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1.4 ! 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@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: OpenXM_contrib2/asir2000/engine/Q.c,v 1.3 2000/05/29 08:54:46 noro Exp $
! 49: */
1.1 noro 50: #include "ca.h"
51: #include "base.h"
52: #include "inline.h"
53:
54: void addq(n1,n2,nr)
55: Q n1,n2,*nr;
56: {
57: N nm,dn,nm1,nm2,nm3,dn0,dn1,dn2,g,g1,g0,m;
58: int sgn;
59: unsigned t,t1;
60:
61: if ( !n1 )
62: *nr = n2;
63: else if ( !n2 )
64: *nr = n1;
65: else if ( INT(n1) )
66: if ( INT(n2) ) {
67: nm1 = NM(n1); nm2 = NM(n2);
68: if ( SGN(n1) == SGN(n2) ) {
69: if ( PL(nm1) == 1 && PL(nm2) == 1 ) {
70: t1 = BD(nm1)[0]; t = t1+BD(nm2)[0];
71: if ( t < t1 ) {
72: m = NALLOC(2); PL(m) = 2; BD(m)[0] = t; BD(m)[1] = 1;
73: } else
74: UTON(t,m);
75: } else
76: addn(NM(n1),NM(n2),&m);
77: NTOQ(m,SGN(n1),*nr);
78: } else {
79: if ( PL(nm1) == 1 && PL(nm2) == 1 ) {
80: t1 = BD(nm1)[0]; t = t1-BD(nm2)[0];
81: if ( !t )
82: sgn = 0;
83: else if ( t > t1 ) {
84: sgn = -1; t = -((int)t); UTON(t,m);
85: } else {
86: sgn = 1; UTON(t,m);
87: }
88: } else
89: sgn = subn(NM(n1),NM(n2),&m);
90: if ( sgn ) {
91: if ( SGN(n1) == sgn )
92: NTOQ(m,1,*nr);
93: else
94: NTOQ(m,-1,*nr);
95: } else
96: *nr = 0;
97: }
98: } else {
99: kmuln(NM(n1),DN(n2),&m);
100: if ( SGN(n1) == SGN(n2) ) {
101: sgn = SGN(n1); addn(m,NM(n2),&nm);
102: } else
103: sgn = SGN(n1)*subn(m,NM(n2),&nm);
104: if ( sgn ) {
105: dn = DN(n2); NDTOQ(nm,dn,sgn,*nr);
106: } else
107: *nr = 0;
108: }
109: else if ( INT(n2) ) {
110: kmuln(NM(n2),DN(n1),&m);
111: if ( SGN(n1) == SGN(n2) ) {
112: sgn = SGN(n1); addn(m,NM(n1),&nm);
113: } else
114: sgn = SGN(n1)*subn(NM(n1),m,&nm);
115: if ( sgn ) {
116: dn = DN(n1); NDTOQ(nm,dn,sgn,*nr);
117: } else
118: *nr = 0;
119: } else {
120: gcdn(DN(n1),DN(n2),&g); divsn(DN(n1),g,&dn1); divsn(DN(n2),g,&dn2);
121: kmuln(NM(n1),dn2,&nm1); kmuln(NM(n2),dn1,&nm2);
122: if ( SGN(n1) == SGN(n2) ) {
123: sgn = SGN(n1); addn(nm1,nm2,&nm3);
124: } else
125: sgn = SGN(n1)*subn(nm1,nm2,&nm3);
126: if ( sgn ) {
127: gcdn(nm3,g,&g1); divsn(nm3,g1,&nm); divsn(g,g1,&g0);
128: kmuln(dn1,dn2,&dn0); kmuln(g0,dn0,&dn);
129: if ( UNIN(dn) )
130: NTOQ(nm,sgn,*nr);
131: else
132: NDTOQ(nm,dn,sgn,*nr);
133: } else
134: *nr = 0;
135: }
136: }
137:
138: void subq(n1,n2,nr)
139: Q n1,n2,*nr;
140: {
141: Q m;
142:
143: if ( !n1 )
144: if ( !n2 )
145: *nr = 0;
