local fmt = require "fmt"

local function entropy(s)
    local m = {}
    for i = 1, #s do
        local c = s[i]
        local d = m[c]
        m[c] = (d) ? d + 1 : 1
    end
    local hm = 0
    for m:keys() as k do
        local c = m[k]
        hm += c * math.log(c, 2)
    end
    local l = #s
    return math.log(l, 2) - hm / l
end

local function fibword(n)
    if n < 2 then return tostring(n) end
    local a = "1"
    local b = "0"
    local i = 3
    while i <= n do
        local c = b .. a
        a, b = b, c
        i += 1
    end
    return b
end

fmt.print("%2s  %10s  %10s  %s", "n", "Length", " Entropy  ", "Fib word")
for i = 1, 37 do
    local fw = fibword(i)
    fmt.print("%2d  %10s  %0.8f  %s", i, fmt.int(#fw), entropy(fw), fmt.abridge(fw, 20))
end