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normal.c
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/** @file normal.c
*
* Mainly the routine Normalize. This routine brings terms to standard
* FORM. Currently it has one serious drawback. Its buffers are all
* in the stack. This means these buffers have a fixed size (NORMSIZE).
* In the past this has caused problems and NORMSIZE had to be increased.
*
* It is not clear whether Normalize can be called recursively.
*/
/* #[ License : */
/*
* Copyright (C) 1984-2023 J.A.M. Vermaseren
* When using this file you are requested to refer to the publication
* J.A.M.Vermaseren "New features of FORM" math-ph/0010025
* This is considered a matter of courtesy as the development was paid
* for by FOM the Dutch physics granting agency and we would like to
* be able to track its scientific use to convince FOM of its value
* for the community.
*
* This file is part of FORM.
*
* FORM is free software: you can redistribute it and/or modify it under the
* terms of the GNU General Public License as published by the Free Software
* Foundation, either version 3 of the License, or (at your option) any later
* version.
*
* FORM is distributed in the hope that it will be useful, but WITHOUT ANY
* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
* FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
* details.
*
* You should have received a copy of the GNU General Public License along
* with FORM. If not, see <http://www.gnu.org/licenses/>.
*/
/* #] License : */
/*
#[ Includes : normal.c
*/
#include "form3.h"
#ifdef WITHFLOAT
#include <gmp.h>
int PackFloat(WORD *,mpf_t);
int UnpackFloat(mpf_t, WORD *);
void RatToFloat(mpf_t result, UWORD *formrat, int ratsize);
#endif
/*
#] Includes :
#[ Normalize :
#[ CompareFunctions :
*/
WORD CompareFunctions(WORD *fleft,WORD *fright)
{
WORD k, kk;
if ( AC.properorderflag ) {
if ( ( *fleft >= (FUNCTION+WILDOFFSET)
&& functions[*fleft-FUNCTION-WILDOFFSET].spec >= TENSORFUNCTION )
|| ( *fleft >= FUNCTION && *fleft < (FUNCTION + WILDOFFSET)
&& functions[*fleft-FUNCTION].spec >= TENSORFUNCTION ) ) {}
else {
WORD *s1, *s2, *ss1, *ss2;
s1 = fleft+FUNHEAD; s2 = fright+FUNHEAD;
ss1 = fleft + fleft[1]; ss2 = fright + fright[1];
while ( s1 < ss1 && s2 < ss2 ) {
k = CompArg(s1,s2);
if ( k > 0 ) return(1);
if ( k < 0 ) return(0);
NEXTARG(s1)
NEXTARG(s2)
}
if ( s1 < ss1 ) return(1);
return(0);
}
k = fleft[1] - FUNHEAD;
kk = fright[1] - FUNHEAD;
fleft += FUNHEAD;
fright += FUNHEAD;
while ( k > 0 && kk > 0 ) {
if ( *fleft < *fright ) return(0);
else if ( *fleft++ > *fright++ ) return(1);
k--; kk--;
}
if ( k > 0 ) return(1);
return(0);
}
else {
k = fleft[1] - FUNHEAD;
kk = fright[1] - FUNHEAD;
fleft += FUNHEAD;
fright += FUNHEAD;
while ( k > 0 && kk > 0 ) {
if ( *fleft < *fright ) return(0);
else if ( *fleft++ > *fright++ ) return(1);
k--; kk--;
}
if ( k > 0 ) return(1);
return(0);
}
}
/*
#] CompareFunctions :
#[ Commute :
This function gets two adjacent function pointers and decides
whether these two functions should be exchanged to obtain a
natural ordering.
Currently there is only an ordering of gamma matrices belonging
to different spin lines.
Note that we skip for now the cases of (F)^(3/2) or 1/F and a few more
of such funny functions.
*/
WORD Commute(WORD *fleft, WORD *fright)
{
WORD fun1, fun2;
if ( *fleft == DOLLAREXPRESSION || *fright == DOLLAREXPRESSION ) return(0);
fun1 = ABS(*fleft); fun2 = ABS(*fright);
if ( *fleft >= GAMMA && *fleft <= GAMMASEVEN
&& *fright >= GAMMA && *fright <= GAMMASEVEN ) {
if ( fleft[FUNHEAD] < AM.OffsetIndex && fleft[FUNHEAD] > fright[FUNHEAD] )
return(1);
return(0);
}
if ( fun1 >= WILDOFFSET ) fun1 -= WILDOFFSET;
if ( fun2 >= WILDOFFSET ) fun2 -= WILDOFFSET;
if ( ( ( functions[fun1-FUNCTION].flags & COULDCOMMUTE ) == 0 )
|| ( ( functions[fun2-FUNCTION].flags & COULDCOMMUTE ) == 0 ) ) return(0);
/*
if other conditions will come here, keep in mind that if *fleft < 0
or *fright < 0 they are arguments in the exponent function as in f^(3/2)
*/
if ( AC.CommuteInSet == 0 ) return(0);
/*
The code for CompareFunctions can be stolen from the commuting case.
