Annotation of OpenXM_contrib2/asir2000/engine/H.c, Revision 1.1
1.1 ! noro 1: /* $OpenXM: OpenXM/src/asir99/engine/H.c,v 1.1.1.1 1999/11/10 08:12:26 noro Exp $ */
! 2: #include "ca.h"
! 3: #include "inline.h"
! 4: #include "base.h"
! 5: #include <math.h>
! 6:
! 7: void modfctrp(P,int,int,DCP *);
! 8: void gensqfrum(int,UM,struct oDUM *);
! 9: void srchum(int,UM,UM,UM);
! 10: UM *resberle(int,UM,UM *);
! 11: int substum(int,UM,int);
! 12: void ddd(int,UM,UM *);
! 13: void canzas(int,UM,int,UM *,UM *);
! 14: int divum(int,UM,UM,UM);
! 15: void randum(int,int,UM);
! 16: void pwrmodum(int,UM,int,UM,UM);
! 17: void spwrum(int,UM,UM *,UM,N,UM);
! 18: void spwrum0(int,UM,UM,N,UM);
! 19: void mulum(int,UM,UM,UM);
! 20: void mulsum(int,UM,int,UM);
! 21: void gcdum(int,UM,UM,UM);
! 22: void mult_mod_tab(UM,int,UM *,UM,int);
! 23: void make_qmat(UM,int,UM *,int ***);
! 24: void null_mod(int **,int,int,int *);
! 25: void null_to_sol(int **,int *,int,int,UM *);
! 26: void newddd(int,UM,UM *);
! 27: int irred_check(UM,int);
! 28: int berlekamp(UM,int,int,UM *,UM *);
! 29: int nfctr_mod(UM,int);
! 30: void minipoly_mod(int,UM,UM,UM);
! 31: int find_root(int,UM,int *);
! 32: void showum(UM);
! 33: void showumat(int **,int);
! 34: #if 1
! 35: #define Mulum mulum
! 36: #define Divum divum
! 37: #define Mulsum mulsum
! 38: #define Gcdum gcdum
! 39: #endif
! 40:
! 41: #define FCTR 0
! 42: #define SQFR 1
! 43: #define DDD 2
! 44: #define NEWDDD 3
! 45:
! 46: LUM LUMALLOC();
! 47:
! 48: struct p_pair {
! 49: UM p0;
! 50: UM p1;
! 51: struct p_pair *next;
! 52: };
! 53:
! 54: void lnf_mod(int,int,UM,UM,struct p_pair *,UM,UM);
! 55:
! 56: void berle(index,count,f,listp)
! 57: int index,count;
! 58: P f;
! 59: ML *listp;
! 60: {
! 61: UM wf,wf1,wf2,wfs,gcd;
! 62: ML flist;
! 63: int fn,fn1,fm,m,n,fhd;
! 64: register int i,j,inv,hd,*ptr,*ptr1;
! 65:
! 66: n = UDEG(f);
! 67: wf = W_UMALLOC(n); wf1 = W_UMALLOC(n); wf2 = W_UMALLOC(n);
! 68: wfs = W_UMALLOC(n); gcd = W_UMALLOC(n);
! 69: for ( j = 0, fn = n + 1; (j < count) && (fn > 1); ) {
! 70: m = sprime[index++];
! 71: if ( !rem(NM((Q)UCOEF(f)),m) )
! 72: continue;
! 73: ptoum(m,f,wf); cpyum(wf,wf1);
! 74: diffum(m,wf1,wf2); gcdum(m,wf1,wf2,gcd);
! 75: if ( DEG(gcd) > 0 )
! 76: continue;
! 77: hd = COEF(wf)[n]; inv = invm(hd,m);
! 78: for ( i = n, ptr = COEF(wf); i >= 0; i-- )
! 79: ptr[i] = ( ptr[i] * inv ) % m;
! 80: fn1 = berlecnt(m,wf);
! 81: if ( fn1 < fn ) {
! 82: fn = fn1; fm = m; fhd = hd;
! 83: for ( i = n, ptr = COEF(wf), ptr1 = COEF(wfs); i >= 0; i-- )
! 84: ptr1[i] = ptr[i];
! 85: }
! 86: j++;
! 87: }
! 88: DEG(wfs) = n;
! 89: *listp = flist = MLALLOC(fn); flist->n = fn; flist->mod = fm;
! 90: /* berlemain(fm,wfs,(UM *)flist->c); */
! 91: if ( fm == 2 )
! 92: berlemain(fm,wfs,(UM *)flist->c);
! 93: else
! 94: newddd(fm,wfs,(UM *)flist->c);
! 95: for ( i = DEG((UM)(flist->c[0])),
! 96: ptr = COEF((UM)(flist->c[0])),
! 97: hd = fhd, m = fm; i >= 0; i-- )
! 98: ptr[i] = ( ptr[i] * hd ) % m;
! 99: }
! 100:
! 101: int berlecnt(mod,f)
! 102: register int mod;
! 103: UM f;
! 104: {
! 105: register int i,j,**c;
! 106: int d,dr,n;
! 107: UM w,q;
! 108: int **almat();
! 109:
! 110: n = DEG(f); c = almat(n,n);
! 111: w = W_UMALLOC(mod + n); q = W_UMALLOC(mod + n);
! 112: for ( i = 1; ( d = ( mod * i ) ) < n; i++ )
! 113: c[d][i - 1] = 1;
! 114: DEG(w) = d; COEF(w)[d] = 1;
! 115: for ( j = d - 1; j >= 0; j-- )
! 116: COEF(w)[j] = 0;
! 117: for ( ; ( i < n ) && ( ( dr = divum(mod,w,f,q) ) != -1 ); i++ ) {
! 118: for ( j = dr; j >= 0; j-- )
! 119: COEF(w)[j + mod] = c[j][i - 1] = COEF(w)[j];
! 120: for ( j = mod - 1; j >= 0; j-- )
! 121: COEF(w)[j] = 0;
! 122: DEG(w) = dr + mod;
! 123: }
! 124: for ( i = 1; i < n; i++ )
! 125: c[i][i - 1] = ( c[i][i - 1] + mod - 1 ) % mod;
! 126: return berlecntmain(mod,n,n-1,c);
! 127: }
! 128:
! 129: /* XXX berlecntmain should not be used for large mod */
! 130:
! 131: int berlecntmain(mod,n,m,c)
! 132: register int mod;
! 133: int n,m;
! 134: register int **c;
! 135: {
! 136: register int *p1,*p2,i,j,k,l,a;
! 137: int *tmp,inv;
! 138: int cfs;
! 139:
! 140: for ( cfs = 1, j = k = 0; j < m; j++ ) {
! 141: for ( i = k; ( n > i ) && ( c[i][j] == 0 ); i++ );
! 142: if ( i == n ) {
! 143: cfs++; continue;
! 144: }
! 145: if ( i != k ) {
! 146: tmp = c[i]; c[i] = c[k]; c[k] = tmp;
! 147: }
! 148: p1 = c[k]; inv = invm((p1[j] + mod) % mod,mod);
! 149: for ( l = j; l < m; l++ )
! 150: p1[l] = ( p1[l] * inv ) % mod;
! 151: for ( i = k + 1; i < n; c[i][j] = 0, i++ )
! 152: if ( i != k && ( a = -c[i][j] ) )
! 153: for ( l = j + 1, p2 = c[i]; l < m; l++ )
! 154: p2[l] = (a*p1[l] + p2[l]) % mod;
! 155: k++;
! 156: }
! 157: return ( cfs );
! 158: }
! 159:
! 160: UM *berlemain(mod,f,fp)
! 161: register int mod;
! 162: UM f;
! 163: UM *fp;
! 164: {
! 165: UM wg,ws,wf,f0,gcd,q;
! 166: int n;
! 167: register int i;
! 168:
! 169: n = DEG(f); wg = W_UMALLOC(n); mini(mod,f,wg);
! 170: if ( DEG(wg) <= 0 ) {
! 171: f0 = UMALLOC(n); cpyum(f,f0); *fp++ = f0;
! 172: return ( fp );
! 173: }
! 174: f0 = W_UMALLOC(n); cpyum(f,f0);
! 175: ws = W_UMALLOC(n); wf = W_UMALLOC(n);
! 176: q = W_UMALLOC(n); gcd = W_UMALLOC(n);
! 177: for ( i = 0; i < mod; i++ ) {
! 178: cpyum(f0,wf); cpyum(wg,ws);
! 179: COEF(ws)[0] = ( COEF(ws)[0] + mod - i ) % mod;
! 180: gcdum(mod,wf,ws,gcd);
! 181: if ( DEG(gcd) > 0 ) {
! 182: if ( DEG(gcd) < n ) {
! 183: divum(mod,f0,gcd,q); f0 = q; fp = berlemain(mod,gcd,fp);
! 184: }
! 185: break;
! 186: }
! 187: }
! 188: fp = berlemain(mod,f0,fp);
! 189: return ( fp );
! 190: }
! 191:
! 192: void hensel(index,count,f,listp)
! 193: int index,count;
! 194: P f;
! 195: ML *listp;
! 196: {
! 197: register int i,j;
! 198: int q,n,bound;
! 199: int *p;
! 200: int **pp;
! 201: ML blist,clist,bqlist,cqlist,rlist;
! 202: UM *b;
! 203: LUM fl,tl;
! 204: LUM *l;
! 205:
! 206: if ( UDEG(f) == 1 ) {
! 207: *listp = blist = MLALLOC(1); blist->n = 1; blist->c[0] = 0;
! 208: return;
! 209: }
! 210: berle(index,count,f,&blist);
! 211: if ( blist->n == 1 ) {
! 212: *listp = blist = MLALLOC(1); blist->n = 1; blist->c[0] = 0;
! 213: return;
! 214: }
! 215: gcdgen(f,blist,&clist); henprep(f,blist,clist,&bqlist,&cqlist);
! 216: n = bqlist->n; q = bqlist->mod;
