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Annotation of OpenXM_contrib2/asir2000/engine/M.c, Revision 1.10

1.2       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
1.3       noro       26:  * e-mail at risa-admin@sec.flab.fujitsu.co.jp of the detailed specification
1.2       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:  *
1.10    ! noro       48:  * $OpenXM: OpenXM_contrib2/asir2000/engine/M.c,v 1.9 2001/10/09 01:36:10 noro Exp $
1.2       noro       49: */
1.1       noro       50: #include "ca.h"
                     51: #include "base.h"
                     52:
1.9       noro       53: void addum(int mod,UM p1,UM p2,UM pr)
1.1       noro       54: {
1.10    ! noro       55:   register int *c1,*c2,*cr,i,dmax,dmin;
        !            56:
        !            57:   if ( DEG(p1) == -1 ) {
        !            58:     cpyum(p2,pr);
        !            59:     return;
        !            60:   }
        !            61:   if ( DEG(p2) == -1 ) {
        !            62:     cpyum(p1,pr);
        !            63:     return;
        !            64:   }
        !            65:   if ( DEG(p1) >= DEG(p2) ) {
        !            66:     c1 = COEF(p1); c2 = COEF(p2); dmax = DEG(p1); dmin = DEG(p2);
        !            67:   } else {
        !            68:     c1 = COEF(p2); c2 = COEF(p1); dmax = DEG(p2); dmin = DEG(p1);
        !            69:   }
        !            70:   for ( i = 0, cr = COEF(pr); i <= dmin; i++ )
        !            71:     cr[i] = ( c1[i] + c2[i] ) % mod;
        !            72:   for ( ; i <= dmax; i++ )
        !            73:     cr[i] = c1[i];
        !            74:   if ( dmax == dmin )
        !            75:     degum(pr,dmax);
        !            76:   else
        !            77:     DEG(pr) = dmax;
1.1       noro       78: }
                     79:
1.9       noro       80: void subum(int mod,UM p1,UM p2,UM pr)
1.1       noro       81: {
1.10    ! noro       82:   register int *c1,*c2,*cr,i;
        !            83:   int dmax,dmin;
1.1       noro       84:
1.10    ! noro       85:   if ( DEG(p1) == -1 ) {
        !            86:     for ( i = DEG(pr) = DEG(p2), c2 = COEF(p2), cr = COEF(pr);
        !            87:         i >= 0; i-- )
        !            88:       cr[i] = ( mod - c2[i] ) % mod;
        !            89:     return;
        !            90:   }
        !            91:   if ( DEG(p2) == -1 ) {
        !            92:     cpyum(p1,pr);
        !            93:     return;
        !            94:   }
        !            95:   c1 = COEF(p1); c2 = COEF(p2); cr = COEF(pr);
        !            96:   if ( DEG(p1) >= DEG(p2) ) {
        !            97:     dmax = DEG(p1); dmin = DEG(p2);
        !            98:     for ( i = 0; i <= dmin; i++ )
        !            99:       cr[i] = ( c1[i] + mod - c2[i] ) % mod;
        !           100:     for ( ; i <= dmax; i++ )
        !           101:       cr[i] = c1[i];
        !           102:   } else {
        !           103:     dmax = DEG(p2); dmin = DEG(p1);
        !           104:     for ( i = 0; i <= dmin; i++ )
        !           105:       cr[i] = ( c1[i] + mod - c2[i] ) % mod;
        !           106:     for ( ; i <= dmax; i++ )
        !           107:       cr[i] = ( mod - c2[i] ) % mod;
        !           108:   }
        !           109:   if ( dmax == dmin )
        !           110:     degum(pr,dmax);
        !           111:   else
        !           112:     DEG(pr) = dmax;
1.1       noro      113: }
1.10    ! noro      114:
1.9       noro      115: void pwrum(int mod,UM p,int e,UM pr)
1.1       noro      116: {
1.10    ! noro      117:   UM wt,ws;
1.1       noro      118:
1.10    ! noro      119:   if ( e == 0 ) {
        !           120:     DEG(pr) = 0; COEF(pr)[0] = 1;
        !           121:   } else if ( DEG(p) < 0 )
        !           122:     DEG(pr) = -1;
        !           123:   else if ( e == 1 )
        !           124:     cpyum(p,pr);
        !           125:   else if ( DEG(p) == 0 ) {
        !           126:     DEG(pr) = 0; COEF(pr)[0] = pwrm(mod,COEF(p)[0],e);
        !           127:   } else {
        !           128:     wt = W_UMALLOC(DEG(p)*e); ws = W_UMALLOC(DEG(p)*e);
        !           129:     pwrum(mod,p,e/2,wt);
        !           130:     if ( !(e%2) )
        !           131:       mulum(mod,wt,wt,pr);
        !           132:     else {
        !           133:       mulum(mod,wt,wt,ws); mulum(mod,ws,p,pr);
        !           134:     }
        !           135:   }
1.1       noro      136: }
                    137:
1.9       noro      138: void gcdum(int mod,UM p1,UM p2,UM pr)
1.1       noro      139: {
1.10    ! noro      140:   register int inv;
        !           141:   UM t1,t2,q,tum;
        !           142:   int drem;
        !           143:
        !           144:   if ( DEG(p1) < 0 )
        !           145:     cpyum(p2,pr);
        !           146:   else if ( DEG(p2) < 0 )
        !           147:     cpyum(p1,pr);
        !           148:   else {
        !           149:     if ( DEG(p1) >= DEG(p2) ) {
        !           150:       t1 = p1; t2 = p2;
        !           151:     } else {
        !           152:       t1 = p2; t2 = p1;
