Annotation of OpenXM_contrib2/asir2000/engine/M.c, Revision 1.1
1.1 ! noro 1: /* $OpenXM: OpenXM/src/asir99/engine/M.c,v 1.1.1.1 1999/11/10 08:12:26 noro Exp $ */
! 2: #include "ca.h"
! 3: #include "base.h"
! 4:
! 5: void addum(mod,p1,p2,pr)
! 6: int mod;
! 7: UM p1,p2,pr;
! 8: {
! 9: register int *c1,*c2,*cr,i,dmax,dmin;
! 10:
! 11: if ( DEG(p1) == -1 ) {
! 12: cpyum(p2,pr);
! 13: return;
! 14: }
! 15: if ( DEG(p2) == -1 ) {
! 16: cpyum(p1,pr);
! 17: return;
! 18: }
! 19: if ( DEG(p1) >= DEG(p2) ) {
! 20: c1 = COEF(p1); c2 = COEF(p2); dmax = DEG(p1); dmin = DEG(p2);
! 21: } else {
! 22: c1 = COEF(p2); c2 = COEF(p1); dmax = DEG(p2); dmin = DEG(p1);
! 23: }
! 24: for ( i = 0, cr = COEF(pr); i <= dmin; i++ )
! 25: cr[i] = ( c1[i] + c2[i] ) % mod;
! 26: for ( ; i <= dmax; i++ )
! 27: cr[i] = c1[i];
! 28: if ( dmax == dmin )
! 29: degum(pr,dmax);
! 30: else
! 31: DEG(pr) = dmax;
! 32: }
! 33:
! 34: void subum(mod,p1,p2,pr)
! 35: int mod;
! 36: UM p1,p2,pr;
! 37: {
! 38: register int *c1,*c2,*cr,i;
! 39: int dmax,dmin;
! 40:
! 41: if ( DEG(p1) == -1 ) {
! 42: for ( i = DEG(pr) = DEG(p2), c2 = COEF(p2), cr = COEF(pr);
! 43: i >= 0; i-- )
! 44: cr[i] = ( mod - c2[i] ) % mod;
! 45: return;
! 46: }
! 47: if ( DEG(p2) == -1 ) {
! 48: cpyum(p1,pr);
! 49: return;
! 50: }
! 51: c1 = COEF(p1); c2 = COEF(p2); cr = COEF(pr);
! 52: if ( DEG(p1) >= DEG(p2) ) {
! 53: dmax = DEG(p1); dmin = DEG(p2);
! 54: for ( i = 0; i <= dmin; i++ )
! 55: cr[i] = ( c1[i] + mod - c2[i] ) % mod;
! 56: for ( ; i <= dmax; i++ )
! 57: cr[i] = c1[i];
! 58: } else {
! 59: dmax = DEG(p2); dmin = DEG(p1);
! 60: for ( i = 0; i <= dmin; i++ )
! 61: cr[i] = ( c1[i] + mod - c2[i] ) % mod;
! 62: for ( ; i <= dmax; i++ )
! 63: cr[i] = ( mod - c2[i] ) % mod;
! 64: }
! 65: if ( dmax == dmin )
! 66: degum(pr,dmax);
! 67: else
! 68: DEG(pr) = dmax;
! 69: }
! 70:
! 71: void pwrum(mod,p,e,pr)
! 72: int mod,e;
! 73: UM p,pr;
! 74: {
! 75: UM wt,ws;
! 76:
! 77: if ( e == 0 ) {
! 78: DEG(pr) = 0; COEF(pr)[0] = 1;
! 79: } else if ( DEG(p) < 0 )
! 80: DEG(pr) = -1;
! 81: else if ( e == 1 )
! 82: cpyum(p,pr);
! 83: else if ( DEG(p) == 0 ) {
! 84: DEG(pr) = 0; COEF(pr)[0] = pwrm(mod,COEF(p)[0],e);
! 85: } else {
! 86: wt = W_UMALLOC(DEG(p)*e); ws = W_UMALLOC(DEG(p)*e);
! 87: pwrum(mod,p,e/2,wt);
! 88: if ( !(e%2) )
! 89: mulum(mod,wt,wt,pr);
! 90: else {
! 91: mulum(mod,wt,wt,ws); mulum(mod,ws,p,pr);
! 92: }
! 93: }
! 94: }
! 95:
! 96: void gcdum(mod,p1,p2,pr)
! 97: register int mod;
! 98: UM p1,p2,pr;
! 99: {
! 100: register int inv;
! 101: UM t1,t2,q,tum;
! 102: int drem;
! 103:
! 104: if ( DEG(p1) < 0 )
! 105: cpyum(p2,pr);
! 106: else if ( DEG(p2) < 0 )
! 107: cpyum(p1,pr);
! 108: else {
! 109: if ( DEG(p1) >= DEG(p2) ) {
! 110: t1 = p1; t2 = p2;
! 111: } else {
! 112: t1 = p2; t2 = p1;
! 113: }
! 114: q = W_UMALLOC(DEG(t1));
! 115: while ( ( drem = divum(mod,t1,t2,q) ) >= 0 ) {
! 116: tum = t1; t1 = t2; t2 = tum; DEG(t2) = drem;
! 117: }
! 118: inv = invm(COEF(t2)[DEG(t2)],mod);