! 217: bqlist->bound = cqlist->bound = bound = mignotte(q,f);
! 218: if ( bound == 1 ) {
! 219: *listp = rlist = MLALLOC(n);
! 220: rlist->n = n; rlist->mod = q; rlist->bound = bound;
! 221: for ( i = 0, b = (UM *)bqlist->c, l = (LUM *)rlist->c; i < n; i++ ) {
! 222: tl = LUMALLOC(DEG(b[i]),1); l[i] = tl; p = COEF(b[i]);
! 223: for ( j = 0, pp = COEF(tl); j <= DEG(tl); j++ )
! 224: pp[j][0] = p[j];
! 225: }
! 226: } else {
! 227: W_LUMALLOC((int)UDEG(f),bound,fl);
! 228: ptolum(q,bound,f,fl); henmain(fl,bqlist,cqlist,listp);
! 229: }
! 230: }
! 231:
! 232: void hsq(index,count,f,nindex,dcp)
! 233: int index,count,*nindex;
! 234: P f;
! 235: DCP *dcp;
! 236: {
! 237: register int i,j,k;
! 238: register int **pp,**fpp;
! 239: register int *px,*py;
! 240: int **wpp;
! 241: int n,dr,tmp,m,b,e,np,dt;
! 242: LUM fpa,wb0,wb1,lcpa,tpa,tlum;
! 243: struct oDUM *dct;
! 244: UM wt,wq0,wq,wr,wm,wm0,wa,ws,wb;
! 245: LUM *llist,*ll;
! 246: UM *dlist,*l,*c;
! 247: ML list,fp,cfp;
! 248: DCP dc;
! 249:
! 250: sqfrum(index,count,f,nindex,&dct,&fp);
! 251: np = fp->n; m = fp->mod;
! 252: if ( ( np == 1 ) && ( dct[0].n == 1 ) ) {
! 253: NEWDC(dc); DEG(dc) = ONE; COEF(dc) = f; NEXT(dc) = 0; *dcp = dc;
! 254: return;
! 255: }
! 256: for ( i = 0, dt = 0; i < np; i++ )
! 257: dt = MAX(DEG(dct[i].f),dt);
! 258: b = mig(m,dt,f); fp->bound = b;
! 259: if ( np == 1 ) {
! 260: nthrootchk(f,dct,fp,dcp);
! 261: return;
! 262: }
! 263: list = W_MLALLOC(np); list->n = np; list->mod = m; list->bound = 1;
! 264: for ( i = 0, ll = (LUM *)list->c; i < np; i++ ) {
! 265: W_LUMALLOC(DEG(dct[i].f),b,ll[i]);
! 266: for ( j = 0, px = COEF(dct[i].f), pp = COEF(ll[i]);
! 267: j <= DEG(ll[i]); j++ )
! 268: pp[j][0] = px[j];
! 269: }
! 270: dtestsql(f,list,dct,&dc);
! 271: if ( dc ) {
! 272: *dcp = dc;
! 273: return;
! 274: }
! 275: n = UDEG(f);
! 276: W_LUMALLOC(n,b,fpa); W_LUMALLOC(0,b,lcpa);
! 277: W_LUMALLOC(n,b,wb0); W_LUMALLOC(n,b,wb1);
! 278: W_LUMALLOC(n,b,tpa);
! 279: wt = W_UMALLOC(n); ws = W_UMALLOC(n);
! 280: wr = W_UMALLOC(n);
! 281: wq = W_UMALLOC(2*n); wq0 = W_UMALLOC(n);
! 282: wm = W_UMALLOC(2*n); wm0 = W_UMALLOC(2*n);
! 283: wa = W_UMALLOC(2*n);
! 284: ptolum(m,b,f,fpa); DEG(lcpa) = 0;
! 285: for ( i = 0, pp = COEF(lcpa), fpp = COEF(fpa); i < b; i++ )
! 286: pp[0][i] = fpp[n][i];
! 287: gcdgen(f,fp,&cfp);
! 288: llist = (LUM *) ALLOCA(np*sizeof(LUM));
! 289: dlist = (UM *) ALLOCA(np*sizeof(UM));
! 290: l = (UM *)fp->c; c = (UM *)cfp->c;
! 291: for ( i = 0; i < np; i++ ) {
! 292: W_LUMALLOC(DEG(l[i]),b,llist[i]);
! 293: for ( j = DEG(l[i]), pp = COEF(llist[i]), px = COEF(l[i]); j >= 0; j-- )
! 294: pp[j][0] = px[j];
! 295: if ( ( e = dct[i].n ) != 1 ) {
! 296: wb = dct[i].f;
! 297: dlist[i] = W_UMALLOC(DEG(wb)*e); cpyum(l[i],dlist[i]);
! 298: divum(m,dlist[i],wb,wq); DEG(dlist[i])= DEG(wq);
! 299: for ( k = 0; k <= DEG(wq); k++ )
! 300: COEF(dlist[i])[k] = dmb(m,COEF(wq)[k],e,&tmp);
! 301: }
! 302: }
! 303: for ( i = 1; i < b; i++ ) {
! 304: mullum(m,i+1,lcpa,llist[0],wb0);
! 305: for ( j = 1; j < np; j++ ) {
! 306: mullum(m,i+1,llist[j],wb0,wb1);
! 307: tlum = wb0; wb0 = wb1; wb1 = tlum;
! 308: }
! 309: for ( j = n, px = COEF(wt), pp = COEF(fpa), wpp = COEF(wb0);
! 310: j >= 0; j-- )
! 311: px[j] = ( pp[j][i] - wpp[j][i] + m ) % m;
! 312: degum(wt,n);
! 313: for ( j = n, px = COEF(wq0); j >= 0; j-- )
! 314: px[j] = 0;
! 315: for ( j = 1; j < np; j++ ) {
! 316: mulum(m,wt,c[j],wm); dr = divum(m,wm,l[j],wq);
! 317: for ( k = DEG(wq), px = COEF(wq0), py = COEF(wq); k >= 0; k-- )
! 318: px[k] = ( px[k] + py[k] ) % m;
! 319: for ( k = dr, pp = COEF(llist[j]), px = COEF(wm); k >= 0; k-- )
! 320: pp[k][i] = px[k];
! 321: }
! 322: degum(wq0,n); mulum(m,wq0,l[0],wm);
! 323: mulum(m,wt,c[0],wm0); addum(m,wm,wm0,wa);
! 324: for ( j = DEG(wa), pp = COEF(llist[0]), px = COEF(wa); j >= 0; j-- )
! 325: pp[j][i] = px[j];
! 326: for ( j = n, px = COEF(wq0); j >= 0; j-- )
! 327: px[j] = 0;
! 328: for ( j = 0; j < np; j++ )
! 329: if ( dct[j].n == 1 )
! 330: for ( k = 0,
! 331: pp = COEF(llist[j]),
! 332: wpp = COEF(((LUM *)list->c)[j]);
! 333: k <= DEG(llist[j]); k++ )
! 334: wpp[k][i] = pp[k][i];
! 335: else {
! 336: pwrlum(m,i+1,((LUM *)list->c)[j],dct[j].n,tpa);
! 337: for ( k = 0,
! 338: pp = COEF(llist[j]),
! 339: wpp = COEF(tpa);
! 340: k <= DEG(l[j]); k++ )
! 341: COEF(wt)[k] = (pp[k][i]-wpp[k][i]+m)%m;
! 342: degum(wt,DEG(l[j])); dr = divum(m,wt,dlist[j],ws);
! 343: if ( dr >= 0 ) {
! 344: *dcp = 0;
! 345: return;
! 346: } else
! 347: for ( k = 0,
! 348: pp = COEF(((LUM *)list->c)[j]);
! 349: k <= DEG(ws); k++ )
! 350: pp[k][i] = COEF(ws)[k];
! 351: }
! 352: list->bound = i+1; dtestsql(f,list,dct,&dc);
! 353: if ( dc ) {
! 354: *dcp = dc;
! 355: return;
! 356: }
! 357: }
! 358: *dcp = 0;
! 359: }
! 360:
! 361: void gcdgen(f,blist,clistp)
! 362: P f;
! 363: ML blist,*clistp;
! 364: {
! 365: register int i;
! 366: int n,d,mod,np;
! 367: UM wf,wm,wx,wy,wu,wv,wa,wb,wg,q,tum;
! 368: UM *in,*out;
! 369: ML clist;
! 370:
! 371: n = UDEG(f); mod = blist->mod; np = blist->n;
! 372: d = 2*n;
! 373: q = W_UMALLOC(d); wf = W_UMALLOC(d);
! 374: wm = W_UMALLOC(d); wx = W_UMALLOC(d);
! 375: wy = W_UMALLOC(d); wu = W_UMALLOC(d);
! 376: wv = W_UMALLOC(d); wg = W_UMALLOC(d);
! 377: wa = W_UMALLOC(d); wb = W_UMALLOC(d);
! 378: ptoum(mod,f,wf); DEG(wg) = 0; COEF(wg)[0] = 1;
! 379: *clistp = clist = MLALLOC(np); clist->mod = mod; clist->n = np;
! 380: for ( i = 0, in = (UM *)blist->c, out = (UM *)clist->c; i < np; i++ ) {
! 381: divum(mod,wf,in[i],q); tum = wf; wf = q; q = tum;
! 382: cpyum(wf,wx); cpyum(in[i],wy);
! 383: eucum(mod,wx,wy,wa,wb); mulum(mod,wa,wg,wm);
! 384: DEG(wm) = divum(mod,wm,in[i],q); out[i] = UMALLOC(DEG(wm));
! 385: cpyum(wm,out[i]); mulum(mod,q,wf,wu);
! 386: mulum(mod,wg,wb,wv); addum(mod,wu,wv,wg);
! 387: }
! 388: }
! 389:
! 390: /*
! 391: henprep(f,&blist,&clist,&bqlist,&cqlist);
! 392: */
! 393:
! 394: void henprep(f,blist,clist,bqlistp,cqlistp)
! 395: P f;
! 396: ML blist,clist,*bqlistp,*cqlistp;
! 397: {
! 398: register int i,j,k,*px,*py,*pz;
! 399: int n,pmax,dr,tmp,p,p1,mod,np,b,q;
! 400: UM w,wm,wn,wa,wt,wq,wf,quot,tum,*in,*inc,*out,*outc;
! 401: ML bqlist,cqlist;
! 402:
! 403: n = UDEG(f); p = mod = blist->mod; np = blist->n;
