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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: *
1.42 ! noro 48: * $OpenXM: OpenXM_contrib2/asir2000/builtin/array.c,v 1.41 2004/12/04 09:39:27 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:
1.24 noro 161: void Pqsort(NODE arg,VECT *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: }
208: MKLIST((LIST)*rp,n);
209: }else {
210: *rp = vect;
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;
761: STOQ(m,q); MKNODE(s,q,0); STOQ(n,q); MKNODE(t,q,s);
762: break;
763: default:
764: error("size : invalid argument"); break;
765: }
766: }
767: MKLIST(*rp,t);
768: }
769:
1.24 noro 770: void Pdet(NODE arg,P *rp)
1.1 noro 771: {
772: MAT m;
773: int n,i,j,mod;
774: P d;
775: P **mat,**w;
776:
777: m = (MAT)ARG0(arg);
778: asir_assert(m,O_MAT,"det");
779: if ( m->row != m->col )
780: error("det : non-square matrix");
781: else if ( argc(arg) == 1 )
782: detp(CO,(P **)BDY(m),m->row,rp);
783: else {
784: n = m->row; mod = QTOS((Q)ARG1(arg)); mat = (P **)BDY(m);
785: w = (P **)almat_pointer(n,n);
786: for ( i = 0; i < n; i++ )
787: for ( j = 0; j < n; j++ )
788: ptomp(mod,mat[i][j],&w[i][j]);
789: detmp(CO,mod,w,n,&d);
790: mptop(d,rp);
1.23 noro 791: }
792: }
793:
1.24 noro 794: void Pinvmat(NODE arg,LIST *rp)
1.23 noro 795: {
796: MAT m,r;
797: int n,i,j,mod;
798: P dn;
799: P **mat,**imat,**w;
800: NODE nd;
801:
802: m = (MAT)ARG0(arg);
803: asir_assert(m,O_MAT,"invmat");
804: if ( m->row != m->col )
805: error("invmat : non-square matrix");
806: else if ( argc(arg) == 1 ) {
807: n = m->row;
808: invmatp(CO,(P **)BDY(m),n,&imat,&dn);
809: NEWMAT(r); r->row = n; r->col = n; r->body = (pointer **)imat;
810: nd = mknode(2,r,dn);
811: MKLIST(*rp,nd);
812: } else {
813: n = m->row; mod = QTOS((Q)ARG1(arg)); mat = (P **)BDY(m);
814: w = (P **)almat_pointer(n,n);
815: for ( i = 0; i < n; i++ )
816: for ( j = 0; j < n; j++ )
817: ptomp(mod,mat[i][j],&w[i][j]);
818: #if 0
819: detmp(CO,mod,w,n,&d);
820: mptop(d,rp);
821: #else
822: error("not implemented yet");
823: #endif
1.1 noro 824: }
1.25 noro 825: }
826:
827: /*
828: input : a row x col matrix A
829: A[I] <-> A[I][0]*x_0+A[I][1]*x_1+...
830:
831: output : [B,R,C]
832: B : a rank(A) x col-rank(A) matrix
833: R : a vector of length rank(A)
834: C : a vector of length col-rank(A)
835: B[I] <-> x_{R[I]}+B[I][0]x_{C[0]}+B[I][1]x_{C[1]}+...
836: */
837:
838: void Pgeneric_gauss_elim(NODE arg,LIST *rp)
839: {
840: NODE n0;
841: MAT m,nm;
842: int *ri,*ci;
843: VECT rind,cind;
844: Q dn,q;
845: int i,j,k,l,row,col,t,rank;
846:
847: asir_assert(ARG0(arg),O_MAT,"generic_gauss_elim");
848: m = (MAT)ARG0(arg);
849: row = m->row; col = m->col;
850: rank = generic_gauss_elim(m,&nm,&dn,&ri,&ci);
851: t = col-rank;
852: MKVECT(rind,rank);
853: MKVECT(cind,t);
854: for ( i = 0; i < rank; i++ ) {
855: STOQ(ri[i],q);
856: BDY(rind)[i] = (pointer)q;
857: }
858: for ( i = 0; i < t; i++ ) {
859: STOQ(ci[i],q);
860: BDY(cind)[i] = (pointer)q;
861: }
862: n0 = mknode(4,nm,dn,rind,cind);
863: MKLIST(*rp,n0);
1.1 noro 864: }
865:
866: /*
867: input : a row x col matrix A
868: A[I] <-> A[I][0]*x_0+A[I][1]*x_1+...
869:
870: output : [B,R,C]
871: B : a rank(A) x col-rank(A) matrix
872: R : a vector of length rank(A)
873: C : a vector of length col-rank(A)
874: B[I] <-> x_{R[I]}+B[I][0]x_{C[0]}+B[I][1]x_{C[1]}+...
875: */
876:
1.24 noro 877: void Pgeneric_gauss_elim_mod(NODE arg,LIST *rp)
1.1 noro 878: {
879: NODE n0;
880: MAT m,mat;
881: VECT rind,cind;
882: Q **tmat;
883: int **wmat;
884: Q *rib,*cib;
885: int *colstat;
886: Q q;
1.24 noro 887: int md,i,j,k,l,row,col,t,rank;
1.1 noro 888:
889: asir_assert(ARG0(arg),O_MAT,"generic_gauss_elim_mod");
890: asir_assert(ARG1(arg),O_N,"generic_gauss_elim_mod");
891: m = (MAT)ARG0(arg); md = QTOS((Q)ARG1(arg));
892: row = m->row; col = m->col; tmat = (Q **)m->body;
893: wmat = (int **)almat(row,col);
894: colstat = (int *)MALLOC_ATOMIC(col*sizeof(int));
895: for ( i = 0; i < row; i++ )
896: for ( j = 0; j < col; j++ )
897: if ( q = (Q)tmat[i][j] ) {
898: t = rem(NM(q),md);
899: if ( t && SGN(q) < 0 )
900: t = (md - t) % md;
901: wmat[i][j] = t;
902: } else
903: wmat[i][j] = 0;
904: rank = generic_gauss_elim_mod(wmat,row,col,md,colstat);
905:
906: MKMAT(mat,rank,col-rank);
907: tmat = (Q **)mat->body;
908: for ( i = 0; i < rank; i++ )
909: for ( j = k = 0; j < col; j++ )
910: if ( !colstat[j] ) {
911: UTOQ(wmat[i][j],tmat[i][k]); k++;
912: }
913:
914: MKVECT(rind,rank);
915: MKVECT(cind,col-rank);
916: rib = (Q *)rind->body; cib = (Q *)cind->body;
917: for ( j = k = l = 0; j < col; j++ )
918: if ( colstat[j] ) {
919: STOQ(j,rib[k]); k++;
920: } else {
921: STOQ(j,cib[l]); l++;
922: }
923: n0 = mknode(3,mat,rind,cind);
924: MKLIST(*rp,n0);
925: }
926:
1.24 noro 927: void Pleqm(NODE arg,VECT *rp)
1.1 noro 928: {
929: MAT m;
930: VECT vect;
931: pointer **mat;
932: Q *v;
933: Q q;
934: int **wmat;
935: int md,i,j,row,col,t,n,status;
936:
937: asir_assert(ARG0(arg),O_MAT,"leqm");
938: asir_assert(ARG1(arg),O_N,"leqm");
939: m = (MAT)ARG0(arg); md = QTOS((Q)ARG1(arg));
940: row = m->row; col = m->col; mat = m->body;
941: wmat = (int **)almat(row,col);
942: for ( i = 0; i < row; i++ )
943: for ( j = 0; j < col; j++ )
944: if ( q = (Q)mat[i][j] ) {
945: t = rem(NM(q),md);
946: if ( SGN(q) < 0 )
947: t = (md - t) % md;
948: wmat[i][j] = t;
949: } else
950: wmat[i][j] = 0;
951: status = gauss_elim_mod(wmat,row,col,md);
952: if ( status < 0 )
953: *rp = 0;
954: else if ( status > 0 )
955: *rp = (VECT)ONE;
956: else {
957: n = col - 1;
958: MKVECT(vect,n);
959: for ( i = 0, v = (Q *)vect->body; i < n; i++ ) {
960: t = (md-wmat[i][n])%md; STOQ(t,v[i]);
961: }
962: *rp = vect;
963: }
964: }
965:
1.24 noro 966: int gauss_elim_mod(int **mat,int row,int col,int md)
1.1 noro 967: {
968: int i,j,k,inv,a,n;
969: int *t,*pivot;
970:
971: n = col - 1;
972: for ( j = 0; j < n; j++ ) {
973: for ( i = j; i < row && !mat[i][j]; i++ );
974: if ( i == row )
975: return 1;
976: if ( i != j ) {
977: t = mat[i]; mat[i] = mat[j]; mat[j] = t;
978: }
979: pivot = mat[j];
980: inv = invm(pivot[j],md);
981: for ( k = j; k <= n; k++ ) {
982: /* pivot[k] = dmar(pivot[k],inv,0,md); */
983: DMAR(pivot[k],inv,0,md,pivot[k])
984: }
985: for ( i = 0; i < row; i++ ) {
986: t = mat[i];
987: if ( i != j && (a = t[j]) )
988: for ( k = j, a = md - a; k <= n; k++ ) {
1.8 noro 989: unsigned int tk;
1.1 noro 990: /* t[k] = dmar(pivot[k],a,t[k],md); */
1.8 noro 991: DMAR(pivot[k],a,t[k],md,tk)
992: t[k] = tk;
1.1 noro 993: }
994: }
995: }
996: for ( i = n; i < row && !mat[i][n]; i++ );
997: if ( i == row )
998: return 0;
999: else
1000: return -1;
1001: }
1002:
1.4 noro 1003: struct oEGT eg_mod,eg_elim,eg_elim1,eg_elim2,eg_chrem,eg_gschk,eg_intrat,eg_symb;
1.31 noro 1004: struct oEGT eg_conv;
1.1 noro 1005:
1.24 noro 1006: int generic_gauss_elim(MAT mat,MAT *nm,Q *dn,int **rindp,int **cindp)
1.1 noro 1007: {
1008: int **wmat;
1009: Q **bmat;
1010: N **tmat;
1011: Q *bmi;
1012: N *tmi;
1013: Q q;
1014: int *wmi;
1015: int *colstat,*wcolstat,*rind,*cind;
1016: int row,col,ind,md,i,j,k,l,t,t1,rank,rank0,inv;
1017: N m1,m2,m3,s,u;
1018: MAT r,crmat;
1019: struct oEGT tmp0,tmp1;
1020: struct oEGT eg_mod_split,eg_elim_split,eg_chrem_split;
1021: struct oEGT eg_intrat_split,eg_gschk_split;
1022: int ret;
1023:
1024: init_eg(&eg_mod_split); init_eg(&eg_chrem_split);
1025: init_eg(&eg_elim_split); init_eg(&eg_intrat_split);
1026: init_eg(&eg_gschk_split);
1027: bmat = (Q **)mat->body;
1028: row = mat->row; col = mat->col;
1029: wmat = (int **)almat(row,col);
1030: colstat = (int *)MALLOC_ATOMIC(col*sizeof(int));
