diff --git a/Crypto/Number/Basic.hs b/Crypto/Number/Basic.hs
--- a/Crypto/Number/Basic.hs
+++ b/Crypto/Number/Basic.hs
@@ -6,6 +6,9 @@
 #if MIN_VERSION_integer_gmp(0,5,1)
 {-# LANGUAGE UnboxedTuples #-}
 #endif
+#ifdef VERSION_integer_gmp
+{-# LANGUAGE MagicHash #-}
+#endif
 -- |
 -- Module      : Crypto.Number.Basic
 -- License     : BSD-style
@@ -18,6 +21,7 @@
     , gcde
     , gcde_binary
     , areEven
+    , log2
     ) where
 
 #if MIN_VERSION_integer_gmp(0,5,1)
@@ -25,6 +29,10 @@
 #else
 import Data.Bits
 #endif
+#ifdef VERSION_integer_gmp
+import GHC.Exts
+import GHC.Integer.Logarithms (integerLog2#)
+#endif
 
 -- | sqrti returns two integer (l,b) so that l <= sqrt i <= b
 -- the implementation is quite naive, use an approximation for the first number
@@ -110,3 +118,18 @@
 -- | check if a list of integer are all even
 areEven :: [Integer] -> Bool
 areEven = and . map even
+
+log2 :: Integer -> Int
+#ifdef VERSION_integer_gmp
+log2 0 = 0
+log2 x = I# (integerLog2# x)
+#else
+-- http://www.haskell.org/pipermail/haskell-cafe/2008-February/039465.html
+log2 = imLog 2
+  where
+    imLog b x = if x < b then 0 else (x `div` b^l) `doDiv` l
+      where
+        l = 2 * imLog (b * b) x
+        doDiv x' l' = if x' < b then l' else (x' `div` b) `doDiv` (l' + 1)
+#endif
+{-# INLINE log2 #-}
diff --git a/Crypto/Number/F2m.hs b/Crypto/Number/F2m.hs
--- a/Crypto/Number/F2m.hs
+++ b/Crypto/Number/F2m.hs
@@ -2,9 +2,6 @@
 #ifndef MIN_VERSION_integer_gmp
 #define MIN_VERSION_integer_gmp(a,b,c) 0
 #endif
-#ifdef VERSION_integer_gmp
-{-# LANGUAGE MagicHash #-}
-#endif
 -- |
 -- Module      : Crypto.Number.F2m
 -- License     : BSD-style
@@ -27,11 +24,7 @@
 
 import Control.Applicative ((<$>))
 import Data.Bits ((.&.),(.|.),xor,shift,testBit)
-
-#ifdef VERSION_integer_gmp
-import GHC.Exts
-import GHC.Integer.Logarithms (integerLog2#)
-#endif
+import Crypto.Number.Basic
 
 -- | Addition over F₂m. This is just a synonym of  'xor'.
 addF2m :: Integer -> Integer -> Integer
@@ -90,12 +83,10 @@
 invF2m fx n = go n fx 1 0
     where
       go u v g1 g2
-          | u == 1 = Just $ modF2m fx g1
-          | otherwise = if j < 0
-                           then go u  (v  `xor` shift  u (-j))
-                                   g1 (g2 `xor` shift g1 (-j))
-                           else go (u  `xor` shift v  j) v
-                                   (g1 `xor` shift g2 j) g2
+          | u == 0    = Nothing
+          | u == 1    = Just $ modF2m fx g1
+          | j < 0     = go u  (v  `xor` shift  u (-j)) g1 (g2 `xor` shift g1 (-j))
+          | otherwise = go (u  `xor` shift v  j) v (g1 `xor` shift g2 j) g2
         where
           j = log2 u - log2 v
 {-# INLINABLE invF2m #-}
@@ -108,18 +99,3 @@
        -> Maybe Integer
 divF2m fx n1 n2 = mulF2m fx n1 <$> invF2m fx n2
 {-# INLINE divF2m #-}
-
-log2 :: Integer -> Int
-#if defined(VERSION_integer_gmp)
-log2 0 = 0
-log2 x = I# (integerLog2# x)
-#else
--- http://www.haskell.org/pipermail/haskell-cafe/2008-February/039465.html
-log2 = imLog 2
-  where
-    imLog b x = if x < b then 0 else (x `div` b^l) `doDiv` l
-      where
-        l = 2 * imLog (b * b) x
-        doDiv x' l' = if x' < b then l' else (x' `div` b) `doDiv` (l' + 1)
-#endif
-{-# INLINE log2 #-}
diff --git a/Crypto/Number/Generate.hs b/Crypto/Number/Generate.hs
--- a/Crypto/Number/Generate.hs
+++ b/Crypto/Number/Generate.hs
@@ -11,20 +11,31 @@
     , generateOfSize
     ) where
 
