#### Rescale

d
```local function downscale(max, new_max, random)
-- We divide `max` into sections of length `new_max`.
-- To not skew the results, we have to ignore a possible last segment of length `< new_max`.
local max_i = max - max % new_max -- all exclusive
return function()
-- Since the probability of landing in this last segment is `< 1/2`,
-- the probability of this loop requiring `i` iterations is at most `(1/2)^(i-1)`;
-- it runs in expected constant time
local i
repeat
i = random()
until i < max_i
return i % new_max
end
end

local function upscale(max, new_max, random)
-- Upscaled, possibly "overscaled" random
local function upscaled_random()
local res, pow = 0, 1
repeat
res = res + pow * random()
pow = pow * max
until pow >= new_max
return res
end
-- This will be dwarfed by calls to `upscaled_random` anyways
local pow = 1
repeat
pow = pow * max
until pow >= new_max
if pow == new_max then
return upscaled_random
end
-- The `upscaled_random` overshoots, so we need to downscale it
return downscale(pow, new_max, upscaled_random)
end

-- Rescales the value range of an equally distributed discrete random source without skewing it
--> discrete random source returning numbers from `0` to `new_max` with equal probabilities
return function(
max, -- maximum value produced by the random source, **exclusive**
new_max, -- new maximum value the rescaled random source should produce, **exclusive**
random -- uniform random source returning integers from 0 (inclusive) to `max` (**exclusive**)
)
if new_max == max then
return random
end
if new_max < max then
return downscale(max, new_max, random)
end
return upscale(max, new_max, random)
end
```