! 119: mulsum(mod,t2,inv,pr);
! 120: }
! 121: }
! 122:
! 123: void eucum(mod,f1,f2,a,b)
! 124: register int mod;
! 125: UM f1,f2,a,b;
! 126: {
! 127: UM g1,g2,a1,a2,a3,wm,q,tum;
! 128: int d,dr;
! 129:
! 130: d = DEG(f1) + DEG(f2) + 10;
! 131: g1 = W_UMALLOC(d); g2 = W_UMALLOC(d); a1 = W_UMALLOC(d);
! 132: a2 = W_UMALLOC(d); a3 = W_UMALLOC(d); wm = W_UMALLOC(d);
! 133: q = W_UMALLOC(d);
! 134: DEG(a1) = 0; COEF(a1)[0] = 1; DEG(a2) = -1;
! 135: cpyum(f1,g1); cpyum(f2,g2);
! 136: while ( 1 ) {
! 137: dr = divum(mod,g1,g2,q); tum = g1; g1 = g2; g2 = tum;
! 138: if ( ( DEG(g2) = dr ) == -1 )
! 139: break;
! 140: mulum(mod,a2,q,wm); subum(mod,a1,wm,a3); dr = divum(mod,a3,f2,q);
! 141: tum = a1; a1 = a2; a2 = a3; a3 = tum; DEG(a3) = dr;
! 142: }
! 143: if ( COEF(g1)[0] != 1 )
! 144: mulsum(mod,a2,invm(COEF(g1)[0],mod),a);
! 145: else
! 146: cpyum(a2,a);
! 147: mulum(mod,a,f1,wm);
! 148: if ( DEG(wm) >= 0 )
! 149: COEF(wm)[0] = ( COEF(wm)[0] + mod - 1 ) % mod;
! 150: else {
! 151: DEG(wm) = 0; COEF(wm)[0] = mod - 1;
! 152: }
! 153: divum(mod,wm,f2,q); mulsum(mod,q,mod-1,b);
! 154: }
! 155:
! 156: void sqfrum(index,count,f,nindex,dcr,pl)
! 157: int index,count,*nindex;
! 158: P f;
! 159: struct oDUM **dcr;
! 160: ML *pl;
! 161: {
! 162: int i,j,m,n,d,dt,mod;
! 163: UM wf,wdf,ws,wt,wgcd,mf,mgcd;
! 164: UM *l;
! 165: struct oDUM *dc;
! 166: ML tp;
! 167:
! 168: n = UDEG(f);
! 169: wf = W_UMALLOC(n);
! 170: wdf = W_UMALLOC(n);
! 171: ws = W_UMALLOC(n);
! 172: wt = W_UMALLOC(n);
! 173: wgcd = W_UMALLOC(n);
! 174:
! 175: mf = W_UMALLOC(n);
! 176: mgcd = W_UMALLOC(n);
! 177:
! 178: for ( j = 0, d = n; j < count && d; ) {
! 179: m = lprime[index++];
! 180: if ( !m )
! 181: error("sqfrum : lprime[] exhausted.");
! 182: if ( rem(NM((Q)COEF(DC(f))),m) == 0 ) continue;
! 183:
! 184: ptoum(m,f,wf);
! 185: diffum(m,wf,wdf);
! 186: cpyum(wf,wt); cpyum(wdf,ws);
! 187: gcdum(m,wt,ws,wgcd);
! 188: dt = DEG(wgcd);
! 189:
! 190: if ( dt < d ) {
! 191: d = dt;
! 192: mod = m;
! 193: cpyum(wf,mf); cpyum(wgcd,mgcd);
! 194: }
! 195: j++;
! 196: }
! 197: *nindex = index;
! 198:
! 199: sqfrummain(mod,mf,mgcd,&dc);
! 200: *dcr = dc;
! 201:
! 202: for ( n = 0; dc[n].f; n++ );
! 203: *pl = tp = MLALLOC(n+1);
! 204: tp->n = n;
! 205: tp->mod = mod;
! 206:
! 207: for ( i = 0, l = (UM *)COEF(tp); dc[i].f; i++ ) {
! 208: l[i] = UMALLOC(DEG(dc[i].f)*dc[i].n);
! 209: pwrum(mod,dc[i].f,dc[i].n,l[i]);
! 210: }
! 211: l[i] = 0;
! 212: }
! 213:
! 214: void sqfrummain(mod,p,gcd,dcp)
! 215: int mod;
! 216: UM p,gcd;
! 217: struct oDUM **dcp;
! 218: {
! 219: int i,j,n;
! 220: UM wp,wdp,wc,wd,ws,wt,wq;
! 221: struct oDUM *dc;
! 222: UM *f;
! 223:
! 224: i = DEG(p);
! 225:
! 226: wp = W_UMALLOC(i);
! 227: wdp = W_UMALLOC(i);
! 228: wt = W_UMALLOC(i);
! 229: ws = W_UMALLOC(i);
! 230: wc = W_UMALLOC(i);
! 231: wd = W_UMALLOC(i);
! 232: wq = W_UMALLOC(i);
! 233:
! 234: f = (UM *) ALLOCA((i+2)*sizeof(UM));
! 235:
! 236: cpyum(p,wp);
! 237: diffum(mod,wp,wdp);
! 238:
! 239: cpyum(wp,wt);
