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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: *
1.47 ! noro 48: * $OpenXM: OpenXM_contrib2/asir2000/builtin/array.c,v 1.46 2005/02/08 18:06:05 saito 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)
1.47 ! noro 879: RN : a vector of length rank(A) indicating useful rows
! 880:
1.1 noro 881: B[I] <-> x_{R[I]}+B[I][0]x_{C[0]}+B[I][1]x_{C[1]}+...
882: */
883:
1.24 noro 884: void Pgeneric_gauss_elim_mod(NODE arg,LIST *rp)
1.1 noro 885: {
886: NODE n0;
887: MAT m,mat;
1.47 ! noro 888: VECT rind,cind,rnum;
1.1 noro 889: Q **tmat;
1.47 ! noro 890: int **wmat,**row0;
! 891: Q *rib,*cib,*rnb;
! 892: int *colstat,*p;
1.1 noro 893: Q q;
1.24 noro 894: int md,i,j,k,l,row,col,t,rank;
1.1 noro 895:
896: asir_assert(ARG0(arg),O_MAT,"generic_gauss_elim_mod");
897: asir_assert(ARG1(arg),O_N,"generic_gauss_elim_mod");
898: m = (MAT)ARG0(arg); md = QTOS((Q)ARG1(arg));
899: row = m->row; col = m->col; tmat = (Q **)m->body;
900: wmat = (int **)almat(row,col);
1.47 ! noro 901:
! 902: row0 = (int **)ALLOCA(row*sizeof(int *));
! 903: for ( i = 0; i < row; i++ ) row0[i] = wmat[i];
! 904:
1.1 noro 905: colstat = (int *)MALLOC_ATOMIC(col*sizeof(int));
906: for ( i = 0; i < row; i++ )
907: for ( j = 0; j < col; j++ )
908: if ( q = (Q)tmat[i][j] ) {
909: t = rem(NM(q),md);
910: if ( t && SGN(q) < 0 )
911: t = (md - t) % md;
912: wmat[i][j] = t;
913: } else
914: wmat[i][j] = 0;
915: rank = generic_gauss_elim_mod(wmat,row,col,md,colstat);
916:
1.47 ! noro 917: MKVECT(rnum,rank);
! 918: rnb = (Q *)rnum->body;
! 919: for ( i = 0; i < rank; i++ )
! 920: for ( j = 0, p = wmat[i]; j < row; j++ )
! 921: if ( p == row0[j] )
! 922: STOQ(j,rnb[i]);
! 923:
1.1 noro 924: MKMAT(mat,rank,col-rank);
925: tmat = (Q **)mat->body;
926: for ( i = 0; i < rank; i++ )
927: for ( j = k = 0; j < col; j++ )
928: if ( !colstat[j] ) {
929: UTOQ(wmat[i][j],tmat[i][k]); k++;
930: }
931:
932: MKVECT(rind,rank);
933: MKVECT(cind,col-rank);
934: rib = (Q *)rind->body; cib = (Q *)cind->body;
935: for ( j = k = l = 0; j < col; j++ )
936: if ( colstat[j] ) {
937: STOQ(j,rib[k]); k++;
938: } else {
939: STOQ(j,cib[l]); l++;
940: }
1.47 ! noro 941: n0 = mknode(4,mat,rind,cind,rnum);
1.1 noro 942: MKLIST(*rp,n0);
943: }
944:
1.24 noro 945: void Pleqm(NODE arg,VECT *rp)
1.1 noro 946: {
947: MAT m;
948: VECT vect;
949: pointer **mat;
950: Q *v;
951: Q q;
952: int **wmat;
953: int md,i,j,row,col,t,n,status;
954:
955: asir_assert(ARG0(arg),O_MAT,"leqm");
956: asir_assert(ARG1(arg),O_N,"leqm");
957: m = (MAT)ARG0(arg); md = QTOS((Q)ARG1(arg));
958: row = m->row; col = m->col; mat = m->body;
959: wmat = (int **)almat(row,col);
960: for ( i = 0; i < row; i++ )
961: for ( j = 0; j < col; j++ )
962: if ( q = (Q)mat[i][j] ) {
963: t = rem(NM(q),md);
964: if ( SGN(q) < 0 )
965: t = (md - t) % md;
966: wmat[i][j] = t;
967: } else
968: wmat[i][j] = 0;
969: status = gauss_elim_mod(wmat,row,col,md);
970: if ( status < 0 )
971: *rp = 0;
972: else if ( status > 0 )
973: *rp = (VECT)ONE;
974: else {
975: n = col - 1;
976: MKVECT(vect,n);
977: for ( i = 0, v = (Q *)vect->body; i < n; i++ ) {
978: t = (md-wmat[i][n])%md; STOQ(t,v[i]);
979: }
980: *rp = vect;
981: }
982: }
983:
1.24 noro 984: int gauss_elim_mod(int **mat,int row,int col,int md)
1.1 noro 985: {
986: int i,j,k,inv,a,n;
987: int *t,*pivot;
988:
989: n = col - 1;
990: for ( j = 0; j < n; j++ ) {
991: for ( i = j; i < row && !mat[i][j]; i++ );
992: if ( i == row )
993: return 1;
994: if ( i != j ) {
995: t = mat[i]; mat[i] = mat[j]; mat[j] = t;
996: }
997: pivot = mat[j];
998: inv = invm(pivot[j],md);
999: for ( k = j; k <= n; k++ ) {
1000: /* pivot[k] = dmar(pivot[k],inv,0,md); */
1001: DMAR(pivot[k],inv,0,md,pivot[k])
1002: }
1003: for ( i = 0; i < row; i++ ) {
1004: t = mat[i];
1005: if ( i != j && (a = t[j]) )
1006: for ( k = j, a = md - a; k <= n; k++ ) {
1.8 noro 1007: unsigned int tk;
1.1 noro 1008: /* t[k] = dmar(pivot[k],a,t[k],md); */
1.8 noro 1009: DMAR(pivot[k],a,t[k],md,tk)
1010: t[k] = tk;
1.1 noro 1011: }
1012: }
1013: }
1014: for ( i = n; i < row && !mat[i][n]; i++ );
1015: if ( i == row )
1016: return 0;
1017: else
1018: return -1;
1019: }
1020:
1.4 noro 1021: struct oEGT eg_mod,eg_elim,eg_elim1,eg_elim2,eg_chrem,eg_gschk,eg_intrat,eg_symb;
1.31 noro 1022: struct oEGT eg_conv;
1.1 noro 1023:
1.24 noro 1024: int generic_gauss_elim(MAT mat,MAT *nm,Q *dn,int **rindp,int **cindp)
1.1 noro 1025: {
1026: int **wmat;
1027: Q **bmat;
1028: N **tmat;
1029: Q *bmi;
1030: N *tmi;
1031: Q q;
1032: int *wmi;
1033: int *colstat,*wcolstat,*rind,*cind;
1034: int row,col,ind,md,i,j,k,l,t,t1,rank,rank0,inv;
1035: N m1,m2,m3,s,u;
1036: MAT r,crmat;
1037: struct oEGT tmp0,tmp1;
1038: struct oEGT eg_mod_split,eg_elim_split,eg_chrem_split;
1039: struct oEGT eg_intrat_split,eg_gschk_split;
1040: int ret;
1041:
1042: init_eg(&eg_mod_split); init_eg(&eg_chrem_split);
1043: init_eg(&eg_elim_split); init_eg(&eg_intrat_split);
1044: init_eg(&eg_gschk_split);
1045: bmat = (Q **)mat->body;
1046: row = mat->row; col = mat->col;
1047: wmat = (int **)almat(row,col);
1048: colstat = (int *)MALLOC_ATOMIC(col*sizeof(int));
1049: wcolstat = (int *)MALLOC_ATOMIC(col*sizeof(int));
1050: for ( ind = 0; ; ind++ ) {
1.11 noro 1051: if ( DP_Print ) {
1.2 noro 1052: fprintf(asir_out,"."); fflush(asir_out);
1053: }
1.12 noro 1054: md = get_lprime(ind);
1.1 noro 1055: get_eg(&tmp0);
1056: for ( i = 0; i < row; i++ )
1057: for ( j = 0, bmi = bmat[i], wmi = wmat[i]; j < col; j++ )
1058: if ( q = (Q)bmi[j] ) {
1059: t = rem(NM(q),md);
1060: if ( t && SGN(q) < 0 )
1061: t = (md - t) % md;
1062: wmi[j] = t;
1063: } else
1064: wmi[j] = 0;
1065: get_eg(&tmp1);
1066: add_eg(&eg_mod,&tmp0,&tmp1);
1067: add_eg(&eg_mod_split,&tmp0,&tmp1);
1068: get_eg(&tmp0);
1069: rank = generic_gauss_elim_mod(wmat,row,col,md,wcolstat);
1070: get_eg(&tmp1);
1071: add_eg(&eg_elim,&tmp0,&tmp1);
1072: add_eg(&eg_elim_split,&tmp0,&tmp1);
1073: if ( !ind ) {
1074: RESET:
1075: UTON(md,m1);
1076: rank0 = rank;
1077: bcopy(wcolstat,colstat,col*sizeof(int));
1078: MKMAT(crmat,rank,col-rank);
1079: MKMAT(r,rank,col-rank); *nm = r;
1080: tmat = (N **)crmat->body;
1081: for ( i = 0; i < rank; i++ )
1082: for ( j = k = 0, tmi = tmat[i], wmi = wmat[i]; j < col; j++ )
1083: if ( !colstat[j] ) {
1084: UTON(wmi[j],tmi[k]); k++;
1085: }
1086: } else {
1087: if ( rank < rank0 ) {
1.11 noro 1088: if ( DP_Print ) {
1.1 noro 1089: fprintf(asir_out,"lower rank matrix; continuing...\n");
1.2 noro 1090: fflush(asir_out);
1091: }
1.1 noro 1092: continue;
1093: } else if ( rank > rank0 ) {
1.11 noro 1094: if ( DP_Print ) {
1.1 noro 1095: fprintf(asir_out,"higher rank matrix; resetting...\n");
1.2 noro 1096: fflush(asir_out);
1097: }
1.1 noro 1098: goto RESET;
1099: } else {
1100: for ( j = 0; (j<col) && (colstat[j]==wcolstat[j]); j++ );
1101: if ( j < col ) {
1.11 noro 1102: if ( DP_Print ) {
1.1 noro 1103: fprintf(asir_out,"inconsitent colstat; resetting...\n");
1.2 noro 1104: fflush(asir_out);
1105: }
1.1 noro 1106: goto RESET;
1107: }
1108: }
1109:
1110: get_eg(&tmp0);
1111: inv = invm(rem(m1,md),md);
1112: UTON(md,m2); muln(m1,m2,&m3);
1113: for ( i = 0; i < rank; i++ )
1114: for ( j = k = 0, tmi = tmat[i], wmi = wmat[i]; j < col; j++ )
