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1.6 noro 1: /*
2: * Copyright (c) 1994-2000 FUJITSU LABORATORIES LIMITED
3: * All rights reserved.
4: *
5: * FUJITSU LABORATORIES LIMITED ("FLL") hereby grants you a limited,
6: * non-exclusive and royalty-free license to use, copy, modify and
7: * redistribute, solely for non-commercial and non-profit purposes, the
8: * computer program, "Risa/Asir" ("SOFTWARE"), subject to the terms and
9: * conditions of this Agreement. For the avoidance of doubt, you acquire
10: * only a limited right to use the SOFTWARE hereunder, and FLL or any
11: * third party developer retains all rights, including but not limited to
12: * copyrights, in and to the SOFTWARE.
13: *
14: * (1) FLL does not grant you a license in any way for commercial
15: * purposes. You may use the SOFTWARE only for non-commercial and
16: * non-profit purposes only, such as academic, research and internal
17: * business use.
18: * (2) The SOFTWARE is protected by the Copyright Law of Japan and
19: * international copyright treaties. If you make copies of the SOFTWARE,
20: * with or without modification, as permitted hereunder, you shall affix
21: * to all such copies of the SOFTWARE the above copyright notice.
22: * (3) An explicit reference to this SOFTWARE and its copyright owner
23: * shall be made on your publication or presentation in any form of the
24: * results obtained by use of the SOFTWARE.
25: * (4) In the event that you modify the SOFTWARE, you shall notify FLL by
1.7 noro 26: * e-mail at risa-admin@sec.flab.fujitsu.co.jp of the detailed specification
1.6 noro 27: * for such modification or the source code of the modified part of the
28: * SOFTWARE.
29: *
30: * THE SOFTWARE IS PROVIDED AS IS WITHOUT ANY WARRANTY OF ANY KIND. FLL
31: * MAKES ABSOLUTELY NO WARRANTIES, EXPRESSED, IMPLIED OR STATUTORY, AND
32: * EXPRESSLY DISCLAIMS ANY IMPLIED WARRANTY OF MERCHANTABILITY, FITNESS
33: * FOR A PARTICULAR PURPOSE OR NONINFRINGEMENT OF THIRD PARTIES'
34: * RIGHTS. NO FLL DEALER, AGENT, EMPLOYEES IS AUTHORIZED TO MAKE ANY
35: * MODIFICATIONS, EXTENSIONS, OR ADDITIONS TO THIS WARRANTY.
36: * UNDER NO CIRCUMSTANCES AND UNDER NO LEGAL THEORY, TORT, CONTRACT,
37: * OR OTHERWISE, SHALL FLL BE LIABLE TO YOU OR ANY OTHER PERSON FOR ANY
38: * DIRECT, INDIRECT, SPECIAL, INCIDENTAL, PUNITIVE OR CONSEQUENTIAL
39: * DAMAGES OF ANY CHARACTER, INCLUDING, WITHOUT LIMITATION, DAMAGES
40: * ARISING OUT OF OR RELATING TO THE SOFTWARE OR THIS AGREEMENT, DAMAGES
41: * FOR LOSS OF GOODWILL, WORK STOPPAGE, OR LOSS OF DATA, OR FOR ANY
42: * DAMAGES, EVEN IF FLL SHALL HAVE BEEN INFORMED OF THE POSSIBILITY OF
43: * SUCH DAMAGES, OR FOR ANY CLAIM BY ANY OTHER PARTY. EVEN IF A PART
44: * OF THE SOFTWARE HAS BEEN DEVELOPED BY A THIRD PARTY, THE THIRD PARTY
45: * DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE,
46: * PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE.
47: *
1.46 ! saito 48: * $OpenXM: OpenXM_contrib2/asir2000/builtin/array.c,v 1.45 2005/01/23 14:03:47 noro Exp $
1.6 noro 49: */
1.1 noro 50: #include "ca.h"
51: #include "base.h"
52: #include "parse.h"
53: #include "inline.h"
1.4 noro 54:
1.38 noro 55: #define F4_INTRAT_PERIOD 8
56:
1.4 noro 57: #if 0
1.1 noro 58: #undef DMAR
59: #define DMAR(a1,a2,a3,d,r) (r)=dmar(a1,a2,a3,d);
1.4 noro 60: #endif
1.1 noro 61:
1.11 noro 62: extern int DP_Print; /* XXX */
1.1 noro 63:
1.24 noro 64:
1.1 noro 65: void Pnewvect(), Pnewmat(), Psepvect(), Psize(), Pdet(), Pleqm(), Pleqm1(), Pgeninvm();
1.23 noro 66: void Pinvmat();
1.9 noro 67: void Pnewbytearray();
1.1 noro 68:
1.25 noro 69: void Pgeneric_gauss_elim();
1.1 noro 70: void Pgeneric_gauss_elim_mod();
71:
72: void Pmat_to_gfmmat(),Plu_gfmmat(),Psolve_by_lu_gfmmat();
1.33 noro 73: void Pgeninvm_swap(), Premainder(), Psremainder(), Pvtol(), Pltov();
1.27 noro 74: void Pgeninv_sf_swap();
1.1 noro 75: void sepvect();
76: void Pmulmat_gf2n();
77: void Pbconvmat_gf2n();
78: void Pmul_vect_mat_gf2n();
79: void PNBmul_gf2n();
80: void Pmul_mat_vect_int();
81: void Psepmat_destructive();
82: void Px962_irredpoly_up2();
83: void Pirredpoly_up2();
84: void Pnbpoly_up2();
85: void Pqsort();
1.14 noro 86: void Pexponent_vector();
1.26 noro 87: void Pmat_swap_row_destructive();
88: void Pmat_swap_col_destructive();
1.28 saito 89: void Pvect();
90: void Pmat();
1.29 saito 91: void Pmatc();
1.36 noro 92: void Pnd_det();
1.1 noro 93:
94: struct ftab array_tab[] = {
95: {"solve_by_lu_gfmmat",Psolve_by_lu_gfmmat,4},
96: {"lu_gfmmat",Plu_gfmmat,2},
97: {"mat_to_gfmmat",Pmat_to_gfmmat,2},
1.25 noro 98: {"generic_gauss_elim",Pgeneric_gauss_elim,1},
1.1 noro 99: {"generic_gauss_elim_mod",Pgeneric_gauss_elim_mod,2},
100: {"newvect",Pnewvect,-2},
1.28 saito 101: {"vect",Pvect,-99999999},
1.14 noro 102: {"vector",Pnewvect,-2},
103: {"exponent_vector",Pexponent_vector,-99999999},
1.1 noro 104: {"newmat",Pnewmat,-3},
1.14 noro 105: {"matrix",Pnewmat,-3},
1.28 saito 106: {"mat",Pmat,-99999999},
1.29 saito 107: {"matr",Pmat,-99999999},
108: {"matc",Pmatc,-99999999},
1.9 noro 109: {"newbytearray",Pnewbytearray,-2},
1.1 noro 110: {"sepmat_destructive",Psepmat_destructive,2},
111: {"sepvect",Psepvect,2},
112: {"qsort",Pqsort,-2},
113: {"vtol",Pvtol,1},
1.33 noro 114: {"ltov",Pltov,1},
1.1 noro 115: {"size",Psize,1},
116: {"det",Pdet,-2},
1.37 noro 117: {"nd_det",Pnd_det,-2},
1.23 noro 118: {"invmat",Pinvmat,-2},
1.1 noro 119: {"leqm",Pleqm,2},
120: {"leqm1",Pleqm1,2},
121: {"geninvm",Pgeninvm,2},
122: {"geninvm_swap",Pgeninvm_swap,2},
1.27 noro 123: {"geninv_sf_swap",Pgeninv_sf_swap,1},
1.1 noro 124: {"remainder",Premainder,2},
125: {"sremainder",Psremainder,2},
126: {"mulmat_gf2n",Pmulmat_gf2n,1},
127: {"bconvmat_gf2n",Pbconvmat_gf2n,-4},
128: {"mul_vect_mat_gf2n",Pmul_vect_mat_gf2n,2},
129: {"mul_mat_vect_int",Pmul_mat_vect_int,2},
130: {"nbmul_gf2n",PNBmul_gf2n,3},
131: {"x962_irredpoly_up2",Px962_irredpoly_up2,2},
132: {"irredpoly_up2",Pirredpoly_up2,2},
133: {"nbpoly_up2",Pnbpoly_up2,2},
1.26 noro 134: {"mat_swap_row_destructive",Pmat_swap_row_destructive,3},
135: {"mat_swap_col_destructive",Pmat_swap_col_destructive,3},
1.1 noro 136: {0,0,0},
137: };
138:
1.24 noro 139: int comp_obj(Obj *a,Obj *b)
1.1 noro 140: {
141: return arf_comp(CO,*a,*b);
142: }
143:
144: static FUNC generic_comp_obj_func;
145: static NODE generic_comp_obj_arg;
146:
1.24 noro 147: int generic_comp_obj(Obj *a,Obj *b)
1.1 noro 148: {
149: Q r;
150:
151: BDY(generic_comp_obj_arg)=(pointer)(*a);
152: BDY(NEXT(generic_comp_obj_arg))=(pointer)(*b);
153: r = (Q)bevalf(generic_comp_obj_func,generic_comp_obj_arg);
154: if ( !r )
155: return 0;
156: else
157: return SGN(r)>0?1:-1;
158: }
159:
160:
1.46 ! saito 161: void Pqsort(NODE arg,LIST *rp)
1.1 noro 162: {
163: VECT vect;
1.35 ohara 164: NODE n,n1;
1.1 noro 165: P p;
166: V v;
1.34 noro 167: FUNC func;
1.35 ohara 168: int len,i;
169: pointer *a;
170: Obj t;
171:
172: t = ARG0(arg);
173: if (OID(t) == O_LIST) {
174: n = (NODE)BDY((LIST)t);
175: len = length(n);
176: MKVECT(vect,len);
177: for ( i = 0; i < len; i++, n = NEXT(n) ) {
178: BDY(vect)[i] = BDY(n);
179: }
180:
181: }else if (OID(t) != O_VECT) {
182: error("qsort : invalid argument");
183: }else {
184: vect = (VECT)t;
185: }
1.1 noro 186: if ( argc(arg) == 1 )
187: qsort(BDY(vect),vect->len,sizeof(Obj),(int (*)(const void *,const void *))comp_obj);
188: else {
189: p = (P)ARG1(arg);
190: if ( !p || OID(p)!=2 )
191: error("qsort : invalid argument");
192: v = VR(p);
1.34 noro 193: gen_searchf(NAME(v),&func);
194: if ( !func ) {
195: if ( (int)v->attr != V_SR )
196: error("qsort : no such function");
197: func = (FUNC)v->priv;
198: }
199: generic_comp_obj_func = func;
1.1 noro 200: MKNODE(n,0,0); MKNODE(generic_comp_obj_arg,0,n);
201: qsort(BDY(vect),vect->len,sizeof(Obj),(int (*)(const void *,const void *))generic_comp_obj);
202: }
1.35 ohara 203: if (OID(t) == O_LIST) {
204: a = BDY(vect);
205: for ( i = len - 1, n = 0; i >= 0; i-- ) {
206: MKNODE(n1,a[i],n); n = n1;
207: }
1.46 ! saito 208: MKLIST(*rp,n);
1.35 ohara 209: }else {
1.46 ! saito 210: *rp = (LIST)vect;
1.35 ohara 211: }
1.1 noro 212: }
213:
1.24 noro 214: void PNBmul_gf2n(NODE arg,GF2N *rp)
1.1 noro 215: {
216: GF2N a,b;
217: GF2MAT mat;
218: int n,w;
219: unsigned int *ab,*bb;
220: UP2 r;
221:
222: a = (GF2N)ARG0(arg);
223: b = (GF2N)ARG1(arg);
224: mat = (GF2MAT)ARG2(arg);
225: if ( !a || !b )
226: *rp = 0;
227: else {
228: n = mat->row;
229: w = (n+BSH-1)/BSH;
230:
231: ab = (unsigned int *)ALLOCA(w*sizeof(unsigned int));
232: bzero((char *)ab,w*sizeof(unsigned int));
233: bcopy(a->body->b,ab,(a->body->w)*sizeof(unsigned int));
234:
235: bb = (unsigned int *)ALLOCA(w*sizeof(unsigned int));
236: bzero((char *)bb,w*sizeof(unsigned int));
237: bcopy(b->body->b,bb,(b->body->w)*sizeof(unsigned int));
238:
239: NEWUP2(r,w);
240: bzero((char *)r->b,w*sizeof(unsigned int));
241: mul_nb(mat,ab,bb,r->b);
242: r->w = w;
243: _adjup2(r);
244: if ( !r->w )
245: *rp = 0;
246: else
247: MKGF2N(r,*rp);
248: }
249: }
250:
1.24 noro 251: void Pmul_vect_mat_gf2n(NODE arg,GF2N *rp)
1.1 noro 252: {
253: GF2N a;
254: GF2MAT mat;
255: int n,w;
256: unsigned int *b;
257: UP2 r;
258:
259: a = (GF2N)ARG0(arg);
260: mat = (GF2MAT)ARG1(arg);
261: if ( !a )
262: *rp = 0;
263: else {
264: n = mat->row;
265: w = (n+BSH-1)/BSH;
266: b = (unsigned int *)ALLOCA(w*sizeof(unsigned int));
267: bzero((char *)b,w*sizeof(unsigned int));
268: bcopy(a->body->b,b,(a->body->w)*sizeof(unsigned int));
269: NEWUP2(r,w);
270: bzero((char *)r->b,w*sizeof(unsigned int));
271: mulgf2vectmat(mat->row,b,mat->body,r->b);
272: r->w = w;
273: _adjup2(r);
274: if ( !r->w )
275: *rp = 0;
276: else {
277: MKGF2N(r,*rp);
278: }
279: }
280: }
281:
1.24 noro 282: void Pbconvmat_gf2n(NODE arg,LIST *rp)
1.1 noro 283: {
284: P p0,p1;
285: int to;
286: GF2MAT p01,p10;
287: GF2N root;
288: NODE n0,n1;
289:
290: p0 = (P)ARG0(arg);
291: p1 = (P)ARG1(arg);
292: to = ARG2(arg)?1:0;
293: if ( argc(arg) == 4 ) {
294: root = (GF2N)ARG3(arg);
295: compute_change_of_basis_matrix_with_root(p0,p1,to,root,&p01,&p10);
296: } else
297: compute_change_of_basis_matrix(p0,p1,to,&p01,&p10);
298: MKNODE(n1,p10,0); MKNODE(n0,p01,n1);
299: MKLIST(*rp,n0);
300: }
301:
1.24 noro 302: void Pmulmat_gf2n(NODE arg,GF2MAT *rp)
1.1 noro 303: {
304: GF2MAT m;
305:
306: if ( !compute_multiplication_matrix((P)ARG0(arg),&m) )
307: error("mulmat_gf2n : input is not a normal polynomial");
308: *rp = m;
309: }
310:
1.24 noro 311: void Psepmat_destructive(NODE arg,LIST *rp)
1.1 noro 312: {
313: MAT mat,mat1;
314: int i,j,row,col;
315: Q **a,**a1;
316: Q ent;
317: N nm,mod,rem,quo;
318: int sgn;
319: NODE n0,n1;
320:
321: mat = (MAT)ARG0(arg); mod = NM((Q)ARG1(arg));
322: row = mat->row; col = mat->col;
323: MKMAT(mat1,row,col);
324: a = (Q **)mat->body; a1 = (Q **)mat1->body;
325: for ( i = 0; i < row; i++ )
326: for ( j = 0; j < col; j++ ) {
327: ent = a[i][j];
328: if ( !ent )
329: continue;
330: nm = NM(ent);
331: sgn = SGN(ent);
332: divn(nm,mod,&quo,&rem);
333: /* if ( quo != nm && rem != nm ) */
334: /* GC_free(nm); */
335: /* GC_free(ent); */
336: NTOQ(rem,sgn,a[i][j]); NTOQ(quo,sgn,a1[i][j]);
337: }
338: MKNODE(n1,mat1,0); MKNODE(n0,mat,n1);
339: MKLIST(*rp,n0);
340: }
341:
1.24 noro 342: void Psepvect(NODE arg,VECT *rp)
1.1 noro 343: {
344: sepvect((VECT)ARG0(arg),QTOS((Q)ARG1(arg)),rp);
345: }
346:
1.24 noro 347: void sepvect(VECT v,int d,VECT *rp)
1.1 noro 348: {
349: int i,j,k,n,q,q1,r;
350: pointer *pv,*pw,*pu;
351: VECT w,u;
352:
353: n = v->len;
354: if ( d > n )
355: d = n;
356: q = n/d; r = n%d; q1 = q+1;
357: MKVECT(w,d); *rp = w;
358: pv = BDY(v); pw = BDY(w); k = 0;
359: for ( i = 0; i < r; i++ ) {
360: MKVECT(u,q1); pw[i] = (pointer)u;
361: for ( pu = BDY(u), j = 0; j < q1; j++, k++ )
362: pu[j] = pv[k];
363: }
364: for ( ; i < d; i++ ) {
