Annotation of OpenXM_contrib2/asir2018/engine/Q.c, Revision 1.14
1.14 ! noro 1: /* $OpenXM: OpenXM_contrib2/asir2018/engine/Q.c,v 1.13 2019/03/18 07:00:33 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);
1.13 noro 518: mpz_fac_ui(a,(unsigned long)n);
1.1 noro 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);
1.11 noro 1232: isqrt(t,&s);
1.1 noro 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 {
1.14 ! noro 1340: mpz_gcd(t,v1,v2);
! 1341: if ( UNIMPZ(t) )
! 1342: mpz_set_ui(r1,0);
! 1343: else {
! 1344: /* v1 /= t, v2 /= t, t=c*v1-v2, r1=t%m */
! 1345: mpz_divexact(v1,v1,t); mpz_divexact(v2,v2,t);
! 1346: mpz_mul(t,c,v1); mpz_sub(t,t,v2); mpz_mod(r1,t,m);
! 1347: }
! 1348: if ( mpz_sgn(r1) ) return 0;
1.8 noro 1349: if ( mpz_sgn(v1)<0 ) {
1350: mpz_neg(dn,v1); mpz_neg(nm,v2);
1351: } else {
1352: mpz_set(dn,v1); mpz_set(nm,v2);
1353: }
1354: return 1;
1355: }
1356: }
1357:
1.1 noro 1358: int inttorat(Z c,Z m,Z b,Z *nmp,Z *dnp)
1359: {
1.14 ! noro 1360: Z qq,t,s,r,u1,v1,r1;
1.1 noro 1361: Z q,u2,v2,r2;
1362:
1363: u1 = 0; v1 = ONE; u2 = m; v2 = c;
1364: while ( cmpz(v2,b) >= 0 ) {
1365: divqrz(u2,v2,&q,&r2); u2 = v2; v2 = r2;
1366: mulz(q,v1,&t); subz(u1,t,&r1); u1 = v1; v1 = r1;
1367: }
1368: if ( cmpz(v1,b) >= 0 ) return 0;
1369: else {
1.14 ! noro 1370: /* reduction and check */
! 1371: /* v2/v1 = u2/u1, c*u1-u2 = 0 mod m? */
! 1372: gcdz(v1,v2,&t);
! 1373: if ( UNIZ(t) ) {
! 1374: u1 = v1; u2 = v2; r = 0;
! 1375: } else {
! 1376: divsz(v1,t,&u1); divsz(v2,t,&u2);
! 1377: mulz(c,u1,&t); subz(t,u2,&s); remz(s,m,&r);
! 1378: }
! 1379: if ( r ) return 0;
! 1380: if ( mpz_sgn(BDY(u1))<0 ) {
! 1381: chsgnz(u1,dnp); chsgnz(u2,nmp);
1.1 noro 1382: } else {
1.14 ! noro 1383: *dnp = u1; *nmp = u2;
1.1 noro 1384: }
1385: return 1;
1386: }
1387: }
1388:
1389: extern int f4_nocheck;
1390:
1.12 noro 1391: int mpz_gensolve_check(MAT mat,mpz_t **nm,mpz_t dn,int rank,int clen,int *rind,int *cind)
1.8 noro 1392: {
1.12 noro 1393: int row,col,i,j,k,l;
1.8 noro 1394: mpz_t t;
1395: mpz_t *w;
1396: Z *mati;
1397: mpz_t *nmk;
1398:
1399: if ( f4_nocheck ) return 1;
1.12 noro 1400: row = mat->row; col = mat->col;
1.8 noro 1401: w = (mpz_t *)MALLOC(clen*sizeof(mpz_t));
1402: mpz_init(t);
1403: for ( i = 0; i < clen; i++ ) mpz_init(w[i]);
1404: for ( i = 0; i < row; i++ ) {
1405: mati = (Z *)mat->body[i];
1406: for ( l = 0; l < clen; l++ ) mpz_set_ui(w[l],0);
1407: for ( k = 0; k < rank; k++ )
1408: for ( l = 0, nmk = (mpz_t *)nm[k]; l < clen; l++ ) {
1409: /* w[l] += mati[rind[k]]*nmk[k] */
1410: if ( mati[rind[k]] ) mpz_addmul(w[l],BDY(mati[rind[k]]),nmk[l]);
1411: }
1412: for ( j = 0; j < clen; j++ ) {
1413: if ( mati[cind[j]] ) mpz_mul(t,dn,BDY(mati[cind[j]]));
1414: else mpz_set_ui(t,0);
1415: if ( mpz_cmp(w[j],t) ) break;
1416: }
1417: if ( j != clen ) break;
1418: }
1419: if ( i != row ) return 0;
1420: else return 1;
1421: }
1422:
1.1 noro 1423: int gensolve_check(MAT mat,MAT nm,Z dn,int *rind,int *cind)
1424: {
1425: int row,col,rank,clen,i,j,k,l;
1426: Z s,t;
1427: Z *w;
1428: Z *mati,*nmk;
1429:
1430: if ( f4_nocheck ) return 1;
1431: row = mat->row; col = mat->col; rank = nm->row; clen = nm->col;
1432: w = (Z *)MALLOC(clen*sizeof(Z));
1433: for ( i = 0; i < row; i++ ) {
1434: mati = (Z *)mat->body[i];
1435: bzero(w,clen*sizeof(Z));
1436: for ( k = 0; k < rank; k++ )
1437: for ( l = 0, nmk = (Z *)nm->body[k]; l < clen; l++ ) {
