GaussianInteger

import church.math.Complex;

// http://www.math.ucsd.edu/~jverstra/Gaussian1.pdf

round2 a b = quotient(a + quotient(sign(a) * b, multiplicative_identity + multiplicative_identity)) b;

complexQuotient(complex a b, complex c d) = {
    na = a * c + b * d;
    nb = b * c - a * d;
    den = c * c + d * d;
    complex(round2 na den, round2 nb den);
}

n % d = n - d * complexQuotient(n, d);