! 240: divum(mod,wt,gcd,wc);
! 241:
! 242: cpyum(wdp,wt);
! 243: divum(mod,wt,gcd,ws);
! 244:
! 245: diffum(mod,wc,wt);
! 246: subum(mod,ws,wt,wd);
! 247:
! 248: for ( i = 1; DEG(wd) >= 0; i++ ) {
! 249: cpyum(wc,ws); cpyum(wd,wt);
! 250: gcdum(mod,ws,wt,wq);
! 251: if ( DEG(wq) > 0 ) {
! 252: f[i] = UMALLOC(DEG(wq));
! 253: cpyum(wq,f[i]);
! 254:
! 255: cpyum(wc,ws);
! 256: divum(mod,ws,f[i],wc);
! 257: divum(mod,wd,f[i],ws);
! 258: diffum(mod,wc,wt);
! 259: subum(mod,ws,wt,wd);
! 260: } else {
! 261: f[i] = 0;
! 262: cpyum(wd,ws);
! 263: diffum(mod,wc,wt);
! 264: subum(mod,ws,wt,wd);
! 265: }
! 266:
! 267: }
! 268:
! 269: if ( DEG(wc) > 0 ) {
! 270: DEG(wq) = 0;
! 271: COEF(wq)[0] = invm(COEF(wc)[DEG(wc)],mod);
! 272: f[i] = UMALLOC(DEG(wc));
! 273: mulum(mod,wc,wq,f[i]);
! 274: f[i+1] = 0;
! 275: n = i + 1;
! 276: } else {
! 277: f[i] = 0;
! 278: n = i;
! 279: }
! 280:
! 281: for ( i = 1, j = 0; i < n; i++ )
! 282: if ( f[i] ) j++;
! 283:
! 284: *dcp = dc = (struct oDUM *) CALLOC(j+1,sizeof(struct oDUM));
! 285:
! 286: for ( i = 1, j = 0; i < n; i++ )
! 287: if ( f[i] ) {
! 288: dc[j].n = i;
! 289: dc[j].f = f[i];
! 290: j++;
! 291: }
! 292: dc[j].n = 0;
! 293: dc[j].f = 0;
! 294: }
! 295:
! 296: void cpyum(p1,p2)
! 297: UM p1,p2;
! 298: {
! 299: register int *c1,*c2,i;
! 300:
! 301: for ( i = DEG(p2) = DEG(p1), c1 = COEF(p1), c2 = COEF(p2);
! 302: i >= 0; i-- )
! 303: c2[i] = c1[i];
! 304: }
! 305:
! 306: void degum(f,n)
! 307: UM f;
! 308: int n;
! 309: {
! 310: register int i,*c;
! 311:
! 312: for ( i = n, c = COEF(f); ( i >= 0 ) && ( c[i] == 0 ); i-- );
! 313: DEG(f) = i;
! 314: }
! 315:
! 316: int deg(v,p)
! 317: V v;
! 318: P p;
! 319: {
! 320: if ( !p )
! 321: return ( -1 );
! 322: else if ( NUM(p) )
! 323: return ( 0 );
! 324: else if ( VR(p) != v )
! 325: return ( 0 );
! 326: else if ( PL(NM(DEG(DC(p)))) > 1 ) {
! 327: error("degree too large");
! 328: return ( -1 );
! 329: } else
! 330: return ( UDEG(p) );
! 331: }
! 332:
! 333: LUM LUMALLOC(n,bound)
! 334: int n,bound;
! 335: {
! 336: LUM p;
! 337: int **c;
! 338: int i;
! 339:
! 340: p = (LUM)MALLOC(TRUESIZE(oLUM,n,int *));
! 341: DEG(p) = n;
! 342: for ( i = 0, c = (int **)COEF(p); i <= n; i++ ) {
! 343: c[i] = (int *)MALLOC_ATOMIC((bound+1)*sizeof(int));
! 344: bzero((char *)c[i],(bound+1)*sizeof(int));
! 345: }
! 346: return p;
! 347: }
! 348:
! 349: void mullum(mod,n,f1,f2,fr)
! 350: int mod,n;
! 351: LUM f1,f2,fr;
! 352: {
! 353: int max;
! 354: register int i,j,**p1,**p2,*px;
! 355: int *w,*w1,*w2;
! 356:
! 357: p1 = (int **)COEF(f1); p2 = (int **)COEF(f2);
! 358: w = W_ALLOC(2*(n+1)); w1 = W_ALLOC(DEG(f1)); w2 = W_ALLOC(DEG(f2));
! 359: for ( i = DEG(f1); i >= 0; i-- ) {
! 360: for ( j = n - 1, px = p1[i]; ( j >= 0 ) && ( px[j] == 0 ); j-- );
! 361: w1[i] = ( j == -1 ? 0 : 1 );
! 362: }
! 363: for ( i = DEG(f2); i >= 0; i-- ) {
! 364: for ( j = n - 1, px = p2[i]; ( j >= 0 ) && ( px[j] == 0 ); j-- );
! 365: w2[i] = ( j == -1 ? 0 : 1 );
! 366: }
