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Revision 1.14, Mon Mar 16 16:43:02 2009 UTC (15 years, 2 months ago) by ohara
Branch: MAIN
CVS Tags: R_1_3_1-2
Changes since 1.13: +2 -2 lines

In asir sources, LONG_IS_32BIT and LONG_IS_64BIT are replaced by SIZEOF_LONG.
Still, these are defined for pari.

/*
 * 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'
 * RIGHTS. NO FLL DEALER, AGENT, EMPLOYEES IS AUTHORIZED TO MAKE ANY
 * MODIFICATIONS, EXTENSIONS, OR ADDITIONS TO THIS WARRANTY.
 * UNDER NO CIRCUMSTANCES AND UNDER NO LEGAL THEORY, TORT, CONTRACT,
 * OR OTHERWISE, SHALL FLL BE LIABLE TO YOU OR ANY OTHER PERSON FOR ANY
 * DIRECT, INDIRECT, SPECIAL, INCIDENTAL, PUNITIVE OR CONSEQUENTIAL
 * DAMAGES OF ANY CHARACTER, INCLUDING, WITHOUT LIMITATION, DAMAGES
 * ARISING OUT OF OR RELATING TO THE SOFTWARE OR THIS AGREEMENT, DAMAGES
 * FOR LOSS OF GOODWILL, WORK STOPPAGE, OR LOSS OF DATA, OR FOR ANY
 * DAMAGES, EVEN IF FLL SHALL HAVE BEEN INFORMED OF THE POSSIBILITY OF
 * SUCH DAMAGES, OR FOR ANY CLAIM BY ANY OTHER PARTY. EVEN IF A PART
 * OF THE SOFTWARE HAS BEEN DEVELOPED BY A THIRD PARTY, THE THIRD PARTY
 * DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE,
 * PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE.
 *
 * $OpenXM: OpenXM_contrib2/asir2000/engine/_distm.c,v 1.14 2009/03/16 16:43:02 ohara Exp $ 
*/
#include "ca.h"
#include "inline.h"

extern int (*cmpdl)();
extern int do_weyl;

MP _mp_free_list;
DP _dp_free_list;
DL _dl_free_list;
int current_dl_length;

void GC_gcollect();

void _free_private_storage()
{
	_mp_free_list = 0;
	_dp_free_list = 0;
	_dl_free_list = 0;
	GC_gcollect();
}

void _DL_alloc()
{
	int *p;
	int i,dl_len;
	static int DL_alloc_count;

/*	fprintf(stderr,"DL_alloc : %d \n",++DL_alloc_count); */
	dl_len = (current_dl_length+1);
#if SIZEOF_LONG == 8
	if ( dl_len & 1 )
		dl_len += 1;
#endif
	for ( i = 0; i < 128; i++, p += dl_len ) {
		p = (int *)GC_malloc(dl_len*sizeof(int));
		*(DL *)p = _dl_free_list;
		_dl_free_list = (DL)p;
	}
}

void _MP_alloc()
{
	MP p;
	int i;
	static int MP_alloc_count;

/*	fprintf(stderr,"MP_alloc : %d \n",++MP_alloc_count); */
	for ( i = 0; i < 1024; i++ ) {
		p = (MP)GC_malloc(sizeof(struct oMP));
		p->next = _mp_free_list; _mp_free_list = p;
	}
}
		
void _DP_alloc()
{
	DP p;
	int i;
	static int DP_alloc_count;

/*	fprintf(stderr,"DP_alloc : %d \n",++DP_alloc_count); */
	for ( i = 0; i < 1024; i++ ) {
		p = (DP)GC_malloc(sizeof(struct oDP));
		p->body = (MP)_dp_free_list; _dp_free_list = p;
	}
}