365: MKVECT(u,q); pw[i] = (pointer)u;
366: for ( pu = BDY(u), j = 0; j < q; j++, k++ )
367: pu[j] = pv[k];
368: }
369: }
370:
1.24 noro 371: void Pnewvect(NODE arg,VECT *rp)
1.1 noro 372: {
373: int len,i,r;
374: VECT vect;
375: pointer *vb;
376: LIST list;
377: NODE tn;
378:
379: asir_assert(ARG0(arg),O_N,"newvect");
380: len = QTOS((Q)ARG0(arg));
1.5 noro 381: if ( len < 0 )
1.1 noro 382: error("newvect : invalid size");
383: MKVECT(vect,len);
384: if ( argc(arg) == 2 ) {
385: list = (LIST)ARG1(arg);
386: asir_assert(list,O_LIST,"newvect");
387: for ( r = 0, tn = BDY(list); tn; r++, tn = NEXT(tn) );
388: if ( r > len ) {
389: *rp = vect;
390: return;
391: }
392: for ( i = 0, tn = BDY(list), vb = BDY(vect); tn; i++, tn = NEXT(tn) )
393: vb[i] = (pointer)BDY(tn);
394: }
395: *rp = vect;
1.14 noro 396: }
397:
1.28 saito 398: void Pvect(NODE arg,VECT *rp) {
399: int len,i,r;
400: VECT vect;
401: pointer *vb;
402: NODE tn;
403:
404: if ( !arg ) {
405: *rp =0;
406: return;
407: }
408:
409: for (len = 0, tn = arg; tn; tn = NEXT(tn), len++);
1.29 saito 410: if ( len == 1 ) {
411: if ( ARG0(arg) != 0 ) {
412: switch ( OID(ARG0(arg)) ) {
413: case O_VECT:
414: *rp = ARG0(arg);
415: return;
416: case O_LIST:
417: for ( len = 0, tn = ARG0(arg); tn; tn = NEXT(tn), len++ );
418: MKVECT(vect,len-1);
419: for ( i = 0, tn = BDY((LIST)ARG0(arg)), vb =BDY(vect);
420: tn; i++, tn = NEXT(tn) )
421: vb[i] = (pointer)BDY(tn);
422: *rp=vect;
423: return;
424: }
425: }
426: }
1.28 saito 427: MKVECT(vect,len);
428: for ( i = 0, tn = arg, vb = BDY(vect); tn; i++, tn = NEXT(tn) )
429: vb[i] = (pointer)BDY(tn);
430: *rp = vect;
431: }
432:
1.24 noro 433: void Pexponent_vector(NODE arg,DP *rp)
1.14 noro 434: {
435: nodetod(arg,rp);
1.9 noro 436: }
437:
1.24 noro 438: void Pnewbytearray(NODE arg,BYTEARRAY *rp)
1.9 noro 439: {
440: int len,i,r;
441: BYTEARRAY array;
442: unsigned char *vb;
1.10 noro 443: char *str;
1.9 noro 444: LIST list;
445: NODE tn;
446:
447: asir_assert(ARG0(arg),O_N,"newbytearray");
448: len = QTOS((Q)ARG0(arg));
449: if ( len < 0 )
450: error("newbytearray : invalid size");
451: MKBYTEARRAY(array,len);
452: if ( argc(arg) == 2 ) {
1.10 noro 453: if ( !ARG1(arg) )
454: error("newbytearray : invalid initialization");
455: switch ( OID((Obj)ARG1(arg)) ) {
456: case O_LIST:
457: list = (LIST)ARG1(arg);
458: asir_assert(list,O_LIST,"newbytearray");
459: for ( r = 0, tn = BDY(list); tn; r++, tn = NEXT(tn) );
460: if ( r <= len ) {
461: for ( i = 0, tn = BDY(list), vb = BDY(array); tn;
462: i++, tn = NEXT(tn) )
463: vb[i] = (unsigned char)QTOS((Q)BDY(tn));
464: }
465: break;
466: case O_STR:
467: str = BDY((STRING)ARG1(arg));
468: r = strlen(str);
469: if ( r <= len )
470: bcopy(str,BDY(array),r);
471: break;
472: default:
473: if ( !ARG1(arg) )
474: error("newbytearray : invalid initialization");
1.9 noro 475: }
476: }
477: *rp = array;
1.1 noro 478: }
479:
1.24 noro 480: void Pnewmat(NODE arg,MAT *rp)
1.1 noro 481: {
482: int row,col;
483: int i,j,r,c;
484: NODE tn,sn;
485: MAT m;
486: pointer **mb;
487: LIST list;
488:
489: asir_assert(ARG0(arg),O_N,"newmat");
490: asir_assert(ARG1(arg),O_N,"newmat");
491: row = QTOS((Q)ARG0(arg)); col = QTOS((Q)ARG1(arg));
1.5 noro 492: if ( row < 0 || col < 0 )
1.1 noro 493: error("newmat : invalid size");
494: MKMAT(m,row,col);
495: if ( argc(arg) == 3 ) {
496: list = (LIST)ARG2(arg);
497: asir_assert(list,O_LIST,"newmat");
498: for ( r = 0, c = 0, tn = BDY(list); tn; r++, tn = NEXT(tn) ) {
499: for ( j = 0, sn = BDY((LIST)BDY(tn)); sn; j++, sn = NEXT(sn) );
500: c = MAX(c,j);
501: }
502: if ( (r > row) || (c > col) ) {
503: *rp = m;
504: return;
505: }
506: for ( i = 0, tn = BDY(list), mb = BDY(m); tn; i++, tn = NEXT(tn) ) {
507: asir_assert(BDY(tn),O_LIST,"newmat");
508: for ( j = 0, sn = BDY((LIST)BDY(tn)); sn; j++, sn = NEXT(sn) )
509: mb[i][j] = (pointer)BDY(sn);
510: }
511: }
1.28 saito 512: *rp = m;
513: }
514:
515: void Pmat(NODE arg, MAT *rp)
516: {
517: int row,col;
1.29 saito 518: int i;
1.28 saito 519: MAT m;
520: pointer **mb;
1.29 saito 521: pointer *ent;
1.28 saito 522: NODE tn, sn;
1.29 saito 523: VECT v;
1.28 saito 524:
525: if ( !arg ) {
526: *rp =0;
527: return;
528: }
529:
530: for (row = 0, tn = arg; tn; tn = NEXT(tn), row++);
1.30 saito 531: if ( row == 1 ) {
532: if ( OID(ARG0(arg)) == O_MAT ) {
533: *rp=ARG0(arg);
534: return;
535: } else if ( !(OID(ARG0(arg)) == O_LIST || OID(ARG0(arg)) == O_VECT)) {
536: error("mat : invalid argument");
537: }
538: }
1.29 saito 539: if ( OID(ARG0(arg)) == O_VECT ) {
540: v = ARG0(arg);
541: col = v->len;
542: } else if ( OID(ARG0(arg)) == O_LIST ) {
543: for (col = 0, tn = BDY((LIST)ARG0(arg)); tn ; tn = NEXT(tn), col++);
1.30 saito 544: } else {
545: error("mat : invalid argument");
1.29 saito 546: }
547:
1.28 saito 548: MKMAT(m,row,col);
1.29 saito 549: for (row = 0, tn = arg, mb = BDY(m); tn; tn = NEXT(tn), row++) {
550: if ( BDY(tn) == 0 ) {
551: error("mat : invalid argument");
552: } else if ( OID(BDY(tn)) == O_VECT ) {
553: v = tn->body;
554: ent = BDY(v);
555: for (i = 0; i < v->len; i++ ) mb[row][i] = (Obj)ent[i];
556: } else if ( OID(BDY(tn)) == O_LIST ) {
557: for (col = 0, sn = BDY((LIST)BDY(tn)); sn; col++, sn = NEXT(sn) )
558: mb[row][col] = (pointer)BDY(sn);
559: } else {
560: error("mat : invalid argument");
561: }
562: }
563: *rp = m;
564: }
565:
566: void Pmatc(NODE arg, MAT *rp)
567: {
568: int row,col;
569: int i;
570: MAT m;
571: pointer **mb;
572: pointer *ent;
573: NODE tn, sn;
574: VECT v;
575:
576: if ( !arg ) {
577: *rp =0;
578: return;
579: }
580:
581: for (col = 0, tn = arg; tn; tn = NEXT(tn), col++);
1.30 saito 582: if ( col == 1 ) {
583: if ( OID(ARG0(arg)) == O_MAT ) {
584: *rp=ARG0(arg);
585: return;
586: } else if ( !(OID(ARG0(arg)) == O_LIST || OID(ARG0(arg)) == O_VECT)) {
587: error("matc : invalid argument");
588: }
589: }
1.29 saito 590: if ( OID(ARG0(arg)) == O_VECT ) {
591: v = ARG0(arg);
592: row = v->len;
593: } else if ( OID(ARG0(arg)) == O_LIST ) {
594: for (row = 0, tn = BDY((LIST)ARG0(arg)); tn ; tn = NEXT(tn), row++);
1.30 saito 595: } else {
596: error("matc : invalid argument");
1.29 saito 597: }
598:
599: MKMAT(m,row,col);
600: for (col = 0, tn = arg, mb = BDY(m); tn; tn = NEXT(tn), col++) {
601: if ( BDY(tn) == 0 ) {
602: error("matc : invalid argument");
603: } else if ( OID(BDY(tn)) == O_VECT ) {
604: v = tn->body;
605: ent = BDY(v);
606: for (i = 0; i < v->len; i++ ) mb[i][col] = (Obj)ent[i];
607: } else if ( OID(BDY(tn)) == O_LIST ) {
608: for (row = 0, sn = BDY((LIST)BDY(tn)); sn; row++, sn = NEXT(sn) )
609: mb[row][col] = (pointer)BDY(sn);
610: } else {
611: error("matc : invalid argument");
612: }
613: }
1.1 noro 614: *rp = m;
615: }
616:
1.24 noro 617: void Pvtol(NODE arg,LIST *rp)
1.1 noro 618: {
619: NODE n,n1;
620: VECT v;
621: pointer *a;
622: int len,i;
623:
624: asir_assert(ARG0(arg),O_VECT,"vtol");
625: v = (VECT)ARG0(arg); len = v->len; a = BDY(v);
626: for ( i = len - 1, n = 0; i >= 0; i-- ) {
627: MKNODE(n1,a[i],n); n = n1;
628: }
629: MKLIST(*rp,n);
1.33 noro 630: }
631:
632: void Pltov(NODE arg,VECT *rp)
633: {
634: NODE n;
635: VECT v;
636: int len,i;
637:
638: asir_assert(ARG0(arg),O_LIST,"ltov");
639: n = (NODE)BDY((LIST)ARG0(arg));
640: len = length(n);
641: MKVECT(v,len);
642: for ( i = 0; i < len; i++, n = NEXT(n) )
643: BDY(v)[i] = BDY(n);
644: *rp = v;
1.1 noro 645: }
646:
1.24 noro 647: void Premainder(NODE arg,Obj *rp)
1.1 noro 648: {
649: Obj a;
650: VECT v,w;
651: MAT m,l;
652: pointer *vb,*wb;
653: pointer **mb,**lb;
654: int id,i,j,n,row,col,t,smd,sgn;
655: Q md,q;
656:
657: a = (Obj)ARG0(arg); md = (Q)ARG1(arg);
658: if ( !a )
659: *rp = 0;
660: else {
661: id = OID(a);
662: switch ( id ) {
663: case O_N:
664: case O_P:
665: cmp(md,(P)a,(P *)rp); break;
666: case O_VECT:
667: smd = QTOS(md);
668: v = (VECT)a; n = v->len; vb = v->body;
669: MKVECT(w,n); wb = w->body;
670: for ( i = 0; i < n; i++ ) {
671: if ( q = (Q)vb[i] ) {
672: sgn = SGN(q); t = rem(NM(q),smd);
673: STOQ(t,q);
674: if ( q )
675: SGN(q) = sgn;
676: }
677: wb[i] = (pointer)q;
678: }
679: *rp = (Obj)w;
680: break;
681: case O_MAT:
682: m = (MAT)a; row = m->row; col = m->col; mb = m->body;
683: MKMAT(l,row,col); lb = l->body;
684: for ( i = 0; i < row; i++ )
685: for ( j = 0, vb = mb[i], wb = lb[i]; j < col; j++ )
686: cmp(md,(P)vb[j],(P *)&wb[j]);
687: *rp = (Obj)l;
688: break;
689: default:
690: error("remainder : invalid argument");
691: }
692: }
693: }
694:
1.24 noro 695: void Psremainder(NODE arg,Obj *rp)
1.1 noro 696: {
697: Obj a;
698: VECT v,w;
699: MAT m,l;
700: pointer *vb,*wb;
701: pointer **mb,**lb;
702: unsigned int t,smd;
703: int id,i,j,n,row,col;
704: Q md,q;
705:
706: a = (Obj)ARG0(arg); md = (Q)ARG1(arg);
707: if ( !a )
708: *rp = 0;
709: else {
710: id = OID(a);
711: switch ( id ) {
712: case O_N:
713: case O_P:
714: cmp(md,(P)a,(P *)rp); break;
715: case O_VECT:
716: smd = QTOS(md);
717: v = (VECT)a; n = v->len; vb = v->body;
718: MKVECT(w,n); wb = w->body;
719: for ( i = 0; i < n; i++ ) {
720: if ( q = (Q)vb[i] ) {
721: t = (unsigned int)rem(NM(q),smd);
722: if ( SGN(q) < 0 )
723: t = (smd - t) % smd;
724: UTOQ(t,q);
725: }
726: wb[i] = (pointer)q;
727: }
728: *rp = (Obj)w;
729: break;
730: case O_MAT:
731: m = (MAT)a; row = m->row; col = m->col; mb = m->body;
732: MKMAT(l,row,col); lb = l->body;
733: for ( i = 0; i < row; i++ )
734: for ( j = 0, vb = mb[i], wb = lb[i]; j < col; j++ )
735: cmp(md,(P)vb[j],(P *)&wb[j]);
736: *rp = (Obj)l;
737: break;
738: default:
739: error("remainder : invalid argument");
740: }
741: }
742: }
743:
1.24 noro 744: void Psize(NODE arg,LIST *rp)
1.1 noro 745: {
746:
747: int n,m;
748: Q q;
749: NODE t,s;
750:
751: if ( !ARG0(arg) )
752: t = 0;
753: else {
754: switch (OID(ARG0(arg))) {
755: case O_VECT:
756: n = ((VECT)ARG0(arg))->len;
757: STOQ(n,q); MKNODE(t,q,0);
758: break;
759: case O_MAT:
760: n = ((MAT)ARG0(arg))->row; m = ((MAT)ARG0(arg))->col;
1.43 saito 761: STOQ(m,q); MKNODE(s,q,0); STOQ(n,q); MKNODE(t,q,s);
762: break;
763: case O_IMAT:
764: n = ((IMAT)ARG0(arg))->row; m = ((IMAT)ARG0(arg))->col;
1.1 noro 765: STOQ(m,q); MKNODE(s,q,0); STOQ(n,q); MKNODE(t,q,s);
766: break;
767: default:
768: error("size : invalid argument"); break;
769: }
770: }
771: MKLIST(*rp,t);
772: }
773:
1.24 noro 774: void Pdet(NODE arg,P *rp)
1.1 noro 775: {
776: MAT m;
777: int n,i,j,mod;
778: P d;
779: P **mat,**w;
780:
781: m = (MAT)ARG0(arg);
782: asir_assert(m,O_MAT,"det");
783: if ( m->row != m->col )
784: error("det : non-square matrix");
785: else if ( argc(arg) == 1 )
786: detp(CO,(P **)BDY(m),m->row,rp);
787: else {
788: n = m->row; mod = QTOS((Q)ARG1(arg)); mat = (P **)BDY(m);
789: w = (P **)almat_pointer(n,n);
790: for ( i = 0; i < n; i++ )
791: for ( j = 0; j < n; j++ )
792: ptomp(mod,mat[i][j],&w[i][j]);
793: detmp(CO,mod,w,n,&d);
794: mptop(d,rp);
1.23 noro 795: }
796: }
797:
1.24 noro 798: void Pinvmat(NODE arg,LIST *rp)
1.23 noro 799: {
800: MAT m,r;
801: int n,i,j,mod;
802: P dn;
803: P **mat,**imat,**w;
804: NODE nd;
805:
806: m = (MAT)ARG0(arg);
807: asir_assert(m,O_MAT,"invmat");
808: if ( m->row != m->col )
809: error("invmat : non-square matrix");
810: else if ( argc(arg) == 1 ) {
811: n = m->row;
812: invmatp(CO,(P **)BDY(m),n,&imat,&dn);
813: NEWMAT(r); r->row = n; r->col = n; r->body = (pointer **)imat;
814: nd = mknode(2,r,dn);
815: MKLIST(*rp,nd);
816: } else {
817: n = m->row; mod = QTOS((Q)ARG1(arg)); mat = (P **)BDY(m);
818: w = (P **)almat_pointer(n,n);
819: for ( i = 0; i < n; i++ )
820: for ( j = 0; j < n; j++ )
821: ptomp(mod,mat[i][j],&w[i][j]);
822: #if 0
823: detmp(CO,mod,w,n,&d);
824: mptop(d,rp);
825: #else
826: error("not implemented yet");
827: #endif
1.1 noro 828: }
1.25 noro 829: }
830:
831: /*
832: input : a row x col matrix A
833: A[I] <-> A[I][0]*x_0+A[I][1]*x_1+...