! 367: for ( j = DEG(fr) = DEG(f1) + DEG(f2); j >= 0; j-- ) {
! 368: for ( i = n - 1, px = COEF(fr)[j]; i >= 0; i-- )
! 369: px[i] = 0;
! 370: for ( max = MIN(DEG(f1),j), i = MAX(0,j-DEG(f2)); i <= max; i++ )
! 371: if ( w1[i] != 0 && w2[j - i] != 0 ) {
! 372: mulpadic(mod,n,p1[i],p2[j - i],w); addpadic(mod,n,w,px);
! 373: }
! 374: }
! 375: }
! 376:
! 377: void cpylum(bound,p,r)
! 378: int bound;
! 379: LUM p,r;
! 380: {
! 381: register int i,j;
! 382: register int **pp,**ppr;
! 383:
! 384: DEG(r) = DEG(p);
! 385: for ( i = 0, pp = COEF(p), ppr = COEF(r);
! 386: i <= DEG(p); i++ )
! 387: for ( j = 0; j < bound; j++ )
! 388: ppr[i][j] = pp[i][j];
! 389: }
! 390:
! 391: void pwrlum(mod,bound,p,n,r)
! 392: int mod,bound,n;
! 393: LUM p,r;
! 394: {
! 395: LUM t,s;
! 396:
! 397: if ( n == 0 ) {
! 398: DEG(r) = 0;
! 399: COEF(r)[0][0] = 1;
! 400: } else if ( DEG(p) < 0 )
! 401: DEG(r) = -1;
! 402: else if ( n == 1 )
! 403: cpylum(bound,p,r);
! 404: else {
! 405: W_LUMALLOC(DEG(p)*n,bound,t);
! 406: pwrlum(mod,bound,p,n/2,t);
! 407: if ( !(n%2) )
! 408: mullum(mod,bound,t,t,r);
! 409: else {
! 410: W_LUMALLOC(DEG(p)*n,bound,s);
! 411: mullum(mod,bound,t,t,s);
! 412: mullum(mod,bound,s,p,r);
! 413: }
! 414: }
! 415: }
! 416:
! 417: int **almat(n,m)
! 418: int n,m;
! 419: {
! 420: int **mat,i;
! 421:
! 422: mat = (int **)MALLOC(n*sizeof(int *));
! 423: for ( i = 0; i < n; i++ )
! 424: mat[i] = (int *)CALLOC(m,sizeof(int));
! 425: return mat;
! 426: }
! 427:
! 428: void mini(mod,f,fr)
! 429: register int mod;
! 430: UM f,fr;
! 431: {
! 432: register int i,j,**c,*ptr;
! 433: int d,dr,dm,n;
! 434: UM w,q;
! 435:
! 436: n = DEG(f); c = (int **)ALLOCA(n*sizeof(int *));
! 437: for ( i = 0; i < n; i++ ) {
! 438: c[i] = (int *)ALLOCA(n*sizeof(int));
! 439: bzero((char *)c[i],(int)(n*sizeof(int)));
! 440: }
! 441: w = W_UMALLOC( mod + n + 10 ); q = W_UMALLOC( mod + n + 10 );
! 442: for ( i = 1; ( d = ( mod * i ) ) < n; i++ ) c[d][i - 1] = 1;
! 443: DEG(w) = d;
! 444: for ( j = 0; j < d; j++ )
! 445: COEF(w)[j] = 0;
! 446: COEF(w)[d] = 1;
! 447: for ( ; (i < n) && ((dr = divum(mod,w,f,q)) >= 0); i++ ) {
! 448: for ( j = dr; j >= 0; j-- )
! 449: COEF(w)[j + mod] = c[j][i - 1] = COEF(w)[j];
! 450: for ( j = mod - 1; j >= 0; j-- )
! 451: COEF(w)[j] = 0;
! 452: DEG(w) = dr + mod;
! 453: }
! 454: for ( i = 1; i < n; i++ )
! 455: c[i][i - 1] = ( c[i][i - 1] + mod - 1 ) % mod;
! 456: if ( ( dm = minimain(mod,n,n - 1,c) ) != -1 )
! 457: for ( i = 0, ptr = COEF(fr), ptr[0] = 0; i <= dm; i++ )
! 458: ptr[i + 1] = c[0][i];
! 459: else
! 460: COEF(fr)[0] = 1;
! 461: DEG(fr) = dm + 1;
! 462: }
! 463:
! 464: int minimain(mod,n,m,c)
! 465: register int mod;
! 466: int n,m;
! 467: register int **c;
! 468: {
! 469: register int *ptr,*ci,*p;
! 470: register int i,l,a,j,b,inv;
! 471: int *tmp;
! 472:
! 473: for ( j = 0; j < m; j++ ) {
! 474: for ( i = j; (n > i) && !c[i][j]; i++ );
! 475: if ( i == n ) {
! 476: for ( i = j, j = j - 1; j >= 0; j-- )
! 477: c[0][j] = c[j][i];
! 478: c[0][i] = mod - 1;
