Annotation of OpenXM_contrib2/asir2000/builtin/array.c, Revision 1.77
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: *
1.77 ! noro 48: * $OpenXM: OpenXM_contrib2/asir2000/builtin/array.c,v 1.76 2018/03/29 01:32:50 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:
1.51 noro 55: #include <sys/types.h>
56: #include <sys/stat.h>
1.58 ohara 57: #if !defined(_MSC_VER)
1.51 noro 58: #include <unistd.h>
1.58 ohara 59: #endif
1.51 noro 60:
1.38 noro 61: #define F4_INTRAT_PERIOD 8
62:
1.4 noro 63: #if 0
1.1 noro 64: #undef DMAR
65: #define DMAR(a1,a2,a3,d,r) (r)=dmar(a1,a2,a3,d);
1.4 noro 66: #endif
1.1 noro 67:
1.11 noro 68: extern int DP_Print; /* XXX */
1.1 noro 69:
1.24 noro 70:
1.71 noro 71: void Pnewvect(), Pnewmat(), Psepvect(), Psize(), Pdet(), Pleqm(), Pleqm1(), Pgeninvm(), Ptriangleq();
1.23 noro 72: void Pinvmat();
1.49 noro 73: void Pnewbytearray(),Pmemoryplot_to_coord();
1.1 noro 74:
1.25 noro 75: void Pgeneric_gauss_elim();
1.1 noro 76: void Pgeneric_gauss_elim_mod();
77:
1.69 noro 78: void Pindep_rows_mod();
79:
1.1 noro 80: void Pmat_to_gfmmat(),Plu_gfmmat(),Psolve_by_lu_gfmmat();
1.33 noro 81: void Pgeninvm_swap(), Premainder(), Psremainder(), Pvtol(), Pltov();
1.27 noro 82: void Pgeninv_sf_swap();
1.1 noro 83: void sepvect();
84: void Pmulmat_gf2n();
85: void Pbconvmat_gf2n();
86: void Pmul_vect_mat_gf2n();
87: void PNBmul_gf2n();
88: void Pmul_mat_vect_int();
89: void Psepmat_destructive();
90: void Px962_irredpoly_up2();
91: void Pirredpoly_up2();
92: void Pnbpoly_up2();
93: void Pqsort();
1.14 noro 94: void Pexponent_vector();
1.26 noro 95: void Pmat_swap_row_destructive();
96: void Pmat_swap_col_destructive();
1.28 saito 97: void Pvect();
98: void Pmat();
1.29 saito 99: void Pmatc();
1.36 noro 100: void Pnd_det();
1.53 noro 101: void Plu_mat();
1.59 ohara 102: void Pmat_col();
1.63 noro 103: void Plusolve_prep();
104: void Plusolve_main();
1.1 noro 105:
106: struct ftab array_tab[] = {
1.76 noro 107: {"lu_mat",Plu_mat,1},
108: {"solve_by_lu_gfmmat",Psolve_by_lu_gfmmat,4},
109: {"lu_gfmmat",Plu_gfmmat,2},
110: {"mat_to_gfmmat",Pmat_to_gfmmat,2},
111: {"generic_gauss_elim",Pgeneric_gauss_elim,1},
112: {"generic_gauss_elim_mod",Pgeneric_gauss_elim_mod,2},
113: {"indep_rows_mod",Pindep_rows_mod,2},
114: {"newvect",Pnewvect,-2},
115: {"vect",Pvect,-99999999},
116: {"vector",Pnewvect,-2},
117: {"exponent_vector",Pexponent_vector,-99999999},
118: {"newmat",Pnewmat,-3},
119: {"matrix",Pnewmat,-3},
120: {"mat",Pmat,-99999999},
121: {"matr",Pmat,-99999999},
122: {"matc",Pmatc,-99999999},
123: {"newbytearray",Pnewbytearray,-2},
124: {"memoryplot_to_coord",Pmemoryplot_to_coord,1},
125: {"sepmat_destructive",Psepmat_destructive,2},
126: {"sepvect",Psepvect,2},
127: {"qsort",Pqsort,-2},
128: {"vtol",Pvtol,1},
129: {"ltov",Pltov,1},
130: {"size",Psize,1},
131: {"det",Pdet,-2},
132: {"nd_det",Pnd_det,-2},
133: {"invmat",Pinvmat,-2},
134: {"leqm",Pleqm,2},
135: {"leqm1",Pleqm1,2},
136: {"geninvm",Pgeninvm,2},
137: {"geninvm_swap",Pgeninvm_swap,2},
138: {"geninv_sf_swap",Pgeninv_sf_swap,1},
139: {"remainder",Premainder,2},
140: {"sremainder",Psremainder,2},
141: {"mulmat_gf2n",Pmulmat_gf2n,1},
142: {"bconvmat_gf2n",Pbconvmat_gf2n,-4},
143: {"mul_vect_mat_gf2n",Pmul_vect_mat_gf2n,2},
144: {"mul_mat_vect_int",Pmul_mat_vect_int,2},
145: {"nbmul_gf2n",PNBmul_gf2n,3},
146: {"x962_irredpoly_up2",Px962_irredpoly_up2,2},
147: {"irredpoly_up2",Pirredpoly_up2,2},
148: {"nbpoly_up2",Pnbpoly_up2,2},
149: {"mat_swap_row_destructive",Pmat_swap_row_destructive,3},
150: {"mat_swap_col_destructive",Pmat_swap_col_destructive,3},
151: {"mat_col",Pmat_col,2},
152: {"lusolve_prep",Plusolve_prep,1},
153: {"lusolve_main",Plusolve_main,1},
154: {"triangleq",Ptriangleq,1},
155: {0,0,0},
1.1 noro 156: };
157:
1.63 noro 158: typedef struct _ent { int j; unsigned int e; } ent;
159:
160: ent *get_row(FILE *,int *l);
161: void put_row(FILE *out,int l,ent *a);
1.72 ohara 162: void lu_elim(int *l,ent **a,int k,int i,int mul,int mod);
163: void lu_append(int *,ent **,int *,int,int,int);
164: void solve_l(int *,ent **,int,int *,int);
165: void solve_u(int *,ent **,int,int *,int);
166:
1.63 noro 167:
168: static int *ul,*ll;
169: static ent **u,**l;
170: static int modulus;
171:
172: void Plusolve_prep(NODE arg,Q *rp)
173: {
1.76 noro 174: char *fname;
175: FILE *in;
176: int len,i,rank;
177: int *rhs;
178:
179: fname = BDY((STRING)ARG0(arg));
180: in = fopen(fname,"r");
181: modulus = getw(in);
182: len = getw(in);
183: ul = (int *)MALLOC_ATOMIC(len*sizeof(int));
184: u = (ent **)MALLOC(len*sizeof(ent *));
185: ll = (int *)MALLOC_ATOMIC(len*sizeof(int));
186: l = (ent **)MALLOC(len*sizeof(ent *));
187: for ( i = 0; i < len; i++ ) {
188: u[i] = get_row(in,&ul[i]);
189: }
190: for ( i = 0; i < len; i++ ) {
191: l[i] = get_row(in,&ll[i]);
192: }
193: fclose(in);
194: *rp = ONE;
1.63 noro 195: }
196:
197: void Plusolve_main(NODE arg,VECT *rp)
198: {
1.76 noro 199: Q *d,*p;
200: VECT v,r;
201: int len,i;
202: int *rhs;
203:
204: v = (VECT)ARG0(arg); len = v->len;
205: d = (Q *)BDY(v);
206: rhs = (int *)MALLOC_ATOMIC(len*sizeof(int));
207: for ( i = 0; i < len; i++ ) rhs[i] = QTOS(d[i]);
208: solve_l(ll,l,len,rhs,modulus);
209: solve_u(ul,u,len,rhs,modulus);
210: NEWVECT(r); r->len = len;
211: r->body = (pointer *)MALLOC(len*sizeof(pointer));
212: p = (Q *)r->body;
213: for ( i = 0; i < len; i++ )
214: STOQ(rhs[i],p[i]);
215: *rp = r;
1.63 noro 216: }
217:
218: ent *get_row(FILE *in,int *l)
219: {
1.76 noro 220: int len,i;
221: ent *a;
1.63 noro 222:
1.76 noro 223: *l = len = getw(in);
224: a = (ent *)MALLOC_ATOMIC(len*sizeof(ent));
225: for ( i = 0; i < len; i++ ) {
226: a[i].j = getw(in);
227: a[i].e = getw(in);
228: }
229: return a;
1.63 noro 230: }
231:
1.72 ohara 232: void lu_gauss(int *ul,ent **u,int *ll,ent **l,int n,int mod)
1.63 noro 233: {
1.76 noro 234: int i,j,k,s,mul;
235: unsigned int inv;
236: int *ll2;
237:
238: ll2 = (int *)MALLOC_ATOMIC(n*sizeof(int));
239: for ( i = 0; i < n; i++ ) ll2[i] = 0;
240: for ( i = 0; i < n; i++ ) {
241: fprintf(stderr,"i=%d\n",i);
242: inv = invm(u[i][0].e,mod);
243: for ( k = i+1; k < n; k++ )
244: if ( u[k][0].j == n-i ) {
245: s = u[k][0].e;
246: DMAR(s,inv,0,mod,mul);
247: lu_elim(ul,u,k,i,mul,mod);
248: lu_append(ll,l,ll2,k,i,mul);
249: }
250: }
1.63 noro 251: }
252:
253: #define INITLEN 10
254:
1.72 ohara 255: void lu_append(int *l,ent **a,int *l2,int k,int i,int mul)
1.63 noro 256: {
1.76 noro 257: int len;
258: ent *p;
1.63 noro 259:
1.76 noro 260: len = l[k];
261: if ( !len ) {
262: a[k] = p = (ent *)MALLOC_ATOMIC(INITLEN*sizeof(ent));
263: p[0].j = i; p[0].e = mul;
264: l[k] = 1; l2[k] = INITLEN;
265: } else {
266: if ( l2[k] == l[k] ) {
267: l2[k] *= 2;
268: a[k] = REALLOC(a[k],l2[k]*sizeof(ent));
269: }
270: p =a[k];
271: p[l[k]].j = i; p[l[k]].e = mul;
272: l[k]++;
273: }
1.63 noro 274: }
275:
276: /* a[k] = a[k]-mul*a[i] */
277:
1.72 ohara 278: void lu_elim(int *l,ent **a,int k,int i,int mul,int mod)
1.63 noro 279: {
1.76 noro 280: ent *ak,*ai,*w;
281: int lk,li,j,m,p,q,r,s,t,j0;
1.63 noro 282:
1.76 noro 283: ak = a[k]; ai = a[i]; lk = l[k]; li = l[i];
284: w = (ent *)alloca((lk+li)*sizeof(ent));
285: p = 0; q = 0; j = 0;
286: mul = mod-mul;
287: while ( p < lk && q < li ) {
288: if ( ak[p].j > ai[q].j ) {
289: w[j] = ak[p]; j++; p++;
290: } else if ( ak[p].j < ai[q].j ) {
291: w[j].j = ai[q].j;
292: t = ai[q].e;
293: DMAR(t,mul,0,mod,r);
294: w[j].e = r;
295: j++; q++;
296: } else {
297: t = ai[q].e; s = ak[p].e;
298: DMAR(t,mul,s,mod,r);
299: if ( r ) {
300: w[j].j = ai[q].j; w[j].e = r; j++;
301: }
302: p++; q++;
303: }
304: }
305: if ( q == li )
306: while ( p < lk ) {
307: w[j] = ak[p]; j++; p++;
308: }
309: else if ( p == lk )
310: while ( q < li ) {
311: w[j].j = ai[q].j;
312: t = ai[q].e;
313: DMAR(t,mul,0,mod,r);
314: w[j].e = r;
315: j++; q++;
316: }
317: if ( j <= lk ) {
318: for ( m = 0; m < j; m++ ) ak[m] = w[m];
319: } else {
320: a[k] = ak = (ent *)MALLOC_ATOMIC(j*sizeof(ent));
321: for ( m = 0; m < j; m++ ) ak[m] = w[m];
322: }
323: l[k] = j;
1.63 noro 324: }
325:
1.72 ohara 326: void solve_l(int *ll,ent **l,int n,int *rhs,int mod)
1.63 noro 327: {
1.76 noro 328: int j,k,s,len;
329: ent *p;
1.63 noro 330:
1.76 noro 331: for ( j = 0; j < n; j++ ) {
332: len = ll[j]; p = l[j];
333: for ( k = 0, s = 0; k < len; k++ )
334: s = dmar(p[k].e,rhs[p[k].j],s,mod);
335: rhs[j] -= s;
336: if ( rhs[j] < 0 ) rhs[j] += mod;
337: }
1.63 noro 338: }
339:
1.72 ohara 340: void solve_u(int *ul,ent **u,int n,int *rhs,int mod)
1.63 noro 341: {
1.76 noro 342: int j,k,s,len,inv;
343: ent *p;
1.63 noro 344:
1.76 noro 345: for ( j = n-1; j >= 0; j-- ) {
346: len = ul[j]; p = u[j];
347: for ( k = 1, s = 0; k < len; k++ )
348: s = dmar(p[k].e,rhs[p[k].j],s,mod);
349: rhs[j] -= s;
350: if ( rhs[j] < 0 ) rhs[j] += mod;
351: inv = invm((unsigned int)p[0].e,mod);
352: rhs[j] = dmar(rhs[j],inv,0,mod);
353: }
1.63 noro 354: }
355:
1.24 noro 356: int comp_obj(Obj *a,Obj *b)
1.1 noro 357: {
1.76 noro 358: return arf_comp(CO,*a,*b);
1.1 noro 359: }
360:
361: static FUNC generic_comp_obj_func;
362: static NODE generic_comp_obj_arg;
1.60 ohara 363: static NODE generic_comp_obj_option;
1.1 noro 364:
1.24 noro 365: int generic_comp_obj(Obj *a,Obj *b)
1.1 noro 366: {
1.76 noro 367: Q r;
368:
369: BDY(generic_comp_obj_arg)=(pointer)(*a);
370: BDY(NEXT(generic_comp_obj_arg))=(pointer)(*b);
371: r = (Q)bevalf_with_opts(generic_comp_obj_func,generic_comp_obj_arg,generic_comp_obj_option);
372: if ( !r )
373: return 0;
374: else
375: return SGN(r)>0?1:-1;
1.1 noro 376: }
377:
378:
1.46 saito 379: void Pqsort(NODE arg,LIST *rp)
1.1 noro 380: {
1.76 noro 381: VECT vect;
382: NODE n,n1;
383: P p;
384: V v;
385: FUNC func;
386: int len,i;
387: pointer *a;
388: Obj t;
1.35 ohara 389:
1.76 noro 390: t = ARG0(arg);
1.35 ohara 391: if (OID(t) == O_LIST) {
392: n = (NODE)BDY((LIST)t);
393: len = length(n);
394: MKVECT(vect,len);
395: for ( i = 0; i < len; i++, n = NEXT(n) ) {
396: BDY(vect)[i] = BDY(n);
397: }
398:
399: }else if (OID(t) != O_VECT) {
400: error("qsort : invalid argument");
401: }else {
402: vect = (VECT)t;
403: }
1.76 noro 404: if ( argc(arg) == 1 )
405: qsort(BDY(vect),vect->len,sizeof(Obj),(int (*)(const void *,const void *))comp_obj);
406: else {
407: p = (P)ARG1(arg);
408: if ( !p || OID(p)!=2 )
409: error("qsort : invalid argument");
410: v = VR(p);
411: gen_searchf(NAME(v),&func);
412: if ( !func ) {
413: if ( (int)v->attr != V_SR )
414: error("qsort : no such function");
415: func = (FUNC)v->priv;
416: }
417: generic_comp_obj_func = func;
418: MKNODE(n,0,0); MKNODE(generic_comp_obj_arg,0,n);
419: generic_comp_obj_option = current_option;
420: qsort(BDY(vect),vect->len,sizeof(Obj),(int (*)(const void *,const void *))generic_comp_obj);
421: }
1.35 ohara 422: if (OID(t) == O_LIST) {
423: a = BDY(vect);
424: for ( i = len - 1, n = 0; i >= 0; i-- ) {
425: MKNODE(n1,a[i],n); n = n1;
426: }
1.46 saito 427: MKLIST(*rp,n);
1.35 ohara 428: }else {
1.46 saito 429: *rp = (LIST)vect;
1.35 ohara 430: }
1.1 noro 431: }
432:
1.24 noro 433: void PNBmul_gf2n(NODE arg,GF2N *rp)
1.1 noro 434: {
1.76 noro 435: GF2N a,b;
436: GF2MAT mat;
437: int n,w;
438: unsigned int *ab,*bb;
439: UP2 r;
440:
441: a = (GF2N)ARG0(arg);
442: b = (GF2N)ARG1(arg);
443: mat = (GF2MAT)ARG2(arg);
444: if ( !a || !b )
445: *rp = 0;
446: else {
447: n = mat->row;
448: w = (n+BSH-1)/BSH;
449:
450: ab = (unsigned int *)ALLOCA(w*sizeof(unsigned int));
451: bzero((char *)ab,w*sizeof(unsigned int));
452: bcopy(a->body->b,ab,(a->body->w)*sizeof(unsigned int));
453:
454: bb = (unsigned int *)ALLOCA(w*sizeof(unsigned int));
455: bzero((char *)bb,w*sizeof(unsigned int));
456: bcopy(b->body->b,bb,(b->body->w)*sizeof(unsigned int));
457:
458: NEWUP2(r,w);
459: bzero((char *)r->b,w*sizeof(unsigned int));
460: mul_nb(mat,ab,bb,r->b);
461: r->w = w;
462: _adjup2(r);
463: if ( !r->w )
464: *rp = 0;
465: else
466: MKGF2N(r,*rp);
467: }
1.1 noro 468: }
469:
1.24 noro 470: void Pmul_vect_mat_gf2n(NODE arg,GF2N *rp)
1.1 noro 471: {
1.76 noro 472: GF2N a;
473: GF2MAT mat;
474: int n,w;
475: unsigned int *b;
476: UP2 r;
477:
478: a = (GF2N)ARG0(arg);
479: mat = (GF2MAT)ARG1(arg);
480: if ( !a )
481: *rp = 0;
482: else {
483: n = mat->row;
484: w = (n+BSH-1)/BSH;
485: b = (unsigned int *)ALLOCA(w*sizeof(unsigned int));
486: bzero((char *)b,w*sizeof(unsigned int));
487: bcopy(a->body->b,b,(a->body->w)*sizeof(unsigned int));
488: NEWUP2(r,w);
489: bzero((char *)r->b,w*sizeof(unsigned int));
490: mulgf2vectmat(mat->row,b,mat->body,r->b);
491: r->w = w;
492: _adjup2(r);
493: if ( !r->w )
494: *rp = 0;
495: else {
496: MKGF2N(r,*rp);
497: }
498: }
1.1 noro 499: }
500:
1.24 noro 501: void Pbconvmat_gf2n(NODE arg,LIST *rp)
1.1 noro 502: {
1.76 noro 503: P p0,p1;
504: int to;
505: GF2MAT p01,p10;
506: GF2N root;
507: NODE n0,n1;
508:
509: p0 = (P)ARG0(arg);
510: p1 = (P)ARG1(arg);
511: to = ARG2(arg)?1:0;
512: if ( argc(arg) == 4 ) {
513: root = (GF2N)ARG3(arg);
514: compute_change_of_basis_matrix_with_root(p0,p1,to,root,&p01,&p10);
515: } else
516: compute_change_of_basis_matrix(p0,p1,to,&p01,&p10);
517: MKNODE(n1,p10,0); MKNODE(n0,p01,n1);
518: MKLIST(*rp,n0);
1.1 noro 519: }
520:
1.24 noro 521: void Pmulmat_gf2n(NODE arg,GF2MAT *rp)
1.1 noro 522: {
1.76 noro 523: GF2MAT m;
1.1 noro 524:
1.76 noro 525: if ( !compute_multiplication_matrix((P)ARG0(arg),&m) )
526: error("mulmat_gf2n : input is not a normal polynomial");
527: *rp = m;
1.1 noro 528: }
529:
1.24 noro 530: void Psepmat_destructive(NODE arg,LIST *rp)
1.1 noro 531: {
1.76 noro 532: MAT mat,mat1;
533: int i,j,row,col;
534: Q **a,**a1;
535: Q ent;
536: N nm,mod,rem,quo;
537: int sgn;
538: NODE n0,n1;
539:
540: mat = (MAT)ARG0(arg); mod = NM((Q)ARG1(arg));
541: row = mat->row; col = mat->col;
542: MKMAT(mat1,row,col);
543: a = (Q **)mat->body; a1 = (Q **)mat1->body;
544: for ( i = 0; i < row; i++ )
545: for ( j = 0; j < col; j++ ) {
546: ent = a[i][j];
547: if ( !ent )
548: continue;
549: nm = NM(ent);
550: sgn = SGN(ent);
551: divn(nm,mod,&quo,&rem);
552: /* if ( quo != nm && rem != nm ) */
553: /* GCFREE(nm); */
554: /* GCFREE(ent); */
555: NTOQ(rem,sgn,a[i][j]); NTOQ(quo,sgn,a1[i][j]);
556: }
557: MKNODE(n1,mat1,0); MKNODE(n0,mat,n1);
558: MKLIST(*rp,n0);
1.1 noro 559: }
560:
1.24 noro 561: void Psepvect(NODE arg,VECT *rp)
1.1 noro 562: {
1.76 noro 563: sepvect((VECT)ARG0(arg),QTOS((Q)ARG1(arg)),rp);
1.1 noro 564: }
565:
1.24 noro 566: void sepvect(VECT v,int d,VECT *rp)
1.1 noro 567: {
1.76 noro 568: int i,j,k,n,q,q1,r;
569: pointer *pv,*pw,*pu;
570: VECT w,u;
571:
572: n = v->len;
573: if ( d > n )
574: d = n;
575: q = n/d; r = n%d; q1 = q+1;
576: MKVECT(w,d); *rp = w;
577: pv = BDY(v); pw = BDY(w); k = 0;
578: for ( i = 0; i < r; i++ ) {
579: MKVECT(u,q1); pw[i] = (pointer)u;
580: for ( pu = BDY(u), j = 0; j < q1; j++, k++ )
581: pu[j] = pv[k];
582: }
583: for ( ; i < d; i++ ) {
584: MKVECT(u,q); pw[i] = (pointer)u;
585: for ( pu = BDY(u), j = 0; j < q; j++, k++ )
586: pu[j] = pv[k];
587: }
1.1 noro 588: }
589:
1.24 noro 590: void Pnewvect(NODE arg,VECT *rp)
1.1 noro 591: {
1.76 noro 592: int len,i,r;
593: VECT vect;
594: pointer *vb;
595: LIST list;
596: NODE tn;
597:
598: asir_assert(ARG0(arg),O_N,"newvect");
599: len = QTOS((Q)ARG0(arg));
600: if ( len < 0 )
601: error("newvect : invalid size");
602: MKVECT(vect,len);
603: if ( argc(arg) == 2 ) {
604: list = (LIST)ARG1(arg);
605: asir_assert(list,O_LIST,"newvect");
1.56 ohara 606: #if 0
1.76 noro 607: for ( r = 0, tn = BDY(list); tn; r++, tn = NEXT(tn) );
608: if ( r > len ) {
609: *rp = vect;
610: return;
611: }
1.56 ohara 612: #endif
1.76 noro 613: for ( i = 0, tn = BDY(list), vb = BDY(vect); tn; i++, tn = NEXT(tn) )
614: vb[i] = (pointer)BDY(tn);
615: }
616: *rp = vect;
1.14 noro 617: }
618:
1.28 saito 619: void Pvect(NODE arg,VECT *rp) {
1.76 noro 620: int len,i;
621: VECT vect;
622: pointer *vb;
623: NODE tn;
624:
625: if ( !arg ) {
626: *rp =0;
627: return;
628: }
629:
630: for (len = 0, tn = arg; tn; tn = NEXT(tn), len++);
631: if ( len == 1 ) {
632: if ( ARG0(arg) != 0 ) {
633: switch ( OID(ARG0(arg)) ) {
634: case O_VECT:
635: *rp = ARG0(arg);
636: return;
637: case O_LIST:
638: for ( len = 0, tn = ARG0(arg); tn; tn = NEXT(tn), len++ );
639: MKVECT(vect,len-1);
640: for ( i = 0, tn = BDY((LIST)ARG0(arg)), vb =BDY(vect);
641: tn; i++, tn = NEXT(tn) )
642: vb[i] = (pointer)BDY(tn);
643: *rp=vect;
644: return;
645: }
646: }
647: }
648: MKVECT(vect,len);
649: for ( i = 0, tn = arg, vb = BDY(vect); tn; i++, tn = NEXT(tn) )
650: vb[i] = (pointer)BDY(tn);
651: *rp = vect;
1.28 saito 652: }
653:
1.24 noro 654: void Pexponent_vector(NODE arg,DP *rp)
1.14 noro 655: {
1.76 noro 656: nodetod(arg,rp);
1.9 noro 657: }
658:
1.24 noro 659: void Pnewbytearray(NODE arg,BYTEARRAY *rp)
1.9 noro 660: {
1.76 noro 661: int len,i,r;
662: BYTEARRAY array;
663: unsigned char *vb;
664: char *str;
665: LIST list;
666: NODE tn;
667: int ac;
668: struct stat sbuf;
669: char *fname;
670: FILE *fp;
671:
672: ac = argc(arg);
673: if ( ac == 1 ) {
674: if ( !OID((Obj)ARG0(arg)) ) error("newbytearray : invalid argument");
675: switch ( OID((Obj)ARG0(arg)) ) {
676: case O_STR:
677: fname = BDY((STRING)ARG0(arg));
678: fp = fopen(fname,"rb");
679: if ( !fp ) error("newbytearray : fopen failed");
680: if ( stat(fname,&sbuf) < 0 )
681: error("newbytearray : stat failed");
682: len = sbuf.st_size;
683: MKBYTEARRAY(array,len);
684: fread(BDY(array),len,sizeof(char),fp);
685: break;
686: case O_N:
687: if ( !RATN(ARG0(arg)) )
688: error("newbytearray : invalid argument");
689: len = QTOS((Q)ARG0(arg));
690: if ( len < 0 )
691: error("newbytearray : invalid size");
692: MKBYTEARRAY(array,len);
693: break;
694: default:
695: error("newbytearray : invalid argument");
696: }
697: } else if ( ac == 2 ) {
698: asir_assert(ARG0(arg),O_N,"newbytearray");
699: len = QTOS((Q)ARG0(arg));
700: if ( len < 0 )
701: error("newbytearray : invalid size");
702: MKBYTEARRAY(array,len);
703: if ( !ARG1(arg) )
704: error("newbytearray : invalid initialization");
705: switch ( OID((Obj)ARG1(arg)) ) {
706: case O_LIST:
707: list = (LIST)ARG1(arg);
708: asir_assert(list,O_LIST,"newbytearray");
709: for ( r = 0, tn = BDY(list); tn; r++, tn = NEXT(tn) );
710: if ( r <= len ) {
711: for ( i = 0, tn = BDY(list), vb = BDY(array); tn;
712: i++, tn = NEXT(tn) )
713: vb[i] = (unsigned char)QTOS((Q)BDY(tn));
714: }
715: break;
716: case O_STR:
717: str = BDY((STRING)ARG1(arg));
718: r = strlen(str);
719: if ( r <= len )
720: bcopy(str,BDY(array),r);
721: break;
722: default:
723: if ( !ARG1(arg) )
724: error("newbytearray : invalid initialization");
725: }
726: } else
727: error("newbytearray : invalid argument");
728: *rp = array;
1.49 noro 729: }
730:
731: #define MEMORY_GETPOINT(a,len,x,y) (((a)[(len)*(y)+((x)>>3)])&(1<<((x)&7)))
732:
733: void Pmemoryplot_to_coord(NODE arg,LIST *rp)
734: {
1.76 noro 735: int len,blen,y,i,j;
736: unsigned char *a;
737: NODE r0,r,n;
738: LIST l;
739: BYTEARRAY ba;
740: Q iq,jq;
741:
742: asir_assert(ARG0(arg),O_LIST,"memoryplot_to_coord");
743: arg = BDY((LIST)ARG0(arg));
744: len = QTOS((Q)ARG0(arg));
745: blen = (len+7)/8;
746: y = QTOS((Q)ARG1(arg));
747: ba = (BYTEARRAY)ARG2(arg); a = ba->body;
748: r0 = 0;
749: for ( j = 0; j < y; j++ )
750: for ( i = 0; i < len; i++ )
751: if ( MEMORY_GETPOINT(a,blen,i,j) ) {
752: NEXTNODE(r0,r);
753: STOQ(i,iq); STOQ(j,jq);
754: n = mknode(2,iq,jq);
755: MKLIST(l,n);
756: BDY(r) = l;
757: }
758: if ( r0 ) NEXT(r) = 0;
759: MKLIST(*rp,r0);
1.1 noro 760: }
761:
1.24 noro 762: void Pnewmat(NODE arg,MAT *rp)
1.1 noro 763: {
1.76 noro 764: int row,col;
765: int i,j,r,c;
766: NODE tn,sn;
767: MAT m;
768: pointer **mb;
769: LIST list;
770:
771: asir_assert(ARG0(arg),O_N,"newmat");
772: asir_assert(ARG1(arg),O_N,"newmat");
773: row = QTOS((Q)ARG0(arg)); col = QTOS((Q)ARG1(arg));
774: if ( row < 0 || col < 0 )
775: error("newmat : invalid size");
776: MKMAT(m,row,col);
777: if ( argc(arg) == 3 ) {
778: list = (LIST)ARG2(arg);
779: asir_assert(list,O_LIST,"newmat");
780: for ( r = 0, c = 0, tn = BDY(list); tn; r++, tn = NEXT(tn) ) {
781: for ( j = 0, sn = BDY((LIST)BDY(tn)); sn; j++, sn = NEXT(sn) );
782: c = MAX(c,j);
783: }
784: if ( (r > row) || (c > col) ) {
785: *rp = m;
786: return;
787: }
788: for ( i = 0, tn = BDY(list), mb = BDY(m); tn; i++, tn = NEXT(tn) ) {
789: asir_assert(BDY(tn),O_LIST,"newmat");
790: for ( j = 0, sn = BDY((LIST)BDY(tn)); sn; j++, sn = NEXT(sn) )
791: mb[i][j] = (pointer)BDY(sn);
792: }
793: }
794: *rp = m;
1.28 saito 795: }
796:
797: void Pmat(NODE arg, MAT *rp)
798: {
1.76 noro 799: int row,col;
800: int i;
801: MAT m;
802: pointer **mb;
803: pointer *ent;
804: NODE tn, sn;
805: VECT v;
806:
807: if ( !arg ) {
808: *rp =0;
809: return;
810: }
811:
812: for (row = 0, tn = arg; tn; tn = NEXT(tn), row++);
813: if ( row == 1 ) {
814: if ( OID(ARG0(arg)) == O_MAT ) {
815: *rp=ARG0(arg);
816: return;
817: } else if ( !(OID(ARG0(arg)) == O_LIST || OID(ARG0(arg)) == O_VECT)) {
818: error("mat : invalid argument");
819: }
820: }
821: if ( OID(ARG0(arg)) == O_VECT ) {
822: v = ARG0(arg);
823: col = v->len;
824: } else if ( OID(ARG0(arg)) == O_LIST ) {
825: for (col = 0, tn = BDY((LIST)ARG0(arg)); tn ; tn = NEXT(tn), col++);
826: } else {
827: error("mat : invalid argument");
828: }
829:
830: MKMAT(m,row,col);
831: for (row = 0, tn = arg, mb = BDY(m); tn; tn = NEXT(tn), row++) {
832: if ( BDY(tn) == 0 ) {
833: error("mat : invalid argument");
834: } else if ( OID(BDY(tn)) == O_VECT ) {
835: v = tn->body;
836: ent = BDY(v);
837: for (i = 0; i < v->len; i++ ) mb[row][i] = (Obj)ent[i];
838: } else if ( OID(BDY(tn)) == O_LIST ) {
839: for (col = 0, sn = BDY((LIST)BDY(tn)); sn; col++, sn = NEXT(sn) )
840: mb[row][col] = (pointer)BDY(sn);
841: } else {
842: error("mat : invalid argument");
843: }
844: }
845: *rp = m;
1.29 saito 846: }
847:
848: void Pmatc(NODE arg, MAT *rp)
849: {
1.76 noro 850: int row,col;
851: int i;
852: MAT m;
853: pointer **mb;
854: pointer *ent;
855: NODE tn, sn;
856: VECT v;
857:
858: if ( !arg ) {
859: *rp =0;
860: return;
861: }
862:
863: for (col = 0, tn = arg; tn; tn = NEXT(tn), col++);
864: if ( col == 1 ) {
865: if ( OID(ARG0(arg)) == O_MAT ) {
866: *rp=ARG0(arg);
867: return;
868: } else if ( !(OID(ARG0(arg)) == O_LIST || OID(ARG0(arg)) == O_VECT)) {
869: error("matc : invalid argument");
870: }
871: }
872: if ( OID(ARG0(arg)) == O_VECT ) {
873: v = ARG0(arg);
874: row = v->len;
875: } else if ( OID(ARG0(arg)) == O_LIST ) {
876: for (row = 0, tn = BDY((LIST)ARG0(arg)); tn ; tn = NEXT(tn), row++);
877: } else {
878: error("matc : invalid argument");
879: }
880:
881: MKMAT(m,row,col);
882: for (col = 0, tn = arg, mb = BDY(m); tn; tn = NEXT(tn), col++) {
883: if ( BDY(tn) == 0 ) {
884: error("matc : invalid argument");
885: } else if ( OID(BDY(tn)) == O_VECT ) {
886: v = tn->body;
887: ent = BDY(v);
888: for (i = 0; i < v->len; i++ ) mb[i][col] = (Obj)ent[i];
889: } else if ( OID(BDY(tn)) == O_LIST ) {
890: for (row = 0, sn = BDY((LIST)BDY(tn)); sn; row++, sn = NEXT(sn) )
891: mb[row][col] = (pointer)BDY(sn);
892: } else {
893: error("matc : invalid argument");
894: }
895: }
896: *rp = m;
1.1 noro 897: }
898:
1.24 noro 899: void Pvtol(NODE arg,LIST *rp)
1.1 noro 900: {
1.76 noro 901: NODE n,n1;
902: VECT v;
903: pointer *a;
904: int len,i;
905:
906: if ( OID(ARG0(arg)) == O_LIST ) {
907: *rp = ARG0(arg);
908: return;
909: }
910: asir_assert(ARG0(arg),O_VECT,"vtol");
911: v = (VECT)ARG0(arg); len = v->len; a = BDY(v);
912: for ( i = len - 1, n = 0; i >= 0; i-- ) {
913: MKNODE(n1,a[i],n); n = n1;
914: }
915: MKLIST(*rp,n);
1.33 noro 916: }
917:
918: void Pltov(NODE arg,VECT *rp)
919: {
1.76 noro 920: NODE n;
921: VECT v,v0;
922: int len,i;
923:
924: if ( OID(ARG0(arg)) == O_VECT ) {
925: v0 = (VECT)ARG0(arg); len = v0->len;
926: MKVECT(v,len);
927: for ( i = 0; i < len; i++ ) {
928: BDY(v)[i] = BDY(v0)[i];
929: }
930: *rp = v;
931: return;
932: }
933: asir_assert(ARG0(arg),O_LIST,"ltov");
934: n = (NODE)BDY((LIST)ARG0(arg));
935: len = length(n);
936: MKVECT(v,len);
937: for ( i = 0; i < len; i++, n = NEXT(n) )
938: BDY(v)[i] = BDY(n);
939: *rp = v;
1.1 noro 940: }
941:
1.24 noro 942: void Premainder(NODE arg,Obj *rp)
1.1 noro 943: {
1.76 noro 944: Obj a;
945: VECT v,w;
946: MAT m,l;
947: pointer *vb,*wb;
948: pointer **mb,**lb;
949: int id,i,j,n,row,col,t,smd,sgn;
950: Q md,q;
951:
952: a = (Obj)ARG0(arg); md = (Q)ARG1(arg);
953: if ( !a )
954: *rp = 0;
955: else {
956: id = OID(a);
957: switch ( id ) {
958: case O_N:
959: case O_P:
960: cmp(md,(P)a,(P *)rp); break;
961: case O_VECT:
962: smd = QTOS(md);
963: v = (VECT)a; n = v->len; vb = v->body;
964: MKVECT(w,n); wb = w->body;
965: for ( i = 0; i < n; i++ ) {
966: if ( q = (Q)vb[i] ) {
967: sgn = SGN(q); t = rem(NM(q),smd);
968: STOQ(t,q);
969: if ( q )
970: SGN(q) = sgn;
971: }
972: wb[i] = (pointer)q;
973: }
974: *rp = (Obj)w;
975: break;
976: case O_MAT:
977: m = (MAT)a; row = m->row; col = m->col; mb = m->body;
978: MKMAT(l,row,col); lb = l->body;
979: for ( i = 0; i < row; i++ )
980: for ( j = 0, vb = mb[i], wb = lb[i]; j < col; j++ )
981: cmp(md,(P)vb[j],(P *)&wb[j]);
982: *rp = (Obj)l;
983: break;
984: default:
985: error("remainder : invalid argument");
986: }
987: }
1.1 noro 988: }
989:
1.24 noro 990: void Psremainder(NODE arg,Obj *rp)
1.1 noro 991: {
1.76 noro 992: Obj a;
993: VECT v,w;
994: MAT m,l;
995: pointer *vb,*wb;
996: pointer **mb,**lb;
997: unsigned int t,smd;
998: int id,i,j,n,row,col;
999: Q md,q;
1000:
1001: a = (Obj)ARG0(arg); md = (Q)ARG1(arg);
1002: if ( !a )
1003: *rp = 0;
1004: else {
1005: id = OID(a);
1006: switch ( id ) {
1007: case O_N:
1008: case O_P:
1009: cmp(md,(P)a,(P *)rp); break;
1010: case O_VECT:
1011: smd = QTOS(md);
1012: v = (VECT)a; n = v->len; vb = v->body;
1013: MKVECT(w,n); wb = w->body;
1014: for ( i = 0; i < n; i++ ) {
1015: if ( q = (Q)vb[i] ) {
1016: t = (unsigned int)rem(NM(q),smd);
1017: if ( SGN(q) < 0 )
1018: t = (smd - t) % smd;
1019: UTOQ(t,q);
1020: }
1021: wb[i] = (pointer)q;
1022: }
1023: *rp = (Obj)w;
1024: break;
1025: case O_MAT:
1026: m = (MAT)a; row = m->row; col = m->col; mb = m->body;
1027: MKMAT(l,row,col); lb = l->body;
1028: for ( i = 0; i < row; i++ )
1029: for ( j = 0, vb = mb[i], wb = lb[i]; j < col; j++ )
1030: cmp(md,(P)vb[j],(P *)&wb[j]);
1031: *rp = (Obj)l;
1032: break;
1033: default:
1034: error("remainder : invalid argument");
1035: }
1036: }
1.1 noro 1037: }
1038:
1.24 noro 1039: void Psize(NODE arg,LIST *rp)
1.1 noro 1040: {
1041:
1.76 noro 1042: int n,m;
1043: Q q;
1044: NODE t,s;
1045:
1046: if ( !ARG0(arg) )
1047: t = 0;
1048: else {
1049: switch (OID(ARG0(arg))) {
1050: case O_VECT:
1051: n = ((VECT)ARG0(arg))->len;
1052: STOQ(n,q); MKNODE(t,q,0);
1053: break;
1054: case O_MAT:
1055: n = ((MAT)ARG0(arg))->row; m = ((MAT)ARG0(arg))->col;
1056: STOQ(m,q); MKNODE(s,q,0); STOQ(n,q); MKNODE(t,q,s);
1057: break;
1058: case O_IMAT:
1059: n = ((IMAT)ARG0(arg))->row; m = ((IMAT)ARG0(arg))->col;
1060: STOQ(m,q); MKNODE(s,q,0); STOQ(n,q); MKNODE(t,q,s);
1061: break;
1062: default:
1063: error("size : invalid argument"); break;
1064: }
1065: }
1066: MKLIST(*rp,t);
1.1 noro 1067: }
1068:
1.24 noro 1069: void Pdet(NODE arg,P *rp)
1.1 noro 1070: {
1.76 noro 1071: MAT m;
1072: int n,i,j,mod;
1073: P d;
1074: P **mat,**w;
1075:
1076: m = (MAT)ARG0(arg);
1077: asir_assert(m,O_MAT,"det");
1078: if ( m->row != m->col )
1079: error("det : non-square matrix");
1080: else if ( argc(arg) == 1 )
1081: detp(CO,(P **)BDY(m),m->row,rp);
1082: else {
1083: n = m->row; mod = QTOS((Q)ARG1(arg)); mat = (P **)BDY(m);
1084: w = (P **)almat_pointer(n,n);
1085: for ( i = 0; i < n; i++ )
1086: for ( j = 0; j < n; j++ )
1087: ptomp(mod,mat[i][j],&w[i][j]);
1088: detmp(CO,mod,w,n,&d);
1089: mptop(d,rp);
1090: }
1.23 noro 1091: }
1092:
1.24 noro 1093: void Pinvmat(NODE arg,LIST *rp)
1.23 noro 1094: {
1.76 noro 1095: MAT m,r;
1096: int n,i,j,mod;
1097: P dn;
1098: P **mat,**imat,**w;
1099: NODE nd;
1100:
1101: m = (MAT)ARG0(arg);
1102: asir_assert(m,O_MAT,"invmat");
1103: if ( m->row != m->col )
1104: error("invmat : non-square matrix");
1105: else if ( argc(arg) == 1 ) {
1106: n = m->row;
1107: invmatp(CO,(P **)BDY(m),n,&imat,&dn);
1108: NEWMAT(r); r->row = n; r->col = n; r->body = (pointer **)imat;
1109: nd = mknode(2,r,dn);
1110: MKLIST(*rp,nd);
1111: } else {
1112: n = m->row; mod = QTOS((Q)ARG1(arg)); mat = (P **)BDY(m);
1113: w = (P **)almat_pointer(n,n);
1114: for ( i = 0; i < n; i++ )
1115: for ( j = 0; j < n; j++ )
1116: ptomp(mod,mat[i][j],&w[i][j]);
1.23 noro 1117: #if 0
1.76 noro 1118: detmp(CO,mod,w,n,&d);
1119: mptop(d,rp);
1.23 noro 1120: #else
1.76 noro 1121: error("not implemented yet");
1.23 noro 1122: #endif
1.76 noro 1123: }
1.25 noro 1124: }
1125:
1126: /*
1.76 noro 1127: input : a row x col matrix A
1128: A[I] <-> A[I][0]*x_0+A[I][1]*x_1+...