834:
1.45 noro 835: output : [B,D,R,C]
1.25 noro 836: B : a rank(A) x col-rank(A) matrix
1.45 noro 837: D : the denominator
1.25 noro 838: R : a vector of length rank(A)
839: C : a vector of length col-rank(A)
1.45 noro 840: B[I] <-> D*x_{R[I]}+B[I][0]x_{C[0]}+B[I][1]x_{C[1]}+...
1.25 noro 841: */
842:
843: void Pgeneric_gauss_elim(NODE arg,LIST *rp)
844: {
845: NODE n0;
846: MAT m,nm;
847: int *ri,*ci;
848: VECT rind,cind;
849: Q dn,q;
850: int i,j,k,l,row,col,t,rank;
851:
852: asir_assert(ARG0(arg),O_MAT,"generic_gauss_elim");
853: m = (MAT)ARG0(arg);
854: row = m->row; col = m->col;
855: rank = generic_gauss_elim(m,&nm,&dn,&ri,&ci);
856: t = col-rank;
857: MKVECT(rind,rank);
858: MKVECT(cind,t);
859: for ( i = 0; i < rank; i++ ) {
860: STOQ(ri[i],q);
861: BDY(rind)[i] = (pointer)q;
862: }
863: for ( i = 0; i < t; i++ ) {
864: STOQ(ci[i],q);
865: BDY(cind)[i] = (pointer)q;
866: }
867: n0 = mknode(4,nm,dn,rind,cind);
868: MKLIST(*rp,n0);
1.1 noro 869: }
870:
871: /*
872: input : a row x col matrix A
873: A[I] <-> A[I][0]*x_0+A[I][1]*x_1+...
874:
875: output : [B,R,C]
876: B : a rank(A) x col-rank(A) matrix
877: R : a vector of length rank(A)
878: C : a vector of length col-rank(A)
879: B[I] <-> x_{R[I]}+B[I][0]x_{C[0]}+B[I][1]x_{C[1]}+...
880: */
881:
1.24 noro 882: void Pgeneric_gauss_elim_mod(NODE arg,LIST *rp)
1.1 noro 883: {
884: NODE n0;
885: MAT m,mat;
886: VECT rind,cind;
887: Q **tmat;
888: int **wmat;
889: Q *rib,*cib;
890: int *colstat;
891: Q q;
1.24 noro 892: int md,i,j,k,l,row,col,t,rank;
1.1 noro 893:
894: asir_assert(ARG0(arg),O_MAT,"generic_gauss_elim_mod");
895: asir_assert(ARG1(arg),O_N,"generic_gauss_elim_mod");
896: m = (MAT)ARG0(arg); md = QTOS((Q)ARG1(arg));
897: row = m->row; col = m->col; tmat = (Q **)m->body;
898: wmat = (int **)almat(row,col);
899: colstat = (int *)MALLOC_ATOMIC(col*sizeof(int));
900: for ( i = 0; i < row; i++ )
901: for ( j = 0; j < col; j++ )
902: if ( q = (Q)tmat[i][j] ) {
903: t = rem(NM(q),md);
904: if ( t && SGN(q) < 0 )
905: t = (md - t) % md;
906: wmat[i][j] = t;
907: } else
908: wmat[i][j] = 0;
909: rank = generic_gauss_elim_mod(wmat,row,col,md,colstat);
910:
911: MKMAT(mat,rank,col-rank);
912: tmat = (Q **)mat->body;
913: for ( i = 0; i < rank; i++ )
914: for ( j = k = 0; j < col; j++ )
915: if ( !colstat[j] ) {
916: UTOQ(wmat[i][j],tmat[i][k]); k++;
917: }
918:
919: MKVECT(rind,rank);
920: MKVECT(cind,col-rank);
921: rib = (Q *)rind->body; cib = (Q *)cind->body;
922: for ( j = k = l = 0; j < col; j++ )
923: if ( colstat[j] ) {
924: STOQ(j,rib[k]); k++;
925: } else {
926: STOQ(j,cib[l]); l++;
927: }
928: n0 = mknode(3,mat,rind,cind);
929: MKLIST(*rp,n0);
930: }
931:
1.24 noro 932: void Pleqm(NODE arg,VECT *rp)
1.1 noro 933: {
934: MAT m;
935: VECT vect;
936: pointer **mat;
937: Q *v;
938: Q q;
939: int **wmat;
940: int md,i,j,row,col,t,n,status;
941:
942: asir_assert(ARG0(arg),O_MAT,"leqm");
943: asir_assert(ARG1(arg),O_N,"leqm");
944: m = (MAT)ARG0(arg); md = QTOS((Q)ARG1(arg));
945: row = m->row; col = m->col; mat = m->body;
946: wmat = (int **)almat(row,col);
947: for ( i = 0; i < row; i++ )
948: for ( j = 0; j < col; j++ )
949: if ( q = (Q)mat[i][j] ) {
950: t = rem(NM(q),md);
951: if ( SGN(q) < 0 )
952: t = (md - t) % md;
953: wmat[i][j] = t;
954: } else
955: wmat[i][j] = 0;
956: status = gauss_elim_mod(wmat,row,col,md);
957: if ( status < 0 )
958: *rp = 0;
959: else if ( status > 0 )
960: *rp = (VECT)ONE;
961: else {
962: n = col - 1;
963: MKVECT(vect,n);
964: for ( i = 0, v = (Q *)vect->body; i < n; i++ ) {
965: t = (md-wmat[i][n])%md; STOQ(t,v[i]);
966: }
967: *rp = vect;
968: }
969: }
970:
1.24 noro 971: int gauss_elim_mod(int **mat,int row,int col,int md)
1.1 noro 972: {
973: int i,j,k,inv,a,n;
974: int *t,*pivot;
975:
976: n = col - 1;
977: for ( j = 0; j < n; j++ ) {
978: for ( i = j; i < row && !mat[i][j]; i++ );
979: if ( i == row )
980: return 1;
981: if ( i != j ) {
982: t = mat[i]; mat[i] = mat[j]; mat[j] = t;
983: }
984: pivot = mat[j];
985: inv = invm(pivot[j],md);
986: for ( k = j; k <= n; k++ ) {
987: /* pivot[k] = dmar(pivot[k],inv,0,md); */
988: DMAR(pivot[k],inv,0,md,pivot[k])
989: }
990: for ( i = 0; i < row; i++ ) {
991: t = mat[i];
992: if ( i != j && (a = t[j]) )
993: for ( k = j, a = md - a; k <= n; k++ ) {
1.8 noro 994: unsigned int tk;
1.1 noro 995: /* t[k] = dmar(pivot[k],a,t[k],md); */
1.8 noro 996: DMAR(pivot[k],a,t[k],md,tk)
997: t[k] = tk;
1.1 noro 998: }
999: }
1000: }
1001: for ( i = n; i < row && !mat[i][n]; i++ );
1002: if ( i == row )
1003: return 0;
1004: else
1005: return -1;
1006: }
1007:
1.4 noro 1008: struct oEGT eg_mod,eg_elim,eg_elim1,eg_elim2,eg_chrem,eg_gschk,eg_intrat,eg_symb;
1.31 noro 1009: struct oEGT eg_conv;
1.1 noro 1010:
1.24 noro 1011: int generic_gauss_elim(MAT mat,MAT *nm,Q *dn,int **rindp,int **cindp)
1.1 noro 1012: {
1013: int **wmat;
1014: Q **bmat;
1015: N **tmat;
1016: Q *bmi;
1017: N *tmi;
1018: Q q;
1019: int *wmi;
1020: int *colstat,*wcolstat,*rind,*cind;
1021: int row,col,ind,md,i,j,k,l,t,t1,rank,rank0,inv;
1022: N m1,m2,m3,s,u;
1023: MAT r,crmat;
1024: struct oEGT tmp0,tmp1;
1025: struct oEGT eg_mod_split,eg_elim_split,eg_chrem_split;
1026: struct oEGT eg_intrat_split,eg_gschk_split;
1027: int ret;
1028:
1029: init_eg(&eg_mod_split); init_eg(&eg_chrem_split);
1030: init_eg(&eg_elim_split); init_eg(&eg_intrat_split);
1031: init_eg(&eg_gschk_split);
1032: bmat = (Q **)mat->body;
1033: row = mat->row; col = mat->col;
1034: wmat = (int **)almat(row,col);
1035: colstat = (int *)MALLOC_ATOMIC(col*sizeof(int));
1036: wcolstat = (int *)MALLOC_ATOMIC(col*sizeof(int));
1037: for ( ind = 0; ; ind++ ) {
1.11 noro 1038: if ( DP_Print ) {
1.2 noro 1039: fprintf(asir_out,"."); fflush(asir_out);
1040: }
1.12 noro 1041: md = get_lprime(ind);
1.1 noro 1042: get_eg(&tmp0);
1043: for ( i = 0; i < row; i++ )
1044: for ( j = 0, bmi = bmat[i], wmi = wmat[i]; j < col; j++ )
1045: if ( q = (Q)bmi[j] ) {
1046: t = rem(NM(q),md);
1047: if ( t && SGN(q) < 0 )
1048: t = (md - t) % md;
1049: wmi[j] = t;
1050: } else
1051: wmi[j] = 0;
1052: get_eg(&tmp1);
1053: add_eg(&eg_mod,&tmp0,&tmp1);
1054: add_eg(&eg_mod_split,&tmp0,&tmp1);
1055: get_eg(&tmp0);
1056: rank = generic_gauss_elim_mod(wmat,row,col,md,wcolstat);
1057: get_eg(&tmp1);
1058: add_eg(&eg_elim,&tmp0,&tmp1);
1059: add_eg(&eg_elim_split,&tmp0,&tmp1);
1060: if ( !ind ) {
1061: RESET:
1062: UTON(md,m1);
1063: rank0 = rank;
1064: bcopy(wcolstat,colstat,col*sizeof(int));
1065: MKMAT(crmat,rank,col-rank);
1066: MKMAT(r,rank,col-rank); *nm = r;
1067: tmat = (N **)crmat->body;
1068: for ( i = 0; i < rank; i++ )
1069: for ( j = k = 0, tmi = tmat[i], wmi = wmat[i]; j < col; j++ )
1070: if ( !colstat[j] ) {
1071: UTON(wmi[j],tmi[k]); k++;
1072: }
1073: } else {
1074: if ( rank < rank0 ) {
1.11 noro 1075: if ( DP_Print ) {
1.1 noro 1076: fprintf(asir_out,"lower rank matrix; continuing...\n");
1.2 noro 1077: fflush(asir_out);
1078: }
1.1 noro 1079: continue;
1080: } else if ( rank > rank0 ) {
1.11 noro 1081: if ( DP_Print ) {
1.1 noro 1082: fprintf(asir_out,"higher rank matrix; resetting...\n");
1.2 noro 1083: fflush(asir_out);
1084: }
1.1 noro 1085: goto RESET;
1086: } else {
1087: for ( j = 0; (j<col) && (colstat[j]==wcolstat[j]); j++ );
1088: if ( j < col ) {
1.11 noro 1089: if ( DP_Print ) {
1.1 noro 1090: fprintf(asir_out,"inconsitent colstat; resetting...\n");
1.2 noro 1091: fflush(asir_out);
1092: }
1.1 noro 1093: goto RESET;
1094: }
1095: }
1096:
1097: get_eg(&tmp0);
1098: inv = invm(rem(m1,md),md);
1099: UTON(md,m2); muln(m1,m2,&m3);
1100: for ( i = 0; i < rank; i++ )
1101: for ( j = k = 0, tmi = tmat[i], wmi = wmat[i]; j < col; j++ )
1102: if ( !colstat[j] ) {
1103: if ( tmi[k] ) {
1104: /* f3 = f1+m1*(m1 mod m2)^(-1)*(f2 - f1 mod m2) */
1105: t = rem(tmi[k],md);
1106: if ( wmi[j] >= t )
1107: t = wmi[j]-t;
1108: else
1109: t = md-(t-wmi[j]);
1110: DMAR(t,inv,0,md,t1)
1111: UTON(t1,u);
1112: muln(m1,u,&s);
1113: addn(tmi[k],s,&u); tmi[k] = u;
1114: } else if ( wmi[j] ) {
1115: /* f3 = m1*(m1 mod m2)^(-1)*f2 */
1116: DMAR(wmi[j],inv,0,md,t)
1117: UTON(t,u);
1118: muln(m1,u,&s); tmi[k] = s;
1119: }
1120: k++;
1121: }
1122: m1 = m3;
1123: get_eg(&tmp1);
1124: add_eg(&eg_chrem,&tmp0,&tmp1);
1125: add_eg(&eg_chrem_split,&tmp0,&tmp1);
1126:
1127: get_eg(&tmp0);
1.38 noro 1128: if ( ind % F4_INTRAT_PERIOD )
1.13 noro 1129: ret = 0;
1130: else
1131: ret = intmtoratm(crmat,m1,*nm,dn);
1.1 noro 1132: get_eg(&tmp1);
1133: add_eg(&eg_intrat,&tmp0,&tmp1);
1134: add_eg(&eg_intrat_split,&tmp0,&tmp1);
1135: if ( ret ) {
1136: *rindp = rind = (int *)MALLOC_ATOMIC(rank*sizeof(int));
1137: *cindp = cind = (int *)MALLOC_ATOMIC((col-rank)*sizeof(int));
1138: for ( j = k = l = 0; j < col; j++ )
1139: if ( colstat[j] )
1140: rind[k++] = j;
1141: else
1142: cind[l++] = j;
1143: get_eg(&tmp0);
1.3 noro 1144: if ( gensolve_check(mat,*nm,*dn,rind,cind) ) {
1145: get_eg(&tmp1);
1146: add_eg(&eg_gschk,&tmp0,&tmp1);
1147: add_eg(&eg_gschk_split,&tmp0,&tmp1);
1.11 noro 1148: if ( DP_Print ) {
1.3 noro 1149: print_eg("Mod",&eg_mod_split);
1150: print_eg("Elim",&eg_elim_split);
1151: print_eg("ChRem",&eg_chrem_split);
1152: print_eg("IntRat",&eg_intrat_split);
1153: print_eg("Check",&eg_gschk_split);
1154: fflush(asir_out);
1155: }
1156: return rank;
1157: }
1158: }
1159: }
1160: }
1161: }
1162:
1.24 noro 1163: int generic_gauss_elim_hensel(MAT mat,MAT *nmmat,Q *dn,int **rindp,int **cindp)
1.3 noro 1164: {
1165: MAT bmat,xmat;
1166: Q **a0,**a,**b,**x,**nm;
1167: Q *ai,*bi,*xi;
1168: int row,col;
1169: int **w;
1170: int *wi;
1171: int **wc;
1172: Q mdq,q,s,u;
1173: N tn;
1174: int ind,md,i,j,k,l,li,ri,rank;
1175: unsigned int t;
1176: int *cinfo,*rinfo;
1177: int *rind,*cind;
1178: int count;
1.41 noro 1179: int ret;
1180: struct oEGT eg_mul,eg_inv,eg_intrat,eg_check,tmp0,tmp1;