! 479: return( i );
! 480: }
! 481: if ( i != j ) {
! 482: tmp = c[i]; c[i] = c[j]; c[j] = tmp;
! 483: }
! 484: ptr = c[j]; inv = invm((ptr[j] + mod) % mod,mod);
! 485: for ( l = j, p = ptr+l; l < m; l++ ) {
! 486: a = (*p * inv) % mod;
! 487: *p++ = (a<0?a+mod:a);
! 488: }
! 489: for ( i = 0; i < n; i++ )
! 490: if ( (a = -c[i][j]) && (i != j) ) {
! 491: for ( l = j+1, p = ptr+l, ci = c[i]+l; l < m; l++ ) {
! 492: b = (*p++ * a + *ci) % mod;
! 493: *ci++ = (b<0?b+mod:b);
! 494: }
! 495: c[i][j] = 0;
! 496: }
! 497: }
! 498: return (-1);
! 499: }
! 500:
! 501: #if defined(__GNUC__) || defined(THINK_C)
! 502: const
! 503: #endif
! 504: int sprime[] = {
! 505: 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,
! 506: 53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,
! 507: 127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,
! 508: 199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,
! 509: 283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,
! 510: 383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,
! 511: 467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,
! 512: 577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,
! 513: 661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,
! 514: 769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,
! 515: 877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,
! 516: 983,991,997,1009,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063,1069,
! 517: 1087,1091,1093,1097,1103,1109,1117,1123,1129,1151,1153,1163,1171,1181,1187,
! 518: 1193,1201,1213,1217,1223,1229,1231,1237,1249,1259,1277,1279,1283,1289,1291,
! 519: 1297,1301,1303,1307,1319,1321,1327,1361,1367,1373,1381,1399,1409,1423,1427,
! 520: 1429,1433,1439,1447,1451,1453,1459,1471,1481,1483,1487,1489,1493,1499,1511,
! 521: 1523,1531,1543,1549,1553,1559,1567,1571,1579,1583,1597,1601,1607,1609,1613,
! 522: 1619,1621,1627,1637,1657,1663,1667,1669,1693,1697,1699,1709,1721,1723,1733,
! 523: 1741,1747,1753,1759,1777,1783,1787,1789,1801,1811,1823,1831,1847,1861,1867,
! 524: 1871,1873,1877,1879,1889,1901,1907,1913,1931,1933,1949,1951,1973,1979,1987,
! 525: 1993,1997,1999,2003,2011,2017,2027,2029,2039,2053,2063,2069,2081,2083,2087,
! 526: 2089,2099,2111,2113,2129,2131,2137,2141,2143,2153,2161,2179,2203,2207,2213,
! 527: 2221,2237,2239,2243,2251,2267,2269,2273,2281,2287,2293,2297,2309,2311,2333,
! 528: 2339,2341,2347,2351,2357,2371,2377,2381,2383,2389,2393,2399,2411,2417,2423,
! 529: 2437,2441,2447,2459,2467,2473,2477,2503,2521,2531,2539,2543,2549,2551,2557,
! 530: 2579,2591,2593,2609,2617,2621,2633,2647,2657,2659,2663,2671,2677,2683,2687,
! 531: 2689,2693,2699,2707,2711,2713,2719,2729,2731,2741,2749,2753,2767,2777,2789,
! 532: 2791,2797,2801,2803,2819,2833,2837,2843,2851,2857,2861,2879,2887,2897,2903,
! 533: 2909,2917,2927,2939,2953,2957,2963,2969,2971,2999,3001,3011,3019,3023,3037,
! 534: 3041,3049,3061,3067,3079,3083,3089,3109,3119,3121,3137,3163,3167,3169,3181,
