/**
* Multiplies the polynomial by another, taking the indices mod N. Does not change this polynomial
* but returns the result as a new polynomial.<br>
* Both polynomials must have the same number of coefficients.
*
* @param poly2 the polynomial to multiply by
* @return a new polynomial
*/
public BigIntPolynomial mult(BigIntPolynomial poly2) {
int N = coeffs.length;
if (poly2.coeffs.length != N) {
throw new IllegalArgumentException("Number of coefficients must be the same");
}
BigIntPolynomial c = multRecursive(poly2);
if (c.coeffs.length > N) {
for (int k = N; k < c.coeffs.length; k++) {
c.coeffs[k - N] = c.coeffs[k - N].add(c.coeffs[k]);
}
c.coeffs = Arrays.copyOf(c.coeffs, N);
}
return c;
}
/** Karazuba multiplication */
private BigIntPolynomial multRecursive(BigIntPolynomial poly2) {
BigInteger[] a = coeffs;
BigInteger[] b = poly2.coeffs;
int n = poly2.coeffs.length;
if (n <= 1) {
BigInteger[] c = Arrays.clone(coeffs);
for (int i = 0; i < coeffs.length; i++) {
c[i] = c[i].multiply(poly2.coeffs[0]);
}
return new BigIntPolynomial(c);
} else {
int n1 = n / 2;
BigIntPolynomial a1 = new BigIntPolynomial(Arrays.copyOf(a, n1));
BigIntPolynomial a2 = new BigIntPolynomial(Arrays.copyOfRange(a, n1, n));
BigIntPolynomial b1 = new BigIntPolynomial(Arrays.copyOf(b, n1));
BigIntPolynomial b2 = new BigIntPolynomial(Arrays.copyOfRange(b, n1, n));
BigIntPolynomial A = (BigIntPolynomial) a1.clone();
A.add(a2);
BigIntPolynomial B = (BigIntPolynomial) b1.clone();
B.add(b2);
BigIntPolynomial c1 = a1.multRecursive(b1);
BigIntPolynomial c2 = a2.multRecursive(b2);
BigIntPolynomial c3 = A.multRecursive(B);
c3.sub(c1);
c3.sub(c2);
BigIntPolynomial c = new BigIntPolynomial(2 * n - 1);
for (int i = 0; i < c1.coeffs.length; i++) {
c.coeffs[i] = c1.coeffs[i];
}
for (int i = 0; i < c3.coeffs.length; i++) {
c.coeffs[n1 + i] = c.coeffs[n1 + i].add(c3.coeffs[i]);
}
for (int i = 0; i < c2.coeffs.length; i++) {
c.coeffs[2 * n1 + i] = c.coeffs[2 * n1 + i].add(c2.coeffs[i]);
}
return c;
}
}