1.39 noro 1181: int period;
1.44 noro 1182: int *wx,*ptr;
1183: int wxsize,nsize;
1184: N wn;
1185: Q wq;
1.3 noro 1186:
1187: a0 = (Q **)mat->body;
1188: row = mat->row; col = mat->col;
1189: w = (int **)almat(row,col);
1190: for ( ind = 0; ; ind++ ) {
1.12 noro 1191: md = get_lprime(ind);
1.3 noro 1192: STOQ(md,mdq);
1193: for ( i = 0; i < row; i++ )
1194: for ( j = 0, ai = a0[i], wi = w[i]; j < col; j++ )
1195: if ( q = (Q)ai[j] ) {
1196: t = rem(NM(q),md);
1197: if ( t && SGN(q) < 0 )
1198: t = (md - t) % md;
1199: wi[j] = t;
1200: } else
1201: wi[j] = 0;
1202:
1.27 noro 1203: rank = find_lhs_and_lu_mod((unsigned int **)w,row,col,md,&rinfo,&cinfo);
1.3 noro 1204: a = (Q **)almat_pointer(rank,rank); /* lhs mat */
1205: MKMAT(bmat,rank,col-rank); b = (Q **)bmat->body; /* lhs mat */
1206: for ( j = li = ri = 0; j < col; j++ )
1207: if ( cinfo[j] ) {
1208: /* the column is in lhs */
1209: for ( i = 0; i < rank; i++ ) {
1210: w[i][li] = w[i][j];
1211: a[i][li] = a0[rinfo[i]][j];
1212: }
1213: li++;
1214: } else {
1215: /* the column is in rhs */
1216: for ( i = 0; i < rank; i++ )
1217: b[i][ri] = a0[rinfo[i]][j];
1218: ri++;
1219: }
1220:
1221: /* solve Ax+B=0; A: rank x rank, B: rank x ri */
1222: MKMAT(xmat,rank,ri); x = (Q **)(xmat)->body;
1223: MKMAT(*nmmat,rank,ri); nm = (Q **)(*nmmat)->body;
1224: /* use the right part of w as work area */
1225: /* ri = col - rank */
1226: wc = (int **)almat(rank,ri);
1227: for ( i = 0; i < rank; i++ )
1228: wc[i] = w[i]+rank;
1229: *rindp = rind = (int *)MALLOC_ATOMIC(rank*sizeof(int));
1230: *cindp = cind = (int *)MALLOC_ATOMIC((ri)*sizeof(int));
1231:
1232: init_eg(&eg_mul); init_eg(&eg_inv);
1.41 noro 1233: init_eg(&eg_check); init_eg(&eg_intrat);
1.39 noro 1234: period = F4_INTRAT_PERIOD;
1.44 noro 1235: nsize = period;
1236: wxsize = rank*ri*nsize;
1237: wx = (int *)MALLOC_ATOMIC(wxsize*sizeof(int));
1238: for ( i = 0; i < wxsize; i++ ) wx[i] = 0;
1239: for ( q = ONE, count = 0; ; ) {
1.42 noro 1240: if ( DP_Print > 3 )
1.41 noro 1241: fprintf(stderr,"o");
1.3 noro 1242: /* wc = -b mod md */
1.44 noro 1243: get_eg(&tmp0);
1.3 noro 1244: for ( i = 0; i < rank; i++ )
1245: for ( j = 0, bi = b[i], wi = wc[i]; j < ri; j++ )
1246: if ( u = (Q)bi[j] ) {
1247: t = rem(NM(u),md);
1248: if ( t && SGN(u) > 0 )
1249: t = (md - t) % md;
1250: wi[j] = t;
1251: } else
1252: wi[j] = 0;
1.44 noro 1253: /* wc = A^(-1)wc; wc is not normalized */
1254: solve_by_lu_mod(w,rank,md,wc,ri,0);
1255: /* wx += q*wc */
1256: ptr = wx;
1257: for ( i = 0; i < rank; i++ )
1258: for ( j = 0, wi = wc[i]; j < ri; j++ ) {
1259: if ( wi[j] )
1260: muln_1(BD(NM(q)),PL(NM(q)),wi[j],ptr);
1261: ptr += nsize;
1262: }
1263: count++;
1.1 noro 1264: get_eg(&tmp1);
1.3 noro 1265: add_eg(&eg_inv,&tmp0,&tmp1);
1266: get_eg(&tmp0);
1267: for ( i = 0; i < rank; i++ )
1268: for ( j = 0; j < ri; j++ ) {
1269: inner_product_mat_int_mod(a,wc,rank,i,j,&u);
1270: addq(b[i][j],u,&s);
1271: if ( s ) {
1272: t = divin(NM(s),md,&tn);
1273: if ( t )
1274: error("generic_gauss_elim_hensel:incosistent");
1275: NTOQ(tn,SGN(s),b[i][j]);
1276: } else
1277: b[i][j] = 0;
1278: }
1279: get_eg(&tmp1);
1280: add_eg(&eg_mul,&tmp0,&tmp1);
1281: /* q = q*md */
1282: mulq(q,mdq,&u); q = u;
1.44 noro 1283: if ( count == period ) {
1.41 noro 1284: get_eg(&tmp0);
1.44 noro 1285: ptr = wx;
1286: for ( i = 0; i < rank; i++ )
1287: for ( j = 0, xi = x[i]; j < ri;
1288: j++, ptr += nsize ) {
1289: for ( k = nsize-1; k >= 0 && !ptr[k]; k-- );
1290: if ( k >= 0 ) {
1291: wn = NALLOC(k+1);
1292: PL(wn) = k+1;
1293: for ( l = 0; l <= k; l++ ) BD(wn)[l] = (unsigned int)ptr[l];
1294: NTOQ(wn,1,wq);
1295: subq(xi[j],wq,&u); xi[j] = u;
1296: }
1297: }
1.41 noro 1298: ret = intmtoratm_q(xmat,NM(q),*nmmat,dn);
1299: get_eg(&tmp1); add_eg(&eg_intrat,&tmp0,&tmp1);
1300: if ( ret ) {
1.39 noro 1301: for ( j = k = l = 0; j < col; j++ )
1302: if ( cinfo[j] )
1303: rind[k++] = j;
1304: else
1305: cind[l++] = j;
1.41 noro 1306: get_eg(&tmp0);
1307: ret = gensolve_check(mat,*nmmat,*dn,rind,cind);
1308: get_eg(&tmp1); add_eg(&eg_check,&tmp0,&tmp1);
1309: if ( ret ) {
1.42 noro 1310: if ( DP_Print > 3 ) {
1.40 noro 1311: fprintf(stderr,"\n");
1312: print_eg("INV",&eg_inv);
1313: print_eg("MUL",&eg_mul);
1.41 noro 1314: print_eg("INTRAT",&eg_intrat);
1315: print_eg("CHECK",&eg_check);
1.40 noro 1316: fflush(asir_out);
1317: }
1.39 noro 1318: return rank;
1319: }
1.44 noro 1320: } else {
1321: period = period*3/2;
1322: count = 0;
1323: nsize += period;
1324: wxsize += rank*ri*nsize;
1325: wx = (int *)REALLOC(wx,wxsize*sizeof(int));
1326: for ( i = 0; i < wxsize; i++ ) wx[i] = 0;
1327: }
1.41 noro 1328: }
1.1 noro 1329: }
1330: }
1331: }
1332:
1333: int f4_nocheck;
1334:
1.24 noro 1335: int gensolve_check(MAT mat,MAT nm,Q dn,int *rind,int *cind)
1.1 noro 1336: {
1337: int row,col,rank,clen,i,j,k,l;
1.24 noro 1338: Q s,t;
1.1 noro 1339: Q *w;
1340: Q *mati,*nmk;
1341:
1342: if ( f4_nocheck )
1343: return 1;
1344: row = mat->row; col = mat->col;
1345: rank = nm->row; clen = nm->col;
1346: w = (Q *)MALLOC(clen*sizeof(Q));
1347: for ( i = 0; i < row; i++ ) {
1348: mati = (Q *)mat->body[i];
1349: #if 1
1350: bzero(w,clen*sizeof(Q));
1351: for ( k = 0; k < rank; k++ )
1352: for ( l = 0, nmk = (Q *)nm->body[k]; l < clen; l++ ) {
1353: mulq(mati[rind[k]],nmk[l],&t);
1354: addq(w[l],t,&s); w[l] = s;
1355: }
1356: for ( j = 0; j < clen; j++ ) {
1357: mulq(dn,mati[cind[j]],&t);
1358: if ( cmpq(w[j],t) )
1359: break;
1360: }
1361: #else
1362: for ( j = 0; j < clen; j++ ) {
1363: for ( k = 0, s = 0; k < rank; k++ ) {
1364: mulq(mati[rind[k]],nm->body[k][j],&t);
1365: addq(s,t,&u); s = u;
1366: }
1367: mulq(dn,mati[cind[j]],&t);
1368: if ( cmpq(s,t) )
1369: break;
1370: }
1371: #endif
1372: if ( j != clen )
1373: break;
1374: }
1375: if ( i != row )
1376: return 0;
1377: else
1378: return 1;
1379: }
1380:
1381: /* assuming 0 < c < m */
1382:
1.24 noro 1383: int inttorat(N c,N m,N b,int *sgnp,N *nmp,N *dnp)
1.1 noro 1384: {
1.24 noro 1385: Q qq,t,u1,v1,r1;
1386: N q,u2,v2,r2;
1.1 noro 1387:
1388: u1 = 0; v1 = ONE; u2 = m; v2 = c;
1389: while ( cmpn(v2,b) >= 0 ) {
1390: divn(u2,v2,&q,&r2); u2 = v2; v2 = r2;
1391: NTOQ(q,1,qq); mulq(qq,v1,&t); subq(u1,t,&r1); u1 = v1; v1 = r1;
1392: }
1393: if ( cmpn(NM(v1),b) >= 0 )
1394: return 0;
1395: else {
1396: *nmp = v2;
1397: *dnp = NM(v1);
1398: *sgnp = SGN(v1);
1399: return 1;
1400: }
1401: }
1402:
1403: /* mat->body = N ** */
1404:
1.24 noro 1405: int intmtoratm(MAT mat,N md,MAT nm,Q *dn)
1.1 noro 1406: {
1407: N t,s,b;
1.24 noro 1408: Q dn0,dn1,nm1,q;
1.1 noro 1409: int i,j,k,l,row,col;
1410: Q **rmat;
1411: N **tmat;
1412: N *tmi;
1413: Q *nmk;
1414: N u,unm,udn;
1415: int sgn,ret;
1416:
1.3 noro 1417: if ( UNIN(md) )
1418: return 0;
1.1 noro 1419: row = mat->row; col = mat->col;
1420: bshiftn(md,1,&t);
1421: isqrt(t,&s);
1422: bshiftn(s,64,&b);
1423: if ( !b )
1424: b = ONEN;
1425: dn0 = ONE;
1426: tmat = (N **)mat->body;
1427: rmat = (Q **)nm->body;
1428: for ( i = 0; i < row; i++ )
1429: for ( j = 0, tmi = tmat[i]; j < col; j++ )
1430: if ( tmi[j] ) {
1431: muln(tmi[j],NM(dn0),&s);
1432: remn(s,md,&u);
1433: ret = inttorat(u,md,b,&sgn,&unm,&udn);
1434: if ( !ret )
1435: return 0;
1436: else {
1437: NTOQ(unm,sgn,nm1);
1438: NTOQ(udn,1,dn1);
1439: if ( !UNIQ(dn1) ) {
1440: for ( k = 0; k < i; k++ )
1441: for ( l = 0, nmk = rmat[k]; l < col; l++ ) {
1442: mulq(nmk[l],dn1,&q); nmk[l] = q;
1443: }
1444: for ( l = 0, nmk = rmat[i]; l < j; l++ ) {
1445: mulq(nmk[l],dn1,&q); nmk[l] = q;
1446: }
1447: }
1448: rmat[i][j] = nm1;
1449: mulq(dn0,dn1,&q); dn0 = q;
1450: }
1451: }
1452: *dn = dn0;
1453: return 1;
1454: }
1455:
1.3 noro 1456: /* mat->body = Q ** */
1457:
1.24 noro 1458: int intmtoratm_q(MAT mat,N md,MAT nm,Q *dn)
1.3 noro 1459: {
1460: N t,s,b;
1.24 noro 1461: Q dn0,dn1,nm1,q;
1.3 noro 1462: int i,j,k,l,row,col;
1463: Q **rmat;
1464: Q **tmat;
1465: Q *tmi;
1466: Q *nmk;
1467: N u,unm,udn;
1468: int sgn,ret;
1469:
1470: if ( UNIN(md) )
1471: return 0;
1472: row = mat->row; col = mat->col;
1473: bshiftn(md,1,&t);
1474: isqrt(t,&s);
1475: bshiftn(s,64,&b);
1476: if ( !b )
1477: b = ONEN;
1478: dn0 = ONE;
1479: tmat = (Q **)mat->body;
1480: rmat = (Q **)nm->body;
1481: for ( i = 0; i < row; i++ )
1482: for ( j = 0, tmi = tmat[i]; j < col; j++ )
1483: if ( tmi[j] ) {
1484: muln(NM(tmi[j]),NM(dn0),&s);
1485: remn(s,md,&u);
1486: ret = inttorat(u,md,b,&sgn,&unm,&udn);
1487: if ( !ret )
1488: return 0;
1489: else {
1490: if ( SGN(tmi[j])<0 )
1491: sgn = -sgn;
1492: NTOQ(unm,sgn,nm1);
1493: NTOQ(udn,1,dn1);
1494: if ( !UNIQ(dn1) ) {
1495: for ( k = 0; k < i; k++ )
1496: for ( l = 0, nmk = rmat[k]; l < col; l++ ) {
1497: mulq(nmk[l],dn1,&q); nmk[l] = q;
1498: }
1499: for ( l = 0, nmk = rmat[i]; l < j; l++ ) {
1500: mulq(nmk[l],dn1,&q); nmk[l] = q;
1501: }
1502: }
1503: rmat[i][j] = nm1;
1504: mulq(dn0,dn1,&q); dn0 = q;
1505: }
1506: }
1507: *dn = dn0;
1508: return 1;
1509: }
1510:
1.4 noro 1511: #define ONE_STEP1 if ( zzz = *s ) { DMAR(zzz,hc,*tj,md,*tj) } tj++; s++;
1512:
1.24 noro 1513: void reduce_reducers_mod(int **mat,int row,int col,int md)
1.4 noro 1514: {
1515: int i,j,k,l,hc,zzz;
1516: int *t,*s,*tj,*ind;
1517:
1518: /* reduce the reducers */
1519: ind = (int *)ALLOCA(row*sizeof(int));
1520: for ( i = 0; i < row; i++ ) {
1521: t = mat[i];
1522: for ( j = 0; j < col && !t[j]; j++ );
1523: /* register the position of the head term */
1524: ind[i] = j;
1525: for ( l = i-1; l >= 0; l-- ) {
1526: /* reduce mat[i] by mat[l] */
1527: if ( hc = t[ind[l]] ) {
1528: /* mat[i] = mat[i]-hc*mat[l] */
1529: j = ind[l];
1530: s = mat[l]+j;
1531: tj = t+j;
1532: hc = md-hc;
1533: k = col-j;
1534: for ( ; k >= 64; k -= 64 ) {
1535: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
1536: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
