module SolaveyStrassen (solaveyStrassen) where

import ModularArithmeticUtils (modExp, jacobi)
import System.Random (randomRIO)


solaveyStrassen :: Integer -> Integer -> IO Bool
solaveyStrassen n k
  | n < 2     = return False
  | n == 2    = return True
  | even n    = return False
  | otherwise = go k
    where
    expHalf = (n - 1) `div` 2

    go 0 = return True
    go i = do
      a <- randomRIO (2, n - 2)
      if gcd a n /= 1
        then return False
        else do
          let x = modExp a expHalf n
              j = jacobi a n `mod` n

          if x /= j
            then return False
            else go (i - 1)