Annotation of OpenXM_contrib2/asir2018/engine/Q.c, Revision 1.10
1.10 ! noro 1: /* $OpenXM: OpenXM_contrib2/asir2018/engine/Q.c,v 1.9 2018/10/19 23:27:38 noro Exp $ */
1.1 noro 2: #include "ca.h"
3: #include "gmp.h"
4: #include "base.h"
5: #include "inline.h"
6:
7: mpz_t ONEMPZ;
8: Z ONE;
9: int lf_lazy;
10: Z current_mod_lf;
11: int current_mod_lf_size;
12: gmp_randstate_t GMP_RAND;
13:
1.9 noro 14: #define F4_INTRAT_PERIOD 4
1.6 noro 15:
16: extern int DP_Print;
17:
1.1 noro 18: void isqrtz(Z a,Z *r);
19: void bshiftz(Z a,int n,Z *r);
20:
21: void *gc_realloc(void *p,size_t osize,size_t nsize)
22: {
23: return (void *)Risa_GC_realloc(p,nsize);
24: }
25:
26: void gc_free(void *p,size_t size)
27: {
28: Risa_GC_free(p);
29: }
30:
31: void init_gmpq()
32: {
1.10 ! noro 33: mp_set_memory_functions(Risa_GC_malloc,gc_realloc,gc_free);
1.1 noro 34:
35: mpz_init(ONEMPZ); mpz_set_ui(ONEMPZ,1); MPZTOZ(ONEMPZ,ONE);
36: gmp_randinit_default(GMP_RAND);
37: }
38:
1.7 noro 39: void printexpr(VL,Obj);
40:
1.3 noro 41: void pmat(Z **a,int row,int col)
42: {
43: int i,j;
44:
45: for ( i = 0; i < row; i++, printf("\n") )
46: for ( j = 0; j < col; j++, printf(" ") )
1.7 noro 47: printexpr(CO,(Obj)a[i][j]);
1.3 noro 48: printf("\n");
49: }
50:
1.1 noro 51: Z utoz(unsigned int u)
52: {
53: mpz_t z;
54: Z r;
55:
56: if ( !u ) return 0;
57: mpz_init(z); mpz_set_ui(z,u); MPZTOZ(z,r); return r;
58: }
59:
60: Z stoz(int s)
61: {
62: mpz_t z;
63: Z r;
64:
65: if ( !s ) return 0;
66: mpz_init(z); mpz_set_si(z,s); MPZTOZ(z,r); return r;
67: }
68:
69: int sgnz(Z z)
70: {
71: if ( !z ) return 0;
72: else return mpz_sgn(BDY(z));
73: }
74:
75: void nmq(Q q,Z *r)
76: {
77: if ( !q ) *r = 0;
78: else if ( INT(q) ) *r = (Z)q;
79: else {
80: MPZTOZ(mpq_numref(BDY(q)),*r);
81: }
82: }
83:
84: void dnq(Q q,Z *r)
85: {
86: if ( !q ) *r = 0;
87: else if ( INT(q) ) *r = ONE;
88: else {
89: MPZTOZ(mpq_denref(BDY(q)),*r);
90: }
91: }
92:
93: int sgnq(Q q)
94: {
95: if ( !q ) return 0;
96: else if ( q->z ) return mpz_sgn(BDY((Z)q));
97: else return mpz_sgn(mpq_numref(BDY(q)));
98: }
99:
100: Q mpqtozq(mpq_t a)
101: {
102: Z z;
103: Q q;
104:
105: if ( INTMPQ(a) ) {
106: MPZTOZ(mpq_numref(a),z); return (Q)z;
107: } else {
108: MPQTOQ(a,q); return q;
109: }
110: }
111:
112: void dupz(Z a,Z *b)
113: {
114: mpz_t t;
115:
116: if ( !a ) *b = a;
117: else {
118: mpz_init(t); mpz_set(t,BDY(a)); MPZTOZ(t,*b);
119: }
120: }
121:
122: int n_bits_z(Z a)
123: {
124: return a ? mpz_sizeinbase(BDY(a),2) : 0;
125: }
126:
127: void addz(Z n1,Z n2,Z *nr)
128: {
129: mpz_t t;
130: int s1,s2;
131:
132: if ( !n1 ) *nr = n2;
133: else if ( !n2 ) *nr = n1;
134: else if ( !n1->z || !n2->z )
135: error("addz : invalid argument");
136: else {
137: mpz_init(t); mpz_add(t,BDY(n1),BDY(n2)); MPZTOZ(t,*nr);
138: }
139: }
140:
141: void subz(Z n1,Z n2,Z *nr)
142: {
143: mpz_t t;
144:
145: if ( !n1 ) {
146: if ( !n2 )
147: *nr = 0;
148: else
149: chsgnz(n2,nr);
150: } else if ( !n2 )
151: *nr = n1;
152: else if ( n1 == n2 )
153: *nr = 0;
154: else if ( !n1->z || !n2->z )
155: error("subz : invalid argument");
156: else {
157: mpz_init(t); mpz_sub(t,BDY(n1),BDY(n2)); MPZTOZ(t,*nr);
158: }
159: }
160:
161: void mulz(Z n1,Z n2,Z *nr)
162: {
163: mpz_t t;
164:
165: if ( !n1 || !n2 ) *nr = 0;
166: else if ( !n1->z || !n2->z )
167: error("mulz : invalid argument");
168: else if ( UNIQ(n1) ) *nr = n2;
169: else if ( UNIQ(n2) ) *nr = n1;
170: else if ( MUNIQ(n1) ) chsgnz(n2,nr);
171: else if ( MUNIQ(n2) ) chsgnz(n1,nr);
172: else {
173: mpz_init(t); mpz_mul(t,BDY(n1),BDY(n2)); MPZTOZ(t,*nr);
174: }
175: }
176:
177: /* nr += n1*n2 */
178:
179: void muladdtoz(Z n1,Z n2,Z *nr)
180: {
1.3 noro 181: #if 0
1.1 noro 182: Z t;
183:
184: if ( n1 && n2 ) {
185: if ( !(*nr) ) {
186: NEWZ(t); mpz_init(BDY(t)); *nr = t;
187: }
188: mpz_addmul(BDY(*nr),BDY(n1),BDY(n2));
1.2 noro 189: if ( !mpz_sgn(BDY(*nr)) )
190: *nr = 0;
1.3 noro 191: }
1.2 noro 192: #else
193: Z t,s;
194:
195: mulz(n1,n2,&t); addz(*nr,t,&s); *nr = s;
196: #endif
1.1 noro 197: }
198:
199: /* nr += n1*u */
200:
201: void mul1addtoz(Z n1,long u,Z *nr)
202: {
1.3 noro 203: #if 0
1.1 noro 204: Z t;
205:
206: if ( n1 && u ) {
207: if ( !(*nr) ) {
208: NEWZ(t); mpz_init(BDY(t)); *nr = t;
209: }
210: if ( u >= 0 )
211: mpz_addmul_ui(BDY(*nr),BDY(n1),(unsigned long)u);
212: else
213: mpz_submul_ui(BDY(*nr),BDY(n1),(unsigned long)(-u));
1.2 noro 214: if ( !mpz_sgn(BDY(*nr)) )
215: *nr = 0;
1.1 noro 216: }
1.3 noro 217: #else
218: Z t,s;
219:
220: mul1z(n1,u,&t); addz(*nr,t,&s); *nr = s;
221: #endif
1.1 noro 222: }
223:
224: void mul1z(Z n1,long n2,Z *nr)
225: {
226: mpz_t t;
227:
228: if ( !n1 || !n2 ) *nr = 0;
229: else {
230: mpz_init(t); mpz_mul_si(t,BDY(n1),n2); MPZTOZ(t,*nr);
231: }
232: }
233:
234: void divz(Z n1,Z n2,Z *nq)
235: {
236: mpz_t t;
237: mpq_t a, b, q;
238:
239: if ( !n2 ) {
240: error("division by 0");
241: *nq = 0;
242: } else if ( !n1 )
243: *nq = 0;
244: else if ( n1 == n2 ) {
245: mpz_init(t); mpz_set_ui(t,1); MPZTOZ(t,*nq);
246: } else {
247: MPZTOMPQ(BDY(n1),a); MPZTOMPQ(BDY(n2),b);
248: mpq_init(q); mpq_div(q,a,b); *nq = (Z)mpqtozq(q);
249: }
250: }
251:
252: void remz(Z n1,Z n2,Z *nr)
253: {
254: mpz_t r;
255:
256: if ( !n2 ) {
257: error("division by 0");
258: *nr = 0;
259: } else if ( !n1 || n1 == n2 )
260: *nr = 0;
261: else if ( !n1->z || !n2->z )
262: error("remz : invalid argument");
263: else {
264: mpz_init(r);
265: mpz_mod(r,BDY(n1),BDY(n2));
266: if ( !mpz_sgn(r) ) *nr = 0;
267: else MPZTOZ(r,*nr);
268: }
269: }
270:
271: void divqrz(Z n1,Z n2,Z *nq,Z *nr)
272: {
273: mpz_t t, a, b, q, r;
274:
275: if ( !n2 ) {
276: error("division by 0");
277: *nq = 0; *nr = 0;
278: } else if ( !n1 ) {
279: *nq = 0; *nr = 0;
280: } else if ( !n1->z || !n2->z )
281: error("divqrz : invalid argument");
282: else if ( n1 == n2 ) {
283: mpz_init(t); mpz_set_ui(t,1); MPZTOZ(t,*nq); *nr = 0;
284: } else {
285: mpz_init(q); mpz_init(r);
286: mpz_fdiv_qr(q,r,BDY(n1),BDY(n2));
287: if ( !mpz_sgn(q) ) *nq = 0;
288: else MPZTOZ(q,*nq);
289: if ( !mpz_sgn(r) ) *nr = 0;
290: else MPZTOZ(r,*nr);
291: }
292: }
293:
294: void divsz(Z n1,Z n2,Z *nq)
295: {
296: mpz_t t;
297: mpq_t a, b, q;
298:
299: if ( !n2 ) {
300: error("division by 0");
301: *nq = 0;
302: } else if ( !n1 )
303: *nq = 0;
304: else if ( !n1->z || !n2->z )
305: error("divsz : invalid argument");
306: else if ( n1 == n2 ) {
307: mpz_init(t); mpz_set_ui(t,1); MPZTOZ(t,*nq);
308: } else {
309: mpz_init(t); mpz_divexact(t,BDY(n1),BDY(n2)); MPZTOZ(t,*nq);
310: }
311: }
312:
313: void chsgnz(Z n,Z *nr)
314: {
315: mpz_t t;
316:
317: if ( !n )
318: *nr = 0;
319: else if ( !n->z )
320: error("chsgnz : invalid argument");
321: else {
322: t[0] = BDY(n)[0]; mpz_neg(t,t); MPZTOZ(t,*nr);
323: }
324: }
325:
326: void absz(Z n,Z *nr)
327: {
328: if ( !n ) *nr = 0;
329: else if ( !n->z )
330: error("absz : invalid argument");
331: else if ( sgnz(n) < 0 ) chsgnz(n,nr);
332: else *nr = n;
333: }
334:
335: int evenz(Z n)
336: {
337: return !n ? 1 : mpz_even_p(BDY(n));
338: }
339:
340: int smallz(Z n)
341: {
342: if ( !n ) return 1;
343: else if ( INT(n) && mpz_fits_sint_p(BDY(n)) ) return 1;
344: else return 0;
345: }
346:
347: void pwrz(Z n1,Z n,Z *nr)
348: {
349: mpq_t t,q;
350: mpz_t z;
351: Q p,r;
352:
353: if ( !n || UNIQ(n1) ) *nr = ONE;
354: else if ( !n1 ) *nr = 0;
355: else if ( !n->z || !n1->z )
356: error("pwrz : invalid argument");
357: else if ( MUNIQ(n1) ) {
358: if ( mpz_even_p(BDY((Z)n)) ) *nr = ONE;
359: else *nr = n1;
360: } else if ( !smallz(n) ) {
361: error("exponent too big."); *nr = 0;
362: } else if ( n1->z && mpz_sgn(BDY((Z)n))>0 ) {
1.5 noro 363: mpz_init(z); mpz_pow_ui(z,BDY(n1),ZTOS(n)); MPZTOZ(z,*nr);
1.1 noro 364: } else {
365: MPZTOMPQ(BDY(n1),q); MPQTOQ(q,r);
366: pwrq(r,(Q)n,&p); *nr = (Z)p;