/* merge p1 and p2 into pr */

void _addmd_destructive(int mod,DP p1,DP p2,DP *pr)
{
	int n;
	MP m1,m2,mr,mr0,s;
	int t;

	if ( !p1 )
		*pr = p2;
	else if ( !p2 )
		*pr = p1;
	else {
		for ( n = NV(p1), m1 = BDY(p1), m2 = BDY(p2), mr0 = 0; m1 && m2; )
			switch ( (*cmpdl)(n,m1->dl,m2->dl) ) {
				case 0:
					t = (ITOS(C(m1))+ITOS(C(m2))) - mod;
					if ( t < 0 )
						t += mod;
					s = m1; m1 = NEXT(m1);
					if ( t ) {
						_NEXTMP2(mr0,mr,s); C(mr) = STOI(t);
					} else {
						_FREEDL(s->dl); _FREEMP(s);
					}
					s = m2; m2 = NEXT(m2); _FREEDL(s->dl); _FREEMP(s);
					break;
				case 1:
					s = m1; m1 = NEXT(m1); _NEXTMP2(mr0,mr,s);
					break;
				case -1:
					s = m2; m2 = NEXT(m2); _NEXTMP2(mr0,mr,s);
					break;
			}
		if ( !mr0 )
			if ( m1 )
				mr0 = m1;
			else if ( m2 )
				mr0 = m2;
			else {
				*pr = 0;
				return;
			}
		else if ( m1 )
			NEXT(mr) = m1;
		else if ( m2 )
			NEXT(mr) = m2;
		else
			NEXT(mr) = 0;
		_MKDP(NV(p1),mr0,*pr);
		if ( *pr )
			(*pr)->sugar = MAX(p1->sugar,p2->sugar);
		_FREEDP(p1); _FREEDP(p2);
	}
}

void _mulmd_dup(int mod,DP p1,DP p2,DP *pr)
{
	if ( !do_weyl )
		_comm_mulmd_dup(mod,p1,p2,pr);
	else
		_weyl_mulmd_dup(mod,p1,p2,pr);
}

void _comm_mulmd_dup(int mod,DP p1,DP p2,DP *pr)
{
	MP m;
	DP s,t,u;
	int i,l,l1;
	static MP *w;
	static int wlen;

	if ( !p1 || !p2 )
		*pr = 0;
	else {
		for ( m = BDY(p1), l1 = 0; m; m = NEXT(m), l1++ );
		for ( m = BDY(p2), l = 0; m; m = NEXT(m), l++ );
		if ( l1 < l ) {
			t = p1; p1 = p2; p2 = t;
			l = l1;
		}
		if ( l > wlen ) {
			if ( w ) GC_free(w);
			w = (MP *)MALLOC(l*sizeof(MP));
			wlen = l;
		}
		for ( m = BDY(p2), i = 0; i < l; m = NEXT(m), i++ )
			w[i] = m;
		for ( s = 0, i = l-1; i >= 0; i-- ) {
			_mulmdm_dup(mod,p1,w[i],&t); _addmd_destructive(mod,s,t,&u); s = u;
		}
		bzero(w,l*sizeof(MP));
		*pr = s;
	}
}

void _weyl_mulmd_dup(int mod,DP p1,DP p2,DP *pr)
{
	MP m;
	DP s,t,u;
	int i,l;
	static MP *w;
	static int wlen;

	if ( !p1 || !p2 )
		*pr = 0;
	else {
		for ( m = BDY(p1), l = 0; m; m = NEXT(m), l++ );
		if ( l > wlen ) {
			if ( w ) GC_free(w);
			w = (MP *)MALLOC(l*sizeof(MP));
			wlen = l;
		}
		for ( m = BDY(p1), i = 0; i < l; m = NEXT(m), i++ )
			w[i] = m;
		for ( s = 0, i = l-1; i >= 0; i-- ) {
			_weyl_mulmdm_dup(mod,w[i],p2,&t); _addmd_destructive(mod,s,t,&u); s = u;
		}
		bzero(w,l*sizeof(MP));
		*pr = s;
	}
}

void _mulmdm_dup(int mod,DP p,MP m0,DP *pr)
{
	MP m,mr,mr0;
	DL d,dt,dm;
	int c,n,i,c1,c2;
	int *pt,*p1,*p2;

	if ( !p )
		*pr = 0;
	else {
		for ( mr0 = 0, m = BDY(p), c = ITOS(C(m0)), d = m0->dl, n = NV(p); 
			m; m = NEXT(m) ) {
			_NEXTMP(mr0,mr);
			c1 = ITOS(C(m));
			DMAR(c1,c,0,mod,c2);
			C(mr) = (P)STOI(c2);
			_NEWDL_NOINIT(dt,n); mr->dl = dt;
			dm = m->dl;
			dt->td = d->td + dm->td;
			for ( i = 0, pt = dt->d, p1=d->d, p2 = dm->d; i < n; i++ )
				*pt++ = *p1++ + *p2++;
		}
		NEXT(mr) = 0; _MKDP(NV(p),mr0,*pr);
		if ( *pr )
			(*pr)->sugar = p->sugar + m0->dl->td;
	}
}