1537: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
1538: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
1539: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
1540: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
1541: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
1542: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
1543: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
1544: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
1545: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
1546: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
1547: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
1548: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
1549: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
1550: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
1551: }
1.16 noro 1552: for ( ; k > 0; k-- ) {
1.4 noro 1553: if ( zzz = *s ) { DMAR(zzz,hc,*tj,md,*tj) } tj++; s++;
1554: }
1555: }
1556: }
1557: }
1558: }
1559:
1560: /*
1561: mat[i] : reducers (i=0,...,nred-1)
1562: spolys (i=nred,...,row-1)
1563: mat[0] < mat[1] < ... < mat[nred-1] w.r.t the term order
1564: 1. reduce the reducers
1565: 2. reduce spolys by the reduced reducers
1566: */
1567:
1.24 noro 1568: void pre_reduce_mod(int **mat,int row,int col,int nred,int md)
1.4 noro 1569: {
1570: int i,j,k,l,hc,inv;
1571: int *t,*s,*tk,*ind;
1572:
1573: #if 1
1574: /* reduce the reducers */
1575: ind = (int *)ALLOCA(row*sizeof(int));
1576: for ( i = 0; i < nred; i++ ) {
1577: /* make mat[i] monic and mat[i] by mat[0],...,mat[i-1] */
1578: t = mat[i];
1579: for ( j = 0; j < col && !t[j]; j++ );
1580: /* register the position of the head term */
1581: ind[i] = j;
1582: inv = invm(t[j],md);
1583: for ( k = j; k < col; k++ )
1584: if ( t[k] )
1585: DMAR(t[k],inv,0,md,t[k])
1586: for ( l = i-1; l >= 0; l-- ) {
1587: /* reduce mat[i] by mat[l] */
1588: if ( hc = t[ind[l]] ) {
1589: /* mat[i] = mat[i]-hc*mat[l] */
1590: for ( k = ind[l], hc = md-hc, s = mat[l]+k, tk = t+k;
1591: k < col; k++, tk++, s++ )
1592: if ( *s )
1593: DMAR(*s,hc,*tk,md,*tk)
1594: }
1595: }
1596: }
1597: /* reduce the spolys */
1598: for ( i = nred; i < row; i++ ) {
1599: t = mat[i];
1600: for ( l = nred-1; l >= 0; l-- ) {
1601: /* reduce mat[i] by mat[l] */
1602: if ( hc = t[ind[l]] ) {
1603: /* mat[i] = mat[i]-hc*mat[l] */
1604: for ( k = ind[l], hc = md-hc, s = mat[l]+k, tk = t+k;
1605: k < col; k++, tk++, s++ )
1606: if ( *s )
1607: DMAR(*s,hc,*tk,md,*tk)
1608: }
1609: }
1610: }
1611: #endif
1612: }
1613: /*
1614: mat[i] : reducers (i=0,...,nred-1)
1615: mat[0] < mat[1] < ... < mat[nred-1] w.r.t the term order
1616: */
1617:
1.24 noro 1618: void reduce_sp_by_red_mod(int *sp,int **redmat,int *ind,int nred,int col,int md)
1.4 noro 1619: {
1620: int i,j,k,hc,zzz;
1.24 noro 1621: int *s,*tj;
1.4 noro 1622:
1623: /* reduce the spolys by redmat */
1624: for ( i = nred-1; i >= 0; i-- ) {
1625: /* reduce sp by redmat[i] */
1626: if ( hc = sp[ind[i]] ) {
1627: /* sp = sp-hc*redmat[i] */
1628: j = ind[i];
1629: hc = md-hc;
1630: s = redmat[i]+j;
1631: tj = sp+j;
1.16 noro 1632: for ( k = col-j; k > 0; k-- ) {
1.4 noro 1633: if ( zzz = *s ) { DMAR(zzz,hc,*tj,md,*tj) } tj++; s++;
1.15 noro 1634: }
1635: }
1.17 noro 1636: }
1637: }
1638:
1639: /*
1.15 noro 1640: mat[i] : compressed reducers (i=0,...,nred-1)
1641: mat[0] < mat[1] < ... < mat[nred-1] w.r.t the term order
1642: */
1643:
1.24 noro 1644: void red_by_compress(int m,unsigned int *p,unsigned int *r,
1645: unsigned int *ri,unsigned int hc,int len)
1.18 noro 1646: {
1.19 noro 1647: unsigned int up,lo;
1.18 noro 1648: unsigned int dmy;
1649: unsigned int *pj;
1650:
1.21 noro 1651: p[*ri] = 0; r++; ri++;
1652: for ( len--; len; len--, r++, ri++ ) {
1653: pj = p+ *ri;
1654: DMA(*r,hc,*pj,up,lo);
1.18 noro 1655: if ( up ) {
1656: DSAB(m,up,lo,dmy,*pj);
1657: } else
1658: *pj = lo;
1659: }
1660: }
1661:
1662: /* p -= hc*r */
1663:
1.24 noro 1664: void red_by_vect(int m,unsigned int *p,unsigned int *r,unsigned int hc,int len)
1.18 noro 1665: {
1666: register unsigned int up,lo;
1667: unsigned int dmy;
1668:
1669: *p++ = 0; r++; len--;
1670: for ( ; len; len--, r++, p++ )
1671: if ( *r ) {
1.20 noro 1672: DMA(*r,hc,*p,up,lo);
1.18 noro 1673: if ( up ) {
1674: DSAB(m,up,lo,dmy,*p);
1675: } else
1676: *p = lo;
1677: }
1678: }
1679:
1.32 noro 1680: void red_by_vect_sf(int m,unsigned int *p,unsigned int *r,unsigned int hc,int len)
1681: {
1682: *p++ = 0; r++; len--;
1683: for ( ; len; len--, r++, p++ )
1684: if ( *r )
1685: *p = _addsf(_mulsf(*r,hc),*p);
1686: }
1687:
1.21 noro 1688: extern unsigned int **psca;
1689:
1.24 noro 1690: void reduce_sp_by_red_mod_compress (int *sp,CDP *redmat,int *ind,
1691: int nred,int col,int md)
1.15 noro 1692: {
1.24 noro 1693: int i,len;
1.15 noro 1694: CDP ri;
1.24 noro 1695: unsigned int hc;
1.18 noro 1696: unsigned int *usp;
1.15 noro 1697:
1.18 noro 1698: usp = (unsigned int *)sp;
1.15 noro 1699: /* reduce the spolys by redmat */
1700: for ( i = nred-1; i >= 0; i-- ) {
1701: /* reduce sp by redmat[i] */
1.18 noro 1702: usp[ind[i]] %= md;
1703: if ( hc = usp[ind[i]] ) {
1.15 noro 1704: /* sp = sp-hc*redmat[i] */
1705: hc = md-hc;
1706: ri = redmat[i];
1707: len = ri->len;
1.21 noro 1708: red_by_compress(md,usp,psca[ri->psindex],ri->body,hc,len);
1.4 noro 1709: }
1710: }
1.18 noro 1711: for ( i = 0; i < col; i++ )
1.24 noro 1712: if ( usp[i] >= (unsigned int)md )
1.18 noro 1713: usp[i] %= md;
1.4 noro 1714: }
1715:
1716: #define ONE_STEP2 if ( zzz = *pk ) { DMAR(zzz,a,*tk,md,*tk) } pk++; tk++;
1717:
1.24 noro 1718: int generic_gauss_elim_mod(int **mat0,int row,int col,int md,int *colstat)
1.1 noro 1719: {
1.24 noro 1720: int i,j,k,l,inv,a,rank;
1721: unsigned int *t,*pivot,*pk;
1.18 noro 1722: unsigned int **mat;
1.1 noro 1723:
1.18 noro 1724: mat = (unsigned int **)mat0;
1.1 noro 1725: for ( rank = 0, j = 0; j < col; j++ ) {
1.18 noro 1726: for ( i = rank; i < row; i++ )
1727: mat[i][j] %= md;
1728: for ( i = rank; i < row; i++ )
1729: if ( mat[i][j] )
1730: break;
1.1 noro 1731: if ( i == row ) {
1732: colstat[j] = 0;
1733: continue;
1734: } else
1735: colstat[j] = 1;
1736: if ( i != rank ) {
1737: t = mat[i]; mat[i] = mat[rank]; mat[rank] = t;
1738: }
1739: pivot = mat[rank];
1740: inv = invm(pivot[j],md);
1.4 noro 1741: for ( k = j, pk = pivot+k; k < col; k++, pk++ )
1742: if ( *pk ) {
1.24 noro 1743: if ( *pk >= (unsigned int)md )
1.18 noro 1744: *pk %= md;
1.4 noro 1745: DMAR(*pk,inv,0,md,*pk)
1.1 noro 1746: }
1747: for ( i = rank+1; i < row; i++ ) {
1748: t = mat[i];
1.18 noro 1749: if ( a = t[j] )
1750: red_by_vect(md,t+j,pivot+j,md-a,col-j);
1.1 noro 1751: }
1752: rank++;
1753: }
1754: for ( j = col-1, l = rank-1; j >= 0; j-- )
1755: if ( colstat[j] ) {
1756: pivot = mat[l];
1757: for ( i = 0; i < l; i++ ) {
1758: t = mat[i];
1.18 noro 1759: t[j] %= md;
1760: if ( a = t[j] )
1761: red_by_vect(md,t+j,pivot+j,md-a,col-j);
1.1 noro 1762: }
1763: l--;
1.18 noro 1764: }
1765: for ( j = 0, l = 0; l < rank; j++ )
1766: if ( colstat[j] ) {
1767: t = mat[l];
1768: for ( k = j; k < col; k++ )
1.24 noro 1769: if ( t[k] >= (unsigned int)md )
1.18 noro 1770: t[k] %= md;
1771: l++;
1.32 noro 1772: }
1773: return rank;
1774: }
1775:
1776: int generic_gauss_elim_sf(int **mat0,int row,int col,int md,int *colstat)
1777: {
1778: int i,j,k,l,inv,a,rank;
1779: unsigned int *t,*pivot,*pk;
1780: unsigned int **mat;
1781:
1782: mat = (unsigned int **)mat0;
1783: for ( rank = 0, j = 0; j < col; j++ ) {
1784: for ( i = rank; i < row; i++ )
1785: if ( mat[i][j] )
1786: break;
1787: if ( i == row ) {
1788: colstat[j] = 0;
1789: continue;
1790: } else
1791: colstat[j] = 1;
1792: if ( i != rank ) {
1793: t = mat[i]; mat[i] = mat[rank]; mat[rank] = t;
1794: }
1795: pivot = mat[rank];
1796: inv = _invsf(pivot[j]);
1797: for ( k = j, pk = pivot+k; k < col; k++, pk++ )
1798: if ( *pk )
1799: *pk = _mulsf(*pk,inv);
1800: for ( i = rank+1; i < row; i++ ) {
1801: t = mat[i];
1802: if ( a = t[j] )
1803: red_by_vect_sf(md,t+j,pivot+j,_chsgnsf(a),col-j);
1804: }
1805: rank++;
1806: }
1807: for ( j = col-1, l = rank-1; j >= 0; j-- )
1808: if ( colstat[j] ) {
1809: pivot = mat[l];
1810: for ( i = 0; i < l; i++ ) {
1811: t = mat[i];
1812: if ( a = t[j] )
1813: red_by_vect_sf(md,t+j,pivot+j,_chsgnsf(a),col-j);
1814: }
1815: l--;
1.1 noro 1816: }
1817: return rank;
1818: }
1819:
1820: /* LU decomposition; a[i][i] = 1/U[i][i] */
1821:
1.24 noro 1822: int lu_gfmmat(GFMMAT mat,unsigned int md,int *perm)
1.1 noro 1823: {
1824: int row,col;
1.24 noro 1825: int i,j,k;
1.1 noro 1826: unsigned int *t,*pivot;
1827: unsigned int **a;
1828: unsigned int inv,m;
1829:
1830: row = mat->row; col = mat->col;
1831: a = mat->body;
1832: bzero(perm,row*sizeof(int));
1833:
1834: for ( i = 0; i < row; i++ )
1835: perm[i] = i;
1836: for ( k = 0; k < col; k++ ) {
1837: for ( i = k; i < row && !a[i][k]; i++ );
1838: if ( i == row )
1839: return 0;
1840: if ( i != k ) {
1841: j = perm[i]; perm[i] = perm[k]; perm[k] = j;
1842: t = a[i]; a[i] = a[k]; a[k] = t;
1843: }
1844: pivot = a[k];
1845: pivot[k] = inv = invm(pivot[k],md);
1846: for ( i = k+1; i < row; i++ ) {
1847: t = a[i];
1848: if ( m = t[k] ) {
1849: DMAR(inv,m,0,md,t[k])
1850: for ( j = k+1, m = md - t[k]; j < col; j++ )
1851: if ( pivot[j] ) {
1.8 noro 1852: unsigned int tj;
1853:
1854: DMAR(m,pivot[j],t[j],md,tj)
1855: t[j] = tj;
1.1 noro 1856: }
1857: }
1858: }
1859: }
1860: return 1;
1861: }
1862:
1.3 noro 1863: /*
1864: Input
1865: a: a row x col matrix
1866: md : a modulus
1867:
1868: Output:
1869: return : d = the rank of mat
1870: a[0..(d-1)][0..(d-1)] : LU decomposition (a[i][i] = 1/U[i][i])
1871: rinfo: array of length row
1872: cinfo: array of length col
1873: i-th row in new a <-> rinfo[i]-th row in old a
1874: cinfo[j]=1 <=> j-th column is contained in the LU decomp.
