ ) {
1293: for ( DEG(t) = -1, i = 0; i <= DEG(w); i++ )
1294: if ( COEF(w)[i] ) {
1295: Mulsum(mod,base[i],COEF(w)[i],s);
1296: addum(mod,s,t,u); cpyum(u,t);
1297: }
1298: cpyum(t,w); cpyum(v,s); subum(mod,w,x,t); Gcdum(mod,s,t,g);
1299: if ( DEG(g) >= 1 ) {
1300: canzas(mod,g,d,base,r+j); j += DEG(g)/d;
1301: Divum(mod,v,g,q); cpyum(q,v);
1302: DEG(w) = Divum(mod,w,v,q);
1303: for ( i = 0; i < DEG(v); i++ )
1304: DEG(base[i]) = Divum(mod,base[i],v,q);
1305: }
1306: }
1307: if ( DEG(v) ) {
1308: r[j] = UMALLOC(DEG(v)); cpyum(v,r[j]); j++;
1309: }
1310: r[j] = 0;
1311: }
1312:
1313: #if 0
1.6 noro 1314: void canzas(int mod,UM f,int d,UM *base,UM *r)
1.1 noro 1315: {
1316: UM t,s,u,w,g,o,q;
1317: N n1,n2,n3,n4,n5;
1318: UM *b;
1319: int n,m,i;
1320:
1321: if ( DEG(f) == d ) {
1322: r[0] = UMALLOC(d); cpyum(f,r[0]);
1323: return;
1324: } else {
1325: n = DEG(f); b = (UM *)ALLOCA(n*sizeof(UM)); bzero((char *)b,n*sizeof(UM));
1326: for ( i = 0, m = 0; i < n; i++ )
1327: m = MAX(m,DEG(base[i]));
1328: q = W_UMALLOC(m);
1329: for ( i = 0; i < n; i++ ) {
1330: b[i] = W_UMALLOC(DEG(base[i])); cpyum(base[i],b[i]);
1331: DEG(b[i]) = Divum(mod,b[i],f,q);
1332: }
1333: t = W_UMALLOC(2*d);
1334: s = W_UMALLOC(DEG(f)); u = W_UMALLOC(DEG(f));
1335: w = W_UMALLOC(DEG(f)); g = W_UMALLOC(DEG(f));
1336: o = W_UMALLOC(0); DEG(o) = 0; COEF(o)[0] = 1;
1337: STON(mod,n1); pwrn(n1,d,&n2); subn(n2,ONEN,&n3);
1338: STON(2,n4); divsn(n3,n4,&n5);
1339: while ( 1 ) {
1340: randum(mod,2*d,t); spwrum(mod,f,b,t,n5,s);
1341: subum(mod,s,o,u); cpyum(f,w); Gcdum(mod,w,u,g);
1342: if ( (DEG(g) >= 1) && (DEG(g) < DEG(f)) ) {
1343: canzas(mod,g,d,b,r);
1344: cpyum(f,w); Divum(mod,w,g,s);
1345: canzas(mod,s,d,b,r+DEG(g)/d);
1346: return;
1347: }
1348: }
1349: }
1350: }
1351: #else
1.6 noro 1352: void canzas(int mod,UM f,int d,UM *base,UM *r)
1.1 noro 1353: {
1354: UM t,s,u,w,g,o,q;
1355: N n1,n2,n3,n4,n5;
1356: UM *b;
1357: int n,m,i;
1358:
1359: if ( DEG(f) == d ) {
1360: r[0] = UMALLOC(d); cpyum(f,r[0]);
1361: return;
1362: } else {
1363: n = DEG(f); b = (UM *)ALLOCA(n*sizeof(UM)); bzero((char *)b,n*sizeof(UM));
1364: for ( i = 0, m = 0; i < n; i++ )
1365: m = MAX(m,DEG(base[i]));
1366: q = W_UMALLOC(m);
1367: for ( i = 0; i < n; i++ ) {
1368: b[i] = W_UMALLOC(DEG(base[i])); cpyum(base[i],b[i]);
1369: DEG(b[i]) = Divum(mod,b[i],f,q);
1370: }
1371: t = W_UMALLOC(2*d);
