private void TestMult()
{
TestMult(BigInteger.ValueOf(0), BigInteger.ValueOf(0));
TestMult(BigInteger.ValueOf(100), BigInteger.ValueOf(100));
TestMult(BigInteger.ValueOf(-394786896548787L), BigInteger.ValueOf(604984572698687L));
TestMult(BigInteger.ValueOf(415338904376L), BigInteger.ValueOf(527401434558L));
TestMult(new BigInteger("9145524700683826415"), new BigInteger("1786442289234590209543"));
BigInteger pow19_1 = BigInteger.ValueOf(1).ShiftLeft((1 << 19) - 1); // 2^(2^19-1)
BigInteger pow20_2 = BigInteger.ValueOf(1).ShiftLeft((1 << 20) - 2); // 2^(2^20-2)
BigInteger pow19 = BigInteger.ValueOf(1).ShiftLeft(1 << 19); // 2^2^19
BigInteger pow20 = BigInteger.ValueOf(1).ShiftLeft(1 << 20); // 2^2^20
if (!Compare.Equals(pow19_1.ShiftLeft(1024).Subtract(pow19_1), SchonhageStrassen.Multiply(pow19_1, BigInteger.ValueOf(1).ShiftLeft(1024).Subtract(BigInteger.One))))
{
throw new Exception("SchönhageStrassen:TestMult test has failed!");
}
if (!Compare.Equals(pow20_2, SchonhageStrassen.Multiply(pow19_1, pow19_1)))
{
throw new Exception("SchönhageStrassen:TestMult test has failed!");
}
if (!Compare.Equals(pow20_2.Subtract(pow19_1), SchonhageStrassen.Multiply(pow19_1, pow19_1.Subtract(BigInteger.One))))
{
throw new Exception("SchönhageStrassen:TestMult test has failed!");
}
if (!Compare.Equals(pow20_2.Add(pow19_1), SchonhageStrassen.Multiply(pow19_1, pow19_1.Add(BigInteger.One))))
{
throw new Exception("SchönhageStrassen:TestMult test has failed!");
}
if (!Compare.Equals(pow20, SchonhageStrassen.Multiply(pow19, pow19)))
{
throw new Exception("SchönhageStrassen:TestMult test has failed!");
}
if (!Compare.Equals(pow20.Subtract(pow19), SchonhageStrassen.Multiply(pow19, pow19.Subtract(BigInteger.One))))
{
throw new Exception("SchönhageStrassen:TestMult test has failed!");
}
if (!Compare.Equals(pow20.Add(pow19), SchonhageStrassen.Multiply(pow19, pow19.Add(BigInteger.One))))
{
throw new Exception("SchönhageStrassen:TestMult test has failed!");
}
OnProgress(new TestEventArgs("Passed Known Value Multiplication test"));
Random rng = new Random();
TestMult(BigInteger.ValueOf(rng.Next(1000000000) + 524288), BigInteger.ValueOf(rng.Next(1000000000) + 524288));
TestMult(BigInteger.ValueOf((rng.Next() >> 1) + 1000), BigInteger.ValueOf((rng.Next() >> 1) + 1000));
TestMult(BigInteger.ValueOf(rng.Next(1000000000) + 524288), BigInteger.ValueOf(rng.Next(1000000000) + 524288));
TestMult(BigInteger.ValueOf((rng.Next() >> 1) + 1000), BigInteger.ValueOf((rng.Next() >> 1) + 1000));
OnProgress(new TestEventArgs("Passed Random Multiplication test"));
int aLength = 80000 + rng.Next(20000);
int bLength = 80000 + rng.Next(20000);
for (int i = 0; i < 2; i++)
{
byte[] aArr = new byte[aLength];
rng.NextBytes(aArr);
byte[] bArr = new byte[bLength];
rng.NextBytes(bArr);
BigInteger a = new BigInteger(aArr);
BigInteger b = new BigInteger(bArr);
TestMult(a, b);
// double the length and test again so an even and an odd m is tested
aLength *= 2;
bLength *= 2;
}
OnProgress(new TestEventArgs("Passed Large Number Multiplication test"));
}
/// <summary>
/// Multiplies the polynomial by another, taking the indices mod N.
/// <para>Does not change this polynomial but returns the result as a new polynomial.
/// Both polynomials must have the same number of coefficients.
/// This method is designed for large polynomials and uses Schönhage-Strassen multiplication
/// in combination with <a href="http://en.wikipedia.org/wiki/Kronecker_substitution">Kronecker substitution</a>.
/// See <a href="http://math.stackexchange.com/questions/58946/karatsuba-vs-schonhage-strassen-for-multiplication-of-polynomials#58955">here</a> for details.</para>
/// </summary>
///
/// <param name="Factor">The polynomial to multiply by</param>
///
/// <returns>The product polynomial</returns>
public BigIntPolynomial MultBig(BigIntPolynomial Factor)
{
int N = Coeffs.Length;
// determine #bits needed per coefficient
int logMinDigits = 32 - IntUtils.NumberOfLeadingZeros(N - 1);
int maxLengthA = 0;
for (int i = 0; i < Coeffs.Length; i++)
{
BigInteger coeff = Coeffs[i];
maxLengthA = Math.Max(maxLengthA, coeff.BitLength);
}
int maxLengthB = 0;
for (int i = 0; i < Factor.Coeffs.Length; i++)
{
BigInteger coeff = Factor.Coeffs[i];
maxLengthB = Math.Max(maxLengthB, coeff.BitLength);
}
int k = logMinDigits + maxLengthA + maxLengthB + 1; // in bits
k = (k + 31) / 32; // in ints
// encode each polynomial into an int[]
int aDeg = Degree();
int bDeg = Factor.Degree();
if (aDeg < 0 || bDeg < 0)
{
return(new BigIntPolynomial(N)); // return zero
}
int[] aInt = ToIntArray(this, k);
int[] bInt = ToIntArray(Factor, k);
int[] cInt = SchonhageStrassen.Multiply(aInt, bInt);
// decode poly coefficients from the product
BigInteger _2k = BigInteger.One.ShiftLeft(k * 32);
BigIntPolynomial cPoly = new BigIntPolynomial(N);
for (int i = 0; i < 2 * N - 1; i++)
{
int[] coeffInt = cInt.CopyOfRange(i * k, (i + 1) * k);
BigInteger coeff = SchonhageStrassen.ToBigInteger(coeffInt);
if (coeffInt[k - 1] < 0)
{ // if coeff > 2^(k-1)
coeff = coeff.Subtract(_2k);
// add 2^k to cInt which is the same as subtracting coeff
bool carry = false;
int cIdx = (i + 1) * k;
do
{
cInt[cIdx]++;
carry = cInt[cIdx] == 0;
cIdx++;
} while (carry);
}
cPoly.Coeffs[i % N] = cPoly.Coeffs[i % N].Add(coeff);
}
int aSign = Coeffs[aDeg].Signum();
int bSign = Factor.Coeffs[bDeg].Signum();
if (aSign * bSign < 0)
{
for (int i = 0; i < N; i++)
{
cPoly.Coeffs[i] = cPoly.Coeffs[i].Negate();
}
}
return(cPoly);
}
private void TestMult(BigInteger a, BigInteger b)
{
Compare.Equals(a.Multiply(b), SchonhageStrassen.Multiply(a, b));
}