def is_a000290(n):
    """Determine whether a non-negative integer is a perfect square.
    Algorithm: Cohen, p. 40.

    Examples of use:
    >>> is_a000290(10 ** 100)
    True
    >>> is_a000290(10 ** 100 + 1)
    False
    """

    def build_residues(m):
        t = [0] * m
        for k in range((m + 1) // 2):
            t[k**2 % m] = 1
        return tuple(t)

    if not isinstance(n, int):
        raise ValueError(f'{n} is not an integer')

    if n < 0:
        return False
    if n == 0:
        return True

    # First time, precompute and store quadratic residues for selected moduli.
    if not hasattr(is_a000290, 'Q64'):
        is_a000290.Q64 = build_residues(64)
        is_a000290.Q135 = build_residues(135)
        is_a000290.Q143 = build_residues(143)
        is_a000290.Q119 = build_residues(119)

    # If n is a quadratic nonresidue for a given modulus, it cannot be a square.
    if not is_a000290.Q64[n % 64]:
        return False
    r = n % (135 * 143 * 119)
    if not (
        is_a000290.Q135[r % 135]
        and is_a000290.Q143[r % 143]
        and is_a000290.Q119[r % 119]
    ):
        return False

    # Use a variant of Newton's method to calculate the integer part of sqrt(n),
    # then check whether the square of that number equals n.
    x = 2 ** sum(divmod(n.bit_length(), 2))
    while True:
        y = (x + (n // x)) // 2
        if y >= x:
            return x**2 == n
        x = y