        !           153:     }
        !           154:     q = W_UMALLOC(DEG(t1));
        !           155:     while ( ( drem = divum(mod,t1,t2,q) ) >= 0 ) {
        !           156:       tum = t1; t1 = t2; t2 = tum; DEG(t2) = drem;
        !           157:     }
        !           158:     inv = invm(COEF(t2)[DEG(t2)],mod);
        !           159:     mulsum(mod,t2,inv,pr);
        !           160:   }
1.1       noro      161: }
                    162:
1.9       noro      163: void eucum(int mod,UM f1,UM f2,UM a,UM b)
1.1       noro      164: {
1.10    ! noro      165:   UM g1,g2,a1,a2,a3,wm,q,tum;
        !           166:   int d,dr;
1.1       noro      167:
1.10    ! noro      168:   d = DEG(f1) + DEG(f2) + 10;
        !           169:   g1 = W_UMALLOC(d); g2 = W_UMALLOC(d); a1 = W_UMALLOC(d);
        !           170:   a2 = W_UMALLOC(d); a3 = W_UMALLOC(d); wm = W_UMALLOC(d);
        !           171:   q = W_UMALLOC(d);
        !           172:   DEG(a1) = 0; COEF(a1)[0] = 1; DEG(a2) = -1;
        !           173:   cpyum(f1,g1); cpyum(f2,g2);
        !           174:   while ( 1 ) {
        !           175:     dr = divum(mod,g1,g2,q); tum = g1; g1 = g2; g2 = tum;
        !           176:     if ( ( DEG(g2) = dr ) == -1 )
        !           177:       break;
        !           178:     mulum(mod,a2,q,wm); subum(mod,a1,wm,a3); dr = divum(mod,a3,f2,q);
        !           179:     tum = a1; a1 = a2; a2 = a3; a3 = tum; DEG(a3) = dr;
        !           180:   }
        !           181:   if ( COEF(g1)[0] != 1 )
        !           182:     mulsum(mod,a2,invm(COEF(g1)[0],mod),a);
        !           183:   else
        !           184:     cpyum(a2,a);
        !           185:   mulum(mod,a,f1,wm);
        !           186:   if ( DEG(wm) >= 0 )
        !           187:     COEF(wm)[0] = ( COEF(wm)[0] + mod - 1 ) % mod;
        !           188:   else {
        !           189:     DEG(wm) = 0; COEF(wm)[0] = mod - 1;
        !           190:   }
        !           191:   divum(mod,wm,f2,q); mulsum(mod,q,mod-1,b);
1.8       noro      192: #if 0
1.10    ! noro      193:   t1 = W_UMALLOC(d);
        !           194:   t2 = W_UMALLOC(d);
        !           195:   t3 = W_UMALLOC(d);
        !           196:   mulum(mod,a,f1,t1);
        !           197:   mulum(mod,b,f2,t2);
        !           198:   addum(mod,t1,t2,t3);
1.8       noro      199: #endif
                    200: }
                    201:
1.9       noro      202: void eucum2(int mod,UM f1,UM f2,UM a,UM b)
1.8       noro      203: {
1.10    ! noro      204:   UM gk,gk1,gk2,ak,ak1,ak2,bk,bk1,bk2,q,t,wm1,wm2,wz;
        !           205:   int d,inv;
        !           206:   UM t1,t2;
        !           207:
        !           208:   d = 2*(DEG(f1) + DEG(f2));
        !           209:   gk = W_UMALLOC(d); gk1 = W_UMALLOC(d); gk2 = W_UMALLOC(d);
        !           210:   ak = W_UMALLOC(d); ak1 = W_UMALLOC(d); ak2 = W_UMALLOC(d);
        !           211:   bk = W_UMALLOC(d); bk1 = W_UMALLOC(d); bk2 = W_UMALLOC(d);
        !           212:   q = W_UMALLOC(d); wm1 = W_UMALLOC(d); wm2 = W_UMALLOC(d);
        !           213:   wz = W_UMALLOC(d);
        !           214:
        !           215:   t1 = UMALLOC(1000);
        !           216:   t2 = UMALLOC(1000);
        !           217:   cpyum(f1,t1);
        !           218:   cpyum(f2,t2);
        !           219:
        !           220:   DEG(ak) = 0; COEF(ak)[0] = 1;
        !           221:   DEG(ak1) = -1;
        !           222:   DEG(bk) = -1;
        !           223:   DEG(bk1) = 0; COEF(bk1)[0] = 1;
        !           224:
        !           225:   cpyum(f1,gk); cpyum(f2,gk1);
        !           226:
        !           227:   while ( 1 ) {
        !           228:     /* ak*f1+bk*f2 = gk, ak1*f1+bk1*f2 = gk1 */
        !           229:     cpyum(gk,gk2);
        !           230:     DEG(gk2) = divum(mod,gk2,gk1,q);
        !           231:     /* gk2 = gk - q*gk1 */
        !           232:     if ( DEG(gk2) == -1 )
        !           233:       break;
        !           234:     /* ak2 = ak - q*ak1, bk2 = bk - q*bk1 */
        !           235:     mulum(mod,ak1,q,wm1); subum(mod,ak,wm1,ak2);
        !           236:     mulum(mod,bk1,q,wm1); subum(mod,bk,wm1,bk2);
        !           237:
        !           238:     /* shift */
        !           239:     t = ak; ak = ak1; ak1 = ak2; ak2 = t;
        !           240:     t = bk; bk = bk1; bk1 = bk2; bk2 = t;
        !           241:     t = gk; gk = gk1; gk1 = gk2; gk2 = t;
        !           242:   }
        !           243:   /* ak1*f1+bk1*f2 = gk1 = GCD(f1,f2) */
        !           244:   mulum(mod,ak1,t1,wm1);
        !           245:   mulum(mod,bk1,t2,wm2);
        !           246:   addum(mod,wm1,wm2,wz);
        !           247:   if ( DEG(wz) != 0 )
        !           248:     error("euc 1");
        !           249:
        !           250:   DEG(ak1) = divum(mod,ak1,f2,q);
        !           251:   DEG(bk1) = divum(mod,bk1,f1,q);
        !           252:   mulum(mod,ak1,f1,wm1);
        !           253:   mulum(mod,bk1,f2,wm2);
        !           254:   addum(mod,wm1,wm2,wz);
        !           255:   if ( DEG(wz) != 0 )