146: else {
147: DUPQ(n2,*nr); SGN(*nr) = -SGN(n2);
148: }
149: else if ( !n2 )
150: *nr = n1;
151: else if ( n1 == n2 )
152: *nr = 0;
153: else {
154: DUPQ(n2,m); SGN(m) = -SGN(n2); addq(n1,m,nr);
155: }
156: }
157:
158: void mulq(n1,n2,nr)
159: Q n1,n2,*nr;
160: {
161: N nm,nm1,nm2,dn,dn1,dn2,g;
162: int sgn;
163: unsigned u,l;
164:
165: if ( !n1 || !n2 ) *nr = 0;
166: else if ( INT(n1) )
167: if ( INT(n2) ) {
168: nm1 = NM(n1); nm2 = NM(n2);
169: if ( PL(nm1) == 1 && PL(nm2) == 1 ) {
170: DM(BD(NM(n1))[0],BD(NM(n2))[0],u,l)
171: if ( u ) {
172: nm = NALLOC(2); PL(nm) = 2; BD(nm)[0] = l; BD(nm)[1] = u;
173: } else {
174: nm = NALLOC(1); PL(nm) = 1; BD(nm)[0] = l;
175: }
176: } else
177: kmuln(nm1,nm2,&nm);
178: sgn = (SGN(n1)==SGN(n2)?1:-1); NTOQ(nm,sgn,*nr);
179: } else {
180: gcdn(NM(n1),DN(n2),&g); divsn(NM(n1),g,&nm1); divsn(DN(n2),g,&dn);
181: kmuln(nm1,NM(n2),&nm); sgn = SGN(n1)*SGN(n2);
182: if ( UNIN(dn) )
183: NTOQ(nm,sgn,*nr);
184: else
185: NDTOQ(nm,dn,sgn,*nr);
186: }
187: else if ( INT(n2) ) {
188: gcdn(NM(n2),DN(n1),&g); divsn(NM(n2),g,&nm2); divsn(DN(n1),g,&dn);
189: kmuln(nm2,NM(n1),&nm); sgn = SGN(n1)*SGN(n2);
190: if ( UNIN(dn) )
191: NTOQ(nm,sgn,*nr);
192: else
193: NDTOQ(nm,dn,sgn,*nr);
194: } else {
195: gcdn(NM(n1),DN(n2),&g); divsn(NM(n1),g,&nm1); divsn(DN(n2),g,&dn2);
196: gcdn(DN(n1),NM(n2),&g); divsn(DN(n1),g,&dn1); divsn(NM(n2),g,&nm2);
197: kmuln(nm1,nm2,&nm); kmuln(dn1,dn2,&dn); sgn = SGN(n1) * SGN(n2);
198: if ( UNIN(dn) )
199: NTOQ(nm,sgn,*nr);
200: else
201: NDTOQ(nm,dn,sgn,*nr);
202: }
203: }
204:
205: void divq(n1,n2,nq)
206: Q n1,n2,*nq;
207: {
208: Q m;
209:
210: if ( !n2 ) {
211: error("division by 0");
212: *nq = 0;
213: return;
214: } else if ( !n1 )
215: *nq = 0;
216: else if ( n1 == n2 )
217: *nq = ONE;
218: else {
219: invq(n2,&m); mulq(n1,m,nq);
220: }
221: }
222:
223: void invq(n,nr)
224: Q n,*nr;
225: {
226: N nm,dn;
227:
228: if ( INT(n) )
229: if ( UNIN(NM(n)) )
230: if ( SGN(n) > 0 )
231: *nr = ONE;
232: else {
233: nm = ONEN; NTOQ(nm,SGN(n),*nr);
234: }
235: else {
236: nm = ONEN; dn = NM(n); NDTOQ(nm,dn,SGN(n),*nr);
237: }
238: else if ( UNIN(NM(n)) ) {
239: nm = DN(n); NTOQ(nm,SGN(n),*nr);
240: } else {
241: nm = DN(n); dn = NM(n); NDTOQ(nm,dn,SGN(n),*nr);
242: }
243: }
244:
245: void chsgnq(n,nr)
246: Q n,*nr;
247: {
248: Q t;
249:
250: if ( !n )
251: *nr = 0;
252: else {
253: DUPQ(n,t); SGN(t) = -SGN(t); *nr = t;
254: }
255: }