+import Crypto.Number.Basic
 import Crypto.Number.Serialize
 import Crypto.Random.API
 import qualified Data.ByteString as B
-import Data.Bits ((.|.))
+import Data.Bits ((.|.), (.&.), shiftL)
 
--- | generate a positive integer x, s.t. 0 <= x < m
---
--- Note that depending on m value, the number distribution
--- generated by this function is not necessarily uniform.
+-- | generate a positive integer x, s.t. 0 <= x < m, uniformly at random
 generateMax :: CPRG g => g -> Integer -> (Integer, g)
-generateMax rng m = withRandomBytes rng (lengthBytes m) $ \bs ->
-    os2ip bs `mod` m
+generateMax rng m
+    | m < 1 = error "generateMax: m must be >= 1"
+    | m == 1 = (0,rng)
+    | otherwise =
+        let (tentativeResult, rng') =
+                withRandomBytes rng (lengthBytes m) $ \bs ->
+                    let lengthBits = (log2 (m-1) + 1)
+                        mask = if lengthBits `mod` 8 == 0
+                               then 0xff
+                               else (1 `shiftL` (lengthBits `mod` 8)) - 1 in
+                    os2ip $ snd $ B.mapAccumL (\acc w -> (0xff, w .&. acc))
+                                      mask bs in
+        if tentativeResult < m
+            then (tentativeResult, rng')
+            else generateMax rng' m
 
--- | generate a number between the inclusive bound [low,high].
+-- | generate a number between the inclusive bound [low,high] uniformly at random.
 generateBetween :: CPRG g => g -> Integer -> Integer -> (Integer, g)
 generateBetween rng low high = (low + v, rng')
     where (v, rng') = generateMax rng (high - low + 1)
diff --git a/Crypto/Number/Serialize.hs b/Crypto/Number/Serialize.hs
--- a/Crypto/Number/Serialize.hs
+++ b/Crypto/Number/Serialize.hs
@@ -23,6 +23,7 @@
 
 import Data.ByteString (ByteString)
 import qualified Data.ByteString.Internal as B
+import qualified Data.ByteString as B
 import Foreign.Ptr
 