! 404: /* for ( b = 1, q = mod; q <= (unsigned int)(LBASE / (L)mod); q *= mod, b++ ); */
! 405: for ( b = 1, q = mod; q <= ((1<<27) / mod); q *= mod, b++ );
! 406: w = W_UMALLOC(n); ptoum(q,f,w);
! 407: wm = W_UMALLOC(2*n); wn = W_UMALLOC(2*n);
! 408: wa = W_UMALLOC(2*n); wt = W_UMALLOC(2*n);
! 409: wq = W_UMALLOC(2*n); wf = W_UMALLOC(2*n);
! 410: quot = W_UMALLOC(2*n);
! 411: *bqlistp = bqlist = MLALLOC(np); *cqlistp = cqlist = MLALLOC(np);
! 412: for ( i = 0; i < n+2; i++ )
! 413: COEF(wq)[i] = 0;
! 414: for ( i = 0,
! 415: in = (UM *)blist->c, inc = (UM *)clist->c,
! 416: out = (UM *)bqlist->c, outc = (UM *)cqlist->c;
! 417: i < np; i++ ) {
! 418: out[i] = C_UMALLOC(n+1); cpyum(in[i],out[i]);
! 419: outc[i] = C_UMALLOC(n+1); cpyum(inc[i],outc[i]);
! 420: }
! 421: for ( pmax = 1, i = b; i > 0; i-- )
! 422: pmax *= mod;
! 423: for ( i = 1; i < b; i++, p = p1 ) {
! 424: cpyum(out[0],wm);
! 425: for ( j = 1; j < np; j++ ) {
! 426: mulum(pmax,wm,out[j],wn);
! 427: tum = wm; wm = wn; wn = tum;
! 428: }
! 429: for ( j = n, px = COEF(w), py = COEF(wm), pz = COEF(wt); j >= 0; j-- ) {
! 430: tmp = ( ( px[j] - py[j] ) / p ) % mod;
! 431: pz[j] = ( tmp >= 0? tmp : tmp + mod );
! 432: }
! 433: degum(wt,n);
! 434: for ( j = 1; j < np; j++ ) {
! 435: mulum(mod,wt,inc[j],wm); dr = divum(mod,wm,in[j],quot);
! 436: for ( k = DEG(quot); k >= 0; k-- )
! 437: COEF(wq)[k] = ( COEF(wq)[k] + COEF(quot)[k] ) % mod;
! 438: for ( k = dr, px = COEF(out[j]), py = COEF(wm); k >= 0; k-- )
! 439: px[k] += p * py[k];
! 440: }
! 441: degum(wq,n); mulum(mod,wq,in[0],wm);
! 442: mulum(mod,wt,inc[0],wn); addum(mod,wm,wn,wa);
! 443: for ( j = DEG(wa), px = COEF(out[0]), py = COEF(wa); j >= 0; j-- )
! 444: px[j] += p * py[j];
! 445: for ( j = n, px = COEF(wq); j >= 0; j-- )
! 446: px[j] = 0;
! 447: p1 = p * mod;
! 448: for ( j = n, px = COEF(wt); j >= 1; j-- )
! 449: px[j] = 0;
! 450: px[0] = 1;
! 451: for ( j = 0; j < np; j++ ) {
! 452: cpyum(w,wf);
! 453: for ( k = DEG(wf), px = COEF(wf); k >= 0; k-- )
! 454: px[k] %= p1;
! 455: divum(p1,wf,out[j],quot); mulum(p1,outc[j],quot,wm);
! 456: for ( k = DEG(wm), px = COEF(wt), py = COEF(wm); k >= 0; k-- )
! 457: px[k] = ( px[k] - py[k] ) % p1;
! 458: }
! 459: degum(wt,n);
! 460: for ( j = DEG(wt), px = COEF(wt); j >= 0; j-- )
! 461: px[j] = ((tmp=(px[j]/p)%mod)>= 0?tmp:tmp + mod);
! 462: for ( j = 0; j < np; j++ ) {
! 463: mulum(mod,wt,outc[j],wm); dr = divum(mod,wm,in[j],quot);
! 464: for ( k = dr, px = COEF(outc[j]), py = COEF(wm); k >= 0; k-- )
! 465: px[k] += p * py[k];
! 466: degum(outc[j],MAX(DEG(outc[j]),dr));
! 467: }
! 468: }
! 469: bqlist->n = cqlist->n = np;
! 470: bqlist->mod = cqlist->mod = q;
! 471: }
! 472:
! 473: /*
! 474: henmain(fl,bqlist,cqlist,listp)
! 475: */
! 476:
! 477: void henmain(f,bqlist,cqlist,listp)
! 478: LUM f;
! 479: ML bqlist,cqlist,*listp;
! 480: {
! 481: register int i,j,k;
! 482: int *px,*py;
! 483: int **pp,**pp1;
! 484: int n,np,mod,bound,dr,tmp;
! 485: UM wt,wq0,wq,wr,wm,wm0,wa,q;
! 486: LUM wb0,wb1,tlum;
! 487: UM *b,*c;
! 488: LUM *l;
! 489: ML list;
! 490:
! 491: n = DEG(f); np = bqlist->n; mod = bqlist->mod; bound = bqlist->bound;
! 492: *listp = list = MLALLOC(n);
! 493: list->n = np; list->mod = mod; list->bound = bound;
! 494: W_LUMALLOC(n,bound,wb0); W_LUMALLOC(n,bound,wb1);
! 495: wt = W_UMALLOC(n); wq0 = W_UMALLOC(n); wq = W_UMALLOC(n);
! 496: wr = W_UMALLOC(n); wm = W_UMALLOC(2*n); wm0 = W_UMALLOC(2*n);
! 497: wa = W_UMALLOC(2*n); q = W_UMALLOC(2*n);
! 498: b = (UM *)bqlist->c; c = (UM *)cqlist->c; l = (LUM *)list->c;
! 499: for ( i = 0; i < np; i++ ) {
! 500: l[i] = LUMALLOC(DEG(b[i]),bound);
! 501: for ( j = DEG(b[i]), pp = COEF(l[i]), px = COEF(b[i]); j >= 0; j-- )
! 502: pp[j][0] = px[j];
! 503: }
! 504: for ( i = 1; i < bound; i++ ) {
! 505: mullum(mod,i+1,l[0],l[1],wb0);
! 506: for ( j = 2; j < np; j++ ) {
! 507: mullum(mod,i+1,l[j],wb0,wb1);
! 508: tlum = wb0; wb0 = wb1; wb1 = tlum;
! 509: }
! 510: for ( j = n, px = COEF(wt); j >= 0; j-- )
! 511: px[j] = 0;
! 512: for ( j = n, pp = COEF(f), pp1 = COEF(wb0); j >= 0; j-- ) {
! 513: tmp = ( pp[j][i] - pp1[j][i] ) % mod;
! 514: COEF(wt)[j] = ( tmp < 0 ? tmp + mod : tmp );
! 515: }
! 516: degum(wt,n);
! 517: for ( j = n, px = COEF(wq0); j >= 0; j-- )
! 518: px[j] = 0;
! 519: for ( j = 1; j < np; j++ ) {
! 520: mulum(mod,wt,c[j],wm); dr = divum(mod,wm,b[j],q);
! 521: for ( k = DEG(q), px = COEF(wq0), py = COEF(q); k >= 0; k-- )
! 522: px[k] = ( px[k] + py[k] ) % mod;
! 523: for ( k = dr, pp = COEF(l[j]), px = COEF(wm); k >= 0; k-- )
! 524: pp[k][i] = px[k];
! 525: }
! 526: degum(wq0,n); mulum(mod,wq0,b[0],wm);
! 527: mulum(mod,wt,c[0],wm0); addum(mod,wm,wm0,wa);
! 528: for ( j = DEG(wa), pp = COEF(l[0]), px = COEF(wa); j >= 0; j-- )
! 529: pp[j][i] = px[j];
! 530: for ( j = n, px = COEF(wq0); j >= 0; j-- )
! 531: px[j] = 0;
! 532: }
! 533: }
! 534:
! 535: static double M;
! 536: static int E;
! 537:
! 538: int mignotte(q,f)
! 539: int q;
! 540: P f;
! 541: {
! 542: int p;
! 543: unsigned int *b;
! 544: N c;
! 545: DCP dc;
! 546:
! 547: for ( dc = DC(f), M = 0, E = 0; dc; dc = NEXT(dc) ) {
! 548: c = NM((Q)COEF(dc)); p = PL(c); b = BD(c);
! 549: sqad(b[p-1],(p-1)*BSH);
! 550: }
! 551: if (E % 2) M *= 2; M = ceil(sqrt(M)); E /= 2;
! 552: c = NM((Q)COEF(DC(f))); p = PL(c); M *= ((double)BD(c)[p-1]+1.0); E += (p-1) * BSH;
! 553: return (int)ceil( (0.31*(E+UDEG(f)+1)+log10((double)M)) / log10((double)q) );
! 554: }
! 555:
! 556: int mig(q,d,f)
! 557: int q,d;
! 558: P f;
! 559: {
! 560: int p;
! 561: unsigned int *b;
! 562: N c;
! 563: DCP dc;
! 564:
! 565: for ( dc = DC(f), M = 0, E = 0; dc; dc = NEXT(dc) ) {
! 566: c = NM((Q)COEF(dc)); p = PL(c); b = BD(c);
! 567: sqad(b[p-1],(p-1)*BSH);
! 568: }
! 569: if (E % 2) M *= 2; M = ceil(sqrt(M)); E /= 2;
! 570: c = NM((Q)COEF(DC(f))); p = PL(c);
! 571: M *= (BD(c)[p-1]+1); E += (p-1) * BSH;
! 572: return (int)ceil( (0.31*(E+d+1)+log10((double)M)) / log10((double)q) );
! 573: }
! 574:
! 575: void sqad(man,exp)
! 576: unsigned int man;
! 577: int exp;
! 578: {
! 579: int e,sqe;
! 580: unsigned int t;
! 581: double man1,d,sqm;
! 582: int diff;
! 583:
! 584: if ( man == BMASK ) {
! 585: e = BSH; man1 = 1.0;
! 586: } else {
! 587: man += 1;
! 588: for ( e = 0, t = man; t; e++, t >>= 1 );
