NTL_CLIENT
// given tau in F_q compute the 'trace of Frob_q' for the curve
// y^2=x^3+a4*x+a6 over the residue field F_q(tau). if D!=0, then
// curve is assumed to be smooth. otherwise, distinguishes between
// mult've and add've red'n and computes correct trace. (D=disc)
long trace_tau(zz_pE& tau, ell_surfaceInfoT::affine_model& model)
{
static zz_pE a4_tau, a6_tau, b, e;
// additive reduction
if (IsZero(eval(model.A, tau)))
return 0;
// split multiplicative reduction
if (IsZero(eval(model.M_sp, tau)))
return +1;
// non-split multiplicative reduction
if (IsZero(eval(model.M_ns, tau)))
return -1;
// good red'n
a4_tau = eval(model.a4, tau);
a6_tau = eval(model.a6, tau);
ell_pE::init(a4_tau, a6_tau);
long order = ell_pE::order();
static ZZ trace;
trace = zz_pE::cardinality()+1-order;
assert(trace.WideSinglePrecision());
return to_long(trace);
}
static void RowTransform(vec_ZZ& A, vec_ZZ& B, const ZZ& MU1)
// x = x - y*MU
{
static ZZ T, MU;
long k;
long n = A.length();
long i;
MU = MU1;
if (MU == 1) {
for (i = 1; i <= n; i++)
sub(A(i), A(i), B(i));
return;
}
if (MU == -1) {
for (i = 1; i <= n; i++)
add(A(i), A(i), B(i));
return;
}
if (MU == 0) return;
if (NumTwos(MU) >= NTL_ZZ_NBITS)
k = MakeOdd(MU);
else
k = 0;
if (MU.WideSinglePrecision()) {
long mu1;
conv(mu1, MU);
for (i = 1; i <= n; i++) {
mul(T, B(i), mu1);
if (k > 0) LeftShift(T, T, k);
sub(A(i), A(i), T);
}
}
else {
for (i = 1; i <= n; i++) {
mul(T, B(i), MU);
if (k > 0) LeftShift(T, T, k);
sub(A(i), A(i), T);
}
}
}
static
void reduce(long k, long l,
mat_ZZ& B, vec_long& P, vec_ZZ& D,
vec_vec_ZZ& lam, mat_ZZ* U)
{
static ZZ t1;
static ZZ r;
if (P(l) == 0) return;
add(t1, lam(k)(P(l)), lam(k)(P(l)));
abs(t1, t1);
if (t1 <= D[P(l)]) return;
long j;
long rr, small_r;
BalDiv(r, lam(k)(P(l)), D[P(l)]);
if (r.WideSinglePrecision()) {
small_r = 1;
rr = to_long(r);
}
else {
small_r = 0;
}
if (small_r) {
MulSubFrom(B(k), B(l), rr);
if (U) MulSubFrom((*U)(k), (*U)(l), rr);
for (j = 1; j <= l-1; j++)
if (P(j) != 0)
MulSubFrom(lam(k)(P(j)), lam(l)(P(j)), rr);
MulSubFrom(lam(k)(P(l)), D[P(l)], rr);
}
else {
MulSubFrom(B(k), B(l), r);
if (U) MulSubFrom((*U)(k), (*U)(l), r);
for (j = 1; j <= l-1; j++)
if (P(j) != 0)
MulSubFrom(lam(k)(P(j)), lam(l)(P(j)), r);
MulSubFrom(lam(k)(P(l)), D[P(l)], r);
}
}