1031: wcolstat = (int *)MALLOC_ATOMIC(col*sizeof(int));
1032: for ( ind = 0; ; ind++ ) {
1.11 noro 1033: if ( DP_Print ) {
1.2 noro 1034: fprintf(asir_out,"."); fflush(asir_out);
1035: }
1.12 noro 1036: md = get_lprime(ind);
1.1 noro 1037: get_eg(&tmp0);
1038: for ( i = 0; i < row; i++ )
1039: for ( j = 0, bmi = bmat[i], wmi = wmat[i]; j < col; j++ )
1040: if ( q = (Q)bmi[j] ) {
1041: t = rem(NM(q),md);
1042: if ( t && SGN(q) < 0 )
1043: t = (md - t) % md;
1044: wmi[j] = t;
1045: } else
1046: wmi[j] = 0;
1047: get_eg(&tmp1);
1048: add_eg(&eg_mod,&tmp0,&tmp1);
1049: add_eg(&eg_mod_split,&tmp0,&tmp1);
1050: get_eg(&tmp0);
1051: rank = generic_gauss_elim_mod(wmat,row,col,md,wcolstat);
1052: get_eg(&tmp1);
1053: add_eg(&eg_elim,&tmp0,&tmp1);
1054: add_eg(&eg_elim_split,&tmp0,&tmp1);
1055: if ( !ind ) {
1056: RESET:
1057: UTON(md,m1);
1058: rank0 = rank;
1059: bcopy(wcolstat,colstat,col*sizeof(int));
1060: MKMAT(crmat,rank,col-rank);
1061: MKMAT(r,rank,col-rank); *nm = r;
1062: tmat = (N **)crmat->body;
1063: for ( i = 0; i < rank; i++ )
1064: for ( j = k = 0, tmi = tmat[i], wmi = wmat[i]; j < col; j++ )
1065: if ( !colstat[j] ) {
1066: UTON(wmi[j],tmi[k]); k++;
1067: }
1068: } else {
1069: if ( rank < rank0 ) {
1.11 noro 1070: if ( DP_Print ) {
1.1 noro 1071: fprintf(asir_out,"lower rank matrix; continuing...\n");
1.2 noro 1072: fflush(asir_out);
1073: }
1.1 noro 1074: continue;
1075: } else if ( rank > rank0 ) {
1.11 noro 1076: if ( DP_Print ) {
1.1 noro 1077: fprintf(asir_out,"higher rank matrix; resetting...\n");
1.2 noro 1078: fflush(asir_out);
1079: }
1.1 noro 1080: goto RESET;
1081: } else {
1082: for ( j = 0; (j<col) && (colstat[j]==wcolstat[j]); j++ );
1083: if ( j < col ) {
1.11 noro 1084: if ( DP_Print ) {
1.1 noro 1085: fprintf(asir_out,"inconsitent colstat; resetting...\n");
1.2 noro 1086: fflush(asir_out);
1087: }
1.1 noro 1088: goto RESET;
1089: }
1090: }
1091:
1092: get_eg(&tmp0);
1093: inv = invm(rem(m1,md),md);
1094: UTON(md,m2); muln(m1,m2,&m3);
1095: for ( i = 0; i < rank; i++ )
1096: for ( j = k = 0, tmi = tmat[i], wmi = wmat[i]; j < col; j++ )
1097: if ( !colstat[j] ) {
1098: if ( tmi[k] ) {
1099: /* f3 = f1+m1*(m1 mod m2)^(-1)*(f2 - f1 mod m2) */
1100: t = rem(tmi[k],md);
1101: if ( wmi[j] >= t )
1102: t = wmi[j]-t;
1103: else
1104: t = md-(t-wmi[j]);
1105: DMAR(t,inv,0,md,t1)
1106: UTON(t1,u);
1107: muln(m1,u,&s);
1108: addn(tmi[k],s,&u); tmi[k] = u;
1109: } else if ( wmi[j] ) {
1110: /* f3 = m1*(m1 mod m2)^(-1)*f2 */
1111: DMAR(wmi[j],inv,0,md,t)
1112: UTON(t,u);
1113: muln(m1,u,&s); tmi[k] = s;
1114: }
1115: k++;
1116: }
1117: m1 = m3;
1118: get_eg(&tmp1);
1119: add_eg(&eg_chrem,&tmp0,&tmp1);
1120: add_eg(&eg_chrem_split,&tmp0,&tmp1);
1121:
1122: get_eg(&tmp0);
1.38 noro 1123: if ( ind % F4_INTRAT_PERIOD )
1.13 noro 1124: ret = 0;
1125: else
1126: ret = intmtoratm(crmat,m1,*nm,dn);
1.1 noro 1127: get_eg(&tmp1);
1128: add_eg(&eg_intrat,&tmp0,&tmp1);
1129: add_eg(&eg_intrat_split,&tmp0,&tmp1);
1130: if ( ret ) {
1131: *rindp = rind = (int *)MALLOC_ATOMIC(rank*sizeof(int));
1132: *cindp = cind = (int *)MALLOC_ATOMIC((col-rank)*sizeof(int));
1133: for ( j = k = l = 0; j < col; j++ )
1134: if ( colstat[j] )
1135: rind[k++] = j;
1136: else
1137: cind[l++] = j;
1138: get_eg(&tmp0);
1.3 noro 1139: if ( gensolve_check(mat,*nm,*dn,rind,cind) ) {
1140: get_eg(&tmp1);
1141: add_eg(&eg_gschk,&tmp0,&tmp1);
1142: add_eg(&eg_gschk_split,&tmp0,&tmp1);
1.11 noro 1143: if ( DP_Print ) {
1.3 noro 1144: print_eg("Mod",&eg_mod_split);
1145: print_eg("Elim",&eg_elim_split);
1146: print_eg("ChRem",&eg_chrem_split);
1147: print_eg("IntRat",&eg_intrat_split);
1148: print_eg("Check",&eg_gschk_split);
1149: fflush(asir_out);
1150: }
1151: return rank;
1152: }
1153: }
1154: }
1155: }
1156: }
1157:
1.24 noro 1158: int generic_gauss_elim_hensel(MAT mat,MAT *nmmat,Q *dn,int **rindp,int **cindp)
1.3 noro 1159: {
1160: MAT bmat,xmat;
1161: Q **a0,**a,**b,**x,**nm;
1162: Q *ai,*bi,*xi;
1163: int row,col;
1164: int **w;
1165: int *wi;
1166: int **wc;
1167: Q mdq,q,s,u;
1168: N tn;
1169: int ind,md,i,j,k,l,li,ri,rank;
1170: unsigned int t;
1171: int *cinfo,*rinfo;
1172: int *rind,*cind;
1173: int count;
1.41 noro 1174: int ret;
1175: struct oEGT eg_mul,eg_inv,eg_intrat,eg_check,tmp0,tmp1;
1.39 noro 1176: int period;
1.3 noro 1177:
1178: a0 = (Q **)mat->body;
1179: row = mat->row; col = mat->col;
1180: w = (int **)almat(row,col);
1181: for ( ind = 0; ; ind++ ) {
1.12 noro 1182: md = get_lprime(ind);
1.3 noro 1183: STOQ(md,mdq);
1184: for ( i = 0; i < row; i++ )
1185: for ( j = 0, ai = a0[i], wi = w[i]; j < col; j++ )
1186: if ( q = (Q)ai[j] ) {
1187: t = rem(NM(q),md);
1188: if ( t && SGN(q) < 0 )
1189: t = (md - t) % md;
1190: wi[j] = t;
1191: } else
1192: wi[j] = 0;
1193:
1.27 noro 1194: rank = find_lhs_and_lu_mod((unsigned int **)w,row,col,md,&rinfo,&cinfo);
1.3 noro 1195: a = (Q **)almat_pointer(rank,rank); /* lhs mat */
1196: MKMAT(bmat,rank,col-rank); b = (Q **)bmat->body; /* lhs mat */
1197: for ( j = li = ri = 0; j < col; j++ )
1198: if ( cinfo[j] ) {
1199: /* the column is in lhs */
1200: for ( i = 0; i < rank; i++ ) {
1201: w[i][li] = w[i][j];
1202: a[i][li] = a0[rinfo[i]][j];
1203: }
1204: li++;
1205: } else {
1206: /* the column is in rhs */
1207: for ( i = 0; i < rank; i++ )
1208: b[i][ri] = a0[rinfo[i]][j];
1209: ri++;
1210: }
1211:
1212: /* solve Ax+B=0; A: rank x rank, B: rank x ri */
1213: MKMAT(xmat,rank,ri); x = (Q **)(xmat)->body;
1214: MKMAT(*nmmat,rank,ri); nm = (Q **)(*nmmat)->body;
1215: /* use the right part of w as work area */
1216: /* ri = col - rank */
1217: wc = (int **)almat(rank,ri);
1218: for ( i = 0; i < rank; i++ )
1219: wc[i] = w[i]+rank;
1220: *rindp = rind = (int *)MALLOC_ATOMIC(rank*sizeof(int));
1221: *cindp = cind = (int *)MALLOC_ATOMIC((ri)*sizeof(int));
1222:
1223: init_eg(&eg_mul); init_eg(&eg_inv);
1.41 noro 1224: init_eg(&eg_check); init_eg(&eg_intrat);
1.39 noro 1225: period = F4_INTRAT_PERIOD;
1.3 noro 1226: for ( q = ONE, count = 0; ; count++ ) {
1.42 ! noro 1227: if ( DP_Print > 3 )
1.41 noro 1228: fprintf(stderr,"o");
1.3 noro 1229: /* wc = -b mod md */
1230: for ( i = 0; i < rank; i++ )
1231: for ( j = 0, bi = b[i], wi = wc[i]; j < ri; j++ )
1232: if ( u = (Q)bi[j] ) {
1233: t = rem(NM(u),md);
1234: if ( t && SGN(u) > 0 )
1235: t = (md - t) % md;
1236: wi[j] = t;
1237: } else
1238: wi[j] = 0;
1239: /* wc = A^(-1)wc; wc is normalized */
1240: get_eg(&tmp0);
1241: solve_by_lu_mod(w,rank,md,wc,ri);
1.1 noro 1242: get_eg(&tmp1);
1.3 noro 1243: add_eg(&eg_inv,&tmp0,&tmp1);
1244: /* x = x-q*wc */
1245: for ( i = 0; i < rank; i++ )
1246: for ( j = 0, xi = x[i], wi = wc[i]; j < ri; j++ ) {
1247: STOQ(wi[j],u); mulq(q,u,&s);
1248: subq(xi[j],s,&u); xi[j] = u;
1249: }
1250: get_eg(&tmp0);
1251: for ( i = 0; i < rank; i++ )
1252: for ( j = 0; j < ri; j++ ) {
1253: inner_product_mat_int_mod(a,wc,rank,i,j,&u);
1254: addq(b[i][j],u,&s);
1255: if ( s ) {
1256: t = divin(NM(s),md,&tn);
1257: if ( t )
1258: error("generic_gauss_elim_hensel:incosistent");
1259: NTOQ(tn,SGN(s),b[i][j]);
1260: } else
1261: b[i][j] = 0;
1262: }
1263: get_eg(&tmp1);
1264: add_eg(&eg_mul,&tmp0,&tmp1);
1265: /* q = q*md */
1266: mulq(q,mdq,&u); q = u;
1.41 noro 1267: if ( !(count % period) ) {
1268: get_eg(&tmp0);
1269: ret = intmtoratm_q(xmat,NM(q),*nmmat,dn);
1270: get_eg(&tmp1); add_eg(&eg_intrat,&tmp0,&tmp1);
1271: if ( ret ) {
1.39 noro 1272: for ( j = k = l = 0; j < col; j++ )
1273: if ( cinfo[j] )
1274: rind[k++] = j;
1275: else
1276: cind[l++] = j;
1.41 noro 1277: get_eg(&tmp0);
1278: ret = gensolve_check(mat,*nmmat,*dn,rind,cind);
1279: get_eg(&tmp1); add_eg(&eg_check,&tmp0,&tmp1);
1280: if ( ret ) {
1.42 ! noro 1281: if ( DP_Print > 3 ) {
