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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: *
1.6 ! noro 48: * $OpenXM: OpenXM_contrib2/asir2000/engine/PD.c,v 1.5 2001/10/09 01:36:11 noro Exp $
1.2 noro 49: */
1.1 noro 50: #ifndef FBASE
51: #define FBASE
52: #endif
53:
54: #include "b.h"
55: #include "ca.h"
56:
1.6 ! noro 57: #include "polydiv.c"
1.1 noro 58:
1.5 noro 59: void plisttop(P *f,V v,int n,P *gp)
1.1 noro 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: }
1.4 noro 82: }
83:
84: /* for multivariate polynomials over fields */
85:
1.5 noro 86: int divtp(VL vl,P p1,P p2,P *q)
1.4 noro 87: {
1.5 noro 88: register int i,j;
1.4 noro 89: register DCP dc1,dc2,dc;
90: P m,m1,s,dvr,t;
91: P *pq,*pr,*pd;
92: V v1,v2;
93: Q 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 = cmpq(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 ( (PL(NM(deg1)) > 1) ) {
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:
1.5 noro 170: int divtdcp(VL vl,P p1,P p2,P *q)
1.4 noro 171: {
172:
173: P m;
1.5 noro 174: register DCP dc,dcr,dcr0;
1.4 noro 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;
1.1 noro 185: }
186:
1.5 noro 187: int divtpz(VL vl,P p1,P p2,P *q)
1.1 noro 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: Q 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 = cmpq(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 ( (PL(NM(deg1)) > 1) ) {
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:
1.5 noro 287: int divtdcpz(VL vl,P p1,P p2,P *q)
1.1 noro 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:
1.5 noro 304: void udivpz(P f1,P f2,P *fqp,P *frp)
1.1 noro 305: {
306: register int n1,n2,i,j;
307: Q *pq,*pr,*pd,d,m,s,q;
308: DCP dc;
309: N qn,rn;
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: divn(NM((Q)f1),NM((Q)f2),&qn,&rn);
319: if ( rn ) {
320: *fqp = *frp = 0;
321: } else {
322: NTOQ(qn,SGN((Q)f1)*SGN((Q)f2),q),*fqp = (P)q; *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,Q,pq);
331: for ( dc = DC(f1); dc; dc = NEXT(dc) ) {
332: divn(NM((Q)COEF(dc)),NM((Q)f2),&qn,&rn);
333: if ( rn ) {
334: *fqp = *frp = 0;
335: return;
336: } else {
337: NTOQ(qn,SGN((Q)COEF(dc))*SGN((Q)f2),s); pq[QTOS(DEG(dc))] = s;
338: }
339: }
340: plisttop((P *)pq,VR(f1),n1,fqp);
341: return;
342: }
343: n1 = UDEG(f1); n2 = UDEG(f2);
344: if ( n1 < n2 ) {
345: *fqp = NULL; *frp = f1;
346: return;
347: }
348: W_CALLOC(n1-n2,Q,pq); W_CALLOC(n1,Q,pr); W_CALLOC(n2,Q,pd);
349: for ( dc = DC(f1); dc; dc = NEXT(dc) )
350: pr[QTOS(DEG(dc))] = (Q)COEF(dc);
351: for ( dc = DC(f2); dc; dc = NEXT(dc) )
352: pd[QTOS(DEG(dc))] = (Q)COEF(dc);
353: for ( d = (Q)UCOEF(f2), i = n1 - n2; i >= 0; i-- ) {
354: if ( !pr[i+n2] )
355: continue;
356: divn(NM(pr[i+n2]),NM(d),&qn,&rn);
357: if ( rn ) {
358: *fqp = *frp = 0;
359: return;
360: }
361: NTOQ(qn,SGN(pr[i+n2])*SGN(d),pq[i]);
362: for ( j = n2; j >= 0; j-- ) {
363: mulq(pq[i],pd[j],&m); subq(pr[i+j],m,&s); pr[i+j] = s;
364: }
365: }
366: plisttop((P *)pq,VR(f1),n1-n2,fqp); plisttop((P *)pr,VR(f1),n2-1,frp);
367: }
368:
1.5 noro 369: void udivpwm(Q mod,P p1,P p2,P *q,P *r)
1.1 noro 370: {
371: P s,t,u,tq,tr;
372:
373: invl((Q)UCOEF(p2),mod,(Q *)&t); mulpq(p2,t,&s); cmp(mod,s,&u);
374: udivpzwm(mod,p1,u,&tq,&tr);
375: cmp(mod,tr,r); mulpq(tq,t,&s); cmp(mod,s,q);
376: }
377:
1.5 noro 378: void udivpzwm(Q mod,P f1,P f2,P *fqp,P *frp)
1.1 noro 379: {
380: register int n1,n2,i,j;
381: Q *pq,*pr,*pd,d,m,s,q;
382: DCP dc;
383: N qn,rn;
384:
385: if ( !f2 )
386: error("udivpz: division by 0");
387: else if ( !f1 ) {
388: *fqp = *frp = 0;
389: return;
390: } else if ( NUM(f1) )
391: if ( NUM(f2) ) {
392: divn(NM((Q)f1),NM((Q)f2),&qn,&rn);
393: if ( rn ) {
394: *fqp = *frp = 0;
395: } else {
396: NTOQ(qn,SGN((Q)f1)*SGN((Q)f2),q),*fqp = (P)q; *frp = 0;
397: }
398: return;
399: } else {
400: *fqp = 0; *frp = f1;
401: return;
402: }
403: else if ( NUM(f2) ) {
404: n1 = UDEG(f1); W_CALLOC(n1,Q,pq);
405: for ( dc = DC(f1); dc; dc = NEXT(dc) ) {
406: divn(NM((Q)COEF(dc)),NM((Q)f2),&qn,&rn);
407: if ( rn ) {
408: *fqp = *frp = 0;
409: return;
410: } else {
411: NTOQ(qn,SGN((Q)COEF(dc))*SGN((Q)f2),s); pq[QTOS(DEG(dc))] = s;
412: }
413: }
414: plisttop((P *)pq,VR(f1),n1,fqp);
415: return;
416: }
417: n1 = UDEG(f1); n2 = UDEG(f2);
418: if ( n1 < n2 ) {
419: *fqp = NULL; *frp = f1;
420: return;
421: }
422: W_CALLOC(n1-n2,Q,pq); W_CALLOC(n1,Q,pr); W_CALLOC(n2,Q,pd);
423: for ( dc = DC(f1); dc; dc = NEXT(dc) )
424: pr[QTOS(DEG(dc))] = (Q)COEF(dc);
425: for ( dc = DC(f2); dc; dc = NEXT(dc) )
426: pd[QTOS(DEG(dc))] = (Q)COEF(dc);
427: for ( d = (Q)UCOEF(f2), i = n1 - n2; i >= 0; i-- ) {
428: if ( !pr[i+n2] )
429: continue;
430: divn(NM(pr[i+n2]),NM(d),&qn,&rn);
431: if ( rn ) {
432: *fqp = *frp = 0;
433: return;
434: }
435: NTOQ(qn,SGN(pr[i+n2])*SGN(d),pq[i]);
436: for ( j = n2; j >= 0; j-- ) {
437: mulq(pq[i],pd[j],&m); remq(m,mod,&s);
438: subq(pr[i+j],s,&m); remq(m,mod,&s); pr[i+j] = s;
439: }
440: }
441: plisttop((P *)pq,VR(f1),n1-n2,fqp); plisttop((P *)pr,VR(f1),n2-1,frp);
442: }