Generate a random value in one range given a function to generate a uniformly-random number from another range.

random_for_random.cpp

std::size_t random_for_random(const std::pair<std::size_t, std::size_t>& base_range,
							  const std::function<std::size_t(void)>& base_function,
							  const std::pair<std::size_t, std::size_t>& target_range)
{
	// The number of values in the base range
	const std::size_t base_size = base_range.second - base_range.first + 1;
	
	// The number of values in the target range
	const std::size_t target_size = target_range.second - target_range.first + 1;
	
	// The smallest value we can generate from the base values
	const std::size_t minimum = base_size * base_range.first + base_range.first;
	
	// The largest value we can generate from the base values
	const std::size_t maximum = base_size * base_range.second + base_range.second;
	
	// The smallest value for the uniform target range
	const std::size_t lower_bound = std::ceil(minimum / target_range.second) * target_range.second;
	
	// The largest value for the uniform target range
	const std::size_t upper_bound = maximum - (maximum % target_size);
	
	while (true)
	{
		// Generate a uniform number
		auto number = base_size * base_function() + base_function();
		
		// If it is in the range we want, we can return it
		// being sure that in this range all values can appear
		// with uniform probability
		if (number >= lower_bound && number < upper_bound)
		{
			return number % target_size;
		}
	}
}