1372: s = W_UMALLOC(DEG(f)); u = W_UMALLOC(DEG(f));
1373: w = W_UMALLOC(DEG(f)); g = W_UMALLOC(DEG(f));
1374: o = W_UMALLOC(0); DEG(o) = 0; COEF(o)[0] = 1;
1375: STON(mod,n1); pwrn(n1,d,&n2); subn(n2,ONEN,&n3);
1376: STON(2,n4); divsn(n3,n4,&n5);
1377: while ( 1 ) {
1378: randum(mod,2*d,t); spwrum0(mod,f,t,n5,s);
1379: subum(mod,s,o,u); cpyum(f,w); Gcdum(mod,w,u,g);
1380: if ( (DEG(g) >= 1) && (DEG(g) < DEG(f)) ) {
1381: canzas(mod,g,d,b,r);
1382: cpyum(f,w); Divum(mod,w,g,s);
1383: canzas(mod,s,d,b,r+DEG(g)/d);
1384: return;
1385: }
1386: }
1387: }
1388: }
1389: #endif
1390:
1.6 noro 1391: void randum(int mod,int d,UM p)
1.1 noro 1392: {
1393: unsigned int n;
1394: int i;
1395:
1396: n = ((unsigned int)random()) % d; DEG(p) = n; COEF(p)[n] = 1;
1397: for ( i = 0; i < (int)n; i++ )
1398: COEF(p)[i] = ((unsigned int)random()) % mod;
1399: }
1400:
1.6 noro 1401: void pwrmodum(int mod,UM p,int e,UM f,UM pr)
1.1 noro 1402: {
1403: UM wt,ws,q;
1404:
1405: if ( e == 0 ) {
1406: DEG(pr) = 0; COEF(pr)[0] = 1;
1407: } else if ( DEG(p) < 0 )
1408: DEG(pr) = -1;
1409: else if ( e == 1 ) {
1410: q = W_UMALLOC(DEG(p)); cpyum(p,pr);
1411: DEG(pr) = divum(mod,pr,f,q);
1412: } else if ( DEG(p) == 0 ) {
1413: DEG(pr) = 0; COEF(pr)[0] = pwrm(mod,COEF(p)[0],e);
1414: } else {
1415: wt = W_UMALLOC(2*DEG(f)); ws = W_UMALLOC(2*DEG(f));
1416: q = W_UMALLOC(2*DEG(f));
1417: pwrmodum(mod,p,e/2,f,wt);
1418: if ( !(e%2) ) {
1419: mulum(mod,wt,wt,pr); DEG(pr) = divum(mod,pr,f,q);
1420: } else {
1421: mulum(mod,wt,wt,ws); DEG(ws) = divum(mod,ws,f,q);
1422: mulum(mod,ws,p,pr); DEG(pr) = divum(mod,pr,f,q);
1423: }
1424: }
1425: }
1426:
1.6 noro 1427: void spwrum(int mod,UM m,UM *base,UM f,N e,UM r)
1.1 noro 1428: {
1429: int a,n,i;
1430: N e1,an;
1431: UM t,s,u,q,r1,r2;
1432:
1433: if ( !e ) {
1434: DEG(r) = 0; COEF(r)[0] = 1;
1435: } else if ( UNIN(e) )
1436: cpyum(f,r);
1437: else if ( (PL(e) == 1) && (BD(e)[0] < (unsigned int)mod) )
1438: spwrum0(mod,m,f,e,r);
1439: else {
1440: a = divin(e,mod,&e1); STON(a,an);
1441: n = DEG(m); t = W_UMALLOC(n); s = W_UMALLOC(n);
1442: u = W_UMALLOC(2*n); q = W_UMALLOC(2*n);
1443: for ( DEG(t) = -1, i = 0; i <= DEG(f); i++ )
1444: if ( COEF(f)[i] ) {
1445: Mulsum(mod,base[i],COEF(f)[i],s);
1446: addum(mod,s,t,u); cpyum(u,t);
1447: }
1448: r1 = W_UMALLOC(n); spwrum0(mod,m,f,an,r1);
1449: r2 = W_UMALLOC(n); spwrum(mod,m,base,t,e1,r2);