We need the syntax:
Commute Fun1,Fun2,...,Fun`n';
For this Fun1,...,Fun`n' need to be noncommuting functions.
These functions will commute with all members of the group.
In the AC.paircommute buffer the representation is
`n'+1,element1,...,element`n',`m'+1,element1,...,element`m',0
A function can belong to more than one group.
If a function commutes with itself, it is most efficient to make a separate
group of two elements for it as in
Commute T,T; -> 3,T,T
*/
if ( fun1 >= fun2 ) {
WORD *group = AC.CommuteInSet, *g1, *g2, *g3;
while ( *group > 0 ) {
g3 = group + *group;
g1 = group+1;
while ( g1 < g3 ) {
if ( *g1 == fun1 || ( fun1 <= GAMMASEVEN && fun1 >= GAMMA
&& *g1 <= GAMMASEVEN && *g1 >= GAMMA ) ) {
g2 = group+1;
while ( g2 < g3 ) {
if ( g1 != g2 && ( *g2 == fun2 ||
( fun2 <= GAMMASEVEN && fun2 >= GAMMA
&& *g2 <= GAMMASEVEN && *g2 >= GAMMA ) ) ) {
if ( fun1 != fun2 ) return(1);
if ( *fleft < 0 ) return(0);
if ( *fright < 0 ) return(1);
return(CompareFunctions(fleft,fright));
}
g2++;
}
break;
}
g1++;
}
group = g3;
}
}
return(0);
}
/*
#] Commute :
#[ Normalize :
This is the big normalization routine. It has a great need
to be economical.
There is a fixed limit to the number of objects coming in.
Something should be done about it.
*/
WORD Normalize(PHEAD WORD *term)
{
/*
#[ Declarations :
*/
GETBIDENTITY
WORD *t, *m, *r, i, j, k, l, nsym, *ss, *tt, *u;
WORD shortnum, stype;
WORD *stop, *to = 0, *from = 0;
/*
The next variables could be better off in the AT.WorkSpace (?)
Now they make stackallocations rather bothersome.
*/
WORD psym[7*NORMSIZE],*ppsym;
WORD pvec[NORMSIZE],*ppvec,nvec;
WORD pdot[3*NORMSIZE],*ppdot,ndot;
WORD pdel[2*NORMSIZE],*ppdel,ndel;
WORD pind[NORMSIZE],nind;
WORD *peps[NORMSIZE/3],neps;
WORD *pden[NORMSIZE/3],nden;
WORD *pcom[NORMSIZE],ncom;
WORD *pnco[NORMSIZE],nnco;
WORD *pcon[2*NORMSIZE],ncon; /* Pointer to contractable indices */
WORD *n_coef, ncoef; /* Accumulator for the coefficient */
WORD *n_llnum, *lnum, nnum;
WORD *termout, oldtoprhs = 0, subtype;
WORD ReplaceType, ReplaceVeto = 0, didcontr, regval = 0;
WORD *ReplaceSub;
WORD *fillsetexp;
CBUF *C = cbuf+AT.ebufnum;
WORD *ANsc = 0, *ANsm = 0, *ANsr = 0, PolyFunMode;
#ifdef WITHFLOAT
WORD withfloat = 0;
WORD *firstfloat = 0;
#endif
LONG oldcpointer = 0, x;
n_coef = TermMalloc("NormCoef");
n_llnum = TermMalloc("n_llnum");
lnum = n_llnum+1;
/*
int termflag;
*/
/*
#] Declarations :
#[ Setup :
PrintTerm(term,"Normalize");
*/
Restart:
didcontr = 0;
ReplaceType = -1;
t = term;
if ( !*t ) { TermFree(n_coef,"NormCoef"); TermFree(n_llnum,"n_llnum"); return(regval); }
r = t + *t;
ncoef = r[-1];
i = ABS(ncoef);
r -= i;
m = r;
t = n_coef;
NCOPY(t,r,i);
termout = AT.WorkPointer;
AT.WorkPointer = (WORD *)(((UBYTE *)(AT.WorkPointer)) + AM.MaxTer);
fillsetexp = termout+1;
AN.PolyNormFlag = 0; PolyFunMode = AN.PolyFunTodo;
