smallest |cos(x)| ?

[Albert Chan]

Trivia: 2 convergents cannot have both even denominator (or both even numerator)

Code:

def genConvergents(coefs):
    'Return generator for convergents of n/d'
    n0, d0, n1, d1 = 0, 1, 1, 0
    for coef in coefs:
        n0, n1 = n1, n0 + coef * n1
        d0, d1 = d1, d0 + coef * d1
        yield (n1, d1)

From the loops, assume d0 is odd, d1 is even (same reasoning for numerator)

d1 ← d0 + coef*d1 = odd + even = odd

With this trivia, our search for "best" denominator = 2k+1 guaranteed exist.