void _weyl_mulmdm_dup(int mod,MP m0,DP p,DP *pr)
{
	DP r,t,t1;
	MP m;
	DL d0;
	int n,n2,l,i,j,tlen;
	static MP *w,*psum;
	static struct cdlm *tab;
	static int wlen;
	static int rtlen;

	if ( !p )
		*pr = 0;
	else {
		for ( m = BDY(p), l = 0; m; m = NEXT(m), l++ );
		if ( l > wlen ) {
			if ( w ) GC_free(w);
			w = (MP *)MALLOC(l*sizeof(MP));
			wlen = l;
		}
		for ( m = BDY(p), i = 0; i < l; m = NEXT(m), i++ )
			w[i] = m;
		n = NV(p); n2 = n>>1;
		d0 = m0->dl;

		for ( i = 0, tlen = 1; i < n2; i++ )
			tlen *= d0->d[n2+i]+1;
		if ( tlen > rtlen ) {
			if ( tab ) GC_free(tab);
			if ( psum ) GC_free(psum);
			rtlen = tlen;
			tab = (struct cdlm *)MALLOC(rtlen*sizeof(struct cdlm));
			psum = (MP *)MALLOC(rtlen*sizeof(MP));
		}
		bzero(psum,tlen*sizeof(MP));
		for ( i = l-1; i >= 0; i-- ) {
			bzero(tab,tlen*sizeof(struct cdlm));
			_weyl_mulmmm_dup(mod,m0,w[i],n,tab,tlen);
			for ( j = 0; j < tlen; j++ ) {
				if ( tab[j].c ) {
					_NEWMP(m); m->dl = tab[j].d;
					C(m) = STOI(tab[j].c); NEXT(m) = psum[j];
					psum[j] = m;
				}
			}
		}
		for ( j = tlen-1, r = 0; j >= 0; j-- ) 
			if ( psum[j] ) {
				_MKDP(n,psum[j],t); _addmd_destructive(mod,r,t,&t1); r = t1;
			}
		if ( r )
			r->sugar = p->sugar + m0->dl->td;
		*pr = r;
	}
}

/* m0 = x0^d0*x1^d1*... * dx0^d(n/2)*dx1^d(n/2+1)*... */

void _weyl_mulmmm_dup(int mod,MP m0,MP m1,int n,struct cdlm *rtab,int rtablen)
{
	int c,c0,c1;
	DL d,d0,d1,dt;
	int i,j,a,b,k,l,n2,s,min,curlen;
	struct cdlm *p;
	static int *ctab;
	static struct cdlm *tab;
	static int tablen;
	static struct cdlm *tmptab;
	static int tmptablen;

	if ( !m0 || !m1 ) {
		rtab[0].c = 0;
		rtab[0].d = 0;
		return;
	}
	c0 = ITOS(C(m0)); c1 = ITOS(C(m1));
	c = dmar(c0,c1,0,mod);
	d0 = m0->dl; d1 = m1->dl;
	n2 = n>>1;
	curlen = 1;

	_NEWDL(d,n);
	if ( n & 1 )
		/* offset of h-degree */
		d->td = d->d[n-1] = d0->d[n-1]+d1->d[n-1];
	else
		d->td = 0;
	rtab[0].c = c;
	rtab[0].d = d;

	if ( rtablen > tmptablen ) {
		if ( tmptab ) GC_free(tmptab);
		tmptab = (struct cdlm *)MALLOC(rtablen*sizeof(struct cdlm));
		tmptablen = rtablen; 
	}

	for ( i = 0; i < n2; i++ ) {
		a = d0->d[i]; b = d1->d[n2+i];
		k = d0->d[n2+i]; l = d1->d[i];