256:
257: void pwrq(n1,n,nr)
258: Q n1,n,*nr;
259: {
260: N nm,dn;
261: int sgn;
262:
263: if ( !n || UNIQ(n1) )
264: *nr = ONE;
265: else if ( !n1 )
266: *nr = 0;
267: else if ( !INT(n) ) {
268: error("can't calculate fractional power."); *nr = 0;
269: } else if ( MUNIQ(n1) )
270: *nr = BD(NM(n))[0]%2 ? n1 : ONE;
271: else if ( PL(NM(n)) > 1 ) {
272: error("exponent too big."); *nr = 0;
273: } else {
274: sgn = ((SGN(n1)>0)||EVENN(NM(n))?1:-1);
275: pwrn(NM(n1),BD(NM(n))[0],&nm);
276: if ( INT(n1) ) {
277: if ( UNIN(nm) )
278: if ( sgn == 1 )
279: *nr = ONE;
280: else
281: NTOQ(ONEN,sgn,*nr);
282: else if ( SGN(n) > 0 )
283: NTOQ(nm,sgn,*nr);
284: else
285: NDTOQ(ONEN,nm,sgn,*nr);
286: } else {
287: pwrn(DN(n1),BD(NM(n))[0],&dn);
288: if ( SGN(n) > 0 )
289: NDTOQ(nm,dn,sgn,*nr);
290: else if ( UNIN(nm) )
291: NTOQ(dn,sgn,*nr);
292: else
293: NDTOQ(dn,nm,sgn,*nr);
294: }
295: }
296: }
297:
298: int cmpq(q1,q2)
299: Q q1,q2;
300: {
301: int sgn;
302: N t,s;
303:
304: if ( !q1 )
305: if ( !q2 )
306: return ( 0 );
307: else
308: return ( -SGN(q2) );
309: else if ( !q2 )
310: return ( SGN(q1) );
311: else if ( SGN(q1) != SGN(q2) )
312: return ( SGN(q1) );
313: else if ( INT(q1) )
314: if ( INT(q2) ) {
315: sgn = cmpn(NM(q1),NM(q2));
316: if ( !sgn )
317: return ( 0 );
318: else
319: return ( SGN(q1)==sgn?1:-1 );
320: } else {
321: kmuln(NM(q1),DN(q2),&t); sgn = cmpn(t,NM(q2));
322: return ( SGN(q1) * sgn );
323: }
324: else if ( INT(q2) ) {
325: kmuln(NM(q2),DN(q1),&t); sgn = cmpn(NM(q1),t);
326: return ( SGN(q1) * sgn );
327: } else {
328: kmuln(NM(q1),DN(q2),&t); kmuln(NM(q2),DN(q1),&s); sgn = cmpn(t,s);
329: return ( SGN(q1) * sgn );
330: }
331: }
332:
333: void remq(n,m,nr)
334: Q n,m;
335: Q *nr;
336: {
337: N q,r,s;
338:
339: if ( !n ) {
340: *nr = 0;
341: return;
342: }
343: divn(NM(n),NM(m),&q,&r);
344: if ( !r )
345: *nr = 0;
346: else if ( SGN(n) > 0 )
347: NTOQ(r,1,*nr);
348: else {
349: subn(NM(m),r,&s); NTOQ(s,1,*nr);
350: }
351: }
352:
1.2 noro 353: /* t = [nC0 nC1 ... nCn] */
354:
1.1 noro 355: void mkbc(n,t)
356: int n;
357: Q *t;
358: {
359: int i;
360: N c,d;
361:
362: for ( t[0] = ONE, i = 1; i <= n/2; i++ ) {
363: c = NALLOC(1); PL(c) = 1; BD(c)[0] = n-i+1;
364: kmuln(NM(t[i-1]),c,&d); divin(d,i,&c); NTOQ(c,1,t[i]);
365: }
366: for ( ; i <= n; i++ )
367: t[i] = t[n-i];
1.2 noro 368: }
369:
370: /*
371: * Dx^k*x^l = W(k,l,0)*x^l*Dx^k+W(k,l,1)*x^(l-1)*x^(k-1)*+...
