void DUPFFformal_deriv2(DUPFF fprime, const DUPFF f)
/* fprime and f may be identical */
{
int df, dans, j, p;
p = CurrentFF.prime;
df = DUPFFdeg(f);
/* find degree of the answer */
for (dans=df; dans >= 1; dans--)
if (f->coeffs[dans] != 0 && (dans%p != 0)) break;
dans--;
if (dans < 0)
{
fprime->deg = -1;
return;
}
if (fprime->maxdeg < dans)
{
JERROR(JERROR_DEG_TOO_LOW);
return;
}
fprime->deg = dans;
for (j = 1; j <= dans+1; j++)
fprime->coeffs[j-1] = FFmul(j%p, f->coeffs[j]);
return;
}
DUPFF DUPFFexgcd(DUPFF *fcofac, DUPFF *gcofac, const DUPFF f, const DUPFF g)
{
DUPFF u, v, uf, ug, vf, vg;
FFelem q, lcu, lcvrecip, p;
int df, dg, du, dv;
if (DUPFFdeg(f) < DUPFFdeg(g)) return DUPFFexgcd(gcofac, fcofac, g, f);
if (DUPFFdeg(f) != 2 || DUPFFdeg(g) != 1) abort();
if (f->coeffs[0] == 0) return f;
p = 2;
df = DUPFFdeg(f); if (df < 0) df = 0; /* both inputs are zero */
dg = DUPFFdeg(g); if (dg < 0) dg = 0; /* one input is zero */
u = DUPFFcopy(f);
v = DUPFFcopy(g);
uf = DUPFFnew(dg); uf->coeffs[0] = 1; uf->deg = 0;
ug = DUPFFnew(df);
vf = DUPFFnew(dg);
vg = DUPFFnew(df); vg->coeffs[0] = 1; vg->deg = 0;
while (DUPFFdeg(v) > 0)
{
dv = DUPFFdeg(v);
lcvrecip = FFmul(1, v->coeffs[dv]);
while (DUPFFdeg(u) >= dv)
{
du = DUPFFdeg(u);
lcu = u->coeffs[du];
q = FFmul(lcu, lcvrecip);
DUPFFshift_add(u, v, du-dv, p-q);
DUPFFshift_add(uf, vf, du-dv, p-q);
DUPFFshift_add(ug, vg, du-dv, p-q);
}
DUPFFswap(u, v);
DUPFFswap(uf, vf);
DUPFFswap(ug, vg);
}
if (DUPFFdeg(v) == 0)
{
DUPFFswap(u, v);
DUPFFswap(uf, vf);
DUPFFswap(ug, vg);
}
DUPFFfree(vf);
DUPFFfree(vg);
DUPFFfree(v);
*fcofac = uf;
*gcofac = ug;
return u;
}
DMPFF DMPFFgcd_aux(DMPFF f, DMPFF g)
{
int var, i, p, nvars;
int *df, *dg, *dans, *substitution;
FF Fp;
DUPFF fx, gx;
DMPFFdegs(df, f);
nvars = 0;
for (var = 0; var < NVARS; var++) if (df[var]) nvars++;
if (nvars == 0) return one;
if (nvars == 1) return DMPFFunivariate_gcd(f, g, var);
/* We have at least two variables . */
DMPFFdegs(dg, g);
/* Predict degrees of the result in each variable. We may guess too high. */
/* For each var map to univariate by random substitution and compute gcd */
p = CurrentFF.prime;
for (var = 0; var < NVARS; var++)
{
if (df[var] == 0) continue;
do
{
for (i=0; i < NVARS; i++)
substitution[i] = rand()%p; /* only need values for SOME variables */
fx = DMPFF_to_DUPFF(f, var, substitution);
gx = DMPFF_to_DUPFF(g, var, substitution);
} while (DUPFFdeg(fx) < df[var] || DUPFFdeg(gx) < dg[var]);
DUPFFgcd2(fx, gx);
dans[var] = DUPFFdeg(fx);
DUPFFdtor(fx);
DUPFFdtor(gx);
if (dans[var] > 0) continue;
/* if var does not appear in the answer, remove it from f and g */
nvars--;
if (nvars == 0) return one;
f = DMPFFcontent(f, var);
g = DMPFFcontent(g, var);
if (nvars == 1) return DMPFFunivariate_gcd(f, g, var);
}
/* At this point the predicted degrees are probably correct. */
printf("Predicted degrees are: ");for(i=0;i<NVARS;i++)printf("%3d ",dans[vars]);printf("\n");
/* Pick the 'main' variable. */
for (var=0; dans[var] == 0; var++);
fc = DMPFFcontent(f, var);
gc = DMPFFcontent(g, var);
f = DMPFFdivexact(f, fc);
g = DMPFFdivexact(g, gc);
hc = DMPFFgcd(fc, gc);
fx = DMPFF_to_DUPFF(f, var, substitution);
gx = DMPFF_to_DUPFF(g, var, substitution);
hx = DUPFFgcd2(fx, gx);
fcofac = DUPFFdiv(fx, hx);
gcofac = DUPFFdiv(gx, hx);
tmp = DUPFFgcd2(fcofac, hx);
if (DUPFFdeg(tmp) == 0)
{
DMPFFlift(f, hx, fcofac, substitution, dans);
}
tmp = DUPFFgcd2(gcofac, hx);
if (DUPFFdeg(tmp) == 0)
{
DMPFFlift(g, hx, gcofac, substitution, dans);
}
for (i=1; i < p; i++)
{
DUPFFadd3(fcofac, fcofac, gcofac);
DUPFFadd3(fx, fx, gx);
DMPFFadd3(f, f, g);
tmp = DUPFFgcd(fcofac, hx);
if (DUPFFdeg(tmp) == 0) break
}
DMPFFlift(f, hx, fcofac, substitution, dans);
}
