=================================================================== RCS file: /home/cvs/OpenXM_contrib2/asir2000/engine/M.c,v retrieving revision 1.1.1.1 retrieving revision 1.10 diff -u -p -r1.1.1.1 -r1.10 --- OpenXM_contrib2/asir2000/engine/M.c 1999/12/03 07:39:08 1.1.1.1 +++ OpenXM_contrib2/asir2000/engine/M.c 2018/03/29 01:32:51 1.10 @@ -1,657 +1,788 @@ -/* $OpenXM: OpenXM/src/asir99/engine/M.c,v 1.1.1.1 1999/11/10 08:12:26 noro Exp $ */ +/* + * Copyright (c) 1994-2000 FUJITSU LABORATORIES LIMITED + * All rights reserved. + * + * FUJITSU LABORATORIES LIMITED ("FLL") hereby grants you a limited, + * non-exclusive and royalty-free license to use, copy, modify and + * redistribute, solely for non-commercial and non-profit purposes, the + * computer program, "Risa/Asir" ("SOFTWARE"), subject to the terms and + * conditions of this Agreement. For the avoidance of doubt, you acquire + * only a limited right to use the SOFTWARE hereunder, and FLL or any + * third party developer retains all rights, including but not limited to + * copyrights, in and to the SOFTWARE. + * + * (1) FLL does not grant you a license in any way for commercial + * purposes. You may use the SOFTWARE only for non-commercial and + * non-profit purposes only, such as academic, research and internal + * business use. + * (2) The SOFTWARE is protected by the Copyright Law of Japan and + * international copyright treaties. If you make copies of the SOFTWARE, + * with or without modification, as permitted hereunder, you shall affix + * to all such copies of the SOFTWARE the above copyright notice. + * (3) An explicit reference to this SOFTWARE and its copyright owner + * shall be made on your publication or presentation in any form of the + * results obtained by use of the SOFTWARE. + * (4) In the event that you modify the SOFTWARE, you shall notify FLL by + * e-mail at risa-admin@sec.flab.fujitsu.co.jp of the detailed specification + * for such modification or the source code of the modified part of the + * SOFTWARE. + * + * THE SOFTWARE IS PROVIDED AS IS WITHOUT ANY WARRANTY OF ANY KIND. FLL + * MAKES ABSOLUTELY NO WARRANTIES, EXPRESSED, IMPLIED OR STATUTORY, AND + * EXPRESSLY DISCLAIMS ANY IMPLIED WARRANTY OF MERCHANTABILITY, FITNESS + * FOR A PARTICULAR PURPOSE OR NONINFRINGEMENT OF THIRD PARTIES' + * RIGHTS. NO FLL DEALER, AGENT, EMPLOYEES IS AUTHORIZED TO MAKE ANY + * MODIFICATIONS, EXTENSIONS, OR ADDITIONS TO THIS WARRANTY. + * UNDER NO CIRCUMSTANCES AND UNDER NO LEGAL THEORY, TORT, CONTRACT, + * OR OTHERWISE, SHALL FLL BE LIABLE TO YOU OR ANY OTHER PERSON FOR ANY + * DIRECT, INDIRECT, SPECIAL, INCIDENTAL, PUNITIVE OR CONSEQUENTIAL + * DAMAGES OF ANY CHARACTER, INCLUDING, WITHOUT LIMITATION, DAMAGES + * ARISING OUT OF OR RELATING TO THE SOFTWARE OR THIS AGREEMENT, DAMAGES + * FOR LOSS OF GOODWILL, WORK STOPPAGE, OR LOSS OF DATA, OR FOR ANY + * DAMAGES, EVEN IF FLL SHALL HAVE BEEN INFORMED OF THE POSSIBILITY OF + * SUCH DAMAGES, OR FOR ANY CLAIM BY ANY OTHER PARTY. EVEN IF A PART + * OF THE SOFTWARE HAS BEEN DEVELOPED BY A THIRD PARTY, THE THIRD PARTY + * DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE, + * PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE. + * + * $OpenXM: OpenXM_contrib2/asir2000/engine/M.c,v 1.9 2001/10/09 01:36:10 noro Exp $ +*/ #include "ca.h" #include "base.h" -void addum(mod,p1,p2,pr) -int mod; -UM p1,p2,pr; +void addum(int mod,UM p1,UM p2,UM pr) { - register int *c1,*c2,*cr,i,dmax,dmin; - - if ( DEG(p1) == -1 ) { - cpyum(p2,pr); - return; - } - if ( DEG(p2) == -1 ) { - cpyum(p1,pr); - return; - } - if ( DEG(p1) >= DEG(p2) ) { - c1 = COEF(p1); c2 = COEF(p2); dmax = DEG(p1); dmin = DEG(p2); - } else { - c1 = COEF(p2); c2 = COEF(p1); dmax = DEG(p2); dmin = DEG(p1); - } - for ( i = 0, cr = COEF(pr); i <= dmin; i++ ) - cr[i] = ( c1[i] + c2[i] ) % mod; - for ( ; i <= dmax; i++ ) - cr[i] = c1[i]; - if ( dmax == dmin ) - degum(pr,dmax); - else - DEG(pr) = dmax; + register int *c1,*c2,*cr,i,dmax,dmin; + + if ( DEG(p1) == -1 ) { + cpyum(p2,pr); + return; + } + if ( DEG(p2) == -1 ) { + cpyum(p1,pr); + return; + } + if ( DEG(p1) >= DEG(p2) ) { + c1 = COEF(p1); c2 = COEF(p2); dmax = DEG(p1); dmin = DEG(p2); + } else { + c1 = COEF(p2); c2 = COEF(p1); dmax = DEG(p2); dmin = DEG(p1); + } + for ( i = 0, cr = COEF(pr); i <= dmin; i++ ) + cr[i] = ( c1[i] + c2[i] ) % mod; + for ( ; i <= dmax; i++ ) + cr[i] = c1[i]; + if ( dmax == dmin ) + degum(pr,dmax); + else + DEG(pr) = dmax; } -void subum(mod,p1,p2,pr) -int mod; -UM p1,p2,pr; +void subum(int mod,UM p1,UM p2,UM pr) { - register int *c1,*c2,*cr,i; - int dmax,dmin; + register int *c1,*c2,*cr,i; + int dmax,dmin; - if ( DEG(p1) == -1 ) { - for ( i = DEG(pr) = DEG(p2), c2 = COEF(p2), cr = COEF(pr); - i >= 0; i-- ) - cr[i] = ( mod - c2[i] ) % mod; - return; - } - if ( DEG(p2) == -1 ) { - cpyum(p1,pr); - return; - } - c1 = COEF(p1); c2 = COEF(p2); cr = COEF(pr); - if ( DEG(p1) >= DEG(p2) ) { - dmax = DEG(p1); dmin = DEG(p2); - for ( i = 0; i <= dmin; i++ ) - cr[i] = ( c1[i] + mod - c2[i] ) % mod; - for ( ; i <= dmax; i++ ) - cr[i] = c1[i]; - } else { - dmax = DEG(p2); dmin = DEG(p1); - for ( i = 0; i <= dmin; i++ ) - cr[i] = ( c1[i] + mod - c2[i] ) % mod; - for ( ; i <= dmax; i++ ) - cr[i] = ( mod - c2[i] ) % mod; - } - if ( dmax == dmin ) - degum(pr,dmax); - else - DEG(pr) = dmax; + if ( DEG(p1) == -1 ) { + for ( i = DEG(pr) = DEG(p2), c2 = COEF(p2), cr = COEF(pr); + i >= 0; i-- ) + cr[i] = ( mod - c2[i] ) % mod; + return; + } + if ( DEG(p2) == -1 ) { + cpyum(p1,pr); + return; + } + c1 = COEF(p1); c2 = COEF(p2); cr = COEF(pr); + if ( DEG(p1) >= DEG(p2) ) { + dmax = DEG(p1); dmin = DEG(p2); + for ( i = 0; i <= dmin; i++ ) + cr[i] = ( c1[i] + mod - c2[i] ) % mod; + for ( ; i <= dmax; i++ ) + cr[i] = c1[i]; + } else { + dmax = DEG(p2); dmin = DEG(p1); + for ( i = 0; i <= dmin; i++ ) + cr[i] = ( c1[i] + mod - c2[i] ) % mod; + for ( ; i <= dmax; i++ ) + cr[i] = ( mod - c2[i] ) % mod; + } + if ( dmax == dmin ) + degum(pr,dmax); + else + DEG(pr) = dmax; } - -void pwrum(mod,p,e,pr) -int mod,e; -UM p,pr; + +void pwrum(int mod,UM p,int e,UM pr) { - UM wt,ws; + UM wt,ws; - if ( e == 0 ) { - DEG(pr) = 0; COEF(pr)[0] = 1; - } else if ( DEG(p) < 0 ) - DEG(pr) = -1; - else if ( e == 1 ) - cpyum(p,pr); - else if ( DEG(p) == 0 ) { - DEG(pr) = 0; COEF(pr)[0] = pwrm(mod,COEF(p)[0],e); - } else { - wt = W_UMALLOC(DEG(p)*e); ws = W_UMALLOC(DEG(p)*e); - pwrum(mod,p,e/2,wt); - if ( !(e%2) ) - mulum(mod,wt,wt,pr); - else { - mulum(mod,wt,wt,ws); mulum(mod,ws,p,pr); - } - } + if ( e == 0 ) { + DEG(pr) = 0; COEF(pr)[0] = 1; + } else if ( DEG(p) < 0 ) + DEG(pr) = -1; + else if ( e == 1 ) + cpyum(p,pr); + else if ( DEG(p) == 0 ) { + DEG(pr) = 0; COEF(pr)[0] = pwrm(mod,COEF(p)[0],e); + } else { + wt = W_UMALLOC(DEG(p)*e); ws = W_UMALLOC(DEG(p)*e); + pwrum(mod,p,e/2,wt); + if ( !(e%2) ) + mulum(mod,wt,wt,pr); + else { + mulum(mod,wt,wt,ws); mulum(mod,ws,p,pr); + } + } } -void gcdum(mod,p1,p2,pr) -register int mod; -UM p1,p2,pr; +void gcdum(int mod,UM p1,UM p2,UM pr) { - register int inv; - UM t1,t2,q,tum; - int drem; + register int inv; + UM t1,t2,q,tum; + int drem; - if ( DEG(p1) < 0 ) - cpyum(p2,pr); - else if ( DEG(p2) < 0 ) - cpyum(p1,pr); - else { - if ( DEG(p1) >= DEG(p2) ) { - t1 = p1; t2 = p2; - } else { - t1 = p2; t2 = p1; - } - q = W_UMALLOC(DEG(t1)); - while ( ( drem = divum(mod,t1,t2,q) ) >= 0 ) { - tum = t1; t1 = t2; t2 = tum; DEG(t2) = drem; - } - inv = invm(COEF(t2)[DEG(t2)],mod); - mulsum(mod,t2,inv,pr); - } + if ( DEG(p1) < 0 ) + cpyum(p2,pr); + else if ( DEG(p2) < 0 ) + cpyum(p1,pr); + else { + if ( DEG(p1) >= DEG(p2) ) { + t1 = p1; t2 = p2; + } else { + t1 = p2; t2 = p1; + } + q = W_UMALLOC(DEG(t1)); + while ( ( drem = divum(mod,t1,t2,q) ) >= 0 ) { + tum = t1; t1 = t2; t2 = tum; DEG(t2) = drem; + } + inv = invm(COEF(t2)[DEG(t2)],mod); + mulsum(mod,t2,inv,pr); + } } -void eucum(mod,f1,f2,a,b) -register int mod; -UM f1,f2,a,b; +void eucum(int mod,UM f1,UM f2,UM a,UM b) { - UM g1,g2,a1,a2,a3,wm,q,tum; - int d,dr; + UM g1,g2,a1,a2,a3,wm,q,tum; + int d,dr; - d = DEG(f1) + DEG(f2) + 10; - g1 = W_UMALLOC(d); g2 = W_UMALLOC(d); a1 = W_UMALLOC(d); - a2 = W_UMALLOC(d); a3 = W_UMALLOC(d); wm = W_UMALLOC(d); - q = W_UMALLOC(d); - DEG(a1) = 0; COEF(a1)[0] = 1; DEG(a2) = -1; - cpyum(f1,g1); cpyum(f2,g2); - while ( 1 ) { - dr = divum(mod,g1,g2,q); tum = g1; g1 = g2; g2 = tum; - if ( ( DEG(g2) = dr ) == -1 ) - break; - mulum(mod,a2,q,wm); subum(mod,a1,wm,a3); dr = divum(mod,a3,f2,q); - tum = a1; a1 = a2; a2 = a3; a3 = tum; DEG(a3) = dr; - } - if ( COEF(g1)[0] != 1 ) - mulsum(mod,a2,invm(COEF(g1)[0],mod),a); - else - cpyum(a2,a); - mulum(mod,a,f1,wm); - if ( DEG(wm) >= 0 ) - COEF(wm)[0] = ( COEF(wm)[0] + mod - 1 ) % mod; - else { - DEG(wm) = 0; COEF(wm)[0] = mod - 1; - } - divum(mod,wm,f2,q); mulsum(mod,q,mod-1,b); + d = DEG(f1) + DEG(f2) + 10; + g1 = W_UMALLOC(d); g2 = W_UMALLOC(d); a1 = W_UMALLOC(d); + a2 = W_UMALLOC(d); a3 = W_UMALLOC(d); wm = W_UMALLOC(d); + q = W_UMALLOC(d); + DEG(a1) = 0; COEF(a1)[0] = 1; DEG(a2) = -1; + cpyum(f1,g1); cpyum(f2,g2); + while ( 1 ) { + dr = divum(mod,g1,g2,q); tum = g1; g1 = g2; g2 = tum; + if ( ( DEG(g2) = dr ) == -1 ) + break; + mulum(mod,a2,q,wm); subum(mod,a1,wm,a3); dr = divum(mod,a3,f2,q); + tum = a1; a1 = a2; a2 = a3; a3 = tum; DEG(a3) = dr; + } + if ( COEF(g1)[0] != 1 ) + mulsum(mod,a2,invm(COEF(g1)[0],mod),a); + else + cpyum(a2,a); + mulum(mod,a,f1,wm); + if ( DEG(wm) >= 0 ) + COEF(wm)[0] = ( COEF(wm)[0] + mod - 1 ) % mod; + else { + DEG(wm) = 0; COEF(wm)[0] = mod - 1; + } + divum(mod,wm,f2,q); mulsum(mod,q,mod-1,b); +#if 0 + t1 = W_UMALLOC(d); + t2 = W_UMALLOC(d); + t3 = W_UMALLOC(d); + mulum(mod,a,f1,t1); + mulum(mod,b,f2,t2); + addum(mod,t1,t2,t3); +#endif } -void sqfrum(index,count,f,nindex,dcr,pl) -int index,count,*nindex; -P f; -struct oDUM **dcr; -ML *pl; +void eucum2(int mod,UM f1,UM f2,UM a,UM b) { - int i,j,m,n,d,dt,mod; - UM wf,wdf,ws,wt,wgcd,mf,mgcd; - UM *l; - struct oDUM *dc; - ML tp; + UM gk,gk1,gk2,ak,ak1,ak2,bk,bk1,bk2,q,t,wm1,wm2,wz; + int d,inv; + UM t1,t2; - n = UDEG(f); - wf = W_UMALLOC(n); - wdf = W_UMALLOC(n); - ws = W_UMALLOC(n); - wt = W_UMALLOC(n); - wgcd = W_UMALLOC(n); + d = 2*(DEG(f1) + DEG(f2)); + gk = W_UMALLOC(d); gk1 = W_UMALLOC(d); gk2 = W_UMALLOC(d); + ak = W_UMALLOC(d); ak1 = W_UMALLOC(d); ak2 = W_UMALLOC(d); + bk = W_UMALLOC(d); bk1 = W_UMALLOC(d); bk2 = W_UMALLOC(d); + q = W_UMALLOC(d); wm1 = W_UMALLOC(d); wm2 = W_UMALLOC(d); + wz = W_UMALLOC(d); + + t1 = UMALLOC(1000); + t2 = UMALLOC(1000); + cpyum(f1,t1); + cpyum(f2,t2); - mf = W_UMALLOC(n); - mgcd = W_UMALLOC(n); + DEG(ak) = 0; COEF(ak)[0] = 1; + DEG(ak1) = -1; + DEG(bk) = -1; + DEG(bk1) = 0; COEF(bk1)[0] = 1; - for ( j = 0, d = n; j < count && d; ) { - m = lprime[index++]; - if ( !m ) - error("sqfrum : lprime[] exhausted."); - if ( rem(NM((Q)COEF(DC(f))),m) == 0 ) continue; + cpyum(f1,gk); cpyum(f2,gk1); - ptoum(m,f,wf); - diffum(m,wf,wdf); - cpyum(wf,wt); cpyum(wdf,ws); - gcdum(m,wt,ws,wgcd); - dt = DEG(wgcd); + while ( 1 ) { + /* ak*f1+bk*f2 = gk, ak1*f1+bk1*f2 = gk1 */ + cpyum(gk,gk2); + DEG(gk2) = divum(mod,gk2,gk1,q); + /* gk2 = gk - q*gk1 */ + if ( DEG(gk2) == -1 ) + break; + /* ak2 = ak - q*ak1, bk2 = bk - q*bk1 */ + mulum(mod,ak1,q,wm1); subum(mod,ak,wm1,ak2); + mulum(mod,bk1,q,wm1); subum(mod,bk,wm1,bk2); - if ( dt < d ) { - d = dt; - mod = m; - cpyum(wf,mf); cpyum(wgcd,mgcd); - } - j++; - } - *nindex = index; + /* shift */ + t = ak; ak = ak1; ak1 = ak2; ak2 = t; + t = bk; bk = bk1; bk1 = bk2; bk2 = t; + t = gk; gk = gk1; gk1 = gk2; gk2 = t; + } + /* ak1*f1+bk1*f2 = gk1 = GCD(f1,f2) */ + mulum(mod,ak1,t1,wm1); + mulum(mod,bk1,t2,wm2); + addum(mod,wm1,wm2,wz); + if ( DEG(wz) != 0 ) + error("euc 1"); - sqfrummain(mod,mf,mgcd,&dc); - *dcr = dc; + DEG(ak1) = divum(mod,ak1,f2,q); + DEG(bk1) = divum(mod,bk1,f1,q); + mulum(mod,ak1,f1,wm1); + mulum(mod,bk1,f2,wm2); + addum(mod,wm1,wm2,wz); + if ( DEG(wz) != 0 ) + error("euc 2"); - for ( n = 0; dc[n].f; n++ ); - *pl = tp = MLALLOC(n+1); - tp->n = n; - tp->mod = mod; - for ( i = 0, l = (UM *)COEF(tp); dc[i].f; i++ ) { - l[i] = UMALLOC(DEG(dc[i].f)*dc[i].n); - pwrum(mod,dc[i].f,dc[i].n,l[i]); - } - l[i] = 0; + if ( COEF(wz)[0] != 1 ) { + inv = invm(COEF(wz)[0],mod); + mulsum(mod,ak1,inv,a); + mulsum(mod,bk1,inv,b); + } else { + cpyum(ak1,a); + cpyum(bk1,b); + } } -void sqfrummain(mod,p,gcd,dcp) -int mod; -UM p,gcd; -struct oDUM **dcp; +void sqfrum(int index,int count,P f,int *nindex,struct oDUM **dcr,ML *pl) { - int i,j,n; - UM wp,wdp,wc,wd,ws,wt,wq; - struct oDUM *dc; - UM *f; + int i,j,m,n,d,dt,mod; + UM wf,wdf,ws,wt,wgcd,mf,mgcd; + UM *l; + struct oDUM *dc; + ML