/*
termflag = 0;
*/
/*
#] Setup :
#[ First scan :
*/
nsym = nvec = ndot = ndel = neps = nden =
nind = ncom = nnco = ncon = 0;
ppsym = psym;
ppvec = pvec;
ppdot = pdot;
ppdel = pdel;
t = term + 1;
conscan:;
if ( t < m ) do {
r = t + t[1];
switch ( *t ) {
case SYMBOL :
t += 2;
from = m;
do {
if ( t[1] == 0 ) {
/* if ( *t == 0 || *t == MAXPOWER ) goto NormZZ; */
t += 2;
goto NextSymbol;
}
if ( *t <= DENOMINATORSYMBOL && *t >= COEFFSYMBOL ) {
/*
if ( AN.NoScrat2 == 0 ) {
AN.NoScrat2 = (UWORD *)Malloc1((AM.MaxTal+2)*sizeof(UWORD),"Normalize");
}
*/
if ( AN.cTerm ) m = AN.cTerm;
else m = term;
m += *m;
ncoef = REDLENG(ncoef);
if ( *t == COEFFSYMBOL ) {
i = t[1];
nnum = REDLENG(m[-1]);
m -= ABS(m[-1]);
if ( i > 0 ) {
while ( i > 0 ) {
if ( MulRat(BHEAD (UWORD *)n_coef,ncoef,(UWORD *)m,nnum,
(UWORD *)n_coef,&ncoef) ) goto FromNorm;
i--;
}
}
else if ( i < 0 ) {
while ( i < 0 ) {
if ( DivRat(BHEAD (UWORD *)n_coef,ncoef,(UWORD *)m,nnum,
(UWORD *)n_coef,&ncoef) ) goto FromNorm;
i++;
}
}
}
else {
i = m[-1];
nnum = (ABS(i)-1)/2;
if ( *t == NUMERATORSYMBOL ) { m -= nnum + 1; }
else { m--; }
while ( *m == 0 && nnum > 1 ) { m--; nnum--; }
m -= nnum;
if ( i < 0 && *t == NUMERATORSYMBOL ) nnum = -nnum;
i = t[1];
if ( i > 0 ) {
while ( i > 0 ) {
if ( Mully(BHEAD (UWORD *)n_coef,&ncoef,(UWORD *)m,nnum) )
goto FromNorm;
i--;
}
}
else if ( i < 0 ) {
while ( i < 0 ) {
if ( Divvy(BHEAD (UWORD *)n_coef,&ncoef,(UWORD *)m,nnum) )
goto FromNorm;
i++;
}
}
}
ncoef = INCLENG(ncoef);
t += 2;
goto NextSymbol;
}
else if ( *t == DIMENSIONSYMBOL ) {
if ( AN.cTerm ) m = AN.cTerm;
else m = term;
k = DimensionTerm(m);
if ( k == 0 ) goto NormZero;
if ( k == MAXPOSITIVE ) {
MLOCK(ErrorMessageLock);
MesPrint("Dimension_ is undefined in term %t");
MUNLOCK(ErrorMessageLock);
goto NormMin;
}
if ( k == -MAXPOSITIVE ) {
MLOCK(ErrorMessageLock);
MesPrint("Dimension_ out of range in term %t");
MUNLOCK(ErrorMessageLock);
goto NormMin;
}
if ( k > 0 ) { *((UWORD *)lnum) = k; nnum = 1; }
else { *((UWORD *)lnum) = -k; nnum = -1; }
ncoef = REDLENG(ncoef);
if ( Mully(BHEAD (UWORD *)n_coef,&ncoef,(UWORD *)lnum,nnum) ) goto FromNorm;
ncoef = INCLENG(ncoef);
t += 2;
goto NextSymbol;
}
if ( ( *t >= MAXPOWER && *t < 2*MAXPOWER )
|| ( *t < -MAXPOWER && *t > -2*MAXPOWER ) ) {
/*
#[ TO SNUMBER :
*/
if ( *t < 0 ) {
*t += MAXPOWER;
*t = -*t;
if ( t[1] & 1 ) ncoef = -ncoef;
}
else if ( *t == MAXPOWER ) {
if ( t[1] > 0 ) goto NormZero;
goto NormInf;
}
else {
*t -= MAXPOWER;
}
lnum[0] = *t;
nnum = 1;
if ( t[1] && RaisPow(BHEAD (UWORD *)lnum,&nnum,(UWORD)(ABS(t[1]))) )
goto FromNorm;
ncoef = REDLENG(ncoef);
if ( t[1] < 0 ) {
if ( Divvy(BHEAD (UWORD *)n_coef,&ncoef,(UWORD *)lnum,nnum) )
goto FromNorm;
}
else if ( t[1] > 0 ) {
if ( Mully(BHEAD (UWORD *)n_coef,&ncoef,(UWORD *)lnum,nnum) )
goto FromNorm;
}
ncoef = INCLENG(ncoef);
/*
#] TO SNUMBER :
*/
t += 2;