! 589: e--; d = (double)(1<<e);
! 590: man1 = ((double)man)/d;
! 591: }
! 592: exp += e; sqm = man1 * man1; sqe = 2 * exp;
! 593: if ( sqm >= 2.0 ) {
! 594: sqm /= 2.0; sqe++;
! 595: }
! 596: diff = E - sqe;
! 597: if ( diff > 18 )
! 598: return;
! 599: if ( diff < -18 ) {
! 600: M = sqm; E = sqe;
! 601: return;
! 602: }
! 603: if ( diff >= 0 )
! 604: M += (sqm / (double)(1<<diff));
! 605: else {
! 606: M = ( ( M / (double)(1<<-diff)) + sqm ); E = sqe;
! 607: }
! 608: if ( M >= 2.0 ) {
! 609: M /= 2.0; E++;
! 610: }
! 611: }
! 612:
! 613: void ptolum(q,bound,f,fl)
! 614: int q,bound;
! 615: P f;
! 616: LUM fl;
! 617: {
! 618: DCP dc;
! 619: int i,j;
! 620: int **pp;
! 621: int d,br,s;
! 622: unsigned int r;
! 623: int *c;
! 624: unsigned int *m,*w;
! 625:
! 626: for ( dc = DC(f), pp = COEF(fl); dc; dc = NEXT(dc) ) {
! 627: d = PL(NM((Q)COEF(dc))); m = BD(NM((Q)COEF(dc)));
! 628: c = pp[QTOS(DEG(dc))]; w = (unsigned int *)W_ALLOC(d);
! 629: for ( i = 0; i < d; i++ )
! 630: w[i] = m[i];
! 631: for ( i = 0; d >= 1; ) {
! 632: for ( j = d - 1, r = 0; j >= 0; j-- ) {
! 633: DSAB(q,r,w[j],w[j],r)
! 634: }
! 635: c[i++] = (int)r;
! 636: if ( !w[d-1] )
! 637: d--;
! 638: }
! 639: if ( SGN((Q)COEF(dc)) < 0 )
! 640: for (i = 0, br = 0; i < bound; i++ )
! 641: if ( ( s = -(c[i] + br) ) < 0 ) {
! 642: c[i] = s + q; br = 1;
! 643: } else {
! 644: c[i] = 0; br = 0;
! 645: }
! 646: }
! 647: }
! 648:
! 649: void modfctrp(p,mod,flag,dcp)
! 650: P p;
! 651: int mod,flag;
! 652: DCP *dcp;
! 653: {
! 654: int cm,n,i,j,k;
! 655: DCP dc,dc0;
! 656: P zp;
! 657: Q c,q;
! 658: UM mp;
! 659: UM *tl;
! 660: struct oDUM *udc,*udc1;
! 661:
! 662: if ( !p ) {
! 663: *dcp = 0; return;
! 664: }
! 665: ptozp(p,1,&c,&zp);
! 666: if ( DN(c) || !(cm = rem(NM(c),mod)) ) {
! 667: *dcp = 0; return;
! 668: }
! 669: mp = W_UMALLOC(UDEG(p));
! 670: ptoum(mod,zp,mp);
! 671: if ( (n = DEG(mp)) < 0 ) {
! 672: *dcp = 0; return;
! 673: } else if ( n == 0 ) {
! 674: cm = dmar(cm,COEF(mp)[0],0,mod); STOQ(cm,q);
! 675: NEWDC(dc); COEF(dc) = (P)q; DEG(dc) = ONE;
! 676: NEXT(dc) = 0; *dcp = dc;
! 677: return;
! 678: }
! 679: if ( COEF(mp)[n] != 1 ) {
! 680: cm = dmar(cm,COEF(mp)[n],0,mod);
! 681: i = invm(COEF(mp)[n],mod);
! 682: for ( j = 0; j <= n; j++ )
! 683: COEF(mp)[j] = dmar(COEF(mp)[j],i,0,mod);
! 684: }
! 685: W_CALLOC(n+1,struct oDUM,udc);
! 686: gensqfrum(mod,mp,udc);
! 687: switch ( flag ) {
! 688: case FCTR:
! 689: tl = (UM *)ALLOCA((n+1)*sizeof(UM));
! 690: W_CALLOC(DEG(mp)+1,struct oDUM,udc1);
! 691: for ( i = 0,j = 0; udc[i].f; i++ )
! 692: if ( DEG(udc[i].f) == 1 ) {
! 693: udc1[j].f = udc[i].f; udc1[j].n = udc[i].n; j++;
! 694: } else {
! 695: bzero((char *)tl,(n+1)*sizeof(UM));
! 696: berlemain(mod,udc[i].f,tl);
! 697: for ( k = 0; tl[k]; k++, j++ ) {
! 698: udc1[j].f = tl[k]; udc1[j].n = udc[i].n;
! 699: }
! 700: }
! 701: udc = udc1; break;
! 702: case SQFR:
! 703: break;
! 704: case DDD:
! 705: tl = (UM *)ALLOCA((n+1)*sizeof(UM));
! 706: W_CALLOC(DEG(mp)+1,struct oDUM,udc1);
! 707: for ( i = 0,j = 0; udc[i].f; i++ )
! 708: if ( DEG(udc[i].f) == 1 ) {
! 709: udc1[j].f = udc[i].f; udc1[j].n = udc[i].n; j++;
! 710: } else {
! 711: bzero((char *)tl,(n+1)*sizeof(UM));
! 712: ddd(mod,udc[i].f,tl);
! 713: for ( k = 0; tl[k]; k++, j++ ) {
! 714: udc1[j].f = tl[k]; udc1[j].n = udc[i].n;
! 715: }
! 716: }
! 717: udc = udc1; break;
! 718: case NEWDDD:
! 719: tl = (UM *)ALLOCA((n+1)*sizeof(UM));
! 720: W_CALLOC(DEG(mp)+1,struct oDUM,udc1);
! 721: for ( i = 0,j = 0; udc[i].f; i++ )
! 722: if ( DEG(udc[i].f) == 1 ) {
! 723: udc1[j].f = udc[i].f; udc1[j].n = udc[i].n; j++;
! 724: } else {
! 725: bzero((char *)tl,(n+1)*sizeof(UM));
! 726: if ( mod == 2 )
! 727: berlemain(mod,udc[i].f,tl);
! 728: else
! 729: newddd(mod,udc[i].f,tl);
! 730: for ( k = 0; tl[k]; k++, j++ ) {
! 731: udc1[j].f = tl[k]; udc1[j].n = udc[i].n;
! 732: }
! 733: }
! 734: udc = udc1; break;
! 735: }
! 736: NEWDC(dc0); STOQ(cm,q); COEF(dc0) = (P)q; DEG(dc0) = ONE; dc = dc0;
! 737: for ( n = 0; udc[n].f; n++ ) {
! 738: NEWDC(NEXT(dc)); dc = NEXT(dc);
! 739: STOQ(udc[n].n,DEG(dc)); umtop(VR(p),udc[n].f,&COEF(dc));
! 740: }
! 741: NEXT(dc) = 0; *dcp = dc0;
! 742: }
! 743:
! 744: void gensqfrum(mod,p,dc)
! 745: int mod;
! 746: UM p;
! 747: struct oDUM *dc;
! 748: {
! 749: int n,i,j,d;
! 750: UM t,s,g,f,f1,b;
! 751:
! 752: if ( (n = DEG(p)) == 1 ) {
! 753: dc[0].f = UMALLOC(DEG(p)); cpyum(p,dc[0].f); dc[0].n = 1;
! 754: return;
! 755: }
! 756: t = W_UMALLOC(n); s = W_UMALLOC(n); g = W_UMALLOC(n);
! 757: f = W_UMALLOC(n); f1 = W_UMALLOC(n); b = W_UMALLOC(n);
! 758: diffum(mod,p,t); cpyum(p,s); Gcdum(mod,t,s,g);
! 759: if ( !DEG(g) ) {
! 760: dc[0].f = UMALLOC(DEG(p)); cpyum(p,dc[0].f); dc[0].n = 1;
! 761: return;
! 762: }
! 763: cpyum(p,b); cpyum(p,t); Divum(mod,t,g,f);
! 764: for ( i = 0, d = 0; DEG(f); i++ ) {
! 765: while ( 1 ) {
! 766: cpyum(b,t);
! 767: if ( Divum(mod,t,f,s) >= 0 )
! 768: break;
! 769: else {
! 770: cpyum(s,b); d++;
! 771: }
! 772: }
! 773: cpyum(b,t); cpyum(f,s); Gcdum(mod,t,s,f1);
! 774: Divum(mod,f,f1,s); cpyum(f1,f);
! 775: dc[i].f = UMALLOC(DEG(s)); cpyum(s,dc[i].f); dc[i].n = d;
! 776: }
! 777: if ( DEG(b) > 0 ) {
! 778: d = 1;
! 779: while ( 1 ) {
! 780: cpyum(b,t);
! 781: for ( j = DEG(t); j >= 0; j-- )
! 782: if ( COEF(t)[j] && (j % mod) )
! 783: break;
! 784: if ( j >= 0 )
! 785: break;
! 786: else {
! 787: DEG(s) = DEG(t)/mod;
! 788: for ( j = 0; j <= DEG(t); j++ )
! 789: COEF(s)[j] = COEF(t)[j*mod];
! 790: cpyum(s,b); d *= mod;
! 791: }
! 792: }
! 793: gensqfrum(mod,b,dc+i);
! 794: for ( j = i; dc[j].f; j++ )
! 795: dc[j].n *= d;
! 796: }
! 797: }
! 798:
! 799: #if 0
! 800: void srchum(mod,p1,p2,gr)
! 801: int mod;
! 802: UM p1,p2,gr;
! 803: {
! 804: UM m,m1,m2,q,r,t,g1,g2;
! 805: int lc,d,d1,d2,i,j,k,l,l1,l2,l3,tmp,adj;
! 806: V v;
! 807:
! 808: d = MAX(DEG(p1),DEG(p2));
! 809: g1 = W_UMALLOC(d); g2 = W_UMALLOC(d);
! 810: bzero((char *)g1,(d+2)*sizeof(int)); bzero((char *)g2,(d+2)*sizeof(int));
! 811: if ( d == DEG(p1) ) {
! 812: cpyum(p1,g1); cpyum(p2,g2);
! 813: } else {
! 814: cpyum(p1,g2); cpyum(p2,g1);
! 815: }
! 816: if ( ( d1 = DEG(g1) ) > ( d2 = DEG(g2) ) ) {
! 817: j = d1 - 1; adj = 1;
! 818: } else
! 819: j = d2;
! 820: lc = 1;