1.40 noro 1282: fprintf(stderr,"\n");
1283: print_eg("INV",&eg_inv);
1284: print_eg("MUL",&eg_mul);
1.41 noro 1285: print_eg("INTRAT",&eg_intrat);
1286: print_eg("CHECK",&eg_check);
1.40 noro 1287: fflush(asir_out);
1288: }
1.39 noro 1289: return rank;
1290: }
1291: } else
1292: period *=2;
1.41 noro 1293: }
1.1 noro 1294: }
1295: }
1296: }
1297:
1298: int f4_nocheck;
1299:
1.24 noro 1300: int gensolve_check(MAT mat,MAT nm,Q dn,int *rind,int *cind)
1.1 noro 1301: {
1302: int row,col,rank,clen,i,j,k,l;
1.24 noro 1303: Q s,t;
1.1 noro 1304: Q *w;
1305: Q *mati,*nmk;
1306:
1307: if ( f4_nocheck )
1308: return 1;
1309: row = mat->row; col = mat->col;
1310: rank = nm->row; clen = nm->col;
1311: w = (Q *)MALLOC(clen*sizeof(Q));
1312: for ( i = 0; i < row; i++ ) {
1313: mati = (Q *)mat->body[i];
1314: #if 1
1315: bzero(w,clen*sizeof(Q));
1316: for ( k = 0; k < rank; k++ )
1317: for ( l = 0, nmk = (Q *)nm->body[k]; l < clen; l++ ) {
1318: mulq(mati[rind[k]],nmk[l],&t);
1319: addq(w[l],t,&s); w[l] = s;
1320: }
1321: for ( j = 0; j < clen; j++ ) {
1322: mulq(dn,mati[cind[j]],&t);
1323: if ( cmpq(w[j],t) )
1324: break;
1325: }
1326: #else
1327: for ( j = 0; j < clen; j++ ) {
1328: for ( k = 0, s = 0; k < rank; k++ ) {
1329: mulq(mati[rind[k]],nm->body[k][j],&t);
1330: addq(s,t,&u); s = u;
1331: }
1332: mulq(dn,mati[cind[j]],&t);
1333: if ( cmpq(s,t) )
1334: break;
1335: }
1336: #endif
1337: if ( j != clen )
1338: break;
1339: }
1340: if ( i != row )
1341: return 0;
1342: else
1343: return 1;
1344: }
1345:
1346: /* assuming 0 < c < m */
1347:
1.24 noro 1348: int inttorat(N c,N m,N b,int *sgnp,N *nmp,N *dnp)
1.1 noro 1349: {
1.24 noro 1350: Q qq,t,u1,v1,r1;
1351: N q,u2,v2,r2;
1.1 noro 1352:
1353: u1 = 0; v1 = ONE; u2 = m; v2 = c;
1354: while ( cmpn(v2,b) >= 0 ) {
1355: divn(u2,v2,&q,&r2); u2 = v2; v2 = r2;
1356: NTOQ(q,1,qq); mulq(qq,v1,&t); subq(u1,t,&r1); u1 = v1; v1 = r1;
1357: }
1358: if ( cmpn(NM(v1),b) >= 0 )
1359: return 0;
1360: else {
1361: *nmp = v2;
1362: *dnp = NM(v1);
1363: *sgnp = SGN(v1);
1364: return 1;
1365: }
1366: }
1367:
1368: /* mat->body = N ** */
1369:
1.24 noro 1370: int intmtoratm(MAT mat,N md,MAT nm,Q *dn)
1.1 noro 1371: {
1372: N t,s,b;
1.24 noro 1373: Q dn0,dn1,nm1,q;
1.1 noro 1374: int i,j,k,l,row,col;
1375: Q **rmat;
1376: N **tmat;
1377: N *tmi;
1378: Q *nmk;
1379: N u,unm,udn;
1380: int sgn,ret;
1381:
1.3 noro 1382: if ( UNIN(md) )
1383: return 0;
1.1 noro 1384: row = mat->row; col = mat->col;
1385: bshiftn(md,1,&t);
1386: isqrt(t,&s);
1387: bshiftn(s,64,&b);
1388: if ( !b )
1389: b = ONEN;
1390: dn0 = ONE;
1391: tmat = (N **)mat->body;
1392: rmat = (Q **)nm->body;
1393: for ( i = 0; i < row; i++ )
1394: for ( j = 0, tmi = tmat[i]; j < col; j++ )
1395: if ( tmi[j] ) {
1396: muln(tmi[j],NM(dn0),&s);
1397: remn(s,md,&u);
1398: ret = inttorat(u,md,b,&sgn,&unm,&udn);
1399: if ( !ret )
1400: return 0;
1401: else {
1402: NTOQ(unm,sgn,nm1);
1403: NTOQ(udn,1,dn1);
1404: if ( !UNIQ(dn1) ) {
1405: for ( k = 0; k < i; k++ )
1406: for ( l = 0, nmk = rmat[k]; l < col; l++ ) {
1407: mulq(nmk[l],dn1,&q); nmk[l] = q;
1408: }
1409: for ( l = 0, nmk = rmat[i]; l < j; l++ ) {
1410: mulq(nmk[l],dn1,&q); nmk[l] = q;
1411: }
1412: }
1413: rmat[i][j] = nm1;
1414: mulq(dn0,dn1,&q); dn0 = q;
1415: }
1416: }
1417: *dn = dn0;
1418: return 1;
1419: }
1420:
1.3 noro 1421: /* mat->body = Q ** */
1422:
1.24 noro 1423: int intmtoratm_q(MAT mat,N md,MAT nm,Q *dn)
1.3 noro 1424: {
1425: N t,s,b;
1.24 noro 1426: Q dn0,dn1,nm1,q;
1.3 noro 1427: int i,j,k,l,row,col;
1428: Q **rmat;
1429: Q **tmat;
1430: Q *tmi;
1431: Q *nmk;
1432: N u,unm,udn;
1433: int sgn,ret;
1434:
1435: if ( UNIN(md) )
1436: return 0;
1437: row = mat->row; col = mat->col;
1438: bshiftn(md,1,&t);
1439: isqrt(t,&s);
1440: bshiftn(s,64,&b);
1441: if ( !b )
1442: b = ONEN;
1443: dn0 = ONE;
1444: tmat = (Q **)mat->body;
1445: rmat = (Q **)nm->body;
1446: for ( i = 0; i < row; i++ )
1447: for ( j = 0, tmi = tmat[i]; j < col; j++ )
1448: if ( tmi[j] ) {
1449: muln(NM(tmi[j]),NM(dn0),&s);
1450: remn(s,md,&u);
1451: ret = inttorat(u,md,b,&sgn,&unm,&udn);
1452: if ( !ret )
1453: return 0;
1454: else {
1455: if ( SGN(tmi[j])<0 )
1456: sgn = -sgn;
1457: NTOQ(unm,sgn,nm1);
1458: NTOQ(udn,1,dn1);
1459: if ( !UNIQ(dn1) ) {
1460: for ( k = 0; k < i; k++ )
1461: for ( l = 0, nmk = rmat[k]; l < col; l++ ) {
1462: mulq(nmk[l],dn1,&q); nmk[l] = q;
1463: }
1464: for ( l = 0, nmk = rmat[i]; l < j; l++ ) {
1465: mulq(nmk[l],dn1,&q); nmk[l] = q;
1466: }
1467: }
1468: rmat[i][j] = nm1;
1469: mulq(dn0,dn1,&q); dn0 = q;
1470: }
1471: }
1472: *dn = dn0;
1473: return 1;
1474: }
1475:
1.4 noro 1476: #define ONE_STEP1 if ( zzz = *s ) { DMAR(zzz,hc,*tj,md,*tj) } tj++; s++;
1477:
1.24 noro 1478: void reduce_reducers_mod(int **mat,int row,int col,int md)
1.4 noro 1479: {
1480: int i,j,k,l,hc,zzz;
1481: int *t,*s,*tj,*ind;
1482:
1483: /* reduce the reducers */
1484: ind = (int *)ALLOCA(row*sizeof(int));
1485: for ( i = 0; i < row; i++ ) {
1486: t = mat[i];
1487: for ( j = 0; j < col && !t[j]; j++ );
1488: /* register the position of the head term */
1489: ind[i] = j;
1490: for ( l = i-1; l >= 0; l-- ) {
1491: /* reduce mat[i] by mat[l] */
1492: if ( hc = t[ind[l]] ) {
1493: /* mat[i] = mat[i]-hc*mat[l] */
1494: j = ind[l];
1495: s = mat[l]+j;
1496: tj = t+j;
1497: hc = md-hc;
1498: k = col-j;
1499: for ( ; k >= 64; k -= 64 ) {
1500: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
1501: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
1502: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
1503: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
1504: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
1505: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
1506: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
1507: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
1508: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
1509: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
1510: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
1511: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
1512: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
1513: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
1514: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
1515: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
1516: }
1.16 noro 1517: for ( ; k > 0; k-- ) {
1.4 noro 1518: if ( zzz = *s ) { DMAR(zzz,hc,*tj,md,*tj) } tj++; s++;
1519: }
1520: }
1521: }
1522: }
1523: }
1524:
1525: /*
1526: mat[i] : reducers (i=0,...,nred-1)
1527: spolys (i=nred,...,row-1)
1528: mat[0] < mat[1] < ... < mat[nred-1] w.r.t the term order
1529: 1. reduce the reducers
1530: 2. reduce spolys by the reduced reducers
1531: */
1532:
1.24 noro 1533: void pre_reduce_mod(int **mat,int row,int col,int nred,int md)
1.4 noro 1534: {
1535: int i,j,k,l,hc,inv;
1536: int *t,*s,*tk,*ind;
1537:
1538: #if 1
1539: /* reduce the reducers */
1540: ind = (int *)ALLOCA(row*sizeof(int));
1541: for ( i = 0; i < nred; i++ ) {
1542: /* make mat[i] monic and mat[i] by mat[0],...,mat[i-1] */
1543: t = mat[i];
1544: for ( j = 0; j < col && !t[j]; j++ );
1545: /* register the position of the head term */
1546: ind[i] = j;
1547: inv = invm(t[j],md);
1548: for ( k = j; k < col; k++ )
1549: if ( t[k] )
1550: DMAR(t[k],inv,0,md,t[k])
1551: for ( l = i-1; l >= 0; l-- ) {
1552: /* reduce mat[i] by mat[l] */
1553: if ( hc = t[ind[l]] ) {
1554: /* mat[i] = mat[i]-hc*mat[l] */
1555: for ( k = ind[l], hc = md-hc, s = mat[l]+k, tk = t+k;
1556: k < col; k++, tk++, s++ )
1557: if ( *s )
1558: DMAR(*s,hc,*tk,md,*tk)
1559: }
1560: }
1561: }
1562: /* reduce the spolys */
1563: for ( i = nred; i < row; i++ ) {
