import datetime

us = datetime.timedelta(microseconds = 1)

def div_nearest(m, n):
    """Nearest integer to m / n for integers m and n."""
    q, r = divmod(m, n)
    # round-half-to-even
    if 2*r > n or 2*r == n and q % 2 == 1:
        q += 1
    return q

def mul_td_float(td, x):
    """Multiply a timedelta td by a float x."""

    n, d = x.as_integer_ratio()
    return div_nearest(td // us * n, d) * us

def div_td_float(td, x):
    """Divide a timedelta td by a float x."""

    n, d = x.as_integer_ratio()
    return div_nearest(td // us * d, n) * us