Annotation of OpenXM_contrib2/asir2018/engine/PD.c, Revision 1.1
1.1 ! 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
! 26: * e-mail at risa-admin@sec.flab.fujitsu.co.jp of the detailed specification
! 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: *
! 48: * $OpenXM$
! 49: */
! 50: #ifndef FBASE
! 51: #define FBASE
! 52: #endif
! 53:
! 54: #include "b.h"
! 55: #include "ca.h"
! 56:
! 57: #include "polydiv.c"
! 58:
! 59: void plisttop(P *f,V v,int n,P *gp)
! 60: {
! 61: int i;
! 62: DCP dc,dc0;
! 63:
! 64: for ( i = n; (i >= 0) && !f[i]; i-- );
! 65: if ( i < 0 )
! 66: *gp = 0;
! 67: else if ( i == 0 )
! 68: *gp = f[0];
! 69: else {
! 70: for ( dc0 = 0; i >= 0; i-- ) {
! 71: if ( !f[i] )
! 72: continue;
! 73: NEXTDC(dc0,dc);
! 74: if ( i )
! 75: STOQ(i,DEG(dc));
! 76: else
! 77: DEG(dc) = 0;
! 78: COEF(dc) = f[i];
! 79: }
! 80: NEXT(dc) = 0; MKP(v,dc0,*gp);
! 81: }
! 82: }
! 83:
! 84: /* for multivariate polynomials over fields */
! 85:
! 86: int divtp(VL vl,P p1,P p2,P *q)
! 87: {
! 88: register int i,j;
! 89: register DCP dc1,dc2,dc;
! 90: P m,m1,s,dvr,t;
! 91: P *pq,*pr,*pd;
! 92: V v1,v2;
! 93: Z deg1,deg2;
! 94: int d1,d2,sgn;
! 95:
! 96: if ( !p1 ) {
! 97: *q = 0;
! 98: return 1;
! 99: } else if ( NUM(p2) ) {
! 100: divsp(vl,p1,p2,q);
! 101: return 1;
! 102: } else if ( NUM(p1) ) {
! 103: *q = 0;
! 104: return 0;
! 105: } else if ( ( v1 = VR(p1) ) == ( v2 = VR(p2) ) ) {
! 106: dc1 = DC(p1); dc2 = DC(p2);
! 107: deg1 = DEG(dc1); deg2 = DEG(dc2);
! 108: sgn = cmpz(deg1,deg2);
! 109: if ( sgn == 0 )
! 110: if ( !divtp(vl,COEF(dc1),COEF(dc2),&m) ) {
! 111: *q = 0;
! 112: return 0;
! 113: } else {
! 114: mulp(vl,p2,m,&m1); subp(vl,p1,m1,&s);
! 115: if ( !s ) {
! 116: *q = m;
! 117: return 1;
! 118: } else {
! 119: *q = 0;
! 120: return 0;
! 121: }
! 122: }
! 123: else if ( sgn < 0 ) {
! 124: *q = 0;
! 125: return 0;
! 126: } else {
! 127: if ( !smallz(deg1) ) {
! 128: error("divtp : invalid input");
! 129: *q = 0;
! 130: return ( 0 );
! 131: }
! 132: d1 = QTOS(deg1); d2 = QTOS(deg2);
! 133: W_CALLOC(d1-d2,P,pq); W_CALLOC(d1,P,pr); W_CALLOC(d2,P,pd);
! 134: for ( dc = dc1; dc; dc = NEXT(dc) )
! 135: pr[QTOS(DEG(dc))] = COEF(dc);
! 136: for ( dc = dc2; dc; dc = NEXT(dc) )
! 137: pd[QTOS(DEG(dc))] = COEF(dc);
! 138: for ( dvr = COEF(dc2), i = d1 - d2; i >= 0; i-- )
! 139: if ( !pr[i+d2] )
! 140: continue;
! 141: else if ( !divtp(vl,pr[i+d2],dvr,&m) ) {
! 142: *q = 0;
! 143: return 0;
! 144: } else {
! 145: pq[i] = m;
! 146: for ( j = d2; j >= 0; j-- ) {
