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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: *
1.4 ! noro 48: * $OpenXM: OpenXM_contrib2/asir2000/engine/A.c,v 1.3 2000/08/22 05:04:03 noro Exp $
1.2 noro 49: */
1.1 noro 50: #include "ca.h"
51:
52: void pdiva(vl,p0,p1,p2,pr)
53: VL vl;
54: P p1,p2,p0;
55: P *pr;
56: {
57: Q m,d;
58: P t,q,r;
59:
60: if ( VR(p2) == VR(p0) ) {
61: *pr = p1;
62: return;
63: }
64: if ( VR(p1) == VR(p0) ) {
65: error("pdiva : ???");
66: return;
67: }
68: subq(DEG(DC(p1)),DEG(DC(p2)),&m); addq(m,ONE,&d);
69: pwrq((Q)COEF(DC(p2)),d,&m); mulp(vl,p1,(P)m,&t);
70: divsrp(vl,t,p2,&q,&r); remsdcp(vl,q,p0,pr);
71: }
72:
73: void rema(vl,p0,p1,p2,pr)
74: VL vl;
75: P p1,p2,p0,*pr;
76: {
77: P m,m1,m2,g,lc,x,t;
78: Q q;
79: V v;
80: int d1,d2;
81:
82: if ( !p1 || !p2 || NUM(p2) || ( VR(p2) == VR(p0) ) )
83: *pr = 0;
84: else if ( NUM(p1) )
85: *pr = p1;
86: else if ( ( v = VR(p1) ) == VR(p0) )
87: remsdcp(vl,p1,p0,pr);
88: else if ( ( d1 = deg(v,p1) ) < ( d2 = deg(v,p2) ) )
89: *pr = p1;
90: else if ( d1 == d2 ) {
91: mulp(vl,p1,LC(p2),&m); mulp(vl,p2,LC(p1),&m1);
92: subp(vl,m,m1,&m2);
93: remsdcp(vl,m2,p0,pr);
94: } else {
95: g = p1; lc = LC(p2); MKV(v,x);
96: while ( ( d1 = deg(v,g) ) >= d2 ) {
97: mulp(vl,g,lc,&m); mulp(vl,p2,LC(g),&m1);
98: STOQ(d1-d2,q); pwrp(vl,x,q,&t);
99: mulp(vl,m1,t,&m2); subp(vl,m,m2,&m1);
100: remsdcp(vl,m1,p0,&g);
101: }
102: *pr = g;
103: }
104: }
105:
106: void gcda(vl,p0,p1,p2,pr)
107: VL vl;
108: P p1,p2,p0,*pr;
109: {
110: P g1,g2,r,t,c;
111:
112: remsdcp(vl,p1,p0,&t); pcp(vl,t,&g1,&c); remsdcp(vl,p2,p0,&g2);
113: while ( 1 ) {
114: if ( NUM(g2) || (VR(g2) == VR(p0)) ) {
115: *pr = (P)ONE;
116: return;
117: }
118: pcp(vl,g2,&t,&c); pmonic(vl,p0,t,&g2); rema(vl,p0,g1,g2,&r);
119: if ( !r ) {
120: pmonic(vl,p0,g2,pr);
121: return;
122: }
123: g1 = g2; g2 = r;
124: }
125: }
126:
127: void sqa(vl,p0,p,dcp)
128: VL vl;
129: P p,p0;
130: DCP *dcp;
131: {
132: V v;
133: int i,j,n;
134: P f,f1,f2,gcd,flat,q,r,t;
135: P *a;
136: int *b;
137: DCP dc,dc0;
138:
139: if ( ( v = VR(p) ) == VR(p0) ) {
140: NEWDC(dc); *dcp = dc; COEF(dc) = (P)ONE; DEG(dc) = ONE;
141: NEXT(dc) = 0;
142: } else {
143: n = deg(v,p); W_CALLOC(n,P,a); W_CALLOC(n,int,b);
144: for ( i = 0, f = p; ;i++ ) {
145: if ( VR(f) != v )
146: break;
147: remsdcp(vl,f,p0,&f1); diffp(vl,f1,VR(f1),&f2);
148: while ( 1 ) {
149: pmonic(vl,p0,f2,&t); f2 = t; rema(vl,p0,f1,f2,&r);
150: if ( !r ) {
151: pmonic(vl,p0,f2,&gcd); pqra(vl,p0,f,gcd,&flat,&r);
152: break;
153: }
154: f1 = f2; f2 = r;
155: }
156: if ( VR(gcd) != v ) {
157: a[i] = f; b[i] = 1;
158: break;
159: }
160: for ( j = 1, f = gcd; ; j++ ) {
161: pqra(vl,p0,f,flat,&q,&r);
162: if ( r )
163: break;
164: else
165: f = q;
166: }
167: a[i] = flat; b[i] = j;
168: }
169: for ( i = 0, j = 0, dc0 = 0; a[i]; i++ ) {
170: NEXTDC(dc0,dc); j += b[i]; STOQ(j,DEG(dc));
171: if ( a[i+1] )
172: pqra(vl,p0,a[i],a[i+1],&COEF(dc),&t);
173: else
174: COEF(dc) = a[i];