367: }
368: }
369:
370: int cmpz(Z q1,Z q2)
371: {
372: int sgn;
373:
374: if ( !q1 ) {
375: if ( !q2 )
376: return 0;
377: else
378: return -mpz_sgn(BDY(q2));
379: } else if ( !q2 )
380: return mpz_sgn(BDY(q1));
381: else if ( !q1->z || !q2->z )
382: error("mpqz : invalid argument");
383: else if ( (sgn = mpz_sgn(BDY(q1))) != mpz_sgn(BDY(q2)) )
384: return sgn;
385: else {
386: sgn = mpz_cmp(BDY(q1),BDY(q2));
387: if ( sgn > 0 ) return 1;
388: else if ( sgn < 0 ) return -1;
389: else return 0;
390: }
391: }
392:
393: void gcdz(Z n1,Z n2,Z *nq)
394: {
395: mpz_t t;
396:
397: if ( !n1 ) *nq = n2;
398: else if ( !n2 ) *nq = n1;
399: else if ( !n1->z || !n2->z )
400: error("gcdz : invalid argument");
401: else {
402: mpz_init(t); mpz_gcd(t,BDY(n1),BDY(n2));
403: MPZTOZ(t,*nq);
404: }
405: }
406:
407: void invz(Z n1,Z n2,Z *nq)
408: {
409: mpz_t t;
410:
411: if ( !n1 || !n2 || !n1->z || !n2->z )
412: error("invz : invalid argument");
413: mpz_init(t); mpz_invert(t,BDY(n1),BDY(n2));
414: MPZTOZ(t,*nq);
415: }
416:
417: void lcmz(Z n1,Z n2,Z *nq)
418: {
419: Z g,t;
420:
421: if ( !n1 || !n2 ) *nq = 0;
422: else if ( !n1->z || !n2->z )
423: error("lcmz : invalid argument");
424: else {
425: gcdz(n1,n2,&g); divsz(n1,g,&t);
426: mulz(n2,t,nq);
427: }
428: }
429:
430: void gcdvz(VECT v,Z *q)
431: {
432: int n,i;
433: Z *b;
434: Z g,g1;
435:
436: n = v->len;
437: b = (Z *)v->body;
438: g = b[0];
439: for ( i = 1; i < n; i++ ) {
440: gcdz(g,b[i],&g1); g = g1;
441: }
442: *q = g;
443: }
444:
445: void gcdvz_estimate(VECT v,Z *q)
446: {
447: int n,m,i;
448: Z s,t,u;
449: Z *b;
450:
451: n = v->len;
452: b = (Z *)v->body;
453: if ( n == 1 ) {
454: if ( mpz_sgn(BDY(b[0]))<0 ) chsgnz(b[0],q);
455: else *q = b[0];
456: }
457: m = n/2;
458: for ( i = 0, s = 0; i < m; i++ ) {
459: if ( b[i] && mpz_sgn(BDY(b[i]))<0 ) subz(s,b[i],&u);
460: else addz(s,b[i],&u);
461: s = u;
462: }
1.4 noro 463: for ( t = 0; i < n; i++ ) {
1.1 noro 464: if ( b[i] && mpz_sgn(BDY(b[i]))<0 ) subz(t,b[i],&u);
465: else addz(t,b[i],&u);
466: t = u;
467: }
468: gcdz(s,t,q);
469: }
470:
1.4 noro 471: void gcdv_mpz_estimate(mpz_t g,mpz_t *b,int n)
472: {
473: int m,m2,i,j;
474: mpz_t s,t;
475:
476: mpz_init(g);
477: for ( i = 0, m = 0; i < n; i++ )
478: if ( mpz_sgn(b[i]) ) m++;
479: if ( !m ) {
480: mpz_set_ui(g,0);
481: return;
482: }
483: if ( m == 1 ) {
484: for ( i = 0, m = 0; i < n; i++ )
485: if ( mpz_sgn(b[i]) ) break;
486: if ( mpz_sgn(b[i])<0 ) mpz_neg(g,b[i]);
487: else mpz_set(g,b[i]);
488: return ;
489: }
490: m2 = m/2;
491: mpz_init_set_ui(s,0);
492: for ( i = j = 0; j < m2; i++ ) {
493: if ( mpz_sgn(b[i]) ) {
494: if ( mpz_sgn(b[i])<0 )
495: mpz_sub(s,s,b[i]);
496: else
497: mpz_add(s,s,b[i]);
498: j++;
499: }
500: }
501: mpz_init_set_ui(t,0);
502: for ( ; i < n; i++ ) {
503: if ( mpz_sgn(b[i]) ) {
504: if ( mpz_sgn(b[i])<0 )
505: mpz_sub(t,t,b[i]);
506: else
507: mpz_add(t,t,b[i]);
508: }
509: }
510: mpz_gcd(g,s,t);
511: }
512:
513:
1.1 noro 514: void factorialz(unsigned int n,Z *nr)
515: {
516: mpz_t a;
517: mpz_init(a);
518: mpz_fac_ui(a,n);
519: MPZTOZ(a,*nr);
520: }
521:
522: void randomz(int blen,Z *nr)
523: {
524: mpz_t z;
525:
526: mpz_init(z);
527: mpz_urandomb(z,GMP_RAND,blen);
528: MPZTOZ(z,*nr);
529: }
530:
531: int tstbitz(Z n,int k)
532: {
533: if ( !n || !n->z )
534: error("tstbitz : invalid argument");
535: return !n ? 0 : mpz_tstbit(BDY(n),k);
536: }
537:
538: void addq(Q n1,Q n2,Q *nr)
539: {
540: mpq_t q1,q2,t;
541:
542: if ( !n1 ) *nr = n2;
543: else if ( !n2 ) *nr = n1;
544: else if ( n1->z && n2->z )
545: addz((Z)n1,(Z)n2,(Z *)nr);
546: else {
547: if ( n1->z ) MPZTOMPQ(BDY((Z)n1),q1);
548: else q1[0] = BDY(n1)[0];
549: if ( n2->z ) MPZTOMPQ(BDY((Z)n2),q2);
550: else q2[0] = BDY(n2)[0];
551: mpq_init(t); mpq_add(t,q1,q2); *nr = mpqtozq(t);
552: }
553: }
554:
555: void subq(Q n1,Q n2,Q *nr)
556: {
557: mpq_t q1,q2,t;
558:
559: if ( !n1 ) {
560: if ( !n2 ) *nr = 0;
561: else if ( n1->z ) chsgnz((Z)n1,(Z *)nr);
562: else {
563: mpq_init(t); mpq_neg(t,BDY(n2)); MPQTOQ(t,*nr);
564: }
565: } else if ( !n2 ) *nr = n1;
566: else if ( n1 == n2 ) *nr = 0;
567: else if ( n1->z && n2->z )
568: subz((Z)n1,(Z)n2,(Z *)nr);
569: else {
570: if ( n1->z ) MPZTOMPQ(BDY((Z)n1),q1);
571: else q1[0] = BDY(n1)[0];
572: if ( n2->z ) MPZTOMPQ(BDY((Z)n2),q2);
573: else q2[0] = BDY(n2)[0];
574: mpq_init(t); mpq_sub(t,q1,q2); *nr = mpqtozq(t);
575: }
576: }
577:
578: void mulq(Q n1,Q n2,Q *nr)
579: {
580: mpq_t t,q1,q2;
581:
582: if ( !n1 || !n2 ) *nr = 0;
583: else if ( n1->z && n2->z )
584: mulz((Z)n1,(Z)n2,(Z *)nr);
585: else {
586: if ( n1->z ) MPZTOMPQ(BDY((Z)n1),q1);
587: else q1[0] = BDY(n1)[0];
588: if ( n2->z ) MPZTOMPQ(BDY((Z)n2),q2);
589: else q2[0] = BDY(n2)[0];
590: mpq_init(t); mpq_mul(t,q1,q2); *nr = mpqtozq(t);
591: }
592: }
593:
594: void divq(Q n1,Q n2,Q *nq)
595: {
596: mpq_t t,q1,q2;
597:
598: if ( !n2 ) {
599: error("division by 0");
600: *nq = 0;
601: return;
602: } else if ( !n1 ) *nq = 0;
603: else if ( n1 == n2 ) *nq = (Q)ONE;
604: else {
605: if ( n1->z ) MPZTOMPQ(BDY((Z)n1),q1);
606: else q1[0] = BDY(n1)[0];
607: if ( n2->z ) MPZTOMPQ(BDY((Z)n2),q2);
608: else q2[0] = BDY(n2)[0];
609: mpq_init(t); mpq_div(t,q1,q2); *nq = mpqtozq(t);
610: }
611: }
612:
613: void invq(Q n,Q *nr)
614: {
615: Z nm,dn;
616:
617: if ( INT(n) )
618: divq((Q)ONE,n,nr);
619: else {
620: nmq(n,&nm);
621: dnq(n,&dn);
622: divq((Q)dn,(Q)nm,nr);
623: }
624: }
625:
626: void chsgnq(Q n,Q *nr)
627: {
628: mpq_t t;
629:
630: if ( !n ) *nr = 0;
631: else if (n->z ) chsgnz((Z)n,(Z *)nr);
632: else {
633: mpq_init(t); mpq_neg(t,BDY(n)); MPQTOQ(t,*nr);
634: }
635: }
636:
637: void absq(Q n,Q *nr)
638: {
639: if ( !n ) *nr = 0;
640: else if ( n->z ) absz((Z)n,(Z *)nr);
641: else if ( sgnq(n) < 0 ) chsgnq(n,nr);
642: else *nr = n;
643: }
644:
645: void pwrq(Q n1,Q n,Q *nr)
646: {
647: int e;
648: mpz_t nm,dn;
649: mpq_t t;
650:
651: if ( !n || UNIQ((Z)n1) || UNIQ(n1) ) *nr = (Q)ONE;
652: else if ( !n1 ) *nr = 0;
653: else if ( !INT(n) ) {
654: error("can't calculate fractional power."); *nr = 0;
655: } else if ( !smallz((Z)n) ) {
656: error("exponent too big."); *nr = 0;
657: } else {
1.5 noro 658: e = ZTOS(n);
1.1 noro 659: if ( e < 0 ) {
660: e = -e;
661: if ( n1->z ) {
662: nm[0] = ONEMPZ[0];
663: dn[0] = BDY((Z)n1)[0];
664: } else {
665: nm[0] = mpq_denref(BDY(n1))[0];
666: dn[0] = mpq_numref(BDY(n1))[0];
667: }
668: } else {
669: if ( n1->z ) {
670: nm[0] = BDY((Z)n1)[0];
671: dn[0] = ONEMPZ[0];
672: } else {
673: nm[0] = mpq_numref(BDY(n1))[0];
674: dn[0] = mpq_denref(BDY(n1))[0];
675: }
676: }
677: mpq_init(t);
678: mpz_pow_ui(mpq_numref(t),nm,e); mpz_pow_ui(mpq_denref(t),dn,e);
679: *nr = mpqtozq(t);
680: }
681: }
682:
683: int cmpq(Q n1,Q n2)
684: {
685: mpq_t q1,q2;
686: int sgn;
687:
688: if ( !n1 ) {
689: if ( !n2 ) return 0;
690: else return (n2->z) ? -mpz_sgn(BDY((Z)n2)) : -mpq_sgn(BDY(n2));
691: } if ( !n2 ) return (n1->z) ? mpz_sgn(BDY((Z)n1)) : mpq_sgn(BDY(n1));
692: else if ( n1->z && n2->z )
693: return cmpz((Z)n1,(Z)n2);
694: else if ( (sgn = mpq_sgn(BDY(n1))) != mpq_sgn(BDY(n2)) ) return sgn;
695: else {
696: if ( n1->z ) MPZTOMPQ(BDY((Z)n1),q1);
697: else q1[0] = BDY(n1)[0];
698: if ( n2->z ) MPZTOMPQ(BDY((Z)n2),q2);
699: else q2[0] = BDY(n2)[0];
700: sgn = mpq_cmp(q1,q2);
701: if ( sgn > 0 ) return 1;
702: else if ( sgn < 0 ) return -1;
703: else return 0;
704: }
705: }
706:
707: /* t = [nC0 nC1 ... nCn] */
708:
709: void mkbc(int n,Z *t)
710: {
711: int i;
712: Z c,d,iq;
713:
714: for ( t[0] = ONE, i = 1; i <= n/2; i++ ) {
1.5 noro 715: STOZ(n-i+1,c); mulz(t[i-1],c,&d);
716: STOZ(i,iq); divsz(d,iq,&t[i]);
1.1 noro 717: }
718: for ( ; i <= n; i++ )
719: t[i] = t[n-i];
720: }
721:
722: /*
723: * Dx^k*x^l = W(k,l,0)*x^l*Dx^k+W(k,l,1)*x^(l-1)*x^(k-1)*+...