! 535: 3187,3191,3203,3209,3217,3221,3229,3251,3253,3257,3259,3271,3299,3301,3307,
! 536: 3313,3319,3323,3329,3331,3343,3347,3359,3361,3371,3373,3389,3391,3407,3413,
! 537: 3433,3449,3457,3461,3463,3467,3469,3491,3499,3511,3517,3527,3529,3533,3539,
! 538: 3541,3547,3557,3559,3571,3581,3583,3593,3607,3613,3617,3623,3631,3637,3643,
! 539: 3659,3671,3673,3677,3691,3697,3701,3709,3719,3727,3733,3739,3761,3767,3769,
! 540: 3779,3793,3797,3803,3821,3823,3833,3847,3851,3853,3863,3877,3881,3889,3907,
! 541: 3911,3917,3919,3923,3929,3931,3943,3947,3967,3989,4001,4003,4007,4013,4019,
! 542: 4021,4027,4049,4051,4057,4073,4079,4091,4093,4099,4111,4127,4129,4133,4139,
! 543: 4153,4157,4159,4177,4201,4211,4217,4219,4229,4231,4241,4243,4253,4259,4261,
! 544: 4271,4273,4283,4289,4297,4327,4337,4339,4349,4357,4363,4373,4391,4397,4409,
! 545: 4421,4423,4441,4447,4451,4457,4463,4481,4483,4493,4507,4513,4517,4519,4523,
! 546: 4547,4549,4561,4567,4583,4591,4597,4603,4621,4637,4639,4643,4649,4651,4657,
! 547: 4663,4673,4679,4691,4703,4721,4723,4729,4733,4751,4759,4783,4787,4789,4793,
! 548: 4799,4801,4813,4817,4831,4861,4871,4877,4889,4903,4909,4919,4931,4933,4937,
! 549: 4943,4951,4957,4967,4969,4973,4987,4993,4999,5003,5009,5011,5021,5023,5039,
! 550: 5051,5059,5077,5081,5087,5099,5101,5107,5113,5119,5147,5153,5167,5171,5179,
! 551: 5189,5197,5209,5227,5231,5233,5237,5261,5273,5279,5281,5297,5303,5309,5323,
! 552: 5333,5347,5351,5381,5387,5393,5399,5407,5413,5417,5419,5431,5437,5441,5443,
! 553: 5449,5471,5477,5479,5483,5501,5503,5507,5519,5521,5527,5531,5557,5563,5569,
! 554: 5573,5581,5591,5623,5639,5641,5647,5651,5653,5657,5659,5669,5683,5689,5693,
! 555: 5701,5711,5717,5737,5741,5743,5749,5779,5783,5791,5801,5807,5813,5821,5827,
! 556: 5839,5843,5849,5851,5857,5861,5867,5869,5879,5881,5897,5903,5923,5927,5939,
! 557: 5953,5981,5987,6007,6011,6029,6037,6043,6047,6053,6067,6073,6079,6089,6091,
! 558: 6101,6113,6121,6131,6133,6143,6151,6163,6173,6197,6199,6203,6211,6217,6221,
! 559: 6229,6247,6257,6263,6269,6271,6277,6287,6299,6301,6311,6317,6323,6329,6337,
! 560: 6343,6353,6359,6361,6367,6373,6379,6389,6397,6421,6427,6449,6451,6469,6473,
! 561: 6481,6491,6521,6529,6547,6551,6553,6563,6569,6571,6577,6581,6599,6607,6619,
! 562: 6637,6653,6659,6661,6673,6679,6689,6691,6701,6703,6709,6719,6733,6737,6761,
! 563: 6763,6779,6781,6791,6793,6803,6823,6827,6829,6833,6841,6857,6863,6869,6871,
! 564: 6883,6899,6907,6911,6917,6947,6949,6959,6961,6967,6971,6977,6983,6991,6997,
! 565: 7001,7013,7019,7027,7039,7043,7057,7069,7079,7103,7109,7121,7127,7129,7151,
! 566: 7159,7177,7187,7193,7207,7211,7213,7219,7229,7237,7243,7247,7253,7283,7297,
! 567: 7307,7309,7321,7331,7333,7349,7351,7369,7393,7411,7417,7433,7451,7457,7459,
! 568: 7477,7481,7487,7489,7499,7507,7517,7523,7529,7537,7541,7547,7549,7559,7561,
! 569: 7573,7577,7583,7589,7591,7603,7607,7621,7639,7643,7649,7669,7673,7681,7687,
! 570: 7691,7699,7703,7717,7723,7727,7741,7753,7757,7759,7789,7793,7817,7823,7829,
