Annotation of OpenXM_contrib2/asir2018/engine/Q.c, Revision 1.7
1.7 ! noro 1: /* $OpenXM: OpenXM_contrib2/asir2018/engine/Q.c,v 1.6 2018/10/01 05:49:06 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:
1.6 noro 14: #define F4_INTRAT_PERIOD 8
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: {
1.3 noro 33: mp_set_memory_functions(Risa_GC_malloc_atomic,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;
903:
1.6 noro 904: #if SIZEOF_LONG == 8
905: return generic_gauss_elim64(mat,nm,dn,rindp,cindp);
906: #endif
1.1 noro 907: bmat = (Z **)mat->body;
908: row = mat->row; col = mat->col;
909: wmat = (int **)almat(row,col);
910: colstat = (int *)MALLOC_ATOMIC(col*sizeof(int));
911: wcolstat = (int *)MALLOC_ATOMIC(col*sizeof(int));
912: for ( ind = 0; ; ind++ ) {
913: if ( DP_Print ) {
914: fprintf(asir_out,"."); fflush(asir_out);
915: }
916: md = get_lprime(ind);
917: for ( i = 0; i < row; i++ )
918: for ( j = 0, bmi = bmat[i], wmi = wmat[i]; j < col; j++ )
919: wmi[j] = remqi((Q)bmi[j],md);
920: rank = generic_gauss_elim_mod(wmat,row,col,md,wcolstat);
921: if ( !ind ) {
922: RESET:
923: m1 = utoz(md);
924: rank0 = rank;
925: bcopy(wcolstat,colstat,col*sizeof(int));
926: MKMAT(crmat,rank,col-rank);
927: MKMAT(r,rank,col-rank); *nm = r;
928: tmat = (Z **)crmat->body;
929: for ( i = 0; i < rank; i++ )
930: for ( j = k = 0, tmi = tmat[i], wmi = wmat[i]; j < col; j++ )
931: if ( !colstat[j] ) tmi[k++] = utoz(wmi[j]);
932: } else {
933: if ( rank < rank0 ) {
934: if ( DP_Print ) {
935: fprintf(asir_out,"lower rank matrix; continuing...\n");
936: fflush(asir_out);
937: }
938: continue;
939: } else if ( rank > rank0 ) {
940: if ( DP_Print ) {
941: fprintf(asir_out,"higher rank matrix; resetting...\n");
942: fflush(asir_out);
943: }
944: goto RESET;
945: } else {
946: for ( j = 0; (j<col) && (colstat[j]==wcolstat[j]); j++ );
947: if ( j < col ) {
948: if ( DP_Print ) {
949: fprintf(asir_out,"inconsitent colstat; resetting...\n");
950: fflush(asir_out);
951: }
952: goto RESET;
953: }
954: }
955:
956: inv = invm(remqi((Q)m1,md),md);
957: m2 = utoz(md); mulz(m1,m2,&m3);
958: for ( i = 0; i < rank; i++ )
959: for ( j = k = 0, tmi = tmat[i], wmi = wmat[i]; j < col; j++ )
960: if ( !colstat[j] ) {
961: if ( tmi[k] ) {
962: /* f3 = f1+m1*(m1 mod m2)^(-1)*(f2 - f1 mod m2) */
963: t = remqi((Q)tmi[k],md);
964: if ( wmi[j] >= t ) t = wmi[j]-t;
965: else t = md-(t-wmi[j]);
966: DMAR(t,inv,0,md,t1)
967: u = utoz(t1); mulz(m1,u,&s);
968: addz(tmi[k],s,&u); tmi[k] = u;
969: } else if ( wmi[j] ) {
970: /* f3 = m1*(m1 mod m2)^(-1)*f2 */
971: DMAR(wmi[j],inv,0,md,t)
972: u = utoz(t); mulz(m1,u,&s); tmi[k] = s;
973: }
974: k++;
975: }
976: m1 = m3;
977: if ( ind % F4_INTRAT_PERIOD )
978: ret = 0;
979: else
980: ret = intmtoratm(crmat,m1,*nm,dn);
981: if ( ret ) {
982: *rindp = rind = (int *)MALLOC_ATOMIC(rank*sizeof(int));
983: *cindp = cind = (int *)MALLOC_ATOMIC((col-rank)*sizeof(int));
984: for ( j = k = l = 0; j < col; j++ )
985: if ( colstat[j] ) rind[k++] = j;
986: else cind[l++] = j;
987: if ( gensolve_check(mat,*nm,*dn,rind,cind) )
988: return rank;
989: }
990: }
991: }
992: }
993:
994: int generic_gauss_elim2(MAT mat,MAT *nm,Z *dn,int **rindp,int **cindp)
995: {
996:
997: MAT full;
998: Z **bmat,**b;
999: Z *bmi;
1000: Z dn0;
1001: int row,col,md,i,j,rank,ret;
1002: int **wmat;
1003: int *wmi;
1004: int *colstat,*rowstat;
1005:
1006: bmat = (Z **)mat->body;
1007: row = mat->row; col = mat->col;
1008: wmat = (int **)almat(row,col);
1009: colstat = (int *)MALLOC_ATOMIC(col*sizeof(int));
1010: rowstat = (int *)MALLOC_ATOMIC(row*sizeof(int));
1011: /* XXX */
1012: md = get_lprime(0);
1013: for ( i = 0; i < row; i++ )