1115: if ( !colstat[j] ) {
1116: if ( tmi[k] ) {
1117: /* f3 = f1+m1*(m1 mod m2)^(-1)*(f2 - f1 mod m2) */
1118: t = rem(tmi[k],md);
1119: if ( wmi[j] >= t )
1120: t = wmi[j]-t;
1121: else
1122: t = md-(t-wmi[j]);
1123: DMAR(t,inv,0,md,t1)
1124: UTON(t1,u);
1125: muln(m1,u,&s);
1126: addn(tmi[k],s,&u); tmi[k] = u;
1127: } else if ( wmi[j] ) {
1128: /* f3 = m1*(m1 mod m2)^(-1)*f2 */
1129: DMAR(wmi[j],inv,0,md,t)
1130: UTON(t,u);
1131: muln(m1,u,&s); tmi[k] = s;
1132: }
1133: k++;
1134: }
1135: m1 = m3;
1136: get_eg(&tmp1);
1137: add_eg(&eg_chrem,&tmp0,&tmp1);
1138: add_eg(&eg_chrem_split,&tmp0,&tmp1);
1139:
1140: get_eg(&tmp0);
1.38 noro 1141: if ( ind % F4_INTRAT_PERIOD )
1.13 noro 1142: ret = 0;
1143: else
1144: ret = intmtoratm(crmat,m1,*nm,dn);
1.1 noro 1145: get_eg(&tmp1);
1146: add_eg(&eg_intrat,&tmp0,&tmp1);
1147: add_eg(&eg_intrat_split,&tmp0,&tmp1);
1148: if ( ret ) {
1149: *rindp = rind = (int *)MALLOC_ATOMIC(rank*sizeof(int));
1150: *cindp = cind = (int *)MALLOC_ATOMIC((col-rank)*sizeof(int));
1151: for ( j = k = l = 0; j < col; j++ )
1152: if ( colstat[j] )
1153: rind[k++] = j;
1154: else
1155: cind[l++] = j;
1156: get_eg(&tmp0);
1.3 noro 1157: if ( gensolve_check(mat,*nm,*dn,rind,cind) ) {
1158: get_eg(&tmp1);
1159: add_eg(&eg_gschk,&tmp0,&tmp1);
1160: add_eg(&eg_gschk_split,&tmp0,&tmp1);
1.11 noro 1161: if ( DP_Print ) {
1.3 noro 1162: print_eg("Mod",&eg_mod_split);
1163: print_eg("Elim",&eg_elim_split);
1164: print_eg("ChRem",&eg_chrem_split);
1165: print_eg("IntRat",&eg_intrat_split);
1166: print_eg("Check",&eg_gschk_split);
1167: fflush(asir_out);
1168: }
1169: return rank;
1170: }
1171: }
1172: }
1173: }
1174: }
1175:
1.24 noro 1176: int generic_gauss_elim_hensel(MAT mat,MAT *nmmat,Q *dn,int **rindp,int **cindp)
1.3 noro 1177: {
1178: MAT bmat,xmat;
1179: Q **a0,**a,**b,**x,**nm;
1180: Q *ai,*bi,*xi;
1181: int row,col;
1182: int **w;
1183: int *wi;
1184: int **wc;
1185: Q mdq,q,s,u;
1186: N tn;
1187: int ind,md,i,j,k,l,li,ri,rank;
1188: unsigned int t;
1189: int *cinfo,*rinfo;
1190: int *rind,*cind;
1191: int count;
1.41 noro 1192: int ret;
1193: struct oEGT eg_mul,eg_inv,eg_intrat,eg_check,tmp0,tmp1;
1.39 noro 1194: int period;
1.44 noro 1195: int *wx,*ptr;
1196: int wxsize,nsize;
1197: N wn;
1198: Q wq;
1.3 noro 1199:
1200: a0 = (Q **)mat->body;
1201: row = mat->row; col = mat->col;
1202: w = (int **)almat(row,col);
1203: for ( ind = 0; ; ind++ ) {
1.12 noro 1204: md = get_lprime(ind);
1.3 noro 1205: STOQ(md,mdq);
1206: for ( i = 0; i < row; i++ )
1207: for ( j = 0, ai = a0[i], wi = w[i]; j < col; j++ )
1208: if ( q = (Q)ai[j] ) {
1209: t = rem(NM(q),md);
1210: if ( t && SGN(q) < 0 )
1211: t = (md - t) % md;
1212: wi[j] = t;
1213: } else
1214: wi[j] = 0;
1215:
1.27 noro 1216: rank = find_lhs_and_lu_mod((unsigned int **)w,row,col,md,&rinfo,&cinfo);
1.3 noro 1217: a = (Q **)almat_pointer(rank,rank); /* lhs mat */
1218: MKMAT(bmat,rank,col-rank); b = (Q **)bmat->body; /* lhs mat */
1219: for ( j = li = ri = 0; j < col; j++ )
1220: if ( cinfo[j] ) {
1221: /* the column is in lhs */
1222: for ( i = 0; i < rank; i++ ) {
1223: w[i][li] = w[i][j];
1224: a[i][li] = a0[rinfo[i]][j];
1225: }
1226: li++;
1227: } else {
1228: /* the column is in rhs */
1229: for ( i = 0; i < rank; i++ )
1230: b[i][ri] = a0[rinfo[i]][j];
1231: ri++;
1232: }
1233:
1234: /* solve Ax+B=0; A: rank x rank, B: rank x ri */
1235: MKMAT(xmat,rank,ri); x = (Q **)(xmat)->body;
1236: MKMAT(*nmmat,rank,ri); nm = (Q **)(*nmmat)->body;
1237: /* use the right part of w as work area */
1238: /* ri = col - rank */
1239: wc = (int **)almat(rank,ri);
1240: for ( i = 0; i < rank; i++ )
1241: wc[i] = w[i]+rank;
1242: *rindp = rind = (int *)MALLOC_ATOMIC(rank*sizeof(int));
1243: *cindp = cind = (int *)MALLOC_ATOMIC((ri)*sizeof(int));
1244:
1245: init_eg(&eg_mul); init_eg(&eg_inv);
1.41 noro 1246: init_eg(&eg_check); init_eg(&eg_intrat);
1.39 noro 1247: period = F4_INTRAT_PERIOD;
1.44 noro 1248: nsize = period;
1249: wxsize = rank*ri*nsize;
1250: wx = (int *)MALLOC_ATOMIC(wxsize*sizeof(int));
1251: for ( i = 0; i < wxsize; i++ ) wx[i] = 0;
1252: for ( q = ONE, count = 0; ; ) {
1.42 noro 1253: if ( DP_Print > 3 )
1.41 noro 1254: fprintf(stderr,"o");
1.3 noro 1255: /* wc = -b mod md */
1.44 noro 1256: get_eg(&tmp0);
1.3 noro 1257: for ( i = 0; i < rank; i++ )
1258: for ( j = 0, bi = b[i], wi = wc[i]; j < ri; j++ )
1259: if ( u = (Q)bi[j] ) {
1260: t = rem(NM(u),md);
1261: if ( t && SGN(u) > 0 )
1262: t = (md - t) % md;
1263: wi[j] = t;
1264: } else
1265: wi[j] = 0;
1.44 noro 1266: /* wc = A^(-1)wc; wc is not normalized */
1267: solve_by_lu_mod(w,rank,md,wc,ri,0);
1268: /* wx += q*wc */
1269: ptr = wx;
1270: for ( i = 0; i < rank; i++ )
1271: for ( j = 0, wi = wc[i]; j < ri; j++ ) {
1272: if ( wi[j] )
1273: muln_1(BD(NM(q)),PL(NM(q)),wi[j],ptr);
1274: ptr += nsize;
1275: }
1276: count++;
1.1 noro 1277: get_eg(&tmp1);
1.3 noro 1278: add_eg(&eg_inv,&tmp0,&tmp1);
1279: get_eg(&tmp0);
1280: for ( i = 0; i < rank; i++ )
1281: for ( j = 0; j < ri; j++ ) {
1282: inner_product_mat_int_mod(a,wc,rank,i,j,&u);
1283: addq(b[i][j],u,&s);
1284: if ( s ) {
1285: t = divin(NM(s),md,&tn);
1286: if ( t )
1287: error("generic_gauss_elim_hensel:incosistent");
1288: NTOQ(tn,SGN(s),b[i][j]);
1289: } else
1290: b[i][j] = 0;
1291: }
1292: get_eg(&tmp1);
1293: add_eg(&eg_mul,&tmp0,&tmp1);
1294: /* q = q*md */
1295: mulq(q,mdq,&u); q = u;
1.44 noro 1296: if ( count == period ) {
1.41 noro 1297: get_eg(&tmp0);
1.44 noro 1298: ptr = wx;
1299: for ( i = 0; i < rank; i++ )
1300: for ( j = 0, xi = x[i]; j < ri;
1301: j++, ptr += nsize ) {
1302: for ( k = nsize-1; k >= 0 && !ptr[k]; k-- );
1303: if ( k >= 0 ) {
1304: wn = NALLOC(k+1);
1305: PL(wn) = k+1;
1306: for ( l = 0; l <= k; l++ ) BD(wn)[l] = (unsigned int)ptr[l];
1307: NTOQ(wn,1,wq);
1308: subq(xi[j],wq,&u); xi[j] = u;
1309: }
1310: }
1.41 noro 1311: ret = intmtoratm_q(xmat,NM(q),*nmmat,dn);
1312: get_eg(&tmp1); add_eg(&eg_intrat,&tmp0,&tmp1);
1313: if ( ret ) {
1.39 noro 1314: for ( j = k = l = 0; j < col; j++ )
1315: if ( cinfo[j] )
1316: rind[k++] = j;
1317: else
1318: cind[l++] = j;
1.41 noro 1319: get_eg(&tmp0);
1320: ret = gensolve_check(mat,*nmmat,*dn,rind,cind);
1321: get_eg(&tmp1); add_eg(&eg_check,&tmp0,&tmp1);
1322: if ( ret ) {
1.42 noro 1323: if ( DP_Print > 3 ) {
1.40 noro 1324: fprintf(stderr,"\n");
1325: print_eg("INV",&eg_inv);
1326: print_eg("MUL",&eg_mul);
1.41 noro 1327: print_eg("INTRAT",&eg_intrat);
1328: print_eg("CHECK",&eg_check);
1.40 noro 1329: fflush(asir_out);
1330: }
1.39 noro 1331: return rank;
1332: }
1.44 noro 1333: } else {
1334: period = period*3/2;
1335: count = 0;
1336: nsize += period;
1337: wxsize += rank*ri*nsize;
1338: wx = (int *)REALLOC(wx,wxsize*sizeof(int));
1339: for ( i = 0; i < wxsize; i++ ) wx[i] = 0;
1340: }
1.41 noro 1341: }
1.1 noro 1342: }
1343: }
1344: }
1345:
1346: int f4_nocheck;
1347:
1.24 noro 1348: int gensolve_check(MAT mat,MAT nm,Q dn,int *rind,int *cind)
1.1 noro 1349: {
1350: int row,col,rank,clen,i,j,k,l;
1.24 noro 1351: Q s,t;
1.1 noro 1352: Q *w;
1353: Q *mati,*nmk;
1354:
1355: if ( f4_nocheck )
1356: return 1;
1357: row = mat->row; col = mat->col;
1358: rank = nm->row; clen = nm->col;
1359: w = (Q *)MALLOC(clen*sizeof(Q));