1875: */
1876:
1.24 noro 1877: int find_lhs_and_lu_mod(unsigned int **a,int row,int col,
1878: unsigned int md,int **rinfo,int **cinfo)
1.3 noro 1879: {
1.24 noro 1880: int i,j,k,d;
1.3 noro 1881: int *rp,*cp;
1882: unsigned int *t,*pivot;
1883: unsigned int inv,m;
1884:
1885: *rinfo = rp = (int *)MALLOC_ATOMIC(row*sizeof(int));
1886: *cinfo = cp = (int *)MALLOC_ATOMIC(col*sizeof(int));
1887: for ( i = 0; i < row; i++ )
1888: rp[i] = i;
1889: for ( k = 0, d = 0; k < col; k++ ) {
1890: for ( i = d; i < row && !a[i][k]; i++ );
1891: if ( i == row ) {
1892: cp[k] = 0;
1893: continue;
1894: } else
1895: cp[k] = 1;
1896: if ( i != d ) {
1897: j = rp[i]; rp[i] = rp[d]; rp[d] = j;
1898: t = a[i]; a[i] = a[d]; a[d] = t;
1899: }
1900: pivot = a[d];
1901: pivot[k] = inv = invm(pivot[k],md);
1902: for ( i = d+1; i < row; i++ ) {
1903: t = a[i];
1904: if ( m = t[k] ) {
1905: DMAR(inv,m,0,md,t[k])
1906: for ( j = k+1, m = md - t[k]; j < col; j++ )
1907: if ( pivot[j] ) {
1.8 noro 1908: unsigned int tj;
1909: DMAR(m,pivot[j],t[j],md,tj)
1910: t[j] = tj;
1.3 noro 1911: }
1912: }
1913: }
1914: d++;
1915: }
1916: return d;
1917: }
1918:
1919: /*
1920: Input
1921: a : n x n matrix; a result of LU-decomposition
1922: md : modulus
1923: b : n x l matrix
1924: Output
1925: b = a^(-1)b
1926: */
1927:
1.44 noro 1928: void solve_by_lu_mod(int **a,int n,int md,int **b,int l,int normalize)
1.3 noro 1929: {
1930: unsigned int *y,*c;
1931: int i,j,k;
1932: unsigned int t,m,m2;
1933:
1934: y = (int *)MALLOC_ATOMIC(n*sizeof(int));
1935: c = (int *)MALLOC_ATOMIC(n*sizeof(int));
1936: m2 = md>>1;
1937: for ( k = 0; k < l; k++ ) {
1938: /* copy b[.][k] to c */
1939: for ( i = 0; i < n; i++ )
1940: c[i] = (unsigned int)b[i][k];
1941: /* solve Ly=c */
1942: for ( i = 0; i < n; i++ ) {
1943: for ( t = c[i], j = 0; j < i; j++ )
1944: if ( a[i][j] ) {
1945: m = md - a[i][j];
1946: DMAR(m,y[j],t,md,t)
1947: }
1948: y[i] = t;
1949: }
1950: /* solve Uc=y */
1951: for ( i = n-1; i >= 0; i-- ) {
1952: for ( t = y[i], j =i+1; j < n; j++ )
1953: if ( a[i][j] ) {
1954: m = md - a[i][j];
1955: DMAR(m,c[j],t,md,t)
1956: }
1957: /* a[i][i] = 1/U[i][i] */
1958: DMAR(t,a[i][i],0,md,c[i])
1959: }
1960: /* copy c to b[.][k] with normalization */
1.44 noro 1961: if ( normalize )
1962: for ( i = 0; i < n; i++ )
1963: b[i][k] = (int)(c[i]>m2 ? c[i]-md : c[i]);
1964: else
1965: for ( i = 0; i < n; i++ )
1966: b[i][k] = c[i];
1.3 noro 1967: }
1968: }
1969:
1.24 noro 1970: void Pleqm1(NODE arg,VECT *rp)
1.1 noro 1971: {
1972: MAT m;
1973: VECT vect;
1974: pointer **mat;
1975: Q *v;
1976: Q q;
1977: int **wmat;
1978: int md,i,j,row,col,t,n,status;
1979:
1980: asir_assert(ARG0(arg),O_MAT,"leqm1");
1981: asir_assert(ARG1(arg),O_N,"leqm1");
1982: m = (MAT)ARG0(arg); md = QTOS((Q)ARG1(arg));
1983: row = m->row; col = m->col; mat = m->body;
1984: wmat = (int **)almat(row,col);
1985: for ( i = 0; i < row; i++ )
1986: for ( j = 0; j < col; j++ )
1987: if ( q = (Q)mat[i][j] ) {
1988: t = rem(NM(q),md);
1989: if ( SGN(q) < 0 )
1990: t = (md - t) % md;
1991: wmat[i][j] = t;
1992: } else
1993: wmat[i][j] = 0;
1994: status = gauss_elim_mod1(wmat,row,col,md);
1995: if ( status < 0 )
1996: *rp = 0;
1997: else if ( status > 0 )
1998: *rp = (VECT)ONE;
1999: else {
2000: n = col - 1;
2001: MKVECT(vect,n);
2002: for ( i = 0, v = (Q *)vect->body; i < n; i++ ) {
2003: t = (md-wmat[i][n])%md; STOQ(t,v[i]);
2004: }
2005: *rp = vect;
2006: }
2007: }
2008:
1.24 noro 2009: int gauss_elim_mod1(int **mat,int row,int col,int md)
1.1 noro 2010: {
2011: int i,j,k,inv,a,n;
2012: int *t,*pivot;
2013:
2014: n = col - 1;
2015: for ( j = 0; j < n; j++ ) {
2016: for ( i = j; i < row && !mat[i][j]; i++ );
2017: if ( i == row )
2018: return 1;
2019: if ( i != j ) {
2020: t = mat[i]; mat[i] = mat[j]; mat[j] = t;
2021: }
2022: pivot = mat[j];
2023: inv = invm(pivot[j],md);
2024: for ( k = j; k <= n; k++ )
2025: pivot[k] = dmar(pivot[k],inv,0,md);
2026: for ( i = j+1; i < row; i++ ) {
2027: t = mat[i];
2028: if ( i != j && (a = t[j]) )
2029: for ( k = j, a = md - a; k <= n; k++ )
2030: t[k] = dmar(pivot[k],a,t[k],md);
2031: }
2032: }
2033: for ( i = n; i < row && !mat[i][n]; i++ );
2034: if ( i == row ) {
2035: for ( j = n-1; j >= 0; j-- ) {
2036: for ( i = j-1, a = (md-mat[j][n])%md; i >= 0; i-- ) {
2037: mat[i][n] = dmar(mat[i][j],a,mat[i][n],md);
2038: mat[i][j] = 0;
2039: }
2040: }
2041: return 0;
2042: } else
2043: return -1;
2044: }
2045:
1.24 noro 2046: void Pgeninvm(NODE arg,LIST *rp)
1.1 noro 2047: {
2048: MAT m;
2049: pointer **mat;
2050: Q **tmat;
2051: Q q;
2052: unsigned int **wmat;
2053: int md,i,j,row,col,t,status;
2054: MAT mat1,mat2;
2055: NODE node1,node2;
2056:
2057: asir_assert(ARG0(arg),O_MAT,"leqm1");
2058: asir_assert(ARG1(arg),O_N,"leqm1");
2059: m = (MAT)ARG0(arg); md = QTOS((Q)ARG1(arg));
2060: row = m->row; col = m->col; mat = m->body;
2061: wmat = (unsigned int **)almat(row,col+row);
2062: for ( i = 0; i < row; i++ ) {
2063: bzero((char *)wmat[i],(col+row)*sizeof(int));
2064: for ( j = 0; j < col; j++ )
2065: if ( q = (Q)mat[i][j] ) {
2066: t = rem(NM(q),md);
2067: if ( SGN(q) < 0 )
2068: t = (md - t) % md;
2069: wmat[i][j] = t;
2070: }
2071: wmat[i][col+i] = 1;
2072: }
2073: status = gauss_elim_geninv_mod(wmat,row,col,md);
2074: if ( status > 0 )
2075: *rp = 0;
2076: else {
2077: MKMAT(mat1,col,row); MKMAT(mat2,row-col,row);
2078: for ( i = 0, tmat = (Q **)mat1->body; i < col; i++ )
2079: for ( j = 0; j < row; j++ )
1.24 noro 2080: UTOQ(wmat[i][j+col],tmat[i][j]);
1.1 noro 2081: for ( tmat = (Q **)mat2->body; i < row; i++ )
2082: for ( j = 0; j < row; j++ )
1.24 noro 2083: UTOQ(wmat[i][j+col],tmat[i-col][j]);
1.1 noro 2084: MKNODE(node2,mat2,0); MKNODE(node1,mat1,node2); MKLIST(*rp,node1);
2085: }
2086: }
2087:
1.24 noro 2088: int gauss_elim_geninv_mod(unsigned int **mat,int row,int col,int md)
1.1 noro 2089: {
2090: int i,j,k,inv,a,n,m;
2091: unsigned int *t,*pivot;
2092:
2093: n = col; m = row+col;
2094: for ( j = 0; j < n; j++ ) {
2095: for ( i = j; i < row && !mat[i][j]; i++ );
2096: if ( i == row )
2097: return 1;
2098: if ( i != j ) {
2099: t = mat[i]; mat[i] = mat[j]; mat[j] = t;
2100: }
2101: pivot = mat[j];
2102: inv = invm(pivot[j],md);
2103: for ( k = j; k < m; k++ )
2104: pivot[k] = dmar(pivot[k],inv,0,md);
2105: for ( i = j+1; i < row; i++ ) {
2106: t = mat[i];
2107: if ( a = t[j] )
2108: for ( k = j, a = md - a; k < m; k++ )
2109: t[k] = dmar(pivot[k],a,t[k],md);
2110: }
2111: }
2112: for ( j = n-1; j >= 0; j-- ) {
2113: pivot = mat[j];
2114: for ( i = j-1; i >= 0; i-- ) {
2115: t = mat[i];
2116: if ( a = t[j] )
2117: for ( k = j, a = md - a; k < m; k++ )
2118: t[k] = dmar(pivot[k],a,t[k],md);
2119: }
2120: }
2121: return 0;
2122: }
2123:
1.24 noro 2124: void Psolve_by_lu_gfmmat(NODE arg,VECT *rp)
1.1 noro 2125: {
2126: GFMMAT lu;
2127: Q *perm,*rhs,*v;
2128: int n,i;
2129: unsigned int md;
2130: unsigned int *b,*sol;
2131: VECT r;
2132:
2133: lu = (GFMMAT)ARG0(arg);
2134: perm = (Q *)BDY((VECT)ARG1(arg));
2135: rhs = (Q *)BDY((VECT)ARG2(arg));
2136: md = (unsigned int)QTOS((Q)ARG3(arg));
2137: n = lu->col;
2138: b = (unsigned int *)MALLOC_ATOMIC(n*sizeof(int));
2139: sol = (unsigned int *)MALLOC_ATOMIC(n*sizeof(int));
2140: for ( i = 0; i < n; i++ )
2141: b[i] = QTOS(rhs[QTOS(perm[i])]);
2142: solve_by_lu_gfmmat(lu,md,b,sol);
2143: MKVECT(r,n);
2144: for ( i = 0, v = (Q *)r->body; i < n; i++ )
1.24 noro 2145: UTOQ(sol[i],v[i]);
1.1 noro 2146: *rp = r;
2147: }
2148:
1.24 noro 2149: void solve_by_lu_gfmmat(GFMMAT lu,unsigned int md,
2150: unsigned int *b,unsigned int *x)
1.1 noro 2151: {
2152: int n;
2153: unsigned int **a;
2154: unsigned int *y;
2155: int i,j;
2156: unsigned int t,m;
2157:
2158: n = lu->col;
2159: a = lu->body;
2160: y = (unsigned int *)MALLOC_ATOMIC(n*sizeof(int));
2161: /* solve Ly=b */
2162: for ( i = 0; i < n; i++ ) {
2163: for ( t = b[i], j = 0; j < i; j++ )
2164: if ( a[i][j] ) {
2165: m = md - a[i][j];
2166: DMAR(m,y[j],t,md,t)
2167: }
2168: y[i] = t;
2169: }
2170: /* solve Ux=y */
2171: for ( i = n-1; i >= 0; i-- ) {
2172: for ( t = y[i], j =i+1; j < n; j++ )
2173: if ( a[i][j] ) {
2174: m = md - a[i][j];
2175: DMAR(m,x[j],t,md,t)
2176: }
2177: /* a[i][i] = 1/U[i][i] */
2178: DMAR(t,a[i][i],0,md,x[i])
2179: }
2180: }
2181:
1.24 noro 2182: void Plu_gfmmat(NODE arg,LIST *rp)
1.1 noro 2183: {
2184: MAT m;
2185: GFMMAT mm;
2186: unsigned int md;
2187: int i,row,col,status;
2188: int *iperm;
2189: Q *v;
2190: VECT perm;
2191: NODE n0;
2192:
2193: asir_assert(ARG0(arg),O_MAT,"mat_to_gfmmat");
2194: asir_assert(ARG1(arg),O_N,"mat_to_gfmmat");
2195: m = (MAT)ARG0(arg); md = (unsigned int)QTOS((Q)ARG1(arg));
2196: mat_to_gfmmat(m,md,&mm);
2197: row = m->row;
2198: col = m->col;
2199: iperm = (int *)MALLOC_ATOMIC(row*sizeof(int));
2200: status = lu_gfmmat(mm,md,iperm);
2201: if ( !status )
2202: n0 = 0;
2203: else {
2204: MKVECT(perm,row);
2205: for ( i = 0, v = (Q *)perm->body; i < row; i++ )
2206: STOQ(iperm[i],v[i]);
2207: n0 = mknode(2,mm,perm);
2208: }
2209: MKLIST(*rp,n0);
2210: }
2211:
1.24 noro 2212: void Pmat_to_gfmmat(NODE arg,GFMMAT *rp)
1.1 noro 2213: {
2214: MAT m;
2215: unsigned int md;
2216:
2217: asir_assert(ARG0(arg),O_MAT,"mat_to_gfmmat");
2218: asir_assert(ARG1(arg),O_N,"mat_to_gfmmat");
2219: m = (MAT)ARG0(arg); md = (unsigned int)QTOS((Q)ARG1(arg));
2220: mat_to_gfmmat(m,md,rp);
2221: }
2222:
1.24 noro 2223: void mat_to_gfmmat(MAT m,unsigned int md,GFMMAT *rp)
1.1 noro 2224: {
2225: unsigned int **wmat;
2226: unsigned int t;
2227: Q **mat;
2228: Q q;
2229: int i,j,row,col;
2230:
2231: row = m->row; col = m->col; mat = (Q **)m->body;
2232: wmat = (unsigned int **)almat(row,col);
2233: for ( i = 0; i < row; i++ ) {
2234: bzero((char *)wmat[i],col*sizeof(unsigned int));
2235: for ( j = 0; j < col; j++ )
2236: if ( q = mat[i][j] ) {
2237: t = (unsigned int)rem(NM(q),md);
2238: if ( SGN(q) < 0 )
2239: t = (md - t) % md;
2240: wmat[i][j] = t;
2241: }
2242: }
2243: TOGFMMAT(row,col,wmat,*rp);
2244: }
2245:
1.27 noro 2246: void Pgeninvm_swap(arg,rp)
2247: NODE arg;
2248: LIST *rp;