1438: mulz(mati[rind[k]],nmk[l],&t); addz(w[l],t,&s); w[l] = s;
1439: }
1440: for ( j = 0; j < clen; j++ ) {
1441: mulz(dn,mati[cind[j]],&t);
1442: if ( cmpz(w[j],t) ) break;
1443: }
1444: if ( j != clen ) break;
1445: }
1446: if ( i != row ) return 0;
1447: else return 1;
1448: }
1449:
1450: int gensolve_check2(MAT mat,MAT nm,Z *dn,int *rind,int *cind)
1451: {
1452: int row,col,rank,clen,i,j,k,l;
1453: Z s,t,u,d;
1454: Z *w,*m;
1455: Z *mati,*nmk;
1456:
1457: if ( f4_nocheck ) return 1;
1458: row = mat->row; col = mat->col; rank = nm->row; clen = nm->col;
1459: w = (Z *)MALLOC(clen*sizeof(Z));
1460: m = (Z *)MALLOC(clen*sizeof(Z));
1461: for ( d = dn[0], i = 1; i < rank; i++ ) {
1462: lcmz(d,dn[i],&t); d = t;
1463: }
1464: for ( i = 0; i < rank; i++ ) divsz(d,dn[i],&m[i]);
1465: for ( i = 0; i < row; i++ ) {
1466: mati = (Z *)mat->body[i];
1467: bzero(w,clen*sizeof(Z));
1468: for ( k = 0; k < rank; k++ ) {
1469: mulz(mati[rind[k]],m[k],&u);
1470: for ( l = 0, nmk = (Z *)nm->body[k]; l < clen; l++ ) {
1471: mulz(u,nmk[l],&t); addz(w[l],t,&s); w[l] = s;
1472: }
1473: }
1474: for ( j = 0; j < clen; j++ ) {
1475: mulz(d,mati[cind[j]],&t);
1476: if ( cmpz(w[j],t) ) break;
1477: }
1478: if ( j != clen ) break;
1479: }
1480: if ( i != row ) return 0;
1481: else return 1;
1482: }
1483:
1484: void isqrtz(Z a,Z *r)
1485: {
1486: int k;
1487: Z x,t,x2,xh,quo,rem;
1488: Z two;
1489:
1490: if ( !a ) *r = 0;
1.11 noro 1491: else if ( UNIZ(a) ) *r = ONE;
1.1 noro 1492: else {
1493: k = z_bits((Q)a); /* a <= 2^k-1 */
1494: bshiftz(ONE,-((k>>1)+(k&1)),&x); /* a <= x^2 */
1.5 noro 1495: STOZ(2,two);
1.1 noro 1496: while ( 1 ) {
1497: pwrz(x,two,&t);
1498: if ( cmpz(t,a) <= 0 ) {
1499: *r = x; return;
1500: } else {
1501: if ( mpz_tstbit(BDY(x),0) ) addz(x,a,&t);
1502: else t = a;
1503: bshiftz(x,-1,&x2); divqrz(t,x2,&quo,&rem);
1504: bshiftz(x,1,&xh); addz(quo,xh,&x);
1505: }
1506: }
1507: }
1508: }
1509:
1510: void bshiftz(Z a,int n,Z *r)
1511: {
1512: mpz_t t;
1513:
1514: if ( !a ) *r = 0;
1515: else if ( n == 0 ) *r = a;
1516: else if ( n < 0 ) {
1517: mpz_init(t); mpz_mul_2exp(t,BDY(a),-n); MPZTOZ(t,*r);
1518: } else {
1519: mpz_init(t); mpz_fdiv_q_2exp(t,BDY(a),n);
1520: if ( !mpz_sgn(t) ) *r = 0;
1521: else MPZTOZ(t,*r);
1522: }
1523: }
1524:
1525: void addlf(Z a,Z b,Z *c)
1526: {
1527: addz(a,b,c);
1528: if ( !lf_lazy ) {
1529: if ( cmpz(*c,current_mod_lf) >= 0 ) {
1530: subz(*c,current_mod_lf,c);
1531: }
1532: }
1533: }
1534:
1535: void sublf(Z a,Z b,Z *c)
1536: {
1537: subz(a,b,c);
1538: if ( !lf_lazy ) {
1539: remz(*c,current_mod_lf,c);
1540: }
1541: }
1542:
1543: void mullf(Z a,Z b,Z *c)
1544: {
1545: mulz(a,b,c);
1546: if ( !lf_lazy ) {
1547: remz(*c,current_mod_lf,c);
1548: }
1549: }
1550:
1551: void divlf(Z a,Z b,Z *c)
1552: {
1553: Z inv;
1554:
1555: invz(b,current_mod_lf,&inv);
1556: mulz(a,inv,c);
1557: if ( !lf_lazy ) {
1558: remz(*c,current_mod_lf,c);
1559: }
1560: }
1561:
1562: void chsgnlf(Z a,Z *c)
1563: {
1564: chsgnz(a,c);
1565: if ( !lf_lazy ) {
1566: remz(*c,current_mod_lf,c);
1567: }
1568: }
1569:
1570: void lmtolf(LM a,Z *b)
1571: {
1572: if ( !a ) *b = 0;
1573: else {
1574: MPZTOZ(BDY(a),*b);
1575: }
1576: }
1577:
1578: void setmod_lf(Z p)
1579: {
1580: current_mod_lf = p;
1581: current_mod_lf_size = mpz_size(BDY(current_mod_lf))+1;
1582: }
1583:
1584: void simplf_force(Z a,Z *b)
1585: {
1586: remz(a,current_mod_lf,b);
1587: }
1588:
1589: int generic_gauss_elim_hensel(MAT mat,MAT *nmmat,Z *dn,int **rindp,int **cindp)
1590: {
1591: MAT bmat,xmat;
1592: Z **a0,**a,**b,**x,**nm;
1593: Z *ai,*bi,*xi;
1594: int row,col;
1595: int **w;
1596: int *wi;
1597: int **wc;
1598: Z mdq,q,s,u;
1599: Z tn;
1600: int ind,md,i,j,k,l,li,ri,rank;
1601: unsigned int t;
1602: int *cinfo,*rinfo;
1603: int *rind,*cind;
1604: int count;
1605: int ret;
1.3 noro 1606: struct oEGT eg_mul1,eg_mul2,tmp0,tmp1,tmp2;
1.1 noro 1607: int period;
1608: int *wx,*ptr;
1609: int wxsize,nsize;
1610: Z wn;
1611: Z wq;
1612:
1.9 noro 1613: #if SIZEOF_LONG == 8
1.11 noro 1614: return generic_gauss_elim_hensel64(mat,nmmat,dn,rindp,cindp,0);
1.9 noro 1615: #endif
1.3 noro 1616: init_eg(&eg_mul1); init_eg(&eg_mul2);
1.1 noro 1617: a0 = (Z **)mat->body;
1618: row = mat->row; col = mat->col;
1619: w = (int **)almat(row,col);
1620: for ( ind = 0; ; ind++ ) {
1621: md = get_lprime(ind);
1.5 noro 1622: STOZ(md,mdq);
1.1 noro 1623: for ( i = 0; i < row; i++ )
1624: for ( j = 0, ai = a0[i], wi = w[i]; j < col; j++ )
1625: wi[j] = remqi((Q)ai[j],md);
1626:
1627: if ( DP_Print > 3 ) {
1628: fprintf(asir_out,"LU decomposition.."); fflush(asir_out);
1629: }
1630: rank = find_lhs_and_lu_mod((unsigned int **)w,row,col,md,&rinfo,&cinfo);
1631: if ( DP_Print > 3 ) {
1632: fprintf(asir_out,"done.\n"); fflush(asir_out);
1633: }
1634: a = (Z **)almat_pointer(rank,rank); /* lhs mat */
1635: MKMAT(bmat,rank,col-rank); b = (Z **)bmat->body; /* lhs mat */
1636: for ( j = li = ri = 0; j < col; j++ )
1637: if ( cinfo[j] ) {
1638: /* the column is in lhs */
1639: for ( i = 0; i < rank; i++ ) {
1640: w[i][li] = w[i][j];
1641: a[i][li] = a0[rinfo[i]][j];
1642: }
1643: li++;
1644: } else {
1645: /* the column is in rhs */
1646: for ( i = 0; i < rank; i++ )
1647: b[i][ri] = a0[rinfo[i]][j];
1648: ri++;
1649: }
1650:
1651: /* solve Ax=B; A: rank x rank, B: rank x ri */
1652: /* algorithm
1653: c <- B
1654: x <- 0
1655: q <- 1
1656: do
1657: t <- A^(-1)c mod p
1658: x <- x+qt
1659: c <- (c-At)/p
1660: q <- qp
1661: end do
1662: then Ax-B=0 mod q and b=(B-Ax)/q hold after "do".
1663: */
1664: MKMAT(xmat,rank,ri); x = (Z **)(xmat)->body;
1665: MKMAT(*nmmat,rank,ri); nm = (Z **)(*nmmat)->body;
1666: wc = (int **)almat(rank,ri);
1667: *rindp = rind = (int *)MALLOC_ATOMIC(rank*sizeof(int));
1668: *cindp = cind = (int *)MALLOC_ATOMIC((ri)*sizeof(int));
1669:
1670: period = F4_INTRAT_PERIOD;
1671: for ( q = ONE, count = 0; ; ) {
1.3 noro 1672: /* check Ax=B mod q */
1.1 noro 1673: if ( DP_Print > 3 )
1674: fprintf(stderr,"o");
1675: /* wc = b mod md */
1676: for ( i = 0; i < rank; i++ )
1.3 noro 1677: for ( j = 0, bi = b[i], wi = wc[i]; j < ri; j++ )
1.1 noro 1678: wi[j] = remqi((Q)bi[j],md);
1.3 noro 1679: /* wc = A^(-1)wc; wc is not normalized */
1680: solve_by_lu_mod(w,rank,md,wc,ri,0);
1.1 noro 1681: /* x += q*wc */
1.3 noro 1682: get_eg(&tmp0);
1.1 noro 1683: for ( i = 0; i < rank; i++ )
1684: for ( j = 0, wi = wc[i]; j < ri; j++ ) mul1addtoz(q,wi[j],&x[i][j]);
1.3 noro 1685: /* b =(b-A*wc)/md */
1686: get_eg(&tmp1); add_eg(&eg_mul1,&tmp0,&tmp1);
1.1 noro 1687: for ( i = 0; i < rank; i++ )
1688: for ( j = 0; j < ri; j++ ) {
1.3 noro 1689: mpz_t uz;
1690:
1691: if ( b[i][j] )
1692: mpz_init_set(uz,BDY(b[i][j]));
1693: else
1694: mpz_init_set_ui(uz,0);
1695: for ( k = 0; k < rank; k++ ) {
1696: if ( a[i][k] && wc[k][j] ) {
1697: if ( wc[k][j] < 0 )