724: *
725: * t = [W(k,l,0) W(k,l,1) ... W(k,l,min(k,l)]
726: * where W(k,l,i) = i! * kCi * lCi
727: */
728:
729: /* mod m table */
730: /* XXX : should be optimized */
731:
732: void mkwcm(int k,int l,int m,int *t)
733: {
734: int i,n;
735: Z *s;
736:
737: n = MIN(k,l);
738: s = (Z *)ALLOCA((n+1)*sizeof(Q));
739: mkwc(k,l,s);
740: for ( i = 0; i <= n; i++ ) {
741: t[i] = remqi((Q)s[i],m);
742: }
743: }
744:
745: void mkwc(int k,int l,Z *t)
746: {
747: mpz_t a,b,q,nm,z,u;
748: int i,n;
749:
750: n = MIN(k,l);
751: mpz_init_set_ui(z,1);
752: mpz_init(u); mpz_set(u,z); MPZTOZ(u,t[0]);
753: mpz_init(a); mpz_init(b); mpz_init(nm);
754: for ( i = 1; i <= n; i++ ) {
755: mpz_set_ui(a,k-i+1); mpz_set_ui(b,l-i+1); mpz_mul(nm,a,b);
756: mpz_mul(z,BDY(t[i-1]),nm); mpz_fdiv_q_ui(z,z,i);
757: mpz_init(u); mpz_set(u,z); MPZTOZ(u,t[i]);
758: }
759: }
760:
761: void lgp(P p,Z *g,Z *l);
762:
763: void ptozp(P p,int sgn,Q *c,P *pr)
764: {
765: Z nm,dn;
766:
767: if ( !p ) {
768: *c = 0; *pr = 0;
769: } else {
770: lgp(p,&nm,&dn);
771: divz(nm,dn,(Z *)c);
772: divsp(CO,p,(P)*c,pr);
773: }
774: }
775:
776: void lgp(P p,Z *g,Z *l)
777: {
778: DCP dc;
779: Z g1,g2,l1,l2,l3,l4;
780:
781: if ( NUM(p) ) {
782: if ( ((Q)p)->z ) {
783: MPZTOZ(BDY((Z)p),*g);
784: *l = ONE;
785: } else {
786: MPZTOZ(mpq_numref(BDY((Q)p)),*g);
787: MPZTOZ(mpq_denref(BDY((Q)p)),*l);
788: }
789: } else {
790: dc = DC(p); lgp(COEF(dc),g,l);
791: for ( dc = NEXT(dc); dc; dc = NEXT(dc) ) {
792: lgp(COEF(dc),&g1,&l1); gcdz(*g,g1,&g2); *g = g2;
793: gcdz(*l,l1,&l2); mulz(*l,l1,&l3); divz(l3,l2,l);
794: }
795: }
796: }
797:
798: void qltozl(Q *w,int n,Z *dvr)
799: {
800: Z nm,dn;
801: Z g,g1,l1,l2,l3;
802: Q c;
803: int i;
804: struct oVECT v;
805:
806: for ( i = 0; i < n; i++ )
807: if ( w[i] && !w[i]->z )
808: break;
809: if ( i == n ) {
810: v.id = O_VECT; v.len = n; v.body = (pointer *)w;
811: gcdvz(&v,dvr); return;
812: }
813: for ( i = 0; !w[i]; i++ );
814: c = w[i];
815: if ( !c->z ) {
816: MPZTOZ(mpq_numref(BDY(c)),nm); MPZTOZ(mpq_denref(BDY(c)),dn);
817: } else {
818: MPZTOZ(BDY((Z)c),nm); dn = ONE;
819: }
820: for ( i++; i < n; i++ ) {
821: c = w[i];
822: if ( !c ) continue;
823: if ( !c->z ) {
824: MPZTOZ(mpq_numref(BDY(c)),g1); MPZTOZ(mpq_denref(BDY(c)),l1);
825: } else {
826: MPZTOZ(BDY((Z)c),g1); l1 = ONE;
827: }
828: gcdz(nm,g1,&g); nm = g;
829: gcdz(dn,l1,&l2); mulz(dn,l1,&l3); divz(l3,l2,&dn);
830: }
831: divz(nm,dn,dvr);
832: }
833:
834: int z_bits(Q q)
835: {
836: if ( !q ) return 0;
837: else if ( q->z ) return mpz_sizeinbase(BDY((Z)q),2);
838: else
839: return mpz_sizeinbase(mpq_numref(BDY(q)),2)
840: + mpz_sizeinbase(mpq_denref(BDY(q)),2);
841: }
842:
843: int zp_mag(P p)
844: {
845: int s;
846: DCP dc;
847:
848: if ( !p ) return 0;
849: else if ( OID(p) == O_N ) return z_bits((Q)p);
850: else {
851: for ( dc = DC(p), s = 0; dc; dc = NEXT(dc) ) s += zp_mag(COEF(dc));
852: return s;
853: }
854: }
855:
856: void makesubstz(VL v,NODE *s)
857: {
858: NODE r,r0;
859: Z q;
860: unsigned int n;
861:
862: for ( r0 = 0; v; v = NEXT(v) ) {
863: NEXTNODE(r0,r); BDY(r) = (pointer)v->v;
864: #if defined(_PA_RISC1_1)
865: n = mrand48()&BMASK; q = utoz(n);
866: #else
867: n = random(); q = utoz(n);
868: #endif
869: NEXTNODE(r0,r); BDY(r) = (pointer)q;
870: }
871: if ( r0 ) NEXT(r) = 0;
872: *s = r0;
873: }
874:
875: unsigned int remqi(Q a,unsigned int mod)
876: {
877: unsigned int c,nm,dn;
878: mpz_t r;
879:
880: if ( !a ) return 0;
881: else if ( a->z ) {
882: mpz_init(r);
883: c = mpz_fdiv_r_ui(r,BDY((Z)a),mod);
884: } else {
885: mpz_init(r);
886: nm = mpz_fdiv_r_ui(r,mpq_numref(BDY(a)),mod);
887: dn = mpz_fdiv_r_ui(r,mpq_denref(BDY(a)),mod);
888: dn = invm(dn,mod);
889: DMAR(nm,dn,0,mod,c);
890: }
891: return c;
892: }
893:
894: int generic_gauss_elim(MAT mat,MAT *nm,Z *dn,int **rindp,int **cindp)
895: {
896: int **wmat;
897: Z **bmat,**tmat,*bmi,*tmi;
898: Z q,m1,m2,m3,s,u;
899: int *wmi,*colstat,*wcolstat,*rind,*cind;
900: int row,col,ind,md,i,j,k,l,t,t1,rank,rank0,inv;
901: MAT r,crmat;
902: int ret;
1.8 noro 903: MAT mat2,nm2;
904: Z dn2;
905: int *rind2,*cind2;
906: int ret2;
1.1 noro 907:
1.6 noro 908: #if SIZEOF_LONG == 8
1.8 noro 909: ret = generic_gauss_elim64(mat,nm,dn,rindp,cindp);
910: return ret;
1.6 noro 911: #endif
1.1 noro 912: bmat = (Z **)mat->body;
913: row = mat->row; col = mat->col;
914: wmat = (int **)almat(row,col);
915: colstat = (int *)MALLOC_ATOMIC(col*sizeof(int));
916: wcolstat = (int *)MALLOC_ATOMIC(col*sizeof(int));
917: for ( ind = 0; ; ind++ ) {
918: if ( DP_Print ) {
919: fprintf(asir_out,"."); fflush(asir_out);
920: }
921: md = get_lprime(ind);
922: for ( i = 0; i < row; i++ )
923: for ( j = 0, bmi = bmat[i], wmi = wmat[i]; j < col; j++ )
924: wmi[j] = remqi((Q)bmi[j],md);
925: rank = generic_gauss_elim_mod(wmat,row,col,md,wcolstat);
926: if ( !ind ) {
927: RESET:
928: m1 = utoz(md);
929: rank0 = rank;
930: bcopy(wcolstat,colstat,col*sizeof(int));
931: MKMAT(crmat,rank,col-rank);
932: MKMAT(r,rank,col-rank); *nm = r;
933: tmat = (Z **)crmat->body;
934: for ( i = 0; i < rank; i++ )
935: for ( j = k = 0, tmi = tmat[i], wmi = wmat[i]; j < col; j++ )
936: if ( !colstat[j] ) tmi[k++] = utoz(wmi[j]);
937: } else {
938: if ( rank < rank0 ) {
939: if ( DP_Print ) {
940: fprintf(asir_out,"lower rank matrix; continuing...\n");
941: fflush(asir_out);
942: }
943: continue;
944: } else if ( rank > rank0 ) {
945: if ( DP_Print ) {
946: fprintf(asir_out,"higher rank matrix; resetting...\n");
947: fflush(asir_out);
948: }
949: goto RESET;
950: } else {
951: for ( j = 0; (j<col) && (colstat[j]==wcolstat[j]); j++ );
952: if ( j < col ) {
953: if ( DP_Print ) {
954: fprintf(asir_out,"inconsitent colstat; resetting...\n");
955: fflush(asir_out);
956: }
957: goto RESET;
958: }
959: }
960:
961: inv = invm(remqi((Q)m1,md),md);
962: m2 = utoz(md); mulz(m1,m2,&m3);
963: for ( i = 0; i < rank; i++ )
964: for ( j = k = 0, tmi = tmat[i], wmi = wmat[i]; j < col; j++ )
965: if ( !colstat[j] ) {
966: if ( tmi[k] ) {
967: /* f3 = f1+m1*(m1 mod m2)^(-1)*(f2 - f1 mod m2) */
968: t = remqi((Q)tmi[k],md);
969: if ( wmi[j] >= t ) t = wmi[j]-t;
970: else t = md-(t-wmi[j]);
971: DMAR(t,inv,0,md,t1)
972: u = utoz(t1); mulz(m1,u,&s);
973: addz(tmi[k],s,&u); tmi[k] = u;
974: } else if ( wmi[j] ) {
975: /* f3 = m1*(m1 mod m2)^(-1)*f2 */
976: DMAR(wmi[j],inv,0,md,t)
977: u = utoz(t); mulz(m1,u,&s); tmi[k] = s;
978: }
979: k++;
980: }
981: m1 = m3;
982: if ( ind % F4_INTRAT_PERIOD )
983: ret = 0;
984: else
985: ret = intmtoratm(crmat,m1,*nm,dn);
986: if ( ret ) {
987: *rindp = rind = (int *)MALLOC_ATOMIC(rank*sizeof(int));
988: *cindp = cind = (int *)MALLOC_ATOMIC((col-rank)*sizeof(int));
989: for ( j = k = l = 0; j < col; j++ )
990: if ( colstat[j] ) rind[k++] = j;
991: else cind[l++] = j;
992: if ( gensolve_check(mat,*nm,*dn,rind,cind) )
993: return rank;
994: }
995: }
996: }
997: }
998:
999: int generic_gauss_elim2(MAT mat,MAT *nm,Z *dn,int **rindp,int **cindp)
1000: {
1001:
1002: MAT full;
1003: Z **bmat,**b;
1004: Z *bmi;
1005: Z dn0;
1006: int row,col,md,i,j,rank,ret;
1007: int **wmat;
1008: int *wmi;
1009: int *colstat,*rowstat;
1010:
1011: bmat = (Z **)mat->body;
1012: row = mat->row; col = mat->col;
1013: wmat = (int **)almat(row,col);
1014: colstat = (int *)MALLOC_ATOMIC(col*sizeof(int));
1015: rowstat = (int *)MALLOC_ATOMIC(row*sizeof(int));
1016: /* XXX */