1.1 noro 2249: {
2250: MAT m;
2251: pointer **mat;
2252: Q **tmat;
2253: Q *tvect;
2254: Q q;
2255: unsigned int **wmat,**invmat;
2256: int *index;
2257: unsigned int t,md;
2258: int i,j,row,col,status;
2259: MAT mat1;
2260: VECT vect1;
2261: NODE node1,node2;
2262:
2263: asir_assert(ARG0(arg),O_MAT,"geninvm_swap");
2264: asir_assert(ARG1(arg),O_N,"geninvm_swap");
2265: m = (MAT)ARG0(arg); md = QTOS((Q)ARG1(arg));
2266: row = m->row; col = m->col; mat = m->body;
2267: wmat = (unsigned int **)almat(row,col+row);
2268: for ( i = 0; i < row; i++ ) {
2269: bzero((char *)wmat[i],(col+row)*sizeof(int));
2270: for ( j = 0; j < col; j++ )
2271: if ( q = (Q)mat[i][j] ) {
2272: t = (unsigned int)rem(NM(q),md);
2273: if ( SGN(q) < 0 )
2274: t = (md - t) % md;
2275: wmat[i][j] = t;
2276: }
2277: wmat[i][col+i] = 1;
2278: }
2279: status = gauss_elim_geninv_mod_swap(wmat,row,col,md,&invmat,&index);
2280: if ( status > 0 )
2281: *rp = 0;
2282: else {
2283: MKMAT(mat1,col,col);
2284: for ( i = 0, tmat = (Q **)mat1->body; i < col; i++ )
2285: for ( j = 0; j < col; j++ )
2286: UTOQ(invmat[i][j],tmat[i][j]);
2287: MKVECT(vect1,row);
2288: for ( i = 0, tvect = (Q *)vect1->body; i < row; i++ )
2289: STOQ(index[i],tvect[i]);
2290: MKNODE(node2,vect1,0); MKNODE(node1,mat1,node2); MKLIST(*rp,node1);
2291: }
2292: }
2293:
1.27 noro 2294: gauss_elim_geninv_mod_swap(mat,row,col,md,invmatp,indexp)
2295: unsigned int **mat;
2296: int row,col;
2297: unsigned int md;
2298: unsigned int ***invmatp;
2299: int **indexp;
1.1 noro 2300: {
2301: int i,j,k,inv,a,n,m;
2302: unsigned int *t,*pivot,*s;
2303: int *index;
2304: unsigned int **invmat;
2305:
2306: n = col; m = row+col;
2307: *indexp = index = (int *)MALLOC_ATOMIC(row*sizeof(int));
2308: for ( i = 0; i < row; i++ )
2309: index[i] = i;
2310: for ( j = 0; j < n; j++ ) {
2311: for ( i = j; i < row && !mat[i][j]; i++ );
2312: if ( i == row ) {
2313: *indexp = 0; *invmatp = 0; return 1;
2314: }
2315: if ( i != j ) {
2316: t = mat[i]; mat[i] = mat[j]; mat[j] = t;
2317: k = index[i]; index[i] = index[j]; index[j] = k;
2318: }
2319: pivot = mat[j];
2320: inv = (unsigned int)invm(pivot[j],md);
2321: for ( k = j; k < m; k++ )
2322: if ( pivot[k] )
2323: pivot[k] = (unsigned int)dmar(pivot[k],inv,0,md);
2324: for ( i = j+1; i < row; i++ ) {
2325: t = mat[i];
2326: if ( a = t[j] )
2327: for ( k = j, a = md - a; k < m; k++ )
2328: if ( pivot[k] )
2329: t[k] = dmar(pivot[k],a,t[k],md);
2330: }
2331: }
2332: for ( j = n-1; j >= 0; j-- ) {
2333: pivot = mat[j];
2334: for ( i = j-1; i >= 0; i-- ) {
2335: t = mat[i];
2336: if ( a = t[j] )
2337: for ( k = j, a = md - a; k < m; k++ )
2338: if ( pivot[k] )
2339: t[k] = dmar(pivot[k],a,t[k],md);
2340: }
2341: }
2342: *invmatp = invmat = (unsigned int **)almat(col,col);
1.27 noro 2343: for ( i = 0; i < col; i++ )
2344: for ( j = 0, s = invmat[i], t = mat[i]; j < col; j++ )
2345: s[j] = t[col+index[j]];
2346: return 0;
2347: }
2348:
2349: void Pgeninv_sf_swap(NODE arg,LIST *rp)
2350: {
2351: MAT m;
2352: GFS **mat,**tmat;
2353: Q *tvect;
2354: GFS q;
2355: int **wmat,**invmat;
2356: int *index;
2357: unsigned int t;
2358: int i,j,row,col,status;
2359: MAT mat1;
2360: VECT vect1;
2361: NODE node1,node2;
2362:
2363: asir_assert(ARG0(arg),O_MAT,"geninv_sf_swap");
2364: m = (MAT)ARG0(arg);
2365: row = m->row; col = m->col; mat = (GFS **)m->body;
2366: wmat = (int **)almat(row,col+row);
2367: for ( i = 0; i < row; i++ ) {
2368: bzero((char *)wmat[i],(col+row)*sizeof(int));
2369: for ( j = 0; j < col; j++ )
2370: if ( q = (GFS)mat[i][j] )
2371: wmat[i][j] = FTOIF(CONT(q));
2372: wmat[i][col+i] = _onesf();
2373: }
2374: status = gauss_elim_geninv_sf_swap(wmat,row,col,&invmat,&index);
2375: if ( status > 0 )
2376: *rp = 0;
2377: else {
2378: MKMAT(mat1,col,col);
2379: for ( i = 0, tmat = (GFS **)mat1->body; i < col; i++ )
2380: for ( j = 0; j < col; j++ )
2381: if ( t = invmat[i][j] ) {
2382: MKGFS(IFTOF(t),tmat[i][j]);
2383: }
2384: MKVECT(vect1,row);
2385: for ( i = 0, tvect = (Q *)vect1->body; i < row; i++ )
2386: STOQ(index[i],tvect[i]);
2387: MKNODE(node2,vect1,0); MKNODE(node1,mat1,node2); MKLIST(*rp,node1);
2388: }
2389: }
2390:
2391: int gauss_elim_geninv_sf_swap(int **mat,int row,int col,
2392: int ***invmatp,int **indexp)
2393: {
2394: int i,j,k,inv,a,n,m,u;
2395: int *t,*pivot,*s;
2396: int *index;
2397: int **invmat;
2398:
2399: n = col; m = row+col;
2400: *indexp = index = (int *)MALLOC_ATOMIC(row*sizeof(int));
2401: for ( i = 0; i < row; i++ )
2402: index[i] = i;
2403: for ( j = 0; j < n; j++ ) {
2404: for ( i = j; i < row && !mat[i][j]; i++ );
2405: if ( i == row ) {
2406: *indexp = 0; *invmatp = 0; return 1;
2407: }
2408: if ( i != j ) {
2409: t = mat[i]; mat[i] = mat[j]; mat[j] = t;
2410: k = index[i]; index[i] = index[j]; index[j] = k;
2411: }
2412: pivot = mat[j];
2413: inv = _invsf(pivot[j]);
2414: for ( k = j; k < m; k++ )
2415: if ( pivot[k] )
2416: pivot[k] = _mulsf(pivot[k],inv);
2417: for ( i = j+1; i < row; i++ ) {
2418: t = mat[i];
2419: if ( a = t[j] )
2420: for ( k = j, a = _chsgnsf(a); k < m; k++ )
2421: if ( pivot[k] ) {
2422: u = _mulsf(pivot[k],a);
2423: t[k] = _addsf(u,t[k]);
2424: }
2425: }
2426: }
2427: for ( j = n-1; j >= 0; j-- ) {
2428: pivot = mat[j];
2429: for ( i = j-1; i >= 0; i-- ) {
2430: t = mat[i];
2431: if ( a = t[j] )
2432: for ( k = j, a = _chsgnsf(a); k < m; k++ )
2433: if ( pivot[k] ) {
2434: u = _mulsf(pivot[k],a);
2435: t[k] = _addsf(u,t[k]);
2436: }
2437: }
2438: }
2439: *invmatp = invmat = (int **)almat(col,col);
1.1 noro 2440: for ( i = 0; i < col; i++ )
2441: for ( j = 0, s = invmat[i], t = mat[i]; j < col; j++ )
2442: s[j] = t[col+index[j]];
2443: return 0;
2444: }
2445:
2446: void _addn(N,N,N);
2447: int _subn(N,N,N);
2448: void _muln(N,N,N);
2449:
1.24 noro 2450: void inner_product_int(Q *a,Q *b,int n,Q *r)
1.1 noro 2451: {
2452: int la,lb,i;
2453: int sgn,sgn1;
2454: N wm,wma,sum,t;
2455:
2456: for ( la = lb = 0, i = 0; i < n; i++ ) {
2457: if ( a[i] )
2458: if ( DN(a[i]) )
2459: error("inner_product_int : invalid argument");
2460: else
2461: la = MAX(PL(NM(a[i])),la);
2462: if ( b[i] )
2463: if ( DN(b[i]) )
2464: error("inner_product_int : invalid argument");
2465: else
2466: lb = MAX(PL(NM(b[i])),lb);
2467: }
2468: sgn = 0;
2469: sum= NALLOC(la+lb+2);
2470: bzero((char *)sum,(la+lb+3)*sizeof(unsigned int));
2471: wm = NALLOC(la+lb+2);
2472: wma = NALLOC(la+lb+2);
2473: for ( i = 0; i < n; i++ ) {
2474: if ( !a[i] || !b[i] )
2475: continue;
2476: _muln(NM(a[i]),NM(b[i]),wm);
2477: sgn1 = SGN(a[i])*SGN(b[i]);
2478: if ( !sgn ) {
2479: sgn = sgn1;
2480: t = wm; wm = sum; sum = t;
2481: } else if ( sgn == sgn1 ) {
2482: _addn(sum,wm,wma);
2483: if ( !PL(wma) )
2484: sgn = 0;
2485: t = wma; wma = sum; sum = t;
2486: } else {
2487: /* sgn*sum+sgn1*wm = sgn*(sum-wm) */
2488: sgn *= _subn(sum,wm,wma);
2489: t = wma; wma = sum; sum = t;
2490: }
2491: }
2492: GC_free(wm);
2493: GC_free(wma);
2494: if ( !sgn ) {
2495: GC_free(sum);
2496: *r = 0;
2497: } else
2498: NTOQ(sum,sgn,*r);
2499: }
2500:
1.3 noro 2501: /* (k,l) element of a*b where a: .x n matrix, b: n x . integer matrix */
2502:
1.24 noro 2503: void inner_product_mat_int_mod(Q **a,int **b,int n,int k,int l,Q *r)
1.3 noro 2504: {
2505: int la,lb,i;
2506: int sgn,sgn1;
2507: N wm,wma,sum,t;
2508: Q aki;
2509: int bil,bilsgn;
2510: struct oN tn;
2511:
2512: for ( la = 0, i = 0; i < n; i++ ) {
2513: if ( aki = a[k][i] )
2514: if ( DN(aki) )
2515: error("inner_product_int : invalid argument");
2516: else
2517: la = MAX(PL(NM(aki)),la);
2518: }
2519: lb = 1;
2520: sgn = 0;
2521: sum= NALLOC(la+lb+2);
2522: bzero((char *)sum,(la+lb+3)*sizeof(unsigned int));
2523: wm = NALLOC(la+lb+2);
2524: wma = NALLOC(la+lb+2);
2525: for ( i = 0; i < n; i++ ) {
2526: if ( !(aki = a[k][i]) || !(bil = b[i][l]) )
2527: continue;
2528: tn.p = 1;
2529: if ( bil > 0 ) {
2530: tn.b[0] = bil; bilsgn = 1;
2531: } else {
2532: tn.b[0] = -bil; bilsgn = -1;
2533: }
2534: _muln(NM(aki),&tn,wm);
2535: sgn1 = SGN(aki)*bilsgn;
2536: if ( !sgn ) {
2537: sgn = sgn1;
2538: t = wm; wm = sum; sum = t;
2539: } else if ( sgn == sgn1 ) {
2540: _addn(sum,wm,wma);
2541: if ( !PL(wma) )
2542: sgn = 0;
2543: t = wma; wma = sum; sum = t;
2544: } else {
2545: /* sgn*sum+sgn1*wm = sgn*(sum-wm) */
2546: sgn *= _subn(sum,wm,wma);
2547: t = wma; wma = sum; sum = t;
2548: }
2549: }
2550: GC_free(wm);
2551: GC_free(wma);
2552: if ( !sgn ) {
2553: GC_free(sum);
2554: *r = 0;
2555: } else
2556: NTOQ(sum,sgn,*r);
2557: }
2558:
1.24 noro 2559: void Pmul_mat_vect_int(NODE arg,VECT *rp)
1.1 noro 2560: {
2561: MAT mat;
2562: VECT vect,r;
2563: int row,col,i;
2564:
2565: mat = (MAT)ARG0(arg);
2566: vect = (VECT)ARG1(arg);
2567: row = mat->row;
2568: col = mat->col;
2569: MKVECT(r,row);
1.24 noro 2570: for ( i = 0; i < row; i++ ) {
2571: inner_product_int((Q *)mat->body[i],(Q *)vect->body,col,(Q *)&r->body[i]);
2572: }
1.1 noro 2573: *rp = r;
2574: }
2575:
1.24 noro 2576: void Pnbpoly_up2(NODE arg,GF2N *rp)
1.1 noro 2577: {
2578: int m,type,ret;
2579: UP2 r;
2580:
2581: m = QTOS((Q)ARG0(arg));
2582: type = QTOS((Q)ARG1(arg));
2583: ret = generate_ONB_polynomial(&r,m,type);
2584: if ( ret == 0 )
2585: MKGF2N(r,*rp);
2586: else
2587: *rp = 0;
2588: }
2589:
1.24 noro 2590: void Px962_irredpoly_up2(NODE arg,GF2N *rp)
1.1 noro 2591: {
1.24 noro 2592: int m,ret,w;
1.1 noro 2593: GF2N prev;
2594: UP2 r;
2595:
2596: m = QTOS((Q)ARG0(arg));
2597: prev = (GF2N)ARG1(arg);
2598: if ( !prev ) {
2599: w = (m>>5)+1; NEWUP2(r,w); r->w = 0;
2600: bzero((char *)r->b,w*sizeof(unsigned int));
2601: } else {
2602: r = prev->body;
2603: if ( degup2(r) != m ) {
2604: w = (m>>5)+1; NEWUP2(r,w); r->w = 0;
2605: bzero((char *)r->b,w*sizeof(unsigned int));
2606: }
2607: }
1.24 noro 2608: ret = _generate_irreducible_polynomial(r,m);
1.1 noro 2609: if ( ret == 0 )
2610: MKGF2N(r,*rp);
2611: else
2612: *rp = 0;
2613: }
2614:
1.24 noro 2615: void Pirredpoly_up2(NODE arg,GF2N *rp)
1.1 noro 2616: {
1.24 noro 2617: int m,ret,w;
1.1 noro 2618: GF2N prev;
2619: UP2 r;
2620:
2621: m = QTOS((Q)ARG0(arg));