		/* degree of xi^a*(Di^k*xi^l)*Di^b */
		a += l;
		b += k;
		s = MUL_WEIGHT(a,i)+MUL_WEIGHT(b,n2+i);

		if ( !k || !l ) {
			for ( j = 0, p = rtab; j < curlen; j++, p++ ) {
				if ( p->c ) {
					dt = p->d;
					dt->d[i] = a;
					dt->d[n2+i] = b;
					dt->td += s;
				}
			}
			curlen *= k+1;
			continue;
		}
		if ( k+1 > tablen ) {
			if ( tab ) GC_free(tab);
			if ( ctab ) GC_free(ctab);
			tablen = k+1;
			tab = (struct cdlm *)MALLOC(tablen*sizeof(struct cdlm));
			ctab = (int *)MALLOC(tablen*sizeof(int));
		}
		/* compute xi^a*(Di^k*xi^l)*Di^b */
		min = MIN(k,l);
		mkwcm(k,l,mod,ctab);
		bzero(tab,(k+1)*sizeof(struct cdlm));
		/* n&1 != 0 => homogenized computation; dx-xd=h^2 */
		if ( n & 1 )
			for ( j = 0; j <= min; j++ ) {
				_NEWDL(d,n);
				d->d[i] = a-j; d->d[n2+i] = b-j;
				d->td = s;
				d->d[n-1] = s-(MUL_WEIGHT(a-j,i)+MUL_WEIGHT(b-j,n2+i)); 
				tab[j].d = d;
				tab[j].c = ctab[j];
			}
		else
			for ( j = 0; j <= min; j++ ) {
				_NEWDL(d,n);
				d->d[i] = a-j; d->d[n2+i] = b-j;
				d->td = MUL_WEIGHT(a-j,i)+MUL_WEIGHT(b-j,n2+i);  /* XXX */
				tab[j].d = d;
				tab[j].c = ctab[j];
			}
#if 0
		_comm_mulmd_tab(mod,n,rtab,curlen,tab,k+1,tmptab);
		for ( j = 0; j < curlen; j++ )
			if ( rtab[j].d ) { _FREEDL(rtab[j].d); }
		for ( j = 0; j <= min; j++ )
			if ( tab[j].d ) { _FREEDL(tab[j].d); }
		curlen *= k+1;
		bcopy(tmptab,rtab,curlen*sizeof(struct cdlm));
#else
		_comm_mulmd_tab_destructive(mod,n,rtab,curlen,tab,k+1);
		for ( j = 0; j <= min; j++ )
			if ( tab[j].d ) { _FREEDL(tab[j].d); }
		curlen *= k+1;
#endif
	}
}

/* direct product of two cdlm tables
  rt[] = [
    t[0]*t1[0],...,t[n-1]*t1[0],
    t[0]*t1[1],...,t[n-1]*t1[1],
    ...
    t[0]*t1[n1-1],...,t[n-1]*t1[n1-1]
  ]
*/

void _comm_mulmd_tab(int mod,int nv,struct cdlm *t,int n,struct cdlm *t1,int n1,struct cdlm *rt)
{
	int i,j;
	struct cdlm *p;
	int c;
	DL d;

	bzero(rt,n*n1*sizeof(struct cdlm));
	for ( j = 0, p = rt; j < n1; j++ ) {
		c = t1[j].c;
		d = t1[j].d;
		if ( !c )
			break;
		for ( i = 0; i < n; i++, p++ ) {
			if ( t[i].c ) {
				p->c = dmar(t[i].c,c,0,mod);
				_adddl_dup(nv,t[i].d,d,&p->d);
			}
		}
	}
}

void _comm_mulmd_tab_destructive(int mod,int nv,struct cdlm *t,int n,struct cdlm *t1,int n1)
{
	int i,j;
	struct cdlm *p;
	int c;
	DL d;

	for ( j = 1, p = t+n; j < n1; j++ ) {
		c = t1[j].c;
		d = t1[j].d;
		if ( !c )
			break;
		for ( i = 0; i < n; i++, p++ ) {
			if ( t[i].c ) {
				p->c = dmar(t[i].c,c,0,mod);
				_adddl_dup(nv,t[i].d,d,&p->d);
			}
		}
	}
	c = t1[0].c;
	d = t1[0].d;
	for ( i = 0, p = t; i < n; i++, p++ )
		if ( t[i].c ) {
			p->c = dmar(t[i].c,c,0,mod);
			/* t[i].d += d */
			adddl_destructive(nv,t[i].d,d);
		}
}