goto NextSymbol;
}
if ( ( *t <= NumSymbols && *t > -MAXPOWER )
&& ( symbols[*t].complex & VARTYPEROOTOFUNITY ) == VARTYPEROOTOFUNITY ) {
if ( t[1] <= 2*MAXPOWER && t[1] >= -2*MAXPOWER ) {
t[1] %= symbols[*t].maxpower;
if ( t[1] < 0 ) t[1] += symbols[*t].maxpower;
if ( ( symbols[*t].complex & VARTYPEMINUS ) == VARTYPEMINUS ) {
if ( ( ( symbols[*t].maxpower & 1 ) == 0 ) &&
( t[1] >= symbols[*t].maxpower/2 ) ) {
t[1] -= symbols[*t].maxpower/2; ncoef = -ncoef;
}
}
if ( t[1] == 0 ) { t += 2; goto NextSymbol; }
}
}
i = nsym;
m = ppsym;
if ( i > 0 ) do {
m -= 2;
if ( *t == *m ) {
t++; m++;
if ( *t > 2*MAXPOWER || *t < -2*MAXPOWER
|| *m > 2*MAXPOWER || *m < -2*MAXPOWER ) {
MLOCK(ErrorMessageLock);
MesPrint("Illegal wildcard power combination.");
MUNLOCK(ErrorMessageLock);
goto NormMin;
}
*m += *t;
if ( ( t[-1] <= NumSymbols && t[-1] > -MAXPOWER )
&& ( symbols[t[-1]].complex & VARTYPEROOTOFUNITY ) == VARTYPEROOTOFUNITY ) {
*m %= symbols[t[-1]].maxpower;
if ( *m < 0 ) *m += symbols[t[-1]].maxpower;
if ( ( symbols[t[-1]].complex & VARTYPEMINUS ) == VARTYPEMINUS ) {
if ( ( ( symbols[t[-1]].maxpower & 1 ) == 0 ) &&
( *m >= symbols[t[-1]].maxpower/2 ) ) {
*m -= symbols[t[-1]].maxpower/2; ncoef = -ncoef;
}
}
}
if ( *m >= 2*MAXPOWER || *m <= -2*MAXPOWER ) {
MLOCK(ErrorMessageLock);
MesPrint("Power overflow during normalization");
MUNLOCK(ErrorMessageLock);
goto NormMin;
}
if ( !*m ) {
m--;
while ( i < nsym )
{ *m = m[2]; m++; *m = m[2]; m++; i++; }
ppsym -= 2;
nsym--;
}
t++;
goto NextSymbol;
}
} while ( *t < *m && --i > 0 );
m = ppsym;
while ( i < nsym )
{ m--; m[2] = *m; m--; m[2] = *m; i++; }
*m++ = *t++;
*m = *t++;
ppsym += 2;
nsym++;
NextSymbol:;
} while ( t < r );
m = from;
break;
case VECTOR :
t += 2;
do {
if ( t[0] == AM.vectorzero ) goto NormZero;
if ( t[1] == FUNNYVEC ) {
pind[nind++] = *t;
t += 2;
}
else if ( t[1] < 0 ) {
if ( *t == NOINDEX && t[1] == NOINDEX ) t += 2;
else {
if ( t[1] == AM.vectorzero ) goto NormZero;
*ppdot++ = *t++; *ppdot++ = *t++; *ppdot++ = 1; ndot++;
}
}
else { *ppvec++ = *t++; *ppvec++ = *t++; nvec += 2; }
} while ( t < r );
break;
case DOTPRODUCT :
t += 2;
do {
if ( t[2] == 0 ) t += 3;
else if ( ndot > 0 && t[0] == ppdot[-3]
&& t[1] == ppdot[-2] ) {
ppdot[-1] += t[2];
t += 3;
if ( ppdot[-1] == 0 ) { ppdot -= 3; ndot--; }
}
else if ( t[0] == AM.vectorzero || t[1] == AM.vectorzero ) {
if ( t[2] > 0 ) goto NormZero;
goto NormInf;
}
else {
*ppdot++ = *t++; *ppdot++ = *t++;
*ppdot++ = *t++; ndot++;
}
} while ( t < r );
break;
case HAAKJE :
break;
case SETSET:
if ( WildFill(BHEAD termout,term,AT.dummysubexp) < 0 ) goto FromNorm;
i = *termout;
t = termout; m = term;
NCOPY(m,t,i);
goto Restart;
case DOLLAREXPRESSION :
/*
We have DOLLAREXPRESSION,4,number,power
Replace by SUBEXPRESSION and exit elegantly to let
TestSub pick it up. Of course look for special cases first.