        !           256:     error("euc 2");
        !           257:
        !           258:
        !           259:   if ( COEF(wz)[0] != 1 ) {
        !           260:     inv = invm(COEF(wz)[0],mod);
        !           261:     mulsum(mod,ak1,inv,a);
        !           262:     mulsum(mod,bk1,inv,b);
        !           263:   } else {
        !           264:     cpyum(ak1,a);
        !           265:     cpyum(bk1,b);
        !           266:   }
1.1       noro      267: }
                    268:
1.9       noro      269: void sqfrum(int index,int count,P f,int *nindex,struct oDUM **dcr,ML *pl)
1.1       noro      270: {
1.10    ! noro      271:   int i,j,m,n,d,dt,mod;
        !           272:   UM wf,wdf,ws,wt,wgcd,mf,mgcd;
        !           273:   UM *l;
        !           274:   struct oDUM *dc;
        !           275:   ML tp;
        !           276:
        !           277:   n = UDEG(f);
        !           278:   wf = W_UMALLOC(n);
        !           279:   wdf = W_UMALLOC(n);
        !           280:   ws = W_UMALLOC(n);
        !           281:   wt = W_UMALLOC(n);
        !           282:   wgcd = W_UMALLOC(n);
        !           283:
        !           284:   mf = W_UMALLOC(n);
        !           285:   mgcd = W_UMALLOC(n);
        !           286:
        !           287:   for ( j = 0, d = n; j < count && d; ) {
        !           288:     m = get_lprime(index++);
        !           289:     if ( rem(NM((Q)COEF(DC(f))),m) == 0 ) continue;
        !           290:
        !           291:     ptoum(m,f,wf);
        !           292:     diffum(m,wf,wdf);
        !           293:     cpyum(wf,wt); cpyum(wdf,ws);
        !           294:     gcdum(m,wt,ws,wgcd);
        !           295:     dt = DEG(wgcd);
        !           296:
        !           297:     if ( dt < d ) {
        !           298:       d = dt;
        !           299:       mod = m;
        !           300:       cpyum(wf,mf); cpyum(wgcd,mgcd);
        !           301:     }
        !           302:     j++;
        !           303:   }
        !           304:   *nindex = index;
        !           305:
        !           306:   sqfrummain(mod,mf,mgcd,&dc);
        !           307:   *dcr = dc;
        !           308:
        !           309:   for ( n = 0; dc[n].f; n++ );
        !           310:   *pl = tp = MLALLOC(n+1);
        !           311:   tp->n = n;
        !           312:   tp->mod = mod;
        !           313:
        !           314:   for ( i = 0, l = (UM *)COEF(tp); dc[i].f; i++ ) {
        !           315:     l[i] = UMALLOC(DEG(dc[i].f)*dc[i].n);
        !           316:     pwrum(mod,dc[i].f,dc[i].n,l[i]);
        !           317:   }
        !           318:   l[i] = 0;
1.1       noro      319: }
                    320:
1.9       noro      321: void sqfrummain(int mod,UM p,UM gcd,struct oDUM **dcp)
1.1       noro      322: {
1.10    ! noro      323:   int i,j,n;
        !           324:   UM wp,wdp,wc,wd,ws,wt,wq;
        !           325:   struct oDUM *dc;
        !           326:   UM *f;
        !           327:
        !           328:   i = DEG(p);
        !           329:
        !           330:   wp = W_UMALLOC(i);
        !           331:   wdp = W_UMALLOC(i);
        !           332:   wt = W_UMALLOC(i);
        !           333:   ws = W_UMALLOC(i);
        !           334:   wc = W_UMALLOC(i);
        !           335:   wd = W_UMALLOC(i);
        !           336:   wq =  W_UMALLOC(i);
        !           337:
        !           338:   f = (UM *) ALLOCA((i+2)*sizeof(UM));
        !           339:
        !           340:   cpyum(p,wp);
        !           341:   diffum(mod,wp,wdp);
        !           342:
        !           343:   cpyum(wp,wt);
        !           344:   divum(mod,wt,gcd,wc);
        !           345:
        !           346:   cpyum(wdp,wt);
        !           347:   divum(mod,wt,gcd,ws);
        !           348:
        !           349:   diffum(mod,wc,wt);
        !           350:   subum(mod,ws,wt,wd);
        !           351:
        !           352:   for ( i = 1; DEG(wd) >= 0; i++ ) {
        !           353:     cpyum(wc,ws); cpyum(wd,wt);
        !           354:     gcdum(mod,ws,wt,wq);
        !           355:     if ( DEG(wq) > 0 ) {
        !           356:       f[i] = UMALLOC(DEG(wq));
        !           357:       cpyum(wq,f[i]);
        !           358:
        !           359:       cpyum(wc,ws);
        !           360:       divum(mod,ws,f[i],wc);
        !           361:       divum(mod,wd,f[i],ws);
        !           362:       diffum(mod,wc,wt);
        !           363:       subum(mod,ws,wt,wd);
        !           364:     } else {
        !           365:       f[i] = 0;
        !           366:       cpyum(wd,ws);
        !           367:       diffum(mod,wc,wt);
        !           368:       subum(mod,ws,wt,wd);
        !           369:     }
        !           370:
        !           371:   }
        !           372:
        !           373:   if ( DEG(wc) > 0 ) {
        !           374:     DEG(wq) = 0;
        !           375:     COEF(wq)[0] = invm(COEF(wc)[DEG(wc)],mod);
        !           376:     f[i] = UMALLOC(DEG(wc));
        !           377:     mulum(mod,wc,wq,f[i]);