1450: Mulum(mod,r1,r2,u); DEG(u) = Divum(mod,u,m,q);
1451: cpyum(u,r);
1452: }
1453: }
1454:
1.6 noro 1455: void spwrum0(int mod,UM m,UM f,N e,UM r)
1.1 noro 1456: {
1457: UM t,s,q;
1458: N e1;
1459: int a;
1460:
1461: if ( !e ) {
1462: DEG(r) = 0; COEF(r)[0] = 1;
1463: } else if ( UNIN(e) )
1464: cpyum(f,r);
1465: else {
1466: a = divin(e,2,&e1);
1467: t = W_UMALLOC(2*DEG(m)); spwrum0(mod,m,f,e1,t);
1468: s = W_UMALLOC(2*DEG(m)); q = W_UMALLOC(2*DEG(m));
1469: Mulum(mod,t,t,s); DEG(s) = Divum(mod,s,m,q);
1470: if ( a ) {
1471: Mulum(mod,s,f,t); DEG(t) = Divum(mod,t,m,q); cpyum(t,r);
1472: } else
1473: cpyum(s,r);
1474: }
1475: }
1476:
1477: #if 0
1.6 noro 1478: void Mulum(int mod,UM p1,UM p2,UM pr)
1.1 noro 1479: {
1480: register int *pc1,*pcr;
1481: register int mul,i,j,d1,d2;
1482: int *c1,*c2,*cr;
1483:
1484: if ( ( (d1 = DEG(p1)) < 0) || ( (d2 = DEG(p2)) < 0 ) ) {
1485: DEG(pr) = -1;
1486: return;
1487: }
1488: c1 = COEF(p1); c2 = COEF(p2); cr = COEF(pr);
1489: bzero((char *)cr,(d1+d2+1)*sizeof(int));
1490: for ( i = 0; i <= d2; i++, cr++ )
1491: if ( mul = *c2++ )
1492: for ( j = 0, pc1 = c1, pcr = cr; j <= d1; j++, pc1++, pcr++ )
1493: *pcr = (*pc1 * mul + *pcr) % mod;
1494: DEG(pr) = d1 + d2;
1495: }
1496:
1.6 noro 1497: void Mulsum(int mod,UM p,int n,UM pr)
1.1 noro 1498: {
1499: register int *sp,*dp;
1500: register int i;
1501:
1502: for ( i = DEG(pr) = DEG(p), sp = COEF(p)+i, dp = COEF(pr)+i;
1503: i >= 0; i--, dp--, sp-- )
1504: *dp = (*sp * n) % mod;
1505: }
1506:
1.6 noro 1507: int Divum(int mod,UM p1,UM p2,UM pq)
1.1 noro 1508: {
1509: register int *pc1,*pct;
1510: register int tmp,i,j,inv;
1511: int *c1,*c2,*ct;
1512: int d1,d2,dd,hd;
1513:
1514: if ( (d1 = DEG(p1)) < (d2 = DEG(p2)) ) {
1515: DEG(pq) = -1;
1516: return( d1 );
1517: }
1518: c1 = COEF(p1); c2 = COEF(p2); dd = d1-d2;
1519: if ( ( hd = c2[d2] ) != 1 ) {
1520: inv = invm(hd,mod);
1521: for ( pc1 = c2 + d2; pc1 >= c2; pc1-- )
1522: *pc1 = (*pc1 * inv) % mod;
1523: } else
1524: inv = 1;
1525: for ( i = dd, ct = c1+d1; i >= 0; i-- )
1526: if ( tmp = *ct-- ) {
1527: tmp = mod - tmp;
1528: for ( j = d2-1, pct = ct, pc1 = c2+j; j >= 0; j--, pct--, pc1-- )
1529: *pct = (*pc1 * tmp + *pct) % mod;
1530: }
1531: if ( inv != 1 ) {
1532: for ( pc1 = c1+d2, pct = c1+d1; pc1 <= pct; pc1++ )
1533: *pc1 = (*pc1 * inv) % mod;
1534: for ( pc1 = c2, pct = c2+d2, inv = hd; pc1 <= pct; pc1++ )