1.25 noro 1129:
1.76 noro 1130: output : [B,D,R,C]
1131: B : a rank(A) x col-rank(A) matrix
1132: D : the denominator
1133: R : a vector of length rank(A)
1134: C : a vector of length col-rank(A)
1135: B[I] <-> D*x_{R[I]}+B[I][0]x_{C[0]}+B[I][1]x_{C[1]}+...
1.25 noro 1136: */
1137:
1138: void Pgeneric_gauss_elim(NODE arg,LIST *rp)
1139: {
1.76 noro 1140: NODE n0,opt,p;
1141: MAT m,nm;
1142: int *ri,*ci;
1143: VECT rind,cind;
1144: Q dn,q;
1145: int i,row,col,t,rank;
1146: int is_hensel = 0;
1147: char *key;
1148: Obj value;
1149:
1150: if ( current_option ) {
1151: for ( opt = current_option; opt; opt = NEXT(opt) ) {
1152: p = BDY((LIST)BDY(opt));
1153: key = BDY((STRING)BDY(p));
1154: value = (Obj)BDY(NEXT(p));
1155: if ( !strcmp(key,"hensel") && value ) {
1156: is_hensel = value ? 1 : 0;
1157: break;
1158: }
1159: }
1160: }
1161: asir_assert(ARG0(arg),O_MAT,"generic_gauss_elim");
1162: m = (MAT)ARG0(arg);
1163: row = m->row; col = m->col;
1164: if ( is_hensel )
1165: rank = generic_gauss_elim_hensel(m,&nm,&dn,&ri,&ci);
1166: else
1167: rank = generic_gauss_elim(m,&nm,&dn,&ri,&ci);
1168: t = col-rank;
1169: MKVECT(rind,rank);
1170: MKVECT(cind,t);
1171: for ( i = 0; i < rank; i++ ) {
1172: STOQ(ri[i],q);
1173: BDY(rind)[i] = (pointer)q;
1174: }
1175: for ( i = 0; i < t; i++ ) {
1176: STOQ(ci[i],q);
1177: BDY(cind)[i] = (pointer)q;
1178: }
1179: n0 = mknode(4,nm,dn,rind,cind);
1180: MKLIST(*rp,n0);
1.1 noro 1181: }
1182:
1.69 noro 1183: void Pindep_rows_mod(NODE arg,VECT *rp)
1184: {
1.76 noro 1185: MAT m,mat;
1186: VECT rind;
1187: Q **tmat;
1188: int **wmat,**row0;
1189: Q *rib;
1190: int *rowstat,*p;
1191: Q q;
1192: int md,i,j,k,l,row,col,t,rank;
1193:
1194: asir_assert(ARG0(arg),O_MAT,"indep_rows_mod");
1195: asir_assert(ARG1(arg),O_N,"indep_rows_mod");
1196: m = (MAT)ARG0(arg); md = QTOS((Q)ARG1(arg));
1197: row = m->row; col = m->col; tmat = (Q **)m->body;
1198: wmat = (int **)almat(row,col);
1199:
1200: row0 = (int **)ALLOCA(row*sizeof(int *));
1201: for ( i = 0; i < row; i++ ) row0[i] = wmat[i];
1202:
1203: rowstat = (int *)MALLOC_ATOMIC(row*sizeof(int));
1204: for ( i = 0; i < row; i++ )
1205: for ( j = 0; j < col; j++ )
1206: if ( q = (Q)tmat[i][j] ) {
1207: t = rem(NM(q),md);
1208: if ( t && SGN(q) < 0 )
1209: t = (md - t) % md;
1210: wmat[i][j] = t;
1211: } else
1212: wmat[i][j] = 0;
1213: rank = indep_rows_mod(wmat,row,col,md,rowstat);
1214:
1215: MKVECT(rind,rank);
1216: rib = (Q *)rind->body;
1217: for ( j = 0; j < rank; j++ ) {
1218: STOQ(rowstat[j],rib[j]);
1219: }
1.69 noro 1220: *rp = rind;
1221: }
1222:
1.1 noro 1223: /*
1.76 noro 1224: input : a row x col matrix A
1225: A[I] <-> A[I][0]*x_0+A[I][1]*x_1+...
1.1 noro 1226:
1.76 noro 1227: output : [B,R,C]
1228: B : a rank(A) x col-rank(A) matrix
1229: R : a vector of length rank(A)
1230: C : a vector of length col-rank(A)
1231: RN : a vector of length rank(A) indicating useful rows
1.47 noro 1232:
1.76 noro 1233: B[I] <-> x_{R[I]}+B[I][0]x_{C[0]}+B[I][1]x_{C[1]}+...
1.1 noro 1234: */
1235:
1.24 noro 1236: void Pgeneric_gauss_elim_mod(NODE arg,LIST *rp)
1.1 noro 1237: {
1.76 noro 1238: NODE n0;
1239: MAT m,mat;
1240: VECT rind,cind,rnum;
1241: Q **tmat;
1242: int **wmat,**row0;
1243: Q *rib,*cib,*rnb;
1244: int *colstat,*p;
1245: Q q;
1246: int md,i,j,k,l,row,col,t,rank;
1247:
1248: asir_assert(ARG0(arg),O_MAT,"generic_gauss_elim_mod");
1249: asir_assert(ARG1(arg),O_N,"generic_gauss_elim_mod");
1250: m = (MAT)ARG0(arg); md = QTOS((Q)ARG1(arg));
1251: row = m->row; col = m->col; tmat = (Q **)m->body;
1252: wmat = (int **)almat(row,col);
1253:
1254: row0 = (int **)ALLOCA(row*sizeof(int *));
1255: for ( i = 0; i < row; i++ ) row0[i] = wmat[i];
1256:
1257: colstat = (int *)MALLOC_ATOMIC(col*sizeof(int));
1258: for ( i = 0; i < row; i++ )
1259: for ( j = 0; j < col; j++ )
1260: if ( q = (Q)tmat[i][j] ) {
1261: t = rem(NM(q),md);
1262: if ( t && SGN(q) < 0 )
1263: t = (md - t) % md;
1264: wmat[i][j] = t;
1265: } else
1266: wmat[i][j] = 0;
1267: rank = generic_gauss_elim_mod(wmat,row,col,md,colstat);
1268:
1269: MKVECT(rnum,rank);
1270: rnb = (Q *)rnum->body;
1271: for ( i = 0; i < rank; i++ )
1272: for ( j = 0, p = wmat[i]; j < row; j++ )
1273: if ( p == row0[j] )
1274: STOQ(j,rnb[i]);
1275:
1276: MKMAT(mat,rank,col-rank);
1277: tmat = (Q **)mat->body;
1278: for ( i = 0; i < rank; i++ )
1279: for ( j = k = 0; j < col; j++ )
1280: if ( !colstat[j] ) {
1281: UTOQ(wmat[i][j],tmat[i][k]); k++;
1282: }
1283:
1284: MKVECT(rind,rank);
1285: MKVECT(cind,col-rank);
1286: rib = (Q *)rind->body; cib = (Q *)cind->body;
1287: for ( j = k = l = 0; j < col; j++ )
1288: if ( colstat[j] ) {
1289: STOQ(j,rib[k]); k++;
1290: } else {
1291: STOQ(j,cib[l]); l++;
1292: }
1293: n0 = mknode(4,mat,rind,cind,rnum);
1294: MKLIST(*rp,n0);
1.1 noro 1295: }
1296:
1.24 noro 1297: void Pleqm(NODE arg,VECT *rp)
1.1 noro 1298: {
1.76 noro 1299: MAT m;
1300: VECT vect;
1301: pointer **mat;
1302: Q *v;
1303: Q q;
1304: int **wmat;
1305: int md,i,j,row,col,t,n,status;
1306:
1307: asir_assert(ARG0(arg),O_MAT,"leqm");
1308: asir_assert(ARG1(arg),O_N,"leqm");
1309: m = (MAT)ARG0(arg); md = QTOS((Q)ARG1(arg));
1310: row = m->row; col = m->col; mat = m->body;
1311: wmat = (int **)almat(row,col);
1312: for ( i = 0; i < row; i++ )
1313: for ( j = 0; j < col; j++ )
1314: if ( q = (Q)mat[i][j] ) {
1315: t = rem(NM(q),md);
1316: if ( SGN(q) < 0 )
1317: t = (md - t) % md;
1318: wmat[i][j] = t;
1319: } else
1320: wmat[i][j] = 0;
1321: status = gauss_elim_mod(wmat,row,col,md);
1322: if ( status < 0 )
1323: *rp = 0;
1324: else if ( status > 0 )
1325: *rp = (VECT)ONE;
1326: else {
1327: n = col - 1;
1328: MKVECT(vect,n);
1329: for ( i = 0, v = (Q *)vect->body; i < n; i++ ) {
1330: t = (md-wmat[i][n])%md; STOQ(t,v[i]);
1331: }
1332: *rp = vect;
1333: }
1.1 noro 1334: }
1335:
1.24 noro 1336: int gauss_elim_mod(int **mat,int row,int col,int md)
1.1 noro 1337: {
1.76 noro 1338: int i,j,k,inv,a,n;
1339: int *t,*pivot;
1.1 noro 1340:
1.76 noro 1341: n = col - 1;
1342: for ( j = 0; j < n; j++ ) {
1343: for ( i = j; i < row && !mat[i][j]; i++ );
1344: if ( i == row )
1345: return 1;
1346: if ( i != j ) {
1347: t = mat[i]; mat[i] = mat[j]; mat[j] = t;
1348: }
1349: pivot = mat[j];
1350: inv = invm(pivot[j],md);
1351: for ( k = j; k <= n; k++ ) {
1352: /* pivot[k] = dmar(pivot[k],inv,0,md); */
1353: DMAR(pivot[k],inv,0,md,pivot[k])
1354: }
1355: for ( i = 0; i < row; i++ ) {
1356: t = mat[i];
1357: if ( i != j && (a = t[j]) )
1358: for ( k = j, a = md - a; k <= n; k++ ) {
1359: unsigned int tk;
1360: /* t[k] = dmar(pivot[k],a,t[k],md); */
1361: DMAR(pivot[k],a,t[k],md,tk)
1362: t[k] = tk;
1363: }
1364: }
1365: }
1366: for ( i = n; i < row && !mat[i][n]; i++ );
1367: if ( i == row )
1368: return 0;
1369: else
1370: return -1;
1.1 noro 1371: }
1372:
1.4 noro 1373: struct oEGT eg_mod,eg_elim,eg_elim1,eg_elim2,eg_chrem,eg_gschk,eg_intrat,eg_symb;
1.31 noro 1374: struct oEGT eg_conv;
1.1 noro 1375:
1.24 noro 1376: int generic_gauss_elim(MAT mat,MAT *nm,Q *dn,int **rindp,int **cindp)
1.1 noro 1377: {
1.76 noro 1378: int **wmat;
1379: Q **bmat;
1380: N **tmat;
1381: Q *bmi;
1382: N *tmi;
1383: Q q;
1384: int *wmi;
1385: int *colstat,*wcolstat,*rind,*cind;
1386: int row,col,ind,md,i,j,k,l,t,t1,rank,rank0,inv;
1387: N m1,m2,m3,s,u;
1388: MAT r,crmat;
1389: struct oEGT tmp0,tmp1;
1390: struct oEGT eg_mod_split,eg_elim_split,eg_chrem_split;
1391: struct oEGT eg_intrat_split,eg_gschk_split;
1392: int ret;
1393:
1394: init_eg(&eg_mod_split); init_eg(&eg_chrem_split);
1395: init_eg(&eg_elim_split); init_eg(&eg_intrat_split);
1396: init_eg(&eg_gschk_split);
1397: bmat = (Q **)mat->body;
1398: row = mat->row; col = mat->col;
1399: wmat = (int **)almat(row,col);
1400: colstat = (int *)MALLOC_ATOMIC(col*sizeof(int));
1401: wcolstat = (int *)MALLOC_ATOMIC(col*sizeof(int));
1402: for ( ind = 0; ; ind++ ) {
1403: if ( DP_Print ) {
1404: fprintf(asir_out,"."); fflush(asir_out);
1405: }
1406: md = get_lprime(ind);
1407: get_eg(&tmp0);
1408: for ( i = 0; i < row; i++ )
1409: for ( j = 0, bmi = bmat[i], wmi = wmat[i]; j < col; j++ )
1410: if ( q = (Q)bmi[j] ) {
1411: t = rem(NM(q),md);
1412: if ( t && SGN(q) < 0 )
1413: t = (md - t) % md;
1414: wmi[j] = t;
1415: } else
1416: wmi[j] = 0;
1417: get_eg(&tmp1);
1418: add_eg(&eg_mod,&tmp0,&tmp1);
1419: add_eg(&eg_mod_split,&tmp0,&tmp1);
1420: get_eg(&tmp0);
1421: rank = generic_gauss_elim_mod(wmat,row,col,md,wcolstat);
1422: get_eg(&tmp1);
1423: add_eg(&eg_elim,&tmp0,&tmp1);
1424: add_eg(&eg_elim_split,&tmp0,&tmp1);
1425: if ( !ind ) {
1.1 noro 1426: RESET:
1.76 noro 1427: UTON(md,m1);
1428: rank0 = rank;
1429: bcopy(wcolstat,colstat,col*sizeof(int));
1430: MKMAT(crmat,rank,col-rank);
1431: MKMAT(r,rank,col-rank); *nm = r;
1432: tmat = (N **)crmat->body;
1433: for ( i = 0; i < rank; i++ )
1434: for ( j = k = 0, tmi = tmat[i], wmi = wmat[i]; j < col; j++ )
1435: if ( !colstat[j] ) {
1436: UTON(wmi[j],tmi[k]); k++;
1437: }
1438: } else {
1439: if ( rank < rank0 ) {
1440: if ( DP_Print ) {
1441: fprintf(asir_out,"lower rank matrix; continuing...\n");
1442: fflush(asir_out);
1443: }
1444: continue;
1445: } else if ( rank > rank0 ) {
1446: if ( DP_Print ) {
1447: fprintf(asir_out,"higher rank matrix; resetting...\n");
1448: fflush(asir_out);
1449: }
1450: goto RESET;
1451: } else {
1452: for ( j = 0; (j<col) && (colstat[j]==wcolstat[j]); j++ );
1453: if ( j < col ) {
1454: if ( DP_Print ) {
1455: fprintf(asir_out,"inconsitent colstat; resetting...\n");
1456: fflush(asir_out);
1457: }
1458: goto RESET;
1459: }
1460: }
1461:
1462: get_eg(&tmp0);
1463: inv = invm(rem(m1,md),md);
1464: UTON(md,m2); muln(m1,m2,&m3);
1465: for ( i = 0; i < rank; i++ )
1466: for ( j = k = 0, tmi = tmat[i], wmi = wmat[i]; j < col; j++ )
1467: if ( !colstat[j] ) {
1468: if ( tmi[k] ) {
1469: /* f3 = f1+m1*(m1 mod m2)^(-1)*(f2 - f1 mod m2) */
1470: t = rem(tmi[k],md);
1471: if ( wmi[j] >= t )
1472: t = wmi[j]-t;
1473: else
1474: t = md-(t-wmi[j]);
1475: DMAR(t,inv,0,md,t1)
1476: UTON(t1,u);
1477: muln(m1,u,&s);
1478: addn(tmi[k],s,&u); tmi[k] = u;
1479: } else if ( wmi[j] ) {
1480: /* f3 = m1*(m1 mod m2)^(-1)*f2 */
1481: DMAR(wmi[j],inv,0,md,t)
1482: UTON(t,u);
1483: muln(m1,u,&s); tmi[k] = s;
1484: }
1485: k++;
1486: }
1487: m1 = m3;
1488: get_eg(&tmp1);
1489: add_eg(&eg_chrem,&tmp0,&tmp1);
1490: add_eg(&eg_chrem_split,&tmp0,&tmp1);
1491:
1492: get_eg(&tmp0);
1493: if ( ind % F4_INTRAT_PERIOD )
1494: ret = 0;
1495: else
1496: ret = intmtoratm(crmat,m1,*nm,dn);
1497: get_eg(&tmp1);
1498: add_eg(&eg_intrat,&tmp0,&tmp1);
1499: add_eg(&eg_intrat_split,&tmp0,&tmp1);
1500: if ( ret ) {
1501: *rindp = rind = (int *)MALLOC_ATOMIC(rank*sizeof(int));
1502: *cindp = cind = (int *)MALLOC_ATOMIC((col-rank)*sizeof(int));
1503: for ( j = k = l = 0; j < col; j++ )
1504: if ( colstat[j] )
1505: rind[k++] = j;
1506: else
1507: cind[l++] = j;
1508: get_eg(&tmp0);
1509: if ( gensolve_check(mat,*nm,*dn,rind,cind) ) {
1510: get_eg(&tmp1);
1511: add_eg(&eg_gschk,&tmp0,&tmp1);
1512: add_eg(&eg_gschk_split,&tmp0,&tmp1);
1513: if ( DP_Print ) {
1514: print_eg("Mod",&eg_mod_split);
1515: print_eg("Elim",&eg_elim_split);
1516: print_eg("ChRem",&eg_chrem_split);
1517: print_eg("IntRat",&eg_intrat_split);
1518: print_eg("Check",&eg_gschk_split);
1519: fflush(asir_out);
1520: }
1521: return rank;
1522: }
1523: }
1524: }
1525: }
1.3 noro 1526: }
1527:
1.64 noro 1528: void lu_dec_cr(MAT mat,MAT lu,Q *dn,int **perm);
1529:
1.53 noro 1530: /* XXX broken */
1.64 noro 1531: void lu_dec_cr(MAT mat,MAT lu,Q *dn,int **perm)
1.53 noro 1532: {
1.76 noro 1533: Q **a0,**b;
1534: Q *aiq;
1535: N **a;
1536: N *ai;
1537: Q q,q1,dn2,a1,q0,bik;
1538: MAT m;
1539: unsigned int md;
1540: int n,ind,i,j,rank,t,inv,t1,ret,min,k;
1541: int **w;
1542: int *wi,*rinfo0,*rinfo;
1543: N m1,m2,m3,u,s;
1544:
1545: a0 = (Q **)mat->body;
1546: n = mat->row;
1547: if ( n != mat->col )
1548: error("lu_dec_cr : non-square matrix");
1549: w = (int **)almat(n,n);
1550: MKMAT(m,n,n);
1551: a = (N **)m->body;
1552: UTON(1,m1);
1553: rinfo0 = 0;
1554: ind = 0;
1555: while ( 1 ) {
1556: md = get_lprime(ind);
1557: /* mat mod md */
1558: for ( i = 0; i < n; i++ )
1559: for ( j = 0, aiq = a0[i], wi = w[i]; j < n; j++ )
1560: if ( q = aiq[j] ) {
1561: t = rem(NM(q),md);
1562: if ( t && SGN(q) < 0 )
1563: t = (md - t) % md;
1564: wi[j] = t;
1565: } else
1566: wi[j] = 0;
1567:
1568: if ( !lu_mod((unsigned int **)w,n,md,&rinfo) ) continue;
1569: printf("."); fflush(stdout);
1570: if ( !rinfo0 )
1571: *perm = rinfo0 = rinfo;
1572: else {
1573: for ( i = 0; i < n; i++ )
1574: if ( rinfo[i] != rinfo0[i] ) break;
1575: if ( i < n ) continue;
1576: }
1577: if ( UNIN(m1) ) {
1578: for ( i = 0; i < n; i++ )
1579: for ( j = 0, ai = a[i], wi = w[i]; j < n; j++ ) {
1580: UTON(wi[j],u); ai[j] = u;
1581: }
1582: UTON(md,m1);
1583: } else {
1584: inv = invm(rem(m1,md),md);
1585: UTON(md,m2); muln(m1,m2,&m3);
1586: for ( i = 0; i < n; i++ )