        !           378:     f[i+1] = 0;
        !           379:     n = i + 1;
        !           380:   } else {
        !           381:     f[i] = 0;
        !           382:     n = i;
        !           383:   }
        !           384:
        !           385:   for ( i = 1, j = 0; i < n; i++ )
        !           386:     if ( f[i] ) j++;
        !           387:
        !           388:   *dcp = dc = (struct oDUM *) CALLOC(j+1,sizeof(struct oDUM));
        !           389:
        !           390:   for ( i = 1, j = 0; i < n; i++ )
        !           391:     if ( f[i] ) {
        !           392:       dc[j].n = i;
        !           393:       dc[j].f = f[i];
        !           394:       j++;
        !           395:     }
        !           396:   dc[j].n = 0;
        !           397:   dc[j].f = 0;
1.1       noro      398: }
                    399:
1.9       noro      400: void cpyum(UM p1,UM p2)
1.1       noro      401: {
1.10    ! noro      402:   register int *c1,*c2,i;
1.1       noro      403:
1.10    ! noro      404:   for ( i = DEG(p2) = DEG(p1), c1 = COEF(p1), c2 = COEF(p2);
        !           405:       i >= 0; i-- )
        !           406:     c2[i] = c1[i];
1.1       noro      407: }
                    408:
1.9       noro      409: void clearum(UM p,int n)
1.7       noro      410: {
1.10    ! noro      411:   DEG(p) = -1;
        !           412:   bzero(COEF(p),(n+1)*sizeof(int));
1.7       noro      413: }
                    414:
1.9       noro      415: void degum(UM f,int n)
1.1       noro      416: {
1.10    ! noro      417:   register int i,*c;
1.1       noro      418:
1.10    ! noro      419:   for ( i = n, c = COEF(f); ( i >= 0 ) && ( c[i] == 0 ); i-- );
        !           420:   DEG(f) = i;
1.1       noro      421: }
                    422:
1.9       noro      423: int deg(V v,P p)
1.1       noro      424: {
1.10    ! noro      425:   if ( !p )
        !           426:     return ( -1 );
        !           427:   else if ( NUM(p) )
        !           428:     return ( 0 );
        !           429:   else if ( VR(p) != v )
        !           430:     return ( 0 );
        !           431:   else if ( PL(NM(DEG(DC(p)))) > 1 ) {
        !           432:     error("degree too large");
        !           433:     return ( -1 );
        !           434:   } else
        !           435:     return ( UDEG(p) );
1.1       noro      436: }
                    437:
1.9       noro      438: LUM LUMALLOC(int n,int bound)
1.1       noro      439: {
1.10    ! noro      440:   LUM p;
        !           441:   int **c;
        !           442:   int i;
        !           443:
        !           444:   p = (LUM)MALLOC(TRUESIZE(oLUM,n,int *));
        !           445:   DEG(p) = n;
        !           446:   for ( i = 0, c = (int **)COEF(p); i <= n; i++ ) {
        !           447:     c[i] = (int *)MALLOC_ATOMIC((bound+1)*sizeof(int));
        !           448:     bzero((char *)c[i],(bound+1)*sizeof(int));
        !           449:   }
        !           450:   return p;
1.6       noro      451: }
                    452:
1.8       noro      453: /* dx = deg in x, dy = deg in y, c[i] <-> the coef of y^i (poly in x) */
1.7       noro      454:
1.9       noro      455: BM BMALLOC(int dx,int dy)
1.6       noro      456: {
1.10    ! noro      457:   BM p;
        !           458:   UM *c;
        !           459:   int i;
        !           460:
        !           461:   p = (BM)MALLOC(TRUESIZE(oBM,dy,UM));
        !           462:   DEG(p) = dy;
        !           463:   for ( i = 0, c = (UM *)COEF(p); i <= dy; i++ ) {
        !           464:     c[i] = UMALLOC(dx);
        !           465:     clearum(c[i],dx);
        !           466:   }
        !           467:   return p;
1.1       noro      468: }
                    469:
1.9       noro      470: void mullum(int mod,int n,LUM f1,LUM f2,LUM fr)
1.1       noro      471: {
1.10    ! noro      472:   int max;
        !           473:   register int i,j,**p1,**p2,*px;
        !           474:   int *w,*w1,*w2;
        !           475:
        !           476:   p1 = (int **)COEF(f1); p2 = (int **)COEF(f2);
        !           477:   w = W_ALLOC(2*(n+1)); w1 = W_ALLOC(DEG(f1)); w2 = W_ALLOC(DEG(f2));
        !           478:   for ( i = DEG(f1); i >= 0; i-- ) {
        !           479:     for ( j = n - 1, px = p1[i]; ( j >= 0 ) && ( px[j] == 0 ); j-- );
        !           480:     w1[i] = ( j == -1 ? 0 : 1 );
        !           481:   }
        !           482:   for ( i = DEG(f2); i >= 0; i-- ) {
        !           483:     for ( j = n - 1, px = p2[i]; ( j >= 0 ) && ( px[j] == 0 ); j-- );
        !           484:     w2[i] = ( j == -1 ? 0 : 1 );
        !           485:   }
        !           486:   for ( j = DEG(fr) = DEG(f1) + DEG(f2); j >= 0; j-- ) {
        !           487:     for ( i = n - 1, px = COEF(fr)[j]; i >= 0; i-- )
        !           488:       px[i] = 0;
        !           489:     for ( max = MIN(DEG(f1),j), i = MAX(0,j-DEG(f2)); i <= max; i++ )
        !           490:       if ( w1[i] != 0 && w2[j - i] != 0 ) {
        !           491:         mulpadic(mod,n,p1[i],p2[j - i],w); addpadic(mod,n,w,px);
        !           492:       }