1535: *pc1 = (*pc1 * inv) % mod;
1536: }
1537: for ( i = d2-1, pc1 = c1+i; i >= 0 && !(*pc1); pc1--, i-- );
1538: for ( DEG(pq) = j = dd, pc1 = c1+d1, pct = COEF(pq)+j; j >= 0; j-- )
1539: *pct-- = *pc1--;
1540: return( i );
1541: }
1542:
1.6 noro 1543: void Gcdum(int mod,UM p1,UM p2,UM pr)
1.1 noro 1544: {
1545: register int *sp,*dp;
1546: register int i,inv;
1547: UM t1,t2,q,tum;
1548: int drem;
1549:
1550: if ( DEG(p1) < 0 )
1551: cpyum(p2,pr);
1552: else if ( DEG(p2) < 0 )
1553: cpyum(p1,pr);
1554: else {
1555: if ( DEG(p1) >= DEG(p2) ) {
1556: t1 = p1; t2 = p2;
1557: } else {
1558: t1 = p2; t2 = p1;
1559: }
1560: q = W_UMALLOC(DEG(t1));
1561: while ( ( drem = Divum(mod,t1,t2,q) ) >= 0 ) {
1562: tum = t1; t1 = t2; t2 = tum; DEG(t2) = drem;
1563: }
1564: inv = invm(COEF(t2)[DEG(t2)],mod);
1565: Mulsum(mod,t2,inv,pr);
1566: }
1567: }
1568: #endif
1569:
1.6 noro 1570: void mult_mod_tab(UM p,int mod,UM *tab,UM r,int d)
1.1 noro 1571: {
1572: UM w,w1,c;
1573: int n,i;
1574: int *pc;
1575:
1576: w = W_UMALLOC(d); w1 = W_UMALLOC(d);
1577: c = W_UMALLOC(1); DEG(c) = 0;
1578: n = DEG(p); DEG(r) = -1;
1579: for ( i = 0, pc = COEF(p); i <= n; i++ )
1580: if ( pc[i] ) {
1581: COEF(c)[0] = pc[i];
1582: mulum(mod,tab[i],c,w);
1583: addum(mod,r,w,w1);
1584: cpyum(w1,r);
1585: }
1586: }
1587:
1.6 noro 1588: void make_qmat(UM p,int mod,UM *tab,int ***mp)
1.1 noro 1589: {
1590: int n,i,j;
1591: int *c;
1592: UM q,r;
1593: int **mat;
1594:
1595: n = DEG(p);
1596: *mp = mat = almat(n,n);
1597: for ( j = 0; j < n; j++ ) {
1598: r = W_UMALLOC(DEG(tab[j])); q = W_UMALLOC(DEG(tab[j]));
1599: cpyum(tab[j],r); DEG(r) = divum(mod,r,p,q);
1600: for ( i = 0, c = COEF(r); i <= DEG(r); i++ )
1601: mat[i][j] = c[i];
1602: }
1603: for ( i = 0; i < n; i++ )
1604: mat[i][i] = (mat[i][i]+mod-1) % mod;
1605: }
1606:
1.6 noro 1607: void null_mod(int **mat,int mod,int n,int *ind)
1.1 noro 1608: {
1609: int i,j,l,s,h,inv;
1610: int *t,*u;
1611:
1612: bzero((char *)ind,n*sizeof(int));
1613: ind[0] = 0;
1614: for ( i = j = 0; j < n; i++, j++ ) {
1615: for ( ; j < n; j++ ) {
1616: for ( l = i; l < n; l++ )
1617: if ( mat[l][j] )
1618: break;
1619: if ( l < n ) {
1620: t = mat[i]; mat[i] = mat[l]; mat[l] = t; break;
1621: } else
1622: ind[j] = 1;
1623: }
1624: if ( j == n )
1625: break;
1626: inv = invm(mat[i][j],mod);
1627: for ( s = j, t = mat[i]; s < n; s++ )
1628: t[s] = dmar(t[s],inv,0,mod);