1698: mpz_addmul_ui(uz,BDY(a[i][k]),-wc[k][j]);
1699: else
1700: mpz_submul_ui(uz,BDY(a[i][k]),wc[k][j]);
1701: }
1702: }
1703: MPZTOZ(uz,u);
1.1 noro 1704: divsz(u,mdq,&b[i][j]);
1705: }
1.3 noro 1706: get_eg(&tmp2); add_eg(&eg_mul2,&tmp1,&tmp2);
1.1 noro 1707: count++;
1708: /* q = q*md */
1709: mulz(q,mdq,&u); q = u;
1710: if ( count == period ) {
1711: ret = intmtoratm(xmat,q,*nmmat,dn);
1712: if ( ret ) {
1.3 noro 1713: print_eg("MUL1",&eg_mul1);
1714: print_eg("MUL2",&eg_mul2);
1.1 noro 1715: for ( j = k = l = 0; j < col; j++ )
1716: if ( cinfo[j] )
1717: rind[k++] = j;
1718: else
1719: cind[l++] = j;
1720: ret = gensolve_check(mat,*nmmat,*dn,rind,cind);
1721: if ( ret ) {
1722: *rindp = rind;
1723: *cindp = cind;
1724: for ( j = k = 0; j < col; j++ )
1725: if ( !cinfo[j] )
1726: cind[k++] = j;
1727: return rank;
1.11 noro 1728: } else
1729: goto reset;
1.1 noro 1730: } else {
1.11 noro 1731: reset:
1.1 noro 1732: period = period*3/2;
1733: count = 0;
1734: }
1735: }
1736: }
1737: }
1738: }
1739:
1740: /* for inv_or_split_dalg */
1741:
1742: int generic_gauss_elim_hensel_dalg(MAT mat,DP *mb,MAT *nmmat,Z *dn,int **rindp,int **cindp)
1743: {
1744: MAT bmat,xmat;
1745: Z **a0,**a,**b,**x,**nm;
1746: Z *ai,*bi,*xi;
1747: int row,col;
1748: int **w;
1749: int *wi;
1750: int **wc;
1751: Z mdq,q,s,u;
1752: Z tn;
1753: int ind,md,i,j,k,l,li,ri,rank;
1754: unsigned int t;
1755: int *cinfo,*rinfo;
1756: int *rind,*cind;
1757: int count;
1758: int ret;
1759: struct oEGT eg_mul,eg_inv,eg_intrat,eg_check,tmp0,tmp1;
1760: int period;
1761: int *wx,*ptr;
1762: int wxsize,nsize;
1763: Z wn;
1764: Z wq;
1765: DP m;
1766:
1.11 noro 1767: #if SIZEOF_LONG == 8
1768: return generic_gauss_elim_hensel64(mat,nmmat,dn,rindp,cindp,mb);
1769: #endif
1.1 noro 1770: a0 = (Z **)mat->body;
1771: row = mat->row; col = mat->col;
1772: w = (int **)almat(row,col);
1773: for ( ind = 0; ; ind++ ) {
1774: md = get_lprime(ind);
1.5 noro 1775: STOZ(md,mdq);
1.1 noro 1776: for ( i = 0; i < row; i++ )
1777: for ( j = 0, ai = a0[i], wi = w[i]; j < col; j++ )
1778: wi[j] = remqi((Q)ai[j],md);
1779:
1780: if ( DP_Print > 3 ) {
1781: fprintf(asir_out,"LU decomposition.."); fflush(asir_out);
1782: }
1783: rank = find_lhs_and_lu_mod((unsigned int **)w,row,col,md,&rinfo,&cinfo);
1784: if ( DP_Print > 3 ) {
1785: fprintf(asir_out,"done.\n"); fflush(asir_out);
1786: }
1787:
1788: /* this part is added for inv_or_split_dalg */
1789: for ( i = 0; i < col-1; i++ ) {
1790: if ( !cinfo[i] ) {
1791: m = mb[i];
1792: for ( j = i+1; j < col-1; j++ )
1793: if ( dp_redble(mb[j],m) )
1794: cinfo[j] = -1;
1795: }
1796: }
1797:
1798: a = (Z **)almat_pointer(rank,rank); /* lhs mat */
1799: MKMAT(bmat,rank,col-rank); b = (Z **)bmat->body; /* lhs mat */
1800: for ( j = li = ri = 0; j < col; j++ )
1.4 noro 1801: if ( cinfo[j] > 0 ) {
1.1 noro 1802: /* the column is in lhs */
1803: for ( i = 0; i < rank; i++ ) {
1804: w[i][li] = w[i][j];
1805: a[i][li] = a0[rinfo[i]][j];
1806: }
1807: li++;
1.4 noro 1808: } else if ( !cinfo[j] ) {
1.1 noro 1809: /* the column is in rhs */
1810: for ( i = 0; i < rank; i++ )
1811: b[i][ri] = a0[rinfo[i]][j];
1812: ri++;
1813: }
1814:
1815: /* solve Ax=B; A: rank x rank, B: rank x ri */
1816: /* algorithm
1817: c <- B
1818: x <- 0
1819: q <- 1
1820: do
1821: t <- A^(-1)c mod p
1822: x <- x+qt
1823: c <- (c-At)/p
1824: q <- qp
1825: end do
1826: then Ax-B=0 mod q and b=(B-Ax)/q hold after "do".