1587: for ( j = 0, ai = a[i], wi = w[i]; j < n; j++ )
1588: if ( ai[i] ) {
1589: /* f3 = f1+m1*(m1 mod m2)^(-1)*(f2 - f1 mod m2) */
1590: t = rem(ai[j],md);
1591: if ( wi[j] >= t )
1592: t = wi[j]-t;
1593: else
1594: t = md-(t-wi[j]);
1595: DMAR(t,inv,0,md,t1)
1596: UTON(t1,u);
1597: muln(m1,u,&s);
1598: addn(ai[j],s,&u); ai[j] = u;
1599: } else if ( wi[j] ) {
1600: /* f3 = m1*(m1 mod m2)^(-1)*f2 */
1601: DMAR(wi[j],inv,0,md,t)
1602: UTON(t,u);
1603: muln(m1,u,&s); ai[j] = s;
1604: }
1605: m1 = m3;
1606: }
1607: if ( (++ind%8) == 0 ) {
1608: ret = intmtoratm(m,m1,lu,dn);
1609: if ( ret ) {
1610: b = (Q **)lu->body;
1611: mulq(*dn,*dn,&dn2);
1612: for ( i = 0; i < n; i++ ) {
1613: for ( j = 0; j < n; j++ ) {
1614: q = 0;
1615: min = MIN(i,j);
1616: for ( k = 0; k <= min; k++ ) {
1617: bik = k==i ? *dn : b[i][k];
1618: mulq(bik,b[k][j],&q0);
1619: addq(q,q0,&q1); q = q1;
1620: }
1621: mulq(a0[rinfo0[i]][j],dn2,&q1);
1622: if ( cmpq(q,q1) ) break;
1623: }
1624: if ( j < n ) break;
1625: }
1626: if ( i == n )
1627: return;
1628: }
1629: }
1630: }
1.53 noro 1631: }
1632:
1.64 noro 1633: void nmat(N **m,int n)
1.53 noro 1634: {
1.76 noro 1635: int i,j;
1.53 noro 1636:
1.76 noro 1637: for ( i = 0; i < n; i++ ) {
1638: for ( j = 0; j < n; j++ ) {
1639: printn(m[i][j]); printf(" ");
1640: }
1641: printf("\n");
1642: }
1.53 noro 1643: }
1644:
1.24 noro 1645: int generic_gauss_elim_hensel(MAT mat,MAT *nmmat,Q *dn,int **rindp,int **cindp)
1.3 noro 1646: {
1.76 noro 1647: MAT bmat,xmat;
1648: Q **a0,**a,**b,**x,**nm;
1649: Q *ai,*bi,*xi;
1650: int row,col;
1651: int **w;
1652: int *wi;
1653: int **wc;
1654: Q mdq,q,s,u;
1655: N tn;
1656: int ind,md,i,j,k,l,li,ri,rank;
1657: unsigned int t;
1658: int *cinfo,*rinfo;
1659: int *rind,*cind;
1660: int count;
1661: int ret;
1662: struct oEGT eg_mul,eg_inv,eg_intrat,eg_check,tmp0,tmp1;
1663: int period;
1664: int *wx,*ptr;
1665: int wxsize,nsize;
1666: N wn;
1667: Q wq;
1668:
1669: a0 = (Q **)mat->body;
1670: row = mat->row; col = mat->col;
1671: w = (int **)almat(row,col);
1672: for ( ind = 0; ; ind++ ) {
1673: md = get_lprime(ind);
1674: STOQ(md,mdq);
1675: for ( i = 0; i < row; i++ )
1676: for ( j = 0, ai = a0[i], wi = w[i]; j < col; j++ )
1677: if ( q = (Q)ai[j] ) {
1678: t = rem(NM(q),md);
1679: if ( t && SGN(q) < 0 )
1680: t = (md - t) % md;
1681: wi[j] = t;
1682: } else
1683: wi[j] = 0;
1684:
1685: if ( DP_Print > 3 ) {
1686: fprintf(asir_out,"LU decomposition.."); fflush(asir_out);
1687: }
1688: rank = find_lhs_and_lu_mod((unsigned int **)w,row,col,md,&rinfo,&cinfo);
1689: if ( DP_Print > 3 ) {
1690: fprintf(asir_out,"done.\n"); fflush(asir_out);
1691: }
1692: a = (Q **)almat_pointer(rank,rank); /* lhs mat */
1693: MKMAT(bmat,rank,col-rank); b = (Q **)bmat->body; /* lhs mat */
1694: for ( j = li = ri = 0; j < col; j++ )
1695: if ( cinfo[j] ) {
1696: /* the column is in lhs */
1697: for ( i = 0; i < rank; i++ ) {
1698: w[i][li] = w[i][j];
1699: a[i][li] = a0[rinfo[i]][j];
1700: }
1701: li++;
1702: } else {
1703: /* the column is in rhs */
1704: for ( i = 0; i < rank; i++ )
1705: b[i][ri] = a0[rinfo[i]][j];
1706: ri++;
1707: }
1708:
1709: /* solve Ax+B=0; A: rank x rank, B: rank x ri */
1710: MKMAT(xmat,rank,ri); x = (Q **)(xmat)->body;
1711: MKMAT(*nmmat,rank,ri); nm = (Q **)(*nmmat)->body;
1712: /* use the right part of w as work area */
1713: /* ri = col - rank */
1714: wc = (int **)almat(rank,ri);
1715: for ( i = 0; i < rank; i++ )
1716: wc[i] = w[i]+rank;
1717: *rindp = rind = (int *)MALLOC_ATOMIC(rank*sizeof(int));
1718: *cindp = cind = (int *)MALLOC_ATOMIC((ri)*sizeof(int));
1719:
1720: init_eg(&eg_mul); init_eg(&eg_inv);
1721: init_eg(&eg_check); init_eg(&eg_intrat);
1722: period = F4_INTRAT_PERIOD;
1723: nsize = period;
1724: wxsize = rank*ri*nsize;
1725: wx = (int *)MALLOC_ATOMIC(wxsize*sizeof(int));
1726: for ( i = 0; i < wxsize; i++ ) wx[i] = 0;
1727: for ( q = ONE, count = 0; ; ) {
1728: if ( DP_Print > 3 )
1729: fprintf(stderr,"o");
1730: /* wc = -b mod md */
1731: get_eg(&tmp0);
1732: for ( i = 0; i < rank; i++ )
1733: for ( j = 0, bi = b[i], wi = wc[i]; j < ri; j++ )
1734: if ( u = (Q)bi[j] ) {
1735: t = rem(NM(u),md);
1736: if ( t && SGN(u) > 0 )
1737: t = (md - t) % md;
1738: wi[j] = t;
1739: } else
1740: wi[j] = 0;
1741: /* wc = A^(-1)wc; wc is not normalized */
1742: solve_by_lu_mod(w,rank,md,wc,ri,0);
1743: /* wx += q*wc */
1744: ptr = wx;
1745: for ( i = 0; i < rank; i++ )
1746: for ( j = 0, wi = wc[i]; j < ri; j++ ) {
1747: if ( wi[j] )
1748: muln_1(BD(NM(q)),PL(NM(q)),wi[j],ptr);
1749: ptr += nsize;
1750: }
1751: count++;
1752: get_eg(&tmp1);
1753: add_eg(&eg_inv,&tmp0,&tmp1);
1754: get_eg(&tmp0);
1755: for ( i = 0; i < rank; i++ )
1756: for ( j = 0; j < ri; j++ ) {
1757: inner_product_mat_int_mod(a,wc,rank,i,j,&u);
1758: addq(b[i][j],u,&s);
1759: if ( s ) {
1760: t = divin(NM(s),md,&tn);
1761: if ( t )
1762: error("generic_gauss_elim_hensel:incosistent");
1763: NTOQ(tn,SGN(s),b[i][j]);
1764: } else
1765: b[i][j] = 0;
1766: }
1767: get_eg(&tmp1);
1768: add_eg(&eg_mul,&tmp0,&tmp1);
1769: /* q = q*md */
1770: mulq(q,mdq,&u); q = u;
1771: if ( count == period ) {
1772: get_eg(&tmp0);
1773: ptr = wx;
1774: for ( i = 0; i < rank; i++ )
1775: for ( j = 0, xi = x[i]; j < ri;
1776: j++, ptr += nsize ) {
1777: for ( k = nsize-1; k >= 0 && !ptr[k]; k-- );
1778: if ( k >= 0 ) {
1779: wn = NALLOC(k+1);
1780: PL(wn) = k+1;
1781: for ( l = 0; l <= k; l++ ) BD(wn)[l] = (unsigned int)ptr[l];
1782: NTOQ(wn,1,wq);
1783: subq(xi[j],wq,&u); xi[j] = u;
1784: }
1785: }
1786: ret = intmtoratm_q(xmat,NM(q),*nmmat,dn);
1787: get_eg(&tmp1); add_eg(&eg_intrat,&tmp0,&tmp1);
1788: if ( ret ) {
1789: rind = (int *)MALLOC_ATOMIC(rank*sizeof(int));
1790: cind = (int *)MALLOC_ATOMIC((col-rank)*sizeof(int));
1791: for ( j = k = l = 0; j < col; j++ )
1792: if ( cinfo[j] )
1793: rind[k++] = j;
1794: else
1795: cind[l++] = j;
1796: get_eg(&tmp0);
1797: ret = gensolve_check(mat,*nmmat,*dn,rind,cind);
1798: get_eg(&tmp1); add_eg(&eg_check,&tmp0,&tmp1);
1799: if ( ret ) {
1800: if ( DP_Print > 3 ) {
1801: fprintf(stderr,"\n");
1802: print_eg("INV",&eg_inv);
1803: print_eg("MUL",&eg_mul);
1804: print_eg("INTRAT",&eg_intrat);
1805: print_eg("CHECK",&eg_check);
1806: fflush(asir_out);
1807: }
1808: *rindp = rind;
1809: *cindp = cind;
1810: for ( j = k = 0; j < col; j++ )
1811: if ( !cinfo[j] )
1812: cind[k++] = j;
1813: return rank;
1814: }
1815: } else {
1816: period = period*3/2;
1817: count = 0;
1818: nsize += period;
1819: wxsize += rank*ri*nsize;
1820: wx = (int *)REALLOC(wx,wxsize*sizeof(int));
1821: for ( i = 0; i < wxsize; i++ ) wx[i] = 0;
1822: }
1823: }
1824: }
1825: }
1.50 noro 1826: }
1827:
1.55 noro 1828: int generic_gauss_elim_hensel_dalg(MAT mat,DP *mb,MAT *nmmat,Q *dn,int **rindp,int **cindp)
1.50 noro 1829: {
1.76 noro 1830: MAT bmat,xmat;
1831: Q **a0,**a,**b,**x,**nm;
1832: Q *ai,*bi,*xi;
1833: int row,col;
1834: int **w;
1835: int *wi;
1836: int **wc;
1837: Q mdq,q,s,u;
1838: N tn;
1839: int ind,md,i,j,k,l,li,ri,rank;
1840: unsigned int t;
1841: int *cinfo,*rinfo;
1842: int *rind,*cind;
1843: int count;
1844: int ret;
1845: struct oEGT eg_mul,eg_inv,eg_intrat,eg_check,tmp0,tmp1;
1846: int period;
1847: int *wx,*ptr;
1848: int wxsize,nsize;
1849: N wn;
1850: Q wq;
1851: NumberField nf;
1852: DP m;
1853: int col1;
1854:
1855: a0 = (Q **)mat->body;
1856: row = mat->row; col = mat->col;
1857: w = (int **)almat(row,col);
1858: for ( ind = 0; ; ind++ ) {
1859: md = get_lprime(ind);
1860: STOQ(md,mdq);
1861: for ( i = 0; i < row; i++ )
1862: for ( j = 0, ai = a0[i], wi = w[i]; j < col; j++ )
1863: if ( q = (Q)ai[j] ) {
1864: t = rem(NM(q),md);
1865: if ( t && SGN(q) < 0 )
1866: t = (md - t) % md;
1867: wi[j] = t;
1868: } else
1869: wi[j] = 0;
1870:
1871: if ( DP_Print ) {
1872: fprintf(asir_out,"LU decomposition.."); fflush(asir_out);
1873: }
1874: rank = find_lhs_and_lu_mod((unsigned int **)w,row,col,md,&rinfo,&cinfo);
1.77 ! noro 1875: printf("\n");
! 1876: for ( i = 0; i < row; i++ ) {
! 1877: for ( j = 0; j < col; j++ )
! 1878: printf("%d ",w[i][j]);
! 1879: printf("\n");
! 1880: }
1.76 noro 1881: if ( DP_Print ) {
1882: fprintf(asir_out,"done.\n"); fflush(asir_out);
1883: }
1884: for ( i = 0; i < col-1; i++ ) {
1885: if ( !cinfo[i] ) {
1886: m = mb[i];
1887: for ( j = i+1; j < col-1; j++ )
1888: if ( dp_redble(mb[j],m) )
1889: cinfo[j] = -1;
1890: }
1891: }
1892: a = (Q **)almat_pointer(rank,rank); /* lhs mat */
1893: MKMAT(bmat,rank,col-rank); b = (Q **)bmat->body; /* lhs mat */
1894: for ( j = li = ri = 0; j < col; j++ )
1895: if ( cinfo[j] > 0 ) {
1896: /* the column is in lhs */
1897: for ( i = 0; i < rank; i++ ) {
1898: w[i][li] = w[i][j];
1899: a[i][li] = a0[rinfo[i]][j];
1900: }
1901: li++;
1902: } else if ( !cinfo[j] ) {
1903: /* the column is in rhs */
1904: for ( i = 0; i < rank; i++ )
1905: b[i][ri] = a0[rinfo[i]][j];
1906: ri++;
1907: }
1908:
1909: /* solve Ax+B=0; A: rank x rank, B: rank x ri */
1910: MKMAT(xmat,rank,ri); x = (Q **)(xmat)->body;
1911: MKMAT(*nmmat,rank,ri); nm = (Q **)(*nmmat)->body;
1912: /* use the right part of w as work area */
1913: wc = (int **)almat(rank,ri);
1914: for ( i = 0; i < rank; i++ )
1915: wc[i] = w[i]+rank;
1916: *rindp = rind = (int *)MALLOC_ATOMIC(rank*sizeof(int));
1917: *cindp = cind = (int *)MALLOC_ATOMIC((col-rank)*sizeof(int));
1918: init_eg(&eg_mul); init_eg(&eg_inv);
1919: init_eg(&eg_check); init_eg(&eg_intrat);
1920: period = F4_INTRAT_PERIOD;
1921: nsize = period;
1922: wxsize = rank*ri*nsize;
1923: wx = (int *)MALLOC_ATOMIC(wxsize*sizeof(int));
1924: for ( i = 0; i < wxsize; i++ ) wx[i] = 0;
1925: for ( q = ONE, count = 0; ; ) {
1926: if ( DP_Print )
1927: fprintf(stderr,"o");
1928: /* wc = -b mod md */
1929: get_eg(&tmp0);
1930: for ( i = 0; i < rank; i++ )
1931: for ( j = 0, bi = b[i], wi = wc[i]; j < ri; j++ )
1932: if ( u = (Q)bi[j] ) {
1933: t = rem(NM(u),md);
1934: if ( t && SGN(u) > 0 )
1935: t = (md - t) % md;
1936: wi[j] = t;
1937: } else
1938: wi[j] = 0;
1939: /* wc = A^(-1)wc; wc is not normalized */
1940: solve_by_lu_mod(w,rank,md,wc,ri,0);
1941: /* wx += q*wc */
1942: ptr = wx;
1943: for ( i = 0; i < rank; i++ )
1944: for ( j = 0, wi = wc[i]; j < ri; j++ ) {
1945: if ( wi[j] )
1946: muln_1(BD(NM(q)),PL(NM(q)),wi[j],ptr);
1947: ptr += nsize;
1948: }
1949: count++;
1950: get_eg(&tmp1);
1951: add_eg(&eg_inv,&tmp0,&tmp1);
1952: get_eg(&tmp0);
1953: for ( i = 0; i < rank; i++ )
1954: for ( j = 0; j < ri; j++ ) {
1955: inner_product_mat_int_mod(a,wc,rank,i,j,&u);
1956: addq(b[i][j],u,&s);
1957: if ( s ) {
1958: t = divin(NM(s),md,&tn);
1959: if ( t )
1960: error("generic_gauss_elim_hensel:incosistent");
1961: NTOQ(tn,SGN(s),b[i][j]);
1962: } else
1963: b[i][j] = 0;
1964: }
1.77 ! noro 1965: printf("\n");
! 1966: for ( i = 0; i < rank; i++ ) {
! 1967: for ( j = 0; j < ri; j++ ) {
! 1968: printexpr(CO,b[i][j]); printf(" ");
! 1969: }
! 1970: printf("\n");
! 1971: }
1.76 noro 1972: get_eg(&tmp1);
1973: add_eg(&eg_mul,&tmp0,&tmp1);
1974: /* q = q*md */
1975: mulq(q,mdq,&u); q = u;
1976: if ( count == period ) {
1977: get_eg(&tmp0);
1978: ptr = wx;
1979: for ( i = 0; i < rank; i++ )
1980: for ( j = 0, xi = x[i]; j < ri;
1981: j++, ptr += nsize ) {
1982: for ( k = nsize-1; k >= 0 && !ptr[k]; k-- );
1983: if ( k >= 0 ) {
1984: wn = NALLOC(k+1);
1985: PL(wn) = k+1;
1986: for ( l = 0; l <= k; l++ ) BD(wn)[l] = (unsigned int)ptr[l];
1987: NTOQ(wn,1,wq);
1988: subq(xi[j],wq,&u); xi[j] = u;
1989: }
1990: }
1991: ret = intmtoratm_q(xmat,NM(q),*nmmat,dn);
1992: get_eg(&tmp1); add_eg(&eg_intrat,&tmp0,&tmp1);
1993: if ( ret ) {
1994: for ( j = k = l = 0; j < col; j++ )
1995: if ( cinfo[j] > 0 )
1996: rind[k++] = j;
1997: else if ( !cinfo[j] )
1998: cind[l++] = j;
1999: get_eg(&tmp0);
2000: ret = gensolve_check(mat,*nmmat,*dn,rind,cind);
2001: get_eg(&tmp1); add_eg(&eg_check,&tmp0,&tmp1);
2002: if ( ret ) {
2003: if ( DP_Print > 3 ) {
2004: fprintf(stderr,"\n");
2005: print_eg("INV",&eg_inv);
2006: print_eg("MUL",&eg_mul);
2007: print_eg("INTRAT",&eg_intrat);
2008: print_eg("CHECK",&eg_check);
2009: fflush(asir_out);
2010: }
2011: return rank;
1.77 ! noro 2012: } else
! 2013: goto reset;
1.76 noro 2014: } else {
1.77 ! noro 2015: reset:
1.76 noro 2016: period = period*3/2;
2017: count = 0;
2018: nsize += period;
2019: wxsize += rank*ri*nsize;
2020: wx = (int *)REALLOC(wx,wxsize*sizeof(int));
2021: for ( i = 0; i < wxsize; i++ ) wx[i] = 0;
2022: }
2023: }
2024: }
2025: }
1.1 noro 2026: }
2027:
2028: int f4_nocheck;
2029:
1.24 noro 2030: int gensolve_check(MAT mat,MAT nm,Q dn,int *rind,int *cind)
1.1 noro 2031: {
1.76 noro 2032: int row,col,rank,clen,i,j,k,l;
2033: Q s,t;
2034: Q *w;
2035: Q *mati,*nmk;
2036:
2037: if ( f4_nocheck )
2038: return 1;
2039: row = mat->row; col = mat->col;
2040: rank = nm->row; clen = nm->col;
2041: w = (Q *)MALLOC(clen*sizeof(Q));
2042: for ( i = 0; i < row; i++ ) {
2043: mati = (Q *)mat->body[i];
1.1 noro 2044: #if 1
