Annotation of OpenXM_contrib2/asir2018/engine/A.c, Revision 1.2
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: *
1.2 ! noro 48: * $OpenXM: OpenXM_contrib2/asir2018/engine/A.c,v 1.1 2018/09/19 05:45:06 noro Exp $
1.1 noro 49: */
50: #include "ca.h"
51: #include "parse.h"
52:
53: int get_lprime();
54:
55: void pdiva(VL vl,P p0,P p1,P p2,P *pr)
56: {
57: Z 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: subz(DEG(DC(p1)),DEG(DC(p2)),&m); addz(m,ONE,&d);
69: pwrz((Z)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 vl,P p0,P p1,P p2,P *pr)
74: {
75: P m,m1,m2,g,lc,x,t;
76: Z q;
77: V v;
78: int d1,d2;
79:
80: if ( !p1 || !p2 || NUM(p2) || ( VR(p2) == VR(p0) ) )
81: *pr = 0;
82: else if ( NUM(p1) )
83: *pr = p1;
84: else if ( ( v = VR(p1) ) == VR(p0) )
85: remsdcp(vl,p1,p0,pr);
86: else if ( ( d1 = deg(v,p1) ) < ( d2 = deg(v,p2) ) )
87: *pr = p1;
88: else if ( d1 == d2 ) {
89: mulp(vl,p1,LC(p2),&m); mulp(vl,p2,LC(p1),&m1);
90: subp(vl,m,m1,&m2);
91: remsdcp(vl,m2,p0,pr);
92: } else {
93: g = p1; lc = LC(p2); MKV(v,x);
94: while ( ( d1 = deg(v,g) ) >= d2 ) {
95: mulp(vl,g,lc,&m); mulp(vl,p2,LC(g),&m1);
1.2 ! noro 96: STOZ(d1-d2,q); pwrp(vl,x,q,&t);
1.1 noro 97: mulp(vl,m1,t,&m2); subp(vl,m,m2,&m1);
98: remsdcp(vl,m1,p0,&g);
99: }
100: *pr = g;
101: }
102: }
103:
104: void gcda(VL vl,P p0,P p1,P p2,P *pr)
105: {
106: P g1,g2,r,t,c;
107:
108: remsdcp(vl,p1,p0,&t); pcp(vl,t,&g1,&c); remsdcp(vl,p2,p0,&g2);
109: while ( 1 ) {
110: if ( NUM(g2) || (VR(g2) == VR(p0)) ) {
111: *pr = (P)ONE;
112: return;
113: }
114: pcp(vl,g2,&t,&c); pmonic(vl,p0,t,&g2); rema(vl,p0,g1,g2,&r);
115: if ( !r ) {
116: pmonic(vl,p0,g2,pr);
117: return;
118: }
119: g1 = g2; g2 = r;
120: }
121: }
122:
123: void sqa(VL vl,P p0,P p,DCP *dcp)
124: {
125: V v;
126: int i,j,n;
127: P f,f1,f2,gcd,flat,q,r,t;
128: P *a;
129: int *b;
130: DCP dc,dc0;
131:
132: if ( ( v = VR(p) ) == VR(p0) ) {
133: NEWDC(dc); *dcp = dc; COEF(dc) = (P)ONE; DEG(dc) = ONE;
134: NEXT(dc) = 0;
135: } else {
136: n = deg(v,p); W_CALLOC(n,P,a); W_CALLOC(n,int,b);
137: for ( i = 0, f = p; ;i++ ) {
138: if ( VR(f) != v )
139: break;
140: remsdcp(vl,f,p0,&f1); diffp(vl,f1,VR(f1),&f2);
141: while ( 1 ) {
142: pmonic(vl,p0,f2,&t); f2 = t; rema(vl,p0,f1,f2,&r);
143: if ( !r ) {
144: pmonic(vl,p0,f2,&gcd); pqra(vl,p0,f,gcd,&flat,&r);
145: break;
146: }
147: f1 = f2; f2 = r;
148: }
149: if ( VR(gcd) != v ) {
150: a[i] = f; b[i] = 1;
151: break;
152: }
153: for ( j = 1, f = gcd; ; j++ ) {
154: pqra(vl,p0,f,flat,&q,&r);