1629: for ( l = 0; l < n; l++ ) {
1630: if ( l == i )
1631: continue;
1632: for ( s = j, u = mat[l], h = (mod-u[j])%mod; s < n; s++ )
1633: u[s] = dmar(h,t[s],u[s],mod);
1634: }
1635: }
1636: }
1637:
1.6 noro 1638: void null_to_sol(int **mat,int *ind,int mod,int n,UM *r)
1.1 noro 1639: {
1640: int i,j,k,l;
1641: int *c;
1642: UM w;
1643:
1644: for ( i = 0, l = 0; i < n; i++ ) {
1645: if ( !ind[i] )
1646: continue;
1647: w = UMALLOC(n);
1648: for ( j = k = 0, c = COEF(w); j < n; j++ )
1649: if ( ind[j] )
1650: c[j] = 0;
1651: else
1652: c[j] = mat[k++][i];
1653: c[i] = mod-1;
1654: for ( j = n; j >= 0; j-- )
1655: if ( c[j] )
1656: break;
1657: DEG(w) = j;
1658: r[l++] = w;
1659: }
1660: }
1661: /*
1662: make_qmat(p,mod,tab,mp)
1663: null_mod(mat,mod,n,ind)
1664: null_to_sol(mat,ind,mod,n,r)
1665: */
1666:
1.6 noro 1667: void newddd(int mod,UM f,UM *r)
1.1 noro 1668: {
1669: register int i,j;
1670: int d,n;
1671: UM q,s,t,u,v,w,g,x,m;
1672: UM *base;
1673:
1674: n = DEG(f); base = (UM *)ALLOCA(n*sizeof(UM)); bzero((char *)base,n*sizeof(UM));
1675: w = W_UMALLOC(2*n); q = W_UMALLOC(2*n); m = W_UMALLOC(2*n);
1676: base[0] = W_UMALLOC(0); DEG(base[0]) = 0; COEF(base[0])[0] = 1;
1677: t = W_UMALLOC(1); DEG(t) = 1; COEF(t)[0] = 0; COEF(t)[1] = 1;
1678: pwrmodum(mod,t,mod,f,w); base[1] = W_UMALLOC(DEG(w)); cpyum(w,base[1]);
1679: for ( i = 2; i < n; i++ ) {
1680: /* fprintf(stderr,"i=%d\n",i); */
1681: mulum(mod,base[i-1],base[1],m); DEG(m) = divum(mod,m,f,q);
1682: base[i] = W_UMALLOC(DEG(m)); cpyum(m,base[i]);
1683: }
1684: v = W_UMALLOC(n); cpyum(f,v);
1685: DEG(w) = 1; COEF(w)[0] = 0; COEF(w)[1] = 1;
1686: x = W_UMALLOC(1); DEG(x) = 1; COEF(x)[0] = 0; COEF(x)[1] = 1;
1687: t = W_UMALLOC(n); s = W_UMALLOC(n); u = W_UMALLOC(n); g = W_UMALLOC(n);
1688: for ( j = 0, d = 1; 2*d <= DEG(v); d++ ) {
1689: /* fprintf(stderr,"d=%d\n",d); */
1690: for ( DEG(t) = -1, i = 0; i <= DEG(w); i++ )
1691: if ( COEF(w)[i] ) {
1692: Mulsum(mod,base[i],COEF(w)[i],s);
1693: addum(mod,s,t,u); cpyum(u,t);
1694: }
1695: cpyum(t,w); cpyum(v,s); subum(mod,w,x,t); Gcdum(mod,s,t,g);
1696: if ( DEG(g) >= 1 ) {
1697: berlekamp(g,mod,d,base,r+j); j += DEG(g)/d;
1698: Divum(mod,v,g,q); cpyum(q,v);
1699: DEG(w) = Divum(mod,w,v,q);
1700: for ( i = 0; i < DEG(v); i++ )
1701: DEG(base[i]) = Divum(mod,base[i],v,q);
1702: }
1703: }
1704: if ( DEG(v) ) {