2622: prev = (GF2N)ARG1(arg);
2623: if ( !prev ) {
2624: w = (m>>5)+1; NEWUP2(r,w); r->w = 0;
2625: bzero((char *)r->b,w*sizeof(unsigned int));
2626: } else {
2627: r = prev->body;
2628: if ( degup2(r) != m ) {
2629: w = (m>>5)+1; NEWUP2(r,w); r->w = 0;
2630: bzero((char *)r->b,w*sizeof(unsigned int));
2631: }
2632: }
1.24 noro 2633: ret = _generate_good_irreducible_polynomial(r,m);
1.1 noro 2634: if ( ret == 0 )
2635: MKGF2N(r,*rp);
2636: else
2637: *rp = 0;
2638: }
2639:
1.26 noro 2640: void Pmat_swap_row_destructive(NODE arg, MAT *m)
2641: {
2642: int i1,i2;
2643: pointer *t;
2644: MAT mat;
2645:
2646: asir_assert(ARG0(arg),O_MAT,"mat_swap_row_destructive");
2647: asir_assert(ARG1(arg),O_N,"mat_swap_row_destructive");
2648: asir_assert(ARG2(arg),O_N,"mat_swap_row_destructive");
2649: mat = (MAT)ARG0(arg);
2650: i1 = QTOS((Q)ARG1(arg));
2651: i2 = QTOS((Q)ARG2(arg));
2652: if ( i1 < 0 || i2 < 0 || i1 >= mat->row || i2 >= mat->row )
2653: error("mat_swap_row_destructive : Out of range");
2654: t = mat->body[i1];
2655: mat->body[i1] = mat->body[i2];
2656: mat->body[i2] = t;
2657: *m = mat;
2658: }
2659:
2660: void Pmat_swap_col_destructive(NODE arg, MAT *m)
2661: {
2662: int j1,j2,i,n;
2663: pointer *mi;
2664: pointer t;
2665: MAT mat;
2666:
2667: asir_assert(ARG0(arg),O_MAT,"mat_swap_col_destructive");
2668: asir_assert(ARG1(arg),O_N,"mat_swap_col_destructive");
2669: asir_assert(ARG2(arg),O_N,"mat_swap_col_destructive");
2670: mat = (MAT)ARG0(arg);
2671: j1 = QTOS((Q)ARG1(arg));
2672: j2 = QTOS((Q)ARG2(arg));
2673: if ( j1 < 0 || j2 < 0 || j1 >= mat->col || j2 >= mat->col )
2674: error("mat_swap_col_destructive : Out of range");
2675: n = mat->row;
2676: for ( i = 0; i < n; i++ ) {
2677: mi = mat->body[i];
2678: t = mi[j1]; mi[j1] = mi[j2]; mi[j2] = t;
2679: }
2680: *m = mat;
2681: }
1.1 noro 2682: /*
2683: * f = type 'type' normal polynomial of degree m if exists
2684: * IEEE P1363 A.7.2
2685: *
2686: * return value : 0 --- exists
2687: * 1 --- does not exist
2688: * -1 --- failure (memory allocation error)
2689: */
2690:
2691: int generate_ONB_polynomial(UP2 *rp,int m,int type)
2692: {
2693: int i,r;
2694: int w;
2695: UP2 f,f0,f1,f2,t;
2696:
2697: w = (m>>5)+1;
2698: switch ( type ) {
2699: case 1:
2700: if ( !TypeT_NB_check(m,1) ) return 1;
2701: NEWUP2(f,w); *rp = f; f->w = w;
2702: /* set all the bits */
2703: for ( i = 0; i < w; i++ )
2704: f->b[i] = 0xffffffff;
2705: /* mask the top word if necessary */
2706: if ( r = (m+1)&31 )
2707: f->b[w-1] &= (1<<r)-1;
2708: return 0;
2709: break;
2710: case 2:
2711: if ( !TypeT_NB_check(m,2) ) return 1;
2712: NEWUP2(f,w); *rp = f;
2713: W_NEWUP2(f0,w);
2714: W_NEWUP2(f1,w);
2715: W_NEWUP2(f2,w);
2716:
2717: /* recursion for genrating Type II normal polynomial */
2718:
2719: /* f0 = 1, f1 = t+1 */
2720: f0->w = 1; f0->b[0] = 1;
2721: f1->w = 1; f1->b[0] = 3;
2722: for ( i = 2; i <= m; i++ ) {
2723: /* f2 = t*f1+f0 */
2724: _bshiftup2(f1,-1,f2);
2725: _addup2_destructive(f2,f0);
2726: /* cyclic change of the variables */
2727: t = f0; f0 = f1; f1 = f2; f2 = t;
2728: }
2729: _copyup2(f1,f);
2730: return 0;
2731: break;
2732: default:
2733: return -1;
2734: break;
2735: }
2736: }
2737:
2738: /*
2739: * f = an irreducible trinomial or pentanomial of degree d 'after' f
2740: * return value : 0 --- exists
2741: * 1 --- does not exist (exhaustion)
2742: */
2743:
2744: int _generate_irreducible_polynomial(UP2 f,int d)
2745: {
2746: int ret,i,j,k,nz,i0,j0,k0;
2747: int w;
2748: unsigned int *fd;
2749:
2750: /*
2751: * if f = x^d+x^i+1 then i0 <- i, j0 <- 0, k0 <-0.
2752: * if f = x^d+x^k+x^j+x^i+1 (k>j>i) then i0 <- i, j0 <- j, k0 <-k.
2753: * otherwise i0,j0,k0 is set to 0.
2754: */
2755:
2756: fd = f->b;
2757: w = (d>>5)+1;
2758: if ( f->w && (d==degup2(f)) ) {
2759: for ( nz = 0, i = d; i >= 0; i-- )
2760: if ( fd[i>>5]&(1<<(i&31)) ) nz++;
2761: switch ( nz ) {
2762: case 3:
2763: for ( i0 = 1; !(fd[i0>>5]&(1<<(i0&31))) ; i0++ );
2764: /* reset i0-th bit */
2765: fd[i0>>5] &= ~(1<<(i0&31));
2766: j0 = k0 = 0;
2767: break;
2768: case 5:
2769: for ( i0 = 1; !(fd[i0>>5]&(1<<(i0&31))) ; i0++ );
2770: /* reset i0-th bit */
2771: fd[i0>>5] &= ~(1<<(i0&31));
2772: for ( j0 = i0+1; !(fd[j0>>5]&(1<<(j0&31))) ; j0++ );
2773: /* reset j0-th bit */
2774: fd[j0>>5] &= ~(1<<(j0&31));
2775: for ( k0 = j0+1; !(fd[k0>>5]&(1<<(k0&31))) ; k0++ );
2776: /* reset k0-th bit */
2777: fd[k0>>5] &= ~(1<<(k0&31));
2778: break;
2779: default:
2780: f->w = 0; break;
2781: }
2782: } else
2783: f->w = 0;
2784:
2785: if ( !f->w ) {
2786: fd = f->b;
2787: f->w = w; fd[0] |= 1; fd[d>>5] |= (1<<(d&31));
2788: i0 = j0 = k0 = 0;
2789: }
2790: /* if j0 > 0 then f is already a pentanomial */
2791: if ( j0 > 0 ) goto PENTA;
2792:
2793: /* searching for an irreducible trinomial */
2794:
2795: for ( i = 1; 2*i <= d; i++ ) {
2796: /* skip the polynomials 'before' f */
2797: if ( i < i0 ) continue;
2798: if ( i == i0 ) { i0 = 0; continue; }
2799: /* set i-th bit */
2800: fd[i>>5] |= (1<<(i&31));
2801: ret = irredcheck_dddup2(f);
2802: if ( ret == 1 ) return 0;
2803: /* reset i-th bit */
2804: fd[i>>5] &= ~(1<<(i&31));
2805: }
2806:
2807: /* searching for an irreducible pentanomial */
2808: PENTA:
2809: for ( i = 1; i < d; i++ ) {
2810: /* skip the polynomials 'before' f */
2811: if ( i < i0 ) continue;
2812: if ( i == i0 ) i0 = 0;
2813: /* set i-th bit */
2814: fd[i>>5] |= (1<<(i&31));
2815: for ( j = i+1; j < d; j++ ) {
2816: /* skip the polynomials 'before' f */
2817: if ( j < j0 ) continue;
2818: if ( j == j0 ) j0 = 0;
2819: /* set j-th bit */
2820: fd[j>>5] |= (1<<(j&31));
2821: for ( k = j+1; k < d; k++ ) {
2822: /* skip the polynomials 'before' f */
2823: if ( k < k0 ) continue;
2824: else if ( k == k0 ) { k0 = 0; continue; }
2825: /* set k-th bit */
2826: fd[k>>5] |= (1<<(k&31));
2827: ret = irredcheck_dddup2(f);
2828: if ( ret == 1 ) return 0;
2829: /* reset k-th bit */
2830: fd[k>>5] &= ~(1<<(k&31));
2831: }
2832: /* reset j-th bit */
2833: fd[j>>5] &= ~(1<<(j&31));
2834: }
2835: /* reset i-th bit */
2836: fd[i>>5] &= ~(1<<(i&31));
2837: }
2838: /* exhausted */
2839: return 1;
2840: }
2841:
2842: /*
2843: * f = an irreducible trinomial or pentanomial of degree d 'after' f
2844: *
2845: * searching strategy:
2846: * trinomial x^d+x^i+1:
2847: * i is as small as possible.
2848: * trinomial x^d+x^i+x^j+x^k+1:
2849: * i is as small as possible.
2850: * For such i, j is as small as possible.
2851: * For such i and j, 'k' is as small as possible.
2852: *
2853: * return value : 0 --- exists
2854: * 1 --- does not exist (exhaustion)
2855: */
2856:
2857: int _generate_good_irreducible_polynomial(UP2 f,int d)
2858: {
2859: int ret,i,j,k,nz,i0,j0,k0;
2860: int w;
2861: unsigned int *fd;
2862:
2863: /*
2864: * if f = x^d+x^i+1 then i0 <- i, j0 <- 0, k0 <-0.
2865: * if f = x^d+x^k+x^j+x^i+1 (k>j>i) then i0 <- i, j0 <- j, k0 <-k.
2866: * otherwise i0,j0,k0 is set to 0.
2867: */
2868:
2869: fd = f->b;
2870: w = (d>>5)+1;
2871: if ( f->w && (d==degup2(f)) ) {
2872: for ( nz = 0, i = d; i >= 0; i-- )
2873: if ( fd[i>>5]&(1<<(i&31)) ) nz++;
2874: switch ( nz ) {
2875: case 3:
2876: for ( i0 = 1; !(fd[i0>>5]&(1<<(i0&31))) ; i0++ );
2877: /* reset i0-th bit */
2878: fd[i0>>5] &= ~(1<<(i0&31));
2879: j0 = k0 = 0;
2880: break;
2881: case 5:
2882: for ( i0 = 1; !(fd[i0>>5]&(1<<(i0&31))) ; i0++ );
2883: /* reset i0-th bit */
2884: fd[i0>>5] &= ~(1<<(i0&31));
2885: for ( j0 = i0+1; !(fd[j0>>5]&(1<<(j0&31))) ; j0++ );
2886: /* reset j0-th bit */
2887: fd[j0>>5] &= ~(1<<(j0&31));
2888: for ( k0 = j0+1; !(fd[k0>>5]&(1<<(k0&31))) ; k0++ );
2889: /* reset k0-th bit */
2890: fd[k0>>5] &= ~(1<<(k0&31));
2891: break;
2892: default:
2893: f->w = 0; break;
2894: }
2895: } else
2896: f->w = 0;
2897:
2898: if ( !f->w ) {
2899: fd = f->b;
2900: f->w = w; fd[0] |= 1; fd[d>>5] |= (1<<(d&31));
2901: i0 = j0 = k0 = 0;
2902: }
2903: /* if j0 > 0 then f is already a pentanomial */
2904: if ( j0 > 0 ) goto PENTA;
2905:
2906: /* searching for an irreducible trinomial */
2907:
2908: for ( i = 1; 2*i <= d; i++ ) {
2909: /* skip the polynomials 'before' f */
2910: if ( i < i0 ) continue;
2911: if ( i == i0 ) { i0 = 0; continue; }
2912: /* set i-th bit */
2913: fd[i>>5] |= (1<<(i&31));
2914: ret = irredcheck_dddup2(f);
2915: if ( ret == 1 ) return 0;
2916: /* reset i-th bit */
2917: fd[i>>5] &= ~(1<<(i&31));
2918: }
2919:
2920: /* searching for an irreducible pentanomial */
2921: PENTA:
2922: for ( i = 3; i < d; i++ ) {
2923: /* skip the polynomials 'before' f */
2924: if ( i < i0 ) continue;
2925: if ( i == i0 ) i0 = 0;
2926: /* set i-th bit */
2927: fd[i>>5] |= (1<<(i&31));
2928: for ( j = 2; j < i; j++ ) {
2929: /* skip the polynomials 'before' f */
2930: if ( j < j0 ) continue;
2931: if ( j == j0 ) j0 = 0;
2932: /* set j-th bit */
2933: fd[j>>5] |= (1<<(j&31));
2934: for ( k = 1; k < j; k++ ) {
2935: /* skip the polynomials 'before' f */
2936: if ( k < k0 ) continue;
2937: else if ( k == k0 ) { k0 = 0; continue; }
2938: /* set k-th bit */
2939: fd[k>>5] |= (1<<(k&31));
2940: ret = irredcheck_dddup2(f);
2941: if ( ret == 1 ) return 0;
2942: /* reset k-th bit */
2943: fd[k>>5] &= ~(1<<(k&31));
2944: }
2945: /* reset j-th bit */
2946: fd[j>>5] &= ~(1<<(j&31));
2947: }
2948: /* reset i-th bit */
2949: fd[i>>5] &= ~(1<<(i&31));
2950: }
2951: /* exhausted */
2952: return 1;
1.3 noro 2953: }
2954:
1.24 noro 2955: void printqmat(Q **mat,int row,int col)
1.3 noro 2956: {
2957: int i,j;
2958:
2959: for ( i = 0; i < row; i++ ) {
2960: for ( j = 0; j < col; j++ ) {
1.8 noro 2961: printnum((Num)mat[i][j]); printf(" ");
1.3 noro 2962: }
2963: printf("\n");
2964: }
2965: }
2966:
1.24 noro 2967: void printimat(int **mat,int row,int col)
1.3 noro 2968: {
2969: int i,j;
2970:
2971: for ( i = 0; i < row; i++ ) {
2972: for ( j = 0; j < col; j++ ) {
2973: printf("%d ",mat[i][j]);
2974: }
2975: printf("\n");
2976: }
1.36 noro 2977: }
2978:
2979: void Pnd_det(NODE arg,P *rp)
2980: {
1.37 noro 2981: if ( argc(arg) == 1 )
2982: nd_det(0,ARG0(arg),rp);
2983: else
2984: nd_det(QTOS((Q)ARG1(arg)),ARG0(arg),rp);
1.1 noro 2985: }