Scaling an 7-state RNG to uniform integers on an arbitrary range

gistfile1.txt

# in R:

rng_7 <- function(n) {
	sample(0:6, size = n, replace = TRUE)
}

scale_rng <- function(m, n) {
	range <- n - m
	n_digits <- ceiling(log10(range) / log10(7))
	exponents <- seq(from = n_digits - 1, to = 0)
	proposal <- n+1
	while (proposal > range) {
		digits <- rng_7(n_digits)
		proposal <- sum(digits * 7^exponents)
	}
	proposal + m
}


-------

# in Python:

from random import randint
from math import log10, ceil

def rng_7(n):
	return [randint(0, 6) for i in range(n)]

def scale_rng(m, n):
	interval = n - m
	n_digits = ceil(log10(interval) / log10(7))
	exponents = range(n_digits - 1, -1, -1)
	proposal = interval + 1
	while(proposal > interval):
		digits = rng_7(n_digits)
		proposal = sum([d * 7**x for d,x in zip(digits, exponents)])
	return proposal + m