/*
* Copyright (c) 1994-2000 FUJITSU LABORATORIES LIMITED
* All rights reserved.
*
* FUJITSU LABORATORIES LIMITED ("FLL") hereby grants you a limited,
* non-exclusive and royalty-free license to use, copy, modify and
* redistribute, solely for non-commercial and non-profit purposes, the
* computer program, "Risa/Asir" ("SOFTWARE"), subject to the terms and
* conditions of this Agreement. For the avoidance of doubt, you acquire
* only a limited right to use the SOFTWARE hereunder, and FLL or any
* third party developer retains all rights, including but not limited to
* copyrights, in and to the SOFTWARE.
*
* (1) FLL does not grant you a license in any way for commercial
* purposes. You may use the SOFTWARE only for non-commercial and
* non-profit purposes only, such as academic, research and internal
* business use.
* (2) The SOFTWARE is protected by the Copyright Law of Japan and
* international copyright treaties. If you make copies of the SOFTWARE,
* with or without modification, as permitted hereunder, you shall affix
* to all such copies of the SOFTWARE the above copyright notice.
* (3) An explicit reference to this SOFTWARE and its copyright owner
* shall be made on your publication or presentation in any form of the
* results obtained by use of the SOFTWARE.
* (4) In the event that you modify the SOFTWARE, you shall notify FLL by
* e-mail at risa-admin@sec.flab.fujitsu.co.jp of the detailed specification
* for such modification or the source code of the modified part of the
* SOFTWARE.
*
* THE SOFTWARE IS PROVIDED AS IS WITHOUT ANY WARRANTY OF ANY KIND. FLL
* MAKES ABSOLUTELY NO WARRANTIES, EXPRESSED, IMPLIED OR STATUTORY, AND
* EXPRESSLY DISCLAIMS ANY IMPLIED WARRANTY OF MERCHANTABILITY, FITNESS
* FOR A PARTICULAR PURPOSE OR NONINFRINGEMENT OF THIRD PARTIES'
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*
* $OpenXM: OpenXM_contrib2/asir2000/engine/A.c,v 1.7 2013/06/13 18:40:31 ohara Exp $
*/
#include "ca.h"
#include "parse.h"
int get_lprime();
void pdiva(vl,p0,p1,p2,pr)
VL vl;
P p1,p2,p0;
P *pr;
{
Q m,d;
P t,q,r;
if ( VR(p2) == VR(p0) ) {
*pr = p1;
return;
}
if ( VR(p1) == VR(p0) ) {
error("pdiva : ???");
return;
}
subq(DEG(DC(p1)),DEG(DC(p2)),&m); addq(m,ONE,&d);
pwrq((Q)COEF(DC(p2)),d,&m); mulp(vl,p1,(P)m,&t);
divsrp(vl,t,p2,&q,&r); remsdcp(vl,q,p0,pr);
}
void rema(vl,p0,p1,p2,pr)
VL vl;
P p1,p2,p0,*pr;
{
P m,m1,m2,g,lc,x,t;
Q q;
V v;
int d1,d2;
if ( !p1 || !p2 || NUM(p2) || ( VR(p2) == VR(p0) ) )
*pr = 0;
else if ( NUM(p1) )
*pr = p1;
else if ( ( v = VR(p1) ) == VR(p0) )
remsdcp(vl,p1,p0,pr);
else if ( ( d1 = deg(v,p1) ) < ( d2 = deg(v,p2) ) )
