Approximate Count with HyperLogLog in Python

import hashlib

class HyperLogLog:
    def __init__(self, precision=4):
        if precision < 4 or precision > 16:
            raise ValueError("precision must be between 4 and 16")
        self.precision = precision
        self.registers = [0] * (1 << precision)

    def _hash(self, value):
        return int(hashlib.md5(str(value).encode()).hexdigest(), 16)

    def add(self, value):
        h = self._hash(value)
        register_index = h & ((1 << self.precision) - 1)
        remaining = h >> self.precision
        rank = 1
        while (remaining & 1) == 0 and rank < 64:
            remaining >>= 1
            rank += 1
        self.registers[register_index] = max(self.registers[register_index], rank)

    def estimate(self):
        alpha = 0.79402  # for m >= 128
        m = len(self.registers)
        inv_sum = sum(2.0 ** -r for r in self.registers)
        raw = alpha * m * m / inv_sum
        if raw <= 2.5 * m:
            zeros = self.registers.count(0)
            if zeros > 0:
                return m * (m / zeros) if zeros > 0 else raw
        return raw

if __name__ == "__main__":
    hll = HyperLogLog(precision=8)
    values = [f"item-{i}" for i in range(1000)]
    for v in values:
        hll.add(v)
    print(f"True count: {len(values)}")
    print(f"Estimated count: {hll.estimate():.1f}")
    print(f"Registers used: {256 - hll.registers.count(0)}/256")