icg_dice_roller600.py

import math
from collections import Counter

# primes chosen to be the 4, 6, 8, 12, 20, 100 primes to match the dice roll
# with this it is at least possible to get a reproducible sequence, for each one
# with length desired

DICE = [4, 6, 8, 12, 20, 100]
PRIME_NUMBERS = [11, 13, 19, 29, 41, 211]


def icg(x0, a, b, p, n=1) -> list[int]:
    """
    Generate a sequence of numbers using inverse congruential generator

    Args:
        x0: the initial starting value (seed)
        a: multiplier
        b: increment
        p: modulus (prime number)
        n: number of values to generate, default=1
    """
    sequence = []
    x = x0
    for _ in range(n):
        x = (a * x + b) % p if x != 0 else b
        sequence.append(x)
    return sequence


def get_dice_roll_sequence(d, offset=0):
    NUM_FULL_SEQUENCES = 2
    p = PRIME_NUMBERS[DICE.index(d)]
    a, b = find_valid_params_with_full_period(p)
    full_sequence = icg(p // 2 + offset, a, b, p, p)
    c = Counter()
    dice_sequence = []
    for x in full_sequence:
        x_roll = (x % d) + 1
        if c[x_roll] < NUM_FULL_SEQUENCES:
            c[x_roll] += 1
            dice_sequence.append(x_roll)
    return dice_sequence


def find_valid_params_with_full_period(
    p, num_iters=None, limit_primes=True, return_median=True
):
    """
    Attempts to find whether or not there are valid parameters
    If num_iters is None tries to brute force all possible parameters, (p**2)
    """
    if limit_primes and p not in PRIME_NUMBERS:
        raise ValueError("ensure that number is a valid prime for checking")

    candidate_solution = []
    iters = 0
    for a in range(p, p * math.ceil(math.log(p))):
        for b in range(1, p + 1):
            sequence = icg(0, a, b, p, p)
            if set(sequence) == set(range(p)):
                candidate_solution.append((a, b))
            iters += 1
            if len(candidate_solution) > p / 2:
                break
            if num_iters is not None and iters > num_iters:
                break
    if return_median:
        return candidate_solution[len(candidate_solution) // 2]
    return candidate_solution


def main():
    print("Hello from icg-pseudo-rand!")
    # get the rolls for 600 events
    output = {}
    for d in DICE:
        seq = []
        iter = 0
        for _ in range(600//d):
            # add a bit of randomness
            seq_temp = get_dice_roll_sequence(d, iter)
            seq.extend(seq_temp)
            iter = seq_temp[-1]
        output[d] = seq
    print(output)


if __name__ == "__main__":
    main()