155: if ( r )
156: break;
157: else
158: f = q;
159: }
160: a[i] = flat; b[i] = j;
161: }
162: for ( i = 0, j = 0, dc0 = 0; a[i]; i++ ) {
1.2 ! noro 163: NEXTDC(dc0,dc); j += b[i]; STOZ(j,DEG(dc));
1.1 noro 164: if ( a[i+1] )
165: pqra(vl,p0,a[i],a[i+1],&COEF(dc),&t);
166: else
167: COEF(dc) = a[i];
168: }
169: NEXT(dc) = 0; *dcp = dc0;
170: }
171: }
172:
173: void pqra(VL vl,P p0,P p1,P p2,P *p,P *pr)
174: {
175: V v,v1;
176: P m,m1,q,r;
177: Z tq;
178: int n;
179:
180: if ( ( v = VR(p1) ) != ( v1 = VR(p2) ) ) {
181: while ( ( VR(vl) != v ) && ( VR(vl) != v1 ) )
182: vl = NEXT(vl);
183: if ( VR(vl) == v ) {
184: *p = p1; *pr = 0;
185: } else {
186: *p = 0; *pr = p1;
187: }
188: } else if ( (n = deg(v,p1) - deg(v,p2)) < 0 ) {
189: *pr = p1; *p = 0;
190: } else {
1.2 ! noro 191: n++; STOZ(n,tq);
1.1 noro 192: pwrp(vl,LC(p2),tq,&m); mulp(vl,m,p1,&m1); divsrp(vl,m1,p2,&q,&r);
193: remsdcp(vl,q,p0,p); remsdcp(vl,r,p0,pr);
194: }
195: }
196:
197: void pmonic(VL vl, P p0, P p, P *pr)
198: {
199: P d,m,pp,c,t;
200:
201: if ( NUM(p) || ( VR(p) == VR(p0) ) )
202: *pr = (P)ONE;
203: else if ( NUM(COEF(DC(p))) )
204: *pr = p;
205: else {
206: ptozp(COEF(DC(p)),1,(Q *)&c,&pp); pinva(p0,pp,&d);
207: mulp(vl,p,d,&m); remsdcp(vl,m,p0,&t); ptozp(t,1,(Q *)&c,pr);
208: }
209: }
210:
211: void remsdcp(VL vl, P p, P p0, P *pr)
212: {
213: P q,r,c;
214: DCP dc,dcr,dcr0;
215:
216: if ( !p )
217: *pr = 0;
218: else if ( NUM(p) )
219: *pr = (P)ONE;
220: else if ( VR(p) == VR(p0) ) {
221: divsrp(vl,p,p0,&q,&r); ptozp(r,1,(Q *)&c,pr);
222: } else {
223: for ( dcr = dcr0 = 0, dc = DC(p); dc; dc = NEXT(dc) ) {
224: divsrp(vl,COEF(dc),p0,&q,&r);
225: if ( r ) {
226: NEXTDC(dcr0,dcr); DEG(dcr) = DEG(dc); COEF(dcr) = r;
227: }
228: }
229: if ( !dcr0 )
230: *pr = 0;
231: else {
232: NEXT(dcr) = 0; MKP(VR(p),dcr0,r); ptozp(r,1,(Q *)&c,pr);
233: }
234: }
235: }
236:
237: void pinva(P p0, P p, P *pr)
238: {
239: V v;
240: Z w,q,q1;
241: Q f;
242: Q t,a,b,s,ts;
243: P c,c1;
244: P tg,th,tr;
245: P z,zz,zzz;
246: UM wg,wh,ws,wt,wm;
247: int n,m,modres,mod,index,i;
248:
249: v = VR(p); n=deg(v,p); m=deg(v,p0);
250: norm(p,&a); norm(p0,&b);
1.2 ! noro 251: STOZ(m,w); pwrq(a,(Q)w,&t); STOZ(n,w); pwrq(b,(Q)w,&s);
1.1 noro 252: mulq(t,s,&ts);
253: factorialz(n+m,&w); mulq(ts,(Q)w,&s); addq(s,s,&f);
254: wg = W_UMALLOC(m+n); wh = W_UMALLOC(m+n);
255: wt = W_UMALLOC(m+n); ws = W_UMALLOC(m+n);
256: wm = W_UMALLOC(m+n);
257: for ( q = ONE, t = 0, c = 0, index = 0; ; ) {