        !           493:   }
1.1       noro      494: }
                    495:
1.9       noro      496: void cpylum(int bound,LUM p,LUM r)
1.1       noro      497: {
1.10    ! noro      498:   register int i,j;
        !           499:   register int **pp,**ppr;
1.1       noro      500:
1.10    ! noro      501:   DEG(r) = DEG(p);
        !           502:   for ( i = 0, pp = COEF(p), ppr = COEF(r);
        !           503:     i <= DEG(p); i++ )
        !           504:     for ( j = 0; j < bound; j++ )
        !           505:       ppr[i][j] = pp[i][j];
1.7       noro      506: }
                    507:
1.9       noro      508: int isequalum(UM f1,UM f2)
1.7       noro      509: {
1.10    ! noro      510:   int i;
1.7       noro      511:
1.10    ! noro      512:   if ( DEG(f1) < 0 )
        !           513:     if ( DEG(f2) < 0 )
        !           514:       return 1;
        !           515:     else
        !           516:       return 0;
        !           517:   else if ( DEG(f2) < 0 )
        !           518:     return 0;
        !           519:   else {
        !           520:     if ( DEG(f1) != DEG(f2) )
        !           521:       return 0;
        !           522:     for ( i = 0; i <= DEG(f1); i++ )
        !           523:       if ( COEF(f1)[i] != COEF(f2)[i] )
        !           524:         break;
        !           525:     if ( i < DEG(f1) )
        !           526:       return 0;
        !           527:     else
        !           528:       return 1;
        !           529:   }
1.1       noro      530: }
                    531:
1.9       noro      532: void pwrlum(int mod,int bound,LUM p,int n,LUM r)
1.1       noro      533: {
1.10    ! noro      534:   LUM t,s;
1.1       noro      535:
1.10    ! noro      536:   if ( n == 0 ) {
        !           537:     DEG(r) = 0;
        !           538:     COEF(r)[0][0] = 1;
        !           539:   } else if ( DEG(p) < 0 )
        !           540:     DEG(r) = -1;
        !           541:   else if ( n == 1 )
        !           542:     cpylum(bound,p,r);
        !           543:   else {
        !           544:     W_LUMALLOC(DEG(p)*n,bound,t);
        !           545:     pwrlum(mod,bound,p,n/2,t);
        !           546:     if ( !(n%2) )
        !           547:       mullum(mod,bound,t,t,r);
        !           548:     else {
        !           549:       W_LUMALLOC(DEG(p)*n,bound,s);
        !           550:       mullum(mod,bound,t,t,s);
        !           551:       mullum(mod,bound,s,p,r);
        !           552:     }
        !           553:   }
1.1       noro      554: }
                    555:
1.9       noro      556: int **almat(int n,int m)
1.1       noro      557: {
1.10    ! noro      558:   int **mat,i;
1.1       noro      559:
1.10    ! noro      560:   mat = (int **)MALLOC(n*sizeof(int *));
        !           561:   for ( i = 0; i < n; i++ )
        !           562:     mat[i] = (int *)CALLOC(m,sizeof(int));
        !           563:   return mat;
1.1       noro      564: }
                    565:
1.9       noro      566: void mini(int mod,UM f,UM fr)
1.1       noro      567: {
1.10    ! noro      568:   register int i,j,**c,*ptr;
        !           569:   int d,dr,dm,n;
        !           570:   UM w,q;
        !           571:
        !           572:   n = DEG(f); c = (int **)ALLOCA(n*sizeof(int *));
        !           573:   for ( i = 0; i < n; i++ ) {
        !           574:     c[i] = (int *)ALLOCA(n*sizeof(int));
        !           575:     bzero((char *)c[i],(int)(n*sizeof(int)));
        !           576:   }
        !           577:   w = W_UMALLOC( mod + n + 10 ); q = W_UMALLOC( mod + n + 10 );
        !           578:   for ( i = 1; ( d = ( mod * i ) ) < n; i++ ) c[d][i - 1] = 1;
        !           579:   DEG(w) = d;
        !           580:   for ( j = 0; j < d; j++ )
        !           581:     COEF(w)[j] = 0;
        !           582:   COEF(w)[d] = 1;
        !           583:   for ( ; (i < n) && ((dr = divum(mod,w,f,q)) >= 0); i++ ) {
        !           584:     for ( j = dr; j >= 0; j-- )
        !           585:       COEF(w)[j + mod] = c[j][i - 1] = COEF(w)[j];
        !           586:     for ( j = mod - 1; j >= 0; j-- )
        !           587:       COEF(w)[j] = 0;
        !           588:     DEG(w) = dr + mod;
        !           589:   }
        !           590:   for ( i = 1; i < n; i++ )
        !           591:     c[i][i - 1] = ( c[i][i - 1] + mod - 1 ) % mod;
        !           592:   if ( ( dm = minimain(mod,n,n - 1,c) ) != -1 )
        !           593:     for ( i = 0, ptr = COEF(fr), ptr[0] = 0; i <= dm; i++ )
        !           594:       ptr[i + 1] = c[0][i];
        !           595:   else
        !           596:     COEF(fr)[0] = 1;
        !           597:   DEG(fr) = dm + 1;
1.1       noro      598: }
                    599:
1.9       noro      600: int minimain(int mod,int n,int m,int **c)
1.1       noro      601: {
1.10    ! noro      602:   register int *ptr,*ci,*p;
        !           603:   register int i,l,a,j,b,inv;
        !           604:   int *tmp;
        !           605:
        !           606:   for ( j = 0; j < m; j++ ) {