1564: t = mat[i];
1565: for ( l = nred-1; l >= 0; l-- ) {
1566: /* reduce mat[i] by mat[l] */
1567: if ( hc = t[ind[l]] ) {
1568: /* mat[i] = mat[i]-hc*mat[l] */
1569: for ( k = ind[l], hc = md-hc, s = mat[l]+k, tk = t+k;
1570: k < col; k++, tk++, s++ )
1571: if ( *s )
1572: DMAR(*s,hc,*tk,md,*tk)
1573: }
1574: }
1575: }
1576: #endif
1577: }
1578: /*
1579: mat[i] : reducers (i=0,...,nred-1)
1580: mat[0] < mat[1] < ... < mat[nred-1] w.r.t the term order
1581: */
1582:
1.24 noro 1583: void reduce_sp_by_red_mod(int *sp,int **redmat,int *ind,int nred,int col,int md)
1.4 noro 1584: {
1585: int i,j,k,hc,zzz;
1.24 noro 1586: int *s,*tj;
1.4 noro 1587:
1588: /* reduce the spolys by redmat */
1589: for ( i = nred-1; i >= 0; i-- ) {
1590: /* reduce sp by redmat[i] */
1591: if ( hc = sp[ind[i]] ) {
1592: /* sp = sp-hc*redmat[i] */
1593: j = ind[i];
1594: hc = md-hc;
1595: s = redmat[i]+j;
1596: tj = sp+j;
1.16 noro 1597: for ( k = col-j; k > 0; k-- ) {
1.4 noro 1598: if ( zzz = *s ) { DMAR(zzz,hc,*tj,md,*tj) } tj++; s++;
1.15 noro 1599: }
1600: }
1.17 noro 1601: }
1602: }
1603:
1604: /*
1.15 noro 1605: mat[i] : compressed reducers (i=0,...,nred-1)
1606: mat[0] < mat[1] < ... < mat[nred-1] w.r.t the term order
1607: */
1608:
1.24 noro 1609: void red_by_compress(int m,unsigned int *p,unsigned int *r,
1610: unsigned int *ri,unsigned int hc,int len)
1.18 noro 1611: {
1.19 noro 1612: unsigned int up,lo;
1.18 noro 1613: unsigned int dmy;
1614: unsigned int *pj;
1615:
1.21 noro 1616: p[*ri] = 0; r++; ri++;
1617: for ( len--; len; len--, r++, ri++ ) {
1618: pj = p+ *ri;
1619: DMA(*r,hc,*pj,up,lo);
1.18 noro 1620: if ( up ) {
1621: DSAB(m,up,lo,dmy,*pj);
1622: } else
1623: *pj = lo;
1624: }
1625: }
1626:
1627: /* p -= hc*r */
1628:
1.24 noro 1629: void red_by_vect(int m,unsigned int *p,unsigned int *r,unsigned int hc,int len)
1.18 noro 1630: {
1631: register unsigned int up,lo;
1632: unsigned int dmy;
1633:
1634: *p++ = 0; r++; len--;
1635: for ( ; len; len--, r++, p++ )
1636: if ( *r ) {
1.20 noro 1637: DMA(*r,hc,*p,up,lo);
1.18 noro 1638: if ( up ) {
1639: DSAB(m,up,lo,dmy,*p);
1640: } else
1641: *p = lo;
1642: }
1643: }
1644:
1.32 noro 1645: void red_by_vect_sf(int m,unsigned int *p,unsigned int *r,unsigned int hc,int len)
1646: {
1647: *p++ = 0; r++; len--;
1648: for ( ; len; len--, r++, p++ )
1649: if ( *r )
1650: *p = _addsf(_mulsf(*r,hc),*p);
1651: }
1652:
1.21 noro 1653: extern unsigned int **psca;
1654:
1.24 noro 1655: void reduce_sp_by_red_mod_compress (int *sp,CDP *redmat,int *ind,
1656: int nred,int col,int md)
1.15 noro 1657: {
1.24 noro 1658: int i,len;
1.15 noro 1659: CDP ri;
1.24 noro 1660: unsigned int hc;
1.18 noro 1661: unsigned int *usp;
1.15 noro 1662:
1.18 noro 1663: usp = (unsigned int *)sp;
1.15 noro 1664: /* reduce the spolys by redmat */
1665: for ( i = nred-1; i >= 0; i-- ) {
1666: /* reduce sp by redmat[i] */
1.18 noro 1667: usp[ind[i]] %= md;
1668: if ( hc = usp[ind[i]] ) {
1.15 noro 1669: /* sp = sp-hc*redmat[i] */
1670: hc = md-hc;
1671: ri = redmat[i];
1672: len = ri->len;
1.21 noro 1673: red_by_compress(md,usp,psca[ri->psindex],ri->body,hc,len);
1.4 noro 1674: }
1675: }
1.18 noro 1676: for ( i = 0; i < col; i++ )
1.24 noro 1677: if ( usp[i] >= (unsigned int)md )
1.18 noro 1678: usp[i] %= md;
1.4 noro 1679: }
1680:
1681: #define ONE_STEP2 if ( zzz = *pk ) { DMAR(zzz,a,*tk,md,*tk) } pk++; tk++;
1682:
1.24 noro 1683: int generic_gauss_elim_mod(int **mat0,int row,int col,int md,int *colstat)
1.1 noro 1684: {
1.24 noro 1685: int i,j,k,l,inv,a,rank;
1686: unsigned int *t,*pivot,*pk;
1.18 noro 1687: unsigned int **mat;
1.1 noro 1688:
1.18 noro 1689: mat = (unsigned int **)mat0;
1.1 noro 1690: for ( rank = 0, j = 0; j < col; j++ ) {
1.18 noro 1691: for ( i = rank; i < row; i++ )
1692: mat[i][j] %= md;
1693: for ( i = rank; i < row; i++ )
1694: if ( mat[i][j] )
1695: break;
1.1 noro 1696: if ( i == row ) {
1697: colstat[j] = 0;
1698: continue;
1699: } else
1700: colstat[j] = 1;
1701: if ( i != rank ) {
1702: t = mat[i]; mat[i] = mat[rank]; mat[rank] = t;
1703: }
1704: pivot = mat[rank];
1705: inv = invm(pivot[j],md);
1.4 noro 1706: for ( k = j, pk = pivot+k; k < col; k++, pk++ )
1707: if ( *pk ) {
1.24 noro 1708: if ( *pk >= (unsigned int)md )
1.18 noro 1709: *pk %= md;
1.4 noro 1710: DMAR(*pk,inv,0,md,*pk)
1.1 noro 1711: }
1712: for ( i = rank+1; i < row; i++ ) {
1713: t = mat[i];
1.18 noro 1714: if ( a = t[j] )
1715: red_by_vect(md,t+j,pivot+j,md-a,col-j);
1.1 noro 1716: }
1717: rank++;
1718: }
1719: for ( j = col-1, l = rank-1; j >= 0; j-- )
1720: if ( colstat[j] ) {
1721: pivot = mat[l];
1722: for ( i = 0; i < l; i++ ) {
1723: t = mat[i];
1.18 noro 1724: t[j] %= md;
1725: if ( a = t[j] )
1726: red_by_vect(md,t+j,pivot+j,md-a,col-j);
1.1 noro 1727: }
1728: l--;
1.18 noro 1729: }
1730: for ( j = 0, l = 0; l < rank; j++ )
1731: if ( colstat[j] ) {
1732: t = mat[l];
1733: for ( k = j; k < col; k++ )
1.24 noro 1734: if ( t[k] >= (unsigned int)md )
1.18 noro 1735: t[k] %= md;
1736: l++;
1.32 noro 1737: }
1738: return rank;
1739: }
1740:
1741: int generic_gauss_elim_sf(int **mat0,int row,int col,int md,int *colstat)
1742: {
1743: int i,j,k,l,inv,a,rank;
1744: unsigned int *t,*pivot,*pk;
1745: unsigned int **mat;
1746:
1747: mat = (unsigned int **)mat0;
1748: for ( rank = 0, j = 0; j < col; j++ ) {
1749: for ( i = rank; i < row; i++ )
1750: if ( mat[i][j] )
1751: break;
1752: if ( i == row ) {
1753: colstat[j] = 0;
1754: continue;
1755: } else
1756: colstat[j] = 1;
1757: if ( i != rank ) {
1758: t = mat[i]; mat[i] = mat[rank]; mat[rank] = t;
1759: }
1760: pivot = mat[rank];
1761: inv = _invsf(pivot[j]);
1762: for ( k = j, pk = pivot+k; k < col; k++, pk++ )
1763: if ( *pk )
1764: *pk = _mulsf(*pk,inv);
1765: for ( i = rank+1; i < row; i++ ) {
1766: t = mat[i];
1767: if ( a = t[j] )
1768: red_by_vect_sf(md,t+j,pivot+j,_chsgnsf(a),col-j);
1769: }
1770: rank++;
1771: }
1772: for ( j = col-1, l = rank-1; j >= 0; j-- )
1773: if ( colstat[j] ) {
1774: pivot = mat[l];
1775: for ( i = 0; i < l; i++ ) {
1776: t = mat[i];
1777: if ( a = t[j] )
1778: red_by_vect_sf(md,t+j,pivot+j,_chsgnsf(a),col-j);
1779: }
1780: l--;
1.1 noro 1781: }
1782: return rank;
1783: }
1784:
1785: /* LU decomposition; a[i][i] = 1/U[i][i] */
1786:
1.24 noro 1787: int lu_gfmmat(GFMMAT mat,unsigned int md,int *perm)
1.1 noro 1788: {
1789: int row,col;
1.24 noro 1790: int i,j,k;
1.1 noro 1791: unsigned int *t,*pivot;
1792: unsigned int **a;
1793: unsigned int inv,m;
1794:
1795: row = mat->row; col = mat->col;
1796: a = mat->body;
1797: bzero(perm,row*sizeof(int));
1798:
1799: for ( i = 0; i < row; i++ )
1800: perm[i] = i;
1801: for ( k = 0; k < col; k++ ) {
1802: for ( i = k; i < row && !a[i][k]; i++ );
1803: if ( i == row )
1804: return 0;
1805: if ( i != k ) {
1806: j = perm[i]; perm[i] = perm[k]; perm[k] = j;
1807: t = a[i]; a[i] = a[k]; a[k] = t;
1808: }
1809: pivot = a[k];
1810: pivot[k] = inv = invm(pivot[k],md);
1811: for ( i = k+1; i < row; i++ ) {
1812: t = a[i];
1813: if ( m = t[k] ) {
1814: DMAR(inv,m,0,md,t[k])
1815: for ( j = k+1, m = md - t[k]; j < col; j++ )
1816: if ( pivot[j] ) {
1.8 noro 1817: unsigned int tj;
1818:
1819: DMAR(m,pivot[j],t[j],md,tj)
1820: t[j] = tj;
1.1 noro 1821: }
1822: }
1823: }
1824: }
1825: return 1;
1826: }
1827:
1.3 noro 1828: /*
1829: Input
1830: a: a row x col matrix
1831: md : a modulus
1832:
1833: Output:
1834: return : d = the rank of mat
1835: a[0..(d-1)][0..(d-1)] : LU decomposition (a[i][i] = 1/U[i][i])
1836: rinfo: array of length row
1837: cinfo: array of length col
1838: i-th row in new a <-> rinfo[i]-th row in old a
1839: cinfo[j]=1 <=> j-th column is contained in the LU decomp.