258: mod = get_lprime(index++);
259: if ( !remqi((Q)LC(p),mod) || !remqi((Q)LC(p0),mod) )
260: continue;
261: ptomp(mod,p,&tg); ptomp(mod,p0,&th); srchump(mod,tg,th,&tr);
262: if ( !tr )
263: continue;
264: else
265: modres = CONT((MQ)tr);
266: mptoum(tg,wg); mptoum(th,wh);
267: eucum(mod,wg,wh,ws,wt); /* wg * ws + wh * wt = 1 */
268: DEG(wm) = 0; COEF(wm)[0] = modres;
269: mulum(mod,ws,wm,wt);
270: for ( i = DEG(wt); i >= 0; i-- )
271: if ( ( COEF(wt)[i] * 2 ) > mod )
272: COEF(wt)[i] -= mod;
273: chnrem(mod,v,c,q,wt,&c1,&q1);
274: if ( !ucmpp(c,c1) ) {
275: mulp(CO,c,p,&z); divsrp(CO,z,p0,&zz,&zzz);
276: if ( NUM(zzz) ) {
277: q = q1; c = c1; break;
278: }
279: }
280: q = q1; c = c1;
281: if ( cmpq(f,(Q)q) < 0 )
282: break;
283: }
284: ptozp(c,1,&s,pr);
285: }
286:
287: /*
288: * compute g s.t. h*p0+g*p = res(v,p0,p)
289: */
290:
291: void inva_chrem(P p0, P p, NODE *pr)
292: {
293: V v;
294: Z w,q,q1;
295: Q f,ts;
296: Q u,t,a,b,s,dn;
297: P c,c0,c1;
298: P tg,th,tr;
299: P z,zz,zzz;
300: UM wg,wh,ws,wt,wm;
301: int n,m,modres,mod,index,i;
302:
303: v = VR(p); n=deg(v,p); m=deg(v,p0);
304: norm(p,&a); norm(p0,&b);
1.2 ! noro 305: STOZ(m,w); pwrq(a,(Q)w,&t); STOZ(n,w); pwrq(b,(Q)w,&s);
1.1 noro 306: mulq(t,s,&ts);
307: factorialz(n+m,&w); mulq(ts,(Q)w,&s); addq(s,s,&f);
308: wg = W_UMALLOC(m+n); wh = W_UMALLOC(m+n);
309: wt = W_UMALLOC(m+n); ws = W_UMALLOC(m+n);
310: wm = W_UMALLOC(m+n);
311: for ( q = ONE, t = 0, c = 0, index = 0; ; ) {
312: mod = get_lprime(index++);
313: if ( !remqi((Q)LC(p),mod) || !remqi((Q)LC(p0),mod) )
314: continue;
315: ptomp(mod,p,&tg); ptomp(mod,p0,&th); srchump(mod,tg,th,&tr);
316: if ( !tr )
317: continue;
318: else
319: modres = CONT((MQ)tr);
320: mptoum(tg,wg); mptoum(th,wh);
321: eucum(mod,wg,wh,ws,wt); /* wg * ws + wh * wt = 1 */
322: DEG(wm) = 0; COEF(wm)[0] = modres;
323: mulum(mod,ws,wm,wt);
324: for ( i = DEG(wt); i >= 0; i-- )
325: if ( ( COEF(wt)[i] * 2 ) > mod )
326: COEF(wt)[i] -= mod;
327: chnrem(mod,v,c,q,wt,&c1,&q1);
328: if ( !ucmpp(c,c1) ) {
329: mulp(CO,c,p,&z); divsrp(CO,z,p0,&zz,&zzz);
330: if ( NUM(zzz) ) {
331: q = (Z)zzz; break;
332: }
333: }
334: q = q1; c = c1;
335: if ( cmpq(f,(Q)q) < 0 ) {
336: mulp(CO,c,p,&z); divsrp(CO,z,p0,&zz,&zzz);
337: q = (Z)zzz;
338: break;
339: }
340: }
341: /* c*p = q mod p0 */
342: /* c = s*c0 */
343: ptozp(c,1,&s,&c0);
344: /* c/q = c0/(q/s) */
345: divq((Q)q,s,&dn);
346: *pr = (NODE)mknode(2,c0,dn);
347: }
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