simulates hashing into 16-cell bins

16_entries_1_choice.py

#!/usr/bin/env python3

import numpy


class BinHasher16EntriesOneChoice:

    def __init__(self, size_exp: int) -> None:
        # each bin is represented by a word-size bitvector
        self.size_exp: int = size_exp
        self.array = numpy.zeros([2 ** (self.size_exp - 4)], dtype='uint16')
        self.overflows: int = 0
        self.bin_mask: numpy.uint64 = numpy.uint64(2 ** (self.size_exp - 4) - 1) << numpy.uint64(64 - self.size_exp)

    """
    Returns True if insert was successful, False on overflow.
    """
    def insert(self, num: int) -> bool:
        # find bin using leftmost {log2(bins)} bits of value
        bin_index: int = numpy.uint64(num & self.bin_mask) >> numpy.uint64(64 - self.size_exp)
        bin_word: numpy.uint16 = self.array[bin_index]

        # if bin is full then increment overflow counter and exit
        if bin_word == 0xffff:
            self.overflows += 1
            return False
        
        # find rightmost unset bit in bin word and set it
        # (this cannot overflow since we already checked for the max word value)
        bin_word = bin_word | numpy.uint16(bin_word + 1)
        self.array[bin_index] = bin_word

        return True


if __name__ == "__main__":
    for size_exp in range(8, 27):
        print(f"Table size: {2 ** size_exp}")
        table = BinHasher16EntriesOneChoice(size_exp)
        first_overflow = False
        for i in range(1, (2 ** table.size_exp) + 1):
            num: int = numpy.random.randint(1, high=numpy.iinfo(numpy.uint64).max, dtype=numpy.uint64)
            if not table.insert(num) and not first_overflow:
                first_overflow = True
                print(f"Overflowed at {i} elements (fraction: {i / (2 ** table.size_exp)})")

        print(f"Overflows for {2 ** table.size_exp} elements: {table.overflows} (fraction: {table.overflows / (2 ** table.size_exp)})")