1840: */
1841:
1.24 noro 1842: int find_lhs_and_lu_mod(unsigned int **a,int row,int col,
1843: unsigned int md,int **rinfo,int **cinfo)
1.3 noro 1844: {
1.24 noro 1845: int i,j,k,d;
1.3 noro 1846: int *rp,*cp;
1847: unsigned int *t,*pivot;
1848: unsigned int inv,m;
1849:
1850: *rinfo = rp = (int *)MALLOC_ATOMIC(row*sizeof(int));
1851: *cinfo = cp = (int *)MALLOC_ATOMIC(col*sizeof(int));
1852: for ( i = 0; i < row; i++ )
1853: rp[i] = i;
1854: for ( k = 0, d = 0; k < col; k++ ) {
1855: for ( i = d; i < row && !a[i][k]; i++ );
1856: if ( i == row ) {
1857: cp[k] = 0;
1858: continue;
1859: } else
1860: cp[k] = 1;
1861: if ( i != d ) {
1862: j = rp[i]; rp[i] = rp[d]; rp[d] = j;
1863: t = a[i]; a[i] = a[d]; a[d] = t;
1864: }
1865: pivot = a[d];
1866: pivot[k] = inv = invm(pivot[k],md);
1867: for ( i = d+1; i < row; i++ ) {
1868: t = a[i];
1869: if ( m = t[k] ) {
1870: DMAR(inv,m,0,md,t[k])
1871: for ( j = k+1, m = md - t[k]; j < col; j++ )
1872: if ( pivot[j] ) {
1.8 noro 1873: unsigned int tj;
1874: DMAR(m,pivot[j],t[j],md,tj)
1875: t[j] = tj;
1.3 noro 1876: }
1877: }
1878: }
1879: d++;
1880: }
1881: return d;
1882: }
1883:
1884: /*
1885: Input
1886: a : n x n matrix; a result of LU-decomposition
1887: md : modulus
1888: b : n x l matrix
1889: Output
1890: b = a^(-1)b
1891: */
1892:
1.24 noro 1893: void solve_by_lu_mod(int **a,int n,int md,int **b,int l)
1.3 noro 1894: {
1895: unsigned int *y,*c;
1896: int i,j,k;
1897: unsigned int t,m,m2;
1898:
1899: y = (int *)MALLOC_ATOMIC(n*sizeof(int));
1900: c = (int *)MALLOC_ATOMIC(n*sizeof(int));
1901: m2 = md>>1;
1902: for ( k = 0; k < l; k++ ) {
1903: /* copy b[.][k] to c */
1904: for ( i = 0; i < n; i++ )
1905: c[i] = (unsigned int)b[i][k];
1906: /* solve Ly=c */
1907: for ( i = 0; i < n; i++ ) {
1908: for ( t = c[i], j = 0; j < i; j++ )
1909: if ( a[i][j] ) {
1910: m = md - a[i][j];
1911: DMAR(m,y[j],t,md,t)
1912: }
1913: y[i] = t;
1914: }
1915: /* solve Uc=y */
1916: for ( i = n-1; i >= 0; i-- ) {
1917: for ( t = y[i], j =i+1; j < n; j++ )
1918: if ( a[i][j] ) {
1919: m = md - a[i][j];
1920: DMAR(m,c[j],t,md,t)
1921: }
1922: /* a[i][i] = 1/U[i][i] */
1923: DMAR(t,a[i][i],0,md,c[i])
1924: }
1925: /* copy c to b[.][k] with normalization */
1926: for ( i = 0; i < n; i++ )
1927: b[i][k] = (int)(c[i]>m2 ? c[i]-md : c[i]);
1928: }
1929: }
1930:
1.24 noro 1931: void Pleqm1(NODE arg,VECT *rp)
1.1 noro 1932: {
1933: MAT m;
1934: VECT vect;
1935: pointer **mat;
1936: Q *v;
1937: Q q;
1938: int **wmat;
1939: int md,i,j,row,col,t,n,status;
1940:
1941: asir_assert(ARG0(arg),O_MAT,"leqm1");
1942: asir_assert(ARG1(arg),O_N,"leqm1");
1943: m = (MAT)ARG0(arg); md = QTOS((Q)ARG1(arg));
1944: row = m->row; col = m->col; mat = m->body;
1945: wmat = (int **)almat(row,col);
1946: for ( i = 0; i < row; i++ )
1947: for ( j = 0; j < col; j++ )
1948: if ( q = (Q)mat[i][j] ) {
1949: t = rem(NM(q),md);
1950: if ( SGN(q) < 0 )
1951: t = (md - t) % md;
1952: wmat[i][j] = t;
1953: } else
1954: wmat[i][j] = 0;
1955: status = gauss_elim_mod1(wmat,row,col,md);
1956: if ( status < 0 )
1957: *rp = 0;
1958: else if ( status > 0 )
1959: *rp = (VECT)ONE;
1960: else {
1961: n = col - 1;
1962: MKVECT(vect,n);
1963: for ( i = 0, v = (Q *)vect->body; i < n; i++ ) {
1964: t = (md-wmat[i][n])%md; STOQ(t,v[i]);
1965: }
1966: *rp = vect;
1967: }
1968: }
1969:
1.24 noro 1970: int gauss_elim_mod1(int **mat,int row,int col,int md)
1.1 noro 1971: {
1972: int i,j,k,inv,a,n;
1973: int *t,*pivot;
1974:
1975: n = col - 1;
1976: for ( j = 0; j < n; j++ ) {
1977: for ( i = j; i < row && !mat[i][j]; i++ );
1978: if ( i == row )
1979: return 1;
1980: if ( i != j ) {
1981: t = mat[i]; mat[i] = mat[j]; mat[j] = t;
1982: }
1983: pivot = mat[j];
1984: inv = invm(pivot[j],md);
1985: for ( k = j; k <= n; k++ )
1986: pivot[k] = dmar(pivot[k],inv,0,md);
1987: for ( i = j+1; i < row; i++ ) {
1988: t = mat[i];
1989: if ( i != j && (a = t[j]) )
1990: for ( k = j, a = md - a; k <= n; k++ )
1991: t[k] = dmar(pivot[k],a,t[k],md);
1992: }
1993: }
1994: for ( i = n; i < row && !mat[i][n]; i++ );
1995: if ( i == row ) {
1996: for ( j = n-1; j >= 0; j-- ) {
1997: for ( i = j-1, a = (md-mat[j][n])%md; i >= 0; i-- ) {
1998: mat[i][n] = dmar(mat[i][j],a,mat[i][n],md);
1999: mat[i][j] = 0;
2000: }
2001: }
2002: return 0;
2003: } else
2004: return -1;
2005: }
2006:
1.24 noro 2007: void Pgeninvm(NODE arg,LIST *rp)
1.1 noro 2008: {
2009: MAT m;
2010: pointer **mat;
2011: Q **tmat;
2012: Q q;
2013: unsigned int **wmat;
2014: int md,i,j,row,col,t,status;
2015: MAT mat1,mat2;
2016: NODE node1,node2;
2017:
2018: asir_assert(ARG0(arg),O_MAT,"leqm1");
2019: asir_assert(ARG1(arg),O_N,"leqm1");
2020: m = (MAT)ARG0(arg); md = QTOS((Q)ARG1(arg));
2021: row = m->row; col = m->col; mat = m->body;
2022: wmat = (unsigned int **)almat(row,col+row);
2023: for ( i = 0; i < row; i++ ) {
2024: bzero((char *)wmat[i],(col+row)*sizeof(int));
2025: for ( j = 0; j < col; j++ )
2026: if ( q = (Q)mat[i][j] ) {
2027: t = rem(NM(q),md);
2028: if ( SGN(q) < 0 )
2029: t = (md - t) % md;
2030: wmat[i][j] = t;
2031: }
2032: wmat[i][col+i] = 1;
2033: }
2034: status = gauss_elim_geninv_mod(wmat,row,col,md);
2035: if ( status > 0 )
2036: *rp = 0;
2037: else {
2038: MKMAT(mat1,col,row); MKMAT(mat2,row-col,row);
2039: for ( i = 0, tmat = (Q **)mat1->body; i < col; i++ )
2040: for ( j = 0; j < row; j++ )
1.24 noro 2041: UTOQ(wmat[i][j+col],tmat[i][j]);
1.1 noro 2042: for ( tmat = (Q **)mat2->body; i < row; i++ )
2043: for ( j = 0; j < row; j++ )
1.24 noro 2044: UTOQ(wmat[i][j+col],tmat[i-col][j]);
1.1 noro 2045: MKNODE(node2,mat2,0); MKNODE(node1,mat1,node2); MKLIST(*rp,node1);
2046: }
2047: }
2048:
1.24 noro 2049: int gauss_elim_geninv_mod(unsigned int **mat,int row,int col,int md)
1.1 noro 2050: {
2051: int i,j,k,inv,a,n,m;
2052: unsigned int *t,*pivot;
2053:
2054: n = col; m = row+col;
2055: for ( j = 0; j < n; j++ ) {
2056: for ( i = j; i < row && !mat[i][j]; i++ );
2057: if ( i == row )
2058: return 1;
2059: if ( i != j ) {
2060: t = mat[i]; mat[i] = mat[j]; mat[j] = t;
2061: }
2062: pivot = mat[j];
2063: inv = invm(pivot[j],md);
2064: for ( k = j; k < m; k++ )
2065: pivot[k] = dmar(pivot[k],inv,0,md);
2066: for ( i = j+1; i < row; i++ ) {
2067: t = mat[i];
2068: if ( a = t[j] )
2069: for ( k = j, a = md - a; k < m; k++ )
2070: t[k] = dmar(pivot[k],a,t[k],md);
2071: }
2072: }
2073: for ( j = n-1; j >= 0; j-- ) {
2074: pivot = mat[j];
2075: for ( i = j-1; i >= 0; i-- ) {
2076: t = mat[i];
2077: if ( a = t[j] )
2078: for ( k = j, a = md - a; k < m; k++ )
2079: t[k] = dmar(pivot[k],a,t[k],md);
2080: }
2081: }
2082: return 0;
2083: }
2084:
1.24 noro 2085: void Psolve_by_lu_gfmmat(NODE arg,VECT *rp)
1.1 noro 2086: {
2087: GFMMAT lu;
2088: Q *perm,*rhs,*v;
2089: int n,i;
2090: unsigned int md;
2091: unsigned int *b,*sol;
2092: VECT r;
2093:
2094: lu = (GFMMAT)ARG0(arg);
2095: perm = (Q *)BDY((VECT)ARG1(arg));
2096: rhs = (Q *)BDY((VECT)ARG2(arg));
2097: md = (unsigned int)QTOS((Q)ARG3(arg));
2098: n = lu->col;
2099: b = (unsigned int *)MALLOC_ATOMIC(n*sizeof(int));
2100: sol = (unsigned int *)MALLOC_ATOMIC(n*sizeof(int));
2101: for ( i = 0; i < n; i++ )
2102: b[i] = QTOS(rhs[QTOS(perm[i])]);
2103: solve_by_lu_gfmmat(lu,md,b,sol);
2104: MKVECT(r,n);
2105: for ( i = 0, v = (Q *)r->body; i < n; i++ )
1.24 noro 2106: UTOQ(sol[i],v[i]);
1.1 noro 2107: *rp = r;
2108: }
2109:
1.24 noro 2110: void solve_by_lu_gfmmat(GFMMAT lu,unsigned int md,
2111: unsigned int *b,unsigned int *x)
1.1 noro 2112: {
2113: int n;
2114: unsigned int **a;
2115: unsigned int *y;
2116: int i,j;
2117: unsigned int t,m;
2118:
2119: n = lu->col;
2120: a = lu->body;
2121: y = (unsigned int *)MALLOC_ATOMIC(n*sizeof(int));
2122: /* solve Ly=b */
2123: for ( i = 0; i < n; i++ ) {
2124: for ( t = b[i], j = 0; j < i; j++ )
2125: if ( a[i][j] ) {
2126: m = md - a[i][j];