1014: for ( j = 0, bmi = bmat[i], wmi = wmat[i]; j < col; j++ )
1015: wmi[j] = remqi((Q)bmi[j],md);
1016: rank = generic_gauss_elim_mod2(wmat,row,col,md,colstat,rowstat);
1017: b = (Z **)MALLOC(rank*sizeof(Z));
1018: for ( i = 0; i < rank; i++ ) b[i] = bmat[rowstat[i]];
1019: NEWMAT(full); full->row = rank; full->col = col; full->body = (pointer **)b;
1020: ret = generic_gauss_elim_full(full,nm,dn,rindp,cindp);
1021: if ( !ret ) {
1022: rank = generic_gauss_elim(mat,nm,&dn0,rindp,cindp);
1023: for ( i = 0; i < rank; i++ ) dn[i] = dn0;
1024: }
1025: return rank;
1026: }
1027:
1028: int generic_gauss_elim_full(MAT mat,MAT *nm,Z *dn,int **rindp,int **cindp)
1029: {
1030: int **wmat;
1031: int *stat;
1032: Z **bmat,**tmat,*bmi,*tmi,*ri;
1033: Z q,m1,m2,m3,s,u;
1034: int *wmi,*colstat,*wcolstat,*rind,*cind;
1035: int row,col,ind,md,i,j,k,l,t,t1,rank,rank0,inv,h;
1036: MAT r,crmat;
1037: int ret,initialized,done;
1038:
1039: initialized = 0;
1040: bmat = (Z **)mat->body;
1041: row = mat->row; col = mat->col;
1042: wmat = (int **)almat(row,col);
1043: stat = (int *)MALLOC_ATOMIC(row*sizeof(int));
1044: for ( i = 0; i < row; i++ ) stat[i] = 0;
1045: colstat = (int *)MALLOC_ATOMIC(col*sizeof(int));
1046: wcolstat = (int *)MALLOC_ATOMIC(col*sizeof(int));
1047: for ( ind = 0; ; ind++ ) {
1048: if ( DP_Print ) {
1049: fprintf(asir_out,"."); fflush(asir_out);
1050: }
1051: md = get_lprime(ind);
1052: for ( i = 0; i < row; i++ )
1053: for ( j = 0, bmi = bmat[i], wmi = wmat[i]; j < col; j++ )
1054: wmi[j] = remqi((Q)bmi[j],md);
1055: rank = generic_gauss_elim_mod(wmat,row,col,md,wcolstat);
1056: if ( rank < row ) continue;
1057: if ( !initialized ) {
1058: m1 = utoz(md);
1059: bcopy(wcolstat,colstat,col*sizeof(int));
1060: MKMAT(crmat,row,col-row);
1061: MKMAT(r,row,col-row); *nm = r;
1062: tmat = (Z **)crmat->body;
1063: for ( i = 0; i < row; i++ )
1064: for ( j = k = 0, tmi = tmat[i], wmi = wmat[i]; j < col; j++ )
1065: if ( !colstat[j] ) tmi[k++] = utoz(wmi[j]);
1066: initialized = 1;
1067: } else {
1068: for ( j = 0; (j<col) && (colstat[j]==wcolstat[j]); j++ );
1069: if ( j < col ) continue;
1070:
1071: inv = invm(remqi((Q)m1,md),md);
1072: m2 = utoz(md); mulz(m1,m2,&m3);
1073: for ( i = 0; i < row; i++ )
1074: switch ( stat[i] ) {
1075: case 1:
1076: /* consistency check */
1077: ri = (Z *)BDY(r)[i]; wmi = wmat[i];
1078: for ( j = 0; j < col; j++ ) if ( colstat[j] ) break;
1079: h = md-remqi((Q)dn[i],md);
1080: for ( j++, k = 0; j < col; j++ )
1081: if ( !colstat[j] ) {
1082: t = remqi((Q)ri[k],md);
1083: DMAR(wmi[i],h,t,md,t1);
1084: if ( t1 ) break;
1085: }
1086: if ( j == col ) { stat[i]++; break; }
1087: else {
1088: /* fall to the case 0 */
1089: stat[i] = 0;
1090: }
1091: case 0:
1092: tmi = tmat[i]; wmi = wmat[i];
1093: for ( j = k = 0; j < col; j++ )
1094: if ( !colstat[j] ) {
1095: if ( tmi[k] ) {
1096: /* f3 = f1+m1*(m1 mod m2)^(-1)*(f2 - f1 mod m2) */
1097: t = remqi((Q)tmi[k],md);
1098: if ( wmi[j] >= t ) t = wmi[j]-t;
1099: else t = md-(t-wmi[j]);
1100: DMAR(t,inv,0,md,t1)
1101: u = utoz(t1); mulz(m1,u,&s);
1102: addz(tmi[k],s,&u); tmi[k] = u;
1103: } else if ( wmi[j] ) {
1104: /* f3 = m1*(m1 mod m2)^(-1)*f2 */
1105: DMAR(wmi[j],inv,0,md,t)
1106: u = utoz(t); mulz(m1,u,&s); tmi[k] = s;
1107: }
1108: k++;
1109: }
1110: break;
1111: case 2: default:
1112: break;
1113: }
1114: m1 = m3;
1115: if ( ind % 4 )
1116: ret = 0;
1117: else
1118: ret = intmtoratm2(crmat,m1,*nm,dn,stat);
1119: if ( ret ) {
1120: *rindp = rind = (int *)MALLOC_ATOMIC(row*sizeof(int));
1121: *cindp = cind = (int *)MALLOC_ATOMIC((col-row)*sizeof(int));
1122: for ( j = k = l = 0; j < col; j++ )