1.76 noro 2045: bzero(w,clen*sizeof(Q));
2046: for ( k = 0; k < rank; k++ )
2047: for ( l = 0, nmk = (Q *)nm->body[k]; l < clen; l++ ) {
2048: mulq(mati[rind[k]],nmk[l],&t);
2049: addq(w[l],t,&s); w[l] = s;
2050: }
2051: for ( j = 0; j < clen; j++ ) {
2052: mulq(dn,mati[cind[j]],&t);
2053: if ( cmpq(w[j],t) )
2054: break;
2055: }
1.1 noro 2056: #else
1.76 noro 2057: for ( j = 0; j < clen; j++ ) {
2058: for ( k = 0, s = 0; k < rank; k++ ) {
2059: mulq(mati[rind[k]],nm->body[k][j],&t);
2060: addq(s,t,&u); s = u;
2061: }
2062: mulq(dn,mati[cind[j]],&t);
2063: if ( cmpq(s,t) )
2064: break;
2065: }
1.1 noro 2066: #endif
1.76 noro 2067: if ( j != clen )
2068: break;
2069: }
2070: if ( i != row )
2071: return 0;
2072: else
2073: return 1;
1.1 noro 2074: }
2075:
2076: /* assuming 0 < c < m */
2077:
1.24 noro 2078: int inttorat(N c,N m,N b,int *sgnp,N *nmp,N *dnp)
1.1 noro 2079: {
1.76 noro 2080: Q qq,t,u1,v1,r1;
2081: N q,u2,v2,r2;
1.1 noro 2082:
1.76 noro 2083: u1 = 0; v1 = ONE; u2 = m; v2 = c;
2084: while ( cmpn(v2,b) >= 0 ) {
2085: divn(u2,v2,&q,&r2); u2 = v2; v2 = r2;
2086: NTOQ(q,1,qq); mulq(qq,v1,&t); subq(u1,t,&r1); u1 = v1; v1 = r1;
2087: }
2088: if ( cmpn(NM(v1),b) >= 0 )
2089: return 0;
2090: else {
2091: *nmp = v2;
2092: *dnp = NM(v1);
2093: *sgnp = SGN(v1);
2094: return 1;
2095: }
1.1 noro 2096: }
2097:
2098: /* mat->body = N ** */
2099:
1.24 noro 2100: int intmtoratm(MAT mat,N md,MAT nm,Q *dn)
1.1 noro 2101: {
1.76 noro 2102: N t,s,b;
2103: Q dn0,dn1,nm1,q;
2104: int i,j,k,l,row,col;
2105: Q **rmat;
2106: N **tmat;
2107: N *tmi;
2108: Q *nmk;
2109: N u,unm,udn;
2110: int sgn,ret;
2111:
2112: if ( UNIN(md) )
2113: return 0;
2114: row = mat->row; col = mat->col;
2115: bshiftn(md,1,&t);
2116: isqrt(t,&s);
2117: bshiftn(s,64,&b);
2118: if ( !b )
2119: b = ONEN;
2120: dn0 = ONE;
2121: tmat = (N **)mat->body;
2122: rmat = (Q **)nm->body;
2123: for ( i = 0; i < row; i++ )
2124: for ( j = 0, tmi = tmat[i]; j < col; j++ )
2125: if ( tmi[j] ) {
2126: muln(tmi[j],NM(dn0),&s);
2127: remn(s,md,&u);
2128: ret = inttorat(u,md,b,&sgn,&unm,&udn);
2129: if ( !ret )
2130: return 0;
2131: else {
2132: NTOQ(unm,sgn,nm1);
2133: NTOQ(udn,1,dn1);
2134: if ( !UNIQ(dn1) ) {
2135: for ( k = 0; k < i; k++ )
2136: for ( l = 0, nmk = rmat[k]; l < col; l++ ) {
2137: mulq(nmk[l],dn1,&q); nmk[l] = q;
2138: }
2139: for ( l = 0, nmk = rmat[i]; l < j; l++ ) {
2140: mulq(nmk[l],dn1,&q); nmk[l] = q;
2141: }
2142: }
2143: rmat[i][j] = nm1;
2144: mulq(dn0,dn1,&q); dn0 = q;
2145: }
2146: }
2147: *dn = dn0;
2148: return 1;
1.1 noro 2149: }
2150:
1.3 noro 2151: /* mat->body = Q ** */
2152:
1.24 noro 2153: int intmtoratm_q(MAT mat,N md,MAT nm,Q *dn)
1.3 noro 2154: {
1.76 noro 2155: N t,s,b;
2156: Q dn0,dn1,nm1,q;
2157: int i,j,k,l,row,col;
2158: Q **rmat;
2159: Q **tmat;
2160: Q *tmi;
2161: Q *nmk;
2162: N u,unm,udn;
2163: int sgn,ret;
2164:
2165: if ( UNIN(md) )
2166: return 0;
2167: row = mat->row; col = mat->col;
2168: bshiftn(md,1,&t);
2169: isqrt(t,&s);
2170: bshiftn(s,64,&b);
2171: if ( !b )
2172: b = ONEN;
2173: dn0 = ONE;
2174: tmat = (Q **)mat->body;
2175: rmat = (Q **)nm->body;
2176: for ( i = 0; i < row; i++ )
2177: for ( j = 0, tmi = tmat[i]; j < col; j++ )
2178: if ( tmi[j] ) {
2179: muln(NM(tmi[j]),NM(dn0),&s);
2180: remn(s,md,&u);
2181: ret = inttorat(u,md,b,&sgn,&unm,&udn);
2182: if ( !ret )
2183: return 0;
2184: else {
2185: if ( SGN(tmi[j])<0 )
2186: sgn = -sgn;
2187: NTOQ(unm,sgn,nm1);
2188: NTOQ(udn,1,dn1);
2189: if ( !UNIQ(dn1) ) {
2190: for ( k = 0; k < i; k++ )
2191: for ( l = 0, nmk = rmat[k]; l < col; l++ ) {
2192: mulq(nmk[l],dn1,&q); nmk[l] = q;
2193: }
2194: for ( l = 0, nmk = rmat[i]; l < j; l++ ) {
2195: mulq(nmk[l],dn1,&q); nmk[l] = q;
2196: }
2197: }
2198: rmat[i][j] = nm1;
2199: mulq(dn0,dn1,&q); dn0 = q;
2200: }
2201: }
2202: *dn = dn0;
2203: return 1;
1.3 noro 2204: }
2205:
1.4 noro 2206: #define ONE_STEP1 if ( zzz = *s ) { DMAR(zzz,hc,*tj,md,*tj) } tj++; s++;
2207:
1.24 noro 2208: void reduce_reducers_mod(int **mat,int row,int col,int md)
1.4 noro 2209: {
1.76 noro 2210: int i,j,k,l,hc,zzz;
2211: int *t,*s,*tj,*ind;
1.4 noro 2212:
1.76 noro 2213: /* reduce the reducers */
2214: ind = (int *)ALLOCA(row*sizeof(int));
2215: for ( i = 0; i < row; i++ ) {
2216: t = mat[i];
2217: for ( j = 0; j < col && !t[j]; j++ );
2218: /* register the position of the head term */
2219: ind[i] = j;
2220: for ( l = i-1; l >= 0; l-- ) {
2221: /* reduce mat[i] by mat[l] */
2222: if ( hc = t[ind[l]] ) {
2223: /* mat[i] = mat[i]-hc*mat[l] */
2224: j = ind[l];
2225: s = mat[l]+j;
2226: tj = t+j;
2227: hc = md-hc;
2228: k = col-j;
2229: for ( ; k >= 64; k -= 64 ) {
2230: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
2231: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
2232: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
2233: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
2234: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
2235: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
2236: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
2237: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
2238: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
2239: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
2240: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
2241: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
2242: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
2243: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
2244: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
2245: ONE_STEP1 ONE_STEP1 ONE_STEP1 ONE_STEP1
2246: }
2247: for ( ; k > 0; k-- ) {
2248: if ( zzz = *s ) { DMAR(zzz,hc,*tj,md,*tj) } tj++; s++;
2249: }
2250: }
2251: }
2252: }
1.4 noro 2253: }
2254:
2255: /*
1.76 noro 2256: mat[i] : reducers (i=0,...,nred-1)
2257: spolys (i=nred,...,row-1)
2258: mat[0] < mat[1] < ... < mat[nred-1] w.r.t the term order
2259: 1. reduce the reducers
2260: 2. reduce spolys by the reduced reducers
1.4 noro 2261: */
2262:
1.24 noro 2263: void pre_reduce_mod(int **mat,int row,int col,int nred,int md)
1.4 noro 2264: {
1.76 noro 2265: int i,j,k,l,hc,inv;
2266: int *t,*s,*tk,*ind;
1.4 noro 2267:
2268: #if 1
1.76 noro 2269: /* reduce the reducers */
2270: ind = (int *)ALLOCA(row*sizeof(int));
2271: for ( i = 0; i < nred; i++ ) {
2272: /* make mat[i] monic and mat[i] by mat[0],...,mat[i-1] */
2273: t = mat[i];
2274: for ( j = 0; j < col && !t[j]; j++ );
2275: /* register the position of the head term */
2276: ind[i] = j;
2277: inv = invm(t[j],md);
2278: for ( k = j; k < col; k++ )
2279: if ( t[k] )
2280: DMAR(t[k],inv,0,md,t[k])
2281: for ( l = i-1; l >= 0; l-- ) {
2282: /* reduce mat[i] by mat[l] */
2283: if ( hc = t[ind[l]] ) {
2284: /* mat[i] = mat[i]-hc*mat[l] */
2285: for ( k = ind[l], hc = md-hc, s = mat[l]+k, tk = t+k;
2286: k < col; k++, tk++, s++ )
2287: if ( *s )
2288: DMAR(*s,hc,*tk,md,*tk)
2289: }
2290: }
2291: }
2292: /* reduce the spolys */
2293: for ( i = nred; i < row; i++ ) {
2294: t = mat[i];
2295: for ( l = nred-1; l >= 0; l-- ) {
2296: /* reduce mat[i] by mat[l] */
2297: if ( hc = t[ind[l]] ) {
2298: /* mat[i] = mat[i]-hc*mat[l] */
2299: for ( k = ind[l], hc = md-hc, s = mat[l]+k, tk = t+k;
2300: k < col; k++, tk++, s++ )
2301: if ( *s )
2302: DMAR(*s,hc,*tk,md,*tk)
2303: }
2304: }
2305: }
1.4 noro 2306: #endif
2307: }
2308: /*
1.76 noro 2309: mat[i] : reducers (i=0,...,nred-1)
2310: mat[0] < mat[1] < ... < mat[nred-1] w.r.t the term order
1.4 noro 2311: */
2312:
1.24 noro 2313: void reduce_sp_by_red_mod(int *sp,int **redmat,int *ind,int nred,int col,int md)
1.4 noro 2314: {
1.76 noro 2315: int i,j,k,hc,zzz;
2316: int *s,*tj;
1.4 noro 2317:
1.76 noro 2318: /* reduce the spolys by redmat */
2319: for ( i = nred-1; i >= 0; i-- ) {
2320: /* reduce sp by redmat[i] */
2321: if ( hc = sp[ind[i]] ) {
2322: /* sp = sp-hc*redmat[i] */
2323: j = ind[i];
2324: hc = md-hc;
2325: s = redmat[i]+j;
2326: tj = sp+j;
2327: for ( k = col-j; k > 0; k-- ) {
2328: if ( zzz = *s ) { DMAR(zzz,hc,*tj,md,*tj) } tj++; s++;
2329: }
2330: }
2331: }
1.17 noro 2332: }
2333:
2334: /*
1.76 noro 2335: mat[i] : compressed reducers (i=0,...,nred-1)
2336: mat[0] < mat[1] < ... < mat[nred-1] w.r.t the term order
1.15 noro 2337: */
2338:
1.24 noro 2339: void red_by_compress(int m,unsigned int *p,unsigned int *r,
1.76 noro 2340: unsigned int *ri,unsigned int hc,int len)
1.18 noro 2341: {
1.76 noro 2342: unsigned int up,lo;
2343: unsigned int dmy;
2344: unsigned int *pj;
2345:
2346: p[*ri] = 0; r++; ri++;
2347: for ( len--; len; len--, r++, ri++ ) {
2348: pj = p+ *ri;
2349: DMA(*r,hc,*pj,up,lo);
2350: if ( up ) {
2351: DSAB(m,up,lo,dmy,*pj);
2352: } else
2353: *pj = lo;
2354: }
1.18 noro 2355: }
2356:
2357: /* p -= hc*r */
2358:
1.24 noro 2359: void red_by_vect(int m,unsigned int *p,unsigned int *r,unsigned int hc,int len)
1.18 noro 2360: {
1.76 noro 2361: unsigned int up,lo,dmy;
1.18 noro 2362:
1.76 noro 2363: *p++ = 0; r++; len--;
2364: for ( ; len; len--, r++, p++ )
2365: if ( *r ) {
2366: DMA(*r,hc,*p,up,lo);
2367: if ( up ) {
2368: DSAB(m,up,lo,dmy,*p);
2369: } else
2370: *p = lo;
2371: }
1.18 noro 2372: }
2373:
1.75 noro 2374: #if defined(__GNUC__) && SIZEOF_LONG==8
1.74 noro 2375: /* 64bit vector += UNIT vector(normalized) */
1.73 noro 2376:
1.74 noro 2377: void red_by_vect64(int m, U64 *p,unsigned int *c,U64 *r,unsigned int hc,int len)
1.73 noro 2378: {
1.74 noro 2379: U64 t;
2380:
2381: /* (p[0],c[0]) is normalized */
2382: *p++ = 0; *c++ = 0; r++; len--;
2383: for ( ; len; len--, r++, p++, c++ )
2384: if ( *r ) {
2385: t = (*p)+(*r)*hc;
2386: if ( t < *p ) (*c)++;
2387: *p = t;
2388: }
1.73 noro 2389: }
2390: #endif
2391:
1.32 noro 2392: void red_by_vect_sf(int m,unsigned int *p,unsigned int *r,unsigned int hc,int len)
2393: {
1.76 noro 2394: *p++ = 0; r++; len--;
2395: for ( ; len; len--, r++, p++ )
2396: if ( *r )
2397: *p = _addsf(_mulsf(*r,hc),*p);
1.32 noro 2398: }
2399:
1.71 noro 2400: extern GZ current_mod_lf;
2401: extern int current_mod_lf_size;
2402:
1.70 noro 2403: void red_by_vect_lf(mpz_t *p,mpz_t *r,mpz_t hc,int len)
2404: {
1.76 noro 2405: mpz_set_ui(*p++,0); r++; len--;
2406: for ( ; len; len--, r++, p++ ) {
1.70 noro 2407: mpz_addmul(*p,*r,hc);
1.71 noro 2408: #if 0
2409: if ( mpz_size(*p) > current_mod_lf_size )
2410: mpz_mod(*p,*p,BDY(current_mod_lf));
2411: #endif
2412: }
1.70 noro 2413: }
2414:
2415:
1.21 noro 2416: extern unsigned int **psca;
2417:
1.24 noro 2418: void reduce_sp_by_red_mod_compress (int *sp,CDP *redmat,int *ind,
1.76 noro 2419: int nred,int col,int md)
1.15 noro 2420: {
1.76 noro 2421: int i,len;
2422: CDP ri;
2423: unsigned int hc;
2424: unsigned int *usp;
2425:
2426: usp = (unsigned int *)sp;
2427: /* reduce the spolys by redmat */
2428: for ( i = nred-1; i >= 0; i-- ) {
2429: /* reduce sp by redmat[i] */
2430: usp[ind[i]] %= md;
2431: if ( hc = usp[ind[i]] ) {
2432: /* sp = sp-hc*redmat[i] */
2433: hc = md-hc;
2434: ri = redmat[i];
2435: len = ri->len;
2436: red_by_compress(md,usp,psca[ri->psindex],ri->body,hc,len);
2437: }
2438: }
2439: for ( i = 0; i < col; i++ )
2440: if ( usp[i] >= (unsigned int)md )
2441: usp[i] %= md;
1.4 noro 2442: }
2443:
2444: #define ONE_STEP2 if ( zzz = *pk ) { DMAR(zzz,a,*tk,md,*tk) } pk++; tk++;
2445:
1.24 noro 2446: int generic_gauss_elim_mod(int **mat0,int row,int col,int md,int *colstat)
1.1 noro 2447: {
1.76 noro 2448: int i,j,k,l,inv,a,rank;
2449: unsigned int *t,*pivot,*pk;
2450: unsigned int **mat;
2451:
2452: mat = (unsigned int **)mat0;
2453: for ( rank = 0, j = 0; j < col; j++ ) {
2454: for ( i = rank; i < row; i++ )
2455: mat[i][j] %= md;
2456: for ( i = rank; i < row; i++ )
2457: if ( mat[i][j] )
2458: break;
2459: if ( i == row ) {
2460: colstat[j] = 0;
2461: continue;
2462: } else
2463: colstat[j] = 1;
2464: if ( i != rank ) {
2465: t = mat[i]; mat[i] = mat[rank]; mat[rank] = t;
2466: }
2467: pivot = mat[rank];
2468: inv = invm(pivot[j],md);
2469: for ( k = j, pk = pivot+k; k < col; k++, pk++ )
2470: if ( *pk ) {
2471: if ( *pk >= (unsigned int)md )
2472: *pk %= md;
2473: DMAR(*pk,inv,0,md,*pk)
2474: }
2475: for ( i = rank+1; i < row; i++ ) {
2476: t = mat[i];
2477: if ( a = t[j] )
2478: red_by_vect(md,t+j,pivot+j,md-a,col-j);
2479: }
2480: rank++;
2481: }
2482: for ( j = col-1, l = rank-1; j >= 0; j-- )
2483: if ( colstat[j] ) {
2484: pivot = mat[l];
2485: for ( i = 0; i < l; i++ ) {
2486: t = mat[i];
2487: t[j] %= md;
2488: if ( a = t[j] )
2489: red_by_vect(md,t+j,pivot+j,md-a,col-j);
2490: }
2491: l--;
2492: }
2493: for ( j = 0, l = 0; l < rank; j++ )
2494: if ( colstat[j] ) {
2495: t = mat[l];
2496: for ( k = j; k < col; k++ )
2497: if ( t[k] >= (unsigned int)md )
2498: t[k] %= md;
2499: l++;
2500: }
2501: return rank;
1.32 noro 2502: }
2503:
1.65 noro 2504: int generic_gauss_elim_mod2(int **mat0,int row,int col,int md,int *colstat,int *rowstat)
2505: {
1.76 noro 2506: int i,j,k,l,inv,a,rank;
2507: unsigned int *t,*pivot,*pk;