        !           607:     for ( i = j; (n > i) && !c[i][j]; i++ );
        !           608:     if ( i == n ) {
        !           609:       for ( i = j, j = j - 1; j >= 0; j-- )
        !           610:         c[0][j] = c[j][i];
        !           611:       c[0][i] = mod - 1;
        !           612:       return( i );
        !           613:     }
        !           614:     if ( i != j ) {
        !           615:       tmp = c[i]; c[i] = c[j]; c[j] = tmp;
        !           616:     }
        !           617:     ptr = c[j]; inv = invm((ptr[j] + mod) % mod,mod);
        !           618:     for ( l = j, p = ptr+l; l < m; l++ ) {
        !           619:       a = (*p * inv) % mod;
        !           620:       *p++ = (a<0?a+mod:a);
        !           621:     }
        !           622:     for ( i = 0; i < n; i++ )
        !           623:       if ( (a = -c[i][j]) && (i != j) ) {
        !           624:         for ( l = j+1, p = ptr+l, ci = c[i]+l; l < m; l++ ) {
        !           625:           b = (*p++ * a + *ci) % mod;
        !           626:           *ci++ = (b<0?b+mod:b);
        !           627:         }
        !           628:         c[i][j] = 0;
        !           629:       }
        !           630:   }
        !           631:   return (-1);
1.1       noro      632: }
                    633:
1.4       noro      634: #if defined(__GNUC__)
1.1       noro      635: const
                    636: #endif
                    637: int sprime[] = {
1.10    ! noro      638:   2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,
        !           639:   53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,
        !           640:   127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,
        !           641:   199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,
        !           642:   283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,
        !           643:   383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,
        !           644:   467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,
        !           645:   577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,
        !           646:   661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,
        !           647:   769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,
        !           648:   877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,
        !           649:   983,991,997,1009,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063,1069,
        !           650:   1087,1091,1093,1097,1103,1109,1117,1123,1129,1151,1153,1163,1171,1181,1187,
        !           651:   1193,1201,1213,1217,1223,1229,1231,1237,1249,1259,1277,1279,1283,1289,1291,
        !           652:   1297,1301,1303,1307,1319,1321,1327,1361,1367,1373,1381,1399,1409,1423,1427,
        !           653:   1429,1433,1439,1447,1451,1453,1459,1471,1481,1483,1487,1489,1493,1499,1511,
        !           654:   1523,1531,1543,1549,1553,1559,1567,1571,1579,1583,1597,1601,1607,1609,1613,
        !           655:   1619,1621,1627,1637,1657,1663,1667,1669,1693,1697,1699,1709,1721,1723,1733,
        !           656:   1741,1747,1753,1759,1777,1783,1787,1789,1801,1811,1823,1831,1847,1861,1867,
        !           657:   1871,1873,1877,1879,1889,1901,1907,1913,1931,1933,1949,1951,1973,1979,1987,
        !           658:   1993,1997,1999,2003,2011,2017,2027,2029,2039,2053,2063,2069,2081,2083,2087,
        !           659:   2089,2099,2111,2113,2129,2131,2137,2141,2143,2153,2161,2179,2203,2207,2213,
        !           660:   2221,2237,2239,2243,2251,2267,2269,2273,2281,2287,2293,2297,2309,2311,2333,
        !           661:   2339,2341,2347,2351,2357,2371,2377,2381,2383,2389,2393,2399,2411,2417,2423,
        !           662:   2437,2441,2447,2459,2467,2473,2477,2503,2521,2531,2539,2543,2549,2551,2557,
        !           663:   2579,2591,2593,2609,2617,2621,2633,2647,2657,2659,2663,2671,2677,2683,2687,
        !           664:   2689,2693,2699,2707,2711,2713,2719,2729,2731,2741,2749,2753,2767,2777,2789,
        !           665:   2791,2797,2801,2803,2819,2833,2837,2843,2851,2857,2861,2879,2887,2897,2903,
        !           666:   2909,2917,2927,2939,2953,2957,2963,2969,2971,2999,3001,3011,3019,3023,3037,
        !           667:   3041,3049,3061,3067,3079,3083,3089,3109,3119,3121,3137,3163,3167,3169,3181,
        !           668:   3187,3191,3203,3209,3217,3221,3229,3251,3253,3257,3259,3271,3299,3301,3307,
        !           669:   3313,3319,3323,3329,3331,3343,3347,3359,3361,3371,3373,3389,3391,3407,3413,
        !           670:   3433,3449,3457,3461,3463,3467,3469,3491,3499,3511,3517,3527,3529,3533,3539,
        !           671:   3541,3547,3557,3559,3571,3581,3583,3593,3607,3613,3617,3623,3631,3637,3643,
        !           672:   3659,3671,3673,3677,3691,3697,3701,3709,3719,3727,3733,3739,3761,3767,3769,
        !           673:   3779,3793,3797,3803,3821,3823,3833,3847,3851,3853,3863,3877,3881,3889,3907,
        !           674:   3911,3917,3919,3923,3929,3931,3943,3947,3967,3989,4001,4003,4007,4013,4019,
        !           675:   4021,4027,4049,4051,4057,4073,4079,4091,4093,4099,4111,4127,4129,4133,4139,