1123: if ( colstat[j] ) rind[k++] = j;
1124: else cind[l++] = j;
1125: return gensolve_check2(mat,*nm,dn,rind,cind);
1126: }
1127: }
1128: }
1129: }
1130:
1131: int generic_gauss_elim_direct(MAT mat,MAT *nm,Z *dn,int **rindp,int **cindp){
1132: Z **bmat,*s;
1133: Z u,v,w,x,d,t,y;
1134: int row,col,i,j,k,l,m,rank;
1135: int *colstat,*colpos,*cind;
1136: MAT r,in;
1137:
1138: row = mat->row; col = mat->col;
1139: MKMAT(in,row,col);
1140: for ( i = 0; i < row; i++ )
1141: for ( j = 0; j < col; j++ ) in->body[i][j] = mat->body[i][j];
1142: bmat = (Z **)in->body;
1143: colstat = (int *)MALLOC_ATOMIC(col*sizeof(int));
1144: *rindp = colpos = (int *)MALLOC_ATOMIC(row*sizeof(int));
1145: for ( j = 0, rank = 0, d = ONE; j < col; j++ ) {
1146: for ( i = rank; i < row && !bmat[i][j]; i++ );
1147: if ( i == row ) { colstat[j] = 0; continue; }
1148: else { colstat[j] = 1; colpos[rank] = j; }
1149: if ( i != rank )
1150: for ( k = j; k < col; k++ ) {
1151: t = bmat[i][k]; bmat[i][k] = bmat[rank][k]; bmat[rank][k] = t;
1152: }
1153: for ( i = rank+1, v = bmat[rank][j]; i < row; i++ )
1154: for ( k = j, u = bmat[i][j]; k < col; k++ ) {
1155: mulz(bmat[i][k],v,&w); mulz(bmat[rank][k],u,&x);
1156: subz(w,x,&y); divsz(y,d,&bmat[i][k]);
1157: }
1158: d = v; rank++;
1159: }
1160: *dn = d;
1161: s = (Z *)MALLOC(col*sizeof(Z));
1162: for ( i = rank-1; i >= 0; i-- ) {
1163: for ( k = colpos[i]; k < col; k++ ) mulz(bmat[i][k],d,&s[k]);
1164: for ( m = rank-1; m > i; m-- ) {
1165: for ( k = colpos[m], u = bmat[i][k]; k < col; k++ ) {
1166: mulz(bmat[m][k],u,&w); subz(s[k],w,&x); s[k] = x;
1167: }
1168: }
1169: for ( k = colpos[i], u = bmat[i][k]; k < col; k++ )
1170: divz(s[k],u,&bmat[i][k]);
1171: }
1172: *cindp = cind = (int *)MALLOC_ATOMIC((col-rank)*sizeof(int));
1173: MKMAT(r,rank,col-rank); *nm = r;
1174: for ( j = 0, k = 0; j < col; j++ )
1175: if ( !colstat[j] ) {
1176: cind[k] = j;
1177: for ( i = 0; i < rank; i++ ) r->body[i][k] = bmat[i][j];
1178: k++;
1179: }
1180: return rank;
1181: }
1182:
1183: int intmtoratm(MAT mat,Z md,MAT nm,Z *dn)
1184: {
1185: Z t,s,b,dn0,dn1,nm1,q,u,unm,udn,dmy;
1186: int i,j,k,l,row,col,sgn,ret;
1187: Z **rmat,**tmat,*tmi,*nmk;
1188:
1189: if ( UNIQ(md) )
1190: return 0;
1191: row = mat->row; col = mat->col;
1192: bshiftz(md,1,&t);
1193: isqrtz(t,&s);
1194: bshiftz(s,64,&b);
1195: if ( !b ) b = ONE;
1196: dn0 = ONE;
1197: tmat = (Z **)mat->body;
1198: rmat = (Z **)nm->body;
1199: for ( i = 0; i < row; i++ )
1200: for ( j = 0, tmi = tmat[i]; j < col; j++ )
1201: if ( tmi[j] ) {
1202: mulz(tmi[j],dn0,&s);
1203: divqrz(s,md,&dmy,&u);
1204: ret = inttorat(u,md,b,&nm1,&dn1);
1205: if ( !ret ) return 0;
1206: else {
1207: if ( !UNIQ(dn1) ) {
1208: for ( k = 0; k < i; k++ )
1209: for ( l = 0, nmk = rmat[k]; l < col; l++ ) {
1210: mulz(nmk[l],dn1,&q); nmk[l] = q;
1211: }
1212: for ( l = 0, nmk = rmat[i]; l < j; l++ ) {
1213: mulz(nmk[l],dn1,&q); nmk[l] = q;
1214: }
1215: }
1216: rmat[i][j] = nm1;
1217: mulz(dn0,dn1,&q); dn0 = q;
1218: }
1219: }
1220: *dn = dn0;
1221: return 1;
1222: }
1223:
1224: int intmtoratm2(MAT mat,Z md,MAT nm,Z *dn,int *stat)
1225: {
1226: int row,col,i,j,ret;
1227: Z dn0,dn1,t,s,b;
1228: Z *w,*tmi;
1229: Z **tmat;
1230:
1231: bshiftz(md,1,&t);
1232: isqrtz(t,&s);
1233: bshiftz(s,64,&b);
1234: tmat = (Z **)mat->body;
1235: if ( UNIQ(md) ) return 0;
1236: row = mat->row; col = mat->col;
1237: dn0 = ONE;
1238: for ( i = 0; i < row; i++ )
1239: if ( cmpz(dn[i],dn0) > 0 ) dn0 = dn[i];
1240: w = (Z *)MALLOC(col*sizeof(Z));
1241: for ( i = 0; i < row; i++ )
1242: if ( stat[i] == 0 ) {
1243: for ( j = 0, tmi = tmat[i]; j < col; j++ )
1244: mulz(tmi[j],dn0,&w[j]);