1705: r[j] = UMALLOC(DEG(v)); cpyum(v,r[j]); j++;
1706: }
1707: r[j] = 0;
1708: }
1709:
1.6 noro 1710: int nfctr_mod(UM f,int mod)
1.1 noro 1711: {
1712: register int i,j;
1713: int d,n;
1714: UM q,s,t,u,v,w,g,x,m;
1715: UM *base;
1716:
1717: n = DEG(f); base = (UM *)ALLOCA(n*sizeof(UM)); bzero((char *)base,n*sizeof(UM));
1718: w = W_UMALLOC(2*n); q = W_UMALLOC(2*n); m = W_UMALLOC(2*n);
1719: base[0] = W_UMALLOC(0); DEG(base[0]) = 0; COEF(base[0])[0] = 1;
1720: t = W_UMALLOC(1); DEG(t) = 1; COEF(t)[0] = 0; COEF(t)[1] = 1;
1721: pwrmodum(mod,t,mod,f,w); base[1] = W_UMALLOC(DEG(w)); cpyum(w,base[1]);
1722: for ( i = 2; i < n; i++ ) {
1723: /* fprintf(stderr,"i=%d\n",i); */
1724: mulum(mod,base[i-1],base[1],m); DEG(m) = divum(mod,m,f,q);
1725: base[i] = W_UMALLOC(DEG(m)); cpyum(m,base[i]);
1726: }
1727: v = W_UMALLOC(n); cpyum(f,v);
1728: DEG(w) = 1; COEF(w)[0] = 0; COEF(w)[1] = 1;
1729: x = W_UMALLOC(1); DEG(x) = 1; COEF(x)[0] = 0; COEF(x)[1] = 1;
1730: t = W_UMALLOC(n); s = W_UMALLOC(n); u = W_UMALLOC(n); g = W_UMALLOC(n);
1731: for ( j = 0, d = 1; 2*d <= DEG(v); d++ ) {
1732: /* fprintf(stderr,"d=%d\n",d); */
1733: for ( DEG(t) = -1, i = 0; i <= DEG(w); i++ )
1734: if ( COEF(w)[i] ) {
1735: Mulsum(mod,base[i],COEF(w)[i],s);
1736: addum(mod,s,t,u); cpyum(u,t);
1737: }
1738: cpyum(t,w); cpyum(v,s); subum(mod,w,x,t); Gcdum(mod,s,t,g);
1739: if ( DEG(g) >= 1 ) {
1740: j += DEG(g)/d;
1741: Divum(mod,v,g,q); cpyum(q,v);
1742: DEG(w) = Divum(mod,w,v,q);
1743: for ( i = 0; i < DEG(v); i++ )
1744: DEG(base[i]) = Divum(mod,base[i],v,q);
1745: }
1746: }
1747: if ( DEG(v) ) j++;
1748: return j;
1749: }
1750:
1.6 noro 1751: int irred_check(UM f,int mod)
1.1 noro 1752: {
1753: register int i,j;
1754: int d,n;
1755: UM q,s,t,u,v,w,g,x,m,f1,b;
1756: UM *base;
1757:
1758: if ( (n = DEG(f)) == 1 )
1759: return 1;
1760: t = W_UMALLOC(n); s = W_UMALLOC(n); g = W_UMALLOC(n);
1761: f1 = W_UMALLOC(n); b = W_UMALLOC(n);
1762: diffum(mod,f,t); cpyum(f,s); Gcdum(mod,t,s,g);
1763: if ( DEG(g) )
1764: return 0;
1765:
1766: base = (UM *)ALLOCA(n*sizeof(UM)); bzero((char *)base,n*sizeof(UM));
1767: w = W_UMALLOC(2*n); q = W_UMALLOC(2*n); m = W_UMALLOC(2*n);
1768: base[0] = W_UMALLOC(0); DEG(base[0]) = 0; COEF(base[0])[0] = 1;
1769: t = W_UMALLOC(1); DEG(t) = 1; COEF(t)[0] = 0; COEF(t)[1] = 1;
1770: pwrmodum(mod,t,mod,f,w); base[1] = W_UMALLOC(DEG(w)); cpyum(w,base[1]);
1771: for ( i = 2; i < n; i++ ) {
