/**
@brief Test if dual SVP reduction returns reduced basis.
@param A input lattice
@param b shortest dual vector
@return
*/
template <class ZT> int test_dsvp_reduce(ZZ_mat<ZT> &A, IntVect &b)
{
IntMatrix u;
int d = A.get_rows();
Float normb;
if (dual_length(normb, A, b))
{
return 1;
}
int status =
lll_reduction(A, u, LLL_DEF_DELTA, LLL_DEF_ETA, LM_WRAPPER, FT_DEFAULT, 0, LLL_DEFAULT);
if (status != RED_SUCCESS)
{
cerr << "LLL reduction failed: " << get_red_status_str(status) << endl;
return status;
}
IntMatrix empty_mat;
MatGSO<Integer, Float> gso(A, empty_mat, empty_mat, GSO_INT_GRAM);
LLLReduction<Integer, Float> lll_obj(gso, LLL_DEF_DELTA, LLL_DEF_ETA, LLL_DEFAULT);
vector<Strategy> strategies;
BKZParam dummy(d, strategies);
BKZReduction<Float> bkz_obj(gso, lll_obj, dummy);
bool clean = true;
bkz_obj.svp_reduction_ex(0, d, dummy, clean, true);
status = bkz_obj.status;
if (status != RED_SUCCESS)
{
cerr << "Failure: " << get_red_status_str(status) << endl;
return status;
}
Float norm_sol;
Integer zero;
zero = 0;
IntVect e_n(d, zero);
e_n[d - 1] = 1;
if (dual_length(norm_sol, A, e_n))
{
return 1;
}
Float error;
error = 1;
error.mul_2si(error, -(int)error.get_prec());
normb += error;
if (norm_sol > normb)
{
cerr << "Last dual vector too long by more than " << error << endl;
return 1;
}
return 0;
}
/**
@brief Compute the norm of a dual vector (specified by coefficients in the dual basis).
@param A input lattice
@param b coefficients of shortest dual vector
@return
*/
template <class ZT> int dual_length(Float &norm, ZZ_mat<ZT> &A, const IntVect &coords)
{
int d = coords.size();
if (A.get_rows() != d)
{
cerr << "DSVP length error: Coefficient vector has wrong dimension: ";
cerr << A.get_rows() << " vs " << d << endl;
return 1;
}
FloatVect coords_d(d);
for (int i = 0; i < d; i++)
{
coords_d[i] = coords[i].get_d();
}
IntMatrix empty_mat;
MatGSO<Integer, Float> gso(A, empty_mat, empty_mat, GSO_INT_GRAM);
if (!gso.update_gso())
{
cerr << "GSO Failure." << endl;
return 1;
}
Float tmp;
gso.get_r(tmp, d - 1, d - 1);
tmp.pow_si(tmp, -1);
FloatVect alpha(d);
Float mu, alpha2, r_inv;
norm = 0.0;
for (int i = 0; i < d; i++)
{
alpha[i] = coords_d[i];
for (int j = 0; j < i; j++)
{
gso.get_mu(mu, i, j);
alpha[i] -= mu * alpha[j];
}
gso.get_r(r_inv, i, i);
r_inv.pow_si(r_inv, -1);
alpha2.pow_si(alpha[i], 2);
norm += alpha2 * r_inv;
}
return 0;
}
template <class ZT> void zeros_last(ZZ_mat<ZT> &b, ZZ_mat<ZT> &u, ZZ_mat<ZT> &u_inv_t)
{
int i, d = b.get_rows();
for (i = 0; i < d && b[i].is_zero(); i++)
{
}
if (i > 0 && i < d)
{
b.rotate(0, i, d - 1);
if (!u.empty())
u.rotate(0, i, d - 1);
if (!u_inv_t.empty())
u_inv_t.rotate(0, i, d - 1);
}
}