1245: ret = intvtoratv(w,col,md,b,(Z *)BDY(nm)[i],&dn[i]);
1246: if ( ret ) {
1247: stat[i] = 1;
1248: mulz(dn0,dn[i],&t); dn[i] = t; dn0 = t;
1249: }
1250: }
1251: for ( i = 0; i < row; i++ ) if ( !stat[i] ) break;
1252: if ( i == row ) return 1;
1253: else return 0;
1254: }
1255:
1256: int intvtoratv(Z *v,int n,Z md,Z b,Z *nm,Z *dn)
1257: {
1258: Z dn0,dn1,q,s,u,nm1,unm,udn,dmy;
1259: Z *nmk;
1260: int j,l,col,ret,sgn;
1261:
1262: for ( j = 0; j < n; j++ ) nm[j] = 0;
1263: dn0 = ONE;
1264: for ( j = 0; j < n; j++ ) {
1265: if ( !v[j] ) continue;
1266: mulz(v[j],dn0,&s);
1267: divqrz(s,md,&dmy,&u);
1268: ret = inttorat(u,md,b,&nm1,&dn1);
1269: if ( !ret ) return 0;
1270: if ( !UNIQ(dn1) )
1271: for ( l = 0; l < j; l++ ) {
1272: mulz(nm[l],dn1,&q); nm[l] = q;
1273: }
1274: nm[j] = nm1;
1275: mulz(dn0,dn1,&q); dn0 = q;
1276: }
1277: *dn = dn0;
1278: return 1;
1279: }
1280:
1281: /* assuming 0 < c < m */
1282:
1283: int inttorat(Z c,Z m,Z b,Z *nmp,Z *dnp)
1284: {
1285: Z qq,t,u1,v1,r1;
1286: Z q,u2,v2,r2;
1287:
1288: u1 = 0; v1 = ONE; u2 = m; v2 = c;
1289: while ( cmpz(v2,b) >= 0 ) {
1290: divqrz(u2,v2,&q,&r2); u2 = v2; v2 = r2;
1291: mulz(q,v1,&t); subz(u1,t,&r1); u1 = v1; v1 = r1;
1292: }
1293: if ( cmpz(v1,b) >= 0 ) return 0;
1294: else {
1295: if ( mpz_sgn(BDY(v1))<0 ) {
1296: chsgnz(v1,dnp); chsgnz(v2,nmp);
1297: } else {
1298: *dnp = v1; *nmp = v2;
1299: }
1300: return 1;
1301: }
1302: }
1303:
1304: extern int f4_nocheck;
1305:
1306: int gensolve_check(MAT mat,MAT nm,Z dn,int *rind,int *cind)
1307: {
1308: int row,col,rank,clen,i,j,k,l;
1309: Z s,t;
1310: Z *w;
1311: Z *mati,*nmk;
1312:
1313: if ( f4_nocheck ) return 1;
1314: row = mat->row; col = mat->col; rank = nm->row; clen = nm->col;
1315: w = (Z *)MALLOC(clen*sizeof(Z));
1316: for ( i = 0; i < row; i++ ) {
1317: mati = (Z *)mat->body[i];
1318: bzero(w,clen*sizeof(Z));
1319: for ( k = 0; k < rank; k++ )
1320: for ( l = 0, nmk = (Z *)nm->body[k]; l < clen; l++ ) {
1321: mulz(mati[rind[k]],nmk[l],&t); addz(w[l],t,&s); w[l] = s;
1322: }
1323: for ( j = 0; j < clen; j++ ) {
1324: mulz(dn,mati[cind[j]],&t);
1325: if ( cmpz(w[j],t) ) break;
1326: }
1327: if ( j != clen ) break;
1328: }
1329: if ( i != row ) return 0;
1330: else return 1;
1331: }
1332:
1333: int gensolve_check2(MAT mat,MAT nm,Z *dn,int *rind,int *cind)
1334: {
1335: int row,col,rank,clen,i,j,k,l;
1336: Z s,t,u,d;
1337: Z *w,*m;
1338: Z *mati,*nmk;
1339:
1340: if ( f4_nocheck ) return 1;
1341: row = mat->row; col = mat->col; rank = nm->row; clen = nm->col;
1342: w = (Z *)MALLOC(clen*sizeof(Z));
1343: m = (Z *)MALLOC(clen*sizeof(Z));
1344: for ( d = dn[0], i = 1; i < rank; i++ ) {
1345: lcmz(d,dn[i],&t); d = t;
1346: }
1347: for ( i = 0; i < rank; i++ ) divsz(d,dn[i],&m[i]);
1348: for ( i = 0; i < row; i++ ) {
1349: mati = (Z *)mat->body[i];
1350: bzero(w,clen*sizeof(Z));
1351: for ( k = 0; k < rank; k++ ) {
1352: mulz(mati[rind[k]],m[k],&u);
1353: for ( l = 0, nmk = (Z *)nm->body[k]; l < clen; l++ ) {
1354: mulz(u,nmk[l],&t); addz(w[l],t,&s); w[l] = s;
1355: }
1356: }
1357: for ( j = 0; j < clen; j++ ) {
1358: mulz(d,mati[cind[j]],&t);
1359: if ( cmpz(w[j],t) ) break;
1360: }
1361: if ( j != clen ) break;
1362: }
1363: if ( i != row ) return 0;
1364: else return 1;
1365: }
1366:
1367: void isqrtz(Z a,Z *r)
1368: {
1369: int k;
1370: Z x,t,x2,xh,quo,rem;
1371: Z two;
1372:
1373: if ( !a ) *r = 0;
1374: else if ( UNIQ(a) ) *r = ONE;
1375: else {
1376: k = z_bits((Q)a); /* a <= 2^k-1 */
1377: bshiftz(ONE,-((k>>1)+(k&1)),&x); /* a <= x^2 */
1.5 noro 1378: STOZ(2,two);
1.1 noro 1379: while ( 1 ) {
1380: pwrz(x,two,&t);
1381: if ( cmpz(t,a) <= 0 ) {
1382: *r = x; return;
1383: } else {