void dlto_dl(DL d,DL *dr)
{
	int i,n;
	DL t;

	n = current_dl_length;
	_NEWDL(t,n); *dr = t;
	t->td = d->td;
	for ( i = 0; i < n; i++ )
		t->d[i] = d->d[i];	
}

void _dltodl(DL d,DL *dr)
{
	int i,n;
	DL t;

	n = current_dl_length;
	NEWDL(t,n); *dr = t;
	t->td = d->td;
	for ( i = 0; i < n; i++ )
		t->d[i] = d->d[i];	
}

void _adddl_dup(int n,DL d1,DL d2,DL *dr)
{
	DL dt;
	int i;

	_NEWDL(dt,n);
	*dr = dt;
	dt->td = d1->td + d2->td;
	for ( i = 0; i < n; i++ )
		dt->d[i] = d1->d[i]+d2->d[i];
}

void _free_dlarray(DL *a,int n)
{
	int i;

	for ( i = 0; i < n; i++ ) { _FREEDL(a[i]); }
}

void _free_dp(DP f)
{
	MP m,s;

	if ( !f )
		return;
	m = f->body;
	while ( m ) {
		s = m; m = NEXT(m); _FREEDL(s->dl); _FREEMP(s);
	}
	_FREEDP(f);
}

void dpto_dp(DP p,DP *r)
{
	MP m,mr0,mr;
	DL t;

	if ( !p )
		*r = 0;
	else {
		/* XXX : dummy call to set current_dl_length */
		_NEWDL_NOINIT(t,NV(p));

		for ( m = BDY(p), mr0 = 0; m; m = NEXT(m) ) {
			_NEXTMP(mr0,mr);
			dlto_dl(m->dl,&mr->dl);
			mr->c = m->c;
		}
		NEXT(mr) = 0;
		_MKDP(p->nv,mr0,*r);
		(*r)->sugar = p->sugar;
	}
}

void _dptodp(DP p,DP *r)
{
	MP m,mr0,mr;

	if ( !p )
		*r = 0;
	else {
		for ( m = BDY(p), mr0 = 0; m; m = NEXT(m) ) {
			NEXTMP(mr0,mr);
			_dltodl(m->dl,&mr->dl);
			mr->c = m->c;
		}
		NEXT(mr) = 0;
		MKDP(p->nv,mr0,*r);
		(*r)->sugar = p->sugar;
	}
}

/* 
 * destructive merge of two list
 *
 * p1, p2 : list of DL
 * return : a merged list
 */

NODE _symb_merge(NODE m1,NODE m2,int n)
{
	NODE top,prev,cur,m,t;

	if ( !m1 )
		return m2;
	else if ( !m2 )
		return m1;
	else {
		switch ( (*cmpdl)(n,(DL)BDY(m1),(DL)BDY(m2)) ) {
			case 0:
				top = m1; _FREEDL((DL)BDY(m2)); m = NEXT(m2);
				break;
			case 1:
				top = m1; m = m2;
				break;
			case -1:
				top = m2; m = m1;
				break;
		}
		prev = top; cur = NEXT(top);
		/* BDY(prev) > BDY(m) always holds */
		while ( cur && m ) {
			switch ( (*cmpdl)(n,(DL)BDY(cur),(DL)BDY(m)) ) {
				case 0:
					_FREEDL(BDY(m)); m = NEXT(m);
					prev = cur; cur = NEXT(cur);
					break;
				case 1:
					t = NEXT(cur); NEXT(cur) = m; m = t;
					prev = cur; cur = NEXT(cur);
					break;
				case -1:
					NEXT(prev) = m; m = cur;
					prev = NEXT(prev); cur = NEXT(prev);
					break;
			}
		}
		if ( !cur )
			NEXT(prev) = m;
		return top;
	}
}

