# Generated by tools/algo/legacy.py from the corpus: do not edit.
# TheAlgorithms' two gcds (maths.viv).
# Element comparisons are routed through lib/algo/legacy/order.viv; nothing else changes.
import algo.legacy.order

# from study/idioms/thealgorithms-python/maths.viv: greatest_common_divisor gcd_by_iterative

#| greatest_common_divisor.py: gcd(a, b) = |b| if a == 0 else gcd(b % a, a).
#| `%` takes the sign of the divisor, as Python's does, which the doctests with negatives rely on.
def greatest_common_divisor(a, b) {
    if a == 0.0 {
        return abs(b)
    }
    return greatest_common_divisor(b % a, a)
}

def gcd_by_iterative(x0, y0) {
    x = x0
    y = y0
    while y != 0.0 {
        r = x % y
        x = y
        y = r
    }
    return abs(x)
}