1384: if ( mpz_tstbit(BDY(x),0) ) addz(x,a,&t);
1385: else t = a;
1386: bshiftz(x,-1,&x2); divqrz(t,x2,&quo,&rem);
1387: bshiftz(x,1,&xh); addz(quo,xh,&x);
1388: }
1389: }
1390: }
1391: }
1392:
1393: void bshiftz(Z a,int n,Z *r)
1394: {
1395: mpz_t t;
1396:
1397: if ( !a ) *r = 0;
1398: else if ( n == 0 ) *r = a;
1399: else if ( n < 0 ) {
1400: mpz_init(t); mpz_mul_2exp(t,BDY(a),-n); MPZTOZ(t,*r);
1401: } else {
1402: mpz_init(t); mpz_fdiv_q_2exp(t,BDY(a),n);
1403: if ( !mpz_sgn(t) ) *r = 0;
1404: else MPZTOZ(t,*r);
1405: }
1406: }
1407:
1408: void addlf(Z a,Z b,Z *c)
1409: {
1410: addz(a,b,c);
1411: if ( !lf_lazy ) {
1412: if ( cmpz(*c,current_mod_lf) >= 0 ) {
1413: subz(*c,current_mod_lf,c);
1414: }
1415: }
1416: }
1417:
1418: void sublf(Z a,Z b,Z *c)
1419: {
1420: subz(a,b,c);
1421: if ( !lf_lazy ) {
1422: remz(*c,current_mod_lf,c);
1423: }
1424: }
1425:
1426: void mullf(Z a,Z b,Z *c)
1427: {
1428: mulz(a,b,c);
1429: if ( !lf_lazy ) {
1430: remz(*c,current_mod_lf,c);
1431: }
1432: }
1433:
1434: void divlf(Z a,Z b,Z *c)
1435: {
1436: Z inv;
1437:
1438: invz(b,current_mod_lf,&inv);
1439: mulz(a,inv,c);
1440: if ( !lf_lazy ) {
1441: remz(*c,current_mod_lf,c);
1442: }
1443: }
1444:
1445: void chsgnlf(Z a,Z *c)
1446: {
1447: chsgnz(a,c);
1448: if ( !lf_lazy ) {
1449: remz(*c,current_mod_lf,c);
1450: }
1451: }
1452:
1453: void lmtolf(LM a,Z *b)
1454: {
1455: if ( !a ) *b = 0;
1456: else {
1457: MPZTOZ(BDY(a),*b);
1458: }
1459: }
1460:
1461: void setmod_lf(Z p)
1462: {
1463: current_mod_lf = p;
1464: current_mod_lf_size = mpz_size(BDY(current_mod_lf))+1;
1465: }
1466:
1467: void simplf_force(Z a,Z *b)
1468: {
1469: remz(a,current_mod_lf,b);
1470: }
1471:
1472: int generic_gauss_elim_hensel(MAT mat,MAT *nmmat,Z *dn,int **rindp,int **cindp)
1473: {
1474: MAT bmat,xmat;
1475: Z **a0,**a,**b,**x,**nm;
1476: Z *ai,*bi,*xi;
1477: int row,col;
1478: int **w;
1479: int *wi;
1480: int **wc;
1481: Z mdq,q,s,u;
1482: Z tn;
1483: int ind,md,i,j,k,l,li,ri,rank;
1484: unsigned int t;
1485: int *cinfo,*rinfo;
1486: int *rind,*cind;
1487: int count;
1488: int ret;
1.3 noro 1489: struct oEGT eg_mul1,eg_mul2,tmp0,tmp1,tmp2;
1.1 noro 1490: int period;
1491: int *wx,*ptr;
1492: int wxsize,nsize;
1493: Z wn;
1494: Z wq;
1495:
1.3 noro 1496: init_eg(&eg_mul1); init_eg(&eg_mul2);
1.1 noro 1497: a0 = (Z **)mat->body;
1498: row = mat->row; col = mat->col;
1499: w = (int **)almat(row,col);
1500: for ( ind = 0; ; ind++ ) {
1501: md = get_lprime(ind);
1.5 noro 1502: STOZ(md,mdq);
1.1 noro 1503: for ( i = 0; i < row; i++ )
1504: for ( j = 0, ai = a0[i], wi = w[i]; j < col; j++ )
1505: wi[j] = remqi((Q)ai[j],md);
1506:
1507: if ( DP_Print > 3 ) {
1508: fprintf(asir_out,"LU decomposition.."); fflush(asir_out);
1509: }
1510: rank = find_lhs_and_lu_mod((unsigned int **)w,row,col,md,&rinfo,&cinfo);
1511: if ( DP_Print > 3 ) {
1512: fprintf(asir_out,"done.\n"); fflush(asir_out);
1513: }
1514: a = (Z **)almat_pointer(rank,rank); /* lhs mat */
1515: MKMAT(bmat,rank,col-rank); b = (Z **)bmat->body; /* lhs mat */
1516: for ( j = li = ri = 0; j < col; j++ )
1517: if ( cinfo[j] ) {
1518: /* the column is in lhs */
1519: for ( i = 0; i < rank; i++ ) {
1520: w[i][li] = w[i][j];
1521: a[i][li] = a0[rinfo[i]][j];
1522: }
1523: li++;
1524: } else {
1525: /* the column is in rhs */
1526: for ( i = 0; i < rank; i++ )
1527: b[i][ri] = a0[rinfo[i]][j];
1528: ri++;
1529: }
1530:
1531: /* solve Ax=B; A: rank x rank, B: rank x ri */
1532: /* algorithm
1533: c <- B
1534: x <- 0
1535: q <- 1
1536: do
1537: t <- A^(-1)c mod p
1538: x <- x+qt
1539: c <- (c-At)/p
1540: q <- qp
1541: end do
1542: then Ax-B=0 mod q and b=(B-Ax)/q hold after "do".