372: *
373: * t = [W(k,l,0) W(k,l,1) ... W(k,l,min(k,l)]
374: * where W(k,l,i) = i! * kCi * lCi
375: */
376:
377: void mkwc(k,l,t)
378: int k,l;
379: Q *t;
380: {
381: int i,n,up,low;
382: N nm,d,c;
383:
384: n = MIN(k,l);
385: for ( t[0] = ONE, i = 1; i <= n; i++ ) {
386: DM(k-i+1,l-i+1,up,low);
387: if ( up ) {
388: nm = NALLOC(2); PL(nm) = 2; BD(nm)[0] = low; BD(nm)[1] = up;
389: } else {
390: nm = NALLOC(1); PL(nm) = 1; BD(nm)[0] = low;
391: }
392: kmuln(NM(t[i-1]),nm,&d); divin(d,i,&c); NTOQ(c,1,t[i]);
1.3 noro 393: }
394: }
395:
396: /* mod m table */
397: /* XXX : should be optimized */
398:
399: void mkwcm(k,l,m,t)
400: int k,l,m;
401: int *t;
402: {
403: int i,n;
404: Q *s;
405:
406: n = MIN(k,l);
407: s = (Q *)ALLOCA((n+1)*sizeof(Q));
408: mkwc(k,l,s);
409: for ( i = 0; i <= n; i++ ) {
410: t[i] = rem(NM(s[i]),m);
1.2 noro 411: }
1.1 noro 412: }
413:
414: void factorial(n,r)
415: int n;
416: Q *r;
417: {
418: Q t,iq,s;
419: unsigned int i,m,m0;
420: unsigned int c;
421:
422: if ( !n )
423: *r = ONE;
424: else if ( n < 0 )
425: *r = 0;
426: else {
427: for ( i = 1, t = ONE; (int)i <= n; ) {
428: for ( m0 = m = 1, c = 0; ((int)i <= n) && !c; i++ ) {
429: m0 = m; DM(m0,i,c,m)
430: }
431: if ( c ) {
432: m = m0; i--;
433: }
434: UTOQ(m,iq); mulq(t,iq,&s); t = s;
435: }
436: *r = t;
437: }
438: }
439:
440: void invl(a,mod,ar)
441: Q a,mod,*ar;
442: {
443: Q f1,f2,a1,a2,q,m,s;
444: N qn,rn;
445:
446: a1 = ONE; a2 = 0;
447: DUPQ(a,f1); SGN(f1) = 1; f2 = mod;
448:
449: while ( 1 ) {
450: divn(NM(f1),NM(f2),&qn,&rn);
451: if ( !qn )
452: q = 0;
453: else
454: NTOQ(qn,1,q);
455:
456: f1 = f2;
457: if ( !rn )
458: break;
459: else
460: NTOQ(rn,1,f2);
461:
462: mulq(a2,q,&m); subq(a1,m,&s); a1 = a2;
463: if ( !s )
464: a2 = 0;
465: else
466: remq(s,mod,&a2);
467: }
468: if ( SGN(a) < 0 )
469: chsgnq(a2,&m);
470: else
471: m = a2;
472:
473: if ( SGN(m) >= 0 )
474: *ar = m;
475: else
476: addq(m,mod,ar);
477: }
478:
479: int kara_mag=100;
480:
481: void kmuln(n1,n2,nr)
482: N n1,n2,*nr;
483: {
484: N n,t,s,m,carry;
485: int d,d1,d2,len,i,l;
486: int *r,*r0;
487:
488: if ( !n1 || !n2 ) {
489: *nr = 0; return;
490: }
491: d1 = PL(n1); d2 = PL(n2);
492: if ( (d1 < kara_mag) || (d2 < kara_mag) ) {
493: muln(n1,n2,nr); return;
494: }
495: if ( d1 < d2 ) {
496: n = n1; n1 = n2; n2 = n;
497: d = d1; d1 = d2; d2 = d;
498: }
499: if ( d2 > (d1+1)/2 ) {
500: kmulnmain(n1,n2,nr); return;