! 571: 7841,7853,7867,7873,7877,7879,7883,7901,7907,7919,7927,7933,7937,7949,7951,
! 572: 7963,7993,8009,8011,8017,8039,8053,8059,8069,8081,8087,8089,8093,8101,8111,
! 573: 8117,8123,8147,8161,8167,8171,8179,8191,8209,8219,8221,8231,8233,8237,8243,
! 574: 8263,8269,8273,8287,8291,8293,8297,8311,8317,8329,8353,8363,8369,8377,8387,
! 575: 8389,8419,8423,8429,8431,8443,8447,8461,8467,8501,8513,8521,8527,8537,8539,
! 576: 8543,8563,8573,8581,8597,8599,8609,8623,8627,8629,8641,8647,8663,8669,8677,
! 577: 8681,8689,8693,8699,8707,8713,8719,8731,8737,8741,8747,8753,8761,8779,8783,
! 578: 8803,8807,8819,8821,8831,8837,8839,8849,8861,8863,8867,8887,8893,8923,8929,
! 579: 8933,8941,8951,8963,8969,8971,8999,9001,9007,9011,9013,9029,9041,9043,9049,
! 580: 9059,9067,9091,9103,9109,9127,9133,9137,9151,9157,9161,9173,9181,9187,9199,
! 581: 9203,9209,9221,9227,9239,9241,9257,9277,9281,9283,9293,9311,9319,9323,9337,
! 582: 9341,9343,9349,9371,9377,9391,9397,9403,9413,9419,9421,9431,9433,9437,9439,
! 583: 9461,9463,9467,9473,9479,9491,9497,9511,9521,9533,9539,9547,9551,9587,9601,
! 584: 9613,9619,9623,9629,9631,9643,9649,9661,9677,9679,9689,9697,9719,9721,9733,
! 585: 9739,9743,9749,9767,9769,9781,9787,9791,9803,9811,9817,9829,9833,9839,9851,
! 586: 9857,9859,9871,9883,9887,9901,9907,9923,9929,9931,9941,9949,9967,9973,10007,
! 587: 10009,10037,10039,10061,10067,10069,10079,10091,10093,10099,
! 588: 10103,10111,10133,10139,10141,10151,10159,10163,10169,10177,
! 589: 10181,10193,10211,10223,10243,10247,10253,10259,10267,10271,
! 590: 10273,10289,10301,10303,10313,10321,10331,10333,10337,10343,
! 591: 10357,10369,10391,10399,10427,10429,10433,10453,10457,10459,
! 592: 10463,10477,10487,10499,10501,10513,10529,10531,10559,10567,
! 593: 10589,10597,10601,10607,10613,10627,10631,10639,10651,10657,
! 594: 10663,10667,10687,10691,10709,10711,10723,10729,10733,10739,
! 595: 10753,10771,10781,10789,10799,10831,10837,10847,10853,10859,
! 596: 10861,10867,10883,10889,10891,10903,10909,10937,10939,10949,
! 597: 10957,10973,10979,10987,10993,11003,11027,11047,11057,11059,
! 598: 11069,11071,11083,11087,11093,11113,11117,11119,11131,11149,
! 599: 11159,11161,11171,11173,11177,11197,11213,11239,11243,11251,
! 600: 11257,11261,11273,11279,11287,11299,11311,11317,11321,11329,
! 601: 11351,11353,11369,11383,11393,11399,11411,11423,11437,11443,
! 602: 11447,11467,11471,11483,11489,11491,11497,11503,11519,11527,
! 603: 11549,11551,11579,11587,11593,11597,11617,11621,11633,11657,
! 604: 11677,11681,11689,11699,11701,11717,11719,11731,11743,11777,
! 605: 11779,11783,11789,11801,11807,11813,11821,11827,11831,11833,
! 606: 11839,11863,11867,11887,11897,11903,11909,11923,11927,11933,
! 607: 11939,11941,11953,11959,11969,11971,11981,11987,12007,12011,
! 608: 12037,12041,12043,12049,12071,12073,12097,12101,12107,12109,
! 609: 12113,12119,12143,12149,12157,12161,12163,12197,12203,12211,
! 610: 12227,12239,12241,12251,12253,12263,12269,12277,12281,12289,
! 611: 12301,12323,12329,12343,12347,12373,12377,12379,12391,12401,