1543: */
1544: MKMAT(xmat,rank,ri); x = (Z **)(xmat)->body;
1545: MKMAT(*nmmat,rank,ri); nm = (Z **)(*nmmat)->body;
1546: wc = (int **)almat(rank,ri);
1547: *rindp = rind = (int *)MALLOC_ATOMIC(rank*sizeof(int));
1548: *cindp = cind = (int *)MALLOC_ATOMIC((ri)*sizeof(int));
1549:
1550: period = F4_INTRAT_PERIOD;
1551: for ( q = ONE, count = 0; ; ) {
1.3 noro 1552: /* check Ax=B mod q */
1.1 noro 1553: if ( DP_Print > 3 )
1554: fprintf(stderr,"o");
1555: /* wc = b mod md */
1556: for ( i = 0; i < rank; i++ )
1.3 noro 1557: for ( j = 0, bi = b[i], wi = wc[i]; j < ri; j++ )
1.1 noro 1558: wi[j] = remqi((Q)bi[j],md);
1.3 noro 1559: /* wc = A^(-1)wc; wc is not normalized */
1560: solve_by_lu_mod(w,rank,md,wc,ri,0);
1.1 noro 1561: /* x += q*wc */
1.3 noro 1562: get_eg(&tmp0);
1.1 noro 1563: for ( i = 0; i < rank; i++ )
1564: for ( j = 0, wi = wc[i]; j < ri; j++ ) mul1addtoz(q,wi[j],&x[i][j]);
1.3 noro 1565: /* b =(b-A*wc)/md */
1566: get_eg(&tmp1); add_eg(&eg_mul1,&tmp0,&tmp1);
1.1 noro 1567: for ( i = 0; i < rank; i++ )
1568: for ( j = 0; j < ri; j++ ) {
1.3 noro 1569: mpz_t uz;
1570:
1571: if ( b[i][j] )
1572: mpz_init_set(uz,BDY(b[i][j]));
1573: else
1574: mpz_init_set_ui(uz,0);
1575: for ( k = 0; k < rank; k++ ) {
1576: if ( a[i][k] && wc[k][j] ) {
1577: if ( wc[k][j] < 0 )
1578: mpz_addmul_ui(uz,BDY(a[i][k]),-wc[k][j]);
1579: else
1580: mpz_submul_ui(uz,BDY(a[i][k]),wc[k][j]);
1581: }
1582: }
1583: MPZTOZ(uz,u);
1.1 noro 1584: divsz(u,mdq,&b[i][j]);
1585: }
1.3 noro 1586: get_eg(&tmp2); add_eg(&eg_mul2,&tmp1,&tmp2);
1.1 noro 1587: count++;
1588: /* q = q*md */
1589: mulz(q,mdq,&u); q = u;
1590: if ( count == period ) {
1591: ret = intmtoratm(xmat,q,*nmmat,dn);
1592: if ( ret ) {
1.3 noro 1593: print_eg("MUL1",&eg_mul1);
1594: print_eg("MUL2",&eg_mul2);
1.1 noro 1595: for ( j = k = l = 0; j < col; j++ )
1596: if ( cinfo[j] )
1597: rind[k++] = j;
1598: else
1599: cind[l++] = j;
1600: ret = gensolve_check(mat,*nmmat,*dn,rind,cind);
1601: if ( ret ) {
1602: *rindp = rind;
1603: *cindp = cind;
1604: for ( j = k = 0; j < col; j++ )
1605: if ( !cinfo[j] )
1606: cind[k++] = j;
1607: return rank;
1608: }
1609: } else {
1610: period = period*3/2;
1611: count = 0;
1612: }
1613: }
1614: }
1615: }
1616: }
1617:
1618: /* for inv_or_split_dalg */
1619:
1620: int generic_gauss_elim_hensel_dalg(MAT mat,DP *mb,MAT *nmmat,Z *dn,int **rindp,int **cindp)
1621: {
1622: MAT bmat,xmat;
1623: Z **a0,**a,**b,**x,**nm;
1624: Z *ai,*bi,*xi;
1625: int row,col;
1626: int **w;
1627: int *wi;
1628: int **wc;
1629: Z mdq,q,s,u;
1630: Z tn;
1631: int ind,md,i,j,k,l,li,ri,rank;
1632: unsigned int t;
1633: int *cinfo,*rinfo;
1634: int *rind,*cind;
1635: int count;
1636: int ret;
1637: struct oEGT eg_mul,eg_inv,eg_intrat,eg_check,tmp0,tmp1;
1638: int period;
1639: int *wx,*ptr;
1640: int wxsize,nsize;
1641: Z wn;
1642: Z wq;
1643: DP m;
1644:
1645: a0 = (Z **)mat->body;
1646: row = mat->row; col = mat->col;
1647: w = (int **)almat(row,col);
1648: for ( ind = 0; ; ind++ ) {
1649: md = get_lprime(ind);
1.5 noro 1650: STOZ(md,mdq);
1.1 noro 1651: for ( i = 0; i < row; i++ )
1652: for ( j = 0, ai = a0[i], wi = w[i]; j < col; j++ )
1653: wi[j] = remqi((Q)ai[j],md);
1654:
1655: if ( DP_Print > 3 ) {
1656: fprintf(asir_out,"LU decomposition.."); fflush(asir_out);
1657: }
1658: rank = find_lhs_and_lu_mod((unsigned int **)w,row,col,md,&rinfo,&cinfo);
1659: if ( DP_Print > 3 ) {