tp; - i = DEG(p); + n = UDEG(f); + wf = W_UMALLOC(n); + wdf = W_UMALLOC(n); + ws = W_UMALLOC(n); + wt = W_UMALLOC(n); + wgcd = W_UMALLOC(n); - wp = W_UMALLOC(i); - wdp = W_UMALLOC(i); - wt = W_UMALLOC(i); - ws = W_UMALLOC(i); - wc = W_UMALLOC(i); - wd = W_UMALLOC(i); - wq = W_UMALLOC(i); + mf = W_UMALLOC(n); + mgcd = W_UMALLOC(n); - f = (UM *) ALLOCA((i+2)*sizeof(UM)); + for ( j = 0, d = n; j < count && d; ) { + m = get_lprime(index++); + if ( rem(NM((Q)COEF(DC(f))),m) == 0 ) continue; - cpyum(p,wp); - diffum(mod,wp,wdp); + ptoum(m,f,wf); + diffum(m,wf,wdf); + cpyum(wf,wt); cpyum(wdf,ws); + gcdum(m,wt,ws,wgcd); + dt = DEG(wgcd); - cpyum(wp,wt); - divum(mod,wt,gcd,wc); + if ( dt < d ) { + d = dt; + mod = m; + cpyum(wf,mf); cpyum(wgcd,mgcd); + } + j++; + } + *nindex = index; - cpyum(wdp,wt); - divum(mod,wt,gcd,ws); + sqfrummain(mod,mf,mgcd,&dc); + *dcr = dc; - diffum(mod,wc,wt); - subum(mod,ws,wt,wd); + for ( n = 0; dc[n].f; n++ ); + *pl = tp = MLALLOC(n+1); + tp->n = n; + tp->mod = mod; - for ( i = 1; DEG(wd) >= 0; i++ ) { - cpyum(wc,ws); cpyum(wd,wt); - gcdum(mod,ws,wt,wq); - if ( DEG(wq) > 0 ) { - f[i] = UMALLOC(DEG(wq)); - cpyum(wq,f[i]); + for ( i = 0, l = (UM *)COEF(tp); dc[i].f; i++ ) { + l[i] = UMALLOC(DEG(dc[i].f)*dc[i].n); + pwrum(mod,dc[i].f,dc[i].n,l[i]); + } + l[i] = 0; +} - cpyum(wc,ws); - divum(mod,ws,f[i],wc); - divum(mod,wd,f[i],ws); - diffum(mod,wc,wt); - subum(mod,ws,wt,wd); - } else { - f[i] = 0; - cpyum(wd,ws); - diffum(mod,wc,wt); - subum(mod,ws,wt,wd); - } - - } +void sqfrummain(int mod,UM p,UM gcd,struct oDUM **dcp) +{ + int i,j,n; + UM wp,wdp,wc,wd,ws,wt,wq; + struct oDUM *dc; + UM *f; - if ( DEG(wc) > 0 ) { - DEG(wq) = 0; - COEF(wq)[0] = invm(COEF(wc)[DEG(wc)],mod); - f[i] = UMALLOC(DEG(wc)); - mulum(mod,wc,wq,f[i]); - f[i+1] = 0; - n = i + 1; - } else { - f[i] = 0; - n = i; - } - - for ( i = 1, j = 0; i < n; i++ ) - if ( f[i] ) j++; + i = DEG(p); - *dcp = dc = (struct oDUM *) CALLOC(j+1,sizeof(struct oDUM)); + wp = W_UMALLOC(i); + wdp = W_UMALLOC(i); + wt = W_UMALLOC(i); + ws = W_UMALLOC(i); + wc = W_UMALLOC(i); + wd = W_UMALLOC(i); + wq = W_UMALLOC(i); - for ( i = 1, j = 0; i < n; i++ ) - if ( f[i] ) { - dc[j].n = i; - dc[j].f = f[i]; - j++; - } - dc[j].n = 0; - dc[j].f = 0; + f = (UM *) ALLOCA((i+2)*sizeof(UM)); + + cpyum(p,wp); + diffum(mod,wp,wdp); + + cpyum(wp,wt); + divum(mod,wt,gcd,wc); + + cpyum(wdp,wt); + divum(mod,wt,gcd,ws); + + diffum(mod,wc,wt); + subum(mod,ws,wt,wd); + + for ( i = 1; DEG(wd) >= 0; i++ ) { + cpyum(wc,ws); cpyum(wd,wt); + gcdum(mod,ws,wt,wq); + if ( DEG(wq) > 0 ) { + f[i] = UMALLOC(DEG(wq)); + cpyum(wq,f[i]); + + cpyum(wc,ws); + divum(mod,ws,f[i],wc); + divum(mod,wd,f[i],ws); + diffum(mod,wc,wt); + subum(mod,ws,wt,wd); + } else { + f[i] = 0; + cpyum(wd,ws); + diffum(mod,wc,wt); + subum(mod,ws,wt,wd); + } + + } + + if ( DEG(wc) > 0 ) { + DEG(wq) = 0; + COEF(wq)[0] = invm(COEF(wc)[DEG(wc)],mod); + f[i] = UMALLOC(DEG(wc)); + mulum(mod,wc,wq,f[i]); + f[i+1] = 0; + n = i + 1; + } else { + f[i] = 0; + n = i; + } + + for ( i = 1, j = 0; i < n; i++ ) + if ( f[i] ) j++; + + *dcp = dc = (struct oDUM *) CALLOC(j+1,sizeof(struct oDUM)); + + for ( i = 1, j = 0; i < n; i++ ) + if ( f[i] ) { + dc[j].n = i; + dc[j].f = f[i]; + j++; + } + dc[j].n = 0; + dc[j].f = 0; } -void cpyum(p1,p2) -UM p1,p2; +void cpyum(UM p1,UM p2) { - register int *c1,*c2,i; + register int *c1,*c2,i; - for ( i = DEG(p2) = DEG(p1), c1 = COEF(p1), c2 = COEF(p2); - i >= 0; i-- ) - c2[i] = c1[i]; + for ( i = DEG(p2) = DEG(p1), c1 = COEF(p1), c2 = COEF(p2); + i >= 0; i-- ) + c2[i] = c1[i]; } -void degum(f,n) -UM f; -int n; +void clearum(UM p,int n) { - register int i,*c; + DEG(p) = -1; + bzero(COEF(p),(n+1)*sizeof(int)); +} - for ( i = n, c = COEF(f); ( i >= 0 ) && ( c[i] == 0 ); i-- ); - DEG(f) = i; +void degum(UM f,int n) +{ + register int i,*c; + + for ( i = n, c = COEF(f); ( i >= 0 ) && ( c[i] == 0 ); i-- ); + DEG(f) = i; } -int deg(v,p) -V v; -P p; +int deg(V v,P p) { - if ( !p ) - return ( -1 ); - else if ( NUM(p) ) - return ( 0 ); - else if ( VR(p) != v ) - return ( 0 ); - else if ( PL(NM(DEG(DC(p)))) > 1 ) { - error("degree too large"); - return ( -1 ); - } else - return ( UDEG(p) ); + if ( !p ) + return ( -1 ); + else if ( NUM(p) ) + return ( 0 ); + else if ( VR(p) != v ) + return ( 0 ); + else if ( PL(NM(DEG(DC(p)))) > 1 ) { + error("degree too large"); + return ( -1 ); + } else + return ( UDEG(p) ); } -LUM LUMALLOC(n,bound) -int n,bound; +LUM LUMALLOC(int n,int bound) { - LUM p; - int **c; - int i; + LUM p; + int **c; + int i; - p = (LUM)MALLOC(TRUESIZE(oLUM,n,int *)); - DEG(p) = n; - for ( i = 0, c = (int **)COEF(p); i <= n; i++ ) { - c[i] = (int *)MALLOC_ATOMIC((bound+1)*sizeof(int)); - bzero((char *)c[i],(bound+1)*sizeof(int)); - } - return p; + p = (LUM)MALLOC(TRUESIZE(oLUM,n,int *)); + DEG(p) = n; + for ( i = 0, c = (int **)COEF(p); i <= n; i++ ) { + c[i] = (int *)MALLOC_ATOMIC((bound+1)*sizeof(int)); + bzero((char *)c[i],(bound+1)*sizeof(int)); + } + return p; } -void mullum(mod,n,f1,f2,fr) -int mod,n; -LUM f1,f2,fr; +/* dx = deg in x, dy = deg in y, c[i] <-> the coef of y^i (poly in x) */ + +BM BMALLOC(int dx,int dy) { - int max; - register int i,j,**p1,**p2,*px; - int *w,*w1,*w2; + BM p; + UM *c; + int i; - p1 = (int **)COEF(f1); p2 = (int **)COEF(f2); - w = W_ALLOC(2*(n+1)); w1 = W_ALLOC(DEG(f1)); w2 = W_ALLOC(DEG(f2)); - for ( i = DEG(f1); i >= 0; i-- ) { - for ( j = n - 1, px = p1[i]; ( j >= 0 ) && ( px[j] == 0 ); j-- ); - w1[i] = ( j == -1 ? 0 : 1 ); - } - for ( i = DEG(f2); i >= 0; i-- ) { - for ( j = n - 1, px = p2[i]; ( j >= 0 ) && ( px[j] == 0 ); j-- ); - w2[i] = ( j == -1 ? 0 : 1 ); - } - for ( j = DEG(fr) = DEG(f1) + DEG(f2); j >= 0; j-- ) { - for ( i = n - 1, px = COEF(fr)[j]; i >= 0; i-- ) - px[i] = 0; - for ( max = MIN(DEG(f1),j), i = MAX(0,j-DEG(f2)); i <= max; i++ ) - if ( w1[i] != 0 && w2[j - i] != 0 ) { - mulpadic(mod,n,p1[i],p2[j - i],w); addpadic(mod,n,w,px); - } - } + p = (BM)MALLOC(TRUESIZE(oBM,dy,UM)); + DEG(p) = dy; + for ( i = 0, c = (UM *)COEF(p); i <= dy; i++ ) { + c[i] = UMALLOC(dx); + clearum(c[i],dx); + } + return p; } -void cpylum(bound,p,r) -int bound; -LUM p,r; +void mullum(int mod,int n,LUM f1,LUM f2,LUM fr) { - register int i,j; - register int **pp,**ppr; + int max; + register int i,j,**p1,**p2,*px; + int *w,*w1,*w2; - DEG(r) = DEG(p); - for ( i = 0, pp = COEF(p), ppr = COEF(r); - i <= DEG(p); i++ ) - for ( j = 0; j < bound; j++ ) - ppr[i][j] = pp[i][j]; + p1 = (int **)COEF(f1); p2 = (int **)COEF(f2); + w = W_ALLOC(2*(n+1)); w1 = W_ALLOC(DEG(f1)); w2 = W_ALLOC(DEG(f2)); + for ( i = DEG(f1); i >= 0; i-- ) { + for ( j = n - 1, px = p1[i]; ( j >= 0 ) && ( px[j] == 0 ); j-- ); + w1[i] = ( j == -1 ? 0 : 1 ); + } + for ( i = DEG(f2); i >= 0; i-- ) { + for ( j = n - 1, px = p2[i]; ( j >= 0 ) && ( px[j] == 0 ); j-- ); + w2[i] = ( j == -1 ? 0 : 1 ); + } + for ( j = DEG(fr) = DEG(f1) + DEG(f2); j >= 0; j-- ) { + for ( i = n - 1, px = COEF(fr)[j]; i >= 0; i-- ) + px[i] = 0; + for ( max = MIN(DEG(f1),j), i = MAX(0,j-DEG(f2)); i <= max; i++ ) + if ( w1[i] != 0 && w2[j - i] != 0 ) { + mulpadic(mod,n,p1[i],p2[j - i],w); addpadic(mod,n,w,px); + } + } } -void pwrlum(mod,bound,p,n,r) -int mod,bound,n; -LUM p,r; +void cpylum(int bound,LUM p,LUM r) { - LUM t,s; + register int i,j; + register int **pp,**ppr; - if ( n == 0 ) { - DEG(r) = 0; - COEF(r)[0][0] = 1; - } else if ( DEG(p) < 0 ) - DEG(r) = -1; - else if ( n == 1 ) - cpylum(bound,p,r); - else { - W_LUMALLOC(DEG(p)*n,bound,t); - pwrlum(mod,bound,p,n/2,t); - if ( !(n%2) ) - mullum(mod,bound,t,t,r); - else { - W_LUMALLOC(DEG(p)*n,bound,s); - mullum(mod,bound,t,t,s); - mullum(mod,bound,s,p,r); - } - } + DEG(r) = DEG(p); + for ( i = 0, pp = COEF(p), ppr = COEF(r); + i <= DEG(p); i++ ) + for ( j = 0; j < bound; j++ ) + ppr[i][j] = pp[i][j]; } -int **almat(n,m) -int n,m; +int isequalum(UM f1,UM f2) { - int **mat,i; + int i; - mat = (int **)MALLOC(n*sizeof(int *)); - for ( i = 0; i < n; i++ ) - mat[i] = (int *)CALLOC(m,sizeof(int)); - return mat; + if ( DEG(f1) < 0 ) + if ( DEG(f2) < 0 ) + return 1; + else + return 0; + else if ( DEG(f2) < 0 ) + return 0; + else { + if ( DEG(f1) != DEG(f2) ) + return 0; + for ( i = 0; i <= DEG(f1); i++ ) + if ( COEF(f1)[i] != COEF(f2)[i] ) + break; + if ( i < DEG(f1) ) + return 0; + else + return 1; + } } -void mini(mod,f,fr) -register int mod; -UM f,fr; +void pwrlum(int mod,int bound,LUM p,int n,LUM r) { - register int