1360: for ( i = 0; i < row; i++ ) {
1361: mati = (Q *)mat->body[i];
1362: #if 1
1363: bzero(w,clen*sizeof(Q));
1364: for ( k = 0; k < rank; k++ )
1365: for ( l = 0, nmk = (Q *)nm->body[k]; l < clen; l++ ) {
1366: mulq(mati[rind[k]],nmk[l],&t);
1367: addq(w[l],t,&s); w[l] = s;
1368: }
1369: for ( j = 0; j < clen; j++ ) {
1370: mulq(dn,mati[cind[j]],&t);
1371: if ( cmpq(w[j],t) )
1372: break;
1373: }
1374: #else
1375: for ( j = 0; j < clen; j++ ) {
1376: for ( k = 0, s = 0; k < rank; k++ ) {
1377: mulq(mati[rind[k]],nm->body[k][j],&t);
1378: addq(s,t,&u); s = u;
1379: }
1380: mulq(dn,mati[cind[j]],&t);
1381: if ( cmpq(s,t) )
1382: break;
1383: }
1384: #endif
1385: if ( j != clen )
1386: break;
1387: }
1388: if ( i != row )
1389: return 0;
1390: else
1391: return 1;
1392: }
1393:
1394: /* assuming 0 < c < m */
1395:
1.24 noro 1396: int inttorat(N c,N m,N b,int *sgnp,N *nmp,N *dnp)
1.1 noro 1397: {
1.24 noro 1398: Q qq,t,u1,v1,r1;
1399: N q,u2,v2,r2;
1.1 noro 1400:
1401: u1 = 0; v1 = ONE; u2 = m; v2 = c;
1402: while ( cmpn(v2,b) >= 0 ) {
1403: divn(u2,v2,&q,&r2); u2 = v2; v2 = r2;
1404: NTOQ(q,1,qq); mulq(qq,v1,&t); subq(u1,t,&r1); u1 = v1; v1 = r1;
1405: }
1406: if ( cmpn(NM(v1),b) >= 0 )
1407: return 0;
1408: else {
1409: *nmp = v2;
1410: *dnp = NM(v1);
1411: *sgnp = SGN(v1);
1412: return 1;
1413: }
1414: }
1415:
1416: /* mat->body = N ** */
1417:
1.24 noro 1418: int intmtoratm(MAT mat,N md,MAT nm,Q *dn)
1.1 noro 1419: {
1420: N t,s,b;
1.24 noro 1421: Q dn0,dn1,nm1,q;
1.1 noro 1422: int i,j,k,l,row,col;
1423: Q **rmat;
1424: N **tmat;
1425: N *tmi;
1426: Q *nmk;
1427: N u,unm,udn;
1428: int sgn,ret;
1429:
1.3 noro 1430: if ( UNIN(md) )
1431: return 0;
1.1 noro 1432: row = mat->row; col = mat->col;
1433: bshiftn(md,1,&t);
1434: isqrt(t,&s);
1435: bshiftn(s,64,&b);
1436: if ( !b )
1437: b = ONEN;
1438: dn0 = ONE;
1439: tmat = (N **)mat->body;
1440: rmat = (Q **)nm->body;
1441: for ( i = 0; i < row; i++ )
1442: for ( j = 0, tmi = tmat[i]; j < col; j++ )
1443: if ( tmi[j] ) {
1444: muln(tmi[j],NM(dn0),&s);
1445: remn(s,md,&u);
1446: ret = inttorat(u,md,b,&sgn,&unm,&udn);
1447: if ( !ret )
1448: return 0;
1449: else {
1450: NTOQ(unm,sgn,nm1);
1451: NTOQ(udn,1,dn1);
1452: if ( !UNIQ(dn1) ) {
1453: for ( k = 0; k < i; k++ )
1454: for ( l = 0, nmk = rmat[k]; l < col; l++ ) {
1455: mulq(nmk[l],dn1,&q); nmk[l] = q;
1456: }
1457: for ( l = 0, nmk = rmat[i]; l < j; l++ ) {
1458: mulq(nmk[l],dn1,&q); nmk[l] = q;
1459: }
1460: }
1461: rmat[i][j] = nm1;
1462: mulq(dn0,dn1,&q); dn0 = q;
1463: }
1464: }
1465: *dn = dn0;
1466: return 1;
1467: }
1468:
1.3 noro 1469: /* mat->body = Q ** */
1470:
1.24 noro 1471: int intmtoratm_q(MAT mat,N md,MAT nm,Q *dn)
1.3 noro 1472: {
1473: N t,s,b;
1.24 noro 1474: Q dn0,dn1,nm1,q;
1.3 noro 1475: int i,j,k,l,row,col;
1476: Q **rmat;
1477: Q **tmat;
1478: Q *tmi;
1479: Q *nmk;
1480: N u,unm,udn;
1481: int sgn,ret;
1482:
1483: if ( UNIN(md) )
1484: return 0;
1485: row = mat->row; col = mat->col;
1486: bshiftn(md,1,&t);
1487: isqrt(t,&s);
1488: bshiftn(s,64,&b);
1489: if ( !b )
1490: b = ONEN;
1491: dn0 = ONE;
1492: tmat = (Q **)mat->body;
1493: rmat = (Q **)nm->body;
1494: for ( i = 0; i < row; i++ )
1495: for ( j = 0, tmi = tmat[i]; j < col; j++ )
1496: if ( tmi[j] ) {
1497: muln(NM(tmi[j]),NM(dn0),&s);
1498: remn(s,md,&u);
1499: ret = inttorat(u,md,b,&sgn,&unm,&udn);
1500: if ( !ret )
1501: return 0;
1502: else {
1503: if ( SGN(tmi[j])<0 )
1504: sgn = -sgn;
1505: NTOQ(unm,sgn,nm1);
1506: NTOQ(udn,1,dn1);
1507: if ( !UNIQ(dn1) ) {
1508: for ( k = 0; k < i; k++ )
1509: for ( l = 0, nmk = rmat[k]; l < col; l++ ) {
1510: mulq(nmk[l],dn1,&q); nmk[l] = q;
1511: }
1512: for ( l = 0, nmk = rmat[i]; l < j; l++ ) {
1513: mulq(nmk[l],dn1,&q); nmk[l] = q;
1514: }
1515: }
1516: rmat[i][j] = nm1;
1517: mulq(dn0,dn1,&q); dn0 = q;
1518: }
1519: }
1520: *dn = dn0;
1521: return 1;
1522: }
1523:
1.4 noro 1524: #define ONE_STEP1 if ( zzz = *s ) { DMAR(zzz,hc,*tj,md,*tj) } tj++; s++;
1525:
1.24 noro 1526: void reduce_reducers_mod(int **mat,int row,int col,int md)
1.4 noro 1527: {
1528: int i,j,k,l,hc,zzz;
1529: int *t,*s,*tj,*ind;
1530:
1531: /* reduce the reducers */
1532: ind = (int *)ALLOCA(row*sizeof(int));
1533: for ( i = 0; i < row; i++ ) {
1534: t = mat[i];
1535: for ( j = 0; j < col && !t[j]; j++ );
1536: /* register the position of the head term */
1537: ind[i] = j;
1538: for ( l = i-1; l >= 0; l-- ) {
1539: /* reduce mat[i] by mat[l] */
1540: if ( hc = t[ind[l]] ) {
1541: /* mat[i] = mat[i]-hc*mat[l] */
1542: j = ind[l];
1543: s = mat[l]+j;
1544: tj = t+j;
1545: hc = md-hc;
1546: k = col-j;
1547: for ( ; k >= 64; k -= 64 ) {
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: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
1552: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
1553: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
1554: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
1555: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
1556: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
1557: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
1558: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
1559: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
1560: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
1561: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
1562: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
1563: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
1564: }
1.16 noro 1565: for ( ; k > 0; k-- ) {
1.4 noro 1566: if ( zzz = *s ) { DMAR(zzz,hc,*tj,md,*tj) } tj++; s++;
1567: }
1568: }
1569: }
1570: }
1571: }
1572:
1573: /*
1574: mat[i] : reducers (i=0,...,nred-1)
1575: spolys (i=nred,...,row-1)
1576: mat[0] < mat[1] < ... < mat[nred-1] w.r.t the term order
1577: 1. reduce the reducers
1578: 2. reduce spolys by the reduced reducers
1579: */
1580:
1.24 noro 1581: void pre_reduce_mod(int **mat,int row,int col,int nred,int md)
1.4 noro 1582: {
1583: int i,j,k,l,hc,inv;
1584: int *t,*s,*tk,*ind;
1585:
1586: #if 1
1587: /* reduce the reducers */
1588: ind = (int *)ALLOCA(row*sizeof(int));
1589: for ( i = 0; i < nred; i++ ) {
1590: /* make mat[i] monic and mat[i] by mat[0],...,mat[i-1] */
1591: t = mat[i];
1592: for ( j = 0; j < col && !t[j]; j++ );
1593: /* register the position of the head term */
1594: ind[i] = j;
1595: inv = invm(t[j],md);
1596: for ( k = j; k < col; k++ )
1597: if ( t[k] )
1598: DMAR(t[k],inv,0,md,t[k])
1599: for ( l = i-1; l >= 0; l-- ) {
1600: /* reduce mat[i] by mat[l] */
1601: if ( hc = t[ind[l]] ) {
1602: /* mat[i] = mat[i]-hc*mat[l] */
1603: for ( k = ind[l], hc = md-hc, s = mat[l]+k, tk = t+k;
1604: k < col; k++, tk++, s++ )
1605: if ( *s )
1606: DMAR(*s,hc,*tk,md,*tk)
1607: }
1608: }
1609: }
1610: /* reduce the spolys */
1611: for ( i = nred; i < row; i++ ) {
1612: t = mat[i];
1613: for ( l = nred-1; l >= 0; l-- ) {
1614: /* reduce mat[i] by mat[l] */
1615: if ( hc = t[ind[l]] ) {
1616: /* mat[i] = mat[i]-hc*mat[l] */
1617: for ( k = ind[l], hc = md-hc, s = mat[l]+k, tk = t+k;
1618: k < col; k++, tk++, s++ )
1619: if ( *s )
1620: DMAR(*s,hc,*tk,md,*tk)
1621: }
1622: }
1623: }
1624: #endif
1625: }
1626: /*
1627: mat[i] : reducers (i=0,...,nred-1)