/* merge p1 and p2 into pr */

void _addd_destructive(VL vl,DP p1,DP p2,DP *pr)
{
	int n;
	MP m1,m2,mr,mr0,s;
	P t;

	if ( !p1 )
		*pr = p2;
	else if ( !p2 )
		*pr = p1;
	else {
		for ( n = NV(p1), m1 = BDY(p1), m2 = BDY(p2), mr0 = 0; m1 && m2; )
			switch ( (*cmpdl)(n,m1->dl,m2->dl) ) {
				case 0:
					addp(vl,C(m1),C(m2),&t);
					s = m1; m1 = NEXT(m1);
					if ( t ) {
						_NEXTMP2(mr0,mr,s); C(mr) = t;
					} else {
						_FREEDL(s->dl); _FREEMP(s);
					}
					s = m2; m2 = NEXT(m2); _FREEDL(s->dl); _FREEMP(s);
					break;
				case 1:
					s = m1; m1 = NEXT(m1); _NEXTMP2(mr0,mr,s);
					break;
				case -1:
					s = m2; m2 = NEXT(m2); _NEXTMP2(mr0,mr,s);
					break;
			}
		if ( !mr0 )
			if ( m1 )
				mr0 = m1;
			else if ( m2 )
				mr0 = m2;
			else {
				*pr = 0;
				return;
			}
		else if ( m1 )
			NEXT(mr) = m1;
		else if ( m2 )
			NEXT(mr) = m2;
		else
			NEXT(mr) = 0;
		_MKDP(NV(p1),mr0,*pr);
		if ( *pr )
			(*pr)->sugar = MAX(p1->sugar,p2->sugar);
		_FREEDP(p1); _FREEDP(p2);
	}
}

void _muld_dup(VL vl,DP p1,DP p2,DP *pr)
{
	if ( !do_weyl )
		_comm_muld_dup(vl,p1,p2,pr);
	else
		_weyl_muld_dup(vl,p1,p2,pr);
}

void _comm_muld_dup(VL vl,DP p1,DP p2,DP *pr)
{
	MP m;
	DP s,t,u;
	int i,l,l1;
	static MP *w;
	static int wlen;

	if ( !p1 || !p2 )
		*pr = 0;
	else {
		for ( m = BDY(p1), l1 = 0; m; m = NEXT(m), l1++ );
		for ( m = BDY(p2), l = 0; m; m = NEXT(m), l++ );
		if ( l1 < l ) {
			t = p1; p1 = p2; p2 = t;
			l = l1;
		}
		if ( l > wlen ) {
			if ( w ) GC_free(w);
			w = (MP *)MALLOC(l*sizeof(MP));
			wlen = l;
		}
		for ( m = BDY(p2), i = 0; i < l; m = NEXT(m), i++ )
			w[i] = m;
		for ( s = 0, i = l-1; i >= 0; i-- ) {
			_muldm_dup(vl,p1,w[i],&t); _addd_destructive(vl,s,t,&u); s = u;
		}
		bzero(w,l*sizeof(MP));
		*pr = s;
	}
}

void _weyl_muld_dup(VL vl,DP p1,DP p2,DP *pr)
{
	MP m;
	DP s,t,u;
	int i,l;
	static MP *w;
	static int wlen;

	if ( !p1 || !p2 )
		*pr = 0;
	else {
		for ( m = BDY(p1), l = 0; m; m = NEXT(m), l++ );
		if ( l > wlen ) {
			if ( w ) GC_free(w);
			w = (MP *)MALLOC(l*sizeof(MP));
			wlen = l;
		}
		for ( m = BDY(p1), i = 0; i < l; m = NEXT(m), i++ )
			w[i] = m;
		for ( s = 0, i = l-1; i >= 0; i-- ) {
			_weyl_muldm_dup(vl,w[i],p2,&t); _addd_destructive(vl,s,t,&u); s = u;
		}
		bzero(w,l*sizeof(MP));
		*pr = s;
	}
}

void _muldm_dup(VL vl,DP p,MP m0,DP *pr)
{
	MP m,mr,mr0;
	DL d,dt,dm;
	P c;
	int n,i;
	int *pt,*p1,*p2;