! 147: mulp(vl,pq[i],pd[j],&m);
! 148: subp(vl,pr[i + j],m,&s); pr[i + j] = s;
! 149: }
! 150: }
! 151: plisttop(pq,v1,d1 - d2,&m); plisttop(pr,v1,d1 - 1,&t);
! 152: if ( t ) {
! 153: *q = 0;
! 154: return 0;
! 155: } else {
! 156: *q = m;
! 157: return 1;
! 158: }
! 159: }
! 160: } else {
! 161: for ( ; (v1 != vl->v) && (v2 != vl->v); vl = NEXT(vl) );
! 162: if ( v2 == vl->v ) {
! 163: *q = 0;
! 164: return 0;
! 165: } else
! 166: return divtdcp(vl,p1,p2,q);
! 167: }
! 168: }
! 169:
! 170: int divtdcp(VL vl,P p1,P p2,P *q)
! 171: {
! 172:
! 173: P m;
! 174: register DCP dc,dcr,dcr0;
! 175:
! 176: for ( dc = DC(p1), dcr0 = 0; dc; dc = NEXT(dc) )
! 177: if ( !divtp(vl,COEF(dc),p2,&m) ) {
! 178: *q = 0;
! 179: return 0;
! 180: } else {
! 181: NEXTDC(dcr0,dcr); DEG(dcr) = DEG(dc); COEF(dcr) = m; NEXT(dcr) = 0;
! 182: }
! 183: MKP(VR(p1),dcr0,*q);
! 184: return 1;
! 185: }
! 186:
! 187: int divtpz(VL vl,P p1,P p2,P *q)
! 188: {
! 189: register int i,j;
! 190: register DCP dc1,dc2,dc;
! 191: P m,m1,s,dvr,t;
! 192: P *pq,*pr,*pd;
! 193: V v1,v2;
! 194: Z deg1,deg2;
! 195: int d1,d2,sgn;
! 196:
! 197: if ( !p1 ) {
! 198: *q = 0;
! 199: return ( 1 );
! 200: } else if ( NUM(p2) )
! 201: if ( NUM(p1) ) {
! 202: divq((Q)p1,(Q)p2,(Q *)&s);
! 203: if ( INT((Q)s) ) {
! 204: *q = s;
! 205: return ( 1 );
! 206: } else {
! 207: *q = 0;
! 208: return ( 0 );
! 209: }
! 210: } else
! 211: return ( divtdcpz(vl,p1,p2,q) );
! 212: else if ( NUM(p1) ) {
! 213: *q = 0;
! 214: return ( 0 );
! 215: } else if ( ( v1 = VR(p1) ) == ( v2 = VR(p2) ) ) {
! 216: Q csum1,csum2;
! 217:
! 218: csump(vl,p1,&csum1); csump(vl,p2,&csum2);
! 219: if ( csum2 && !divtpz(vl,(P)csum1,(P)csum2,&t) ) {
! 220: *q = 0;
! 221: return 0;
! 222: }
! 223: dc1 = DC(p1); dc2 = DC(p2);
! 224: deg1 = DEG(dc1); deg2 = DEG(dc2);
! 225: sgn = cmpz(deg1,deg2);
! 226: if ( sgn == 0 )
! 227: if ( !divtpz(vl,COEF(dc1),COEF(dc2),&m) ) {
! 228: *q = 0;
! 229: return ( 0 );
! 230: } else {
! 231: mulp(vl,p2,m,&m1); subp(vl,p1,m1,&s);
! 232: if ( !s ) {
! 233: *q = m;
! 234: return ( 1 );
! 235: } else {
! 236: *q = 0;
! 237: return ( 0 );
! 238: }
! 239: }
! 240: else if ( sgn < 0 ) {
! 241: *q = 0;
! 242: return ( 0 );
! 243: } else {
! 244: if ( !smallz(deg1) ) {
! 245: error("divtpz : invalid input");
! 246: *q = 0;
! 247: return ( 0 );
! 248: }
! 249: d1 = QTOS(deg1); d2 = QTOS(deg2);
! 250: W_CALLOC(d1-d2,P,pq); W_CALLOC(d1,P,pr); W_CALLOC(d2,P,pd);
! 251: for ( dc = dc1; dc; dc = NEXT(dc) )
! 252: pr[QTOS(DEG(dc))] = COEF(dc);