501: }
502: d = (d1/d2)+((d1%d2)!=0);
503: len = (d+1)*d2;
504: r0 = (int *)ALLOCA(len*sizeof(int));
505: bzero((char *)r0,len*sizeof(int));
506: for ( carry = 0, i = 0, r = r0; i < d; i++, r += d2 ) {
507: extractn(n1,i*d2,d2,&m);
508: if ( m ) {
509: kmuln(m,n2,&t);
510: addn(t,carry,&s);
511: copyn(s,d2,r);
512: extractn(s,d2,d2,&carry);
513: } else {
514: copyn(carry,d2,r);
515: carry = 0;
516: }
517: }
518: copyn(carry,d2,r);
519: for ( l = len - 1; !r0[l]; l-- );
520: l++;
521: *nr = t = NALLOC(l); PL(t) = l;
522: bcopy((char *)r0,(char *)BD(t),l*sizeof(int));
523: }
524:
525: void extractn(n,index,len,nr)
526: N n;
527: int index,len;
528: N *nr;
529: {
530: unsigned int *m;
531: int l;
532: N t;
533:
534: if ( !n ) {
535: *nr = 0; return;
536: }
537: m = BD(n)+index;
538: if ( (l = PL(n)-index) >= len ) {
539: for ( l = len - 1; (l >= 0) && !m[l]; l-- );
540: l++;
541: }
542: if ( l <= 0 ) {
543: *nr = 0; return;
544: } else {
545: *nr = t = NALLOC(l); PL(t) = l;
546: bcopy((char *)m,(char *)BD(t),l*sizeof(int));
547: }
548: }
549:
550: void copyn(n,len,p)
551: N n;
552: int len;
553: int *p;
554: {
555: if ( n )
556: bcopy((char *)BD(n),(char *)p,MIN(PL(n),len)*sizeof(int));
557: }
558:
559: void dupn(n,p)
560: N n;
561: N p;
562: {
563: if ( n )
564: bcopy((char *)n,(char *)p,(1+PL(n))*sizeof(int));
565: }
566:
567: void kmulnmain(n1,n2,nr)
568: N n1,n2,*nr;
569: {
570: int d1,d2,h,sgn,sgn1,sgn2,len;
571: N n1lo,n1hi,n2lo,n2hi,hi,lo,mid1,mid2,mid,s1,s2,t1,t2;
572:
573: d1 = PL(n1); d2 = PL(n2); h = (d1+1)/2;
574: extractn(n1,0,h,&n1lo); extractn(n1,h,d1-h,&n1hi);
575: extractn(n2,0,h,&n2lo); extractn(n2,h,d2-h,&n2hi);
576: kmuln(n1hi,n2hi,&hi); kmuln(n1lo,n2lo,&lo);
577: len = PL(hi)+2*h; t1 = NALLOC(len); PL(t1) = len;
578: bzero((char *)BD(t1),len*sizeof(int));
579: if ( lo )
580: bcopy((char *)BD(lo),(char *)BD(t1),PL(lo)*sizeof(int));
581: if ( hi )
582: bcopy((char *)BD(hi),(char *)(BD(t1)+2*h),PL(hi)*sizeof(int));
583:
584: addn(hi,lo,&mid1);
585: sgn1 = subn(n1hi,n1lo,&s1); sgn2 = subn(n2lo,n2hi,&s2);
586: kmuln(s1,s2,&mid2); sgn = sgn1*sgn2;
587: if ( sgn > 0 )
588: addn(mid1,mid2,&mid);
589: else
590: subn(mid1,mid2,&mid);
591: if ( mid ) {
592: len = PL(mid)+h; t2 = NALLOC(len); PL(t2) = len;
593: bzero((char *)BD(t2),len*sizeof(int));
594: bcopy((char *)BD(mid),(char *)(BD(t2)+h),PL(mid)*sizeof(int));
595: addn(t1,t2,nr);
596: } else
597: *nr = t1;
598: }