#!/usr/bin/env python3

from math import erfc, sqrt


def monobit_test(bitseq: str):
    """
    Frequency (Monobit) Test for a binary sequence. This tests count the number of '1' and '0' in a bit sequence and make a test statistics

    This test is based on the NIST SP 800-22 document, that describe how to perform tests for PRNG algorithms:
    https://nvlpubs.nist.gov/nistpubs/legacy/sp/nistspecialpublication800-22r1a.pdf

    Returns:
        p_value (float): larger p-values suggest consistency with randomness.
    """

    n = len(bitseq)
    if n == 0:
        raise ValueError("bitseq must not be empty")

    if any(c not in "01" for c in bitseq):
        raise ValueError("bitseq must contain only '0' and '1'")

    # Count ones and zeros via +/-1 sum
    s = sum(1 if c == "1" else -1 for c in bitseq)

    # Compute the test statistic
    sobs = abs(s) / sqrt(n)

    # Compute p-value, based on the Complementary Error Function (erfc)
    p_value = erfc(sobs / sqrt(2))
    return p_value