2508: unsigned int **mat;
2509:
2510: for ( i = 0; i < row; i++ ) rowstat[i] = i;
2511: mat = (unsigned int **)mat0;
2512: for ( rank = 0, j = 0; j < col; j++ ) {
2513: for ( i = rank; i < row; i++ )
2514: mat[i][j] %= md;
2515: for ( i = rank; i < row; i++ )
2516: if ( mat[i][j] )
2517: break;
2518: if ( i == row ) {
2519: colstat[j] = 0;
2520: continue;
2521: } else
2522: colstat[j] = 1;
2523: if ( i != rank ) {
2524: t = mat[i]; mat[i] = mat[rank]; mat[rank] = t;
2525: k = rowstat[i]; rowstat[i] = rowstat[rank]; rowstat[rank] = k;
2526: }
2527: pivot = mat[rank];
2528: inv = invm(pivot[j],md);
2529: for ( k = j, pk = pivot+k; k < col; k++, pk++ )
2530: if ( *pk ) {
2531: if ( *pk >= (unsigned int)md )
2532: *pk %= md;
2533: DMAR(*pk,inv,0,md,*pk)
2534: }
2535: for ( i = rank+1; i < row; i++ ) {
2536: t = mat[i];
2537: if ( a = t[j] )
2538: red_by_vect(md,t+j,pivot+j,md-a,col-j);
2539: }
2540: rank++;
2541: }
2542: for ( j = col-1, l = rank-1; j >= 0; j-- )
2543: if ( colstat[j] ) {
2544: pivot = mat[l];
2545: for ( i = 0; i < l; i++ ) {
2546: t = mat[i];
2547: t[j] %= md;
2548: if ( a = t[j] )
2549: red_by_vect(md,t+j,pivot+j,md-a,col-j);
2550: }
2551: l--;
2552: }
2553: for ( j = 0, l = 0; l < rank; j++ )
2554: if ( colstat[j] ) {
2555: t = mat[l];
2556: for ( k = j; k < col; k++ )
2557: if ( t[k] >= (unsigned int)md )
2558: t[k] %= md;
2559: l++;
2560: }
2561: return rank;
1.65 noro 2562: }
2563:
1.69 noro 2564: int indep_rows_mod(int **mat0,int row,int col,int md,int *rowstat)
2565: {
1.76 noro 2566: int i,j,k,l,inv,a,rank;
2567: unsigned int *t,*pivot,*pk;
2568: unsigned int **mat;
2569:
2570: for ( i = 0; i < row; i++ ) rowstat[i] = i;
2571: mat = (unsigned int **)mat0;
2572: for ( rank = 0, j = 0; j < col; j++ ) {
2573: for ( i = rank; i < row; i++ )
2574: mat[i][j] %= md;
2575: for ( i = rank; i < row; i++ )
2576: if ( mat[i][j] )
2577: break;
2578: if ( i == row ) continue;
2579: if ( i != rank ) {
2580: t = mat[i]; mat[i] = mat[rank]; mat[rank] = t;
2581: k = rowstat[i]; rowstat[i] = rowstat[rank]; rowstat[rank] = k;
2582: }
2583: pivot = mat[rank];
2584: inv = invm(pivot[j],md);
2585: for ( k = j, pk = pivot+k; k < col; k++, pk++ )
2586: if ( *pk ) {
2587: if ( *pk >= (unsigned int)md )
2588: *pk %= md;
2589: DMAR(*pk,inv,0,md,*pk)
2590: }
2591: for ( i = rank+1; i < row; i++ ) {
2592: t = mat[i];
2593: if ( a = t[j] )
2594: red_by_vect(md,t+j,pivot+j,md-a,col-j);
2595: }
2596: rank++;
2597: }
2598: return rank;
1.69 noro 2599: }
2600:
1.32 noro 2601: int generic_gauss_elim_sf(int **mat0,int row,int col,int md,int *colstat)
2602: {
1.76 noro 2603: int i,j,k,l,inv,a,rank;
2604: unsigned int *t,*pivot,*pk;
2605: unsigned int **mat;
2606:
2607: mat = (unsigned int **)mat0;
2608: for ( rank = 0, j = 0; j < col; j++ ) {
2609: for ( i = rank; i < row; i++ )
2610: if ( mat[i][j] )
2611: break;
2612: if ( i == row ) {
2613: colstat[j] = 0;
2614: continue;
2615: } else
2616: colstat[j] = 1;
2617: if ( i != rank ) {
2618: t = mat[i]; mat[i] = mat[rank]; mat[rank] = t;
2619: }
2620: pivot = mat[rank];
2621: inv = _invsf(pivot[j]);
2622: for ( k = j, pk = pivot+k; k < col; k++, pk++ )
2623: if ( *pk )
2624: *pk = _mulsf(*pk,inv);
2625: for ( i = rank+1; i < row; i++ ) {
2626: t = mat[i];
2627: if ( a = t[j] )
2628: red_by_vect_sf(md,t+j,pivot+j,_chsgnsf(a),col-j);
2629: }
2630: rank++;
2631: }
2632: for ( j = col-1, l = rank-1; j >= 0; j-- )
2633: if ( colstat[j] ) {
2634: pivot = mat[l];
2635: for ( i = 0; i < l; i++ ) {
2636: t = mat[i];
2637: if ( a = t[j] )
2638: red_by_vect_sf(md,t+j,pivot+j,_chsgnsf(a),col-j);
2639: }
2640: l--;
2641: }
2642: return rank;
1.1 noro 2643: }
2644:
2645: /* LU decomposition; a[i][i] = 1/U[i][i] */
2646:
1.24 noro 2647: int lu_gfmmat(GFMMAT mat,unsigned int md,int *perm)
1.1 noro 2648: {
1.76 noro 2649: int row,col;
2650: int i,j,k;
2651: unsigned int *t,*pivot;
2652: unsigned int **a;
2653: unsigned int inv,m;
2654:
2655: row = mat->row; col = mat->col;
2656: a = mat->body;
2657: bzero(perm,row*sizeof(int));
2658:
2659: for ( i = 0; i < row; i++ )
2660: perm[i] = i;
2661: for ( k = 0; k < col; k++ ) {
2662: for ( i = k; i < row && !a[i][k]; i++ );
2663: if ( i == row )
2664: return 0;
2665: if ( i != k ) {
2666: j = perm[i]; perm[i] = perm[k]; perm[k] = j;
2667: t = a[i]; a[i] = a[k]; a[k] = t;
2668: }
2669: pivot = a[k];
2670: pivot[k] = inv = invm(pivot[k],md);
2671: for ( i = k+1; i < row; i++ ) {
2672: t = a[i];
2673: if ( m = t[k] ) {
2674: DMAR(inv,m,0,md,t[k])
2675: for ( j = k+1, m = md - t[k]; j < col; j++ )
2676: if ( pivot[j] ) {
2677: unsigned int tj;
2678:
2679: DMAR(m,pivot[j],t[j],md,tj)
2680: t[j] = tj;
2681: }
2682: }
2683: }
2684: }
2685: return 1;
1.1 noro 2686: }
2687:
1.3 noro 2688: /*
2689: Input
1.76 noro 2690: a: a row x col matrix
2691: md : a modulus
1.3 noro 2692:
2693: Output:
1.76 noro 2694: return : d = the rank of mat
2695: a[0..(d-1)][0..(d-1)] : LU decomposition (a[i][i] = 1/U[i][i])
2696: rinfo: array of length row
2697: cinfo: array of length col
1.3 noro 2698: i-th row in new a <-> rinfo[i]-th row in old a
1.76 noro 2699: cinfo[j]=1 <=> j-th column is contained in the LU decomp.
1.3 noro 2700: */
2701:
1.24 noro 2702: int find_lhs_and_lu_mod(unsigned int **a,int row,int col,
1.76 noro 2703: unsigned int md,int **rinfo,int **cinfo)
1.3 noro 2704: {
1.76 noro 2705: int i,j,k,d;
2706: int *rp,*cp;
2707: unsigned int *t,*pivot;
2708: unsigned int inv,m;
2709:
2710: *rinfo = rp = (int *)MALLOC_ATOMIC(row*sizeof(int));
2711: *cinfo = cp = (int *)MALLOC_ATOMIC(col*sizeof(int));
2712: for ( i = 0; i < row; i++ )
2713: rp[i] = i;
2714: for ( k = 0, d = 0; k < col; k++ ) {
2715: for ( i = d; i < row && !a[i][k]; i++ );
2716: if ( i == row ) {
2717: cp[k] = 0;
2718: continue;
2719: } else
2720: cp[k] = 1;
2721: if ( i != d ) {
2722: j = rp[i]; rp[i] = rp[d]; rp[d] = j;
2723: t = a[i]; a[i] = a[d]; a[d] = t;
2724: }
2725: pivot = a[d];
2726: pivot[k] = inv = invm(pivot[k],md);
2727: for ( i = d+1; i < row; i++ ) {
2728: t = a[i];
2729: if ( m = t[k] ) {
2730: DMAR(inv,m,0,md,t[k])
2731: for ( j = k+1, m = md - t[k]; j < col; j++ )
2732: if ( pivot[j] ) {
2733: unsigned int tj;
2734: DMAR(m,pivot[j],t[j],md,tj)
2735: t[j] = tj;
2736: }
2737: }
2738: }
2739: d++;
2740: }
2741: return d;
1.3 noro 2742: }
2743:
1.53 noro 2744: int lu_mod(unsigned int **a,int n,unsigned int md,int **rinfo)
2745: {
1.76 noro 2746: int i,j,k;
2747: int *rp;
2748: unsigned int *t,*pivot;
2749: unsigned int inv,m;
2750:
2751: *rinfo = rp = (int *)MALLOC_ATOMIC(n*sizeof(int));
2752: for ( i = 0; i < n; i++ ) rp[i] = i;
2753: for ( k = 0; k < n; k++ ) {
2754: for ( i = k; i < n && !a[i][k]; i++ );
2755: if ( i == n ) return 0;
2756: if ( i != k ) {
2757: j = rp[i]; rp[i] = rp[k]; rp[k] = j;
2758: t = a[i]; a[i] = a[k]; a[k] = t;
2759: }
2760: pivot = a[k];
2761: inv = invm(pivot[k],md);
2762: for ( i = k+1; i < n; i++ ) {
2763: t = a[i];
2764: if ( m = t[k] ) {
2765: DMAR(inv,m,0,md,t[k])
2766: for ( j = k+1, m = md - t[k]; j < n; j++ )
2767: if ( pivot[j] ) {
2768: unsigned int tj;
2769: DMAR(m,pivot[j],t[j],md,tj)
2770: t[j] = tj;
2771: }
2772: }
2773: }
2774: }
2775: return 1;
1.53 noro 2776: }
2777:
1.3 noro 2778: /*
2779: Input
1.76 noro 2780: a : n x n matrix; a result of LU-decomposition
2781: md : modulus
2782: b : n x l matrix
1.3 noro 2783: Output
1.76 noro 2784: b = a^(-1)b
1.3 noro 2785: */
2786:
1.44 noro 2787: void solve_by_lu_mod(int **a,int n,int md,int **b,int l,int normalize)
1.3 noro 2788: {
1.76 noro 2789: unsigned int *y,*c;
2790: int i,j,k;
2791: unsigned int t,m,m2;
2792:
2793: y = (int *)MALLOC_ATOMIC(n*sizeof(int));
2794: c = (int *)MALLOC_ATOMIC(n*sizeof(int));
2795: m2 = md>>1;
2796: for ( k = 0; k < l; k++ ) {
2797: /* copy b[.][k] to c */
2798: for ( i = 0; i < n; i++ )
2799: c[i] = (unsigned int)b[i][k];
2800: /* solve Ly=c */
2801: for ( i = 0; i < n; i++ ) {
2802: for ( t = c[i], j = 0; j < i; j++ )
2803: if ( a[i][j] ) {
2804: m = md - a[i][j];
2805: DMAR(m,y[j],t,md,t)
2806: }
2807: y[i] = t;
2808: }
2809: /* solve Uc=y */
2810: for ( i = n-1; i >= 0; i-- ) {
2811: for ( t = y[i], j =i+1; j < n; j++ )
2812: if ( a[i][j] ) {
2813: m = md - a[i][j];
2814: DMAR(m,c[j],t,md,t)
2815: }
2816: /* a[i][i] = 1/U[i][i] */
2817: DMAR(t,a[i][i],0,md,c[i])
2818: }
2819: /* copy c to b[.][k] with normalization */
2820: if ( normalize )
2821: for ( i = 0; i < n; i++ )
2822: b[i][k] = (int)(c[i]>m2 ? c[i]-md : c[i]);
2823: else
2824: for ( i = 0; i < n; i++ )
2825: b[i][k] = c[i];
2826: }
1.3 noro 2827: }
2828:
1.24 noro 2829: void Pleqm1(NODE arg,VECT *rp)
1.1 noro 2830: {
1.76 noro 2831: MAT m;
2832: VECT vect;
2833: pointer **mat;
2834: Q *v;
2835: Q q;
2836: int **wmat;
2837: int md,i,j,row,col,t,n,status;
2838:
2839: asir_assert(ARG0(arg),O_MAT,"leqm1");
2840: asir_assert(ARG1(arg),O_N,"leqm1");
2841: m = (MAT)ARG0(arg); md = QTOS((Q)ARG1(arg));
2842: row = m->row; col = m->col; mat = m->body;
2843: wmat = (int **)almat(row,col);
2844: for ( i = 0; i < row; i++ )
2845: for ( j = 0; j < col; j++ )
2846: if ( q = (Q)mat[i][j] ) {
2847: t = rem(NM(q),md);
2848: if ( SGN(q) < 0 )
2849: t = (md - t) % md;
2850: wmat[i][j] = t;
2851: } else
2852: wmat[i][j] = 0;
2853: status = gauss_elim_mod1(wmat,row,col,md);
2854: if ( status < 0 )
2855: *rp = 0;
2856: else if ( status > 0 )
2857: *rp = (VECT)ONE;
2858: else {
2859: n = col - 1;
2860: MKVECT(vect,n);
2861: for ( i = 0, v = (Q *)vect->body; i < n; i++ ) {
2862: t = (md-wmat[i][n])%md; STOQ(t,v[i]);
2863: }
2864: *rp = vect;
2865: }
1.1 noro 2866: }
2867:
1.24 noro 2868: int gauss_elim_mod1(int **mat,int row,int col,int md)
1.1 noro 2869: {
1.76 noro 2870: int i,j,k,inv,a,n;
2871: int *t,*pivot;
1.1 noro 2872:
1.76 noro 2873: n = col - 1;
2874: for ( j = 0; j < n; j++ ) {
2875: for ( i = j; i < row && !mat[i][j]; i++ );
2876: if ( i == row )
2877: return 1;
2878: if ( i != j ) {
2879: t = mat[i]; mat[i] = mat[j]; mat[j] = t;
2880: }
2881: pivot = mat[j];
2882: inv = invm(pivot[j],md);
2883: for ( k = j; k <= n; k++ )
2884: pivot[k] = dmar(pivot[k],inv,0,md);
2885: for ( i = j+1; i < row; i++ ) {
2886: t = mat[i];
2887: if ( i != j && (a = t[j]) )
2888: for ( k = j, a = md - a; k <= n; k++ )
2889: t[k] = dmar(pivot[k],a,t[k],md);
2890: }
2891: }
2892: for ( i = n; i < row && !mat[i][n]; i++ );
2893: if ( i == row ) {
2894: for ( j = n-1; j >= 0; j-- ) {
2895: for ( i = j-1, a = (md-mat[j][n])%md; i >= 0; i-- ) {
2896: mat[i][n] = dmar(mat[i][j],a,mat[i][n],md);
2897: mat[i][j] = 0;
2898: }
2899: }
2900: return 0;
2901: } else
2902: return -1;
1.1 noro 2903: }
2904:
1.24 noro 2905: void Pgeninvm(NODE arg,LIST *rp)
1.1 noro 2906: {
1.76 noro 2907: MAT m;
2908: pointer **mat;
2909: Q **tmat;
2910: Q q;
2911: unsigned int **wmat;
2912: int md,i,j,row,col,t,status;
2913: MAT mat1,mat2;
2914: NODE node1,node2;
2915:
2916: asir_assert(ARG0(arg),O_MAT,"leqm1");
2917: asir_assert(ARG1(arg),O_N,"leqm1");
2918: m = (MAT)ARG0(arg); md = QTOS((Q)ARG1(arg));
2919: row = m->row; col = m->col; mat = m->body;
2920: wmat = (unsigned int **)almat(row,col+row);
2921: for ( i = 0; i < row; i++ ) {
2922: bzero((char *)wmat[i],(col+row)*sizeof(int));
2923: for ( j = 0; j < col; j++ )
2924: if ( q = (Q)mat[i][j] ) {
2925: t = rem(NM(q),md);
2926: if ( SGN(q) < 0 )
2927: t = (md - t) % md;
2928: wmat[i][j] = t;
2929: }
2930: wmat[i][col+i] = 1;
2931: }
2932: status = gauss_elim_geninv_mod(wmat,row,col,md);
2933: if ( status > 0 )
2934: *rp = 0;
2935: else {
2936: MKMAT(mat1,col,row); MKMAT(mat2,row-col,row);
2937: for ( i = 0, tmat = (Q **)mat1->body; i < col; i++ )
2938: for ( j = 0; j < row; j++ )
2939: UTOQ(wmat[i][j+col],tmat[i][j]);
2940: for ( tmat = (Q **)mat2->body; i < row; i++ )
2941: for ( j = 0; j < row; j++ )
2942: UTOQ(wmat[i][j+col],tmat[i-col][j]);
2943: MKNODE(node2,mat2,0); MKNODE(node1,mat1,node2); MKLIST(*rp,node1);
2944: }
1.1 noro 2945: }
2946:
1.24 noro 2947: int gauss_elim_geninv_mod(unsigned int **mat,int row,int col,int md)
1.1 noro 2948: {
1.76 noro 2949: int i,j,k,inv,a,n,m;
2950: unsigned int *t,*pivot;
1.1 noro 2951:
1.76 noro 2952: n = col; m = row+col;
2953: for ( j = 0; j < n; j++ ) {
2954: for ( i = j; i < row && !mat[i][j]; i++ );
2955: if ( i == row )
2956: return 1;
2957: if ( i != j ) {
2958: t = mat[i]; mat[i] = mat[j]; mat[j] = t;
2959: }
2960: pivot = mat[j];
2961: inv = invm(pivot[j],md);
2962: for ( k = j; k < m; k++ )
2963: pivot[k] = dmar(pivot[k],inv,0,md);
2964: for ( i = j+1; i < row; i++ ) {
2965: t = mat[i];
2966: if ( a = t[j] )
2967: for ( k = j, a = md - a; k < m; k++ )
2968: t[k] = dmar(pivot[k],a,t[k],md);
2969: }
2970: }
2971: for ( j = n-1; j >= 0; j-- ) {
2972: pivot = mat[j];
2973: for ( i = j-1; i >= 0; i-- ) {
2974: t = mat[i];
2975: if ( a = t[j] )
2976: for ( k = j, a = md - a; k < m; k++ )
2977: t[k] = dmar(pivot[k],a,t[k],md);
2978: }
2979: }
2980: return 0;
1.1 noro 2981: }
2982:
1.24 noro 2983: void Psolve_by_lu_gfmmat(NODE arg,VECT *rp)
1.1 noro 2984: {
1.76 noro 2985: GFMMAT lu;
2986: Q *perm,*rhs,*v;
2987: int n,i;
2988: unsigned int md;
2989: unsigned int *b,*sol;
2990: VECT r;
2991:
2992: lu = (GFMMAT)ARG0(arg);
2993: perm = (Q *)BDY((VECT)ARG1(arg));
2994: rhs = (Q *)BDY((VECT)ARG2(arg));
2995: md = (unsigned int)QTOS((Q)ARG3(arg));
2996: n = lu->col;
2997: b = (unsigned int *)MALLOC_ATOMIC(n*sizeof(int));
2998: sol = (unsigned int *)MALLOC_ATOMIC(n*sizeof(int));
2999: for ( i = 0; i < n; i++ )
3000: b[i] = QTOS(rhs[QTOS(perm[i])]);
3001: solve_by_lu_gfmmat(lu,md,b,sol);
3002: MKVECT(r,n);
3003: for ( i = 0, v = (Q *)r->body; i < n; i++ )
3004: UTOQ(sol[i],v[i]);
3005: *rp = r;
1.1 noro 3006: }
3007:
1.24 noro 3008: void solve_by_lu_gfmmat(GFMMAT lu,unsigned int md,
1.76 noro 3009: unsigned int *b,unsigned int *x)
1.1 noro 3010: {
1.76 noro 3011: int n;
3012: unsigned int **a;
3013: unsigned int *y;
3014: int i,j;
3015: unsigned int t,m;
3016:
3017: n = lu->col;
3018: a = lu->body;
3019: y = (unsigned int *)MALLOC_ATOMIC(n*sizeof(int));
3020: /* solve Ly=b */
3021: for ( i = 0; i < n; i++ ) {
3022: for ( t = b[i], j = 0; j < i; j++ )
3023: if ( a[i][j] ) {
3024: m = md - a[i][j];
3025: DMAR(m,y[j],t,md,t)
3026: }
3027: y[i] = t;
3028: }
3029: /* solve Ux=y */
3030: for ( i = n-1; i >= 0; i-- ) {
3031: for ( t = y[i], j =i+1; j < n; j++ )
3032: if ( a[i][j] ) {
3033: m = md - a[i][j];
3034: DMAR(m,x[j],t,md,t)
3035: }
3036: /* a[i][i] = 1/U[i][i] */
3037: DMAR(t,a[i][i],0,md,x[i])
3038: }
1.1 noro 3039: }
3040:
1.53 noro 3041: void Plu_mat(NODE arg,LIST *rp)
3042: {
1.76 noro 3043: MAT m,lu;
3044: Q dn;
3045: Q *v;
3046: int n,i;
3047: int *iperm;
3048: VECT perm;
3049: NODE n0;
3050:
3051: asir_assert(ARG0(arg),O_MAT,"lu_mat");
3052: m = (MAT)ARG0(arg);
3053: n = m->row;
3054: MKMAT(lu,n,n);
3055: lu_dec_cr(m,lu,&dn,&iperm);
3056: MKVECT(perm,n);
3057: for ( i = 0, v = (Q *)perm->body; i < n; i++ )
3058: STOQ(iperm[i],v[i]);
3059: n0 = mknode(3,lu,dn,perm);
3060: MKLIST(*rp,n0);
1.53 noro 3061: }
3062:
1.24 noro 3063: void Plu_gfmmat(NODE arg,LIST *rp)
1.1 noro 3064: {
1.76 noro 3065: MAT m;
3066: GFMMAT mm;
3067: unsigned int md;
3068: int i,row,col,status;
3069: int *iperm;
3070: Q *v;
3071: VECT perm;
3072: NODE n0;
3073:
3074: asir_assert(ARG0(arg),O_MAT,"lu_gfmmat");
3075: asir_assert(ARG1(arg),O_N,"lu_gfmmat");
3076: m = (MAT)ARG0(arg); md = (unsigned int)QTOS((Q)ARG1(arg));
3077: mat_to_gfmmat(m,md,&mm);
3078: row = m->row;
3079: col = m->col;
3080: iperm = (int *)MALLOC_ATOMIC(row*sizeof(int));
3081: status = lu_gfmmat(mm,md,iperm);
3082: if ( !status )
3083: n0 = 0;
3084: else {
3085: MKVECT(perm,row);
3086: for ( i = 0, v = (Q *)perm->body; i < row; i++ )
3087: STOQ(iperm[i],v[i]);
3088: n0 = mknode(2,mm,perm);
3089: }
3090: MKLIST(*rp,n0);
1.1 noro 3091: }
3092:
1.24 noro 3093: void Pmat_to_gfmmat(NODE arg,GFMMAT *rp)
1.1 noro 3094: {
1.76 noro 3095: MAT m;
3096: unsigned int md;
1.1 noro 3097:
1.76 noro 3098: asir_assert(ARG0(arg),O_MAT,"mat_to_gfmmat");
3099: asir_assert(ARG1(arg),O_N,"mat_to_gfmmat");
3100: m = (MAT)ARG0(arg); md = (unsigned int)QTOS((Q)ARG1(arg));
3101: mat_to_gfmmat(m,md,rp);
1.1 noro 3102: }
3103:
1.24 noro 3104: void mat_to_gfmmat(MAT m,unsigned int md,GFMMAT *rp)
1.1 noro 3105: {
1.76 noro 3106: unsigned int **wmat;
3107: unsigned int t;
3108: Q **mat;
3109: Q q;
3110: int i,j,row,col;
3111:
3112: row = m->row; col = m->col; mat = (Q **)m->body;
3113: wmat = (unsigned int **)almat(row,col);
3114: for ( i = 0; i < row; i++ ) {
3115: bzero((char *)wmat[i],col*sizeof(unsigned int));
3116: for ( j = 0; j < col; j++ )
3117: if ( q = mat[i][j] ) {
3118: t = (unsigned int)rem(NM(q),md);
3119: if ( SGN(q) < 0 )
3120: t = (md - t) % md;
3121: wmat[i][j] = t;
3122: }
3123: }
3124: TOGFMMAT(row,col,wmat,*rp);
1.1 noro 3125: }
3126:
1.72 ohara 3127: void Pgeninvm_swap(NODE arg,LIST *rp)
1.1 noro 3128: {
1.76 noro 3129: MAT m;
3130: pointer **mat;
3131: Q **tmat;
3132: Q *tvect;
3133: Q q;
3134: unsigned int **wmat,**invmat;
3135: int *index;
3136: unsigned int t,md;
3137: int i,j,row,col,status;
3138: MAT mat1;
3139: VECT vect1;
3140: NODE node1,node2;
3141:
3142: asir_assert(ARG0(arg),O_MAT,"geninvm_swap");
3143: asir_assert(ARG1(arg),O_N,"geninvm_swap");
3144: m = (MAT)ARG0(arg); md = QTOS((Q)ARG1(arg));
3145: row = m->row; col = m->col; mat = m->body;
3146: wmat = (unsigned int **)almat(row,col+row);
3147: for ( i = 0; i < row; i++ ) {
3148: bzero((char *)wmat[i],(col+row)*sizeof(int));
3149: for ( j = 0; j < col; j++ )
3150: if ( q = (Q)mat[i][j] ) {
3151: t = (unsigned int)rem(NM(q),md);
3152: if ( SGN(q) < 0 )
3153: t = (md - t) % md;
3154: wmat[i][j] = t;
3155: }
3156: wmat[i][col+i] = 1;
3157: }
3158: status = gauss_elim_geninv_mod_swap(wmat,row,col,md,&invmat,&index);
3159: if ( status > 0 )
3160: *rp = 0;
3161: else {
3162: MKMAT(mat1,col,col);
3163: for ( i = 0, tmat = (Q **)mat1->body; i < col; i++ )
3164: for ( j = 0; j < col; j++ )
3165: UTOQ(invmat[i][j],tmat[i][j]);
3166: MKVECT(vect1,row);
3167: for ( i = 0, tvect = (Q *)vect1->body; i < row; i++ )
3168: STOQ(index[i],tvect[i]);
3169: MKNODE(node2,vect1,0); MKNODE(node1,mat1,node2); MKLIST(*rp,node1);
3170: }
1.1 noro 3171: }
3172:
1.72 ohara 3173: int gauss_elim_geninv_mod_swap(unsigned int **mat,int row,int col,unsigned int md,
3174: unsigned int ***invmatp,int **indexp)
1.1 noro 3175: {
1.76 noro 3176: int i,j,k,inv,a,n,m;
3177: unsigned int *t,*pivot,*s;
3178: int *index;
3179: unsigned int **invmat;
3180:
3181: n = col; m = row+col;
3182: *indexp = index = (int *)MALLOC_ATOMIC(row*sizeof(int));
3183: for ( i = 0; i < row; i++ )
3184: index[i] = i;
3185: for ( j = 0; j < n; j++ ) {
3186: for ( i = j; i < row && !mat[i][j]; i++ );
3187: if ( i == row ) {
3188: *indexp = 0; *invmatp = 0; return 1;
3189: }
3190: if ( i != j ) {
3191: t = mat[i]; mat[i] = mat[j]; mat[j] = t;
3192: k = index[i]; index[i] = index[j]; index[j] = k;
3193: }
3194: pivot = mat[j];
3195: inv = (unsigned int)invm(pivot[j],md);
3196: for ( k = j; k < m; k++ )
3197: if ( pivot[k] )
3198: pivot[k] = (unsigned int)dmar(pivot[k],inv,0,md);
3199: for ( i = j+1; i < row; i++ ) {
3200: t = mat[i];
3201: if ( a = t[j] )
3202: for ( k = j, a = md - a; k < m; k++ )
3203: if ( pivot[k] )
3204: t[k] = dmar(pivot[k],a,t[k],md);
3205: }
3206: }
3207: for ( j = n-1; j >= 0; j-- ) {
3208: pivot = mat[j];
3209: for ( i = j-1; i >= 0; i-- ) {
3210: t = mat[i];
3211: if ( a = t[j] )
3212: for ( k = j, a = md - a; k < m; k++ )
3213: if ( pivot[k] )
3214: t[k] = dmar(pivot[k],a,t[k],md);
3215: }
3216: }
3217: *invmatp = invmat = (unsigned int **)almat(col,col);
3218: for ( i = 0; i < col; i++ )
3219: for ( j = 0, s = invmat[i], t = mat[i]; j < col; j++ )
3220: s[j] = t[col+index[j]];
3221: return 0;
1.27 noro 3222: }
3223:
3224: void Pgeninv_sf_swap(NODE arg,LIST *rp)
3225: {
1.76 noro 3226: MAT m;
3227: GFS **mat,**tmat;
3228: Q *tvect;
3229: GFS q;
3230: int **wmat,**invmat;
3231: int *index;
3232: unsigned int t;
3233: int i,j,row,col,status;
3234: MAT mat1;
3235: VECT vect1;
3236: NODE node1,node2;
3237:
3238: asir_assert(ARG0(arg),O_MAT,"geninv_sf_swap");
3239: m = (MAT)ARG0(arg);
3240: row = m->row; col = m->col; mat = (GFS **)m->body;
3241: wmat = (int **)almat(row,col+row);
3242: for ( i = 0; i < row; i++ ) {
3243: bzero((char *)wmat[i],(col+row)*sizeof(int));
3244: for ( j = 0; j < col; j++ )
3245: if ( q = (GFS)mat[i][j] )
3246: wmat[i][j] = FTOIF(CONT(q));
3247: wmat[i][col+i] = _onesf();
3248: }
3249: status = gauss_elim_geninv_sf_swap(wmat,row,col,&invmat,&index);
3250: if ( status > 0 )
3251: *rp = 0;
3252: else {
3253: MKMAT(mat1,col,col);
3254: for ( i = 0, tmat = (GFS **)mat1->body; i < col; i++ )
3255: for ( j = 0; j < col; j++ )
3256: if ( t = invmat[i][j] ) {
3257: MKGFS(IFTOF(t),tmat[i][j]);
3258: }
3259: MKVECT(vect1,row);
3260: for ( i = 0, tvect = (Q *)vect1->body; i < row; i++ )
3261: STOQ(index[i],tvect[i]);
3262: MKNODE(node2,vect1,0); MKNODE(node1,mat1,node2); MKLIST(*rp,node1);
3263: }
1.27 noro 3264: }
3265:
3266: int gauss_elim_geninv_sf_swap(int **mat,int row,int col,
1.76 noro 3267: int ***invmatp,int **indexp)
1.27 noro 3268: {
1.76 noro 3269: int i,j,k,inv,a,n,m,u;
3270: int *t,*pivot,*s;
3271: int *index;
3272: int **invmat;
3273:
3274: n = col; m = row+col;
3275: *indexp = index = (int *)MALLOC_ATOMIC(row*sizeof(int));
3276: for ( i = 0; i < row; i++ )
3277: index[i] = i;
3278: for ( j = 0; j < n; j++ ) {
3279: for ( i = j; i < row && !mat[i][j]; i++ );
3280: if ( i == row ) {
3281: *indexp = 0; *invmatp = 0; return 1;
3282: }
3283: if ( i != j ) {
3284: t = mat[i]; mat[i] = mat[j]; mat[j] = t;
3285: k = index[i]; index[i] = index[j]; index[j] = k;
3286: }
3287: pivot = mat[j];
3288: inv = _invsf(pivot[j]);
3289: for ( k = j; k < m; k++ )
3290: if ( pivot[k] )
3291: pivot[k] = _mulsf(pivot[k],inv);
3292: for ( i = j+1; i < row; i++ ) {
3293: t = mat[i];
3294: if ( a = t[j] )
3295: for ( k = j, a = _chsgnsf(a); k < m; k++ )
3296: if ( pivot[k] ) {
3297: u = _mulsf(pivot[k],a);
3298: t[k] = _addsf(u,t[k]);
3299: }
3300: }
3301: }
3302: for ( j = n-1; j >= 0; j-- ) {
3303: pivot = mat[j];
3304: for ( i = j-1; i >= 0; i-- ) {
3305: t = mat[i];
3306: if ( a = t[j] )
3307: for ( k = j, a = _chsgnsf(a); k < m; k++ )
3308: if ( pivot[k] ) {
3309: u = _mulsf(pivot[k],a);
3310: t[k] = _addsf(u,t[k]);
3311: }
3312: }
3313: }
3314: *invmatp = invmat = (int **)almat(col,col);
3315: for ( i = 0; i < col; i++ )
3316: for ( j = 0, s = invmat[i], t = mat[i]; j < col; j++ )
3317: s[j] = t[col+index[j]];
3318: return 0;
1.1 noro 3319: }
3320:
3321: void _addn(N,N,N);
3322: int _subn(N,N,N);
3323: void _muln(N,N,N);
3324:
1.24 noro 3325: void inner_product_int(Q *a,Q *b,int n,Q *r)
1.1 noro 3326: {
1.76 noro 3327: int la,lb,i;
3328: int sgn,sgn1;
3329: N wm,wma,sum,t;
3330:
3331: for ( la = lb = 0, i = 0; i < n; i++ ) {
3332: if ( a[i] )
3333: if ( DN(a[i]) )
3334: error("inner_product_int : invalid argument");
3335: else
3336: la = MAX(PL(NM(a[i])),la);
3337: if ( b[i] )
3338: if ( DN(b[i]) )
3339: error("inner_product_int : invalid argument");
3340: else
3341: lb = MAX(PL(NM(b[i])),lb);
3342: }
3343: sgn = 0;
3344: sum= NALLOC(la+lb+2);
3345: bzero((char *)sum,(la+lb+3)*sizeof(unsigned int));
3346: wm = NALLOC(la+lb+2);
3347: wma = NALLOC(la+lb+2);
3348: for ( i = 0; i < n; i++ ) {
3349: if ( !a[i] || !b[i] )
3350: continue;
3351: _muln(NM(a[i]),NM(b[i]),wm);
3352: sgn1 = SGN(a[i])*SGN(b[i]);
3353: if ( !sgn ) {
3354: sgn = sgn1;
3355: t = wm; wm = sum; sum = t;
3356: } else if ( sgn == sgn1 ) {
3357: _addn(sum,wm,wma);
3358: if ( !PL(wma) )
3359: sgn = 0;
3360: t = wma; wma = sum; sum = t;
3361: } else {
3362: /* sgn*sum+sgn1*wm = sgn*(sum-wm) */
3363: sgn *= _subn(sum,wm,wma);
3364: t = wma; wma = sum; sum = t;
3365: }
3366: }
3367: GCFREE(wm);
3368: GCFREE(wma);
3369: if ( !sgn ) {
3370: GCFREE(sum);
3371: *r = 0;
3372: } else
3373: NTOQ(sum,sgn,*r);
1.1 noro 3374: }
3375:
1.3 noro 3376: /* (k,l) element of a*b where a: .x n matrix, b: n x . integer matrix */
3377:
1.24 noro 3378: void inner_product_mat_int_mod(Q **a,int **b,int n,int k,int l,Q *r)
1.3 noro 3379: {
1.76 noro 3380: int la,lb,i;
3381: int sgn,sgn1;
3382: N wm,wma,sum,t;
3383: Q aki;
3384: int bil,bilsgn;
3385: struct oN tn;
3386:
3387: for ( la = 0, i = 0; i < n; i++ ) {
3388: if ( aki = a[k][i] )
3389: if ( DN(aki) )
3390: error("inner_product_int : invalid argument");
3391: else
3392: la = MAX(PL(NM(aki)),la);
3393: }
3394: lb = 1;
3395: sgn = 0;
3396: sum= NALLOC(la+lb+2);
3397: bzero((char *)sum,(la+lb+3)*sizeof(unsigned int));
3398: wm = NALLOC(la+lb+2);
3399: wma = NALLOC(la+lb+2);
3400: for ( i = 0; i < n; i++ ) {
3401: if ( !(aki = a[k][i]) || !(bil = b[i][l]) )
3402: continue;
3403: tn.p = 1;
3404: if ( bil > 0 ) {
3405: tn.b[0] = bil; bilsgn = 1;
3406: } else {
3407: tn.b[0] = -bil; bilsgn = -1;
3408: }
3409: _muln(NM(aki),&tn,wm);
3410: sgn1 = SGN(aki)*bilsgn;
3411: if ( !sgn ) {
3412: sgn = sgn1;
3413: t = wm; wm = sum; sum = t;
3414: } else if ( sgn == sgn1 ) {
3415: _addn(sum,wm,wma);
3416: if ( !PL(wma) )
3417: sgn = 0;
3418: t = wma; wma = sum; sum = t;
3419: } else {
3420: /* sgn*sum+sgn1*wm = sgn*(sum-wm) */
3421: sgn *= _subn(sum,wm,wma);
3422: t = wma; wma = sum; sum = t;
3423: }
3424: }
3425: GCFREE(wm);
3426: GCFREE(wma);
3427: if ( !sgn ) {
3428: GCFREE(sum);
3429: *r = 0;
3430: } else
3431: NTOQ(sum,sgn,*r);
1.3 noro 3432: }
3433:
1.24 noro 3434: void Pmul_mat_vect_int(NODE arg,VECT *rp)
1.1 noro 3435: {
1.76 noro 3436: MAT mat;
3437: VECT vect,r;
3438: int row,col,i;
3439:
3440: mat = (MAT)ARG0(arg);
3441: vect = (VECT)ARG1(arg);
3442: row = mat->row;
3443: col = mat->col;
3444: MKVECT(r,row);
3445: for ( i = 0; i < row; i++ ) {
3446: inner_product_int((Q *)mat->body[i],(Q *)vect->body,col,(Q *)&r->body[i]);
3447: }
3448: *rp = r;
1.1 noro 3449: }
3450:
