
local entries   = ARGV[2]
local precision = ARGV[3]
local count     = redis.call('GET', ARGV[1] .. ':count')

if not count then
  return 0
end

local factor = math.ceil((entries + count) / entries)
-- 0.69314718055995 = ln(2)
local index = math.ceil(math.log(factor) / 0.69314718055995)
local scale = math.pow(2, index - 1) * entries

local hash = redis.sha1hex(ARGV[4])

-- This uses a variation on:
-- 'Less Hashing, Same Performance: Building a Better Bloom Filter'
-- https://www.eecs.harvard.edu/~michaelm/postscripts/tr-02-05.pdf
local h = { }
h[0] = tonumber(string.sub(hash, 1 , 8 ), 16)
h[1] = tonumber(string.sub(hash, 9 , 16), 16)
h[2] = tonumber(string.sub(hash, 17, 24), 16)
h[3] = tonumber(string.sub(hash, 25, 32), 16)

-- Based on the math from: http://en.wikipedia.org/wiki/Bloom_filter#Probability_of_false_positives
-- Combined with: http://www.sciencedirect.com/science/article/pii/S0020019006003127
-- 0.4804530139182 = ln(2)^2
local maxbits = math.floor((scale * math.log(precision * math.pow(0.5, index))) / -0.4804530139182)

-- 0.69314718055995 = ln(2)
local maxk = math.floor(0.69314718055995 * maxbits / scale)
local b    = { }

for i=1, maxk do
  table.insert(b, h[i % 2] + i * h[2 + (((i + (i % 2)) % 4) / 2)])
end

for n=1, index do
  local key    = ARGV[1] .. ':' .. n
  local found  = true
  local scalen = math.pow(2, n - 1) * entries

  -- 0.4804530139182 = ln(2)^2
  local bits = math.floor((scalen * math.log(precision * math.pow(0.5, n))) / -0.4804530139182)

  -- 0.69314718055995 = ln(2)
  local k = math.floor(0.69314718055995 * bits / scalen)

  for i=1, k do
    if redis.call('GETBIT', key, b[i] % bits) == 0 then
      found = false
      break
    end
  end

  if found then
    return 1
  end
end

return 0