1660: fprintf(asir_out,"done.\n"); fflush(asir_out);
1661: }
1662:
1663: /* this part is added for inv_or_split_dalg */
1664: for ( i = 0; i < col-1; i++ ) {
1665: if ( !cinfo[i] ) {
1666: m = mb[i];
1667: for ( j = i+1; j < col-1; j++ )
1668: if ( dp_redble(mb[j],m) )
1669: cinfo[j] = -1;
1670: }
1671: }
1672:
1673: a = (Z **)almat_pointer(rank,rank); /* lhs mat */
1674: MKMAT(bmat,rank,col-rank); b = (Z **)bmat->body; /* lhs mat */
1675: for ( j = li = ri = 0; j < col; j++ )
1.4 noro 1676: if ( cinfo[j] > 0 ) {
1.1 noro 1677: /* the column is in lhs */
1678: for ( i = 0; i < rank; i++ ) {
1679: w[i][li] = w[i][j];
1680: a[i][li] = a0[rinfo[i]][j];
1681: }
1682: li++;
1.4 noro 1683: } else if ( !cinfo[j] ) {
1.1 noro 1684: /* the column is in rhs */
1685: for ( i = 0; i < rank; i++ )
1686: b[i][ri] = a0[rinfo[i]][j];
1687: ri++;
1688: }
1689:
1690: /* solve Ax=B; A: rank x rank, B: rank x ri */
1691: /* algorithm
1692: c <- B
1693: x <- 0
1694: q <- 1
1695: do
1696: t <- A^(-1)c mod p
1697: x <- x+qt
1698: c <- (c-At)/p
1699: q <- qp
1700: end do
1701: then Ax-B=0 mod q and b=(B-Ax)/q hold after "do".
1702: */
1703: MKMAT(xmat,rank,ri); x = (Z **)(xmat)->body;
1704: MKMAT(*nmmat,rank,ri); nm = (Z **)(*nmmat)->body;
1705: wc = (int **)almat(rank,ri);
1706: *rindp = rind = (int *)MALLOC_ATOMIC(rank*sizeof(int));
1707: *cindp = cind = (int *)MALLOC_ATOMIC((ri)*sizeof(int));
1708:
1709: period = F4_INTRAT_PERIOD;
1710: for ( q = ONE, count = 0; ; ) {
1711: if ( DP_Print > 3 )
1712: fprintf(stderr,"o");
1713: /* wc = b mod md */
1714: for ( i = 0; i < rank; i++ )
1.3 noro 1715: for ( j = 0, bi = b[i], wi = wc[i]; j < ri; j++ )
1.1 noro 1716: wi[j] = remqi((Q)bi[j],md);
1717: /* wc = A^(-1)wc; wc is normalized */
1718: solve_by_lu_mod(w,rank,md,wc,ri,1);
1719: /* x += q*wc */
1720: for ( i = 0; i < rank; i++ )
1721: for ( j = 0, wi = wc[i]; j < ri; j++ ) mul1addtoz(q,wi[j],&x[i][j]);
1.3 noro 1722: /* b =(b-A*wc)/md */
1.1 noro 1723: for ( i = 0; i < rank; i++ )
1724: for ( j = 0; j < ri; j++ ) {
1.3 noro 1725: mpz_t uz;
1726:
1727: if ( b[i][j] )
1728: mpz_init_set(uz,BDY(b[i][j]));
1729: else
1730: mpz_init_set_ui(uz,0);
1731: for ( k = 0; k < rank; k++ ) {
1732: if ( a[i][k] && wc[k][j] ) {
1733: if ( wc[k][j] < 0 )
1734: mpz_addmul_ui(uz,BDY(a[i][k]),-wc[k][j]);
1735: else
1736: mpz_submul_ui(uz,BDY(a[i][k]),wc[k][j]);
1737: }
1738: }
1739: MPZTOZ(uz,u);
1.1 noro 1740: divsz(u,mdq,&b[i][j]);
1741: }
1742: count++;
1743: /* q = q*md */
1744: mulz(q,mdq,&u); q = u;
1745: if ( count == period ) {
1746: ret = intmtoratm(xmat,q,*nmmat,dn);
1747: if ( ret ) {
1748: for ( j = k = l = 0; j < col; j++ )
1749: if ( cinfo[j] > 0 )
1750: rind[k++] = j;
1751: else if ( !cinfo[j] )
1752: cind[l++] = j;
1753: ret = gensolve_check(mat,*nmmat,*dn,rind,cind);
1754: if ( ret ) {
1755: *rindp = rind;
1756: *cindp = cind;
1757: for ( j = k = 0; j < col; j++ )
1758: if ( !cinfo[j] )
1759: cind[k++] = j;
1760: return rank;
1761: }
1762: } else {
1763: period = period*3/2;
1764: count = 0;
1765: }
1766: }
1767: }
1768: }
1769: }
1.6 noro 1770:
1771: #if SIZEOF_LONG == 8
1772: mp_limb_t remqi64(Q a,mp_limb_t mod)
1773: {
1774: mp_limb_t c,nm,dn;
1775: mpz_t r;
1776:
1777: if ( !a ) return 0;
1778: else if ( a->z ) {
1779: mpz_init(r);
1780: c = mpz_fdiv_r_ui(r,BDY((Z)a),mod);
1781: } else {
1782: mpz_init(r);
1783: nm = mpz_fdiv_r_ui(r,mpq_numref(BDY(a)),mod);