1017: md = get_lprime(0);
1018: for ( i = 0; i < row; i++ )
1019: for ( j = 0, bmi = bmat[i], wmi = wmat[i]; j < col; j++ )
1020: wmi[j] = remqi((Q)bmi[j],md);
1021: rank = generic_gauss_elim_mod2(wmat,row,col,md,colstat,rowstat);
1022: b = (Z **)MALLOC(rank*sizeof(Z));
1023: for ( i = 0; i < rank; i++ ) b[i] = bmat[rowstat[i]];
1024: NEWMAT(full); full->row = rank; full->col = col; full->body = (pointer **)b;
1025: ret = generic_gauss_elim_full(full,nm,dn,rindp,cindp);
1026: if ( !ret ) {
1027: rank = generic_gauss_elim(mat,nm,&dn0,rindp,cindp);
1028: for ( i = 0; i < rank; i++ ) dn[i] = dn0;
1029: }
1030: return rank;
1031: }
1032:
1033: int generic_gauss_elim_full(MAT mat,MAT *nm,Z *dn,int **rindp,int **cindp)
1034: {
1035: int **wmat;
1036: int *stat;
1037: Z **bmat,**tmat,*bmi,*tmi,*ri;
1038: Z q,m1,m2,m3,s,u;
1039: int *wmi,*colstat,*wcolstat,*rind,*cind;
1040: int row,col,ind,md,i,j,k,l,t,t1,rank,rank0,inv,h;
1041: MAT r,crmat;
1042: int ret,initialized,done;
1043:
1044: initialized = 0;
1045: bmat = (Z **)mat->body;
1046: row = mat->row; col = mat->col;
1047: wmat = (int **)almat(row,col);
1048: stat = (int *)MALLOC_ATOMIC(row*sizeof(int));
1049: for ( i = 0; i < row; i++ ) stat[i] = 0;
1050: colstat = (int *)MALLOC_ATOMIC(col*sizeof(int));
1051: wcolstat = (int *)MALLOC_ATOMIC(col*sizeof(int));
1052: for ( ind = 0; ; ind++ ) {
1053: if ( DP_Print ) {
1054: fprintf(asir_out,"."); fflush(asir_out);
1055: }
1056: md = get_lprime(ind);
1057: for ( i = 0; i < row; i++ )
1058: for ( j = 0, bmi = bmat[i], wmi = wmat[i]; j < col; j++ )
1059: wmi[j] = remqi((Q)bmi[j],md);
1060: rank = generic_gauss_elim_mod(wmat,row,col,md,wcolstat);
1061: if ( rank < row ) continue;
1062: if ( !initialized ) {
1063: m1 = utoz(md);
1064: bcopy(wcolstat,colstat,col*sizeof(int));
1065: MKMAT(crmat,row,col-row);
1066: MKMAT(r,row,col-row); *nm = r;
1067: tmat = (Z **)crmat->body;
1068: for ( i = 0; i < row; i++ )
1069: for ( j = k = 0, tmi = tmat[i], wmi = wmat[i]; j < col; j++ )
1070: if ( !colstat[j] ) tmi[k++] = utoz(wmi[j]);
1071: initialized = 1;
1072: } else {
1073: for ( j = 0; (j<col) && (colstat[j]==wcolstat[j]); j++ );
1074: if ( j < col ) continue;
1075:
1076: inv = invm(remqi((Q)m1,md),md);
1077: m2 = utoz(md); mulz(m1,m2,&m3);
1078: for ( i = 0; i < row; i++ )
1079: switch ( stat[i] ) {
1080: case 1:
1081: /* consistency check */
1082: ri = (Z *)BDY(r)[i]; wmi = wmat[i];
1083: for ( j = 0; j < col; j++ ) if ( colstat[j] ) break;
1084: h = md-remqi((Q)dn[i],md);
1085: for ( j++, k = 0; j < col; j++ )
1086: if ( !colstat[j] ) {
1087: t = remqi((Q)ri[k],md);
1088: DMAR(wmi[i],h,t,md,t1);
1089: if ( t1 ) break;
1090: }
1091: if ( j == col ) { stat[i]++; break; }
1092: else {
1093: /* fall to the case 0 */
1094: stat[i] = 0;
1095: }
1096: case 0:
1097: tmi = tmat[i]; wmi = wmat[i];
1098: for ( j = k = 0; j < col; j++ )
1099: if ( !colstat[j] ) {
1100: if ( tmi[k] ) {
1101: /* f3 = f1+m1*(m1 mod m2)^(-1)*(f2 - f1 mod m2) */
1102: t = remqi((Q)tmi[k],md);
1103: if ( wmi[j] >= t ) t = wmi[j]-t;
1104: else t = md-(t-wmi[j]);
1105: DMAR(t,inv,0,md,t1)
1106: u = utoz(t1); mulz(m1,u,&s);
1107: addz(tmi[k],s,&u); tmi[k] = u;
1108: } else if ( wmi[j] ) {
1109: /* f3 = m1*(m1 mod m2)^(-1)*f2 */
1110: DMAR(wmi[j],inv,0,md,t)
1111: u = utoz(t); mulz(m1,u,&s); tmi[k] = s;
1112: }
1113: k++;
1114: }
1115: break;
1116: case 2: default:
1117: break;
1118: }
1119: m1 = m3;
1120: if ( ind % 4 )
1121: ret = 0;
1122: else
1123: ret = intmtoratm2(crmat,m1,*nm,dn,stat);
1124: if ( ret ) {
1125: *rindp = rind = (int *)MALLOC_ATOMIC(row*sizeof(int));
1126: *cindp = cind = (int *)MALLOC_ATOMIC((col-row)*sizeof(int));
1127: for ( j = k = l = 0; j < col; j++ )
1128: if ( colstat[j] ) rind[k++] = j;
1129: else cind[l++] = j;
1130: return gensolve_check2(mat,*nm,dn,rind,cind);
1131: }
1132: }
1133: }
1134: }
1135:
1136: int generic_gauss_elim_direct(MAT mat,MAT *nm,Z *dn,int **rindp,int **cindp){
1137: Z **bmat,*s;
1138: Z u,v,w,x,d,t,y;
1139: int row,col,i,j,k,l,m,rank;
1140: int *colstat,*colpos,*cind;
1141: MAT r,in;
1142:
1143: row = mat->row; col = mat->col;
1144: MKMAT(in,row,col);
1145: for ( i = 0; i < row; i++ )
1146: for ( j = 0; j < col; j++ ) in->body[i][j] = mat->body[i][j];
1147: bmat = (Z **)in->body;
1148: colstat = (int *)MALLOC_ATOMIC(col*sizeof(int));
1149: *rindp = colpos = (int *)MALLOC_ATOMIC(row*sizeof(int));
1150: for ( j = 0, rank = 0, d = ONE; j < col; j++ ) {
1151: for ( i = rank; i < row && !bmat[i][j]; i++ );
1152: if ( i == row ) { colstat[j] = 0; continue; }
1153: else { colstat[j] = 1; colpos[rank] = j; }
1154: if ( i != rank )
1155: for ( k = j; k < col; k++ ) {
1156: t = bmat[i][k]; bmat[i][k] = bmat[rank][k]; bmat[rank][k] = t;
1157: }
1158: for ( i = rank+1, v = bmat[rank][j]; i < row; i++ )
1159: for ( k = j, u = bmat[i][j]; k < col; k++ ) {
1160: mulz(bmat[i][k],v,&w); mulz(bmat[rank][k],u,&x);
1161: subz(w,x,&y); divsz(y,d,&bmat[i][k]);
1162: }
1163: d = v; rank++;
1164: }
1165: *dn = d;
1166: s = (Z *)MALLOC(col*sizeof(Z));
1167: for ( i = rank-1; i >= 0; i-- ) {
1168: for ( k = colpos[i]; k < col; k++ ) mulz(bmat[i][k],d,&s[k]);
1169: for ( m = rank-1; m > i; m-- ) {
1170: for ( k = colpos[m], u = bmat[i][k]; k < col; k++ ) {
1171: mulz(bmat[m][k],u,&w); subz(s[k],w,&x); s[k] = x;
1172: }
1173: }
1174: for ( k = colpos[i], u = bmat[i][k]; k < col; k++ )
1175: divz(s[k],u,&bmat[i][k]);
1176: }
1177: *cindp = cind = (int *)MALLOC_ATOMIC((col-rank)*sizeof(int));
1178: MKMAT(r,rank,col-rank); *nm = r;
1179: for ( j = 0, k = 0; j < col; j++ )
1180: if ( !colstat[j] ) {
1181: cind[k] = j;
1182: for ( i = 0; i < rank; i++ ) r->body[i][k] = bmat[i][j];
1183: k++;
1184: }
1185: return rank;
1186: }
1187:
1.8 noro 1188: int mpz_intmtoratm(mpz_t **mat,int row,int col,mpz_t md,mpz_t **nm,mpz_t dn)
1189: {
1190: mpz_t t,s,b,u,nm1,dn1;
1191: int i,j,k,l,ret;
1192: mpz_t *mi,*nmk;
1193:
1194: if ( UNIMPZ(md) )
1195: return 0;
1196: mpz_init(t); mpz_init(s); mpz_init(b); mpz_init(u);
1197: mpz_init(nm1); mpz_init(dn1);
1198: mpz_fdiv_q_2exp(t,md,1); mpz_sqrt(s,t); mpz_fdiv_q_2exp(b,s,64);
1199: if ( !mpz_sgn(b) ) mpz_set_ui(b,1);
1200: mpz_set_ui(dn,1);
1201: for ( i = 0; i < row; i++ )
1202: for ( j = 0, mi = mat[i]; j < col; j++ )
1203: if ( mpz_sgn(mi[j]) ) {
1204: mpz_mul(s,mi[j],dn);
1205: mpz_mod(u,s,md);
1206: ret = mpz_inttorat(u,md,b,nm1,dn1);
1207: if ( !ret )
1208: return 0;
1209: else {
1210: if ( !UNIMPZ(dn1) ) {
1211: for ( k = 0; k < i; k++ )
1212: for ( l = 0, nmk = nm[k]; l < col; l++ ) mpz_mul(nmk[l],nmk[l],dn1);
1213: for ( l = 0, nmk = nm[i]; l < j; l++ ) mpz_mul(nmk[l],nmk[l],dn1);
1214: }
1215: mpz_set(nm[i][j],nm1);
1216: mpz_mul(dn,dn,dn1);
1217: }
1218: }
1219: return 1;
1220: }
1221:
1.1 noro 1222: int intmtoratm(MAT mat,Z md,MAT nm,Z *dn)
1223: {
1224: Z t,s,b,dn0,dn1,nm1,q,u,unm,udn,dmy;
1225: int i,j,k,l,row,col,sgn,ret;
1226: Z **rmat,**tmat,*tmi,*nmk;
1227:
1228: if ( UNIQ(md) )
1229: return 0;
1230: row = mat->row; col = mat->col;
1231: bshiftz(md,1,&t);
1232: isqrtz(t,&s);
1233: bshiftz(s,64,&b);
1234: if ( !b ) b = ONE;
1235: dn0 = ONE;
1236: tmat = (Z **)mat->body;
1237: rmat = (Z **)nm->body;
1238: for ( i = 0; i < row; i++ )
1239: for ( j = 0, tmi = tmat[i]; j < col; j++ )
1240: if ( tmi[j] ) {
1241: mulz(tmi[j],dn0,&s);
1242: divqrz(s,md,&dmy,&u);
1243: ret = inttorat(u,md,b,&nm1,&dn1);
1244: if ( !ret ) return 0;