Note that we have a special compiler buffer for the values.
*/
if ( AR.Eside != LHSIDE ) {
DOLLARS d = Dollars + t[2];
#ifdef WITHPTHREADS
int nummodopt, ptype = -1;
if ( AS.MultiThreaded ) {
for ( nummodopt = 0; nummodopt < NumModOptdollars; nummodopt++ ) {
if ( t[2] == ModOptdollars[nummodopt].number ) break;
}
if ( nummodopt < NumModOptdollars ) {
ptype = ModOptdollars[nummodopt].type;
if ( ptype == MODLOCAL ) {
d = ModOptdollars[nummodopt].dstruct+AT.identity;
}
else {
LOCK(d->pthreadslockread);
}
}
}
#endif
if ( d->type == DOLZERO ) {
#ifdef WITHPTHREADS
if ( ptype > 0 && ptype != MODLOCAL ) { UNLOCK(d->pthreadslockread); }
#endif
if ( t[3] == 0 ) goto NormZZ;
if ( t[3] < 0 ) goto NormInf;
goto NormZero;
}
else if ( d->type == DOLNUMBER ) {
nnum = d->where[0];
if ( nnum > 0 ) {
nnum = d->where[nnum-1];
if ( nnum < 0 ) { ncoef = -ncoef; nnum = -nnum; }
nnum = (nnum-1)/2;
for ( i = 1; i <= nnum; i++ ) lnum[i-1] = d->where[i];
}
if ( nnum == 0 || ( nnum == 1 && lnum[0] == 0 ) ) {
#ifdef WITHPTHREADS
if ( ptype > 0 && ptype != MODLOCAL ) { UNLOCK(d->pthreadslockread); }
#endif
if ( t[3] < 0 ) goto NormInf;
else if ( t[3] == 0 ) goto NormZZ;
goto NormZero;
}
if ( t[3] && RaisPow(BHEAD (UWORD *)lnum,&nnum,(UWORD)(ABS(t[3]))) ) goto FromNorm;
ncoef = REDLENG(ncoef);
if ( t[3] < 0 ) {
if ( Divvy(BHEAD (UWORD *)n_coef,&ncoef,(UWORD *)lnum,nnum) ) {
#ifdef WITHPTHREADS
if ( ptype > 0 && ptype != MODLOCAL ) { UNLOCK(d->pthreadslockread); }
#endif
goto FromNorm;
}
}
else if ( t[3] > 0 ) {
if ( Mully(BHEAD (UWORD *)n_coef,&ncoef,(UWORD *)lnum,nnum) ) {
#ifdef WITHPTHREADS
if ( ptype > 0 && ptype != MODLOCAL ) { UNLOCK(d->pthreadslockread); }
#endif
goto FromNorm;
}
}
ncoef = INCLENG(ncoef);
}
else if ( d->type == DOLINDEX ) {
if ( d->index == 0 ) {
#ifdef WITHPTHREADS
if ( ptype > 0 && ptype != MODLOCAL ) { UNLOCK(d->pthreadslockread); }
#endif
goto NormZero;
}
if ( d->index != NOINDEX ) pind[nind++] = d->index;
}
else if ( d->type == DOLTERMS ) {
if ( t[3] >= MAXPOWER || t[3] <= -MAXPOWER ) {
if ( d->where[0] == 0 ) goto NormZero;
if ( d->where[d->where[0]] != 0 ) {
IllDollarExp:
MLOCK(ErrorMessageLock);
MesPrint("!!!Illegal $ expansion with wildcard power!!!");
MUNLOCK(ErrorMessageLock);
goto FromNorm;
}
/*
At this point we should only admit symbols and dotproducts
We expand the dollar directly and do not send it back.