1827: */
1828: MKMAT(xmat,rank,ri); x = (Z **)(xmat)->body;
1829: MKMAT(*nmmat,rank,ri); nm = (Z **)(*nmmat)->body;
1830: wc = (int **)almat(rank,ri);
1831: *rindp = rind = (int *)MALLOC_ATOMIC(rank*sizeof(int));
1832: *cindp = cind = (int *)MALLOC_ATOMIC((ri)*sizeof(int));
1833:
1834: period = F4_INTRAT_PERIOD;
1835: for ( q = ONE, count = 0; ; ) {
1836: if ( DP_Print > 3 )
1837: fprintf(stderr,"o");
1838: /* wc = b mod md */
1839: for ( i = 0; i < rank; i++ )
1.3 noro 1840: for ( j = 0, bi = b[i], wi = wc[i]; j < ri; j++ )
1.1 noro 1841: wi[j] = remqi((Q)bi[j],md);
1.11 noro 1842: /* wc = A^(-1)wc; wc is not normalized */
1843: solve_by_lu_mod(w,rank,md,wc,ri,0);
1.1 noro 1844: /* x += q*wc */
1845: for ( i = 0; i < rank; i++ )
1846: for ( j = 0, wi = wc[i]; j < ri; j++ ) mul1addtoz(q,wi[j],&x[i][j]);
1.3 noro 1847: /* b =(b-A*wc)/md */
1.1 noro 1848: for ( i = 0; i < rank; i++ )
1849: for ( j = 0; j < ri; j++ ) {
1.3 noro 1850: mpz_t uz;
1851:
1852: if ( b[i][j] )
1853: mpz_init_set(uz,BDY(b[i][j]));
1854: else
1855: mpz_init_set_ui(uz,0);
1.11 noro 1856: for ( k = 0; k < rank; k++ )
1857: if ( a[i][k] && wc[k][j] )
1.3 noro 1858: mpz_submul_ui(uz,BDY(a[i][k]),wc[k][j]);
1859: MPZTOZ(uz,u);
1.1 noro 1860: divsz(u,mdq,&b[i][j]);
1861: }
1.11 noro 1862:
1.1 noro 1863: count++;
1864: /* q = q*md */
1865: mulz(q,mdq,&u); q = u;
1866: if ( count == period ) {
1867: ret = intmtoratm(xmat,q,*nmmat,dn);
1868: if ( ret ) {
1869: for ( j = k = l = 0; j < col; j++ )
1870: if ( cinfo[j] > 0 )
1871: rind[k++] = j;
1872: else if ( !cinfo[j] )
1873: cind[l++] = j;
1874: ret = gensolve_check(mat,*nmmat,*dn,rind,cind);
1875: if ( ret ) {
1876: *rindp = rind;
1877: *cindp = cind;
1878: for ( j = k = 0; j < col; j++ )
1879: if ( !cinfo[j] )
1880: cind[k++] = j;
1881: return rank;
1.11 noro 1882: } else
1883: goto reset;
1.1 noro 1884: } else {
1.11 noro 1885: reset:
1.1 noro 1886: period = period*3/2;
1887: count = 0;
1888: }
1889: }
1890: }
1891: }
1892: }
1.6 noro 1893:
1894: #if SIZEOF_LONG == 8
1895: mp_limb_t remqi64(Q a,mp_limb_t mod)
1896: {
1897: mp_limb_t c,nm,dn;
1898: mpz_t r;
1899:
1900: if ( !a ) return 0;
1901: else if ( a->z ) {
1902: mpz_init(r);
1903: c = mpz_fdiv_r_ui(r,BDY((Z)a),mod);
1904: } else {
1905: mpz_init(r);
1906: nm = mpz_fdiv_r_ui(r,mpq_numref(BDY(a)),mod);
1907: dn = mpz_fdiv_r_ui(r,mpq_denref(BDY(a)),mod);
1908: dn = invmod64(dn,mod);
1909: c = mulmod64(nm,dn,mod);
1910: }
1911: return c;
1912: }
1913:
1914: int generic_gauss_elim_mod64(mp_limb_t **mat,int row,int col,mp_limb_t md,int *colstat);
1915: mp_limb_t get_lprime64(int ind);
1916:
1.8 noro 1917: void mpz_print(mpz_t a)
1918: {
1919: mpz_out_str(stdout,10,a); printf("\n");
1920: }
1921:
1922: void mpz_printmat(mpz_t **a,int row,int col)
1923: {
1924: int i,j;
1925: for ( i = 0; i < row; i++ ) {
1926: for ( j = 0; j < col; j++ ) {
1927: mpz_out_str(stdout,10,a[i][j]); printf(" ");
1928: }
1929: printf("\n");
1930: }
1931: }
1932:
1933: mpz_t **mpz_allocmat(int row,int col)
1934: {
1935: mpz_t **p;
1936: int i,j;
1937:
1938: p = (mpz_t **)MALLOC(row*sizeof(mpz_t *));
1939: for ( i = 0; i < row; i++ ) {
1940: p[i] = (mpz_t *)MALLOC(col*sizeof(mpz_t));
1941: for ( j = 0; j < col; j++ ) mpz_init(p[i][j]);
1942: }
1943: return p;
1944: }
1945:
1946: #if 1
1947: int generic_gauss_elim64(MAT mat,MAT *nm,Z *dn,int **rindp,int **cindp)
1948: {
1949: mp_limb_t **wmat;
1950: mp_limb_t *wmi;
1951: mp_limb_t md,inv,t,t1;
1952: Z z;
1953: Z **bmat,*bmi;
1954: mpz_t **tmat,**num;
1955: mpz_t *tmi;
1956: mpz_t den;
1957: mpz_t q,m1,m3,s,u;
1958: int *colstat,*wcolstat,*rind,*cind;