2127: DMAR(m,y[j],t,md,t)
2128: }
2129: y[i] = t;
2130: }
2131: /* solve Ux=y */
2132: for ( i = n-1; i >= 0; i-- ) {
2133: for ( t = y[i], j =i+1; j < n; j++ )
2134: if ( a[i][j] ) {
2135: m = md - a[i][j];
2136: DMAR(m,x[j],t,md,t)
2137: }
2138: /* a[i][i] = 1/U[i][i] */
2139: DMAR(t,a[i][i],0,md,x[i])
2140: }
2141: }
2142:
1.24 noro 2143: void Plu_gfmmat(NODE arg,LIST *rp)
1.1 noro 2144: {
2145: MAT m;
2146: GFMMAT mm;
2147: unsigned int md;
2148: int i,row,col,status;
2149: int *iperm;
2150: Q *v;
2151: VECT perm;
2152: NODE n0;
2153:
2154: asir_assert(ARG0(arg),O_MAT,"mat_to_gfmmat");
2155: asir_assert(ARG1(arg),O_N,"mat_to_gfmmat");
2156: m = (MAT)ARG0(arg); md = (unsigned int)QTOS((Q)ARG1(arg));
2157: mat_to_gfmmat(m,md,&mm);
2158: row = m->row;
2159: col = m->col;
2160: iperm = (int *)MALLOC_ATOMIC(row*sizeof(int));
2161: status = lu_gfmmat(mm,md,iperm);
2162: if ( !status )
2163: n0 = 0;
2164: else {
2165: MKVECT(perm,row);
2166: for ( i = 0, v = (Q *)perm->body; i < row; i++ )
2167: STOQ(iperm[i],v[i]);
2168: n0 = mknode(2,mm,perm);
2169: }
2170: MKLIST(*rp,n0);
2171: }
2172:
1.24 noro 2173: void Pmat_to_gfmmat(NODE arg,GFMMAT *rp)
1.1 noro 2174: {
2175: MAT m;
2176: unsigned int md;
2177:
2178: asir_assert(ARG0(arg),O_MAT,"mat_to_gfmmat");
2179: asir_assert(ARG1(arg),O_N,"mat_to_gfmmat");
2180: m = (MAT)ARG0(arg); md = (unsigned int)QTOS((Q)ARG1(arg));
2181: mat_to_gfmmat(m,md,rp);
2182: }
2183:
1.24 noro 2184: void mat_to_gfmmat(MAT m,unsigned int md,GFMMAT *rp)
1.1 noro 2185: {
2186: unsigned int **wmat;
2187: unsigned int t;
2188: Q **mat;
2189: Q q;
2190: int i,j,row,col;
2191:
2192: row = m->row; col = m->col; mat = (Q **)m->body;
2193: wmat = (unsigned int **)almat(row,col);
2194: for ( i = 0; i < row; i++ ) {
2195: bzero((char *)wmat[i],col*sizeof(unsigned int));
2196: for ( j = 0; j < col; j++ )
2197: if ( q = mat[i][j] ) {
2198: t = (unsigned int)rem(NM(q),md);
2199: if ( SGN(q) < 0 )
2200: t = (md - t) % md;
2201: wmat[i][j] = t;
2202: }
2203: }
2204: TOGFMMAT(row,col,wmat,*rp);
2205: }
2206:
1.27 noro 2207: void Pgeninvm_swap(arg,rp)
2208: NODE arg;
2209: LIST *rp;
1.1 noro 2210: {
2211: MAT m;
2212: pointer **mat;
2213: Q **tmat;
2214: Q *tvect;
2215: Q q;
2216: unsigned int **wmat,**invmat;
2217: int *index;
2218: unsigned int t,md;
2219: int i,j,row,col,status;
2220: MAT mat1;
2221: VECT vect1;
2222: NODE node1,node2;
2223:
2224: asir_assert(ARG0(arg),O_MAT,"geninvm_swap");
2225: asir_assert(ARG1(arg),O_N,"geninvm_swap");
2226: m = (MAT)ARG0(arg); md = QTOS((Q)ARG1(arg));
2227: row = m->row; col = m->col; mat = m->body;
2228: wmat = (unsigned int **)almat(row,col+row);
2229: for ( i = 0; i < row; i++ ) {
2230: bzero((char *)wmat[i],(col+row)*sizeof(int));
2231: for ( j = 0; j < col; j++ )
2232: if ( q = (Q)mat[i][j] ) {
2233: t = (unsigned int)rem(NM(q),md);
2234: if ( SGN(q) < 0 )
2235: t = (md - t) % md;
2236: wmat[i][j] = t;
2237: }
2238: wmat[i][col+i] = 1;
2239: }
2240: status = gauss_elim_geninv_mod_swap(wmat,row,col,md,&invmat,&index);
2241: if ( status > 0 )
2242: *rp = 0;
2243: else {
2244: MKMAT(mat1,col,col);
2245: for ( i = 0, tmat = (Q **)mat1->body; i < col; i++ )
2246: for ( j = 0; j < col; j++ )
2247: UTOQ(invmat[i][j],tmat[i][j]);
2248: MKVECT(vect1,row);
2249: for ( i = 0, tvect = (Q *)vect1->body; i < row; i++ )
2250: STOQ(index[i],tvect[i]);
2251: MKNODE(node2,vect1,0); MKNODE(node1,mat1,node2); MKLIST(*rp,node1);
2252: }
2253: }
2254:
1.27 noro 2255: gauss_elim_geninv_mod_swap(mat,row,col,md,invmatp,indexp)
2256: unsigned int **mat;
2257: int row,col;
2258: unsigned int md;
2259: unsigned int ***invmatp;
2260: int **indexp;
1.1 noro 2261: {
2262: int i,j,k,inv,a,n,m;
2263: unsigned int *t,*pivot,*s;
2264: int *index;
2265: unsigned int **invmat;
2266:
2267: n = col; m = row+col;
2268: *indexp = index = (int *)MALLOC_ATOMIC(row*sizeof(int));
2269: for ( i = 0; i < row; i++ )
2270: index[i] = i;
2271: for ( j = 0; j < n; j++ ) {
2272: for ( i = j; i < row && !mat[i][j]; i++ );
2273: if ( i == row ) {
2274: *indexp = 0; *invmatp = 0; return 1;
2275: }
2276: if ( i != j ) {
2277: t = mat[i]; mat[i] = mat[j]; mat[j] = t;
2278: k = index[i]; index[i] = index[j]; index[j] = k;
2279: }
2280: pivot = mat[j];
2281: inv = (unsigned int)invm(pivot[j],md);
2282: for ( k = j; k < m; k++ )
2283: if ( pivot[k] )
2284: pivot[k] = (unsigned int)dmar(pivot[k],inv,0,md);
2285: for ( i = j+1; i < row; i++ ) {
2286: t = mat[i];
2287: if ( a = t[j] )
2288: for ( k = j, a = md - a; k < m; k++ )
2289: if ( pivot[k] )
2290: t[k] = dmar(pivot[k],a,t[k],md);
2291: }
2292: }
2293: for ( j = n-1; j >= 0; j-- ) {
2294: pivot = mat[j];
2295: for ( i = j-1; i >= 0; i-- ) {
2296: t = mat[i];
2297: if ( a = t[j] )
2298: for ( k = j, a = md - a; k < m; k++ )
2299: if ( pivot[k] )
2300: t[k] = dmar(pivot[k],a,t[k],md);
2301: }
2302: }
2303: *invmatp = invmat = (unsigned int **)almat(col,col);
1.27 noro 2304: for ( i = 0; i < col; i++ )
2305: for ( j = 0, s = invmat[i], t = mat[i]; j < col; j++ )
2306: s[j] = t[col+index[j]];
2307: return 0;
2308: }
2309:
2310: void Pgeninv_sf_swap(NODE arg,LIST *rp)
2311: {
2312: MAT m;
2313: GFS **mat,**tmat;
2314: Q *tvect;
2315: GFS q;
2316: int **wmat,**invmat;
2317: int *index;
2318: unsigned int t;
2319: int i,j,row,col,status;
2320: MAT mat1;
2321: VECT vect1;
2322: NODE node1,node2;
2323:
2324: asir_assert(ARG0(arg),O_MAT,"geninv_sf_swap");
2325: m = (MAT)ARG0(arg);
2326: row = m->row; col = m->col; mat = (GFS **)m->body;
2327: wmat = (int **)almat(row,col+row);
2328: for ( i = 0; i < row; i++ ) {
2329: bzero((char *)wmat[i],(col+row)*sizeof(int));
2330: for ( j = 0; j < col; j++ )
2331: if ( q = (GFS)mat[i][j] )
2332: wmat[i][j] = FTOIF(CONT(q));
2333: wmat[i][col+i] = _onesf();
2334: }
2335: status = gauss_elim_geninv_sf_swap(wmat,row,col,&invmat,&index);
2336: if ( status > 0 )
2337: *rp = 0;
2338: else {
2339: MKMAT(mat1,col,col);
2340: for ( i = 0, tmat = (GFS **)mat1->body; i < col; i++ )
2341: for ( j = 0; j < col; j++ )
2342: if ( t = invmat[i][j] ) {
2343: MKGFS(IFTOF(t),tmat[i][j]);
2344: }
2345: MKVECT(vect1,row);
2346: for ( i = 0, tvect = (Q *)vect1->body; i < row; i++ )
2347: STOQ(index[i],tvect[i]);
2348: MKNODE(node2,vect1,0); MKNODE(node1,mat1,node2); MKLIST(*rp,node1);
2349: }
2350: }
2351:
2352: int gauss_elim_geninv_sf_swap(int **mat,int row,int col,
2353: int ***invmatp,int **indexp)
2354: {
2355: int i,j,k,inv,a,n,m,u;
2356: int *t,*pivot,*s;
2357: int *index;
2358: int **invmat;
2359:
2360: n = col; m = row+col;
2361: *indexp = index = (int *)MALLOC_ATOMIC(row*sizeof(int));
2362: for ( i = 0; i < row; i++ )
2363: index[i] = i;
2364: for ( j = 0; j < n; j++ ) {
2365: for ( i = j; i < row && !mat[i][j]; i++ );
2366: if ( i == row ) {
2367: *indexp = 0; *invmatp = 0; return 1;
2368: }
2369: if ( i != j ) {
2370: t = mat[i]; mat[i] = mat[j]; mat[j] = t;
2371: k = index[i]; index[i] = index[j]; index[j] = k;
2372: }
2373: pivot = mat[j];
2374: inv = _invsf(pivot[j]);
2375: for ( k = j; k < m; k++ )
2376: if ( pivot[k] )
2377: pivot[k] = _mulsf(pivot[k],inv);
2378: for ( i = j+1; i < row; i++ ) {
2379: t = mat[i];
2380: if ( a = t[j] )
2381: for ( k = j, a = _chsgnsf(a); k < m; k++ )
2382: if ( pivot[k] ) {
2383: u = _mulsf(pivot[k],a);
2384: t[k] = _addsf(u,t[k]);
2385: }
2386: }
2387: }
2388: for ( j = n-1; j >= 0; j-- ) {
2389: pivot = mat[j];
2390: for ( i = j-1; i >= 0; i-- ) {
2391: t = mat[i];
2392: if ( a = t[j] )
2393: for ( k = j, a = _chsgnsf(a); k < m; k++ )
2394: if ( pivot[k] ) {
2395: u = _mulsf(pivot[k],a);
2396: t[k] = _addsf(u,t[k]);
2397: }
2398: }
2399: }
2400: *invmatp = invmat = (int **)almat(col,col);
1.1 noro 2401: for ( i = 0; i < col; i++ )
2402: for ( j = 0, s = invmat[i], t = mat[i]; j < col; j++ )
2403: s[j] = t[col+index[j]];
2404: return 0;
2405: }