        !           676:   4153,4157,4159,4177,4201,4211,4217,4219,4229,4231,4241,4243,4253,4259,4261,
        !           677:   4271,4273,4283,4289,4297,4327,4337,4339,4349,4357,4363,4373,4391,4397,4409,
        !           678:   4421,4423,4441,4447,4451,4457,4463,4481,4483,4493,4507,4513,4517,4519,4523,
        !           679:   4547,4549,4561,4567,4583,4591,4597,4603,4621,4637,4639,4643,4649,4651,4657,
        !           680:   4663,4673,4679,4691,4703,4721,4723,4729,4733,4751,4759,4783,4787,4789,4793,
        !           681:   4799,4801,4813,4817,4831,4861,4871,4877,4889,4903,4909,4919,4931,4933,4937,
        !           682:   4943,4951,4957,4967,4969,4973,4987,4993,4999,5003,5009,5011,5021,5023,5039,
        !           683:   5051,5059,5077,5081,5087,5099,5101,5107,5113,5119,5147,5153,5167,5171,5179,
        !           684:   5189,5197,5209,5227,5231,5233,5237,5261,5273,5279,5281,5297,5303,5309,5323,
        !           685:   5333,5347,5351,5381,5387,5393,5399,5407,5413,5417,5419,5431,5437,5441,5443,
        !           686:   5449,5471,5477,5479,5483,5501,5503,5507,5519,5521,5527,5531,5557,5563,5569,
        !           687:   5573,5581,5591,5623,5639,5641,5647,5651,5653,5657,5659,5669,5683,5689,5693,
        !           688:   5701,5711,5717,5737,5741,5743,5749,5779,5783,5791,5801,5807,5813,5821,5827,
        !           689:   5839,5843,5849,5851,5857,5861,5867,5869,5879,5881,5897,5903,5923,5927,5939,
        !           690:   5953,5981,5987,6007,6011,6029,6037,6043,6047,6053,6067,6073,6079,6089,6091,
        !           691:   6101,6113,6121,6131,6133,6143,6151,6163,6173,6197,6199,6203,6211,6217,6221,
        !           692:   6229,6247,6257,6263,6269,6271,6277,6287,6299,6301,6311,6317,6323,6329,6337,
        !           693:   6343,6353,6359,6361,6367,6373,6379,6389,6397,6421,6427,6449,6451,6469,6473,
        !           694:   6481,6491,6521,6529,6547,6551,6553,6563,6569,6571,6577,6581,6599,6607,6619,
        !           695:   6637,6653,6659,6661,6673,6679,6689,6691,6701,6703,6709,6719,6733,6737,6761,
        !           696:   6763,6779,6781,6791,6793,6803,6823,6827,6829,6833,6841,6857,6863,6869,6871,
        !           697:   6883,6899,6907,6911,6917,6947,6949,6959,6961,6967,6971,6977,6983,6991,6997,
        !           698:   7001,7013,7019,7027,7039,7043,7057,7069,7079,7103,7109,7121,7127,7129,7151,
        !           699:   7159,7177,7187,7193,7207,7211,7213,7219,7229,7237,7243,7247,7253,7283,7297,
        !           700:   7307,7309,7321,7331,7333,7349,7351,7369,7393,7411,7417,7433,7451,7457,7459,
        !           701:   7477,7481,7487,7489,7499,7507,7517,7523,7529,7537,7541,7547,7549,7559,7561,
        !           702:   7573,7577,7583,7589,7591,7603,7607,7621,7639,7643,7649,7669,7673,7681,7687,
        !           703:   7691,7699,7703,7717,7723,7727,7741,7753,7757,7759,7789,7793,7817,7823,7829,
        !           704:   7841,7853,7867,7873,7877,7879,7883,7901,7907,7919,7927,7933,7937,7949,7951,
        !           705:   7963,7993,8009,8011,8017,8039,8053,8059,8069,8081,8087,8089,8093,8101,8111,
        !           706:   8117,8123,8147,8161,8167,8171,8179,8191,8209,8219,8221,8231,8233,8237,8243,
        !           707:   8263,8269,8273,8287,8291,8293,8297,8311,8317,8329,8353,8363,8369,8377,8387,
        !           708:   8389,8419,8423,8429,8431,8443,8447,8461,8467,8501,8513,8521,8527,8537,8539,
        !           709:   8543,8563,8573,8581,8597,8599,8609,8623,8627,8629,8641,8647,8663,8669,8677,
        !           710:   8681,8689,8693,8699,8707,8713,8719,8731,8737,8741,8747,8753,8761,8779,8783,
        !           711:   8803,8807,8819,8821,8831,8837,8839,8849,8861,8863,8867,8887,8893,8923,8929,
        !           712:   8933,8941,8951,8963,8969,8971,8999,9001,9007,9011,9013,9029,9041,9043,9049,
        !           713:   9059,9067,9091,9103,9109,9127,9133,9137,9151,9157,9161,9173,9181,9187,9199,
        !           714:   9203,9209,9221,9227,9239,9241,9257,9277,9281,9283,9293,9311,9319,9323,9337,
        !           715:   9341,9343,9349,9371,9377,9391,9397,9403,9413,9419,9421,9431,9433,9437,9439,
        !           716:   9461,9463,9467,9473,9479,9491,9497,9511,9521,9533,9539,9547,9551,9587,9601,
        !           717:   9613,9619,9623,9629,9631,9643,9649,9661,9677,9679,9689,9697,9719,9721,9733,
        !           718:   9739,9743,9749,9767,9769,9781,9787,9791,9803,9811,9817,9829,9833,9839,9851,
        !           719:   9857,9859,9871,9883,9887,9901,9907,9923,9929,9931,9941,9949,9967,9973,10007,
        !           720:   10009,10037,10039,10061,10067,10069,10079,10091,10093,10099,
        !           721:   10103,10111,10133,10139,10141,10151,10159,10163,10169,10177,
        !           722:   10181,10193,10211,10223,10243,10247,10253,10259,10267,10271,
        !           723:   10273,10289,10301,10303,10313,10321,10331,10333,10337,10343,
        !           724:   10357,10369,10391,10399,10427,10429,10433,10453,10457,10459,
        !           725:   10463,10477,10487,10499,10501,10513,10529,10531,10559,10567,
        !           726:   10589,10597,10601,10607,10613,10627,10631,10639,10651,10657,
        !           727:   10663,10667,10687,10691,10709,10711,10723,10729,10733,10739,
        !           728:   10753,10771,10781,10789,10799,10831,10837,10847,10853,10859,