i,j,**c,*ptr; - int d,dr,dm,n; - UM w,q; + LUM t,s; - n = DEG(f); c = (int **)ALLOCA(n*sizeof(int *)); - for ( i = 0; i < n; i++ ) { - c[i] = (int *)ALLOCA(n*sizeof(int)); - bzero((char *)c[i],(int)(n*sizeof(int))); - } - w = W_UMALLOC( mod + n + 10 ); q = W_UMALLOC( mod + n + 10 ); - for ( i = 1; ( d = ( mod * i ) ) < n; i++ ) c[d][i - 1] = 1; - DEG(w) = d; - for ( j = 0; j < d; j++ ) - COEF(w)[j] = 0; - COEF(w)[d] = 1; - for ( ; (i < n) && ((dr = divum(mod,w,f,q)) >= 0); i++ ) { - for ( j = dr; j >= 0; j-- ) - COEF(w)[j + mod] = c[j][i - 1] = COEF(w)[j]; - for ( j = mod - 1; j >= 0; j-- ) - COEF(w)[j] = 0; - DEG(w) = dr + mod; - } - for ( i = 1; i < n; i++ ) - c[i][i - 1] = ( c[i][i - 1] + mod - 1 ) % mod; - if ( ( dm = minimain(mod,n,n - 1,c) ) != -1 ) - for ( i = 0, ptr = COEF(fr), ptr[0] = 0; i <= dm; i++ ) - ptr[i + 1] = c[0][i]; - else - COEF(fr)[0] = 1; - DEG(fr) = dm + 1; + if ( n == 0 ) { + DEG(r) = 0; + COEF(r)[0][0] = 1; + } else if ( DEG(p) < 0 ) + DEG(r) = -1; + else if ( n == 1 ) + cpylum(bound,p,r); + else { + W_LUMALLOC(DEG(p)*n,bound,t); + pwrlum(mod,bound,p,n/2,t); + if ( !(n%2) ) + mullum(mod,bound,t,t,r); + else { + W_LUMALLOC(DEG(p)*n,bound,s); + mullum(mod,bound,t,t,s); + mullum(mod,bound,s,p,r); + } + } } -int minimain(mod,n,m,c) -register int mod; -int n,m; -register int **c; +int **almat(int n,int m) { - register int *ptr,*ci,*p; - register int i,l,a,j,b,inv; - int *tmp; + int **mat,i; - for ( j = 0; j < m; j++ ) { - for ( i = j; (n > i) && !c[i][j]; i++ ); - if ( i == n ) { - for ( i = j, j = j - 1; j >= 0; j-- ) - c[0][j] = c[j][i]; - c[0][i] = mod - 1; - return( i ); - } - if ( i != j ) { - tmp = c[i]; c[i] = c[j]; c[j] = tmp; - } - ptr = c[j]; inv = invm((ptr[j] + mod) % mod,mod); - for ( l = j, p = ptr+l; l < m; l++ ) { - a = (*p * inv) % mod; - *p++ = (a<0?a+mod:a); - } - for ( i = 0; i < n; i++ ) - if ( (a = -c[i][j]) && (i != j) ) { - for ( l = j+1, p = ptr+l, ci = c[i]+l; l < m; l++ ) { - b = (*p++ * a + *ci) % mod; - *ci++ = (b<0?b+mod:b); - } - c[i][j] = 0; - } - } - return (-1); + mat = (int **)MALLOC(n*sizeof(int *)); + for ( i = 0; i < n; i++ ) + mat[i] = (int *)CALLOC(m,sizeof(int)); + return mat; } -#if defined(__GNUC__) || defined(THINK_C) +void mini(int mod,UM f,UM fr) +{ + register int i,j,**c,*ptr; + int d,dr,dm,n; + UM w,q; + + n = DEG(f); c = (int **)ALLOCA(n*sizeof(int *)); + for ( i = 0; i < n; i++ ) { + c[i] = (int *)ALLOCA(n*sizeof(int)); + bzero((char *)c[i],(int)(n*sizeof(int))); + } + w = W_UMALLOC( mod + n + 10 ); q = W_UMALLOC( mod + n + 10 ); + for ( i = 1; ( d = ( mod * i ) ) < n; i++ ) c[d][i - 1] = 1; + DEG(w) = d; + for ( j = 0; j < d; j++ ) + COEF(w)[j] = 0; + COEF(w)[d] = 1; + for ( ; (i < n) && ((dr = divum(mod,w,f,q)) >= 0); i++ ) { + for ( j = dr; j >= 0; j-- ) + COEF(w)[j + mod] = c[j][i - 1] = COEF(w)[j]; + for ( j = mod - 1; j >= 0; j-- ) + COEF(w)[j] = 0; + DEG(w) = dr + mod; + } + for ( i = 1; i < n; i++ ) + c[i][i - 1] = ( c[i][i - 1] + mod - 1 ) % mod; + if ( ( dm = minimain(mod,n,n - 1,c) ) != -1 ) + for ( i = 0, ptr = COEF(fr), ptr[0] = 0; i <= dm; i++ ) + ptr[i + 1] = c[0][i]; + else + COEF(fr)[0] = 1; + DEG(fr) = dm + 1; +} + +int minimain(int mod,int n,int m,int **c) +{ + register int *ptr,*ci,*p; + register int i,l,a,j,b,inv; + int *tmp; + + for ( j = 0; j < m; j++ ) { + for ( i = j; (n > i) && !c[i][j]; i++ ); + if ( i == n ) { + for ( i = j, j = j - 1; j >= 0; j-- ) + c[0][j] = c[j][i]; + c[0][i] = mod - 1; + return( i ); + } + if ( i != j ) { + tmp = c[i]; c[i] = c[j]; c[j] = tmp; + } + ptr = c[j]; inv = invm((ptr[j] + mod) % mod,mod); + for ( l = j, p = ptr+l; l < m; l++ ) { + a = (*p * inv) % mod; + *p++ = (a<0?a+mod:a); + } + for ( i = 0; i < n; i++ ) + if ( (a = -c[i][j]) && (i != j) ) { + for ( l = j+1, p = ptr+l, ci = c[i]+l; l < m; l++ ) { + b = (*p++ * a + *ci) % mod; + *ci++ = (b<0?b+mod:b); + } + c[i][j] = 0; + } + } + return (-1); +} + +#if defined(__GNUC__) const #endif int sprime[] = { - 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47, - 53,59,61,67,71,73,79,83,89,97,101,103,107,109,113, - 127,131,137,139,149,151,157,163,167,173,179,181,191,193,197, - 199,211,223,227,229,233,239,241,251,257,263,269,271,277,281, - 