//[TestMethod]
public void SmallDegreePolyGF2PrimesTest()
{
var last = 3ul;
int len = 0;
foreach (var p in SmallDegreePolyGF2.Primes().Skip(2))
{
if (p.Coefficients > ushort.MaxValue)
{
break;
}
var s = ((p.Coefficients - last) / 2 - 1).ToString() + ", ";
if (len + s.Length > 100)
{
Trace.WriteLine("");
len = 0;
}
Trace.Write(s);
len += s.Length;
last = p.Coefficients;
}
}
public void SmallDegreePolyGF2MultTest()
{
var p = new SmallDegreePolyGF2(0, 2, 5, 17);
var q = new SmallDegreePolyGF2(0, 2, 3);
var z = p * q;
Assert.AreEqual(20, z.Degree);
Assert.AreEqual(0x1A0199ul, z.Coefficients);
}
public void SobolCoefficients()
{
Trace.WriteLine("s\ta\tP");
foreach (var p in SmallDegreePolyGF2.Primes().Skip(1).Take(1000))
{
var a = p.Coefficients;
a ^= 1ul << p.Degree;
a >>= 1;
Trace.WriteLine($"{p.Degree}\t{a}\t{p}");
}
}
public void SmallDegreePolyGF2DivRemTest()
{
var p = new SmallDegreePolyGF2(0x1A0199ul);
var q = new SmallDegreePolyGF2(0, 2, 3);
SmallDegreePolyGF2 r;
var d = SmallDegreePolyGF2.DivRem(p, q, out r);
Assert.AreEqual(0ul, r.Coefficients);
Assert.AreEqual(0x20025ul, d.Coefficients);
d = SmallDegreePolyGF2.DivRem(p, d, out r);
Assert.AreEqual(0ul, r.Coefficients);
Assert.AreEqual(0xDul, d.Coefficients);
}
/// <summary>
/// Sequence of irreducible polynomials over GF(2).
/// </summary>
public static IEnumerable <SmallDegreePolyGF2> Primes()
{
yield return(new SmallDegreePolyGF2(2ul)); // x
yield return(new SmallDegreePolyGF2(3ul)); // x + 1
yield return(new SmallDegreePolyGF2(7ul)); // x² + x + 1
for (ulong u = 9; u > 0; u += 2)
{
var p = new SmallDegreePolyGF2(u);
if (p.IsIrreducible())
{
yield return(p);
}
}
}
public void SmallDegreePolyGF2FactorsTest()
{
foreach (var p in Enumerable.Range(2, 100).Select(i => new SmallDegreePolyGF2((ulong)i)))
{
Trace.Write($"{p} = ");
foreach (var f in p.GetFactors())
{
if (f.Value.Coefficients == 2)
{
Trace.Write(f.Value);
}
else
{
Trace.Write($"({f.Value})");
}
Trace.Write(SmallDegreePolyGF2.Superscript(f.Exponent));
}
Trace.WriteLine("");
}
}
/// <summary>
/// Divide with remainder.
/// </summary>
/// <param name="p">Dividend.</param>
/// <param name="q">Divisor.</param>
/// <param name="rem">Remainder.</param>
/// <returns>Quotient.</returns>
public static SmallDegreePolyGF2 DivRem(SmallDegreePolyGF2 p, SmallDegreePolyGF2 q, out SmallDegreePolyGF2 rem)
{
if (q == Zero)
{
throw new DivideByZeroException();
}
if (p.Degree < q.Degree)
{
rem = p;
return(Zero);
}
int shift = p.Degree - q.Degree;
var d = new SmallDegreePolyGF2(1ul << shift);
var e = new SmallDegreePolyGF2(1ul << p.Degree);
q <<= shift;
var qu = new SmallDegreePolyGF2(0ul);
while (shift-- >= 0)
{
if ((p & e) != Zero)
{
p += q;
qu += d;
}
q >>= 1;
d >>= 1;
e >>= 1;
}
rem = p;
return(qu);
}
public void SmallDegreePolyGF2DegreeTest()
{
var p = new SmallDegreePolyGF2(0x17Bul);
Assert.AreEqual(8, p.Degree);
}