Miller Rabin primality test

ModularArithmeticUtils.hs

@@ -1,4 +1,4 @@
-module ModularArithmeticUtils (modExp, modMul, legendre) where
+module ModularArithmeticUtils (modExp, modMul, legendre, factorOutTwos) where
 
 import Data.Bits (testBit, shiftR)
 
@@ -17,3 +17,11 @@ modMul a b m = (a * b) `mod` m
 -- (a/p) in {-1, 0, 1}
 legendre :: Integer -> Integer -> Integer
 legendre a p = modExp a ((p - 1) `div` 2) p
+
+-- Factor p-1 as q * 2^s, where q is odd
+factorOutTwos :: Integer -> (Integer, Integer)
+factorOutTwos n = go n 0
+  where
+    go x s
+      | even x    = go (x `div` 2) (s + 1)
+      | otherwise = (x, s)