        !           729:   10861,10867,10883,10889,10891,10903,10909,10937,10939,10949,
        !           730:   10957,10973,10979,10987,10993,11003,11027,11047,11057,11059,
        !           731:   11069,11071,11083,11087,11093,11113,11117,11119,11131,11149,
        !           732:   11159,11161,11171,11173,11177,11197,11213,11239,11243,11251,
        !           733:   11257,11261,11273,11279,11287,11299,11311,11317,11321,11329,
        !           734:   11351,11353,11369,11383,11393,11399,11411,11423,11437,11443,
        !           735:   11447,11467,11471,11483,11489,11491,11497,11503,11519,11527,
        !           736:   11549,11551,11579,11587,11593,11597,11617,11621,11633,11657,
        !           737:   11677,11681,11689,11699,11701,11717,11719,11731,11743,11777,
        !           738:   11779,11783,11789,11801,11807,11813,11821,11827,11831,11833,
        !           739:   11839,11863,11867,11887,11897,11903,11909,11923,11927,11933,
        !           740:   11939,11941,11953,11959,11969,11971,11981,11987,12007,12011,
        !           741:   12037,12041,12043,12049,12071,12073,12097,12101,12107,12109,
        !           742:   12113,12119,12143,12149,12157,12161,12163,12197,12203,12211,
        !           743:   12227,12239,12241,12251,12253,12263,12269,12277,12281,12289,
        !           744:   12301,12323,12329,12343,12347,12373,12377,12379,12391,12401,
        !           745:   12409,12413,12421,12433,12437,12451,12457,12473,12479,12487,
        !           746:   12491,12497,12503,12511,12517,12527,12539,12541,12547,12553,
        !           747:   12569,12577,12583,12589,12601,12611,12613,12619,12637,12641,
        !           748:   12647,12653,12659,12671,12689,12697,12703,12713,12721,12739,
        !           749:   12743,12757,12763,12781,12791,12799,12809,12821,12823,12829,
        !           750:   12841,12853,12889,12893,12899,12907,12911,12917,12919,12923,
        !           751:   12941,12953,12959,12967,12973,12979,12983,13001,13003,13007,
        !           752:   13009,13033,13037,13043,13049,13063,13093,13099,13103,13109,
        !           753:   13121,13127,13147,13151,13159,13163,13171,13177,13183,13187,
        !           754:   13217,13219,13229,13241,13249,13259,13267,13291,13297,13309,
        !           755:   13313,13327,13331,13337,13339,13367,13381,13397,13399,13411,
        !           756:   13417,13421,13441,13451,13457,13463,13469,13477,13487,13499,
        !           757:   13513,13523,13537,13553,13567,13577,13591,13597,13613,13619,
        !           758:   13627,13633,13649,13669,13679,13681,13687,13691,13693,13697,
        !           759:   13709,13711,13721,13723,13729,13751,13757,13759,13763,13781,
        !           760:   13789,13799,13807,13829,13831,13841,13859,13873,13877,13879,
        !           761:   13883,13901,13903,13907,13913,13921,13931,13933,13963,13967,
        !           762:   13997,13999,14009,14011,14029,14033,14051,14057,14071,14081,
        !           763:   14083,14087,14107,14143,14149,14153,14159,14173,14177,14197,
        !           764:   14207,14221,14243,14249,14251,14281,14293,14303,14321,14323,
        !           765:   14327,14341,14347,14369,14387,14389,14401,14407,14411,14419,
        !           766:   14423,14431,14437,14447,14449,14461,14479,14489,14503,14519,
        !           767:   14533,14537,14543,14549,14551,14557,14561,14563,14591,14593,
        !           768:   14621,14627,14629,14633,14639,14653,14657,14669,14683,14699,
        !           769:   14713,14717,14723,14731,14737,14741,14747,14753,14759,14767,
        !           770:   14771,14779,14783,14797,14813,14821,14827,14831,14843,14851,
        !           771:   14867,14869,14879,14887,14891,14897,14923,14929,14939,14947,
        !           772:   14951,14957,14969,14983,15013,15017,15031,15053,15061,15073,
        !           773:   15077,15083,15091,15101,15107,15121,15131,15137,15139,15149,
        !           774:   15161,15173,15187,15193,15199,15217,15227,15233,15241,15259,
        !           775:   15263,15269,15271,15277,15287,15289,15299,15307,15313,15319,
        !           776:   15329,15331,15349,15359,15361,15373,15377,15383,15391,15401,
        !           777:   15413,15427,15439,15443,15451,15461,15467,15473,15493,15497,
        !           778:   15511,15527,15541,15551,15559,15569,15581,15583,15601,15607,
        !           779:   15619,15629,15641,15643,15647,15649,15661,15667,15671,15679,
        !           780:   15683,15727,15731,15733,15737,15739,15749,15761,15767,15773,
        !           781:   15787,15791,15797,15803,15809,15817,15823,15859,15877,15881,
        !           782:   15887,15889,15901,15907,15913,15919,15923,15937,15959,15971,
        !           783:   15973,15991,16001,16007,16033,16057,16061,16063,16067,16069,
        !           784:   16073,16087,16091,16097,16103,16111,16127,16139,16141,16183,
        !           785:   16187,16189,16193,16217,16223,16229,16231,16249,16253,16267,
        !           786:   16273,16301,16319,16333,16339,16349,16361,16363,16369,16381,
        !           787:   0
1.1       noro      788: };

FreeBSD-CVSweb <freebsd-cvsweb@FreeBSD.org>