void GF_print(GF & gf)
{
int n, p, q;
n = gf.n;
p = gf.p;
q = gf.q;
if (q > 999)
{
PRINT_OUTPUT("Warning q=%d will overflow print field.\n", q);
}
PRINT_OUTPUT("\nFor GF(%d) p=%d n=%d\n", q, p, n);
PRINT_OUTPUT("x**n = (");
for (int i = 0; i < n - 1; i++)
{
PRINT_OUTPUT("%d,", gf.xton[i]);
}
PRINT_OUTPUT("%d)\n", gf.xton[n - 1]);
PRINT_OUTPUT("\n\nGF(%d) Polynomial coefficients:\n", q);
for (int i = 0; i < q; i++)
{
PRINT_OUTPUT(" %3d ", i);
for (int j = 0; j < n; j++)
{
PRINT_OUTPUT("%3d ", gf.poly(i,j));
}
PRINT_OUTPUT("\n");
}
PRINT_OUTPUT("\n\nGF(%d) Addition Table\n", q);
for (int i = 0; i < q; i++)
{
PRINT_OUTPUT(" ");
for (int j = 0; j < q; j++)
{
PRINT_OUTPUT(" %3d", gf.plus(i,j));
}
PRINT_OUTPUT("\n");
}
PRINT_OUTPUT("\n\nGF(%d) Multiplication table\n", q);
for (int i = 0; i < q; i++)
{
PRINT_OUTPUT(" ");
for (int j = 0; j < q; j++)
{
PRINT_OUTPUT(" %3d", gf.times(i,j));
}
PRINT_OUTPUT("\n");
}
PRINT_OUTPUT("\n\nGF(%d) Reciprocals\n", q);
for (int i = 1; i < q; i++)
{
PRINT_OUTPUT(" %3d %3d\n", i, gf.inv[i]);
}
PRINT_OUTPUT("\n\nGF(%d) Negatives\n", q);
for (int i = 0; i < q; i++)
{
PRINT_OUTPUT(" %3d %3d\n", i, gf.neg[i]);
}
PRINT_OUTPUT("\n\nGF(%d) Square roots\n", q);
for (int i = 0; i < q; i++)
{
PRINT_OUTPUT(" %3d %3d\n", i, gf.root[i]);
}
}
/*
Make ready the Galois Field
*/
int GF_ready(GF & gf, int p, int n, std::vector<int> & xton)
{
size_t q;
std::ostringstream msg;
std::vector<int> poly(n);
gf.n = n;
gf.p = p;
q = 1;
for (int i = 0; i < n; i++)
{
q *= p;
}
gf.q = q;
gf.xton = std::vector<int>(n);
for (size_t i = 0; i < static_cast<size_t>(n); i++)
{
gf.xton[i] = xton[i];
}
gf.plus = bclib::matrix<int>(q,q);
gf.times = bclib::matrix<int>(q,q);
gf.inv = std::vector<int>(q);
gf.neg = std::vector<int>(q);
gf.root = std::vector<int>(q);
gf.poly = bclib::matrix<int>(q, n);
for (size_t i = 0; i < static_cast<size_t>(n); i++)
{
gf.poly(0,i) = 0;
}
for (size_t i = 1; i < q; i++)
{
size_t click;
for (click = 0; gf.poly(i - 1,click) == (p - 1); click++)
{
gf.poly(i,click) = 0;
}
gf.poly(i,click) = gf.poly(i - 1,click) + 1;
for (size_t j = click + 1; j < static_cast<size_t>(n); j++)
{
gf.poly(i,j) = gf.poly(i - 1,j);
}
}
for (size_t i = 0; i < q; i++)
{
for (size_t j = 0; j < q; j++)
{
//GF_poly_sum(p, n, gf.poly[i], gf.poly[j], poly);
GF_poly_sum(p, n, gf.poly.getrow(i), gf.poly.getrow(j), poly);
gf.plus(i,j) = GF_poly2int(p, n, poly);
GF_poly_prod(p, n, xton, gf.poly.getrow(i), gf.poly.getrow(j), poly);
gf.times(i,j) = GF_poly2int(p, n, poly);
}
}
for (size_t i = 0; i < q; i++)
{
gf.inv[i] = -1;
for (size_t j = 0; j < q; j++)
{
if (gf.times(i,j) == 1)
{
gf.inv[i] = j;
}
}
if (i > 0 && gf.inv[i] <= 0)
{
msg << "There is something wrong with the Galois field\n";
msg << "used for q=" << q << ". Element " << i << "has no reciprocal.\n";
throw std::runtime_error(msg.str().c_str());
}
}
for (size_t i = 0; i < q; i++)
{
gf.neg[i] = -1;
for (size_t j = 0; j < q; j++)
if (gf.plus(i,j) == 0)
gf.neg[i] = j;
if (i > 0 && gf.neg[i] <= 0)
{
msg << "There is something wrong with the Galois field\n";
msg << "used for q=" << q << ". Element " << i << " has no negative.\n";
throw std::runtime_error(msg.str().c_str());
}
}
for (size_t i = 0; i < q; i++)
{
gf.root[i] = -1;
for (size_t j = 0; j < q; j++)
{
if (gf.times(j,j) == static_cast<int>(i))
{
gf.root[i] = j;
}
}
}
return 1;
}