1959: int row,col,ind,i,j,k,l,rank,rank0;
1960: MAT r;
1961: int ret;
1962:
1963: bmat = (Z **)mat->body;
1964: row = mat->row; col = mat->col;
1965: wmat = (mp_limb_t **)almat64(row,col);
1966: colstat = (int *)MALLOC_ATOMIC(col*sizeof(int));
1967: wcolstat = (int *)MALLOC_ATOMIC(col*sizeof(int));
1968: mpz_init(m1); mpz_init(m3); mpz_init(den);
1969: for ( ind = 0; ; ind++ ) {
1970: if ( DP_Print ) {
1971: fprintf(asir_out,"."); fflush(asir_out);
1972: }
1973: md = get_lprime64(ind);
1974: for ( i = 0; i < row; i++ )
1975: for ( j = 0, bmi = bmat[i], wmi = wmat[i]; j < col; j++ )
1976: wmi[j] = bmi[j]==0?0:mpz_fdiv_ui(BDY(bmi[j]),md);
1977: rank = generic_gauss_elim_mod64(wmat,row,col,md,wcolstat);
1978: if ( !ind ) {
1979: RESET:
1980: mpz_set_ui(m1,md);
1981: rank0 = rank;
1982: bcopy(wcolstat,colstat,col*sizeof(int));
1983: // crmat
1984: tmat = mpz_allocmat(rank,col-rank);
1985: //
1986: num = mpz_allocmat(rank,col-rank);
1987: for ( i = 0; i < rank; i++ )
1988: for ( j = k = 0, tmi = tmat[i], wmi = wmat[i]; j < col; j++ )
1989: if ( !colstat[j] ) { mpz_set_ui(tmi[k],wmi[j]); k++; }
1990: } else {
1991: if ( rank < rank0 ) {
1992: if ( DP_Print ) {
1993: fprintf(asir_out,"lower rank matrix; continuing...\n");
1994: fflush(asir_out);
1995: }
1996: continue;
1997: } else if ( rank > rank0 ) {
1998: if ( DP_Print ) {
1999: fprintf(asir_out,"higher rank matrix; resetting...\n");
2000: fflush(asir_out);
2001: }
2002: goto RESET;
2003: } else {
2004: for ( j = 0; (j<col) && (colstat[j]==wcolstat[j]); j++ );
2005: if ( j < col ) {
2006: if ( DP_Print ) {
2007: fprintf(asir_out,"inconsitent colstat; resetting...\n");
2008: fflush(asir_out);
2009: }
2010: goto RESET;
2011: }
2012: }
2013:
2014: inv = invmod64(mpz_fdiv_ui(m1,md),md);
2015: mpz_mul_ui(m3,m1,md);
2016: for ( i = 0; i < rank; i++ )
2017: for ( j = k = 0, tmi = tmat[i], wmi = wmat[i]; j < col; j++ )
2018: if ( !colstat[j] ) {
2019: if ( mpz_sgn(tmi[k]) ) {
2020: /* f3 = f1+m1*(m1 mod md)^(-1)*(f2 - f1 mod md) */
2021: t = mpz_fdiv_ui(tmi[k],md);
2022: if ( wmi[j] >= t ) t = wmi[j]-t;
2023: else t = md-(t-wmi[j]);
2024: mpz_addmul_ui(tmi[k],m1,mulmod64(t,inv,md));
2025: } else if ( wmi[j] ) {
2026: /* f3 = m1*(m1 mod m2)^(-1)*f2 */
2027: mpz_mul_ui(tmi[k],m1,mulmod64(wmi[j],inv,md));
2028: }
2029: k++;
2030: }
2031: mpz_set(m1,m3);
2032: if ( ind % F4_INTRAT_PERIOD )
2033: ret = 0;
2034: else
2035: ret = mpz_intmtoratm(tmat,rank,col-rank,m1,num,den);
2036: if ( ret ) {
2037: *rindp = rind = (int *)MALLOC_ATOMIC(rank*sizeof(int));
2038: *cindp = cind = (int *)MALLOC_ATOMIC((col-rank)*sizeof(int));
2039: for ( j = k = l = 0; j < col; j++ )
2040: if ( colstat[j] ) rind[k++] = j;
2041: else cind[l++] = j;
1.12 noro 2042: if ( mpz_gensolve_check(mat,num,den,rank,col-rank,rind,cind) ) {
1.8 noro 2043: MKMAT(r,rank,col-rank); *nm = r;
2044: for ( i = 0; i < rank; i++ )
2045: for ( j = 0; j < col-rank; j++ ) {
2046: MPZTOZ(num[i][j],z); BDY(r)[i][j] = z;
2047: }
2048: MPZTOZ(den,*dn);
2049: return rank;
2050: }
2051: }
2052: }
2053: }
2054: }
2055: #else
1.6 noro 2056: int generic_gauss_elim64(MAT mat,MAT *nm,Z *dn,int **rindp,int **cindp)
2057: {
2058: mp_limb_t **wmat;
2059: mp_limb_t *wmi;
2060: mp_limb_t md,inv,t,t1;
2061: Z **bmat,**tmat,*bmi,*tmi;
2062: Z q,m1,m2,m3,s,u;
2063: int *colstat,*wcolstat,*rind,*cind;
2064: int row,col,ind,i,j,k,l,rank,rank0;
2065: MAT r,crmat;
2066: int ret;
2067:
2068: bmat = (Z **)mat->body;
2069: row = mat->row; col = mat->col;
2070: wmat = (mp_limb_t **)almat64(row,col);
2071: colstat = (int *)MALLOC_ATOMIC(col*sizeof(int));
2072: wcolstat = (int *)MALLOC_ATOMIC(col*sizeof(int));