*/
{ WORD *td, *tdstop, dj;
td = d->where+1;
tdstop = d->where+d->where[0];
if ( tdstop[-1] != 3 || tdstop[-2] != 1
|| tdstop[-3] != 1 ) goto IllDollarExp;
tdstop -= 3;
if ( td >= tdstop ) goto IllDollarExp;
while ( td < tdstop ) {
if ( *td == SYMBOL ) {
for ( dj = 2; dj < td[1]; dj += 2 ) {
if ( td[dj+1] == 1 ) {
*ppsym++ = td[dj];
*ppsym++ = t[3];
nsym++;
}
else if ( td[dj+1] == -1 ) {
*ppsym++ = td[dj];
*ppsym++ = -t[3];
nsym++;
}
else goto IllDollarExp;
}
}
else if ( *td == DOTPRODUCT ) {
for ( dj = 2; dj < td[1]; dj += 3 ) {
if ( td[dj+2] == 1 ) {
*ppdot++ = td[dj];
*ppdot++ = td[dj+1];
*ppdot++ = t[3];
ndot++;
}
else if ( td[dj+2] == -1 ) {
*ppdot++ = td[dj];
*ppdot++ = td[dj+1];
*ppdot++ = -t[3];
ndot++;
}
else goto IllDollarExp;
}
}
else goto IllDollarExp;
td += td[1];
}
regval = 2;
break;
}
}
t[0] = SUBEXPRESSION;
t[4] = AM.dbufnum;
if ( t[3] == 0 ) {
#ifdef WITHPTHREADS
if ( ptype > 0 && ptype != MODLOCAL ) { UNLOCK(d->pthreadslockread); }
#endif
break;
}
regval = 2;
t = r;
while ( t < m ) {
if ( *t == DOLLAREXPRESSION ) {
#ifdef WITHPTHREADS
if ( ptype > 0 && ptype != MODLOCAL ) { UNLOCK(d->pthreadslockread); }
#endif
d = Dollars + t[2];
#ifdef WITHPTHREADS
if ( AS.MultiThreaded ) {
for ( nummodopt = 0; nummodopt < NumModOptdollars; nummodopt++ ) {
if ( t[2] == ModOptdollars[nummodopt].number ) break;
}
if ( nummodopt < NumModOptdollars ) {
ptype = ModOptdollars[nummodopt].type;
if ( ptype == MODLOCAL ) {
d = ModOptdollars[nummodopt].dstruct+AT.identity;
}
else {
LOCK(d->pthreadslockread);
}
}
}
#endif
if ( d->type == DOLTERMS ) {
t[0] = SUBEXPRESSION;
t[4] = AM.dbufnum;
}
}
t += t[1];
}
#ifdef WITHPTHREADS
if ( ptype > 0 && ptype != MODLOCAL ) { UNLOCK(d->pthreadslockread); }
#endif
goto RegEnd;
}
else {
#ifdef WITHPTHREADS
if ( ptype > 0 && ptype != MODLOCAL ) { UNLOCK(d->pthreadslockread); }
#endif
MLOCK(ErrorMessageLock);
MesPrint("!!!This $ variation has not been implemented yet!!!");
MUNLOCK(ErrorMessageLock);
goto NormMin;
}
#ifdef WITHPTHREADS
if ( ptype > 0 && ptype != MODLOCAL ) { UNLOCK(d->pthreadslockread); }
#endif
}
else {
pnco[nnco++] = t;
/*
The next statement should be safe as the value is used
only by the compiler (ie the master).
*/
AC.lhdollarflag = 1;
}
break;
case DELTA :
t += 2;
do {
if ( *t < 0 ) {
if ( *t == SUMMEDIND ) {
if ( t[1] < -NMIN4SHIFT ) {
k = -t[1]-NMIN4SHIFT;
k = ExtraSymbol(k,1,nsym,ppsym,&ncoef);
nsym += k;
ppsym += (k * 2);
}
else if ( t[1] == 0 ) goto NormZero;
else {
if ( t[1] < 0 ) {
lnum[0] = -t[1];
nnum = -1;
}
else {
lnum[0] = t[1];
nnum = 1;
}
ncoef = REDLENG(ncoef);
if ( Mully(BHEAD (UWORD *)n_coef,&ncoef,(UWORD *)lnum,nnum) )
goto FromNorm;
ncoef = INCLENG(ncoef);
}
t += 2;
}
else if ( *t == NOINDEX && t[1] == NOINDEX ) t += 2;
else if ( *t == EMPTYINDEX && t[1] == EMPTYINDEX ) {
*ppdel++ = *t++; *ppdel++ = *t++; ndel += 2;
}
else
if ( t[1] < 0 ) {
*ppdot++ = *t++; *ppdot++ = *t++; *ppdot++ = 1; ndot++;
}
else {
*ppvec++ = *t++; *ppvec++ = *t++; nvec += 2;