! 253: for ( dc = dc2; dc; dc = NEXT(dc) )
! 254: pd[QTOS(DEG(dc))] = COEF(dc);
! 255: for ( dvr = COEF(dc2), i = d1 - d2; i >= 0; i-- )
! 256: if ( !pr[i+d2] )
! 257: continue;
! 258: else if ( !divtpz(vl,pr[i+d2],dvr,&m) ) {
! 259: *q = 0;
! 260: return ( 0 );
! 261: } else {
! 262: pq[i] = m;
! 263: for ( j = d2; j >= 0; j-- ) {
! 264: mulp(vl,pq[i],pd[j],&m);
! 265: subp(vl,pr[i + j],m,&s); pr[i + j] = s;
! 266: }
! 267: }
! 268: plisttop(pq,v1,d1 - d2,&m); plisttop(pr,v1,d1 - 1,&t);
! 269: if ( t ) {
! 270: *q = 0;
! 271: return ( 0 );
! 272: } else {
! 273: *q = m;
! 274: return ( 1 );
! 275: }
! 276: }
! 277: } else {
! 278: for ( ; (v1 != vl->v) && (v2 != vl->v); vl = NEXT(vl) );
! 279: if ( v2 == vl->v ) {
! 280: *q = 0;
! 281: return ( 0 );
! 282: } else
! 283: return ( divtdcpz(vl,p1,p2,q) ) ;
! 284: }
! 285: }
! 286:
! 287: int divtdcpz(VL vl,P p1,P p2,P *q)
! 288: {
! 289:
! 290: P m;
! 291: register DCP dc,dcr,dcr0;
! 292:
! 293: for ( dc = DC(p1), dcr0 = 0; dc; dc = NEXT(dc) )
! 294: if ( !divtpz(vl,COEF(dc),p2,&m) ) {
! 295: *q = 0;
! 296: return ( 0 );
! 297: } else {
! 298: NEXTDC(dcr0,dcr); DEG(dcr) = DEG(dc); COEF(dcr) = m; NEXT(dcr) = 0;
! 299: }
! 300: MKP(VR(p1),dcr0,*q);
! 301: return ( 1 );
! 302: }
! 303:
! 304: void udivpz(P f1,P f2,P *fqp,P *frp)
! 305: {
! 306: int n1,n2,i,j,sgn;
! 307: Z *pq,*pr,*pd,d,m,s;
! 308: DCP dc;
! 309: Z qn,rn,q;
! 310:
! 311: if ( !f2 )
! 312: error("udivpz: division by 0");
! 313: else if ( !f1 ) {
! 314: *fqp = *frp = 0;
! 315: return;
! 316: } else if ( NUM(f1) ) {
! 317: if ( NUM(f2) ) {
! 318: divqrz((Z)f1,(Z)f2,&qn,&rn);
! 319: if ( rn ) {
! 320: *fqp = *frp = 0;
! 321: } else {
! 322: *fqp = (P)qn; *frp = 0;
! 323: }
! 324: return;
! 325: } else {
! 326: *fqp = 0; *frp = f1;
! 327: return;
! 328: }
! 329: } else if ( NUM(f2) ) {
! 330: n1 = UDEG(f1); W_CALLOC(n1,Z,pq);
! 331: for ( dc = DC(f1); dc; dc = NEXT(dc) ) {
! 332: divqrz((Z)COEF(dc),(Z)f2,&qn,&rn);
! 333: if ( rn ) {
! 334: *fqp = *frp = 0;
! 335: return;
! 336: } else {
! 337: pq[QTOS(DEG(dc))] = qn;
! 338: }
! 339: }
! 340: plisttop((P *)pq,VR(f1),n1,fqp);
! 341: *frp = 0;
! 342: return;
! 343: }
! 344: n1 = UDEG(f1); n2 = UDEG(f2);
! 345: if ( n1 < n2 ) {
! 346: *fqp = NULL; *frp = f1;
! 347: return;
! 348: }
! 349: W_CALLOC(n1-n2,Z,pq); W_CALLOC(n1,Z,pr); W_CALLOC(n2,Z,pd);
! 350: for ( dc = DC(f1); dc; dc = NEXT(dc) )
! 351: pr[QTOS(DEG(dc))] = (Z)COEF(dc);
! 352: for ( dc = DC(f2); dc; dc = NEXT(dc) )
! 353: pd[QTOS(DEG(dc))] = (Z)COEF(dc);
