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package org.bouncycastle.pqc.math.ntru.polynomial;
import java.math.BigDecimal;
/**
* A polynomial with {@link BigDecimal} coefficients.
* Some methods (like add) change the polynomial, others (like mult) do
* not but return the result as a new polynomial.
*/
public class BigDecimalPolynomial
{
private static final BigDecimal ZERO = new BigDecimal("0");
private static final BigDecimal ONE_HALF = new BigDecimal("0.5");
BigDecimal[] coeffs;
/**
* Constructs a new polynomial with N coefficients initialized to 0.
*
* @param N the number of coefficients
*/
BigDecimalPolynomial(int N)
{
coeffs = new BigDecimal[N];
for (int i = 0; i < N; i++)
{
coeffs[i] = ZERO;
}
}
/**
* Constructs a new polynomial with a given set of coefficients.
*
* @param coeffs the coefficients
*/
BigDecimalPolynomial(BigDecimal[] coeffs)
{
this.coeffs = coeffs;
}
/**
* Constructs a BigDecimalPolynomial from a BigIntPolynomial. The two polynomials are independent of each other.
*
* @param p the original polynomial
*/
public BigDecimalPolynomial(BigIntPolynomial p)
{
int N = p.coeffs.length;
coeffs = new BigDecimal[N];
for (int i = 0; i < N; i++)
{
coeffs[i] = new BigDecimal(p.coeffs[i]);
}
}
/**
* Divides all coefficients by 2.
*/
public void halve()
{
for (int i = 0; i < coeffs.length; i++)
{
coeffs[i] = coeffs[i].multiply(ONE_HALF);
}
}
/**
* Multiplies the polynomial by another. Does not change this polynomial
* but returns the result as a new polynomial.
*
* @param poly2 the polynomial to multiply by
* @return a new polynomial
*/
public BigDecimalPolynomial mult(BigIntPolynomial poly2)
{
return mult(new BigDecimalPolynomial(poly2));
}
/**
* Multiplies the polynomial by another, taking the indices mod N. Does not
* change this polynomial but returns the result as a new polynomial.
*
* @param poly2 the polynomial to multiply by
* @return a new polynomial
*/
public BigDecimalPolynomial mult(BigDecimalPolynomial poly2)
{
int N = coeffs.length;
if (poly2.coeffs.length != N)
{
throw new IllegalArgumentException("Number of coefficients must be the same");
}
BigDecimalPolynomial 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 = copyOf(c.coeffs, N);
}
return c;
}
/**
* Karazuba multiplication
*/
private BigDecimalPolynomial multRecursive(BigDecimalPolynomial poly2)
{
BigDecimal[] a = coeffs;
BigDecimal[] b = poly2.coeffs;
int n = poly2.coeffs.length;
if (n <= 1)
{
BigDecimal[] c = coeffs.clone();
for (int i = 0; i < coeffs.length; i++)
{
c[i] = c[i].multiply(poly2.coeffs[0]);
}
return new BigDecimalPolynomial(c);
}
else
{
int n1 = n / 2;
BigDecimalPolynomial a1 = new BigDecimalPolynomial(copyOf(a, n1));
BigDecimalPolynomial a2 = new BigDecimalPolynomial(copyOfRange(a, n1, n));
BigDecimalPolynomial b1 = new BigDecimalPolynomial(copyOf(b, n1));
BigDecimalPolynomial b2 = new BigDecimalPolynomial(copyOfRange(b, n1, n));
BigDecimalPolynomial A = (BigDecimalPolynomial)a1.clone();
A.add(a2);
BigDecimalPolynomial B = (BigDecimalPolynomial)b1.clone();
B.add(b2);
BigDecimalPolynomial c1 = a1.multRecursive(b1);
BigDecimalPolynomial c2 = a2.multRecursive(b2);
BigDecimalPolynomial c3 = A.multRecursive(B);
c3.sub(c1);
c3.sub(c2);
BigDecimalPolynomial c = new BigDecimalPolynomial(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;
}
}
/**
* Adds another polynomial which can have a different number of coefficients.
*
* @param b another polynomial
*/
public void add(BigDecimalPolynomial b)
{
if (b.coeffs.length > coeffs.length)
{
int N = coeffs.length;
coeffs = copyOf(coeffs, b.coeffs.length);
for (int i = N; i < coeffs.length; i++)
{
coeffs[i] = ZERO;
}
}
for (int i = 0; i < b.coeffs.length; i++)
{
coeffs[i] = coeffs[i].add(b.coeffs[i]);
}
}
/**
* Subtracts another polynomial which can have a different number of coefficients.
*
* @param b
*/
void sub(BigDecimalPolynomial b)
{
if (b.coeffs.length > coeffs.length)
{
int N = coeffs.length;
coeffs = copyOf(coeffs, b.coeffs.length);
for (int i = N; i < coeffs.length; i++)
{
coeffs[i] = ZERO;
}
}
for (int i = 0; i < b.coeffs.length; i++)
{
coeffs[i] = coeffs[i].subtract(b.coeffs[i]);
}
}
/**
* Rounds all coefficients to the nearest integer.
*
* @return a new polynomial with BigInteger coefficients
*/
public BigIntPolynomial round()
{
int N = coeffs.length;
BigIntPolynomial p = new BigIntPolynomial(N);
for (int i = 0; i < N; i++)
{
p.coeffs[i] = coeffs[i].setScale(0, BigDecimal.ROUND_HALF_EVEN).toBigInteger();
}
return p;
}
/**
* Makes a copy of the polynomial that is independent of the original.
*/
public Object clone()
{
return new BigDecimalPolynomial(coeffs.clone());
}
private BigDecimal[] copyOf(BigDecimal[] a, int length)
{
BigDecimal[] tmp = new BigDecimal[length];
System.arraycopy(a, 0, tmp, 0, a.length < length ? a.length : length);
return tmp;
}
private BigDecimal[] copyOfRange(BigDecimal[] a, int from, int to)
{
int newLength = to - from;
BigDecimal[] tmp = new BigDecimal[to - from];
System.arraycopy(a, from, tmp, 0, (a.length - from) < newLength ? (a.length - from) : newLength);
return tmp;
}
public BigDecimal[] getCoeffs()
{
BigDecimal[] tmp = new BigDecimal[coeffs.length];
System.arraycopy(coeffs, 0, tmp, 0, coeffs.length);
return tmp;
}
}