! 821: r = W_UMALLOC(d1+d2); q = W_UMALLOC(d1+d2);
! 822: m1 = W_UMALLOC(d1+d2); t = W_UMALLOC(d1+d2);
! 823: bzero((char *)r,(d1+d2+2)*sizeof(int)); bzero((char *)q,(d1+d2+2)*sizeof(int));
! 824: bzero((char *)m1,(d1+d2+2)*sizeof(int)); bzero((char *)t,(d1+d2+2)*sizeof(int));
! 825: m = W_UMALLOC(0); bzero((char *)m,2*sizeof(int));
! 826: adj = pwrm(mod,COEF(g2)[DEG(g2)],DEG(g1));
! 827: DEG(m) = 0; COEF(m)[0] = invm(COEF(g2)[DEG(g2)],mod);
! 828: Mulum(mod,g2,m,r); cpyum(r,g2);
! 829: while ( 1 ) {
! 830: if ( ( k = DEG(g2) ) < 0 ) {
! 831: DEG(gr) = -1;
! 832: return;
! 833: }
! 834: if ( k == j ) {
! 835: if ( k == 0 ) {
! 836: DEG(m) = 0; COEF(m)[0] = adj;
! 837: Mulum(mod,g2,m,gr);
! 838: return;
! 839: } else {
! 840: DEG(m) = 0;
! 841: COEF(m)[0] = pwrm(mod,COEF(g2)[k],DEG(g1)-k+1);
! 842: Mulum(mod,g1,m,r); DEG(r) = Divum(mod,r,g2,t);
! 843: DEG(m) = 0; COEF(m)[0] = dmb(mod,lc,lc,&tmp);
! 844: Divum(mod,r,m,q); cpyum(g2,g1); cpyum(q,g2);
! 845: lc = COEF(g1)[DEG(g1)]; j = k - 1;
! 846: }
! 847: } else {
! 848: d = j - k;
! 849: DEG(m) = 0; COEF(m)[0] = pwrm(mod,COEF(g2)[DEG(g2)],d);
! 850: Mulum(mod,g2,m,m1); l = pwrm(mod,lc,d);
! 851: DEG(m) = 0; COEF(m)[0] = l; Divum(mod,m1,m,t);
! 852: if ( k == 0 ) {
! 853: DEG(m) = 0; COEF(m)[0] = adj;
! 854: Mulum(mod,t,m,gr);
! 855: return;
! 856: } else {
! 857: DEG(m) = 0;
! 858: COEF(m)[0] = pwrm(mod,COEF(g2)[k],DEG(g1)-k+1);
! 859: Mulum(mod,g1,m,r); DEG(r) = Divum(mod,r,g2,q);
! 860: l1 = dmb(mod,lc,lc,&tmp); l2 = dmb(mod,l,l1,&tmp);
! 861: DEG(m) = 0; COEF(m)[0] = l2;
! 862: Divum(mod,r,m,q); cpyum(t,g1); cpyum(q,g2);
! 863: if ( d % 2 )
! 864: for ( i = DEG(g2); i >= 0; i-- )
! 865: COEF(g2)[i] = ( mod - COEF(g2)[i] ) % mod;
! 866: lc = COEF(g1)[DEG(g1)]; j = k - 1;
! 867: }
! 868: }
! 869: }
! 870: }
! 871:
! 872: UM *resberle(mod,f,fp)
! 873: register int mod;
! 874: UM f;
! 875: UM *fp;
! 876: {
! 877: UM w,wg,ws,wf,f0,gcd,q,res;
! 878: int n;
! 879: register int i;
! 880:
! 881: n = DEG(f); wg = W_UMALLOC(n); mini(mod,f,wg);
! 882: if ( DEG(wg) <= 0 ) {
! 883: f0 = UMALLOC(n); cpyum(f,f0); *fp++ = f0;
! 884: return ( fp );
! 885: }
! 886: f0 = W_UMALLOC(n); cpyum(f,f0);
! 887: ws = W_UMALLOC(n); wf = W_UMALLOC(n);
! 888: q = W_UMALLOC(n); gcd = W_UMALLOC(n);
! 889: res = W_UMALLOC(2*n);
! 890: srchum(mod,f,wg,res);
! 891: for ( i = 0; i < mod; i++ ) {
! 892: if ( substum(mod,res,i) )
! 893: continue;
! 894: cpyum(f0,wf); cpyum(wg,ws);
! 895: COEF(ws)[0] = ( COEF(ws)[0] + mod - i ) % mod;
! 896: Gcdum(mod,wf,ws,gcd);
! 897: if ( DEG(gcd) > 0 ) {
! 898: if ( DEG(gcd) < n ) {
! 899: Divum(mod,f0,gcd,q); f0 = q; fp = resberle(mod,gcd,fp);
! 900: }
! 901: break;
! 902: }
! 903: }
! 904: fp = resberle(mod,f0,fp);
! 905: return ( fp );
! 906: }
! 907:
! 908: int substum(mod,p,a)
! 909: int mod;
! 910: UM p;
! 911: int a;
! 912: {
! 913: int i,j,s;
! 914: int *c;
! 915:
! 916: if ( DEG(p) < 0 )
! 917: return 0;
! 918: if ( DEG(p) == 0 )
! 919: return COEF(p)[0];
! 920: for ( i = DEG(p), c = COEF(p), s = c[i]; i >= 0; ) {
! 921: for ( j = i--; (i>=0) && !c[i]; i-- );
! 922: if ( i >= 0 )
! 923: s = (s*pwrm(mod,a,j-i)%mod+c[i])%mod;
! 924: else
! 925: s = s*pwrm(mod,a,j)%mod;
! 926: }
! 927: return s;
! 928: }
! 929: #endif
! 930:
! 931: void ddd(mod,f,r)
! 932: int mod;
! 933: UM f,*r;
! 934: {
! 935: register int i,j;
! 936: int d,n;
! 937: UM q,s,t,u,v,w,g,x,m;
! 938: UM *base;
! 939:
! 940: n = DEG(f);
! 941: if ( n == 1 ) {
! 942: r[0] = UMALLOC(1); cpyum(f,r[0]); r[1] = 0; return;
! 943: }
! 944: base = (UM *)ALLOCA(n*sizeof(UM)); bzero((char *)base,n*sizeof(UM));
! 945: w = W_UMALLOC(2*n); q = W_UMALLOC(2*n); m = W_UMALLOC(2*n);
! 946: base[0] = W_UMALLOC(0); DEG(base[0]) = 0; COEF(base[0])[0] = 1;
! 947: t = W_UMALLOC(1); DEG(t) = 1; COEF(t)[0] = 0; COEF(t)[1] = 1;
! 948: pwrmodum(mod,t,mod,f,w); base[1] = W_UMALLOC(DEG(w)); cpyum(w,base[1]);
! 949: for ( i = 2; i < n; i++ ) {
! 950: mulum(mod,base[i-1],base[1],m); DEG(m) = divum(mod,m,f,q);
! 951: base[i] = W_UMALLOC(DEG(m)); cpyum(m,base[i]);
! 952: }
! 953: v = W_UMALLOC(n); cpyum(f,v);
! 954: DEG(w) = 1; COEF(w)[0] = 0; COEF(w)[1] = 1;
! 955: x = W_UMALLOC(1); DEG(x) = 1; COEF(x)[0] = 0; COEF(x)[1] = 1;
! 956: t = W_UMALLOC(n); s = W_UMALLOC(n); u = W_UMALLOC(n); g = W_UMALLOC(n);
! 957: for ( j = 0, d = 1; 2*d <= DEG(v); d++ ) {
! 958: for ( DEG(t) = -1, i = 0; i <= DEG(w); i++ )
! 959: if ( COEF(w)[i] ) {
! 960: Mulsum(mod,base[i],COEF(w)[i],s);
! 961: addum(mod,s,t,u); cpyum(u,t);
! 962: }
! 963: cpyum(t,w); cpyum(v,s); subum(mod,w,x,t); Gcdum(mod,s,t,g);
! 964: if ( DEG(g) >= 1 ) {
! 965: canzas(mod,g,d,base,r+j); j += DEG(g)/d;
! 966: Divum(mod,v,g,q); cpyum(q,v);
! 967: DEG(w) = Divum(mod,w,v,q);
! 968: for ( i = 0; i < DEG(v); i++ )
! 969: DEG(base[i]) = Divum(mod,base[i],v,q);
! 970: }
! 971: }
! 972: if ( DEG(v) ) {
! 973: r[j] = UMALLOC(DEG(v)); cpyum(v,r[j]); j++;
! 974: }
! 975: r[j] = 0;
! 976: }
! 977:
! 978: #if 0
! 979: void canzas(mod,f,d,base,r)
! 980: int mod;
! 981: UM f,*base,*r;
! 982: {
! 983: UM t,s,u,w,g,o,q;
! 984: N n1,n2,n3,n4,n5;
! 985: UM *b;
! 986: int n,m,i;
! 987:
! 988: if ( DEG(f) == d ) {
! 989: r[0] = UMALLOC(d); cpyum(f,r[0]);
! 990: return;
! 991: } else {
! 992: n = DEG(f); b = (UM *)ALLOCA(n*sizeof(UM)); bzero((char *)b,n*sizeof(UM));
! 993: for ( i = 0, m = 0; i < n; i++ )
! 994: m = MAX(m,DEG(base[i]));
! 995: q = W_UMALLOC(m);
! 996: for ( i = 0; i < n; i++ ) {
! 997: b[i] = W_UMALLOC(DEG(base[i])); cpyum(base[i],b[i]);
! 998: DEG(b[i]) = Divum(mod,b[i],f,q);
! 999: }
! 1000: t = W_UMALLOC(2*d);
! 1001: s = W_UMALLOC(DEG(f)); u = W_UMALLOC(DEG(f));
! 1002: w = W_UMALLOC(DEG(f)); g = W_UMALLOC(DEG(f));
! 1003: o = W_UMALLOC(0); DEG(o) = 0; COEF(o)[0] = 1;
! 1004: STON(mod,n1); pwrn(n1,d,&n2); subn(n2,ONEN,&n3);
! 1005: STON(2,n4); divsn(n3,n4,&n5);
! 1006: while ( 1 ) {
! 1007: randum(mod,2*d,t); spwrum(mod,f,b,t,n5,s);
! 1008: subum(mod,s,o,u); cpyum(f,w); Gcdum(mod,w,u,g);
! 1009: if ( (DEG(g) >= 1) && (DEG(g) < DEG(f)) ) {
! 1010: canzas(mod,g,d,b,r);
! 1011: cpyum(f,w); Divum(mod,w,g,s);
! 1012: canzas(mod,s,d,b,r+DEG(g)/d);
! 1013: return;
! 1014: }
! 1015: }
! 1016: }
! 1017: }
! 1018: #else
! 1019: void canzas(mod,f,d,base,r)
! 1020: int mod;