1784: dn = mpz_fdiv_r_ui(r,mpq_denref(BDY(a)),mod);
1785: dn = invmod64(dn,mod);
1786: c = mulmod64(nm,dn,mod);
1787: }
1788: return c;
1789: }
1790:
1791: int generic_gauss_elim_mod64(mp_limb_t **mat,int row,int col,mp_limb_t md,int *colstat);
1792: mp_limb_t get_lprime64(int ind);
1793:
1794: int generic_gauss_elim64(MAT mat,MAT *nm,Z *dn,int **rindp,int **cindp)
1795: {
1796: mp_limb_t **wmat;
1797: mp_limb_t *wmi;
1798: mp_limb_t md,inv,t,t1;
1799: Z **bmat,**tmat,*bmi,*tmi;
1800: Z q,m1,m2,m3,s,u;
1801: int *colstat,*wcolstat,*rind,*cind;
1802: int row,col,ind,i,j,k,l,rank,rank0;
1803: MAT r,crmat;
1804: int ret;
1805:
1806: bmat = (Z **)mat->body;
1807: row = mat->row; col = mat->col;
1808: wmat = (mp_limb_t **)almat64(row,col);
1809: colstat = (int *)MALLOC_ATOMIC(col*sizeof(int));
1810: wcolstat = (int *)MALLOC_ATOMIC(col*sizeof(int));
1811: for ( ind = 0; ; ind++ ) {
1812: if ( DP_Print ) {
1813: fprintf(asir_out,"."); fflush(asir_out);
1814: }
1815: md = get_lprime64(ind);
1816: for ( i = 0; i < row; i++ )
1817: for ( j = 0, bmi = bmat[i], wmi = wmat[i]; j < col; j++ )
1818: wmi[j] = remqi64((Q)bmi[j],md);
1819: rank = generic_gauss_elim_mod64(wmat,row,col,md,wcolstat);
1820: if ( !ind ) {
1821: RESET:
1822: UTOZ(md,m1);
1823: rank0 = rank;
1824: bcopy(wcolstat,colstat,col*sizeof(int));
1825: MKMAT(crmat,rank,col-rank);
1826: MKMAT(r,rank,col-rank); *nm = r;
1827: tmat = (Z **)crmat->body;
1828: for ( i = 0; i < rank; i++ )
1829: for ( j = k = 0, tmi = tmat[i], wmi = wmat[i]; j < col; j++ )
1830: if ( !colstat[j] ) { UTOZ(wmi[j],tmi[k]); k++; }
1831: } else {
1832: if ( rank < rank0 ) {
1833: if ( DP_Print ) {
1834: fprintf(asir_out,"lower rank matrix; continuing...\n");
1835: fflush(asir_out);
1836: }
1837: continue;
1838: } else if ( rank > rank0 ) {
1839: if ( DP_Print ) {
1840: fprintf(asir_out,"higher rank matrix; resetting...\n");
1841: fflush(asir_out);
1842: }
1843: goto RESET;
1844: } else {
1845: for ( j = 0; (j<col) && (colstat[j]==wcolstat[j]); j++ );
1846: if ( j < col ) {
1847: if ( DP_Print ) {
1848: fprintf(asir_out,"inconsitent colstat; resetting...\n");
1849: fflush(asir_out);
1850: }
1851: goto RESET;
1852: }
1853: }
1854:
1855: inv = invmod64(remqi64((Q)m1,md),md);
1856: UTOZ(md,m2); mulz(m1,m2,&m3);
1857: for ( i = 0; i < rank; i++ )
1858: for ( j = k = 0, tmi = tmat[i], wmi = wmat[i]; j < col; j++ )
1859: if ( !colstat[j] ) {
1860: if ( tmi[k] ) {
1861: /* f3 = f1+m1*(m1 mod m2)^(-1)*(f2 - f1 mod m2) */
1862: t = remqi64((Q)tmi[k],md);
1863: if ( wmi[j] >= t ) t = wmi[j]-t;
1864: else t = md-(t-wmi[j]);
1865: t1 = mulmod64(t,inv,md);
1866: UTOZ(t1,u); mulz(m1,u,&s);
1867: addz(tmi[k],s,&u); tmi[k] = u;
1868: } else if ( wmi[j] ) {
1869: /* f3 = m1*(m1 mod m2)^(-1)*f2 */
1870: t = mulmod64(wmi[j],inv,md);
1871: UTOZ(t,u); mulz(m1,u,&s); tmi[k] = s;
1872: }
1873: k++;
1874: }
1875: m1 = m3;
1876: if ( ind % F4_INTRAT_PERIOD )
1877: ret = 0;
1878: else
1879: ret = intmtoratm(crmat,m1,*nm,dn);
1880: if ( ret ) {
1881: *rindp = rind = (int *)MALLOC_ATOMIC(rank*sizeof(int));
1882: *cindp = cind = (int *)MALLOC_ATOMIC((col-rank)*sizeof(int));
1883: for ( j = k = l = 0; j < col; j++ )
1884: if ( colstat[j] ) rind[k++] = j;
1885: else cind[l++] = j;
1886: if ( gensolve_check(mat,*nm,*dn,rind,cind) )
1887: return rank;
1888: }
1889: }
1890: }
1891: }
1892: #endif
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