175: }
176: NEXT(dc) = 0; *dcp = dc0;
177: }
178: }
179:
180: void pqra(vl, p0, p1, p2, p, pr)
181: VL vl;
182: P p0,p1,p2;
183: P *p,*pr;
184: {
185: V v,v1;
186: P m,m1,q,r;
187: Q tq;
188: int n;
189:
190: if ( ( v = VR(p1) ) != ( v1 = VR(p2) ) ) {
191: while ( ( VR(vl) != v ) && ( VR(vl) != v1 ) )
192: vl = NEXT(vl);
193: if ( VR(vl) == v ) {
194: *p = p1; *pr = 0;
195: } else {
196: *p = 0; *pr = p1;
197: }
198: } else if ( (n = deg(v,p1) - deg(v,p2)) < 0 ) {
199: *pr = p1; *p = 0;
200: } else {
201: n++; STOQ(n,tq);
202: pwrp(vl,LC(p2),tq,&m); mulp(vl,m,p1,&m1); divsrp(vl,m1,p2,&q,&r);
203: remsdcp(vl,q,p0,p); remsdcp(vl,r,p0,pr);
204: }
205: }
206:
207: void pmonic(vl, p0, p, pr)
208: VL vl;
209: P p,p0,*pr;
210: {
211: P d,m,pp,c,t;
212:
213: if ( NUM(p) || ( VR(p) == VR(p0) ) )
214: *pr = (P)ONE;
215: else if ( NUM(COEF(DC(p))) )
216: *pr = p;
217: else {
218: ptozp(COEF(DC(p)),1,(Q *)&c,&pp); pinva(p0,pp,&d);
219: mulp(vl,p,d,&m); remsdcp(vl,m,p0,&t); ptozp(t,1,(Q *)&c,pr);
220: }
221: }
222:
223: void remsdcp(vl, p, p0, pr)
224: VL vl;
225: P p,p0,*pr;
226: {
227: P q,r,c;
228: DCP dc,dcr,dcr0;
229:
230: if ( !p )
231: *pr = 0;
232: else if ( NUM(p) )
233: *pr = (P)ONE;
234: else if ( VR(p) == VR(p0) ) {
235: divsrp(vl,p,p0,&q,&r); ptozp(r,1,(Q *)&c,pr);
236: } else {
237: for ( dcr = dcr0 = 0, dc = DC(p); dc; dc = NEXT(dc) ) {
238: divsrp(vl,COEF(dc),p0,&q,&r);
239: if ( r ) {
240: NEXTDC(dcr0,dcr); DEG(dcr) = DEG(dc); COEF(dcr) = r;
241: }
242: }
243: if ( !dcr0 )
244: *pr = 0;
245: else {
246: NEXT(dcr) = 0; MKP(VR(p),dcr0,r); ptozp(r,1,(Q *)&c,pr);
247: }
248: }
249: }
250:
251: void pinva(p0, p, pr)
252: P p,p0,*pr;
253: {
254: V v;
255: Q f,q,q1;
256: Q u,t,a,b,s;
257: P c,c1;
258: P tg,th,tr;
259: P z,zz,zzz;
260: UM wg,wh,ws,wt,wm;
261: int n,m,modres,mod,index,i;
262:
263: v = VR(p); n=deg(v,p); m=deg(v,p0);
264: norm(p,&a); norm(p0,&b);
265: STOQ(m,u); pwrq(a,u,&t); STOQ(n,u); pwrq(b,u,&s);
266: mulq(t,s,&u);
267: factorial(n+m,&t); mulq(u,t,&s); addq(s,s,&f);
268: wg = W_UMALLOC(m+n); wh = W_UMALLOC(m+n);
269: wt = W_UMALLOC(m+n); ws = W_UMALLOC(m+n);
270: wm = W_UMALLOC(m+n);
271: for ( q = ONE, t = 0, c = 0, index = 0; ; ) {
1.4 ! noro 272: mod = get_lprime(index++);
1.1 noro 273: if ( !rem(NM((Q)LC(p)),mod) || !rem(NM((Q)LC(p0)),mod) )
274: continue;
275: ptomp(mod,p,&tg); ptomp(mod,p0,&th); srchump(mod,tg,th,&tr);
276: if ( !tr )
277: continue;
278: else
279: modres = CONT((MQ)tr);
280: mptoum(tg,wg); mptoum(th,wh);
281: eucum(mod,wg,wh,ws,wt); /* wg * ws + wh * wt = 1 */
282: DEG(wm) = 0; COEF(wm)[0] = modres;
283: mulum(mod,ws,wm,wt);
284: for ( i = DEG(wt); i >= 0; i-- )
285: if ( ( COEF(wt)[i] * 2 ) > mod )
286: COEF(wt)[i] -= mod;
287: chnrem(mod,v,c,q,wt,&c1,&q1);
288: if ( !ucmpp(c,c1) ) {
289: mulp(CO,c,p,&z); divsrp(CO,z,p0,&zz,&zzz);
290: if ( NUM(zzz) ) {
291: q = q1; c = c1; break;
292: }
293: }
294: q = q1; c = c1;
295: if ( cmpq(f,q) < 0 )
296: break;
297: }
298: ptozp(c,1,&s,pr);
299: }