	if ( !p )
		*pr = 0;
	else {
		for ( mr0 = 0, m = BDY(p), c = C(m0), d = m0->dl, n = NV(p); 
			m; m = NEXT(m) ) {
			_NEXTMP(mr0,mr);
			mulp(vl,C(m),c,&C(mr));
			_NEWDL_NOINIT(dt,n); mr->dl = dt;
			dm = m->dl;
			dt->td = d->td + dm->td;
			for ( i = 0, pt = dt->d, p1=d->d, p2 = dm->d; i < n; i++ )
				*pt++ = *p1++ + *p2++;
		}
		NEXT(mr) = 0; _MKDP(NV(p),mr0,*pr);
		if ( *pr )
			(*pr)->sugar = p->sugar + m0->dl->td;
	}
}

void _weyl_muldm_dup(VL vl,MP m0,DP p,DP *pr)
{
	DP r,t,t1;
	MP m;
	DL d0;
	int n,n2,l,i,j,tlen;
	static MP *w,*psum;
	static struct cdl *tab;
	static int wlen;
	static int rtlen;

	if ( !p )
		*pr = 0;
	else {
		for ( m = BDY(p), l = 0; m; m = NEXT(m), l++ );
		if ( l > wlen ) {
			if ( w ) GC_free(w);
			w = (MP *)MALLOC(l*sizeof(MP));
			wlen = l;
		}
		for ( m = BDY(p), i = 0; i < l; m = NEXT(m), i++ )
			w[i] = m;
		n = NV(p); n2 = n>>1;
		d0 = m0->dl;

		for ( i = 0, tlen = 1; i < n2; i++ )
			tlen *= d0->d[n2+i]+1;
		if ( tlen > rtlen ) {
			if ( tab ) GC_free(tab);
			if ( psum ) GC_free(psum);
			rtlen = tlen;
			tab = (struct cdl *)MALLOC(rtlen*sizeof(struct cdl));
			psum = (MP *)MALLOC(rtlen*sizeof(MP));
		}
		bzero(psum,tlen*sizeof(MP));
		for ( i = l-1; i >= 0; i-- ) {
			bzero(tab,tlen*sizeof(struct cdl));
			_weyl_mulmm_dup(vl,m0,w[i],n,tab,tlen);
			for ( j = 0; j < tlen; j++ ) {
				if ( tab[j].c ) {
					_NEWMP(m); m->dl = tab[j].d;
					C(m) = tab[j].c; NEXT(m) = psum[j];
					psum[j] = m;
				}
			}
		}
		for ( j = tlen-1, r = 0; j >= 0; j-- ) 
			if ( psum[j] ) {
				_MKDP(n,psum[j],t); _addd_destructive(vl,r,t,&t1); r = t1;
			}
		if ( r )
			r->sugar = p->sugar + m0->dl->td;
		*pr = r;
	}
}

/* m0 = x0^d0*x1^d1*... * dx0^d(n/2)*dx1^d(n/2+1)*... */

void _weyl_mulmm_dup(VL vl,MP m0,MP m1,int n,struct cdl *rtab,int rtablen)
{
	P c;
	DL d,d0,d1,dt;
	int i,j,a,b,k,l,n2,s,min,curlen;
	struct cdl *p;
	static Q *ctab;
	static struct cdl *tab;
	static int tablen;
	static struct cdl *tmptab;
	static int tmptablen;

	if ( !m0 || !m1 ) {
		rtab[0].c = 0;
		rtab[0].d = 0;
		return;
	}
	mulp(vl,C(m0),C(m1),&c);
	d0 = m0->dl; d1 = m1->dl;
	n2 = n>>1;
	curlen = 1;

	_NEWDL(d,n);
	if ( n & 1 )
		/* offset of h-degree */
		d->td = d->d[n-1] = d0->d[n-1]+d1->d[n-1];
	else
		d->td = 0;
	rtab[0].c = c;
	rtab[0].d = d;

	if ( rtablen > tmptablen ) {
		if ( tmptab ) GC_free(tmptab);
		tmptab = (struct cdl *)MALLOC(rtablen*sizeof(struct cdl));
		tmptablen = rtablen; 
	}

	for ( i = 0; i < n2; i++ ) {
		a = d0->d[i]; b = d1->d[n2+i];
		k = d0->d[n2+i]; l = d1->d[i];