1772: /* fprintf(stderr,"i=%d\n",i); */
1773: mulum(mod,base[i-1],base[1],m); DEG(m) = divum(mod,m,f,q);
1774: base[i] = W_UMALLOC(DEG(m)); cpyum(m,base[i]);
1775: }
1776: v = W_UMALLOC(n); cpyum(f,v);
1777: DEG(w) = 1; COEF(w)[0] = 0; COEF(w)[1] = 1;
1778: x = W_UMALLOC(1); DEG(x) = 1; COEF(x)[0] = 0; COEF(x)[1] = 1;
1779: t = W_UMALLOC(n); s = W_UMALLOC(n); u = W_UMALLOC(n); g = W_UMALLOC(n);
1780: for ( j = 0, d = 1; 2*d <= n; d++ ) {
1781: /* fprintf(stderr,"d=%d\n",d); */
1782: for ( DEG(t) = -1, i = 0; i <= DEG(w); i++ )
1783: if ( COEF(w)[i] ) {
1784: Mulsum(mod,base[i],COEF(w)[i],s);
1785: addum(mod,s,t,u); cpyum(u,t);
1786: }
1787: cpyum(t,w); cpyum(v,s); subum(mod,w,x,t); Gcdum(mod,s,t,g);
1788: if ( DEG(g) >= 1 )
1789: return 0;
1790: }
1791: return 1;
1792: }
1793:
1.6 noro 1794: int berlekamp(UM p,int mod,int df,UM *tab,UM *r)
1.1 noro 1795: {
1796: int n,i,j,k,nf,d,nr;
1797: int **mat;
1798: int *ind;
1799: UM mp,w,q,gcd,w1,w2;
1800: UM *u;
1801: int *root;
1802:
1803: n = DEG(p);
1804: ind = ALLOCA(n*sizeof(int));
1805: make_qmat(p,mod,tab,&mat);
1806: null_mod(mat,mod,n,ind);
1807: for ( i = 0, d = 0; i < n; i++ )
1808: if ( ind[i] )
1809: d++;
1810: if ( d == 1 ) {
1811: r[0] = UMALLOC(n); cpyum(p,r[0]); return 1;
1812: }
1813: u = ALLOCA(d*sizeof(UM *));
1814: r[0] = UMALLOC(n); cpyum(p,r[0]);
1815: null_to_sol(mat,ind,mod,n,u);
1816: root = ALLOCA(d*sizeof(int));
1817: w = W_UMALLOC(n); mp = W_UMALLOC(d);
1818: w1 = W_UMALLOC(n); w2 = W_UMALLOC(n);
1819: for ( i = 1, nf = 1; i < d; i++ ) {
1820: minipoly_mod(mod,u[i],p,mp);
1821: nr = find_root(mod,mp,root);
1822: for ( j = 0; j < nf; j++ ) {
1823: if ( DEG(r[j]) == df )
1824: continue;
1825: for ( k = 0; k < nr; k++ ) {
1826: cpyum(u[i],w1); cpyum(r[j],w2);
1827: COEF(w1)[0] = (mod-root[k]) % mod;
1828: gcdum(mod,w1,w2,w);
1829: if ( DEG(w) > 0 && DEG(w) < DEG(r[j]) ) {
1830: gcd = UMALLOC(DEG(w));
1831: q = UMALLOC(DEG(r[j])-DEG(w));
1832: cpyum(w,gcd); divum(mod,r[j],w,q);
1833: r[j] = q; r[nf++] = gcd;
1834: }
1835: if ( nf == d )
1836: return d;
1837: }
1838: }
1839: }
1.6 noro 1840: /* NOTREACHED */
1841: error("berlekamp : cannot happen");
1842: return -1;
1.1 noro 1843: }
1844:
1.6 noro 1845: void minipoly_mod(int mod,UM f,UM p,UM mp)
1.1 noro 1846: {
1847: struct p_pair *list,*l,*l1,*lprev;
1848: int n,d;
1849: UM u,p0,p1,np0,np1,q,w;
1850:
1851: list = (struct p_pair *)MALLOC(sizeof(struct p_pair));
1852: list->p0 = u = W_UMALLOC(0); DEG(u) = 0; COEF(u)[0] = 1;
1853: list->p1 = W_UMALLOC(0); cpyum(list->p0,list->p1);
1854: list->next = 0;
1855: n = DEG(p); w = UMALLOC(2*n);
1856: p0 = UMALLOC(2*n); cpyum(list->p0,p0);
1857: p1 = UMALLOC(2*n); cpyum(list->p1,p1);
1858: q = W_UMALLOC(2*n);
1859: while ( 1 ) {
1860: COEF(p0)[DEG(p0)] = 0; DEG(p0)++; COEF(p0)[DEG(p0)] = 1;
1861: mulum(mod,f,p1,w); DEG(w) = divum(mod,w,p,q); cpyum(w,p1);
1862: np0 = UMALLOC(n); np1 = UMALLOC(n);
1863: lnf_mod(mod,n,p0,p1,list,np0,np1);
1864: if ( DEG(np1) < 0 ) {
1865: cpyum(np0,mp); return;
1866: } else {
1867: l1 = (struct p_pair *)MALLOC(sizeof(struct p_pair));
1868: l1->p0 = np0; l1->p1 = np1;
1869: for ( l = list, lprev = 0, d = DEG(np1);
1870: l && (DEG(l->p1) > d); lprev = l, l = l->next );
1871: if ( lprev ) {
1872: lprev->next = l1; l1->next = l;
1873: } else {
1874: l1->next = list; list = l1;
1875: }
1876: }
1877: }
1878: }
1879:
1.6 noro 1880: void lnf_mod(int mod,int n,UM p0,UM p1,struct p_pair *list,UM np0,UM np1)
1.1 noro 1881: {
1882: int inv,h,d1;
1883: UM t0,t1,s0,s1;
1884: struct p_pair *l;
1885:
1886: cpyum(p0,np0); cpyum(p1,np1);
1887: t0 = W_UMALLOC(n); t1 = W_UMALLOC(n);
1888: s0 = W_UMALLOC(n); s1 = W_UMALLOC(n);
1889: for ( l = list; l; l = l->next ) {
1890: d1 = DEG(np1);
1891: if ( d1 == DEG(l->p1) ) {
1892: inv = invm((mod-COEF(l->p1)[d1])%mod,mod);
1893: h = dmar(COEF(np1)[d1],inv,0,mod);
1894: mulsum(mod,l->p0,h,t0); addum(mod,np0,t0,s0); cpyum(s0,np0);
1895: mulsum(mod,l->p1,h,t1); addum(mod,np1,t1,s1); cpyum(s1,np1);
1896: }
1897: }
1898: }
1899:
1.6 noro 1900: int find_root(int mod,UM p,int *root)
1.1 noro 1901: {
1902: UM *r;
1903: int i,j;
1904:
1905: r = ALLOCA((DEG(p)+1)*sizeof(UM));
1906: ddd(mod,p,r);
1907: for ( i = 0, j = 0; r[i]; i++ )
1908: if ( DEG(r[i]) == 1 )
1909: root[j++] = (mod - COEF(r[i])[0]) % mod;
1910: return j;
1911: }
1912:
1.6 noro 1913: void showum(UM p)
1.1 noro 1914: {
1915: int i;
1916: int *c;
1917:
1918: for ( i = DEG(p), c = COEF(p); i >= 0; i-- )
1919: if ( c[i] )
1920: printf("+%dx^%d",c[i],i);
1921: printf("\n");
1922: }
1923:
1.6 noro 1924: void showumat(int **mat,int n)
1.1 noro 1925: {
1926: int i,j;
1927:
1928: for ( i = 0; i < n; i++ ) {
1929: for ( j = 0; j < n; j++ )
1930: printf("%d ",mat[i][j]);
1931: printf("\n");
1932: }
1933: }