! 612: 12409,12413,12421,12433,12437,12451,12457,12473,12479,12487,
! 613: 12491,12497,12503,12511,12517,12527,12539,12541,12547,12553,
! 614: 12569,12577,12583,12589,12601,12611,12613,12619,12637,12641,
! 615: 12647,12653,12659,12671,12689,12697,12703,12713,12721,12739,
! 616: 12743,12757,12763,12781,12791,12799,12809,12821,12823,12829,
! 617: 12841,12853,12889,12893,12899,12907,12911,12917,12919,12923,
! 618: 12941,12953,12959,12967,12973,12979,12983,13001,13003,13007,
! 619: 13009,13033,13037,13043,13049,13063,13093,13099,13103,13109,
! 620: 13121,13127,13147,13151,13159,13163,13171,13177,13183,13187,
! 621: 13217,13219,13229,13241,13249,13259,13267,13291,13297,13309,
! 622: 13313,13327,13331,13337,13339,13367,13381,13397,13399,13411,
! 623: 13417,13421,13441,13451,13457,13463,13469,13477,13487,13499,
! 624: 13513,13523,13537,13553,13567,13577,13591,13597,13613,13619,
! 625: 13627,13633,13649,13669,13679,13681,13687,13691,13693,13697,
! 626: 13709,13711,13721,13723,13729,13751,13757,13759,13763,13781,
! 627: 13789,13799,13807,13829,13831,13841,13859,13873,13877,13879,
! 628: 13883,13901,13903,13907,13913,13921,13931,13933,13963,13967,
! 629: 13997,13999,14009,14011,14029,14033,14051,14057,14071,14081,
! 630: 14083,14087,14107,14143,14149,14153,14159,14173,14177,14197,
! 631: 14207,14221,14243,14249,14251,14281,14293,14303,14321,14323,
! 632: 14327,14341,14347,14369,14387,14389,14401,14407,14411,14419,
! 633: 14423,14431,14437,14447,14449,14461,14479,14489,14503,14519,
! 634: 14533,14537,14543,14549,14551,14557,14561,14563,14591,14593,
! 635: 14621,14627,14629,14633,14639,14653,14657,14669,14683,14699,
! 636: 14713,14717,14723,14731,14737,14741,14747,14753,14759,14767,
! 637: 14771,14779,14783,14797,14813,14821,14827,14831,14843,14851,
! 638: 14867,14869,14879,14887,14891,14897,14923,14929,14939,14947,
! 639: 14951,14957,14969,14983,15013,15017,15031,15053,15061,15073,
! 640: 15077,15083,15091,15101,15107,15121,15131,15137,15139,15149,
! 641: 15161,15173,15187,15193,15199,15217,15227,15233,15241,15259,
! 642: 15263,15269,15271,15277,15287,15289,15299,15307,15313,15319,
! 643: 15329,15331,15349,15359,15361,15373,15377,15383,15391,15401,
! 644: 15413,15427,15439,15443,15451,15461,15467,15473,15493,15497,
! 645: 15511,15527,15541,15551,15559,15569,15581,15583,15601,15607,
! 646: 15619,15629,15641,15643,15647,15649,15661,15667,15671,15679,
! 647: 15683,15727,15731,15733,15737,15739,15749,15761,15767,15773,
! 648: 15787,15791,15797,15803,15809,15817,15823,15859,15877,15881,
! 649: 15887,15889,15901,15907,15913,15919,15923,15937,15959,15971,
! 650: 15973,15991,16001,16007,16033,16057,16061,16063,16067,16069,
! 651: 16073,16087,16091,16097,16103,16111,16127,16139,16141,16183,
! 652: 16187,16189,16193,16217,16223,16229,16231,16249,16253,16267,
! 653: 16273,16301,16319,16333,16339,16349,16361,16363,16369,16381,
! 654: 0
! 655: };
! 656:
! 657: #include "prime.h"
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