}
}
else {
if ( t[1] < 0 ) {
*ppvec++ = t[1]; *ppvec++ = *t; t+=2; nvec += 2;
}
else { *ppdel++ = *t++; *ppdel++ = *t++; ndel += 2; }
}
} while ( t < r );
break;
case FACTORIAL :
/*
(FACTORIAL,FUNHEAD+2,..,-SNUMBER,number)
*/
if ( t[FUNHEAD] == -SNUMBER && t[1] == FUNHEAD+2
&& t[FUNHEAD+1] >= 0 ) {
if ( Factorial(BHEAD t[FUNHEAD+1],(UWORD *)lnum,&nnum) )
goto FromNorm;
MulIn:
ncoef = REDLENG(ncoef);
if ( Mully(BHEAD (UWORD *)n_coef,&ncoef,(UWORD *)lnum,nnum) ) goto FromNorm;
ncoef = INCLENG(ncoef);
}
else pcom[ncom++] = t;
break;
case BERNOULLIFUNCTION :
/*
(BERNOULLIFUNCTION,FUNHEAD+2,..,-SNUMBER,number)
*/
if ( ( t[FUNHEAD] == -SNUMBER && t[FUNHEAD+1] >= 0 )
&& ( t[1] == FUNHEAD+2 || ( t[1] == FUNHEAD+4 &&
t[FUNHEAD+2] == -SNUMBER && ABS(t[FUNHEAD+3]) == 1 ) ) ) {
WORD inum, mnum;
if ( Bernoulli(t[FUNHEAD+1],(UWORD *)lnum,&nnum) )
goto FromNorm;
if ( nnum == 0 ) goto NormZero;
inum = nnum; if ( inum < 0 ) inum = -inum;
inum--; inum /= 2;
mnum = inum;
while ( lnum[mnum-1] == 0 ) mnum--;
if ( nnum < 0 ) mnum = -mnum;
ncoef = REDLENG(ncoef);
if ( Mully(BHEAD (UWORD *)n_coef,&ncoef,(UWORD *)lnum,mnum) ) goto FromNorm;
mnum = inum;
while ( lnum[inum+mnum-1] == 0 ) mnum--;
if ( Divvy(BHEAD (UWORD *)n_coef,&ncoef,(UWORD *)(lnum+inum),mnum) ) goto FromNorm;
ncoef = INCLENG(ncoef);
if ( t[1] == FUNHEAD+4 && t[FUNHEAD+1] == 1
&& t[FUNHEAD+3] == -1 ) ncoef = -ncoef;
}
else pcom[ncom++] = t;
break;
case NUMARGSFUN:
/*
Numerical function giving the number of arguments.
*/
k = 0;
t += FUNHEAD;
while ( t < r ) {
k++;
NEXTARG(t);
}
if ( k == 0 ) goto NormZero;
*((UWORD *)lnum) = k;
nnum = 1;
goto MulIn;
case NUMFACTORS:
/*
Numerical function giving the number of factors in an expression.
*/
t += FUNHEAD;
if ( *t == -EXPRESSION ) {
k = AS.OldNumFactors[t[1]];
}
else if ( *t == -DOLLAREXPRESSION ) {
k = Dollars[t[1]].nfactors;
}
else {
pcom[ncom++] = t;
break;
}
if ( k == 0 ) goto NormZero;
*((UWORD *)lnum) = k;
nnum = 1;
goto MulIn;
case NUMTERMSFUN:
/*
Numerical function giving the number of terms in the single argument.
*/
if ( t[FUNHEAD] < 0 ) {
if ( t[FUNHEAD] <= -FUNCTION && t[1] == FUNHEAD+1 ) break;
if ( t[FUNHEAD] > -FUNCTION && t[1] == FUNHEAD+2 ) {
if ( t[FUNHEAD] == -SNUMBER && t[FUNHEAD+1] == 0 ) goto NormZero;
break;
}
pcom[ncom++] = t;
break;
}
if ( t[FUNHEAD] > 0 && t[FUNHEAD] == t[1]-FUNHEAD ) {
k = 0;
t += FUNHEAD+ARGHEAD;
while ( t < r ) {
k++;
t += *t;
}
if ( k == 0 ) goto NormZero;
*((UWORD *)lnum) = k;
nnum = 1;
goto MulIn;
}
else pcom[ncom++] = t;
break;
case COUNTFUNCTION:
if ( AN.cTerm ) {
k = CountFun(AN.cTerm,t);
}
else {
k = CountFun(term,t);
}
if ( k == 0 ) goto NormZero;
if ( k > 0 ) { *((UWORD *)lnum) = k; nnum = 1; }
else { *((UWORD *)lnum) = -k; nnum = -1; }
goto MulIn;
break;
case MAKERATIONAL:
if ( t[FUNHEAD] == -SNUMBER && t[FUNHEAD+2] == -SNUMBER
&& t[1] == FUNHEAD+4 && t[FUNHEAD+3] > 1 ) {
WORD x1[2], sgn;
if ( t[FUNHEAD+1] == 0 ) goto NormZero;