1628: mat[0] < mat[1] < ... < mat[nred-1] w.r.t the term order
1629: */
1630:
1.24 noro 1631: void reduce_sp_by_red_mod(int *sp,int **redmat,int *ind,int nred,int col,int md)
1.4 noro 1632: {
1633: int i,j,k,hc,zzz;
1.24 noro 1634: int *s,*tj;
1.4 noro 1635:
1636: /* reduce the spolys by redmat */
1637: for ( i = nred-1; i >= 0; i-- ) {
1638: /* reduce sp by redmat[i] */
1639: if ( hc = sp[ind[i]] ) {
1640: /* sp = sp-hc*redmat[i] */
1641: j = ind[i];
1642: hc = md-hc;
1643: s = redmat[i]+j;
1644: tj = sp+j;
1.16 noro 1645: for ( k = col-j; k > 0; k-- ) {
1.4 noro 1646: if ( zzz = *s ) { DMAR(zzz,hc,*tj,md,*tj) } tj++; s++;
1.15 noro 1647: }
1648: }
1.17 noro 1649: }
1650: }
1651:
1652: /*
1.15 noro 1653: mat[i] : compressed reducers (i=0,...,nred-1)
1654: mat[0] < mat[1] < ... < mat[nred-1] w.r.t the term order
1655: */
1656:
1.24 noro 1657: void red_by_compress(int m,unsigned int *p,unsigned int *r,
1658: unsigned int *ri,unsigned int hc,int len)
1.18 noro 1659: {
1.19 noro 1660: unsigned int up,lo;
1.18 noro 1661: unsigned int dmy;
1662: unsigned int *pj;
1663:
1.21 noro 1664: p[*ri] = 0; r++; ri++;
1665: for ( len--; len; len--, r++, ri++ ) {
1666: pj = p+ *ri;
1667: DMA(*r,hc,*pj,up,lo);
1.18 noro 1668: if ( up ) {
1669: DSAB(m,up,lo,dmy,*pj);
1670: } else
1671: *pj = lo;
1672: }
1673: }
1674:
1675: /* p -= hc*r */
1676:
1.24 noro 1677: void red_by_vect(int m,unsigned int *p,unsigned int *r,unsigned int hc,int len)
1.18 noro 1678: {
1679: register unsigned int up,lo;
1680: unsigned int dmy;
1681:
1682: *p++ = 0; r++; len--;
1683: for ( ; len; len--, r++, p++ )
1684: if ( *r ) {
1.20 noro 1685: DMA(*r,hc,*p,up,lo);
1.18 noro 1686: if ( up ) {
1687: DSAB(m,up,lo,dmy,*p);
1688: } else
1689: *p = lo;
1690: }
1691: }
1692:
1.32 noro 1693: void red_by_vect_sf(int m,unsigned int *p,unsigned int *r,unsigned int hc,int len)
1694: {
1695: *p++ = 0; r++; len--;
1696: for ( ; len; len--, r++, p++ )
1697: if ( *r )
1698: *p = _addsf(_mulsf(*r,hc),*p);
1699: }
1700:
1.21 noro 1701: extern unsigned int **psca;
1702:
1.24 noro 1703: void reduce_sp_by_red_mod_compress (int *sp,CDP *redmat,int *ind,
1704: int nred,int col,int md)
1.15 noro 1705: {
1.24 noro 1706: int i,len;
1.15 noro 1707: CDP ri;
1.24 noro 1708: unsigned int hc;
1.18 noro 1709: unsigned int *usp;
1.15 noro 1710:
1.18 noro 1711: usp = (unsigned int *)sp;
1.15 noro 1712: /* reduce the spolys by redmat */
1713: for ( i = nred-1; i >= 0; i-- ) {
1714: /* reduce sp by redmat[i] */
1.18 noro 1715: usp[ind[i]] %= md;
1716: if ( hc = usp[ind[i]] ) {
1.15 noro 1717: /* sp = sp-hc*redmat[i] */
1718: hc = md-hc;
1719: ri = redmat[i];
1720: len = ri->len;
1.21 noro 1721: red_by_compress(md,usp,psca[ri->psindex],ri->body,hc,len);
1.4 noro 1722: }
1723: }
1.18 noro 1724: for ( i = 0; i < col; i++ )
1.24 noro 1725: if ( usp[i] >= (unsigned int)md )
1.18 noro 1726: usp[i] %= md;
1.4 noro 1727: }
1728:
1729: #define ONE_STEP2 if ( zzz = *pk ) { DMAR(zzz,a,*tk,md,*tk) } pk++; tk++;
1730:
1.24 noro 1731: int generic_gauss_elim_mod(int **mat0,int row,int col,int md,int *colstat)
1.1 noro 1732: {
1.24 noro 1733: int i,j,k,l,inv,a,rank;
1734: unsigned int *t,*pivot,*pk;
1.18 noro 1735: unsigned int **mat;
1.1 noro 1736:
1.18 noro 1737: mat = (unsigned int **)mat0;
1.1 noro 1738: for ( rank = 0, j = 0; j < col; j++ ) {
1.18 noro 1739: for ( i = rank; i < row; i++ )
1740: mat[i][j] %= md;
1741: for ( i = rank; i < row; i++ )
1742: if ( mat[i][j] )
1743: break;
1.1 noro 1744: if ( i == row ) {
1745: colstat[j] = 0;
1746: continue;
1747: } else
1748: colstat[j] = 1;
1749: if ( i != rank ) {
1750: t = mat[i]; mat[i] = mat[rank]; mat[rank] = t;
1751: }
1752: pivot = mat[rank];
1753: inv = invm(pivot[j],md);
1.4 noro 1754: for ( k = j, pk = pivot+k; k < col; k++, pk++ )
1755: if ( *pk ) {
1.24 noro 1756: if ( *pk >= (unsigned int)md )
1.18 noro 1757: *pk %= md;
1.4 noro 1758: DMAR(*pk,inv,0,md,*pk)
1.1 noro 1759: }
1760: for ( i = rank+1; i < row; i++ ) {
1761: t = mat[i];
1.18 noro 1762: if ( a = t[j] )
1763: red_by_vect(md,t+j,pivot+j,md-a,col-j);
1.1 noro 1764: }
1765: rank++;
1766: }
1767: for ( j = col-1, l = rank-1; j >= 0; j-- )
1768: if ( colstat[j] ) {
1769: pivot = mat[l];
1770: for ( i = 0; i < l; i++ ) {
1771: t = mat[i];
1.18 noro 1772: t[j] %= md;
1773: if ( a = t[j] )
1774: red_by_vect(md,t+j,pivot+j,md-a,col-j);
1.1 noro 1775: }
1776: l--;
1.18 noro 1777: }
1778: for ( j = 0, l = 0; l < rank; j++ )
1779: if ( colstat[j] ) {
1780: t = mat[l];
1781: for ( k = j; k < col; k++ )
1.24 noro 1782: if ( t[k] >= (unsigned int)md )
1.18 noro 1783: t[k] %= md;
1784: l++;
1.32 noro 1785: }
1786: return rank;
1787: }
1788:
1789: int generic_gauss_elim_sf(int **mat0,int row,int col,int md,int *colstat)
1790: {
1791: int i,j,k,l,inv,a,rank;
1792: unsigned int *t,*pivot,*pk;
1793: unsigned int **mat;
1794:
1795: mat = (unsigned int **)mat0;
1796: for ( rank = 0, j = 0; j < col; j++ ) {
1797: for ( i = rank; i < row; i++ )
1798: if ( mat[i][j] )
1799: break;
1800: if ( i == row ) {
1801: colstat[j] = 0;
1802: continue;
1803: } else
1804: colstat[j] = 1;
1805: if ( i != rank ) {
1806: t = mat[i]; mat[i] = mat[rank]; mat[rank] = t;
1807: }
1808: pivot = mat[rank];
1809: inv = _invsf(pivot[j]);
1810: for ( k = j, pk = pivot+k; k < col; k++, pk++ )
1811: if ( *pk )
1812: *pk = _mulsf(*pk,inv);
1813: for ( i = rank+1; i < row; i++ ) {
1814: t = mat[i];
1815: if ( a = t[j] )
1816: red_by_vect_sf(md,t+j,pivot+j,_chsgnsf(a),col-j);
1817: }
1818: rank++;
1819: }
1820: for ( j = col-1, l = rank-1; j >= 0; j-- )
1821: if ( colstat[j] ) {
1822: pivot = mat[l];
1823: for ( i = 0; i < l; i++ ) {
1824: t = mat[i];
1825: if ( a = t[j] )
1826: red_by_vect_sf(md,t+j,pivot+j,_chsgnsf(a),col-j);
1827: }
1828: l--;
1.1 noro 1829: }
1830: return rank;
1831: }
1832:
1833: /* LU decomposition; a[i][i] = 1/U[i][i] */
1834:
1.24 noro 1835: int lu_gfmmat(GFMMAT mat,unsigned int md,int *perm)
1.1 noro 1836: {
1837: int row,col;
1.24 noro 1838: int i,j,k;
1.1 noro 1839: unsigned int *t,*pivot;
1840: unsigned int **a;
1841: unsigned int inv,m;
1842:
1843: row = mat->row; col = mat->col;
1844: a = mat->body;
1845: bzero(perm,row*sizeof(int));
1846:
1847: for ( i = 0; i < row; i++ )
1848: perm[i] = i;
1849: for ( k = 0; k < col; k++ ) {
1850: for ( i = k; i < row && !a[i][k]; i++ );
1851: if ( i == row )
1852: return 0;
1853: if ( i != k ) {
1854: j = perm[i]; perm[i] = perm[k]; perm[k] = j;
1855: t = a[i]; a[i] = a[k]; a[k] = t;
1856: }
1857: pivot = a[k];
1858: pivot[k] = inv = invm(pivot[k],md);
1859: for ( i = k+1; i < row; i++ ) {
1860: t = a[i];
1861: if ( m = t[k] ) {
1862: DMAR(inv,m,0,md,t[k])
1863: for ( j = k+1, m = md - t[k]; j < col; j++ )
1864: if ( pivot[j] ) {
1.8 noro 1865: unsigned int tj;
1866:
1867: DMAR(m,pivot[j],t[j],md,tj)
1868: t[j] = tj;
1.1 noro 1869: }
1870: }
1871: }
1872: }
1873: return 1;
1874: }
1875:
1.3 noro 1876: /*
1877: Input
1878: a: a row x col matrix
1879: md : a modulus
1880:
1881: Output:
1882: return : d = the rank of mat
1883: a[0..(d-1)][0..(d-1)] : LU decomposition (a[i][i] = 1/U[i][i])
1884: rinfo: array of length row
1885: cinfo: array of length col
1886: i-th row in new a <-> rinfo[i]-th row in old a
1887: cinfo[j]=1 <=> j-th column is contained in the LU decomp.