1245: else {
1246: if ( !UNIQ(dn1) ) {
1247: for ( k = 0; k < i; k++ )
1248: for ( l = 0, nmk = rmat[k]; l < col; l++ ) {
1249: mulz(nmk[l],dn1,&q); nmk[l] = q;
1250: }
1251: for ( l = 0, nmk = rmat[i]; l < j; l++ ) {
1252: mulz(nmk[l],dn1,&q); nmk[l] = q;
1253: }
1254: }
1255: rmat[i][j] = nm1;
1256: mulz(dn0,dn1,&q); dn0 = q;
1257: }
1258: }
1259: *dn = dn0;
1260: return 1;
1261: }
1262:
1263: int intmtoratm2(MAT mat,Z md,MAT nm,Z *dn,int *stat)
1264: {
1265: int row,col,i,j,ret;
1266: Z dn0,dn1,t,s,b;
1267: Z *w,*tmi;
1268: Z **tmat;
1269:
1270: bshiftz(md,1,&t);
1271: isqrtz(t,&s);
1272: bshiftz(s,64,&b);
1273: tmat = (Z **)mat->body;
1274: if ( UNIQ(md) ) return 0;
1275: row = mat->row; col = mat->col;
1276: dn0 = ONE;
1277: for ( i = 0; i < row; i++ )
1278: if ( cmpz(dn[i],dn0) > 0 ) dn0 = dn[i];
1279: w = (Z *)MALLOC(col*sizeof(Z));
1280: for ( i = 0; i < row; i++ )
1281: if ( stat[i] == 0 ) {
1282: for ( j = 0, tmi = tmat[i]; j < col; j++ )
1283: mulz(tmi[j],dn0,&w[j]);
1284: ret = intvtoratv(w,col,md,b,(Z *)BDY(nm)[i],&dn[i]);
1285: if ( ret ) {
1286: stat[i] = 1;
1287: mulz(dn0,dn[i],&t); dn[i] = t; dn0 = t;
1288: }
1289: }
1290: for ( i = 0; i < row; i++ ) if ( !stat[i] ) break;
1291: if ( i == row ) return 1;
1292: else return 0;
1293: }
1294:
1295: int intvtoratv(Z *v,int n,Z md,Z b,Z *nm,Z *dn)
1296: {
1297: Z dn0,dn1,q,s,u,nm1,unm,udn,dmy;
1298: Z *nmk;
1299: int j,l,col,ret,sgn;
1300:
1301: for ( j = 0; j < n; j++ ) nm[j] = 0;
1302: dn0 = ONE;
1303: for ( j = 0; j < n; j++ ) {
1304: if ( !v[j] ) continue;
1305: mulz(v[j],dn0,&s);
1306: divqrz(s,md,&dmy,&u);
1307: ret = inttorat(u,md,b,&nm1,&dn1);
1308: if ( !ret ) return 0;
1309: if ( !UNIQ(dn1) )
1310: for ( l = 0; l < j; l++ ) {
1311: mulz(nm[l],dn1,&q); nm[l] = q;
1312: }
1313: nm[j] = nm1;
1314: mulz(dn0,dn1,&q); dn0 = q;
1315: }
1316: *dn = dn0;
1317: return 1;
1318: }
1319:
1320: /* assuming 0 < c < m */
1321:
1.8 noro 1322: int mpz_inttorat(mpz_t c,mpz_t m,mpz_t b,mpz_t nm,mpz_t dn)
1323: {
1324: mpz_t u1,v1,u2,v2,r1,r2;
1325: mpz_t q,t;
1326:
1327: mpz_init_set_ui(u1,0); mpz_init_set_ui(v1,1);
1328: mpz_init_set(u2,m); mpz_init_set(v2,c);
1329: mpz_init(q); mpz_init(t); mpz_init(r1); mpz_init(r2);
1330: while ( mpz_cmp(v2,b) >= 0 ) {
1331: /* r2 = u2-q*v2 */
1332: mpz_fdiv_qr(q,r2,u2,v2);
1333: mpz_set(u2,v2); mpz_set(v2,r2);
1334: /* r1 = u1-q*v1 */
1335: mpz_mul(t,q,v1); mpz_sub(r1,u1,t);
1336: mpz_set(u1,v1); mpz_set(v1,r1);
1337: }
1338: if ( mpz_cmp(v1,b) >= 0 ) return 0;
1339: else {
1340: if ( mpz_sgn(v1)<0 ) {
1341: mpz_neg(dn,v1); mpz_neg(nm,v2);
1342: } else {
1343: mpz_set(dn,v1); mpz_set(nm,v2);
1344: }
1345: return 1;
1346: }
1347: }
1348:
1.1 noro 1349: int inttorat(Z c,Z m,Z b,Z *nmp,Z *dnp)
1350: {
1351: Z qq,t,u1,v1,r1;
1352: Z q,u2,v2,r2;
1353:
1354: u1 = 0; v1 = ONE; u2 = m; v2 = c;
1355: while ( cmpz(v2,b) >= 0 ) {
1356: divqrz(u2,v2,&q,&r2); u2 = v2; v2 = r2;
1357: mulz(q,v1,&t); subz(u1,t,&r1); u1 = v1; v1 = r1;
1358: }
1359: if ( cmpz(v1,b) >= 0 ) return 0;
1360: else {
1361: if ( mpz_sgn(BDY(v1))<0 ) {
1362: chsgnz(v1,dnp); chsgnz(v2,nmp);
1363: } else {
1364: *dnp = v1; *nmp = v2;
1365: }
1366: return 1;
1367: }
1368: }
1369:
1370: extern int f4_nocheck;
1371:
1.8 noro 1372: int mpz_gensolve_check(MAT mat,mpz_t **nm,mpz_t dn,int rank,int *rind,int *cind)
1373: {
1374: int row,col,clen,i,j,k,l;
1375: mpz_t t;
1376: mpz_t *w;
1377: Z *mati;
1378: mpz_t *nmk;
1379:
1380: if ( f4_nocheck ) return 1;
1381: row = mat->row; col = mat->col; clen = col-rank;
1382: w = (mpz_t *)MALLOC(clen*sizeof(mpz_t));
1383: mpz_init(t);
1384: for ( i = 0; i < clen; i++ ) mpz_init(w[i]);
1385: for ( i = 0; i < row; i++ ) {
1386: mati = (Z *)mat->body[i];
1387: for ( l = 0; l < clen; l++ ) mpz_set_ui(w[l],0);
1388: for ( k = 0; k < rank; k++ )
1389: for ( l = 0, nmk = (mpz_t *)nm[k]; l < clen; l++ ) {
1390: /* w[l] += mati[rind[k]]*nmk[k] */
1391: if ( mati[rind[k]] ) mpz_addmul(w[l],BDY(mati[rind[k]]),nmk[l]);
1392: }
1393: for ( j = 0; j < clen; j++ ) {
1394: if ( mati[cind[j]] ) mpz_mul(t,dn,BDY(mati[cind[j]]));
1395: else mpz_set_ui(t,0);
1396: if ( mpz_cmp(w[j],t) ) break;
1397: }
1398: if ( j != clen ) break;
1399: }
1400: if ( i != row ) return 0;
1401: else return 1;
1402: }
1403:
1.1 noro 1404: int gensolve_check(MAT mat,MAT nm,Z dn,int *rind,int *cind)
1405: {
1406: int row,col,rank,clen,i,j,k,l;
1407: Z s,t;
1408: Z *w;
1409: Z *mati,*nmk;
1410:
1411: if ( f4_nocheck ) return 1;
1412: row = mat->row; col = mat->col; rank = nm->row; clen = nm->col;
1413: w = (Z *)MALLOC(clen*sizeof(Z));
1414: for ( i = 0; i < row; i++ ) {
1415: mati = (Z *)mat->body[i];
1416: bzero(w,clen*sizeof(Z));
1417: for ( k = 0; k < rank; k++ )
1418: for ( l = 0, nmk = (Z *)nm->body[k]; l < clen; l++ ) {
1419: mulz(mati[rind[k]],nmk[l],&t); addz(w[l],t,&s); w[l] = s;
1420: }
1421: for ( j = 0; j < clen; j++ ) {
1422: mulz(dn,mati[cind[j]],&t);
1423: if ( cmpz(w[j],t) ) break;
1424: }
1425: if ( j != clen ) break;
1426: }
1427: if ( i != row ) return 0;
1428: else return 1;
1429: }
1430:
1431: int gensolve_check2(MAT mat,MAT nm,Z *dn,int *rind,int *cind)
1432: {
1433: int row,col,rank,clen,i,j,k,l;
1434: Z s,t,u,d;
1435: Z *w,*m;
1436: Z *mati,*nmk;
1437:
1438: if ( f4_nocheck ) return 1;
1439: row = mat->row; col = mat->col; rank = nm->row; clen = nm->col;
1440: w = (Z *)MALLOC(clen*sizeof(Z));
1441: m = (Z *)MALLOC(clen*sizeof(Z));
1442: for ( d = dn[0], i = 1; i < rank; i++ ) {
1443: lcmz(d,dn[i],&t); d = t;
1444: }
1445: for ( i = 0; i < rank; i++ ) divsz(d,dn[i],&m[i]);
1446: for ( i = 0; i < row; i++ ) {
1447: mati = (Z *)mat->body[i];
1448: bzero(w,clen*sizeof(Z));
1449: for ( k = 0; k < rank; k++ ) {
1450: mulz(mati[rind[k]],m[k],&u);
1451: for ( l = 0, nmk = (Z *)nm->body[k]; l < clen; l++ ) {
1452: mulz(u,nmk[l],&t); addz(w[l],t,&s); w[l] = s;
1453: }
1454: }
1455: for ( j = 0; j < clen; j++ ) {
1456: mulz(d,mati[cind[j]],&t);
1457: if ( cmpz(w[j],t) ) break;
1458: }
1459: if ( j != clen ) break;
1460: }
1461: if ( i != row ) return 0;
1462: else return 1;
1463: }
1464:
1465: void isqrtz(Z a,Z *r)
1466: {
1467: int k;
1468: Z x,t,x2,xh,quo,rem;
1469: Z two;
1470:
1471: if ( !a ) *r = 0;
1472: else if ( UNIQ(a) ) *r = ONE;
1473: else {
1474: k = z_bits((Q)a); /* a <= 2^k-1 */
1475: bshiftz(ONE,-((k>>1)+(k&1)),&x); /* a <= x^2 */
1.5 noro 1476: STOZ(2,two);
1.1 noro 1477: while ( 1 ) {
1478: pwrz(x,two,&t);
1479: if ( cmpz(t,a) <= 0 ) {
1480: *r = x; return;
1481: } else {
1482: if ( mpz_tstbit(BDY(x),0) ) addz(x,a,&t);
1483: else t = a;
1484: bshiftz(x,-1,&x2); divqrz(t,x2,&quo,&rem);
1485: bshiftz(x,1,&xh); addz(quo,xh,&x);
1486: }
1487: }
1488: }
1489: }
1490:
1491: void bshiftz(Z a,int n,Z *r)
1492: {
1493: mpz_t t;
1494:
1495: if ( !a ) *r = 0;
1496: else if ( n == 0 ) *r = a;
1497: else if ( n < 0 ) {
1498: mpz_init(t); mpz_mul_2exp(t,BDY(a),-n); MPZTOZ(t,*r);
1499: } else {
1500: mpz_init(t); mpz_fdiv_q_2exp(t,BDY(a),n);
1501: if ( !mpz_sgn(t) ) *r = 0;
1502: else MPZTOZ(t,*r);
1503: }
1504: }
1505:
1506: void addlf(Z a,Z b,Z *c)
1507: {
1508: addz(a,b,c);
1509: if ( !lf_lazy ) {
1510: if ( cmpz(*c,current_mod_lf) >= 0 ) {
1511: subz(*c,current_mod_lf,c);
1512: }
1513: }
1514: }
1515:
1516: void sublf(Z a,Z b,Z *c)
1517: {
1518: subz(a,b,c);
1519: if ( !lf_lazy ) {
1520: remz(*c,current_mod_lf,c);
1521: }
1522: }
1523:
1524: void mullf(Z a,Z b,Z *c)
1525: {