if ( t[FUNHEAD+1] < 0 ) { t[FUNHEAD+1] = -t[FUNHEAD+1]; sgn = -1; }
else sgn = 1;
if ( MakeRational(t[FUNHEAD+1],t[FUNHEAD+3],x1,x1+1) ) {
static int warnflag = 1;
if ( warnflag ) {
MesPrint("%w Warning: fraction could not be reconstructed in MakeRational_");
warnflag = 0;
}
x1[0] = t[FUNHEAD+1]; x1[1] = 1;
}
if ( sgn < 0 ) { t[FUNHEAD+1] = -t[FUNHEAD+1]; x1[0] = -x1[0]; }
if ( x1[0] < 0 ) { sgn = -1; x1[0] = -x1[0]; }
else sgn = 1;
ncoef = REDLENG(ncoef);
if ( MulRat(BHEAD (UWORD *)n_coef,ncoef,(UWORD *)x1,sgn,
(UWORD *)n_coef,&ncoef) ) goto FromNorm;
ncoef = INCLENG(ncoef);
}
else {
WORD narg = 0, *tt, *ttstop, *arg1 = 0, *arg2 = 0;
UWORD *x1, *x2, *xx;
WORD nx1,nx2,nxx;
ttstop = t + t[1]; tt = t+FUNHEAD;
while ( tt < ttstop ) {
narg++;
if ( narg == 1 ) arg1 = tt;
else arg2 = tt;
NEXTARG(tt);
}
if ( narg != 2 ) goto defaultcase;
if ( *arg2 == -SNUMBER && arg2[1] <= 1 ) goto defaultcase;
else if ( *arg2 > 0 && ttstop[-1] < 0 ) goto defaultcase;
x1 = NumberMalloc("Norm-MakeRational");
if ( *arg1 == -SNUMBER ) {
if ( arg1[1] == 0 ) {
NumberFree(x1,"Norm-MakeRational");
goto NormZero;
}
if ( arg1[1] < 0 ) { x1[0] = -arg1[1]; nx1 = -1; }
else { x1[0] = arg1[1]; nx1 = 1; }
}
else if ( *arg1 > 0 ) {
WORD *tc;
nx1 = (ABS(arg2[-1])-1)/2;
tc = arg1+ARGHEAD+1+nx1;
if ( tc[0] != 1 ) {
NumberFree(x1,"Norm-MakeRational");
goto defaultcase;
}
for ( i = 1; i < nx1; i++ ) if ( tc[i] != 0 ) {
NumberFree(x1,"Norm-MakeRational");
goto defaultcase;
}
tc = arg1+ARGHEAD+1;
for ( i = 0; i < nx1; i++ ) x1[i] = tc[i];
if ( arg2[-1] < 0 ) nx1 = -nx1;
}
else {
NumberFree(x1,"Norm-MakeRational");
goto defaultcase;
}
x2 = NumberMalloc("Norm-MakeRational");
if ( *arg2 == -SNUMBER ) {
if ( arg2[1] <= 1 ) {
NumberFree(x2,"Norm-MakeRational");
NumberFree(x1,"Norm-MakeRational");
goto defaultcase;
}
else { x2[0] = arg2[1]; nx2 = 1; }
}
else if ( *arg2 > 0 ) {
WORD *tc;
nx2 = (ttstop[-1]-1)/2;
tc = arg2+ARGHEAD+1+nx2;
if ( tc[0] != 1 ) {
NumberFree(x2,"Norm-MakeRational");
NumberFree(x1,"Norm-MakeRational");
goto defaultcase;
}
for ( i = 1; i < nx2; i++ ) if ( tc[i] != 0 ) {
NumberFree(x2,"Norm-MakeRational");
NumberFree(x1,"Norm-MakeRational");
goto defaultcase;
}
tc = arg2+ARGHEAD+1;
for ( i = 0; i < nx2; i++ ) x2[i] = tc[i];
}
else {
NumberFree(x2,"Norm-MakeRational");
NumberFree(x1,"Norm-MakeRational");
goto defaultcase;
}
if ( BigLong(x1,ABS(nx1),x2,nx2) >= 0 ) {
UWORD *x3 = NumberMalloc("Norm-MakeRational");
UWORD *x4 = NumberMalloc("Norm-MakeRational");
WORD nx3, nx4;
DivLong(x1,nx1,x2,nx2,x3,&nx3,x4,&nx4);
for ( i = 0; i < ABS(nx4); i++ ) x1[i] = x4[i];
nx1 = nx4;
NumberFree(x4,"Norm-MakeRational");
NumberFree(x3,"Norm-MakeRational");
}
xx = (UWORD *)(TermMalloc("Norm-MakeRational"));
if ( MakeLongRational(BHEAD x1,nx1,x2,nx2,xx,&nxx) ) {
static int warnflag = 1;
if ( warnflag ) {
MesPrint("%w Warning: fraction could not be reconstructed in MakeRational_");
warnflag = 0;
}
ncoef = REDLENG(ncoef);
if ( Mully(BHEAD (UWORD *)n_coef,&ncoef,x1,nx1) )
goto FromNorm;