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gf2m: fixed defining polynomial generation

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This commit is contained in:
Mirek Kratochvil 2012-06-09 23:52:20 +02:00
parent d24550c126
commit 16d1ebd78b
2 changed files with 38 additions and 21 deletions
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51
lib/gf2m.cpp
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@ -64,7 +64,7 @@ bool is_irreducible_gf2_poly (uint p)
if (!p) return false; if (!p) return false;
int d = gf2p_degree (p) / 2; int d = gf2p_degree (p) / 2;
uint test = 2; //x^1+0 uint test = 2; //x^1+0
for (int i = 0; i <= d; ++i) { for (int i = 1; i <= d; ++i) {
test = gf2p_modmult (test, test, p); test = gf2p_modmult (test, test, p);
if (gf2p_gcd (test ^ 2 /* test - x^1 */, p) != 1) if (gf2p_gcd (test ^ 2 /* test - x^1 */, p) != 1)
@ -88,28 +88,45 @@ bool gf2m::create (uint M)
n = 1 << m; n = 1 << m;
if (!n) return false; //too big. if (!n) return false; //too big.
poly = 0; poly = 0;
//FIXME fails for M>=12. Why?
for (uint t = (1 << m) + 1, e = 1 << (m + 1); t < e; t += 2) /*
if (is_irreducible_gf2_poly (t) ) { * find a conway polynomial for given degree. First we "filter out" the
* possibilities that cannot be conway (reducible ones), then we check
* that Z2[x]/poly is a field.
*/
for (uint t = (1 << m) + 1, e = 1 << (m + 1); t < e; t += 2) {
if (!is_irreducible_gf2_poly (t) ) continue;
//try to prepare log and antilog tables
log.resize (n, 0);
antilog.resize (n, 0);
log[0] = n - 1;
antilog[n-1] = 0;
uint i, xi = 1; //x^0
for (i = 0; i < n - 1; ++i) {
if (log[xi] != 0) { //not a cyclic group
log.clear();
antilog.clear();
break;
}
log[xi] = i;
antilog[i] = xi;
xi <<= 1; //multiply by x
xi = gf2p_mod (xi, t);
}
//if it broke...
if (i < n - 1) continue;
poly = t; poly = t;
break; break;
} }
if (!poly) return false; if (!poly) return false;
log.resize (n); return true;
antilog.resize (n);
log[0] = n - 1;
antilog[n-1] = 0;
uint xi = 1; //x^0
for (uint i = 0; i < n - 1; ++i) {
log[xi] = i;
antilog[i] = xi;
xi <<= 1; //multiply by x
xi = gf2p_mod (xi, poly);
}
} }
uint gf2m::add (uint a, uint b) uint gf2m::add (uint a, uint b)

4
lib/polynomial.cpp
View file

@ -111,9 +111,9 @@ bool polynomial::is_irreducible (gf2m&fld) const
xi = xmodf; xi = xmodf;
xmodf.mod (*this, fld); //mod f xmodf.mod (*this, fld); //mod f
uint d = degree(); int d = degree();
if (d < 0) return false; if (d < 0) return false;
for (uint i = 1; i <= (d / 2); ++i) { for (uint i = 1; i <= (uint) (d / 2); ++i) {
for (uint j = 0; j < fld.m; ++j) { for (uint j = 0; j < fld.m; ++j) {
t = xi; t = xi;
t.mult (xi, fld); t.mult (xi, fld);