1526: mulz(a,b,c);
1527: if ( !lf_lazy ) {
1528: remz(*c,current_mod_lf,c);
1529: }
1530: }
1531:
1532: void divlf(Z a,Z b,Z *c)
1533: {
1534: Z inv;
1535:
1536: invz(b,current_mod_lf,&inv);
1537: mulz(a,inv,c);
1538: if ( !lf_lazy ) {
1539: remz(*c,current_mod_lf,c);
1540: }
1541: }
1542:
1543: void chsgnlf(Z a,Z *c)
1544: {
1545: chsgnz(a,c);
1546: if ( !lf_lazy ) {
1547: remz(*c,current_mod_lf,c);
1548: }
1549: }
1550:
1551: void lmtolf(LM a,Z *b)
1552: {
1553: if ( !a ) *b = 0;
1554: else {
1555: MPZTOZ(BDY(a),*b);
1556: }
1557: }
1558:
1559: void setmod_lf(Z p)
1560: {
1561: current_mod_lf = p;
1562: current_mod_lf_size = mpz_size(BDY(current_mod_lf))+1;
1563: }
1564:
1565: void simplf_force(Z a,Z *b)
1566: {
1567: remz(a,current_mod_lf,b);
1568: }
1569:
1570: int generic_gauss_elim_hensel(MAT mat,MAT *nmmat,Z *dn,int **rindp,int **cindp)
1571: {
1572: MAT bmat,xmat;
1573: Z **a0,**a,**b,**x,**nm;
1574: Z *ai,*bi,*xi;
1575: int row,col;
1576: int **w;
1577: int *wi;
1578: int **wc;
1579: Z mdq,q,s,u;
1580: Z tn;
1581: int ind,md,i,j,k,l,li,ri,rank;
1582: unsigned int t;
1583: int *cinfo,*rinfo;
1584: int *rind,*cind;
1585: int count;
1586: int ret;
1.3 noro 1587: struct oEGT eg_mul1,eg_mul2,tmp0,tmp1,tmp2;
1.1 noro 1588: int period;
1589: int *wx,*ptr;
1590: int wxsize,nsize;
1591: Z wn;
1592: Z wq;
1593:
1.9 noro 1594: #if SIZEOF_LONG == 8
1595: return generic_gauss_elim_hensel64(mat,nmmat,dn,rindp,cindp);
1596: #endif
1.3 noro 1597: init_eg(&eg_mul1); init_eg(&eg_mul2);
1.1 noro 1598: a0 = (Z **)mat->body;
1599: row = mat->row; col = mat->col;
1600: w = (int **)almat(row,col);
1601: for ( ind = 0; ; ind++ ) {
1602: md = get_lprime(ind);
1.5 noro 1603: STOZ(md,mdq);
1.1 noro 1604: for ( i = 0; i < row; i++ )
1605: for ( j = 0, ai = a0[i], wi = w[i]; j < col; j++ )
1606: wi[j] = remqi((Q)ai[j],md);
1607:
1608: if ( DP_Print > 3 ) {
1609: fprintf(asir_out,"LU decomposition.."); fflush(asir_out);
1610: }
1611: rank = find_lhs_and_lu_mod((unsigned int **)w,row,col,md,&rinfo,&cinfo);
1612: if ( DP_Print > 3 ) {
1613: fprintf(asir_out,"done.\n"); fflush(asir_out);
1614: }
1615: a = (Z **)almat_pointer(rank,rank); /* lhs mat */
1616: MKMAT(bmat,rank,col-rank); b = (Z **)bmat->body; /* lhs mat */
1617: for ( j = li = ri = 0; j < col; j++ )
1618: if ( cinfo[j] ) {
1619: /* the column is in lhs */
1620: for ( i = 0; i < rank; i++ ) {
1621: w[i][li] = w[i][j];
1622: a[i][li] = a0[rinfo[i]][j];
1623: }
1624: li++;
1625: } else {
1626: /* the column is in rhs */
1627: for ( i = 0; i < rank; i++ )
1628: b[i][ri] = a0[rinfo[i]][j];
1629: ri++;
1630: }
1631:
1632: /* solve Ax=B; A: rank x rank, B: rank x ri */
1633: /* algorithm
1634: c <- B
1635: x <- 0
1636: q <- 1
1637: do
1638: t <- A^(-1)c mod p
1639: x <- x+qt
1640: c <- (c-At)/p
1641: q <- qp
1642: end do
1643: then Ax-B=0 mod q and b=(B-Ax)/q hold after "do".
1644: */
1645: MKMAT(xmat,rank,ri); x = (Z **)(xmat)->body;
1646: MKMAT(*nmmat,rank,ri); nm = (Z **)(*nmmat)->body;
1647: wc = (int **)almat(rank,ri);
1648: *rindp = rind = (int *)MALLOC_ATOMIC(rank*sizeof(int));
1649: *cindp = cind = (int *)MALLOC_ATOMIC((ri)*sizeof(int));
1650:
1651: period = F4_INTRAT_PERIOD;
1652: for ( q = ONE, count = 0; ; ) {
1.3 noro 1653: /* check Ax=B mod q */
1.1 noro 1654: if ( DP_Print > 3 )
1655: fprintf(stderr,"o");
1656: /* wc = b mod md */
1657: for ( i = 0; i < rank; i++ )
1.3 noro 1658: for ( j = 0, bi = b[i], wi = wc[i]; j < ri; j++ )
1.1 noro 1659: wi[j] = remqi((Q)bi[j],md);
1.3 noro 1660: /* wc = A^(-1)wc; wc is not normalized */
1661: solve_by_lu_mod(w,rank,md,wc,ri,0);
1.1 noro 1662: /* x += q*wc */
1.3 noro 1663: get_eg(&tmp0);
1.1 noro 1664: for ( i = 0; i < rank; i++ )
1665: for ( j = 0, wi = wc[i]; j < ri; j++ ) mul1addtoz(q,wi[j],&x[i][j]);
1.3 noro 1666: /* b =(b-A*wc)/md */
1667: get_eg(&tmp1); add_eg(&eg_mul1,&tmp0,&tmp1);
1.1 noro 1668: for ( i = 0; i < rank; i++ )
1669: for ( j = 0; j < ri; j++ ) {
1.3 noro 1670: mpz_t uz;
1671:
1672: if ( b[i][j] )
1673: mpz_init_set(uz,BDY(b[i][j]));
1674: else
1675: mpz_init_set_ui(uz,0);
1676: for ( k = 0; k < rank; k++ ) {
1677: if ( a[i][k] && wc[k][j] ) {
1678: if ( wc[k][j] < 0 )
1679: mpz_addmul_ui(uz,BDY(a[i][k]),-wc[k][j]);
1680: else
1681: mpz_submul_ui(uz,BDY(a[i][k]),wc[k][j]);
1682: }
1683: }
1684: MPZTOZ(uz,u);
1.1 noro 1685: divsz(u,mdq,&b[i][j]);
1686: }
1.3 noro 1687: get_eg(&tmp2); add_eg(&eg_mul2,&tmp1,&tmp2);
1.1 noro 1688: count++;
1689: /* q = q*md */
1690: mulz(q,mdq,&u); q = u;
1691: if ( count == period ) {
1692: ret = intmtoratm(xmat,q,*nmmat,dn);
1693: if ( ret ) {
1.3 noro 1694: print_eg("MUL1",&eg_mul1);
1695: print_eg("MUL2",&eg_mul2);
1.1 noro 1696: for ( j = k = l = 0; j < col; j++ )
1697: if ( cinfo[j] )
1698: rind[k++] = j;
1699: else
1700: cind[l++] = j;
1701: ret = gensolve_check(mat,*nmmat,*dn,rind,cind);
1702: if ( ret ) {
1703: *rindp = rind;
1704: *cindp = cind;
1705: for ( j = k = 0; j < col; j++ )
1706: if ( !cinfo[j] )
1707: cind[k++] = j;
1708: return rank;
1709: }
1710: } else {
1711: period = period*3/2;
1712: count = 0;
1713: }
1714: }
1715: }
1716: }
1717: }
1718:
1719: /* for inv_or_split_dalg */
1720:
1721: int generic_gauss_elim_hensel_dalg(MAT mat,DP *mb,MAT *nmmat,Z *dn,int **rindp,int **cindp)
1722: {
1723: MAT bmat,xmat;
1724: Z **a0,**a,**b,**x,**nm;
1725: Z *ai,*bi,*xi;
1726: int row,col;
1727: int **w;
1728: int *wi;
1729: int **wc;
1730: Z mdq,q,s,u;
1731: Z tn;
1732: int ind,md,i,j,k,l,li,ri,rank;
1733: unsigned int t;
1734: int *cinfo,*rinfo;
1735: int *rind,*cind;
1736: int count;
1737: int ret;
1738: struct oEGT eg_mul,eg_inv,eg_intrat,eg_check,tmp0,tmp1;
1739: int period;
1740: int *wx,*ptr;
1741: int wxsize,nsize;
1742: Z wn;
1743: Z wq;
1744: DP m;
1745:
1746: a0 = (Z **)mat->body;
1747: row = mat->row; col = mat->col;
1748: w = (int **)almat(row,col);
1749: for ( ind = 0; ; ind++ ) {
1750: md = get_lprime(ind);
1.5 noro 1751: STOZ(md,mdq);
1.1 noro 1752: for ( i = 0; i < row; i++ )
1753: for ( j = 0, ai = a0[i], wi = w[i]; j < col; j++ )
1754: wi[j] = remqi((Q)ai[j],md);
1755:
1756: if ( DP_Print > 3 ) {
1757: fprintf(asir_out,"LU decomposition.."); fflush(asir_out);
1758: }
1759: rank = find_lhs_and_lu_mod((unsigned int **)w,row,col,md,&rinfo,&cinfo);
1760: if ( DP_Print > 3 ) {
1761: fprintf(asir_out,"done.\n"); fflush(asir_out);
1762: }
1763:
1764: /* this part is added for inv_or_split_dalg */
1765: for ( i = 0; i < col-1; i++ ) {
1766: if ( !cinfo[i] ) {
1767: m = mb[i];
1768: for ( j = i+1; j < col-1; j++ )
1769: if ( dp_redble(mb[j],m) )
1770: cinfo[j] = -1;
1771: }
1772: }
1773:
1774: a = (Z **)almat_pointer(rank,rank); /* lhs mat */
1775: MKMAT(bmat,rank,col-rank); b = (Z **)bmat->body; /* lhs mat */
1776: for ( j = li = ri = 0; j < col; j++ )
1.4 noro 1777: if ( cinfo[j] > 0 ) {
1.1 noro 1778: /* the column is in lhs */
1779: for ( i = 0; i < rank; i++ ) {
1780: w[i][li] = w[i][j];
1781: a[i][li] = a0[rinfo[i]][j];
1782: }
1783: li++;
1.4 noro 1784: } else if ( !cinfo[j] ) {
1.1 noro 1785: /* the column is in rhs */
1786: for ( i = 0; i < rank; i++ )
1787: b[i][ri] = a0[rinfo[i]][j];
1788: ri++;
1789: }
1790:
1791: /* solve Ax=B; A: rank x rank, B: rank x ri */
1792: /* algorithm
1793: c <- B
1794: x <- 0
1795: q <- 1
1796: do
1797: t <- A^(-1)c mod p
1798: x <- x+qt
1799: c <- (c-At)/p
1800: q <- qp
1801: end do
1802: then Ax-B=0 mod q and b=(B-Ax)/q hold after "do".