1888: */
1889:
1.24 noro 1890: int find_lhs_and_lu_mod(unsigned int **a,int row,int col,
1891: unsigned int md,int **rinfo,int **cinfo)
1.3 noro 1892: {
1.24 noro 1893: int i,j,k,d;
1.3 noro 1894: int *rp,*cp;
1895: unsigned int *t,*pivot;
1896: unsigned int inv,m;
1897:
1898: *rinfo = rp = (int *)MALLOC_ATOMIC(row*sizeof(int));
1899: *cinfo = cp = (int *)MALLOC_ATOMIC(col*sizeof(int));
1900: for ( i = 0; i < row; i++ )
1901: rp[i] = i;
1902: for ( k = 0, d = 0; k < col; k++ ) {
1903: for ( i = d; i < row && !a[i][k]; i++ );
1904: if ( i == row ) {
1905: cp[k] = 0;
1906: continue;
1907: } else
1908: cp[k] = 1;
1909: if ( i != d ) {
1910: j = rp[i]; rp[i] = rp[d]; rp[d] = j;
1911: t = a[i]; a[i] = a[d]; a[d] = t;
1912: }
1913: pivot = a[d];
1914: pivot[k] = inv = invm(pivot[k],md);
1915: for ( i = d+1; i < row; i++ ) {
1916: t = a[i];
1917: if ( m = t[k] ) {
1918: DMAR(inv,m,0,md,t[k])
1919: for ( j = k+1, m = md - t[k]; j < col; j++ )
1920: if ( pivot[j] ) {
1.8 noro 1921: unsigned int tj;
1922: DMAR(m,pivot[j],t[j],md,tj)
1923: t[j] = tj;
1.3 noro 1924: }
1925: }
1926: }
1927: d++;
1928: }
1929: return d;
1930: }
1931:
1932: /*
1933: Input
1934: a : n x n matrix; a result of LU-decomposition
1935: md : modulus
1936: b : n x l matrix
1937: Output
1938: b = a^(-1)b
1939: */
1940:
1.44 noro 1941: void solve_by_lu_mod(int **a,int n,int md,int **b,int l,int normalize)
1.3 noro 1942: {
1943: unsigned int *y,*c;
1944: int i,j,k;
1945: unsigned int t,m,m2;
1946:
1947: y = (int *)MALLOC_ATOMIC(n*sizeof(int));
1948: c = (int *)MALLOC_ATOMIC(n*sizeof(int));
1949: m2 = md>>1;
1950: for ( k = 0; k < l; k++ ) {
1951: /* copy b[.][k] to c */
1952: for ( i = 0; i < n; i++ )
1953: c[i] = (unsigned int)b[i][k];
1954: /* solve Ly=c */
1955: for ( i = 0; i < n; i++ ) {
1956: for ( t = c[i], j = 0; j < i; j++ )
1957: if ( a[i][j] ) {
1958: m = md - a[i][j];
1959: DMAR(m,y[j],t,md,t)
1960: }
1961: y[i] = t;
1962: }
1963: /* solve Uc=y */
1964: for ( i = n-1; i >= 0; i-- ) {
1965: for ( t = y[i], j =i+1; j < n; j++ )
1966: if ( a[i][j] ) {
1967: m = md - a[i][j];
1968: DMAR(m,c[j],t,md,t)
1969: }
1970: /* a[i][i] = 1/U[i][i] */
1971: DMAR(t,a[i][i],0,md,c[i])
1972: }
1973: /* copy c to b[.][k] with normalization */
1.44 noro 1974: if ( normalize )
1975: for ( i = 0; i < n; i++ )
1976: b[i][k] = (int)(c[i]>m2 ? c[i]-md : c[i]);
1977: else
1978: for ( i = 0; i < n; i++ )
1979: b[i][k] = c[i];
1.3 noro 1980: }
1981: }
1982:
1.24 noro 1983: void Pleqm1(NODE arg,VECT *rp)
1.1 noro 1984: {
1985: MAT m;
1986: VECT vect;
1987: pointer **mat;
1988: Q *v;
1989: Q q;
1990: int **wmat;
1991: int md,i,j,row,col,t,n,status;
1992:
1993: asir_assert(ARG0(arg),O_MAT,"leqm1");
1994: asir_assert(ARG1(arg),O_N,"leqm1");
1995: m = (MAT)ARG0(arg); md = QTOS((Q)ARG1(arg));
1996: row = m->row; col = m->col; mat = m->body;
1997: wmat = (int **)almat(row,col);
1998: for ( i = 0; i < row; i++ )
1999: for ( j = 0; j < col; j++ )
2000: if ( q = (Q)mat[i][j] ) {
2001: t = rem(NM(q),md);
2002: if ( SGN(q) < 0 )
2003: t = (md - t) % md;
2004: wmat[i][j] = t;
2005: } else
2006: wmat[i][j] = 0;
2007: status = gauss_elim_mod1(wmat,row,col,md);
2008: if ( status < 0 )
2009: *rp = 0;
2010: else if ( status > 0 )
2011: *rp = (VECT)ONE;
2012: else {
2013: n = col - 1;
2014: MKVECT(vect,n);
2015: for ( i = 0, v = (Q *)vect->body; i < n; i++ ) {
2016: t = (md-wmat[i][n])%md; STOQ(t,v[i]);
2017: }
2018: *rp = vect;
2019: }
2020: }
2021:
1.24 noro 2022: int gauss_elim_mod1(int **mat,int row,int col,int md)
1.1 noro 2023: {
2024: int i,j,k,inv,a,n;
2025: int *t,*pivot;
2026:
2027: n = col - 1;
2028: for ( j = 0; j < n; j++ ) {
2029: for ( i = j; i < row && !mat[i][j]; i++ );
2030: if ( i == row )
2031: return 1;
2032: if ( i != j ) {
2033: t = mat[i]; mat[i] = mat[j]; mat[j] = t;
2034: }
2035: pivot = mat[j];
2036: inv = invm(pivot[j],md);
2037: for ( k = j; k <= n; k++ )
2038: pivot[k] = dmar(pivot[k],inv,0,md);
2039: for ( i = j+1; i < row; i++ ) {
2040: t = mat[i];
2041: if ( i != j && (a = t[j]) )
2042: for ( k = j, a = md - a; k <= n; k++ )
2043: t[k] = dmar(pivot[k],a,t[k],md);
2044: }
2045: }
2046: for ( i = n; i < row && !mat[i][n]; i++ );
2047: if ( i == row ) {
2048: for ( j = n-1; j >= 0; j-- ) {
2049: for ( i = j-1, a = (md-mat[j][n])%md; i >= 0; i-- ) {
2050: mat[i][n] = dmar(mat[i][j],a,mat[i][n],md);
2051: mat[i][j] = 0;
2052: }
2053: }
2054: return 0;
2055: } else
2056: return -1;
2057: }
2058:
1.24 noro 2059: void Pgeninvm(NODE arg,LIST *rp)
1.1 noro 2060: {
2061: MAT m;
2062: pointer **mat;
2063: Q **tmat;
2064: Q q;
2065: unsigned int **wmat;
2066: int md,i,j,row,col,t,status;
2067: MAT mat1,mat2;
2068: NODE node1,node2;
2069:
2070: asir_assert(ARG0(arg),O_MAT,"leqm1");
2071: asir_assert(ARG1(arg),O_N,"leqm1");
2072: m = (MAT)ARG0(arg); md = QTOS((Q)ARG1(arg));
2073: row = m->row; col = m->col; mat = m->body;
2074: wmat = (unsigned int **)almat(row,col+row);
2075: for ( i = 0; i < row; i++ ) {
2076: bzero((char *)wmat[i],(col+row)*sizeof(int));
2077: for ( j = 0; j < col; j++ )
2078: if ( q = (Q)mat[i][j] ) {
2079: t = rem(NM(q),md);
2080: if ( SGN(q) < 0 )
2081: t = (md - t) % md;
2082: wmat[i][j] = t;
2083: }
2084: wmat[i][col+i] = 1;
2085: }
2086: status = gauss_elim_geninv_mod(wmat,row,col,md);
2087: if ( status > 0 )
2088: *rp = 0;
2089: else {
2090: MKMAT(mat1,col,row); MKMAT(mat2,row-col,row);
2091: for ( i = 0, tmat = (Q **)mat1->body; i < col; i++ )
2092: for ( j = 0; j < row; j++ )
1.24 noro 2093: UTOQ(wmat[i][j+col],tmat[i][j]);
1.1 noro 2094: for ( tmat = (Q **)mat2->body; i < row; i++ )
2095: for ( j = 0; j < row; j++ )
1.24 noro 2096: UTOQ(wmat[i][j+col],tmat[i-col][j]);
1.1 noro 2097: MKNODE(node2,mat2,0); MKNODE(node1,mat1,node2); MKLIST(*rp,node1);
2098: }
2099: }
2100:
1.24 noro 2101: int gauss_elim_geninv_mod(unsigned int **mat,int row,int col,int md)
1.1 noro 2102: {
2103: int i,j,k,inv,a,n,m;
2104: unsigned int *t,*pivot;
2105:
2106: n = col; m = row+col;
2107: for ( j = 0; j < n; j++ ) {
2108: for ( i = j; i < row && !mat[i][j]; i++ );
2109: if ( i == row )
2110: return 1;
2111: if ( i != j ) {
2112: t = mat[i]; mat[i] = mat[j]; mat[j] = t;
2113: }
2114: pivot = mat[j];
2115: inv = invm(pivot[j],md);
2116: for ( k = j; k < m; k++ )
2117: pivot[k] = dmar(pivot[k],inv,0,md);
2118: for ( i = j+1; i < row; i++ ) {
2119: t = mat[i];
2120: if ( a = t[j] )
2121: for ( k = j, a = md - a; k < m; k++ )
2122: t[k] = dmar(pivot[k],a,t[k],md);
2123: }
2124: }
2125: for ( j = n-1; j >= 0; j-- ) {
2126: pivot = mat[j];
2127: for ( i = j-1; i >= 0; i-- ) {
2128: t = mat[i];
2129: if ( a = t[j] )
2130: for ( k = j, a = md - a; k < m; k++ )
2131: t[k] = dmar(pivot[k],a,t[k],md);
2132: }
2133: }
2134: return 0;
2135: }
2136:
1.24 noro 2137: void Psolve_by_lu_gfmmat(NODE arg,VECT *rp)
1.1 noro 2138: {
2139: GFMMAT lu;
2140: Q *perm,*rhs,*v;
2141: int n,i;
2142: unsigned int md;
2143: unsigned int *b,*sol;
2144: VECT r;
2145:
2146: lu = (GFMMAT)ARG0(arg);
2147: perm = (Q *)BDY((VECT)ARG1(arg));
2148: rhs = (Q *)BDY((VECT)ARG2(arg));
2149: md = (unsigned int)QTOS((Q)ARG3(arg));
2150: n = lu->col;
2151: b = (unsigned int *)MALLOC_ATOMIC(n*sizeof(int));
2152: sol = (unsigned int *)MALLOC_ATOMIC(n*sizeof(int));
2153: for ( i = 0; i < n; i++ )
2154: b[i] = QTOS(rhs[QTOS(perm[i])]);
2155: solve_by_lu_gfmmat(lu,md,b,sol);
2156: MKVECT(r,n);
2157: for ( i = 0, v = (Q *)r->body; i < n; i++ )
1.24 noro 2158: UTOQ(sol[i],v[i]);
1.1 noro 2159: *rp = r;
2160: }
2161:
1.24 noro 2162: void solve_by_lu_gfmmat(GFMMAT lu,unsigned int md,
2163: unsigned int *b,unsigned int *x)
1.1 noro 2164: {
2165: int n;
2166: unsigned int **a;
2167: unsigned int *y;
2168: int i,j;
2169: unsigned int t,m;
2170:
2171: n = lu->col;
2172: a = lu->body;
2173: y = (unsigned int *)MALLOC_ATOMIC(n*sizeof(int));
2174: /* solve Ly=b */
2175: for ( i = 0; i < n; i++ ) {
2176: for ( t = b[i], j = 0; j < i; j++ )
2177: if ( a[i][j] ) {