1.24 noro 3451: void Pnbpoly_up2(NODE arg,GF2N *rp)
1.1 noro 3452: {
1.76 noro 3453: int m,type,ret;
3454: UP2 r;
1.1 noro 3455:
1.76 noro 3456: m = QTOS((Q)ARG0(arg));
3457: type = QTOS((Q)ARG1(arg));
3458: ret = generate_ONB_polynomial(&r,m,type);
3459: if ( ret == 0 )
3460: MKGF2N(r,*rp);
3461: else
3462: *rp = 0;
1.1 noro 3463: }
3464:
1.24 noro 3465: void Px962_irredpoly_up2(NODE arg,GF2N *rp)
1.1 noro 3466: {
1.76 noro 3467: int m,ret,w;
3468: GF2N prev;
3469: UP2 r;
3470:
3471: m = QTOS((Q)ARG0(arg));
3472: prev = (GF2N)ARG1(arg);
3473: if ( !prev ) {
3474: w = (m>>5)+1; NEWUP2(r,w); r->w = 0;
3475: bzero((char *)r->b,w*sizeof(unsigned int));
3476: } else {
3477: r = prev->body;
3478: if ( degup2(r) != m ) {
3479: w = (m>>5)+1; NEWUP2(r,w); r->w = 0;
3480: bzero((char *)r->b,w*sizeof(unsigned int));
3481: }
3482: }
3483: ret = _generate_irreducible_polynomial(r,m);
3484: if ( ret == 0 )
3485: MKGF2N(r,*rp);
3486: else
3487: *rp = 0;
1.1 noro 3488: }
3489:
1.24 noro 3490: void Pirredpoly_up2(NODE arg,GF2N *rp)
1.1 noro 3491: {
1.76 noro 3492: int m,ret,w;
3493: GF2N prev;
3494: UP2 r;
3495:
3496: m = QTOS((Q)ARG0(arg));
3497: prev = (GF2N)ARG1(arg);
3498: if ( !prev ) {
3499: w = (m>>5)+1; NEWUP2(r,w); r->w = 0;
3500: bzero((char *)r->b,w*sizeof(unsigned int));
3501: } else {
3502: r = prev->body;
3503: if ( degup2(r) != m ) {
3504: w = (m>>5)+1; NEWUP2(r,w); r->w = 0;
3505: bzero((char *)r->b,w*sizeof(unsigned int));
3506: }
3507: }
3508: ret = _generate_good_irreducible_polynomial(r,m);
3509: if ( ret == 0 )
3510: MKGF2N(r,*rp);
3511: else
3512: *rp = 0;
1.1 noro 3513: }
3514:
1.26 noro 3515: void Pmat_swap_row_destructive(NODE arg, MAT *m)
3516: {
1.76 noro 3517: int i1,i2;
3518: pointer *t;
3519: MAT mat;
3520:
3521: asir_assert(ARG0(arg),O_MAT,"mat_swap_row_destructive");
3522: asir_assert(ARG1(arg),O_N,"mat_swap_row_destructive");
3523: asir_assert(ARG2(arg),O_N,"mat_swap_row_destructive");
3524: mat = (MAT)ARG0(arg);
3525: i1 = QTOS((Q)ARG1(arg));
3526: i2 = QTOS((Q)ARG2(arg));
3527: if ( i1 < 0 || i2 < 0 || i1 >= mat->row || i2 >= mat->row )
3528: error("mat_swap_row_destructive : Out of range");
3529: t = mat->body[i1];
3530: mat->body[i1] = mat->body[i2];
3531: mat->body[i2] = t;
3532: *m = mat;
1.26 noro 3533: }
3534:
3535: void Pmat_swap_col_destructive(NODE arg, MAT *m)
3536: {
1.76 noro 3537: int j1,j2,i,n;
3538: pointer *mi;
3539: pointer t;
3540: MAT mat;
3541:
3542: asir_assert(ARG0(arg),O_MAT,"mat_swap_col_destructive");
3543: asir_assert(ARG1(arg),O_N,"mat_swap_col_destructive");
3544: asir_assert(ARG2(arg),O_N,"mat_swap_col_destructive");
3545: mat = (MAT)ARG0(arg);
3546: j1 = QTOS((Q)ARG1(arg));
3547: j2 = QTOS((Q)ARG2(arg));
3548: if ( j1 < 0 || j2 < 0 || j1 >= mat->col || j2 >= mat->col )
3549: error("mat_swap_col_destructive : Out of range");
3550: n = mat->row;
3551: for ( i = 0; i < n; i++ ) {
3552: mi = mat->body[i];
3553: t = mi[j1]; mi[j1] = mi[j2]; mi[j2] = t;
3554: }
3555: *m = mat;
1.26 noro 3556: }
1.1 noro 3557: /*
3558: * f = type 'type' normal polynomial of degree m if exists
3559: * IEEE P1363 A.7.2
3560: *
3561: * return value : 0 --- exists
3562: * 1 --- does not exist
3563: * -1 --- failure (memory allocation error)
3564: */
3565:
3566: int generate_ONB_polynomial(UP2 *rp,int m,int type)
3567: {
1.76 noro 3568: int i,r;
3569: int w;
3570: UP2 f,f0,f1,f2,t;
3571:
3572: w = (m>>5)+1;
3573: switch ( type ) {
3574: case 1:
3575: if ( !TypeT_NB_check(m,1) ) return 1;
3576: NEWUP2(f,w); *rp = f; f->w = w;
3577: /* set all the bits */
3578: for ( i = 0; i < w; i++ )
3579: f->b[i] = 0xffffffff;
3580: /* mask the top word if necessary */
3581: if ( r = (m+1)&31 )
3582: f->b[w-1] &= (1<<r)-1;
3583: return 0;
3584: break;
3585: case 2:
3586: if ( !TypeT_NB_check(m,2) ) return 1;
3587: NEWUP2(f,w); *rp = f;
3588: W_NEWUP2(f0,w);
3589: W_NEWUP2(f1,w);
3590: W_NEWUP2(f2,w);
3591:
3592: /* recursion for genrating Type II normal polynomial */
3593:
3594: /* f0 = 1, f1 = t+1 */
3595: f0->w = 1; f0->b[0] = 1;
3596: f1->w = 1; f1->b[0] = 3;
3597: for ( i = 2; i <= m; i++ ) {
3598: /* f2 = t*f1+f0 */
3599: _bshiftup2(f1,-1,f2);
3600: _addup2_destructive(f2,f0);
3601: /* cyclic change of the variables */
3602: t = f0; f0 = f1; f1 = f2; f2 = t;
3603: }
3604: _copyup2(f1,f);
3605: return 0;
3606: break;
3607: default:
3608: return -1;
3609: break;
3610: }
1.1 noro 3611: }
3612:
3613: /*
3614: * f = an irreducible trinomial or pentanomial of degree d 'after' f
3615: * return value : 0 --- exists
3616: * 1 --- does not exist (exhaustion)
3617: */
3618:
3619: int _generate_irreducible_polynomial(UP2 f,int d)
3620: {
1.76 noro 3621: int ret,i,j,k,nz,i0,j0,k0;
3622: int w;
3623: unsigned int *fd;
3624:
3625: /*
3626: * if f = x^d+x^i+1 then i0 <- i, j0 <- 0, k0 <-0.
3627: * if f = x^d+x^k+x^j+x^i+1 (k>j>i) then i0 <- i, j0 <- j, k0 <-k.
3628: * otherwise i0,j0,k0 is set to 0.
3629: */
3630:
3631: fd = f->b;
3632: w = (d>>5)+1;
3633: if ( f->w && (d==degup2(f)) ) {
3634: for ( nz = 0, i = d; i >= 0; i-- )
3635: if ( fd[i>>5]&(1<<(i&31)) ) nz++;
3636: switch ( nz ) {
3637: case 3:
3638: for ( i0 = 1; !(fd[i0>>5]&(1<<(i0&31))) ; i0++ );
3639: /* reset i0-th bit */
3640: fd[i0>>5] &= ~(1<<(i0&31));
3641: j0 = k0 = 0;
3642: break;
3643: case 5:
3644: for ( i0 = 1; !(fd[i0>>5]&(1<<(i0&31))) ; i0++ );
3645: /* reset i0-th bit */
3646: fd[i0>>5] &= ~(1<<(i0&31));
3647: for ( j0 = i0+1; !(fd[j0>>5]&(1<<(j0&31))) ; j0++ );
3648: /* reset j0-th bit */
3649: fd[j0>>5] &= ~(1<<(j0&31));
3650: for ( k0 = j0+1; !(fd[k0>>5]&(1<<(k0&31))) ; k0++ );
3651: /* reset k0-th bit */
3652: fd[k0>>5] &= ~(1<<(k0&31));
3653: break;
3654: default:
3655: f->w = 0; break;
3656: }
3657: } else
3658: f->w = 0;
3659:
3660: if ( !f->w ) {
3661: fd = f->b;
3662: f->w = w; fd[0] |= 1; fd[d>>5] |= (1<<(d&31));
3663: i0 = j0 = k0 = 0;
3664: }
3665: /* if j0 > 0 then f is already a pentanomial */
3666: if ( j0 > 0 ) goto PENTA;
1.1 noro 3667:
1.76 noro 3668: /* searching for an irreducible trinomial */
3669:
3670: for ( i = 1; 2*i <= d; i++ ) {
3671: /* skip the polynomials 'before' f */
3672: if ( i < i0 ) continue;
3673: if ( i == i0 ) { i0 = 0; continue; }
3674: /* set i-th bit */
3675: fd[i>>5] |= (1<<(i&31));
3676: ret = irredcheck_dddup2(f);
3677: if ( ret == 1 ) return 0;
3678: /* reset i-th bit */
3679: fd[i>>5] &= ~(1<<(i&31));
3680: }
3681:
3682: /* searching for an irreducible pentanomial */
1.1 noro 3683: PENTA:
1.76 noro 3684: for ( i = 1; i < d; i++ ) {
3685: /* skip the polynomials 'before' f */
3686: if ( i < i0 ) continue;
3687: if ( i == i0 ) i0 = 0;
3688: /* set i-th bit */
3689: fd[i>>5] |= (1<<(i&31));
3690: for ( j = i+1; j < d; j++ ) {
3691: /* skip the polynomials 'before' f */
3692: if ( j < j0 ) continue;
3693: if ( j == j0 ) j0 = 0;
3694: /* set j-th bit */
3695: fd[j>>5] |= (1<<(j&31));
3696: for ( k = j+1; k < d; k++ ) {
3697: /* skip the polynomials 'before' f */
3698: if ( k < k0 ) continue;
3699: else if ( k == k0 ) { k0 = 0; continue; }
3700: /* set k-th bit */
3701: fd[k>>5] |= (1<<(k&31));
3702: ret = irredcheck_dddup2(f);
3703: if ( ret == 1 ) return 0;
3704: /* reset k-th bit */
3705: fd[k>>5] &= ~(1<<(k&31));
3706: }
3707: /* reset j-th bit */
3708: fd[j>>5] &= ~(1<<(j&31));
3709: }
3710: /* reset i-th bit */
3711: fd[i>>5] &= ~(1<<(i&31));
3712: }
3713: /* exhausted */
3714: return 1;
1.1 noro 3715: }
3716:
3717: /*
3718: * f = an irreducible trinomial or pentanomial of degree d 'after' f
3719: *
3720: * searching strategy:
3721: * trinomial x^d+x^i+1:
3722: * i is as small as possible.
3723: * trinomial x^d+x^i+x^j+x^k+1:
3724: * i is as small as possible.
3725: * For such i, j is as small as possible.
3726: * For such i and j, 'k' is as small as possible.
3727: *
3728: * return value : 0 --- exists
3729: * 1 --- does not exist (exhaustion)
3730: */
3731:
3732: int _generate_good_irreducible_polynomial(UP2 f,int d)
3733: {
1.76 noro 3734: int ret,i,j,k,nz,i0,j0,k0;
3735: int w;
3736: unsigned int *fd;
3737:
3738: /*
3739: * if f = x^d+x^i+1 then i0 <- i, j0 <- 0, k0 <-0.
3740: * if f = x^d+x^k+x^j+x^i+1 (k>j>i) then i0 <- i, j0 <- j, k0 <-k.
3741: * otherwise i0,j0,k0 is set to 0.
3742: */
3743:
3744: fd = f->b;
3745: w = (d>>5)+1;
3746: if ( f->w && (d==degup2(f)) ) {
3747: for ( nz = 0, i = d; i >= 0; i-- )
3748: if ( fd[i>>5]&(1<<(i&31)) ) nz++;
3749: switch ( nz ) {
3750: case 3:
3751: for ( i0 = 1; !(fd[i0>>5]&(1<<(i0&31))) ; i0++ );
3752: /* reset i0-th bit */
3753: fd[i0>>5] &= ~(1<<(i0&31));
3754: j0 = k0 = 0;
3755: break;
3756: case 5:
3757: for ( i0 = 1; !(fd[i0>>5]&(1<<(i0&31))) ; i0++ );
3758: /* reset i0-th bit */
3759: fd[i0>>5] &= ~(1<<(i0&31));
3760: for ( j0 = i0+1; !(fd[j0>>5]&(1<<(j0&31))) ; j0++ );
3761: /* reset j0-th bit */
3762: fd[j0>>5] &= ~(1<<(j0&31));
3763: for ( k0 = j0+1; !(fd[k0>>5]&(1<<(k0&31))) ; k0++ );
3764: /* reset k0-th bit */
3765: fd[k0>>5] &= ~(1<<(k0&31));
3766: break;
3767: default:
3768: f->w = 0; break;
3769: }
3770: } else
3771: f->w = 0;
3772:
3773: if ( !f->w ) {
3774: fd = f->b;
3775: f->w = w; fd[0] |= 1; fd[d>>5] |= (1<<(d&31));
3776: i0 = j0 = k0 = 0;
3777: }
3778: /* if j0 > 0 then f is already a pentanomial */
3779: if ( j0 > 0 ) goto PENTA;
1.1 noro 3780:
1.76 noro 3781: /* searching for an irreducible trinomial */
3782:
3783: for ( i = 1; 2*i <= d; i++ ) {
3784: /* skip the polynomials 'before' f */
3785: if ( i < i0 ) continue;
3786: if ( i == i0 ) { i0 = 0; continue; }
3787: /* set i-th bit */
3788: fd[i>>5] |= (1<<(i&31));
3789: ret = irredcheck_dddup2(f);
3790: if ( ret == 1 ) return 0;
3791: /* reset i-th bit */
3792: fd[i>>5] &= ~(1<<(i&31));
3793: }
3794:
3795: /* searching for an irreducible pentanomial */
1.1 noro 3796: PENTA:
1.76 noro 3797: for ( i = 3; i < d; i++ ) {
3798: /* skip the polynomials 'before' f */
3799: if ( i < i0 ) continue;
3800: if ( i == i0 ) i0 = 0;
3801: /* set i-th bit */
3802: fd[i>>5] |= (1<<(i&31));
3803: for ( j = 2; j < i; j++ ) {
3804: /* skip the polynomials 'before' f */
3805: if ( j < j0 ) continue;
3806: if ( j == j0 ) j0 = 0;
3807: /* set j-th bit */
3808: fd[j>>5] |= (1<<(j&31));
3809: for ( k = 1; k < j; k++ ) {
3810: /* skip the polynomials 'before' f */
3811: if ( k < k0 ) continue;
3812: else if ( k == k0 ) { k0 = 0; continue; }
3813: /* set k-th bit */
3814: fd[k>>5] |= (1<<(k&31));
3815: ret = irredcheck_dddup2(f);
3816: if ( ret == 1 ) return 0;
3817: /* reset k-th bit */
3818: fd[k>>5] &= ~(1<<(k&31));
3819: }
3820: /* reset j-th bit */
3821: fd[j>>5] &= ~(1<<(j&31));
3822: }
3823: /* reset i-th bit */
3824: fd[i>>5] &= ~(1<<(i&31));
3825: }
3826: /* exhausted */
3827: return 1;
1.3 noro 3828: }
3829:
1.24 noro 3830: void printqmat(Q **mat,int row,int col)
1.3 noro 3831: {
1.76 noro 3832: int i,j;
1.3 noro 3833:
1.76 noro 3834: for ( i = 0; i < row; i++ ) {
3835: for ( j = 0; j < col; j++ ) {
3836: printnum((Num)mat[i][j]); printf(" ");
3837: }
3838: printf("\n");
3839: }
1.3 noro 3840: }
3841:
1.24 noro 3842: void printimat(int **mat,int row,int col)
1.3 noro 3843: {
1.76 noro 3844: int i,j;
1.3 noro 3845:
1.76 noro 3846: for ( i = 0; i < row; i++ ) {
3847: for ( j = 0; j < col; j++ ) {
3848: printf("%d ",mat[i][j]);
3849: }
3850: printf("\n");
3851: }
1.36 noro 3852: }
3853:
3854: void Pnd_det(NODE arg,P *rp)
3855: {
1.76 noro 3856: if ( argc(arg) == 1 )
3857: nd_det(0,ARG0(arg),rp);
3858: else
3859: nd_det(QTOS((Q)ARG1(arg)),ARG0(arg),rp);
1.1 noro 3860: }
1.59 ohara 3861:
1.62 ohara 3862: void Pmat_col(NODE arg,VECT *rp)
1.59 ohara 3863: {
1.76 noro 3864: int i,j,n;
3865: MAT mat;
3866: VECT vect;
3867:
3868: asir_assert(ARG0(arg),O_MAT,"mat_col");
3869: asir_assert(ARG1(arg),O_N,"mat_col");
3870: mat = (MAT)ARG0(arg);
3871: j = QTOS((Q)ARG1(arg));
3872: if ( j < 0 || j >= mat->col) {
3873: error("mat_col : Out of range");
3874: }
3875: n = mat->row;
3876: MKVECT(vect,n);
3877: for(i=0; i<n; i++) {
3878: BDY(vect)[i] = BDY(mat)[i][j];
3879: }
3880: *rp = vect;
1.59 ohara 3881: }
1.71 noro 3882:
3883: NODE triangleq(NODE e)
3884: {
3885: int n,i,k;
3886: V v;
3887: VL vl;
3888: P *p;
3889: NODE r,r1;
3890:
3891: n = length(e);
3892: p = (P *)MALLOC(n*sizeof(P));
3893: for ( i = 0; i < n; i++, e = NEXT(e) ) p[i] = (P)BDY(e);
3894: i = 0;
3895: while ( 1 ) {
3896: for ( ; i < n && !p[i]; i++ );
3897: if ( i == n ) break;
3898: if ( OID(p[i]) == O_N ) return 0;
3899: v = p[i]->v;
3900: for ( k = i+1; k < n; k++ )
3901: if ( p[k] ) {
3902: if ( OID(p[k]) == O_N ) return 0;
3903: if ( p[k]->v == v ) p[k] = 0;
3904: }
3905: i++;
3906: }
3907: for ( r = 0, i = 0; i < n; i++ ) {
3908: if ( p[i] ) {
3909: MKNODE(r1,p[i],r); r = r1;
3910: }
3911: }
3912: return r;
3913: }
3914:
3915: void Ptriangleq(NODE arg,LIST *rp)
3916: {
3917: NODE ret;
3918:
3919: asir_assert(ARG0(arg),O_LIST,"sparseleq");
3920: ret = triangleq(BDY((LIST)ARG0(arg)));
3921: MKLIST(*rp,ret);
3922: }
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