1803: */
1804: MKMAT(xmat,rank,ri); x = (Z **)(xmat)->body;
1805: MKMAT(*nmmat,rank,ri); nm = (Z **)(*nmmat)->body;
1806: wc = (int **)almat(rank,ri);
1807: *rindp = rind = (int *)MALLOC_ATOMIC(rank*sizeof(int));
1808: *cindp = cind = (int *)MALLOC_ATOMIC((ri)*sizeof(int));
1809:
1810: period = F4_INTRAT_PERIOD;
1811: for ( q = ONE, count = 0; ; ) {
1812: if ( DP_Print > 3 )
1813: fprintf(stderr,"o");
1814: /* wc = b mod md */
1815: for ( i = 0; i < rank; i++ )
1.3 noro 1816: for ( j = 0, bi = b[i], wi = wc[i]; j < ri; j++ )
1.1 noro 1817: wi[j] = remqi((Q)bi[j],md);
1818: /* wc = A^(-1)wc; wc is normalized */
1819: solve_by_lu_mod(w,rank,md,wc,ri,1);
1820: /* x += q*wc */
1821: for ( i = 0; i < rank; i++ )
1822: for ( j = 0, wi = wc[i]; j < ri; j++ ) mul1addtoz(q,wi[j],&x[i][j]);
1.3 noro 1823: /* b =(b-A*wc)/md */
1.1 noro 1824: for ( i = 0; i < rank; i++ )
1825: for ( j = 0; j < ri; j++ ) {
1.3 noro 1826: mpz_t uz;
1827:
1828: if ( b[i][j] )
1829: mpz_init_set(uz,BDY(b[i][j]));
1830: else
1831: mpz_init_set_ui(uz,0);
1832: for ( k = 0; k < rank; k++ ) {
1833: if ( a[i][k] && wc[k][j] ) {
1834: if ( wc[k][j] < 0 )
1835: mpz_addmul_ui(uz,BDY(a[i][k]),-wc[k][j]);
1836: else
1837: mpz_submul_ui(uz,BDY(a[i][k]),wc[k][j]);
1838: }
1839: }
1840: MPZTOZ(uz,u);
1.1 noro 1841: divsz(u,mdq,&b[i][j]);
1842: }
1843: count++;
1844: /* q = q*md */
1845: mulz(q,mdq,&u); q = u;
1846: if ( count == period ) {
1847: ret = intmtoratm(xmat,q,*nmmat,dn);
1848: if ( ret ) {
1849: for ( j = k = l = 0; j < col; j++ )
1850: if ( cinfo[j] > 0 )
1851: rind[k++] = j;
1852: else if ( !cinfo[j] )
1853: cind[l++] = j;
1854: ret = gensolve_check(mat,*nmmat,*dn,rind,cind);
1855: if ( ret ) {
1856: *rindp = rind;
1857: *cindp = cind;
1858: for ( j = k = 0; j < col; j++ )
1859: if ( !cinfo[j] )
1860: cind[k++] = j;
1861: return rank;
1862: }
1863: } else {
1864: period = period*3/2;
1865: count = 0;
1866: }
1867: }
1868: }
1869: }
1870: }
1.6 noro 1871:
1872: #if SIZEOF_LONG == 8
1873: mp_limb_t remqi64(Q a,mp_limb_t mod)
1874: {
1875: mp_limb_t c,nm,dn;
1876: mpz_t r;
1877:
1878: if ( !a ) return 0;
1879: else if ( a->z ) {
1880: mpz_init(r);
1881: c = mpz_fdiv_r_ui(r,BDY((Z)a),mod);
1882: } else {
1883: mpz_init(r);
1884: nm = mpz_fdiv_r_ui(r,mpq_numref(BDY(a)),mod);
1885: dn = mpz_fdiv_r_ui(r,mpq_denref(BDY(a)),mod);
1886: dn = invmod64(dn,mod);
1887: c = mulmod64(nm,dn,mod);
1888: }
1889: return c;
1890: }
1891:
1892: int generic_gauss_elim_mod64(mp_limb_t **mat,int row,int col,mp_limb_t md,int *colstat);
1893: mp_limb_t get_lprime64(int ind);
1894:
1.8 noro 1895: void mpz_print(mpz_t a)
1896: {
1897: mpz_out_str(stdout,10,a); printf("\n");
1898: }
1899:
1900: void mpz_printmat(mpz_t **a,int row,int col)
1901: {
1902: int i,j;
1903: for ( i = 0; i < row; i++ ) {
1904: for ( j = 0; j < col; j++ ) {
1905: mpz_out_str(stdout,10,a[i][j]); printf(" ");
1906: }
1907: printf("\n");
1908: }
1909: }
1910:
1911: mpz_t **mpz_allocmat(int row,int col)
1912: {
1913: mpz_t **p;
1914: int i,j;
1915:
1916: p = (mpz_t **)MALLOC(row*sizeof(mpz_t *));
1917: for ( i = 0; i < row; i++ ) {
1918: p[i] = (mpz_t *)MALLOC(col*sizeof(mpz_t));
1919: for ( j = 0; j < col; j++ ) mpz_init(p[i][j]);
1920: }
1921: return p;
1922: }
1923:
1924: #if 1
1925: int generic_gauss_elim64(MAT mat,MAT *nm,Z *dn,int **rindp,int **cindp)
1926: {
1927: mp_limb_t **wmat;
1928: mp_limb_t *wmi;
1929: mp_limb_t md,inv,t,t1;
1930: Z z;
1931: Z **bmat,*bmi;
1932: mpz_t **tmat,**num;
1933: mpz_t *tmi;
1934: mpz_t den;
1935: mpz_t q,m1,m3,s,u;
1936: int *colstat,*wcolstat,*rind,*cind;
1937: int row,col,ind,i,j,k,l,rank,rank0;
1938: MAT r;
1939: int ret;
1940:
1941: bmat = (Z **)mat->body;
1942: row = mat->row; col = mat->col;
1943: wmat = (mp_limb_t **)almat64(row,col);
1944: colstat = (int *)MALLOC_ATOMIC(col*sizeof(int));
1945: wcolstat = (int *)MALLOC_ATOMIC(col*sizeof(int));
1946: mpz_init(m1); mpz_init(m3); mpz_init(den);
1947: for ( ind = 0; ; ind++ ) {
1948: if ( DP_Print ) {
1949: fprintf(asir_out,"."); fflush(asir_out);
1950: }
1951: md = get_lprime64(ind);
1952: for ( i = 0; i < row; i++ )
1953: for ( j = 0, bmi = bmat[i], wmi = wmat[i]; j < col; j++ )
1954: wmi[j] = bmi[j]==0?0:mpz_fdiv_ui(BDY(bmi[j]),md);
1955: rank = generic_gauss_elim_mod64(wmat,row,col,md,wcolstat);
1956: if ( !ind ) {
1957: RESET:
1958: mpz_set_ui(m1,md);
1959: rank0 = rank;
1960: bcopy(wcolstat,colstat,col*sizeof(int));
1961: // crmat
1962: tmat = mpz_allocmat(rank,col-rank);
1963: //
1964: num = mpz_allocmat(rank,col-rank);
1965: for ( i = 0; i < rank; i++ )
1966: for ( j = k = 0, tmi = tmat[i], wmi = wmat[i]; j < col; j++ )
1967: if ( !colstat[j] ) { mpz_set_ui(tmi[k],wmi[j]); k++; }
1968: } else {
1969: if ( rank < rank0 ) {
1970: if ( DP_Print ) {
1971: fprintf(asir_out,"lower rank matrix; continuing...\n");
1972: fflush(asir_out);
1973: }
1974: continue;
1975: } else if ( rank > rank0 ) {
1976: if ( DP_Print ) {
1977: fprintf(asir_out,"higher rank matrix; resetting...\n");
1978: fflush(asir_out);
1979: }
1980: goto RESET;
1981: } else {
1982: for ( j = 0; (j<col) && (colstat[j]==wcolstat[j]); j++ );
1983: if ( j < col ) {
1984: if ( DP_Print ) {
1985: fprintf(asir_out,"inconsitent colstat; resetting...\n");
1986: fflush(asir_out);
1987: }
1988: goto RESET;
1989: }
1990: }
1991:
1992: inv = invmod64(mpz_fdiv_ui(m1,md),md);
1993: mpz_mul_ui(m3,m1,md);
1994: for ( i = 0; i < rank; i++ )
1995: for ( j = k = 0, tmi = tmat[i], wmi = wmat[i]; j < col; j++ )
1996: if ( !colstat[j] ) {
1997: if ( mpz_sgn(tmi[k]) ) {
1998: /* f3 = f1+m1*(m1 mod md)^(-1)*(f2 - f1 mod md) */
1999: t = mpz_fdiv_ui(tmi[k],md);
2000: if ( wmi[j] >= t ) t = wmi[j]-t;
2001: else t = md-(t-wmi[j]);
2002: mpz_addmul_ui(tmi[k],m1,mulmod64(t,inv,md));
2003: } else if ( wmi[j] ) {
2004: /* f3 = m1*(m1 mod m2)^(-1)*f2 */
2005: mpz_mul_ui(tmi[k],m1,mulmod64(wmi[j],inv,md));
2006: }
2007: k++;
2008: }
2009: mpz_set(m1,m3);
2010: if ( ind % F4_INTRAT_PERIOD )
2011: ret = 0;
2012: else
2013: ret = mpz_intmtoratm(tmat,rank,col-rank,m1,num,den);
2014: if ( ret ) {
2015: *rindp = rind = (int *)MALLOC_ATOMIC(rank*sizeof(int));
2016: *cindp = cind = (int *)MALLOC_ATOMIC((col-rank)*sizeof(int));
2017: for ( j = k = l = 0; j < col; j++ )
2018: if ( colstat[j] ) rind[k++] = j;
2019: else cind[l++] = j;
2020: if ( mpz_gensolve_check(mat,num,den,rank,rind,cind) ) {
2021: MKMAT(r,rank,col-rank); *nm = r;
2022: for ( i = 0; i < rank; i++ )
2023: for ( j = 0; j < col-rank; j++ ) {
2024: MPZTOZ(num[i][j],z); BDY(r)[i][j] = z;
2025: }
2026: MPZTOZ(den,*dn);
2027: return rank;
2028: }
2029: }
2030: }
2031: }
2032: }
2033: #else
1.6 noro 2034: int generic_gauss_elim64(MAT mat,MAT *nm,Z *dn,int **rindp,int **cindp)
2035: {
2036: mp_limb_t **wmat;
2037: mp_limb_t *wmi;
2038: mp_limb_t md,inv,t,t1;
2039: Z **bmat,**tmat,*bmi,*tmi;
2040: Z q,m1,m2,m3,s,u;
2041: int *colstat,*wcolstat,*rind,*cind;
2042: int row,col,ind,i,j,k,l,rank,rank0;
2043: MAT r,crmat;