2178: m = md - a[i][j];
2179: DMAR(m,y[j],t,md,t)
2180: }
2181: y[i] = t;
2182: }
2183: /* solve Ux=y */
2184: for ( i = n-1; i >= 0; i-- ) {
2185: for ( t = y[i], j =i+1; j < n; j++ )
2186: if ( a[i][j] ) {
2187: m = md - a[i][j];
2188: DMAR(m,x[j],t,md,t)
2189: }
2190: /* a[i][i] = 1/U[i][i] */
2191: DMAR(t,a[i][i],0,md,x[i])
2192: }
2193: }
2194:
1.24 noro 2195: void Plu_gfmmat(NODE arg,LIST *rp)
1.1 noro 2196: {
2197: MAT m;
2198: GFMMAT mm;
2199: unsigned int md;
2200: int i,row,col,status;
2201: int *iperm;
2202: Q *v;
2203: VECT perm;
2204: NODE n0;
2205:
2206: asir_assert(ARG0(arg),O_MAT,"mat_to_gfmmat");
2207: asir_assert(ARG1(arg),O_N,"mat_to_gfmmat");
2208: m = (MAT)ARG0(arg); md = (unsigned int)QTOS((Q)ARG1(arg));
2209: mat_to_gfmmat(m,md,&mm);
2210: row = m->row;
2211: col = m->col;
2212: iperm = (int *)MALLOC_ATOMIC(row*sizeof(int));
2213: status = lu_gfmmat(mm,md,iperm);
2214: if ( !status )
2215: n0 = 0;
2216: else {
2217: MKVECT(perm,row);
2218: for ( i = 0, v = (Q *)perm->body; i < row; i++ )
2219: STOQ(iperm[i],v[i]);
2220: n0 = mknode(2,mm,perm);
2221: }
2222: MKLIST(*rp,n0);
2223: }
2224:
1.24 noro 2225: void Pmat_to_gfmmat(NODE arg,GFMMAT *rp)
1.1 noro 2226: {
2227: MAT m;
2228: unsigned int md;
2229:
2230: asir_assert(ARG0(arg),O_MAT,"mat_to_gfmmat");
2231: asir_assert(ARG1(arg),O_N,"mat_to_gfmmat");
2232: m = (MAT)ARG0(arg); md = (unsigned int)QTOS((Q)ARG1(arg));
2233: mat_to_gfmmat(m,md,rp);
2234: }
2235:
1.24 noro 2236: void mat_to_gfmmat(MAT m,unsigned int md,GFMMAT *rp)
1.1 noro 2237: {
2238: unsigned int **wmat;
2239: unsigned int t;
2240: Q **mat;
2241: Q q;
2242: int i,j,row,col;
2243:
2244: row = m->row; col = m->col; mat = (Q **)m->body;
2245: wmat = (unsigned int **)almat(row,col);
2246: for ( i = 0; i < row; i++ ) {
2247: bzero((char *)wmat[i],col*sizeof(unsigned int));
2248: for ( j = 0; j < col; j++ )
2249: if ( q = mat[i][j] ) {
2250: t = (unsigned int)rem(NM(q),md);
2251: if ( SGN(q) < 0 )
2252: t = (md - t) % md;
2253: wmat[i][j] = t;
2254: }
2255: }
2256: TOGFMMAT(row,col,wmat,*rp);
2257: }
2258:
1.27 noro 2259: void Pgeninvm_swap(arg,rp)
2260: NODE arg;
2261: LIST *rp;
1.1 noro 2262: {
2263: MAT m;
2264: pointer **mat;
2265: Q **tmat;
2266: Q *tvect;
2267: Q q;
2268: unsigned int **wmat,**invmat;
2269: int *index;
2270: unsigned int t,md;
2271: int i,j,row,col,status;
2272: MAT mat1;
2273: VECT vect1;
2274: NODE node1,node2;
2275:
2276: asir_assert(ARG0(arg),O_MAT,"geninvm_swap");
2277: asir_assert(ARG1(arg),O_N,"geninvm_swap");
2278: m = (MAT)ARG0(arg); md = QTOS((Q)ARG1(arg));
2279: row = m->row; col = m->col; mat = m->body;
2280: wmat = (unsigned int **)almat(row,col+row);
2281: for ( i = 0; i < row; i++ ) {
2282: bzero((char *)wmat[i],(col+row)*sizeof(int));
2283: for ( j = 0; j < col; j++ )
2284: if ( q = (Q)mat[i][j] ) {
2285: t = (unsigned int)rem(NM(q),md);
2286: if ( SGN(q) < 0 )
2287: t = (md - t) % md;
2288: wmat[i][j] = t;
2289: }
2290: wmat[i][col+i] = 1;
2291: }
2292: status = gauss_elim_geninv_mod_swap(wmat,row,col,md,&invmat,&index);
2293: if ( status > 0 )
2294: *rp = 0;
2295: else {
2296: MKMAT(mat1,col,col);
2297: for ( i = 0, tmat = (Q **)mat1->body; i < col; i++ )
2298: for ( j = 0; j < col; j++ )
2299: UTOQ(invmat[i][j],tmat[i][j]);
2300: MKVECT(vect1,row);
2301: for ( i = 0, tvect = (Q *)vect1->body; i < row; i++ )
2302: STOQ(index[i],tvect[i]);
2303: MKNODE(node2,vect1,0); MKNODE(node1,mat1,node2); MKLIST(*rp,node1);
2304: }
2305: }
2306:
1.27 noro 2307: gauss_elim_geninv_mod_swap(mat,row,col,md,invmatp,indexp)
2308: unsigned int **mat;
2309: int row,col;
2310: unsigned int md;
2311: unsigned int ***invmatp;
2312: int **indexp;
1.1 noro 2313: {
2314: int i,j,k,inv,a,n,m;
2315: unsigned int *t,*pivot,*s;
2316: int *index;
2317: unsigned int **invmat;
2318:
2319: n = col; m = row+col;
2320: *indexp = index = (int *)MALLOC_ATOMIC(row*sizeof(int));
2321: for ( i = 0; i < row; i++ )
2322: index[i] = i;
2323: for ( j = 0; j < n; j++ ) {
2324: for ( i = j; i < row && !mat[i][j]; i++ );
2325: if ( i == row ) {
2326: *indexp = 0; *invmatp = 0; return 1;
2327: }
2328: if ( i != j ) {
2329: t = mat[i]; mat[i] = mat[j]; mat[j] = t;
2330: k = index[i]; index[i] = index[j]; index[j] = k;
2331: }
2332: pivot = mat[j];
2333: inv = (unsigned int)invm(pivot[j],md);
2334: for ( k = j; k < m; k++ )
2335: if ( pivot[k] )
2336: pivot[k] = (unsigned int)dmar(pivot[k],inv,0,md);
2337: for ( i = j+1; i < row; i++ ) {
2338: t = mat[i];
2339: if ( a = t[j] )
2340: for ( k = j, a = md - a; k < m; k++ )
2341: if ( pivot[k] )
2342: t[k] = dmar(pivot[k],a,t[k],md);
2343: }
2344: }
2345: for ( j = n-1; j >= 0; j-- ) {
2346: pivot = mat[j];
2347: for ( i = j-1; i >= 0; i-- ) {
2348: t = mat[i];
2349: if ( a = t[j] )
2350: for ( k = j, a = md - a; k < m; k++ )
2351: if ( pivot[k] )
2352: t[k] = dmar(pivot[k],a,t[k],md);
2353: }
2354: }
2355: *invmatp = invmat = (unsigned int **)almat(col,col);
1.27 noro 2356: for ( i = 0; i < col; i++ )
2357: for ( j = 0, s = invmat[i], t = mat[i]; j < col; j++ )
2358: s[j] = t[col+index[j]];
2359: return 0;
2360: }
2361:
2362: void Pgeninv_sf_swap(NODE arg,LIST *rp)
2363: {
2364: MAT m;
2365: GFS **mat,**tmat;
2366: Q *tvect;
2367: GFS q;
2368: int **wmat,**invmat;
2369: int *index;
2370: unsigned int t;
2371: int i,j,row,col,status;
2372: MAT mat1;
2373: VECT vect1;
2374: NODE node1,node2;
2375:
2376: asir_assert(ARG0(arg),O_MAT,"geninv_sf_swap");
2377: m = (MAT)ARG0(arg);
2378: row = m->row; col = m->col; mat = (GFS **)m->body;
2379: wmat = (int **)almat(row,col+row);
2380: for ( i = 0; i < row; i++ ) {
2381: bzero((char *)wmat[i],(col+row)*sizeof(int));
2382: for ( j = 0; j < col; j++ )
2383: if ( q = (GFS)mat[i][j] )
2384: wmat[i][j] = FTOIF(CONT(q));
2385: wmat[i][col+i] = _onesf();
2386: }
2387: status = gauss_elim_geninv_sf_swap(wmat,row,col,&invmat,&index);
2388: if ( status > 0 )
2389: *rp = 0;
2390: else {
2391: MKMAT(mat1,col,col);
2392: for ( i = 0, tmat = (GFS **)mat1->body; i < col; i++ )
2393: for ( j = 0; j < col; j++ )
2394: if ( t = invmat[i][j] ) {
2395: MKGFS(IFTOF(t),tmat[i][j]);
2396: }
2397: MKVECT(vect1,row);
2398: for ( i = 0, tvect = (Q *)vect1->body; i < row; i++ )
2399: STOQ(index[i],tvect[i]);
2400: MKNODE(node2,vect1,0); MKNODE(node1,mat1,node2); MKLIST(*rp,node1);
2401: }
2402: }
2403:
2404: int gauss_elim_geninv_sf_swap(int **mat,int row,int col,
2405: int ***invmatp,int **indexp)
2406: {
2407: int i,j,k,inv,a,n,m,u;
2408: int *t,*pivot,*s;
2409: int *index;
2410: int **invmat;
2411:
2412: n = col; m = row+col;
2413: *indexp = index = (int *)MALLOC_ATOMIC(row*sizeof(int));
2414: for ( i = 0; i < row; i++ )
2415: index[i] = i;
2416: for ( j = 0; j < n; j++ ) {
2417: for ( i = j; i < row && !mat[i][j]; i++ );
2418: if ( i == row ) {
2419: *indexp = 0; *invmatp = 0; return 1;
2420: }
2421: if ( i != j ) {
2422: t = mat[i]; mat[i] = mat[j]; mat[j] = t;
2423: k = index[i]; index[i] = index[j]; index[j] = k;
2424: }
2425: pivot = mat[j];
2426: inv = _invsf(pivot[j]);
2427: for ( k = j; k < m; k++ )
2428: if ( pivot[k] )
2429: pivot[k] = _mulsf(pivot[k],inv);
2430: for ( i = j+1; i < row; i++ ) {
2431: t = mat[i];
2432: if ( a = t[j] )
2433: for ( k = j, a = _chsgnsf(a); k < m; k++ )
2434: if ( pivot[k] ) {
2435: u = _mulsf(pivot[k],a);
2436: t[k] = _addsf(u,t[k]);
2437: }
2438: }
2439: }
2440: for ( j = n-1; j >= 0; j-- ) {
2441: pivot = mat[j];
2442: for ( i = j-1; i >= 0; i-- ) {
2443: t = mat[i];
2444: if ( a = t[j] )
2445: for ( k = j, a = _chsgnsf(a); k < m; k++ )
2446: if ( pivot[k] ) {
2447: u = _mulsf(pivot[k],a);
2448: t[k] = _addsf(u,t[k]);
2449: }
2450: }
2451: }
2452: *invmatp = invmat = (int **)almat(col,col);
1.1 noro 2453: for ( i = 0; i < col; i++ )
2454: for ( j = 0, s = invmat[i], t = mat[i]; j < col; j++ )
2455: s[j] = t[col+index[j]];
2456: return 0;
2457: }
2458:
2459: void _addn(N,N,N);
2460: int _subn(N,N,N);