! 1021: UM f,*base,*r;
! 1022: {
! 1023: UM t,s,u,w,g,o,q;
! 1024: N n1,n2,n3,n4,n5;
! 1025: UM *b;
! 1026: int n,m,i;
! 1027:
! 1028: if ( DEG(f) == d ) {
! 1029: r[0] = UMALLOC(d); cpyum(f,r[0]);
! 1030: return;
! 1031: } else {
! 1032: n = DEG(f); b = (UM *)ALLOCA(n*sizeof(UM)); bzero((char *)b,n*sizeof(UM));
! 1033: for ( i = 0, m = 0; i < n; i++ )
! 1034: m = MAX(m,DEG(base[i]));
! 1035: q = W_UMALLOC(m);
! 1036: for ( i = 0; i < n; i++ ) {
! 1037: b[i] = W_UMALLOC(DEG(base[i])); cpyum(base[i],b[i]);
! 1038: DEG(b[i]) = Divum(mod,b[i],f,q);
! 1039: }
! 1040: t = W_UMALLOC(2*d);
! 1041: s = W_UMALLOC(DEG(f)); u = W_UMALLOC(DEG(f));
! 1042: w = W_UMALLOC(DEG(f)); g = W_UMALLOC(DEG(f));
! 1043: o = W_UMALLOC(0); DEG(o) = 0; COEF(o)[0] = 1;
! 1044: STON(mod,n1); pwrn(n1,d,&n2); subn(n2,ONEN,&n3);
! 1045: STON(2,n4); divsn(n3,n4,&n5);
! 1046: while ( 1 ) {
! 1047: randum(mod,2*d,t); spwrum0(mod,f,t,n5,s);
! 1048: subum(mod,s,o,u); cpyum(f,w); Gcdum(mod,w,u,g);
! 1049: if ( (DEG(g) >= 1) && (DEG(g) < DEG(f)) ) {
! 1050: canzas(mod,g,d,b,r);
! 1051: cpyum(f,w); Divum(mod,w,g,s);
! 1052: canzas(mod,s,d,b,r+DEG(g)/d);
! 1053: return;
! 1054: }
! 1055: }
! 1056: }
! 1057: }
! 1058: #endif
! 1059:
! 1060: void randum(mod,d,p)
! 1061: int mod,d;
! 1062: UM p;
! 1063: {
! 1064: unsigned int n;
! 1065: int i;
! 1066:
! 1067: n = ((unsigned int)random()) % d; DEG(p) = n; COEF(p)[n] = 1;
! 1068: for ( i = 0; i < (int)n; i++ )
! 1069: COEF(p)[i] = ((unsigned int)random()) % mod;
! 1070: }
! 1071:
! 1072: void pwrmodum(mod,p,e,f,pr)
! 1073: int mod,e;
! 1074: UM p,f,pr;
! 1075: {
! 1076: UM wt,ws,q;
! 1077:
! 1078: if ( e == 0 ) {
! 1079: DEG(pr) = 0; COEF(pr)[0] = 1;
! 1080: } else if ( DEG(p) < 0 )
! 1081: DEG(pr) = -1;
! 1082: else if ( e == 1 ) {
! 1083: q = W_UMALLOC(DEG(p)); cpyum(p,pr);
! 1084: DEG(pr) = divum(mod,pr,f,q);
! 1085: } else if ( DEG(p) == 0 ) {
! 1086: DEG(pr) = 0; COEF(pr)[0] = pwrm(mod,COEF(p)[0],e);
! 1087: } else {
! 1088: wt = W_UMALLOC(2*DEG(f)); ws = W_UMALLOC(2*DEG(f));
! 1089: q = W_UMALLOC(2*DEG(f));
! 1090: pwrmodum(mod,p,e/2,f,wt);
! 1091: if ( !(e%2) ) {
! 1092: mulum(mod,wt,wt,pr); DEG(pr) = divum(mod,pr,f,q);
! 1093: } else {
! 1094: mulum(mod,wt,wt,ws); DEG(ws) = divum(mod,ws,f,q);
! 1095: mulum(mod,ws,p,pr); DEG(pr) = divum(mod,pr,f,q);
! 1096: }
! 1097: }
! 1098: }
! 1099:
! 1100: void spwrum(mod,m,base,f,e,r)
! 1101: int mod;
! 1102: UM f,m,r;
! 1103: UM *base;
! 1104: N e;
! 1105: {
! 1106: int a,n,i;
! 1107: N e1,an;
! 1108: UM t,s,u,q,r1,r2;
! 1109:
! 1110: if ( !e ) {
! 1111: DEG(r) = 0; COEF(r)[0] = 1;
! 1112: } else if ( UNIN(e) )
! 1113: cpyum(f,r);
! 1114: else if ( (PL(e) == 1) && (BD(e)[0] < (unsigned int)mod) )
! 1115: spwrum0(mod,m,f,e,r);
! 1116: else {
! 1117: a = divin(e,mod,&e1); STON(a,an);
! 1118: n = DEG(m); t = W_UMALLOC(n); s = W_UMALLOC(n);
! 1119: u = W_UMALLOC(2*n); q = W_UMALLOC(2*n);
! 1120: for ( DEG(t) = -1, i = 0; i <= DEG(f); i++ )
! 1121: if ( COEF(f)[i] ) {
! 1122: Mulsum(mod,base[i],COEF(f)[i],s);
! 1123: addum(mod,s,t,u); cpyum(u,t);
! 1124: }
! 1125: r1 = W_UMALLOC(n); spwrum0(mod,m,f,an,r1);
! 1126: r2 = W_UMALLOC(n); spwrum(mod,m,base,t,e1,r2);
! 1127: Mulum(mod,r1,r2,u); DEG(u) = Divum(mod,u,m,q);
! 1128: cpyum(u,r);
! 1129: }
! 1130: }
! 1131:
! 1132: void spwrum0(mod,m,f,e,r)
! 1133: int mod;
! 1134: UM f,m,r;
! 1135: N e;
! 1136: {
! 1137: UM t,s,q;
! 1138: N e1;
! 1139: int a;
! 1140:
! 1141: if ( !e ) {
! 1142: DEG(r) = 0; COEF(r)[0] = 1;
! 1143: } else if ( UNIN(e) )
! 1144: cpyum(f,r);
! 1145: else {
! 1146: a = divin(e,2,&e1);
! 1147: t = W_UMALLOC(2*DEG(m)); spwrum0(mod,m,f,e1,t);
! 1148: s = W_UMALLOC(2*DEG(m)); q = W_UMALLOC(2*DEG(m));
! 1149: Mulum(mod,t,t,s); DEG(s) = Divum(mod,s,m,q);
! 1150: if ( a ) {
! 1151: Mulum(mod,s,f,t); DEG(t) = Divum(mod,t,m,q); cpyum(t,r);
! 1152: } else
! 1153: cpyum(s,r);
! 1154: }
! 1155: }
! 1156:
! 1157: #if 0
! 1158: void Mulum(mod,p1,p2,pr)
! 1159: register int mod;
! 1160: UM p1,p2,pr;
! 1161: {
! 1162: register int *pc1,*pcr;
! 1163: register int mul,i,j,d1,d2;
! 1164: int *c1,*c2,*cr;
! 1165:
! 1166: if ( ( (d1 = DEG(p1)) < 0) || ( (d2 = DEG(p2)) < 0 ) ) {
! 1167: DEG(pr) = -1;
! 1168: return;
! 1169: }
! 1170: c1 = COEF(p1); c2 = COEF(p2); cr = COEF(pr);
! 1171: bzero((char *)cr,(d1+d2+1)*sizeof(int));
! 1172: for ( i = 0; i <= d2; i++, cr++ )
! 1173: if ( mul = *c2++ )
! 1174: for ( j = 0, pc1 = c1, pcr = cr; j <= d1; j++, pc1++, pcr++ )
! 1175: *pcr = (*pc1 * mul + *pcr) % mod;
! 1176: DEG(pr) = d1 + d2;
! 1177: }
! 1178:
! 1179: void Mulsum(mod,p,n,pr)
! 1180: register int mod,n;
! 1181: UM p,pr;
! 1182: {
! 1183: register int *sp,*dp;
! 1184: register int i;
! 1185:
! 1186: for ( i = DEG(pr) = DEG(p), sp = COEF(p)+i, dp = COEF(pr)+i;
! 1187: i >= 0; i--, dp--, sp-- )
! 1188: *dp = (*sp * n) % mod;
! 1189: }
! 1190:
! 1191: int Divum(mod,p1,p2,pq)
! 1192: register int mod;
! 1193: UM p1,p2,pq;
! 1194: {
! 1195: register int *pc1,*pct;
! 1196: register int tmp,i,j,inv;
! 1197: int *c1,*c2,*ct;
! 1198: int d1,d2,dd,hd;
! 1199:
! 1200: if ( (d1 = DEG(p1)) < (d2 = DEG(p2)) ) {
! 1201: DEG(pq) = -1;
! 1202: return( d1 );
! 1203: }
! 1204: c1 = COEF(p1); c2 = COEF(p2); dd = d1-d2;
! 1205: if ( ( hd = c2[d2] ) != 1 ) {
! 1206: inv = invm(hd,mod);
! 1207: for ( pc1 = c2 + d2; pc1 >= c2; pc1-- )
! 1208: *pc1 = (*pc1 * inv) % mod;
! 1209: } else
! 1210: inv = 1;
! 1211: for ( i = dd, ct = c1+d1; i >= 0; i-- )
! 1212: if ( tmp = *ct-- ) {
! 1213: tmp = mod - tmp;
! 1214: for ( j = d2-1, pct = ct, pc1 = c2+j; j >= 0; j--, pct--, pc1-- )
! 1215: *pct = (*pc1 * tmp + *pct) % mod;
! 1216: }
! 1217: if ( inv != 1 ) {
! 1218: for ( pc1 = c1+d2, pct = c1+d1; pc1 <= pct; pc1++ )
! 1219: *pc1 = (*pc1 * inv) % mod;
! 1220: for ( pc1 = c2, pct = c2+d2, inv = hd; pc1 <= pct; pc1++ )
! 1221: *pc1 = (*pc1 * inv) % mod;
! 1222: }
! 1223: for ( i = d2-1, pc1 = c1+i; i >= 0 && !(*pc1); pc1--, i-- );
! 1224: for ( DEG(pq) = j = dd, pc1 = c1+d1, pct = COEF(pq)+j; j >= 0; j-- )
! 1225: *pct-- = *pc1--;
! 1226: return( i );
! 1227: }
! 1228:
! 1229: void Gcdum(mod,p1,p2,pr)
! 1230: register int mod;
! 1231: UM p1,p2,pr;
! 1232: {
! 1233: register int *sp,*dp;
! 1234: register int i,inv;
! 1235: UM t1,t2,q,tum;