		/* degree of xi^a*(Di^k*xi^l)*Di^b */
		a += l;
		b += k;
		s = MUL_WEIGHT(a,i)+MUL_WEIGHT(b,n2+i);

		if ( !k || !l ) {
			for ( j = 0, p = rtab; j < curlen; j++, p++ ) {
				if ( p->c ) {
					dt = p->d;
					dt->d[i] = a;
					dt->d[n2+i] = b;
					dt->td += s;
				}
			}
			curlen *= k+1;
			continue;
		}
		if ( k+1 > tablen ) {
			if ( tab ) GC_free(tab);
			if ( ctab ) GC_free(ctab);
			tablen = k+1;
			tab = (struct cdl *)MALLOC(tablen*sizeof(struct cdl));
			ctab = (Q *)MALLOC(tablen*sizeof(P));
		}
		/* compute xi^a*(Di^k*xi^l)*Di^b */
		min = MIN(k,l);
		mkwc(k,l,ctab);
		bzero(tab,(k+1)*sizeof(struct cdl));
		/* n&1 != 0 => homogenized computation; dx-xd=h^2 */
		if ( n & 1 )
			for ( j = 0; j <= min; j++ ) {
				_NEWDL(d,n);
				d->d[i] = a-j; d->d[n2+i] = b-j;
				d->td = s;
				d->d[n-1] = s-(MUL_WEIGHT(a-j,i)+MUL_WEIGHT(b-j,n2+i));
				tab[j].d = d;
				tab[j].c = (P)ctab[j];
			}
		else
			for ( j = 0; j <= min; j++ ) {
				_NEWDL(d,n);
				d->d[i] = a-j; d->d[n2+i] = b-j;
				d->td = MUL_WEIGHT(a-j,i)+MUL_WEIGHT(b-j,n2+i); /* XXX */
				tab[j].d = d;
				tab[j].c = (P)ctab[j];
			}
#if 0
		_comm_muld_tab(vl,n,rtab,curlen,tab,k+1,tmptab);
		for ( j = 0; j < curlen; j++ )
			if ( rtab[j].d ) { _FREEDL(rtab[j].d); }
		for ( j = 0; j <= min; j++ )
			if ( tab[j].d ) { _FREEDL(tab[j].d); }
		curlen *= k+1;
		bcopy(tmptab,rtab,curlen*sizeof(struct cdl));
#else
		_comm_muld_tab_destructive(vl,n,rtab,curlen,tab,k+1);
		for ( j = 0; j <= min; j++ )
			if ( tab[j].d ) { _FREEDL(tab[j].d); }
		curlen *= k+1;
#endif
	}
}

/* direct product of two cdl tables
  rt[] = [
    t[0]*t1[0],...,t[n-1]*t1[0],
    t[0]*t1[1],...,t[n-1]*t1[1],
    ...
    t[0]*t1[n1-1],...,t[n-1]*t1[n1-1]
  ]
*/

void _comm_muld_tab(VL vl,int nv,struct cdl *t,int n,struct cdl *t1,int n1,struct cdl *rt)
{
	int i,j;
	struct cdl *p;
	P c;
	DL d;

	bzero(rt,n*n1*sizeof(struct cdl));
	for ( j = 0, p = rt; j < n1; j++ ) {
		c = t1[j].c;
		d = t1[j].d;
		if ( !c )
			break;
		for ( i = 0; i < n; i++, p++ ) {
			if ( t[i].c ) {
				mulp(vl,t[i].c,c,&p->c);
				_adddl_dup(nv,t[i].d,d,&p->d);
			}
		}
	}
}

void _comm_muld_tab_destructive(VL vl,int nv,struct cdl *t,int n,struct cdl *t1,int n1)
{
	int i,j;
	struct cdl *p;
	P c;
	DL d;

	for ( j = 1, p = t+n; j < n1; j++ ) {
		c = t1[j].c;
		d = t1[j].d;
		if ( !c )
			break;
		for ( i = 0; i < n; i++, p++ ) {
			if ( t[i].c ) {
				mulp(vl,t[i].c,c,&p->c);
				_adddl_dup(nv,t[i].d,d,&p->d);
			}
		}
	}
	c = t1[0].c;
	d = t1[0].d;
	for ( i = 0, p = t; i < n; i++, p++ )
		if ( t[i].c ) {
			mulp(vl,t[i].c,c,&p->c);
			/* t[i].d += d */
			adddl_destructive(nv,t[i].d,d);
		}
}