2461: void _muln(N,N,N);
2462:
1.24 noro 2463: void inner_product_int(Q *a,Q *b,int n,Q *r)
1.1 noro 2464: {
2465: int la,lb,i;
2466: int sgn,sgn1;
2467: N wm,wma,sum,t;
2468:
2469: for ( la = lb = 0, i = 0; i < n; i++ ) {
2470: if ( a[i] )
2471: if ( DN(a[i]) )
2472: error("inner_product_int : invalid argument");
2473: else
2474: la = MAX(PL(NM(a[i])),la);
2475: if ( b[i] )
2476: if ( DN(b[i]) )
2477: error("inner_product_int : invalid argument");
2478: else
2479: lb = MAX(PL(NM(b[i])),lb);
2480: }
2481: sgn = 0;
2482: sum= NALLOC(la+lb+2);
2483: bzero((char *)sum,(la+lb+3)*sizeof(unsigned int));
2484: wm = NALLOC(la+lb+2);
2485: wma = NALLOC(la+lb+2);
2486: for ( i = 0; i < n; i++ ) {
2487: if ( !a[i] || !b[i] )
2488: continue;
2489: _muln(NM(a[i]),NM(b[i]),wm);
2490: sgn1 = SGN(a[i])*SGN(b[i]);
2491: if ( !sgn ) {
2492: sgn = sgn1;
2493: t = wm; wm = sum; sum = t;
2494: } else if ( sgn == sgn1 ) {
2495: _addn(sum,wm,wma);
2496: if ( !PL(wma) )
2497: sgn = 0;
2498: t = wma; wma = sum; sum = t;
2499: } else {
2500: /* sgn*sum+sgn1*wm = sgn*(sum-wm) */
2501: sgn *= _subn(sum,wm,wma);
2502: t = wma; wma = sum; sum = t;
2503: }
2504: }
2505: GC_free(wm);
2506: GC_free(wma);
2507: if ( !sgn ) {
2508: GC_free(sum);
2509: *r = 0;
2510: } else
2511: NTOQ(sum,sgn,*r);
2512: }
2513:
1.3 noro 2514: /* (k,l) element of a*b where a: .x n matrix, b: n x . integer matrix */
2515:
1.24 noro 2516: void inner_product_mat_int_mod(Q **a,int **b,int n,int k,int l,Q *r)
1.3 noro 2517: {
2518: int la,lb,i;
2519: int sgn,sgn1;
2520: N wm,wma,sum,t;
2521: Q aki;
2522: int bil,bilsgn;
2523: struct oN tn;
2524:
2525: for ( la = 0, i = 0; i < n; i++ ) {
2526: if ( aki = a[k][i] )
2527: if ( DN(aki) )
2528: error("inner_product_int : invalid argument");
2529: else
2530: la = MAX(PL(NM(aki)),la);
2531: }
2532: lb = 1;
2533: sgn = 0;
2534: sum= NALLOC(la+lb+2);
2535: bzero((char *)sum,(la+lb+3)*sizeof(unsigned int));
2536: wm = NALLOC(la+lb+2);
2537: wma = NALLOC(la+lb+2);
2538: for ( i = 0; i < n; i++ ) {
2539: if ( !(aki = a[k][i]) || !(bil = b[i][l]) )
2540: continue;
2541: tn.p = 1;
2542: if ( bil > 0 ) {
2543: tn.b[0] = bil; bilsgn = 1;
2544: } else {
2545: tn.b[0] = -bil; bilsgn = -1;
2546: }
2547: _muln(NM(aki),&tn,wm);
2548: sgn1 = SGN(aki)*bilsgn;
2549: if ( !sgn ) {
2550: sgn = sgn1;
2551: t = wm; wm = sum; sum = t;
2552: } else if ( sgn == sgn1 ) {
2553: _addn(sum,wm,wma);
2554: if ( !PL(wma) )
2555: sgn = 0;
2556: t = wma; wma = sum; sum = t;
2557: } else {
2558: /* sgn*sum+sgn1*wm = sgn*(sum-wm) */
2559: sgn *= _subn(sum,wm,wma);
2560: t = wma; wma = sum; sum = t;
2561: }
2562: }
2563: GC_free(wm);
2564: GC_free(wma);
2565: if ( !sgn ) {
2566: GC_free(sum);
2567: *r = 0;
2568: } else
2569: NTOQ(sum,sgn,*r);
2570: }
2571:
1.24 noro 2572: void Pmul_mat_vect_int(NODE arg,VECT *rp)
1.1 noro 2573: {
2574: MAT mat;
2575: VECT vect,r;
2576: int row,col,i;
2577:
2578: mat = (MAT)ARG0(arg);
2579: vect = (VECT)ARG1(arg);
2580: row = mat->row;
2581: col = mat->col;
2582: MKVECT(r,row);
1.24 noro 2583: for ( i = 0; i < row; i++ ) {
2584: inner_product_int((Q *)mat->body[i],(Q *)vect->body,col,(Q *)&r->body[i]);
2585: }
1.1 noro 2586: *rp = r;
2587: }
2588:
1.24 noro 2589: void Pnbpoly_up2(NODE arg,GF2N *rp)
1.1 noro 2590: {
2591: int m,type,ret;
2592: UP2 r;
2593:
2594: m = QTOS((Q)ARG0(arg));
2595: type = QTOS((Q)ARG1(arg));
2596: ret = generate_ONB_polynomial(&r,m,type);
2597: if ( ret == 0 )
2598: MKGF2N(r,*rp);
2599: else
2600: *rp = 0;
2601: }
2602:
1.24 noro 2603: void Px962_irredpoly_up2(NODE arg,GF2N *rp)
1.1 noro 2604: {
1.24 noro 2605: int m,ret,w;
1.1 noro 2606: GF2N prev;
2607: UP2 r;
2608:
2609: m = QTOS((Q)ARG0(arg));
2610: prev = (GF2N)ARG1(arg);
2611: if ( !prev ) {
2612: w = (m>>5)+1; NEWUP2(r,w); r->w = 0;
2613: bzero((char *)r->b,w*sizeof(unsigned int));
2614: } else {
2615: r = prev->body;
2616: if ( degup2(r) != m ) {
2617: w = (m>>5)+1; NEWUP2(r,w); r->w = 0;
2618: bzero((char *)r->b,w*sizeof(unsigned int));
2619: }
2620: }
1.24 noro 2621: ret = _generate_irreducible_polynomial(r,m);
1.1 noro 2622: if ( ret == 0 )
2623: MKGF2N(r,*rp);
2624: else
2625: *rp = 0;
2626: }
2627:
1.24 noro 2628: void Pirredpoly_up2(NODE arg,GF2N *rp)
1.1 noro 2629: {
1.24 noro 2630: int m,ret,w;
1.1 noro 2631: GF2N prev;
2632: UP2 r;
2633:
2634: m = QTOS((Q)ARG0(arg));
2635: prev = (GF2N)ARG1(arg);
2636: if ( !prev ) {
2637: w = (m>>5)+1; NEWUP2(r,w); r->w = 0;
2638: bzero((char *)r->b,w*sizeof(unsigned int));
2639: } else {
2640: r = prev->body;
2641: if ( degup2(r) != m ) {
2642: w = (m>>5)+1; NEWUP2(r,w); r->w = 0;
2643: bzero((char *)r->b,w*sizeof(unsigned int));
2644: }
2645: }
1.24 noro 2646: ret = _generate_good_irreducible_polynomial(r,m);
1.1 noro 2647: if ( ret == 0 )
2648: MKGF2N(r,*rp);
2649: else
2650: *rp = 0;
2651: }
2652:
1.26 noro 2653: void Pmat_swap_row_destructive(NODE arg, MAT *m)
2654: {
2655: int i1,i2;
2656: pointer *t;
2657: MAT mat;
2658:
2659: asir_assert(ARG0(arg),O_MAT,"mat_swap_row_destructive");
2660: asir_assert(ARG1(arg),O_N,"mat_swap_row_destructive");
2661: asir_assert(ARG2(arg),O_N,"mat_swap_row_destructive");
2662: mat = (MAT)ARG0(arg);
2663: i1 = QTOS((Q)ARG1(arg));
2664: i2 = QTOS((Q)ARG2(arg));
2665: if ( i1 < 0 || i2 < 0 || i1 >= mat->row || i2 >= mat->row )
2666: error("mat_swap_row_destructive : Out of range");
2667: t = mat->body[i1];
2668: mat->body[i1] = mat->body[i2];
2669: mat->body[i2] = t;
2670: *m = mat;
2671: }
2672:
2673: void Pmat_swap_col_destructive(NODE arg, MAT *m)
2674: {
2675: int j1,j2,i,n;
2676: pointer *mi;
2677: pointer t;
2678: MAT mat;
2679:
2680: asir_assert(ARG0(arg),O_MAT,"mat_swap_col_destructive");
2681: asir_assert(ARG1(arg),O_N,"mat_swap_col_destructive");
2682: asir_assert(ARG2(arg),O_N,"mat_swap_col_destructive");
2683: mat = (MAT)ARG0(arg);
2684: j1 = QTOS((Q)ARG1(arg));
2685: j2 = QTOS((Q)ARG2(arg));
2686: if ( j1 < 0 || j2 < 0 || j1 >= mat->col || j2 >= mat->col )
2687: error("mat_swap_col_destructive : Out of range");
2688: n = mat->row;
2689: for ( i = 0; i < n; i++ ) {
2690: mi = mat->body[i];
2691: t = mi[j1]; mi[j1] = mi[j2]; mi[j2] = t;
2692: }
2693: *m = mat;
2694: }
1.1 noro 2695: /*
2696: * f = type 'type' normal polynomial of degree m if exists
2697: * IEEE P1363 A.7.2
2698: *
2699: * return value : 0 --- exists
2700: * 1 --- does not exist
2701: * -1 --- failure (memory allocation error)
2702: */
2703:
2704: int generate_ONB_polynomial(UP2 *rp,int m,int type)
2705: {
2706: int i,r;
2707: int w;
2708: UP2 f,f0,f1,f2,t;
2709:
2710: w = (m>>5)+1;
2711: switch ( type ) {
2712: case 1:
2713: if ( !TypeT_NB_check(m,1) ) return 1;
2714: NEWUP2(f,w); *rp = f; f->w = w;
2715: /* set all the bits */
2716: for ( i = 0; i < w; i++ )
2717: f->b[i] = 0xffffffff;
2718: /* mask the top word if necessary */
2719: if ( r = (m+1)&31 )
2720: f->b[w-1] &= (1<<r)-1;
2721: return 0;
2722: break;
2723: case 2:
2724: if ( !TypeT_NB_check(m,2) ) return 1;
2725: NEWUP2(f,w); *rp = f;
2726: W_NEWUP2(f0,w);
2727: W_NEWUP2(f1,w);
2728: W_NEWUP2(f2,w);
2729:
2730: /* recursion for genrating Type II normal polynomial */
2731:
2732: /* f0 = 1, f1 = t+1 */
2733: f0->w = 1; f0->b[0] = 1;
2734: f1->w = 1; f1->b[0] = 3;
2735: for ( i = 2; i <= m; i++ ) {
2736: /* f2 = t*f1+f0 */
2737: _bshiftup2(f1,-1,f2);
2738: _addup2_destructive(f2,f0);
2739: /* cyclic change of the variables */
2740: t = f0; f0 = f1; f1 = f2; f2 = t;
2741: }
2742: _copyup2(f1,f);
2743: return 0;
2744: break;
2745: default:
2746: return -1;
2747: break;
2748: }
2749: }
2750:
2751: /*
2752: * f = an irreducible trinomial or pentanomial of degree d 'after' f
2753: * return value : 0 --- exists
2754: * 1 --- does not exist (exhaustion)
2755: */
2756:
2757: int _generate_irreducible_polynomial(UP2 f,int d)
2758: {
2759: int ret,i,j,k,nz,i0,j0,k0;
2760: int w;
2761: unsigned int *fd;
2762:
2763: /*
2764: * if f = x^d+x^i+1 then i0 <- i, j0 <- 0, k0 <-0.