2406:
2407: void _addn(N,N,N);
2408: int _subn(N,N,N);
2409: void _muln(N,N,N);
2410:
1.24 noro 2411: void inner_product_int(Q *a,Q *b,int n,Q *r)
1.1 noro 2412: {
2413: int la,lb,i;
2414: int sgn,sgn1;
2415: N wm,wma,sum,t;
2416:
2417: for ( la = lb = 0, i = 0; i < n; i++ ) {
2418: if ( a[i] )
2419: if ( DN(a[i]) )
2420: error("inner_product_int : invalid argument");
2421: else
2422: la = MAX(PL(NM(a[i])),la);
2423: if ( b[i] )
2424: if ( DN(b[i]) )
2425: error("inner_product_int : invalid argument");
2426: else
2427: lb = MAX(PL(NM(b[i])),lb);
2428: }
2429: sgn = 0;
2430: sum= NALLOC(la+lb+2);
2431: bzero((char *)sum,(la+lb+3)*sizeof(unsigned int));
2432: wm = NALLOC(la+lb+2);
2433: wma = NALLOC(la+lb+2);
2434: for ( i = 0; i < n; i++ ) {
2435: if ( !a[i] || !b[i] )
2436: continue;
2437: _muln(NM(a[i]),NM(b[i]),wm);
2438: sgn1 = SGN(a[i])*SGN(b[i]);
2439: if ( !sgn ) {
2440: sgn = sgn1;
2441: t = wm; wm = sum; sum = t;
2442: } else if ( sgn == sgn1 ) {
2443: _addn(sum,wm,wma);
2444: if ( !PL(wma) )
2445: sgn = 0;
2446: t = wma; wma = sum; sum = t;
2447: } else {
2448: /* sgn*sum+sgn1*wm = sgn*(sum-wm) */
2449: sgn *= _subn(sum,wm,wma);
2450: t = wma; wma = sum; sum = t;
2451: }
2452: }
2453: GC_free(wm);
2454: GC_free(wma);
2455: if ( !sgn ) {
2456: GC_free(sum);
2457: *r = 0;
2458: } else
2459: NTOQ(sum,sgn,*r);
2460: }
2461:
1.3 noro 2462: /* (k,l) element of a*b where a: .x n matrix, b: n x . integer matrix */
2463:
1.24 noro 2464: void inner_product_mat_int_mod(Q **a,int **b,int n,int k,int l,Q *r)
1.3 noro 2465: {
2466: int la,lb,i;
2467: int sgn,sgn1;
2468: N wm,wma,sum,t;
2469: Q aki;
2470: int bil,bilsgn;
2471: struct oN tn;
2472:
2473: for ( la = 0, i = 0; i < n; i++ ) {
2474: if ( aki = a[k][i] )
2475: if ( DN(aki) )
2476: error("inner_product_int : invalid argument");
2477: else
2478: la = MAX(PL(NM(aki)),la);
2479: }
2480: lb = 1;
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 ( !(aki = a[k][i]) || !(bil = b[i][l]) )
2488: continue;
2489: tn.p = 1;
2490: if ( bil > 0 ) {
2491: tn.b[0] = bil; bilsgn = 1;
2492: } else {
2493: tn.b[0] = -bil; bilsgn = -1;
2494: }
2495: _muln(NM(aki),&tn,wm);
2496: sgn1 = SGN(aki)*bilsgn;
2497: if ( !sgn ) {
2498: sgn = sgn1;
2499: t = wm; wm = sum; sum = t;
2500: } else if ( sgn == sgn1 ) {
2501: _addn(sum,wm,wma);
2502: if ( !PL(wma) )
2503: sgn = 0;
2504: t = wma; wma = sum; sum = t;
2505: } else {
2506: /* sgn*sum+sgn1*wm = sgn*(sum-wm) */
2507: sgn *= _subn(sum,wm,wma);
2508: t = wma; wma = sum; sum = t;
2509: }
2510: }
2511: GC_free(wm);
2512: GC_free(wma);
2513: if ( !sgn ) {
2514: GC_free(sum);
2515: *r = 0;
2516: } else
2517: NTOQ(sum,sgn,*r);
2518: }
2519:
1.24 noro 2520: void Pmul_mat_vect_int(NODE arg,VECT *rp)
1.1 noro 2521: {
2522: MAT mat;
2523: VECT vect,r;
2524: int row,col,i;
2525:
2526: mat = (MAT)ARG0(arg);
2527: vect = (VECT)ARG1(arg);
2528: row = mat->row;
2529: col = mat->col;
2530: MKVECT(r,row);
1.24 noro 2531: for ( i = 0; i < row; i++ ) {
2532: inner_product_int((Q *)mat->body[i],(Q *)vect->body,col,(Q *)&r->body[i]);
2533: }
1.1 noro 2534: *rp = r;
2535: }
2536:
1.24 noro 2537: void Pnbpoly_up2(NODE arg,GF2N *rp)
1.1 noro 2538: {
2539: int m,type,ret;
2540: UP2 r;
2541:
2542: m = QTOS((Q)ARG0(arg));
2543: type = QTOS((Q)ARG1(arg));
2544: ret = generate_ONB_polynomial(&r,m,type);
2545: if ( ret == 0 )
2546: MKGF2N(r,*rp);
2547: else
2548: *rp = 0;
2549: }
2550:
1.24 noro 2551: void Px962_irredpoly_up2(NODE arg,GF2N *rp)
1.1 noro 2552: {
1.24 noro 2553: int m,ret,w;
1.1 noro 2554: GF2N prev;
2555: UP2 r;
2556:
2557: m = QTOS((Q)ARG0(arg));
2558: prev = (GF2N)ARG1(arg);
2559: if ( !prev ) {
2560: w = (m>>5)+1; NEWUP2(r,w); r->w = 0;
2561: bzero((char *)r->b,w*sizeof(unsigned int));
2562: } else {
2563: r = prev->body;
2564: if ( degup2(r) != m ) {
2565: w = (m>>5)+1; NEWUP2(r,w); r->w = 0;
2566: bzero((char *)r->b,w*sizeof(unsigned int));
2567: }
2568: }
1.24 noro 2569: ret = _generate_irreducible_polynomial(r,m);
1.1 noro 2570: if ( ret == 0 )
2571: MKGF2N(r,*rp);
2572: else
2573: *rp = 0;
2574: }
2575:
1.24 noro 2576: void Pirredpoly_up2(NODE arg,GF2N *rp)
1.1 noro 2577: {
1.24 noro 2578: int m,ret,w;
1.1 noro 2579: GF2N prev;
2580: UP2 r;
2581:
2582: m = QTOS((Q)ARG0(arg));
2583: prev = (GF2N)ARG1(arg);
2584: if ( !prev ) {
2585: w = (m>>5)+1; NEWUP2(r,w); r->w = 0;
2586: bzero((char *)r->b,w*sizeof(unsigned int));
2587: } else {
2588: r = prev->body;
2589: if ( degup2(r) != m ) {
2590: w = (m>>5)+1; NEWUP2(r,w); r->w = 0;
2591: bzero((char *)r->b,w*sizeof(unsigned int));
2592: }
2593: }
1.24 noro 2594: ret = _generate_good_irreducible_polynomial(r,m);
1.1 noro 2595: if ( ret == 0 )
2596: MKGF2N(r,*rp);
2597: else
2598: *rp = 0;
2599: }
2600:
1.26 noro 2601: void Pmat_swap_row_destructive(NODE arg, MAT *m)
2602: {
2603: int i1,i2;
2604: pointer *t;
2605: MAT mat;
2606:
2607: asir_assert(ARG0(arg),O_MAT,"mat_swap_row_destructive");
2608: asir_assert(ARG1(arg),O_N,"mat_swap_row_destructive");
2609: asir_assert(ARG2(arg),O_N,"mat_swap_row_destructive");
2610: mat = (MAT)ARG0(arg);
2611: i1 = QTOS((Q)ARG1(arg));
2612: i2 = QTOS((Q)ARG2(arg));
2613: if ( i1 < 0 || i2 < 0 || i1 >= mat->row || i2 >= mat->row )
2614: error("mat_swap_row_destructive : Out of range");
2615: t = mat->body[i1];
2616: mat->body[i1] = mat->body[i2];
2617: mat->body[i2] = t;
2618: *m = mat;
2619: }
2620:
2621: void Pmat_swap_col_destructive(NODE arg, MAT *m)
2622: {
2623: int j1,j2,i,n;
2624: pointer *mi;
2625: pointer t;
2626: MAT mat;
2627:
2628: asir_assert(ARG0(arg),O_MAT,"mat_swap_col_destructive");
2629: asir_assert(ARG1(arg),O_N,"mat_swap_col_destructive");
2630: asir_assert(ARG2(arg),O_N,"mat_swap_col_destructive");
2631: mat = (MAT)ARG0(arg);
2632: j1 = QTOS((Q)ARG1(arg));
2633: j2 = QTOS((Q)ARG2(arg));
2634: if ( j1 < 0 || j2 < 0 || j1 >= mat->col || j2 >= mat->col )
2635: error("mat_swap_col_destructive : Out of range");
2636: n = mat->row;
2637: for ( i = 0; i < n; i++ ) {
2638: mi = mat->body[i];
2639: t = mi[j1]; mi[j1] = mi[j2]; mi[j2] = t;
2640: }
2641: *m = mat;
2642: }
1.1 noro 2643: /*
2644: * f = type 'type' normal polynomial of degree m if exists
2645: * IEEE P1363 A.7.2
2646: *
2647: * return value : 0 --- exists
2648: * 1 --- does not exist
2649: * -1 --- failure (memory allocation error)
2650: */
2651:
2652: int generate_ONB_polynomial(UP2 *rp,int m,int type)
2653: {
2654: int i,r;
2655: int w;
2656: UP2 f,f0,f1,f2,t;
2657:
2658: w = (m>>5)+1;
2659: switch ( type ) {
2660: case 1:
2661: if ( !TypeT_NB_check(m,1) ) return 1;
2662: NEWUP2(f,w); *rp = f; f->w = w;
2663: /* set all the bits */
2664: for ( i = 0; i < w; i++ )
2665: f->b[i] = 0xffffffff;
2666: /* mask the top word if necessary */
2667: if ( r = (m+1)&31 )
2668: f->b[w-1] &= (1<<r)-1;
2669: return 0;
2670: break;
2671: case 2:
2672: if ( !TypeT_NB_check(m,2) ) return 1;
2673: NEWUP2(f,w); *rp = f;
2674: W_NEWUP2(f0,w);
2675: W_NEWUP2(f1,w);
2676: W_NEWUP2(f2,w);
2677:
2678: /* recursion for genrating Type II normal polynomial */
2679:
2680: /* f0 = 1, f1 = t+1 */
2681: f0->w = 1; f0->b[0] = 1;
2682: f1->w = 1; f1->b[0] = 3;
2683: for ( i = 2; i <= m; i++ ) {
2684: /* f2 = t*f1+f0 */
2685: _bshiftup2(f1,-1,f2);
2686: _addup2_destructive(f2,f0);
2687: /* cyclic change of the variables */
2688: t = f0; f0 = f1; f1 = f2; f2 = t;
2689: }
2690: _copyup2(f1,f);
2691: return 0;
2692: break;
2693: default:
2694: return -1;
2695: break;
2696: }
2697: }
2698:
2699: /*
2700: * f = an irreducible trinomial or pentanomial of degree d 'after' f
2701: * return value : 0 --- exists
2702: * 1 --- does not exist (exhaustion)
2703: */
2704:
2705: int _generate_irreducible_polynomial(UP2 f,int d)
2706: {
2707: int ret,i,j,k,nz,i0,j0,k0;
2708: int w;
2709: unsigned int *fd;
2710:
2711: /*
2712: * if f = x^d+x^i+1 then i0 <- i, j0 <- 0, k0 <-0.