*pr = p1;
else if ( d1 == d2 ) {
mulp(vl,p1,LC(p2),&m); mulp(vl,p2,LC(p1),&m1);
subp(vl,m,m1,&m2);
remsdcp(vl,m2,p0,pr);
} else {
g = p1; lc = LC(p2); MKV(v,x);
while ( ( d1 = deg(v,g) ) >= d2 ) {
mulp(vl,g,lc,&m); mulp(vl,p2,LC(g),&m1);
STOQ(d1-d2,q); pwrp(vl,x,q,&t);
mulp(vl,m1,t,&m2); subp(vl,m,m2,&m1);
remsdcp(vl,m1,p0,&g);
}
*pr = g;
}
}
void gcda(vl,p0,p1,p2,pr)
VL vl;
P p1,p2,p0,*pr;
{
P g1,g2,r,t,c;
remsdcp(vl,p1,p0,&t); pcp(vl,t,&g1,&c); remsdcp(vl,p2,p0,&g2);
while ( 1 ) {
if ( NUM(g2) || (VR(g2) == VR(p0)) ) {
*pr = (P)ONE;
return;
}
pcp(vl,g2,&t,&c); pmonic(vl,p0,t,&g2); rema(vl,p0,g1,g2,&r);
if ( !r ) {
pmonic(vl,p0,g2,pr);
return;
}
g1 = g2; g2 = r;
}
}
void sqa(vl,p0,p,dcp)
VL vl;
P p,p0;
DCP *dcp;
{
V v;
int i,j,n;
P f,f1,f2,gcd,flat,q,r,t;
P *a;
int *b;
DCP dc,dc0;
if ( ( v = VR(p) ) == VR(p0) ) {
NEWDC(dc); *dcp = dc; COEF(dc) = (P)ONE; DEG(dc) = ONE;
NEXT(dc) = 0;
} else {
n = deg(v,p); W_CALLOC(n,P,a); W_CALLOC(n,int,b);
for ( i = 0, f = p; ;i++ ) {
if ( VR(f) != v )
break;
remsdcp(vl,f,p0,&f1); diffp(vl,f1,VR(f1),&f2);
while ( 1 ) {
pmonic(vl,p0,f2,&t); f2 = t; rema(vl,p0,f1,f2,&r);
if ( !r ) {
pmonic(vl,p0,f2,&gcd); pqra(vl,p0,f,gcd,&flat,&r);
break;
}
f1 = f2; f2 = r;
}
if ( VR(gcd) != v ) {
a[i] = f; b[i] = 1;
break;
}
for ( j = 1, f = gcd; ; j++ ) {
pqra(vl,p0,f,flat,&q,&r);
if ( r )
break;
else
f = q;
}
a[i] = flat; b[i] = j;
}
for ( i = 0, j = 0, dc0 = 0; a[i]; i++ ) {
NEXTDC(dc0,dc); j += b[i]; STOQ(j,DEG(dc));
if ( a[i+1] )
pqra(vl,p0,a[i],a[i+1],&COEF(dc),&t);
else
COEF(dc) = a[i];
}
NEXT(dc) = 0; *dcp = dc0;
}
}
void pqra(vl, p0, p1, p2, p, pr)
VL vl;
P p0,p1,p2;
P *p,*pr;
{
V v,v1;
P m,m1,q,r;
Q tq;
int n;
if ( ( v = VR(p1) ) != ( v1 = VR(p2) ) ) {
while ( ( VR(vl) != v ) && ( VR(vl) != v1 ) )
vl = NEXT(vl);
if ( VR(vl) == v ) {
*p = p1; *pr = 0;
} else {
*p = 0; *pr = p1;
}
} else if ( (n = deg(v,p1) - deg(v,p2)) < 0 ) {
*pr = p1; *p = 0;
} else {
n++; STOQ(n,tq);
pwrp(vl,LC(p2),tq,&m); mulp(vl,m,p1,&m1); divsrp(vl,m1,p2,&q,&r);
remsdcp(vl,q,p0,p); remsdcp(vl,r,p0,pr);
}
}
void pmonic(vl, p0, p, pr)
VL vl;
P p,p0,*pr;
{
P d,m,pp,c,t;
if ( NUM(p) || ( VR(p) == VR(p0) ) )
*pr = (P)ONE;
else if ( NUM(COEF(DC(p))) )
*pr = p;
else {
ptozp(COEF(DC(p)),1,(Q *)&c,&pp); pinva(p0,pp,&d);
mulp(vl,p,d,&m); remsdcp(vl,m,p0,&t); ptozp(t,1,(Q *)&c,pr);
}
}
void remsdcp(vl, p, p0, pr)
VL vl;
P p,p0,*pr;
{
P q,r,c;
DCP dc,dcr,dcr0;
if ( !p )
*pr = 0;
else if ( NUM(p) )
*pr = (P)ONE;
else if ( VR(p) == VR(p0) ) {
divsrp(vl,p,p0,&q,&r); ptozp(r,1,(Q *)&c,pr);
} else {
for ( dcr = dcr0 = 0, dc = DC(p); dc; dc = NEXT(dc) ) {