2073: for ( ind = 0; ; ind++ ) {
2074: if ( DP_Print ) {
2075: fprintf(asir_out,"."); fflush(asir_out);
2076: }
2077: md = get_lprime64(ind);
2078: for ( i = 0; i < row; i++ )
2079: for ( j = 0, bmi = bmat[i], wmi = wmat[i]; j < col; j++ )
2080: wmi[j] = remqi64((Q)bmi[j],md);
2081: rank = generic_gauss_elim_mod64(wmat,row,col,md,wcolstat);
2082: if ( !ind ) {
2083: RESET:
2084: UTOZ(md,m1);
2085: rank0 = rank;
2086: bcopy(wcolstat,colstat,col*sizeof(int));
2087: MKMAT(crmat,rank,col-rank);
2088: MKMAT(r,rank,col-rank); *nm = r;
2089: tmat = (Z **)crmat->body;
2090: for ( i = 0; i < rank; i++ )
2091: for ( j = k = 0, tmi = tmat[i], wmi = wmat[i]; j < col; j++ )
2092: if ( !colstat[j] ) { UTOZ(wmi[j],tmi[k]); k++; }
2093: } else {
2094: if ( rank < rank0 ) {
2095: if ( DP_Print ) {
2096: fprintf(asir_out,"lower rank matrix; continuing...\n");
2097: fflush(asir_out);
2098: }
2099: continue;
2100: } else if ( rank > rank0 ) {
2101: if ( DP_Print ) {
2102: fprintf(asir_out,"higher rank matrix; resetting...\n");
2103: fflush(asir_out);
2104: }
2105: goto RESET;
2106: } else {
2107: for ( j = 0; (j<col) && (colstat[j]==wcolstat[j]); j++ );
2108: if ( j < col ) {
2109: if ( DP_Print ) {
2110: fprintf(asir_out,"inconsitent colstat; resetting...\n");
2111: fflush(asir_out);
2112: }
2113: goto RESET;
2114: }
2115: }
2116:
2117: inv = invmod64(remqi64((Q)m1,md),md);
2118: UTOZ(md,m2); mulz(m1,m2,&m3);
2119: for ( i = 0; i < rank; i++ )
2120: for ( j = k = 0, tmi = tmat[i], wmi = wmat[i]; j < col; j++ )
2121: if ( !colstat[j] ) {
2122: if ( tmi[k] ) {
2123: /* f3 = f1+m1*(m1 mod m2)^(-1)*(f2 - f1 mod m2) */
2124: t = remqi64((Q)tmi[k],md);
2125: if ( wmi[j] >= t ) t = wmi[j]-t;
2126: else t = md-(t-wmi[j]);
2127: t1 = mulmod64(t,inv,md);
2128: UTOZ(t1,u); mulz(m1,u,&s);
2129: addz(tmi[k],s,&u); tmi[k] = u;
2130: } else if ( wmi[j] ) {
2131: /* f3 = m1*(m1 mod m2)^(-1)*f2 */
2132: t = mulmod64(wmi[j],inv,md);
2133: UTOZ(t,u); mulz(m1,u,&s); tmi[k] = s;
2134: }
2135: k++;
2136: }
2137: m1 = m3;
2138: if ( ind % F4_INTRAT_PERIOD )
2139: ret = 0;
2140: else
2141: ret = intmtoratm(crmat,m1,*nm,dn);
2142: if ( ret ) {
2143: *rindp = rind = (int *)MALLOC_ATOMIC(rank*sizeof(int));
2144: *cindp = cind = (int *)MALLOC_ATOMIC((col-rank)*sizeof(int));
2145: for ( j = k = l = 0; j < col; j++ )
2146: if ( colstat[j] ) rind[k++] = j;
2147: else cind[l++] = j;
2148: if ( gensolve_check(mat,*nm,*dn,rind,cind) )
2149: return rank;
2150: }
2151: }
2152: }
2153: }
2154: #endif
1.8 noro 2155:
1.11 noro 2156: int generic_gauss_elim_hensel64(MAT mat,MAT *nmmat,Z *dn,int **rindp,int **cindp,DP *mb)
1.9 noro 2157: {
2158: MAT r;
2159: Z z;
2160: Z **a0;
2161: Z *ai;
2162: mpz_t **a,**b,**x,**nm;
2163: mpz_t *bi,*xi;
2164: mpz_t q,u,den;
2165: mp_limb_t **w;
2166: mp_limb_t *wi;
2167: mp_limb_t **wc;
2168: mp_limb_t md;
2169: int row,col;
2170: int ind,i,j,k,l,li,ri,rank;
2171: int *cinfo,*rinfo;
2172: int *rind,*cind;
2173: int count;
2174: int ret;
2175: int period;
1.11 noro 2176: DP m;
1.9 noro 2177:
2178: a0 = (Z **)mat->body;
2179: row = mat->row; col = mat->col;
2180: w = (mp_limb_t **)almat64(row,col);
2181: for ( ind = 0; ; ind++ ) {
2182: md = get_lprime64(ind);
2183: for ( i = 0; i < row; i++ )
2184: for ( j = 0, ai = a0[i], wi = w[i]; j < col; j++ )
2185: wi[j] = remqi64((Q)ai[j],md);
2186:
2187: if ( DP_Print > 3 ) {
2188: fprintf(asir_out,"LU decomposition.."); fflush(asir_out);
2189: }
2190: rank = find_lhs_and_lu_mod64(w,row,col,md,&rinfo,&cinfo);
2191: if ( DP_Print > 3 ) {
2192: fprintf(asir_out,"done.\n"); fflush(asir_out);
2193: }
1.11 noro 2194:
2195: if ( mb ) {