2765: * if f = x^d+x^k+x^j+x^i+1 (k>j>i) then i0 <- i, j0 <- j, k0 <-k.
2766: * otherwise i0,j0,k0 is set to 0.
2767: */
2768:
2769: fd = f->b;
2770: w = (d>>5)+1;
2771: if ( f->w && (d==degup2(f)) ) {
2772: for ( nz = 0, i = d; i >= 0; i-- )
2773: if ( fd[i>>5]&(1<<(i&31)) ) nz++;
2774: switch ( nz ) {
2775: case 3:
2776: for ( i0 = 1; !(fd[i0>>5]&(1<<(i0&31))) ; i0++ );
2777: /* reset i0-th bit */
2778: fd[i0>>5] &= ~(1<<(i0&31));
2779: j0 = k0 = 0;
2780: break;
2781: case 5:
2782: for ( i0 = 1; !(fd[i0>>5]&(1<<(i0&31))) ; i0++ );
2783: /* reset i0-th bit */
2784: fd[i0>>5] &= ~(1<<(i0&31));
2785: for ( j0 = i0+1; !(fd[j0>>5]&(1<<(j0&31))) ; j0++ );
2786: /* reset j0-th bit */
2787: fd[j0>>5] &= ~(1<<(j0&31));
2788: for ( k0 = j0+1; !(fd[k0>>5]&(1<<(k0&31))) ; k0++ );
2789: /* reset k0-th bit */
2790: fd[k0>>5] &= ~(1<<(k0&31));
2791: break;
2792: default:
2793: f->w = 0; break;
2794: }
2795: } else
2796: f->w = 0;
2797:
2798: if ( !f->w ) {
2799: fd = f->b;
2800: f->w = w; fd[0] |= 1; fd[d>>5] |= (1<<(d&31));
2801: i0 = j0 = k0 = 0;
2802: }
2803: /* if j0 > 0 then f is already a pentanomial */
2804: if ( j0 > 0 ) goto PENTA;
2805:
2806: /* searching for an irreducible trinomial */
2807:
2808: for ( i = 1; 2*i <= d; i++ ) {
2809: /* skip the polynomials 'before' f */
2810: if ( i < i0 ) continue;
2811: if ( i == i0 ) { i0 = 0; continue; }
2812: /* set i-th bit */
2813: fd[i>>5] |= (1<<(i&31));
2814: ret = irredcheck_dddup2(f);
2815: if ( ret == 1 ) return 0;
2816: /* reset i-th bit */
2817: fd[i>>5] &= ~(1<<(i&31));
2818: }
2819:
2820: /* searching for an irreducible pentanomial */
2821: PENTA:
2822: for ( i = 1; i < d; i++ ) {
2823: /* skip the polynomials 'before' f */
2824: if ( i < i0 ) continue;
2825: if ( i == i0 ) i0 = 0;
2826: /* set i-th bit */
2827: fd[i>>5] |= (1<<(i&31));
2828: for ( j = i+1; j < d; j++ ) {
2829: /* skip the polynomials 'before' f */
2830: if ( j < j0 ) continue;
2831: if ( j == j0 ) j0 = 0;
2832: /* set j-th bit */
2833: fd[j>>5] |= (1<<(j&31));
2834: for ( k = j+1; k < d; k++ ) {
2835: /* skip the polynomials 'before' f */
2836: if ( k < k0 ) continue;
2837: else if ( k == k0 ) { k0 = 0; continue; }
2838: /* set k-th bit */
2839: fd[k>>5] |= (1<<(k&31));
2840: ret = irredcheck_dddup2(f);
2841: if ( ret == 1 ) return 0;
2842: /* reset k-th bit */
2843: fd[k>>5] &= ~(1<<(k&31));
2844: }
2845: /* reset j-th bit */
2846: fd[j>>5] &= ~(1<<(j&31));
2847: }
2848: /* reset i-th bit */
2849: fd[i>>5] &= ~(1<<(i&31));
2850: }
2851: /* exhausted */
2852: return 1;
2853: }
2854:
2855: /*
2856: * f = an irreducible trinomial or pentanomial of degree d 'after' f
2857: *
2858: * searching strategy:
2859: * trinomial x^d+x^i+1:
2860: * i is as small as possible.
2861: * trinomial x^d+x^i+x^j+x^k+1:
2862: * i is as small as possible.
2863: * For such i, j is as small as possible.
2864: * For such i and j, 'k' is as small as possible.
2865: *
2866: * return value : 0 --- exists
2867: * 1 --- does not exist (exhaustion)
2868: */
2869:
2870: int _generate_good_irreducible_polynomial(UP2 f,int d)
2871: {
2872: int ret,i,j,k,nz,i0,j0,k0;
2873: int w;
2874: unsigned int *fd;
2875:
2876: /*
2877: * if f = x^d+x^i+1 then i0 <- i, j0 <- 0, k0 <-0.
2878: * if f = x^d+x^k+x^j+x^i+1 (k>j>i) then i0 <- i, j0 <- j, k0 <-k.
2879: * otherwise i0,j0,k0 is set to 0.
2880: */
2881:
2882: fd = f->b;
2883: w = (d>>5)+1;
2884: if ( f->w && (d==degup2(f)) ) {
2885: for ( nz = 0, i = d; i >= 0; i-- )
2886: if ( fd[i>>5]&(1<<(i&31)) ) nz++;
2887: switch ( nz ) {
2888: case 3:
2889: for ( i0 = 1; !(fd[i0>>5]&(1<<(i0&31))) ; i0++ );
2890: /* reset i0-th bit */
2891: fd[i0>>5] &= ~(1<<(i0&31));
2892: j0 = k0 = 0;
2893: break;
2894: case 5:
2895: for ( i0 = 1; !(fd[i0>>5]&(1<<(i0&31))) ; i0++ );
2896: /* reset i0-th bit */
2897: fd[i0>>5] &= ~(1<<(i0&31));
2898: for ( j0 = i0+1; !(fd[j0>>5]&(1<<(j0&31))) ; j0++ );
2899: /* reset j0-th bit */
2900: fd[j0>>5] &= ~(1<<(j0&31));
2901: for ( k0 = j0+1; !(fd[k0>>5]&(1<<(k0&31))) ; k0++ );
2902: /* reset k0-th bit */
2903: fd[k0>>5] &= ~(1<<(k0&31));
2904: break;
2905: default:
2906: f->w = 0; break;
2907: }
2908: } else
2909: f->w = 0;
2910:
2911: if ( !f->w ) {
2912: fd = f->b;
2913: f->w = w; fd[0] |= 1; fd[d>>5] |= (1<<(d&31));
2914: i0 = j0 = k0 = 0;
2915: }
2916: /* if j0 > 0 then f is already a pentanomial */
2917: if ( j0 > 0 ) goto PENTA;
2918:
2919: /* searching for an irreducible trinomial */
2920:
2921: for ( i = 1; 2*i <= d; i++ ) {
2922: /* skip the polynomials 'before' f */
2923: if ( i < i0 ) continue;
2924: if ( i == i0 ) { i0 = 0; continue; }
2925: /* set i-th bit */
2926: fd[i>>5] |= (1<<(i&31));
2927: ret = irredcheck_dddup2(f);
2928: if ( ret == 1 ) return 0;
2929: /* reset i-th bit */
2930: fd[i>>5] &= ~(1<<(i&31));
2931: }
2932:
2933: /* searching for an irreducible pentanomial */
2934: PENTA:
2935: for ( i = 3; i < d; i++ ) {
2936: /* skip the polynomials 'before' f */
2937: if ( i < i0 ) continue;
2938: if ( i == i0 ) i0 = 0;
2939: /* set i-th bit */
2940: fd[i>>5] |= (1<<(i&31));
2941: for ( j = 2; j < i; j++ ) {
2942: /* skip the polynomials 'before' f */
2943: if ( j < j0 ) continue;
2944: if ( j == j0 ) j0 = 0;
2945: /* set j-th bit */
2946: fd[j>>5] |= (1<<(j&31));
2947: for ( k = 1; k < j; k++ ) {
2948: /* skip the polynomials 'before' f */
2949: if ( k < k0 ) continue;
2950: else if ( k == k0 ) { k0 = 0; continue; }
2951: /* set k-th bit */
2952: fd[k>>5] |= (1<<(k&31));
2953: ret = irredcheck_dddup2(f);
2954: if ( ret == 1 ) return 0;
2955: /* reset k-th bit */
2956: fd[k>>5] &= ~(1<<(k&31));
2957: }
2958: /* reset j-th bit */
2959: fd[j>>5] &= ~(1<<(j&31));
2960: }
2961: /* reset i-th bit */
2962: fd[i>>5] &= ~(1<<(i&31));
2963: }
2964: /* exhausted */
2965: return 1;
1.3 noro 2966: }
2967:
1.24 noro 2968: void printqmat(Q **mat,int row,int col)
1.3 noro 2969: {
2970: int i,j;
2971:
2972: for ( i = 0; i < row; i++ ) {
2973: for ( j = 0; j < col; j++ ) {
1.8 noro 2974: printnum((Num)mat[i][j]); printf(" ");
1.3 noro 2975: }
2976: printf("\n");
2977: }
2978: }
2979:
1.24 noro 2980: void printimat(int **mat,int row,int col)
1.3 noro 2981: {
2982: int i,j;
2983:
2984: for ( i = 0; i < row; i++ ) {
2985: for ( j = 0; j < col; j++ ) {
2986: printf("%d ",mat[i][j]);
2987: }
2988: printf("\n");
2989: }
1.36 noro 2990: }
2991:
2992: void Pnd_det(NODE arg,P *rp)
2993: {
1.37 noro 2994: if ( argc(arg) == 1 )
2995: nd_det(0,ARG0(arg),rp);
2996: else
2997: nd_det(QTOS((Q)ARG1(arg)),ARG0(arg),rp);
1.1 noro 2998: }