283,293,307,311,313,317,331,337,347,349,353,359,367,373,379, - 383,389,397,401,409,419,421,431,433,439,443,449,457,461,463, - 467,479,487,491,499,503,509,521,523,541,547,557,563,569,571, - 577,587,593,599,601,607,613,617,619,631,641,643,647,653,659, - 661,673,677,683,691,701,709,719,727,733,739,743,751,757,761, - 769,773,787,797,809,811,821,823,827,829,839,853,857,859,863, - 877,881,883,887,907,911,919,929,937,941,947,953,967,971,977, - 983,991,997,1009,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063,1069, - 1087,1091,1093,1097,1103,1109,1117,1123,1129,1151,1153,1163,1171,1181,1187, - 1193,1201,1213,1217,1223,1229,1231,1237,1249,1259,1277,1279,1283,1289,1291, - 1297,1301,1303,1307,1319,1321,1327,1361,1367,1373,1381,1399,1409,1423,1427, - 1429,1433,1439,1447,1451,1453,1459,1471,1481,1483,1487,1489,1493,1499,1511, - 1523,1531,1543,1549,1553,1559,1567,1571,1579,1583,1597,1601,1607,1609,1613, - 1619,1621,1627,1637,1657,1663,1667,1669,1693,1697,1699,1709,1721,1723,1733, - 1741,1747,1753,1759,1777,1783,1787,1789,1801,1811,1823,1831,1847,1861,1867, - 1871,1873,1877,1879,1889,1901,1907,1913,1931,1933,1949,1951,1973,1979,1987, - 1993,1997,1999,2003,2011,2017,2027,2029,2039,2053,2063,2069,2081,2083,2087, - 2089,2099,2111,2113,2129,2131,2137,2141,2143,2153,2161,2179,2203,2207,2213, - 2221,2237,2239,2243,2251,2267,2269,2273,2281,2287,2293,2297,2309,2311,2333, - 2339,2341,2347,2351,2357,2371,2377,2381,2383,2389,2393,2399,2411,2417,2423, - 2437,2441,2447,2459,2467,2473,2477,2503,2521,2531,2539,2543,2549,2551,2557, - 2579,2591,2593,2609,2617,2621,2633,2647,2657,2659,2663,2671,2677,2683,2687, - 2689,2693,2699,2707,2711,2713,2719,2729,2731,2741,2749,2753,2767,2777,2789, - 2791,2797,2801,2803,2819,2833,2837,2843,2851,2857,2861,2879,2887,2897,2903, - 2909,2917,2927,2939,2953,2957,2963,2969,2971,2999,3001,3011,3019,3023,3037, - 3041,3049,3061,3067,3079,3083,3089,3109,3119,3121,3137,3163,3167,3169,3181, - 3187,3191,3203,3209,3217,3221,3229,3251,3253,3257,3259,3271,3299,3301,3307, - 3313,3319,3323,3329,3331,3343,3347,3359,3361,3371,3373,3389,3391,3407,3413, - 3433,3449,3457,3461,3463,3467,3469,3491,3499,3511,3517,3527,3529,3533,3539, - 3541,3547,3557,3559,3571,3581,3583,3593,3607,3613,3617,3623,3631,3637,3643, - 3659,3671,3673,3677,3691,3697,3701,3709,3719,3727,3733,3739,3761,3767,3769, - 3779,3793,3797,3803,3821,3823,3833,3847,3851,3853,3863,3877,3881,3889,3907, - 3911,3917,3919,3923,3929,3931,3943,3947,3967,3989,4001,4003,4007,4013,4019, - 4021,4027,4049,4051,4057,4073,4079,4091,4093,4099,4111,4127,4129,4133,4139, - 4153,4157,4159,4177,4201,4211,4217,4219,4229,4231,4241,4243,4253,4259,4261, - 4271,4273,4283,4289,4297,4327,4337,4339,4349,4357,4363,4373,4391,4397,4409, - 4421,4423,4441,4447,4451,4457,4463,4481,4483,4493,4507,4513,4517,4519,4523, - 4547,4549,4561,4567,4583,4591,4597,4603,4621,4637,4639,4643,4649,4651,4657, - 4663,4673,4679,4691,4703,4721,4723,4729,4733,4751,4759,4783,4787,4789,4793, - 4799,4801,4813,4817,4831,4861,4871,4877,4889,4903,4909,4919,4931,4933,4937, - 4943,4951,4957,4967,4969,4973,4987,4993,4999,5003,5009,5011,5021,5023,5039, - 5051,5059,5077,5081,5087,5099,5101,5107,5113,5119,5147,5153,5167,5171,5179, - 5189,5197,5209,5227,5231,5233,5237,5261,5273,5279,5281,5297,5303,5309,5323, - 5333,5347,5351,5381,5387,5393,5399,5407,5413,5417,5419,5431,5437,5441,5443, - 5449,5471,5477,5479,5483,5501,5503,5507,5519,5521,5527,5531,5557,5563,5569, - 5573,5581,5591,5623,5639,5641,5647,5651,5653,5657,5659,5669,5683,5689,5693, - 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8933,8941,8951,8963,8969,8971,8999,9001,9007,9011,9013,9029,9041,9043,9049, + 9059,9067,9091,9103,9109,9127,9133,9137,9151,9157,9161,9173,9181,9187,9199, + 9203,9209,9221,9227,9239,9241,9257,9277,9281,9283,9293,9311,9319,9323,9337, + 9341,9343,9349,9371,9377,9391,9397,9403,9413,9419,9421,9431,9433,9437,9439, + 9461,9463,9467,9473,9479,9491,9497,9511,9521,9533,9539,9547,9551,9587,9601, + 9613,9619,9623,9629,9631,9643,9649,9661,9677,9679,9689,9697,9719,9721,9733, + 9739,9743,9749,9767,9769,9781,9787,9791,9803,9811,9817,9829,9833,9839,9851, + 9857,9859,9871,9883,9887,9901,9907,9923,9929,9931,9941,9949,9967,9973,10007, + 10009,10037,10039,10061,10067,10069,10079,10091,10093,10099, + 