2196: /* this part is added for inv_or_split_dalg */
2197: for ( i = 0; i < col-1; i++ ) {
2198: if ( !cinfo[i] ) {
2199: m = mb[i];
2200: for ( j = i+1; j < col-1; j++ )
2201: if ( dp_redble(mb[j],m) )
2202: cinfo[j] = -1;
2203: }
2204: }
2205: }
2206:
1.9 noro 2207: a = (mpz_t **)mpz_allocmat(rank,rank); /* lhs mat */
2208: b = (mpz_t **)mpz_allocmat(rank,col-rank);
2209: for ( j = li = ri = 0; j < col; j++ )
1.11 noro 2210: if ( cinfo[j] > 0 ) {
1.9 noro 2211: /* the column is in lhs */
2212: for ( i = 0; i < rank; i++ ) {
2213: w[i][li] = w[i][j];
2214: if ( a0[rinfo[i]][j] )
2215: mpz_set(a[i][li],BDY(a0[rinfo[i]][j]));
2216: else
2217: mpz_set_ui(a[i][li],0);
2218: }
2219: li++;
1.11 noro 2220: } else if ( !cinfo[j] ) {
1.9 noro 2221: /* the column is in rhs */
2222: for ( i = 0; i < rank; i++ ) {
2223: if ( a0[rinfo[i]][j] )
2224: mpz_set(b[i][ri],BDY(a0[rinfo[i]][j]));
2225: else
2226: mpz_set_ui(b[i][ri],0);
2227: }
2228: ri++;
2229: }
2230:
2231: /* solve Ax=B; A: rank x rank, B: rank x ri */
2232: /* algorithm
2233: c <- B
2234: x <- 0
2235: q <- 1
2236: do
2237: t <- A^(-1)c mod p
2238: x <- x+qt
2239: c <- (c-At)/p
2240: q <- qp
2241: end do
2242: then Ax-B=0 mod q and b=(B-Ax)/q hold after "do".
2243: */
2244: x = (mpz_t **)mpz_allocmat(rank,ri);
2245: nm = (mpz_t **)mpz_allocmat(rank,ri);
2246: wc = (mp_limb_t **)almat64(rank,ri);
2247: *rindp = rind = (int *)MALLOC_ATOMIC(rank*sizeof(int));
2248: *cindp = cind = (int *)MALLOC_ATOMIC((ri)*sizeof(int));
2249:
2250: period = F4_INTRAT_PERIOD;
2251: mpz_init_set_ui(q,1);
2252: mpz_init(u);
2253: mpz_init(den);
2254: for ( count = 0; ; ) {
2255: /* check Ax=B mod q */
2256: if ( DP_Print > 3 )
2257: fprintf(stderr,"o");
2258: /* wc = b mod md */
2259: for ( i = 0; i < rank; i++ )
2260: for ( j = 0, bi = b[i], wi = wc[i]; j < ri; j++ )
2261: wi[j] = mpz_fdiv_ui(bi[j],md);
2262: /* wc = A^(-1)wc; wc is not normalized */
2263: solve_by_lu_mod64(w,rank,md,wc,ri,0);
2264: /* x += q*wc */
2265: for ( i = 0; i < rank; i++ )
2266: for ( j = 0, wi = wc[i]; j < ri; j++ )
2267: if ( wi[j] > 0 )
2268: mpz_addmul_ui(x[i][j],q,wi[j]);
2269: else if ( wi[j] < 0 )
2270: mpz_submul_ui(x[i][j],q,-wi[j]);
2271: /* b =(b-A*wc)/md */
2272: for ( i = 0; i < rank; i++ )
2273: for ( j = 0; j < ri; j++ ) {
2274: mpz_set(u,b[i][j]);
2275: for ( k = 0; k < rank; k++ ) {
2276: if ( a[i][k] && wc[k][j] ) {
2277: if ( wc[k][j] < 0 )
2278: mpz_addmul_ui(u,a[i][k],-wc[k][j]);
2279: else
2280: mpz_submul_ui(u,a[i][k],wc[k][j]);
2281: }
2282: }
2283: mpz_divexact_ui(b[i][j],u,md);
2284: }
2285: count++;
2286: /* q = q*md */
2287: mpz_mul_ui(q,q,md);
2288: if ( count == period ) {
2289: ret = mpz_intmtoratm(x,rank,ri,q,nm,den);
2290: if ( ret ) {
2291: for ( j = k = l = 0; j < col; j++ )
1.11 noro 2292: if ( cinfo[j] > 0 )
1.9 noro 2293: rind[k++] = j;
1.11 noro 2294: else if ( !cinfo[j] )
1.9 noro 2295: cind[l++] = j;
1.12 noro 2296: ret = mpz_gensolve_check(mat,nm,den,rank,ri,rind,cind);
1.9 noro 2297: if ( ret ) {
2298: *rindp = rind;
2299: *cindp = cind;
2300: for ( j = k = 0; j < col; j++ )
2301: if ( !cinfo[j] )
2302: cind[k++] = j;
2303: MKMAT(r,rank,ri); *nmmat = r;
2304: for ( i = 0; i < rank; i++ )
2305: for ( j = 0; j < ri; j++ ) {
2306: MPZTOZ(nm[i][j],z); BDY(r)[i][j] = z;
2307: }
2308: MPZTOZ(den,*dn);
2309: return rank;
1.11 noro 2310: } else
2311: goto reset;
1.9 noro 2312: } else {
1.11 noro 2313: reset:
1.9 noro 2314: fprintf(stderr,"F");
2315: period = period*3/2;
2316: count = 0;
2317: }
2318: }
2319: }
2320: }
2321: }
2322:
1.8 noro 2323: #endif
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