! 1236: int drem;
! 1237:
! 1238: if ( DEG(p1) < 0 )
! 1239: cpyum(p2,pr);
! 1240: else if ( DEG(p2) < 0 )
! 1241: cpyum(p1,pr);
! 1242: else {
! 1243: if ( DEG(p1) >= DEG(p2) ) {
! 1244: t1 = p1; t2 = p2;
! 1245: } else {
! 1246: t1 = p2; t2 = p1;
! 1247: }
! 1248: q = W_UMALLOC(DEG(t1));
! 1249: while ( ( drem = Divum(mod,t1,t2,q) ) >= 0 ) {
! 1250: tum = t1; t1 = t2; t2 = tum; DEG(t2) = drem;
! 1251: }
! 1252: inv = invm(COEF(t2)[DEG(t2)],mod);
! 1253: Mulsum(mod,t2,inv,pr);
! 1254: }
! 1255: }
! 1256: #endif
! 1257:
! 1258: void mult_mod_tab(p,mod,tab,r,d)
! 1259: UM p,r;
! 1260: UM *tab;
! 1261: int mod,d;
! 1262: {
! 1263: UM w,w1,c;
! 1264: int n,i;
! 1265: int *pc;
! 1266:
! 1267: w = W_UMALLOC(d); w1 = W_UMALLOC(d);
! 1268: c = W_UMALLOC(1); DEG(c) = 0;
! 1269: n = DEG(p); DEG(r) = -1;
! 1270: for ( i = 0, pc = COEF(p); i <= n; i++ )
! 1271: if ( pc[i] ) {
! 1272: COEF(c)[0] = pc[i];
! 1273: mulum(mod,tab[i],c,w);
! 1274: addum(mod,r,w,w1);
! 1275: cpyum(w1,r);
! 1276: }
! 1277: }
! 1278:
! 1279: void make_qmat(p,mod,tab,mp)
! 1280: UM p;
! 1281: int mod;
! 1282: UM *tab;
! 1283: int ***mp;
! 1284: {
! 1285: int n,i,j;
! 1286: int *c;
! 1287: UM q,r;
! 1288: int **mat;
! 1289:
! 1290: n = DEG(p);
! 1291: *mp = mat = almat(n,n);
! 1292: for ( j = 0; j < n; j++ ) {
! 1293: r = W_UMALLOC(DEG(tab[j])); q = W_UMALLOC(DEG(tab[j]));
! 1294: cpyum(tab[j],r); DEG(r) = divum(mod,r,p,q);
! 1295: for ( i = 0, c = COEF(r); i <= DEG(r); i++ )
! 1296: mat[i][j] = c[i];
! 1297: }
! 1298: for ( i = 0; i < n; i++ )
! 1299: mat[i][i] = (mat[i][i]+mod-1) % mod;
! 1300: }
! 1301:
! 1302: void null_mod(mat,mod,n,ind)
! 1303: int **mat;
! 1304: int *ind;
! 1305: int mod,n;
! 1306: {
! 1307: int i,j,l,s,h,inv;
! 1308: int *t,*u;
! 1309:
! 1310: bzero((char *)ind,n*sizeof(int));
! 1311: ind[0] = 0;
! 1312: for ( i = j = 0; j < n; i++, j++ ) {
! 1313: for ( ; j < n; j++ ) {
! 1314: for ( l = i; l < n; l++ )
! 1315: if ( mat[l][j] )
! 1316: break;
! 1317: if ( l < n ) {
! 1318: t = mat[i]; mat[i] = mat[l]; mat[l] = t; break;
! 1319: } else
! 1320: ind[j] = 1;
! 1321: }
! 1322: if ( j == n )
! 1323: break;
! 1324: inv = invm(mat[i][j],mod);
! 1325: for ( s = j, t = mat[i]; s < n; s++ )
! 1326: t[s] = dmar(t[s],inv,0,mod);
! 1327: for ( l = 0; l < n; l++ ) {
! 1328: if ( l == i )
! 1329: continue;
! 1330: for ( s = j, u = mat[l], h = (mod-u[j])%mod; s < n; s++ )
! 1331: u[s] = dmar(h,t[s],u[s],mod);
! 1332: }
! 1333: }
! 1334: }
! 1335:
! 1336: void null_to_sol(mat,ind,mod,n,r)
! 1337: int **mat;
! 1338: int *ind;
! 1339: int mod,n;
! 1340: UM *r;
! 1341: {
! 1342: int i,j,k,l;
! 1343: int *c;
! 1344: UM w;
! 1345:
! 1346: for ( i = 0, l = 0; i < n; i++ ) {
! 1347: if ( !ind[i] )
! 1348: continue;
! 1349: w = UMALLOC(n);
! 1350: for ( j = k = 0, c = COEF(w); j < n; j++ )
! 1351: if ( ind[j] )
! 1352: c[j] = 0;
! 1353: else
! 1354: c[j] = mat[k++][i];
! 1355: c[i] = mod-1;
! 1356: for ( j = n; j >= 0; j-- )
! 1357: if ( c[j] )
! 1358: break;
! 1359: DEG(w) = j;
! 1360: r[l++] = w;
! 1361: }
! 1362: }
! 1363: /*
! 1364: make_qmat(p,mod,tab,mp)
! 1365: null_mod(mat,mod,n,ind)
! 1366: null_to_sol(mat,ind,mod,n,r)
! 1367: */
! 1368:
! 1369: void newddd(mod,f,r)
! 1370: int mod;
! 1371: UM f,*r;
! 1372: {
! 1373: register int i,j;
! 1374: int d,n;
! 1375: UM q,s,t,u,v,w,g,x,m;
! 1376: UM *base;
! 1377:
! 1378: n = DEG(f); base = (UM *)ALLOCA(n*sizeof(UM)); bzero((char *)base,n*sizeof(UM));
! 1379: w = W_UMALLOC(2*n); q = W_UMALLOC(2*n); m = W_UMALLOC(2*n);
! 1380: base[0] = W_UMALLOC(0); DEG(base[0]) = 0; COEF(base[0])[0] = 1;
! 1381: t = W_UMALLOC(1); DEG(t) = 1; COEF(t)[0] = 0; COEF(t)[1] = 1;
! 1382: pwrmodum(mod,t,mod,f,w); base[1] = W_UMALLOC(DEG(w)); cpyum(w,base[1]);
! 1383: for ( i = 2; i < n; i++ ) {
! 1384: /* fprintf(stderr,"i=%d\n",i); */
! 1385: mulum(mod,base[i-1],base[1],m); DEG(m) = divum(mod,m,f,q);
! 1386: base[i] = W_UMALLOC(DEG(m)); cpyum(m,base[i]);
! 1387: }
! 1388: v = W_UMALLOC(n); cpyum(f,v);
! 1389: DEG(w) = 1; COEF(w)[0] = 0; COEF(w)[1] = 1;
! 1390: x = W_UMALLOC(1); DEG(x) = 1; COEF(x)[0] = 0; COEF(x)[1] = 1;
! 1391: t = W_UMALLOC(n); s = W_UMALLOC(n); u = W_UMALLOC(n); g = W_UMALLOC(n);
! 1392: for ( j = 0, d = 1; 2*d <= DEG(v); d++ ) {
! 1393: /* fprintf(stderr,"d=%d\n",d); */
! 1394: for ( DEG(t) = -1, i = 0; i <= DEG(w); i++ )
! 1395: if ( COEF(w)[i] ) {
! 1396: Mulsum(mod,base[i],COEF(w)[i],s);
! 1397: addum(mod,s,t,u); cpyum(u,t);
! 1398: }
! 1399: cpyum(t,w); cpyum(v,s); subum(mod,w,x,t); Gcdum(mod,s,t,g);
! 1400: if ( DEG(g) >= 1 ) {
! 1401: berlekamp(g,mod,d,base,r+j); j += DEG(g)/d;
! 1402: Divum(mod,v,g,q); cpyum(q,v);
! 1403: DEG(w) = Divum(mod,w,v,q);
! 1404: for ( i = 0; i < DEG(v); i++ )
! 1405: DEG(base[i]) = Divum(mod,base[i],v,q);
! 1406: }
! 1407: }
! 1408: if ( DEG(v) ) {
! 1409: r[j] = UMALLOC(DEG(v)); cpyum(v,r[j]); j++;
! 1410: }
! 1411: r[j] = 0;
! 1412: }
! 1413:
! 1414: int nfctr_mod(f,mod)
! 1415: int mod;
! 1416: UM f;
! 1417: {
! 1418: register int i,j;
! 1419: int d,n;
! 1420: UM q,s,t,u,v,w,g,x,m;
! 1421: UM *base;
! 1422:
! 1423: n = DEG(f); base = (UM *)ALLOCA(n*sizeof(UM)); bzero((char *)base,n*sizeof(UM));
! 1424: w = W_UMALLOC(2*n); q = W_UMALLOC(2*n); m = W_UMALLOC(2*n);
! 1425: base[0] = W_UMALLOC(0); DEG(base[0]) = 0; COEF(base[0])[0] = 1;
! 1426: t = W_UMALLOC(1); DEG(t) = 1; COEF(t)[0] = 0; COEF(t)[1] = 1;
! 1427: pwrmodum(mod,t,mod,f,w); base[1] = W_UMALLOC(DEG(w)); cpyum(w,base[1]);
! 1428: for ( i = 2; i < n; i++ ) {
! 1429: /* fprintf(stderr,"i=%d\n",i); */
! 1430: mulum(mod,base[i-1],base[1],m); DEG(m) = divum(mod,m,f,q);
! 1431: base[i] = W_UMALLOC(DEG(m)); cpyum(m,base[i]);
! 1432: }
! 1433: v = W_UMALLOC(n); cpyum(f,v);
! 1434: DEG(w) = 1; COEF(w)[0] = 0; COEF(w)[1] = 1;
! 1435: x = W_UMALLOC(1); DEG(x) = 1; COEF(x)[0] = 0; COEF(x)[1] = 1;
! 1436: t = W_UMALLOC(n); s = W_UMALLOC(n); u = W_UMALLOC(n); g = W_UMALLOC(n);
! 1437: for ( j = 0, d = 1; 2*d <= DEG(v); d++ ) {
! 1438: /* fprintf(stderr,"d=%d\n",d); */
! 1439: for ( DEG(t) = -1, i = 0; i <= DEG(w); i++ )
! 1440: if ( COEF(w)[i] ) {
! 1441: Mulsum(mod,base[i],COEF(w)[i],s);
! 1442: addum(mod,s,t,u); cpyum(u,t);
! 1443: }
! 1444: cpyum(t,w); cpyum(v,s); subum(mod,w,x,t); Gcdum(mod,s,t,g);