2044: int ret;
2045:
2046: bmat = (Z **)mat->body;
2047: row = mat->row; col = mat->col;
2048: wmat = (mp_limb_t **)almat64(row,col);
2049: colstat = (int *)MALLOC_ATOMIC(col*sizeof(int));
2050: wcolstat = (int *)MALLOC_ATOMIC(col*sizeof(int));
2051: for ( ind = 0; ; ind++ ) {
2052: if ( DP_Print ) {
2053: fprintf(asir_out,"."); fflush(asir_out);
2054: }
2055: md = get_lprime64(ind);
2056: for ( i = 0; i < row; i++ )
2057: for ( j = 0, bmi = bmat[i], wmi = wmat[i]; j < col; j++ )
2058: wmi[j] = remqi64((Q)bmi[j],md);
2059: rank = generic_gauss_elim_mod64(wmat,row,col,md,wcolstat);
2060: if ( !ind ) {
2061: RESET:
2062: UTOZ(md,m1);
2063: rank0 = rank;
2064: bcopy(wcolstat,colstat,col*sizeof(int));
2065: MKMAT(crmat,rank,col-rank);
2066: MKMAT(r,rank,col-rank); *nm = r;
2067: tmat = (Z **)crmat->body;
2068: for ( i = 0; i < rank; i++ )
2069: for ( j = k = 0, tmi = tmat[i], wmi = wmat[i]; j < col; j++ )
2070: if ( !colstat[j] ) { UTOZ(wmi[j],tmi[k]); k++; }
2071: } else {
2072: if ( rank < rank0 ) {
2073: if ( DP_Print ) {
2074: fprintf(asir_out,"lower rank matrix; continuing...\n");
2075: fflush(asir_out);
2076: }
2077: continue;
2078: } else if ( rank > rank0 ) {
2079: if ( DP_Print ) {
2080: fprintf(asir_out,"higher rank matrix; resetting...\n");
2081: fflush(asir_out);
2082: }
2083: goto RESET;
2084: } else {
2085: for ( j = 0; (j<col) && (colstat[j]==wcolstat[j]); j++ );
2086: if ( j < col ) {
2087: if ( DP_Print ) {
2088: fprintf(asir_out,"inconsitent colstat; resetting...\n");
2089: fflush(asir_out);
2090: }
2091: goto RESET;
2092: }
2093: }
2094:
2095: inv = invmod64(remqi64((Q)m1,md),md);
2096: UTOZ(md,m2); mulz(m1,m2,&m3);
2097: for ( i = 0; i < rank; i++ )
2098: for ( j = k = 0, tmi = tmat[i], wmi = wmat[i]; j < col; j++ )
2099: if ( !colstat[j] ) {
2100: if ( tmi[k] ) {
2101: /* f3 = f1+m1*(m1 mod m2)^(-1)*(f2 - f1 mod m2) */
2102: t = remqi64((Q)tmi[k],md);
2103: if ( wmi[j] >= t ) t = wmi[j]-t;
2104: else t = md-(t-wmi[j]);
2105: t1 = mulmod64(t,inv,md);
2106: UTOZ(t1,u); mulz(m1,u,&s);
2107: addz(tmi[k],s,&u); tmi[k] = u;
2108: } else if ( wmi[j] ) {
2109: /* f3 = m1*(m1 mod m2)^(-1)*f2 */
2110: t = mulmod64(wmi[j],inv,md);
2111: UTOZ(t,u); mulz(m1,u,&s); tmi[k] = s;
2112: }
2113: k++;
2114: }
2115: m1 = m3;
2116: if ( ind % F4_INTRAT_PERIOD )
2117: ret = 0;
2118: else
2119: ret = intmtoratm(crmat,m1,*nm,dn);
2120: if ( ret ) {
2121: *rindp = rind = (int *)MALLOC_ATOMIC(rank*sizeof(int));
2122: *cindp = cind = (int *)MALLOC_ATOMIC((col-rank)*sizeof(int));
2123: for ( j = k = l = 0; j < col; j++ )
2124: if ( colstat[j] ) rind[k++] = j;
2125: else cind[l++] = j;
2126: if ( gensolve_check(mat,*nm,*dn,rind,cind) )
2127: return rank;
2128: }
2129: }
2130: }
2131: }
2132: #endif
1.8 noro 2133:
1.9 noro 2134: int generic_gauss_elim_hensel64(MAT mat,MAT *nmmat,Z *dn,int **rindp,int **cindp)
2135: {
2136: MAT r;
2137: Z z;
2138: Z **a0;
2139: Z *ai;
2140: mpz_t **a,**b,**x,**nm;
2141: mpz_t *bi,*xi;
2142: mpz_t q,u,den;
2143: mp_limb_t **w;
2144: mp_limb_t *wi;
2145: mp_limb_t **wc;
2146: mp_limb_t md;
2147: int row,col;
2148: int ind,i,j,k,l,li,ri,rank;
2149: int *cinfo,*rinfo;
2150: int *rind,*cind;
2151: int count;
2152: int ret;
2153: int period;
2154:
2155: a0 = (Z **)mat->body;
2156: row = mat->row; col = mat->col;
2157: w = (mp_limb_t **)almat64(row,col);
2158: for ( ind = 0; ; ind++ ) {
2159: md = get_lprime64(ind);
2160: for ( i = 0; i < row; i++ )
2161: for ( j = 0, ai = a0[i], wi = w[i]; j < col; j++ )
2162: wi[j] = remqi64((Q)ai[j],md);
2163:
2164: if ( DP_Print > 3 ) {
2165: fprintf(asir_out,"LU decomposition.."); fflush(asir_out);
2166: }
2167: rank = find_lhs_and_lu_mod64(w,row,col,md,&rinfo,&cinfo);
2168: if ( DP_Print > 3 ) {
2169: fprintf(asir_out,"done.\n"); fflush(asir_out);
2170: }
2171: a = (mpz_t **)mpz_allocmat(rank,rank); /* lhs mat */
2172: b = (mpz_t **)mpz_allocmat(rank,col-rank);
2173: for ( j = li = ri = 0; j < col; j++ )
2174: if ( cinfo[j] ) {
2175: /* the column is in lhs */
2176: for ( i = 0; i < rank; i++ ) {
2177: w[i][li] = w[i][j];
2178: if ( a0[rinfo[i]][j] )
2179: mpz_set(a[i][li],BDY(a0[rinfo[i]][j]));
2180: else
2181: mpz_set_ui(a[i][li],0);
2182: }
2183: li++;
2184: } else {
2185: /* the column is in rhs */
2186: for ( i = 0; i < rank; i++ ) {
2187: if ( a0[rinfo[i]][j] )
2188: mpz_set(b[i][ri],BDY(a0[rinfo[i]][j]));
2189: else
2190: mpz_set_ui(b[i][ri],0);
2191: }
2192: ri++;
2193: }
2194:
2195: /* solve Ax=B; A: rank x rank, B: rank x ri */
2196: /* algorithm
2197: c <- B
2198: x <- 0
2199: q <- 1
2200: do
2201: t <- A^(-1)c mod p
2202: x <- x+qt
2203: c <- (c-At)/p
2204: q <- qp
2205: end do
2206: then Ax-B=0 mod q and b=(B-Ax)/q hold after "do".
2207: */
2208: x = (mpz_t **)mpz_allocmat(rank,ri);
2209: nm = (mpz_t **)mpz_allocmat(rank,ri);
2210: wc = (mp_limb_t **)almat64(rank,ri);
2211: *rindp = rind = (int *)MALLOC_ATOMIC(rank*sizeof(int));
2212: *cindp = cind = (int *)MALLOC_ATOMIC((ri)*sizeof(int));
2213:
2214: period = F4_INTRAT_PERIOD;
2215: mpz_init_set_ui(q,1);
2216: mpz_init(u);
2217: mpz_init(den);
2218: for ( count = 0; ; ) {
2219: /* check Ax=B mod q */
2220: if ( DP_Print > 3 )
2221: fprintf(stderr,"o");
2222: /* wc = b mod md */
2223: for ( i = 0; i < rank; i++ )
2224: for ( j = 0, bi = b[i], wi = wc[i]; j < ri; j++ )
2225: wi[j] = mpz_fdiv_ui(bi[j],md);
2226: /* wc = A^(-1)wc; wc is not normalized */
2227: solve_by_lu_mod64(w,rank,md,wc,ri,0);
2228: /* x += q*wc */
2229: for ( i = 0; i < rank; i++ )
2230: for ( j = 0, wi = wc[i]; j < ri; j++ )
2231: if ( wi[j] > 0 )
2232: mpz_addmul_ui(x[i][j],q,wi[j]);
2233: else if ( wi[j] < 0 )
2234: mpz_submul_ui(x[i][j],q,-wi[j]);
2235: /* b =(b-A*wc)/md */
2236: for ( i = 0; i < rank; i++ )
2237: for ( j = 0; j < ri; j++ ) {
2238: mpz_set(u,b[i][j]);
2239: for ( k = 0; k < rank; k++ ) {
2240: if ( a[i][k] && wc[k][j] ) {
2241: if ( wc[k][j] < 0 )
2242: mpz_addmul_ui(u,a[i][k],-wc[k][j]);
2243: else
2244: mpz_submul_ui(u,a[i][k],wc[k][j]);
2245: }
2246: }
2247: mpz_divexact_ui(b[i][j],u,md);
2248: }
2249: count++;
2250: /* q = q*md */
2251: mpz_mul_ui(q,q,md);
2252: fprintf(stderr,".");
2253: if ( count == period ) {
2254: ret = mpz_intmtoratm(x,rank,ri,q,nm,den);
2255: if ( ret ) {
2256: for ( j = k = l = 0; j < col; j++ )
2257: if ( cinfo[j] )
2258: rind[k++] = j;
2259: else
2260: cind[l++] = j;
2261: ret = mpz_gensolve_check(mat,nm,den,rank,rind,cind);
2262: if ( ret ) {
2263: *rindp = rind;
2264: *cindp = cind;
2265: for ( j = k = 0; j < col; j++ )
2266: if ( !cinfo[j] )
2267: cind[k++] = j;
2268: MKMAT(r,rank,ri); *nmmat = r;
2269: for ( i = 0; i < rank; i++ )
2270: for ( j = 0; j < ri; j++ ) {
2271: MPZTOZ(nm[i][j],z); BDY(r)[i][j] = z;
2272: }
2273: MPZTOZ(den,*dn);
2274: return rank;
2275: }
2276: } else {
2277: fprintf(stderr,"F");
2278: period = period*3/2;
2279: count = 0;
2280: }
2281: }
2282: }
2283: }
2284: }
2285:
1.8 noro 2286: #endif
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