! 354: for ( d = (Z)UCOEF(f2), i = n1 - n2; i >= 0; i-- ) {
! 355: if ( !pr[i+n2] )
! 356: continue;
! 357: divqrz(pr[i+n2],d,&qn,&rn);
! 358: if ( rn ) {
! 359: *fqp = *frp = 0;
! 360: return;
! 361: }
! 362: pq[i] = qn;
! 363: for ( j = n2; j >= 0; j-- ) {
! 364: mulz(pq[i],pd[j],&m); subz(pr[i+j],m,&s); pr[i+j] = s;
! 365: }
! 366: }
! 367: plisttop((P *)pq,VR(f1),n1-n2,fqp); plisttop((P *)pr,VR(f1),n2-1,frp);
! 368: }
! 369:
! 370: /* YYY */
! 371:
! 372: void udivpwm(Z mod,P p1,P p2,P *q,P *r)
! 373: {
! 374: P s,t,u,tq,tr;
! 375:
! 376: invz((Z)UCOEF(p2),mod,(Z *)&t); mulpq(p2,t,&s); cmp(mod,s,&u);
! 377: udivpzwm(mod,p1,u,&tq,&tr);
! 378: cmp(mod,tr,r); mulpq(tq,t,&s); cmp(mod,s,q);
! 379: }
! 380:
! 381: void udivpzwm(Z mod,P f1,P f2,P *fqp,P *frp)
! 382: {
! 383: int n1,n2,i,j;
! 384: Z *pq,*pr,*pd,d,m,s;
! 385: DCP dc;
! 386: Z qn,rn,q;
! 387:
! 388: if ( !f2 )
! 389: error("udivpz: division by 0");
! 390: else if ( !f1 ) {
! 391: *fqp = *frp = 0;
! 392: return;
! 393: } else if ( NUM(f1) ) {
! 394: if ( NUM(f2) ) {
! 395: divqrz((Z)f1,(Z)f2,&qn,&rn);
! 396: if ( rn ) {
! 397: *fqp = *frp = 0;
! 398: } else {
! 399: *fqp = (P)qn; *frp = 0;
! 400: }
! 401: return;
! 402: } else {
! 403: *fqp = 0; *frp = f1;
! 404: return;
! 405: }
! 406: } else if ( NUM(f2) ) {
! 407: n1 = UDEG(f1); W_CALLOC(n1,Z,pq);
! 408: for ( dc = DC(f1); dc; dc = NEXT(dc) ) {
! 409: divqrz((Z)COEF(dc),(Z)f2,&qn,&rn);
! 410: if ( rn ) {
! 411: *fqp = *frp = 0;
! 412: return;
! 413: } else {
! 414: pq[QTOS(DEG(dc))] = qn;
! 415: }
! 416: }
! 417: plisttop((P *)pq,VR(f1),n1,fqp);
! 418: *frp = 0;
! 419: return;
! 420: }
! 421: n1 = UDEG(f1); n2 = UDEG(f2);
! 422: if ( n1 < n2 ) {
! 423: *fqp = NULL; *frp = f1;
! 424: return;
! 425: }
! 426: W_CALLOC(n1-n2,Z,pq); W_CALLOC(n1,Z,pr); W_CALLOC(n2,Z,pd);
! 427: for ( dc = DC(f1); dc; dc = NEXT(dc) )
! 428: pr[QTOS(DEG(dc))] = (Z)COEF(dc);
! 429: for ( dc = DC(f2); dc; dc = NEXT(dc) )
! 430: pd[QTOS(DEG(dc))] = (Z)COEF(dc);
! 431: for ( d = (Z)UCOEF(f2), i = n1 - n2; i >= 0; i-- ) {
! 432: if ( !pr[i+n2] )
! 433: continue;
! 434: divqrz(pr[i+n2],d,&qn,&rn);
! 435: if ( rn ) {
! 436: *fqp = *frp = 0;
! 437: return;
! 438: } else
! 439: pq[i] = qn;
! 440: for ( j = n2; j >= 0; j-- ) {
! 441: mulz(pq[i],pd[j],&m); remz(m,mod,&s);
! 442: subz(pr[i+j],s,&m); remz(m,mod,&s); pr[i+j] = s;
! 443: }
! 444: }
! 445: plisttop((P *)pq,VR(f1),n1-n2,fqp); plisttop((P *)pr,VR(f1),n2-1,frp);
! 446: }
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