! 1445: if ( DEG(g) >= 1 ) {
! 1446: j += DEG(g)/d;
! 1447: Divum(mod,v,g,q); cpyum(q,v);
! 1448: DEG(w) = Divum(mod,w,v,q);
! 1449: for ( i = 0; i < DEG(v); i++ )
! 1450: DEG(base[i]) = Divum(mod,base[i],v,q);
! 1451: }
! 1452: }
! 1453: if ( DEG(v) ) j++;
! 1454: return j;
! 1455: }
! 1456:
! 1457: int irred_check(f,mod)
! 1458: UM f;
! 1459: int mod;
! 1460: {
! 1461: register int i,j;
! 1462: int d,n;
! 1463: UM q,s,t,u,v,w,g,x,m,f1,b;
! 1464: UM *base;
! 1465:
! 1466: if ( (n = DEG(f)) == 1 )
! 1467: return 1;
! 1468: t = W_UMALLOC(n); s = W_UMALLOC(n); g = W_UMALLOC(n);
! 1469: f1 = W_UMALLOC(n); b = W_UMALLOC(n);
! 1470: diffum(mod,f,t); cpyum(f,s); Gcdum(mod,t,s,g);
! 1471: if ( DEG(g) )
! 1472: return 0;
! 1473:
! 1474: base = (UM *)ALLOCA(n*sizeof(UM)); bzero((char *)base,n*sizeof(UM));
! 1475: w = W_UMALLOC(2*n); q = W_UMALLOC(2*n); m = W_UMALLOC(2*n);
! 1476: base[0] = W_UMALLOC(0); DEG(base[0]) = 0; COEF(base[0])[0] = 1;
! 1477: t = W_UMALLOC(1); DEG(t) = 1; COEF(t)[0] = 0; COEF(t)[1] = 1;
! 1478: pwrmodum(mod,t,mod,f,w); base[1] = W_UMALLOC(DEG(w)); cpyum(w,base[1]);
! 1479: for ( i = 2; i < n; i++ ) {
! 1480: /* fprintf(stderr,"i=%d\n",i); */
! 1481: mulum(mod,base[i-1],base[1],m); DEG(m) = divum(mod,m,f,q);
! 1482: base[i] = W_UMALLOC(DEG(m)); cpyum(m,base[i]);
! 1483: }
! 1484: v = W_UMALLOC(n); cpyum(f,v);
! 1485: DEG(w) = 1; COEF(w)[0] = 0; COEF(w)[1] = 1;
! 1486: x = W_UMALLOC(1); DEG(x) = 1; COEF(x)[0] = 0; COEF(x)[1] = 1;
! 1487: t = W_UMALLOC(n); s = W_UMALLOC(n); u = W_UMALLOC(n); g = W_UMALLOC(n);
! 1488: for ( j = 0, d = 1; 2*d <= n; d++ ) {
! 1489: /* fprintf(stderr,"d=%d\n",d); */
! 1490: for ( DEG(t) = -1, i = 0; i <= DEG(w); i++ )
! 1491: if ( COEF(w)[i] ) {
! 1492: Mulsum(mod,base[i],COEF(w)[i],s);
! 1493: addum(mod,s,t,u); cpyum(u,t);
! 1494: }
! 1495: cpyum(t,w); cpyum(v,s); subum(mod,w,x,t); Gcdum(mod,s,t,g);
! 1496: if ( DEG(g) >= 1 )
! 1497: return 0;
! 1498: }
! 1499: return 1;
! 1500: }
! 1501:
! 1502: int berlekamp(p,mod,df,tab,r)
! 1503: UM p;
! 1504: int mod,df;
! 1505: UM *tab,*r;
! 1506: {
! 1507: int n,i,j,k,nf,d,nr;
! 1508: int **mat;
! 1509: int *ind;
! 1510: UM mp,w,q,gcd,w1,w2;
! 1511: UM *u;
! 1512: int *root;
! 1513:
! 1514: n = DEG(p);
! 1515: ind = ALLOCA(n*sizeof(int));
! 1516: make_qmat(p,mod,tab,&mat);
! 1517: null_mod(mat,mod,n,ind);
! 1518: for ( i = 0, d = 0; i < n; i++ )
! 1519: if ( ind[i] )
! 1520: d++;
! 1521: if ( d == 1 ) {
! 1522: r[0] = UMALLOC(n); cpyum(p,r[0]); return 1;
! 1523: }
! 1524: u = ALLOCA(d*sizeof(UM *));
! 1525: r[0] = UMALLOC(n); cpyum(p,r[0]);
! 1526: null_to_sol(mat,ind,mod,n,u);
! 1527: root = ALLOCA(d*sizeof(int));
! 1528: w = W_UMALLOC(n); mp = W_UMALLOC(d);
! 1529: w1 = W_UMALLOC(n); w2 = W_UMALLOC(n);
! 1530: for ( i = 1, nf = 1; i < d; i++ ) {
! 1531: minipoly_mod(mod,u[i],p,mp);
! 1532: nr = find_root(mod,mp,root);
! 1533: for ( j = 0; j < nf; j++ ) {
! 1534: if ( DEG(r[j]) == df )
! 1535: continue;
! 1536: for ( k = 0; k < nr; k++ ) {
! 1537: cpyum(u[i],w1); cpyum(r[j],w2);
! 1538: COEF(w1)[0] = (mod-root[k]) % mod;
! 1539: gcdum(mod,w1,w2,w);
! 1540: if ( DEG(w) > 0 && DEG(w) < DEG(r[j]) ) {
! 1541: gcd = UMALLOC(DEG(w));
! 1542: q = UMALLOC(DEG(r[j])-DEG(w));
! 1543: cpyum(w,gcd); divum(mod,r[j],w,q);
! 1544: r[j] = q; r[nf++] = gcd;
! 1545: }
! 1546: if ( nf == d )
! 1547: return d;
! 1548: }
! 1549: }
! 1550: }
! 1551: }
! 1552:
! 1553: void minipoly_mod(mod,f,p,mp)
! 1554: int mod;
! 1555: UM f,p,mp;
! 1556: {
! 1557: struct p_pair *list,*l,*l1,*lprev;
! 1558: int n,d;
! 1559: UM u,p0,p1,np0,np1,q,w;
! 1560:
! 1561: list = (struct p_pair *)MALLOC(sizeof(struct p_pair));
! 1562: list->p0 = u = W_UMALLOC(0); DEG(u) = 0; COEF(u)[0] = 1;
! 1563: list->p1 = W_UMALLOC(0); cpyum(list->p0,list->p1);
! 1564: list->next = 0;
! 1565: n = DEG(p); w = UMALLOC(2*n);
! 1566: p0 = UMALLOC(2*n); cpyum(list->p0,p0);
! 1567: p1 = UMALLOC(2*n); cpyum(list->p1,p1);
! 1568: q = W_UMALLOC(2*n);
! 1569: while ( 1 ) {
! 1570: COEF(p0)[DEG(p0)] = 0; DEG(p0)++; COEF(p0)[DEG(p0)] = 1;
! 1571: mulum(mod,f,p1,w); DEG(w) = divum(mod,w,p,q); cpyum(w,p1);
! 1572: np0 = UMALLOC(n); np1 = UMALLOC(n);
! 1573: lnf_mod(mod,n,p0,p1,list,np0,np1);
! 1574: if ( DEG(np1) < 0 ) {
! 1575: cpyum(np0,mp); return;
! 1576: } else {
! 1577: l1 = (struct p_pair *)MALLOC(sizeof(struct p_pair));
! 1578: l1->p0 = np0; l1->p1 = np1;
! 1579: for ( l = list, lprev = 0, d = DEG(np1);
! 1580: l && (DEG(l->p1) > d); lprev = l, l = l->next );
! 1581: if ( lprev ) {
! 1582: lprev->next = l1; l1->next = l;
! 1583: } else {
! 1584: l1->next = list; list = l1;
! 1585: }
! 1586: }
! 1587: }
! 1588: }
! 1589:
! 1590: void lnf_mod(mod,n,p0,p1,list,np0,np1)
! 1591: int mod,n;
! 1592: UM p0,p1;
! 1593: struct p_pair *list;
! 1594: UM np0,np1;
! 1595: {
! 1596: int inv,h,d1;
! 1597: UM t0,t1,s0,s1;
! 1598: struct p_pair *l;
! 1599:
! 1600: cpyum(p0,np0); cpyum(p1,np1);
! 1601: t0 = W_UMALLOC(n); t1 = W_UMALLOC(n);
! 1602: s0 = W_UMALLOC(n); s1 = W_UMALLOC(n);
! 1603: for ( l = list; l; l = l->next ) {
! 1604: d1 = DEG(np1);
! 1605: if ( d1 == DEG(l->p1) ) {
! 1606: inv = invm((mod-COEF(l->p1)[d1])%mod,mod);
! 1607: h = dmar(COEF(np1)[d1],inv,0,mod);
! 1608: mulsum(mod,l->p0,h,t0); addum(mod,np0,t0,s0); cpyum(s0,np0);
! 1609: mulsum(mod,l->p1,h,t1); addum(mod,np1,t1,s1); cpyum(s1,np1);
! 1610: }
! 1611: }
! 1612: }
! 1613:
! 1614: int find_root(mod,p,root)
! 1615: int mod;
! 1616: UM p;
! 1617: int *root;
! 1618: {
! 1619: UM *r;
! 1620: int i,j;
! 1621:
! 1622: r = ALLOCA((DEG(p)+1)*sizeof(UM));
! 1623: ddd(mod,p,r);
! 1624: for ( i = 0, j = 0; r[i]; i++ )
! 1625: if ( DEG(r[i]) == 1 )
! 1626: root[j++] = (mod - COEF(r[i])[0]) % mod;
! 1627: return j;
! 1628: }
! 1629:
! 1630: void showum(p)
! 1631: UM p;
! 1632: {
! 1633: int i;
! 1634: int *c;
! 1635:
! 1636: for ( i = DEG(p), c = COEF(p); i >= 0; i-- )
! 1637: if ( c[i] )
! 1638: printf("+%dx^%d",c[i],i);
! 1639: printf("\n");
! 1640: }
! 1641:
! 1642: void showumat(mat,n)
! 1643: int **mat;
! 1644: int n;
! 1645: {
! 1646: int i,j;
! 1647:
! 1648: for ( i = 0; i < n; i++ ) {
! 1649: for ( j = 0; j < n; j++ )
! 1650: printf("%d ",mat[i][j]);
! 1651: printf("\n");
! 1652: }
! 1653: }
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