divsrp(vl,COEF(dc),p0,&q,&r);
if ( r ) {
NEXTDC(dcr0,dcr); DEG(dcr) = DEG(dc); COEF(dcr) = r;
}
}
if ( !dcr0 )
*pr = 0;
else {
NEXT(dcr) = 0; MKP(VR(p),dcr0,r); ptozp(r,1,(Q *)&c,pr);
}
}
}
void pinva(p0, p, pr)
P p,p0,*pr;
{
V v;
Q f,q,q1;
Q u,t,a,b,s;
P c,c1;
P tg,th,tr;
P z,zz,zzz;
UM wg,wh,ws,wt,wm;
int n,m,modres,mod,index,i;
v = VR(p); n=deg(v,p); m=deg(v,p0);
norm(p,&a); norm(p0,&b);
STOQ(m,u); pwrq(a,u,&t); STOQ(n,u); pwrq(b,u,&s);
mulq(t,s,&u);
factorial(n+m,&t); mulq(u,t,&s); addq(s,s,&f);
wg = W_UMALLOC(m+n); wh = W_UMALLOC(m+n);
wt = W_UMALLOC(m+n); ws = W_UMALLOC(m+n);
wm = W_UMALLOC(m+n);
for ( q = ONE, t = 0, c = 0, index = 0; ; ) {
mod = get_lprime(index++);
if ( !rem(NM((Q)LC(p)),mod) || !rem(NM((Q)LC(p0)),mod) )
continue;
ptomp(mod,p,&tg); ptomp(mod,p0,&th); srchump(mod,tg,th,&tr);
if ( !tr )
continue;
else
modres = CONT((MQ)tr);
mptoum(tg,wg); mptoum(th,wh);
eucum(mod,wg,wh,ws,wt); /* wg * ws + wh * wt = 1 */
DEG(wm) = 0; COEF(wm)[0] = modres;
mulum(mod,ws,wm,wt);
for ( i = DEG(wt); i >= 0; i-- )
if ( ( COEF(wt)[i] * 2 ) > mod )
COEF(wt)[i] -= mod;
chnrem(mod,v,c,q,wt,&c1,&q1);
if ( !ucmpp(c,c1) ) {
mulp(CO,c,p,&z); divsrp(CO,z,p0,&zz,&zzz);
if ( NUM(zzz) ) {
q = q1; c = c1; break;
}
}
q = q1; c = c1;
if ( cmpq(f,q) < 0 )
break;
}
ptozp(c,1,&s,pr);
}
/*
* compute g s.t. h*p0+g*p = res(v,p0,p)
*/
void inva_chrem(P p0, P p, NODE *pr)
{
V v;
Q f,q,q1;
Q u,t,a,b,s,dn;
P c,c0,c1;
P tg,th,tr;
P z,zz,zzz;
UM wg,wh,ws,wt,wm;
int n,m,modres,mod,index,i;
v = VR(p); n=deg(v,p); m=deg(v,p0);
norm(p,&a); norm(p0,&b);
STOQ(m,u); pwrq(a,u,&t); STOQ(n,u); pwrq(b,u,&s);
mulq(t,s,&u);
factorial(n+m,&t); mulq(u,t,&s); addq(s,s,&f);
wg = W_UMALLOC(m+n); wh = W_UMALLOC(m+n);
wt = W_UMALLOC(m+n); ws = W_UMALLOC(m+n);
wm = W_UMALLOC(m+n);
for ( q = ONE, t = 0, c = 0, index = 0; ; ) {
mod = get_lprime(index++);
if ( !rem(NM((Q)LC(p)),mod) || !rem(NM((Q)LC(p0)),mod) )
continue;
ptomp(mod,p,&tg); ptomp(mod,p0,&th); srchump(mod,tg,th,&tr);
if ( !tr )
continue;
else
modres = CONT((MQ)tr);
mptoum(tg,wg); mptoum(th,wh);
eucum(mod,wg,wh,ws,wt); /* wg * ws + wh * wt = 1 */
DEG(wm) = 0; COEF(wm)[0] = modres;
mulum(mod,ws,wm,wt);
for ( i = DEG(wt); i >= 0; i-- )
if ( ( COEF(wt)[i] * 2 ) > mod )
COEF(wt)[i] -= mod;
chnrem(mod,v,c,q,wt,&c1,&q1);
if ( !ucmpp(c,c1) ) {
mulp(CO,c,p,&z); divsrp(CO,z,p0,&zz,&zzz);
if ( NUM(zzz) ) {
q = (Q)zzz; break;
}
}
q = q1; c = c1;
if ( cmpq(f,q) < 0 ) {
mulp(CO,c,p,&z); divsrp(CO,z,p0,&zz,&zzz);
q = (Q)zzz;
break;
}
}
/* c*p = q mod p0 */
/* c = s*c0 */
ptozp(c,1,&s,&c0);
/* c/q = c0/(q/s) */
divq(q,s,&dn);
*pr = (NODE)mknode(2,c0,dn);
}