10103,10111,10133,10139,10141,10151,10159,10163,10169,10177, + 10181,10193,10211,10223,10243,10247,10253,10259,10267,10271, + 10273,10289,10301,10303,10313,10321,10331,10333,10337,10343, + 10357,10369,10391,10399,10427,10429,10433,10453,10457,10459, + 10463,10477,10487,10499,10501,10513,10529,10531,10559,10567, + 10589,10597,10601,10607,10613,10627,10631,10639,10651,10657, + 10663,10667,10687,10691,10709,10711,10723,10729,10733,10739, + 10753,10771,10781,10789,10799,10831,10837,10847,10853,10859, + 10861,10867,10883,10889,10891,10903,10909,10937,10939,10949, + 10957,10973,10979,10987,10993,11003,11027,11047,11057,11059, + 11069,11071,11083,11087,11093,11113,11117,11119,11131,11149, + 11159,11161,11171,11173,11177,11197,11213,11239,11243,11251, + 11257,11261,11273,11279,11287,11299,11311,11317,11321,11329, + 11351,11353,11369,11383,11393,11399,11411,11423,11437,11443, + 11447,11467,11471,11483,11489,11491,11497,11503,11519,11527, + 11549,11551,11579,11587,11593,11597,11617,11621,11633,11657, + 11677,11681,11689,11699,11701,11717,11719,11731,11743,11777, + 11779,11783,11789,11801,11807,11813,11821,11827,11831,11833, + 11839,11863,11867,11887,11897,11903,11909,11923,11927,11933, + 11939,11941,11953,11959,11969,11971,11981,11987,12007,12011, + 12037,12041,12043,12049,12071,12073,12097,12101,12107,12109, + 12113,12119,12143,12149,12157,12161,12163,12197,12203,12211, + 12227,12239,12241,12251,12253,12263,12269,12277,12281,12289, + 12301,12323,12329,12343,12347,12373,12377,12379,12391,12401, + 12409,12413,12421,12433,12437,12451,12457,12473,12479,12487, + 12491,12497,12503,12511,12517,12527,12539,12541,12547,12553, + 12569,12577,12583,12589,12601,12611,12613,12619,12637,12641, + 12647,12653,12659,12671,12689,12697,12703,12713,12721,12739, + 12743,12757,12763,12781,12791,12799,12809,12821,12823,12829, + 12841,12853,12889,12893,12899,12907,12911,12917,12919,12923, + 12941,12953,12959,12967,12973,12979,12983,13001,13003,13007, + 13009,13033,13037,13043,13049,13063,13093,13099,13103,13109, + 13121,13127,13147,13151,13159,13163,13171,13177,13183,13187, + 13217,13219,13229,13241,13249,13259,13267,13291,13297,13309, + 13313,13327,13331,13337,13339,13367,13381,13397,13399,13411, + 13417,13421,13441,13451,13457,13463,13469,13477,13487,13499, + 13513,13523,13537,13553,13567,13577,13591,13597,13613,13619, + 13627,13633,13649,13669,13679,13681,13687,13691,13693,13697, + 13709,13711,13721,13723,13729,13751,13757,13759,13763,13781, + 13789,13799,13807,13829,13831,13841,13859,13873,13877,13879, + 13883,13901,13903,13907,13913,13921,13931,13933,13963,13967, + 13997,13999,14009,14011,14029,14033,14051,14057,14071,14081, + 14083,14087,14107,14143,14149,14153,14159,14173,14177,14197, + 14207,14221,14243,14249,14251,14281,14293,14303,14321,14323, + 14327,14341,14347,14369,14387,14389,14401,14407,14411,14419, + 14423,14431,14437,14447,14449,14461,14479,14489,14503,14519, + 14533,14537,14543,14549,14551,14557,14561,14563,14591,14593, + 14621,14627,14629,14633,14639,14653,14657,14669,14683,14699, + 14713,14717,14723,14731,14737,14741,14747,14753,14759,14767, + 14771,14779,14783,14797,14813,14821,14827,14831,14843,14851, + 14867,14869,14879,14887,14891,14897,14923,14929,14939,14947, + 14951,14957,14969,14983,15013,15017,15031,15053,15061,15073, + 15077,15083,15091,15101,15107,15121,15131,15137,15139,15149, + 15161,15173,15187,15193,15199,15217,15227,15233,15241,15259, + 15263,15269,15271,15277,15287,15289,15299,15307,15313,15319, + 15329,15331,15349,15359,15361,15373,15377,15383,15391,15401, + 15413,15427,15439,15443,15451,15461,15467,15473,15493,15497, + 15511,15527,15541,15551,15559,15569,15581,15583,15601,15607, + 15619,15629,15641,15643,15647,15649,15661,15667,15671,15679, + 15683,15727,15731,15733,15737,15739,15749,15761,15767,15773, + 15787,15791,15797,15803,15809,15817,15823,15859,15877,15881, + 15887,15889,15901,15907,15913,15919,15923,15937,15959,15971, + 15973,15991,16001,16007,16033,16057,16061,16063,16067,16069, + 16073,16087,16091,16097,16103,16111,16127,16139,16141,16183, + 16187,16189,16193,16217,16223,16229,16231,16249,16253,16267, + 16273,16301,16319,16333,16339,16349,16361,16363,16369,16381, + 0 }; - -#include "prime.h"