2713: * if f = x^d+x^k+x^j+x^i+1 (k>j>i) then i0 <- i, j0 <- j, k0 <-k.
2714: * otherwise i0,j0,k0 is set to 0.
2715: */
2716:
2717: fd = f->b;
2718: w = (d>>5)+1;
2719: if ( f->w && (d==degup2(f)) ) {
2720: for ( nz = 0, i = d; i >= 0; i-- )
2721: if ( fd[i>>5]&(1<<(i&31)) ) nz++;
2722: switch ( nz ) {
2723: case 3:
2724: for ( i0 = 1; !(fd[i0>>5]&(1<<(i0&31))) ; i0++ );
2725: /* reset i0-th bit */
2726: fd[i0>>5] &= ~(1<<(i0&31));
2727: j0 = k0 = 0;
2728: break;
2729: case 5:
2730: for ( i0 = 1; !(fd[i0>>5]&(1<<(i0&31))) ; i0++ );
2731: /* reset i0-th bit */
2732: fd[i0>>5] &= ~(1<<(i0&31));
2733: for ( j0 = i0+1; !(fd[j0>>5]&(1<<(j0&31))) ; j0++ );
2734: /* reset j0-th bit */
2735: fd[j0>>5] &= ~(1<<(j0&31));
2736: for ( k0 = j0+1; !(fd[k0>>5]&(1<<(k0&31))) ; k0++ );
2737: /* reset k0-th bit */
2738: fd[k0>>5] &= ~(1<<(k0&31));
2739: break;
2740: default:
2741: f->w = 0; break;
2742: }
2743: } else
2744: f->w = 0;
2745:
2746: if ( !f->w ) {
2747: fd = f->b;
2748: f->w = w; fd[0] |= 1; fd[d>>5] |= (1<<(d&31));
2749: i0 = j0 = k0 = 0;
2750: }
2751: /* if j0 > 0 then f is already a pentanomial */
2752: if ( j0 > 0 ) goto PENTA;
2753:
2754: /* searching for an irreducible trinomial */
2755:
2756: for ( i = 1; 2*i <= d; i++ ) {
2757: /* skip the polynomials 'before' f */
2758: if ( i < i0 ) continue;
2759: if ( i == i0 ) { i0 = 0; continue; }
2760: /* set i-th bit */
2761: fd[i>>5] |= (1<<(i&31));
2762: ret = irredcheck_dddup2(f);
2763: if ( ret == 1 ) return 0;
2764: /* reset i-th bit */
2765: fd[i>>5] &= ~(1<<(i&31));
2766: }
2767:
2768: /* searching for an irreducible pentanomial */
2769: PENTA:
2770: for ( i = 1; i < d; i++ ) {
2771: /* skip the polynomials 'before' f */
2772: if ( i < i0 ) continue;
2773: if ( i == i0 ) i0 = 0;
2774: /* set i-th bit */
2775: fd[i>>5] |= (1<<(i&31));
2776: for ( j = i+1; j < d; j++ ) {
2777: /* skip the polynomials 'before' f */
2778: if ( j < j0 ) continue;
2779: if ( j == j0 ) j0 = 0;
2780: /* set j-th bit */
2781: fd[j>>5] |= (1<<(j&31));
2782: for ( k = j+1; k < d; k++ ) {
2783: /* skip the polynomials 'before' f */
2784: if ( k < k0 ) continue;
2785: else if ( k == k0 ) { k0 = 0; continue; }
2786: /* set k-th bit */
2787: fd[k>>5] |= (1<<(k&31));
2788: ret = irredcheck_dddup2(f);
2789: if ( ret == 1 ) return 0;
2790: /* reset k-th bit */
2791: fd[k>>5] &= ~(1<<(k&31));
2792: }
2793: /* reset j-th bit */
2794: fd[j>>5] &= ~(1<<(j&31));
2795: }
2796: /* reset i-th bit */
2797: fd[i>>5] &= ~(1<<(i&31));
2798: }
2799: /* exhausted */
2800: return 1;
2801: }
2802:
2803: /*
2804: * f = an irreducible trinomial or pentanomial of degree d 'after' f
2805: *
2806: * searching strategy:
2807: * trinomial x^d+x^i+1:
2808: * i is as small as possible.
2809: * trinomial x^d+x^i+x^j+x^k+1:
2810: * i is as small as possible.
2811: * For such i, j is as small as possible.
2812: * For such i and j, 'k' is as small as possible.
2813: *
2814: * return value : 0 --- exists
2815: * 1 --- does not exist (exhaustion)
2816: */
2817:
2818: int _generate_good_irreducible_polynomial(UP2 f,int d)
2819: {
2820: int ret,i,j,k,nz,i0,j0,k0;
2821: int w;
2822: unsigned int *fd;
2823:
2824: /*
2825: * if f = x^d+x^i+1 then i0 <- i, j0 <- 0, k0 <-0.
2826: * if f = x^d+x^k+x^j+x^i+1 (k>j>i) then i0 <- i, j0 <- j, k0 <-k.
2827: * otherwise i0,j0,k0 is set to 0.
2828: */
2829:
2830: fd = f->b;
2831: w = (d>>5)+1;
2832: if ( f->w && (d==degup2(f)) ) {
2833: for ( nz = 0, i = d; i >= 0; i-- )
2834: if ( fd[i>>5]&(1<<(i&31)) ) nz++;
2835: switch ( nz ) {
2836: case 3:
2837: for ( i0 = 1; !(fd[i0>>5]&(1<<(i0&31))) ; i0++ );
2838: /* reset i0-th bit */
2839: fd[i0>>5] &= ~(1<<(i0&31));
2840: j0 = k0 = 0;
2841: break;
2842: case 5:
2843: for ( i0 = 1; !(fd[i0>>5]&(1<<(i0&31))) ; i0++ );
2844: /* reset i0-th bit */
2845: fd[i0>>5] &= ~(1<<(i0&31));
2846: for ( j0 = i0+1; !(fd[j0>>5]&(1<<(j0&31))) ; j0++ );
2847: /* reset j0-th bit */
2848: fd[j0>>5] &= ~(1<<(j0&31));
2849: for ( k0 = j0+1; !(fd[k0>>5]&(1<<(k0&31))) ; k0++ );
2850: /* reset k0-th bit */
2851: fd[k0>>5] &= ~(1<<(k0&31));
2852: break;
2853: default:
2854: f->w = 0; break;
2855: }
2856: } else
2857: f->w = 0;
2858:
2859: if ( !f->w ) {
2860: fd = f->b;
2861: f->w = w; fd[0] |= 1; fd[d>>5] |= (1<<(d&31));
2862: i0 = j0 = k0 = 0;
2863: }
2864: /* if j0 > 0 then f is already a pentanomial */
2865: if ( j0 > 0 ) goto PENTA;
2866:
2867: /* searching for an irreducible trinomial */
2868:
2869: for ( i = 1; 2*i <= d; i++ ) {
2870: /* skip the polynomials 'before' f */
2871: if ( i < i0 ) continue;
2872: if ( i == i0 ) { i0 = 0; continue; }
2873: /* set i-th bit */
2874: fd[i>>5] |= (1<<(i&31));
2875: ret = irredcheck_dddup2(f);
2876: if ( ret == 1 ) return 0;
2877: /* reset i-th bit */
2878: fd[i>>5] &= ~(1<<(i&31));
2879: }
2880:
2881: /* searching for an irreducible pentanomial */
2882: PENTA:
2883: for ( i = 3; i < d; i++ ) {
2884: /* skip the polynomials 'before' f */
2885: if ( i < i0 ) continue;
2886: if ( i == i0 ) i0 = 0;
2887: /* set i-th bit */
2888: fd[i>>5] |= (1<<(i&31));
2889: for ( j = 2; j < i; j++ ) {
2890: /* skip the polynomials 'before' f */
2891: if ( j < j0 ) continue;
2892: if ( j == j0 ) j0 = 0;
2893: /* set j-th bit */
2894: fd[j>>5] |= (1<<(j&31));
2895: for ( k = 1; k < j; k++ ) {
2896: /* skip the polynomials 'before' f */
2897: if ( k < k0 ) continue;
2898: else if ( k == k0 ) { k0 = 0; continue; }
2899: /* set k-th bit */
2900: fd[k>>5] |= (1<<(k&31));
2901: ret = irredcheck_dddup2(f);
2902: if ( ret == 1 ) return 0;
2903: /* reset k-th bit */
2904: fd[k>>5] &= ~(1<<(k&31));
2905: }
2906: /* reset j-th bit */
2907: fd[j>>5] &= ~(1<<(j&31));
2908: }
2909: /* reset i-th bit */
2910: fd[i>>5] &= ~(1<<(i&31));
2911: }
2912: /* exhausted */
2913: return 1;
1.3 noro 2914: }
2915:
1.24 noro 2916: void printqmat(Q **mat,int row,int col)
1.3 noro 2917: {
2918: int i,j;
2919:
2920: for ( i = 0; i < row; i++ ) {
2921: for ( j = 0; j < col; j++ ) {
1.8 noro 2922: printnum((Num)mat[i][j]); printf(" ");
1.3 noro 2923: }
2924: printf("\n");
2925: }
2926: }
2927:
1.24 noro 2928: void printimat(int **mat,int row,int col)
1.3 noro 2929: {
2930: int i,j;
2931:
2932: for ( i = 0; i < row; i++ ) {
2933: for ( j = 0; j < col; j++ ) {
2934: printf("%d ",mat[i][j]);
2935: }
2936: printf("\n");
2937: }
1.36 noro 2938: }
2939:
2940: void Pnd_det(NODE arg,P *rp)
2941: {
1.37 noro 2942: if ( argc(arg) == 1 )
2943: nd_det(0,ARG0(arg),rp);
2944: else
2945: nd_det(QTOS((Q)ARG1(arg)),ARG0(arg),rp);
1.1 noro 2946: }