 #if MIN_VERSION_integer_gmp(0,5,1)
@@ -32,7 +33,6 @@
 import System.IO.Unsafe
 import Foreign.ForeignPtr
 #else
-import qualified Data.ByteString as B
 import Foreign.Storable
 import Data.Bits
 #endif
@@ -48,7 +48,11 @@
 #if MIN_VERSION_integer_gmp(0,5,1)
 os2ip bs = unsafePerformIO $ withForeignPtr fptr $ \ptr ->
     let !(Ptr ad) = (ptr `plusPtr` ofs)
+#if __GLASGOW_HASKELL__ >= 710
+     in importIntegerFromAddr ad (int2Word# n) 1#
+#else
      in IO $ \s -> importIntegerFromAddr ad (int2Word# n) 1# s
+#endif
   where !(fptr, ofs, !(I# n)) = B.toForeignPtr bs
 {-# NOINLINE os2ip #-}
 #else
@@ -59,10 +63,15 @@
 -- | i2osp converts a positive integer into a byte string
 i2osp :: Integer -> ByteString
 #if MIN_VERSION_integer_gmp(0,5,1)
+i2osp 0 = B.singleton 0
 i2osp m = B.unsafeCreate (I# (word2Int# sz)) fillPtr
   where !sz = sizeInBaseInteger m 256#
+#if __GLASGOW_HASKELL__ >= 710
+        fillPtr (Ptr srcAddr) = exportIntegerToAddr m srcAddr 1#
+#else
         fillPtr (Ptr srcAddr) = IO $ \s -> case exportIntegerToAddr m srcAddr 1# s of
                                                 (# s2, _ #) -> (# s2, () #)
+#endif
 {-# NOINLINE i2osp #-}
 #else
 i2osp m
@@ -107,14 +116,22 @@
             | len < isz  = error "cannot compute i2ospOf_ with integer larger than output bytes"
             | len == isz =
                 let !(Ptr srcAddr) = ptr in
+#if __GLASGOW_HASKELL__ >= 710
+                exportIntegerToAddr m srcAddr 1#
+#else
                 IO $ \s -> case exportIntegerToAddr m srcAddr 1# s of
                                 (# s2, _ #) -> (# s2, () #)
+#endif
             | otherwise = do
                 let z = len-isz
                 _ <- B.memset ptr 0 (fromIntegral len)
                 let !(Ptr addr) = ptr `plusPtr` z
+#if __GLASGOW_HASKELL__ >= 710
+                exportIntegerToAddr m addr 1#
+#else
                 IO $ \s -> case exportIntegerToAddr m addr 1# s of
                                 (# s2, _ #) -> (# s2, () #)
+#endif
 {-# NOINLINE i2ospOf_ #-}
 #else
 i2ospOf_ len m = B.unsafeCreate len fillPtr
diff --git a/Tests/Tests.hs b/Tests/Tests.hs
--- a/Tests/Tests.hs
+++ b/Tests/Tests.hs
@@ -1,12 +1,8 @@
 {-# LANGUAGE OverloadedStrings #-}
 
-import Test.Framework (defaultMain, testGroup, Test)
-import Test.Framework.Providers.QuickCheck2 (testProperty)
-import Test.Framework.Providers.HUnit (testCase)
-
-import Test.QuickCheck
-import Test.HUnit ((@?=))
---import Test.QuickCheck.Test
+import Test.Tasty
+import Test.Tasty.QuickCheck
+import Test.Tasty.HUnit
 
 import Control.Applicative ((<$>))
 
@@ -68,7 +64,8 @@
      in (v >= 0 && v < h)
 
 prop_invF2m_valid :: Fx -> PositiveLarge -> Bool
-prop_invF2m_valid (Fx fx) (PositiveLarge a) = maybe True ((1 ==) . mulF2m fx a) (invF2m fx a)
+prop_invF2m_valid (Fx fx) (PositiveLarge a) =
+    maybe True ((1 ==) . mulF2m fx a) (invF2m fx a)
 
 prop_squareF2m_valid :: Fx -> PositiveLarge -> Bool
 prop_squareF2m_valid (Fx fx) (PositiveLarge a) = mulF2m fx a a == squareF2m fx a
@@ -123,7 +120,7 @@
 instance Arbitrary Seed where
     arbitrary = arbitrary >>= \(Positive i) -> return (Seed i)
 
-serializationKATTests :: [Test]
+serializationKATTests :: [TestTree]
 serializationKATTests = concatMap f vectors
     where f (v, bs) = [ testCase ("i2osp " ++ show v) (i2osp v  @?= bs)
                       , testCase ("os2ip " ++ show v) (os2ip bs @?= v)
@@ -136,7 +133,7 @@
             , (0x7521908421feabd21490, "u!\144\132!\254\171\210\DC4\144")
             ]
 
-serializationOfKATTests :: [Test]
+serializationOfKATTests :: [TestTree]
 serializationOfKATTests = concatMap f vectors
     where f (elen, v, bs) = [ testCase ("i2osp " ++ show v) (i2ospOf elen v @?= Just bs)
                             , testCase ("os2ip " ++ show v) (os2ip bs @?= v)
@@ -150,7 +147,7 @@
             ]
 
 main :: IO ()
-main = defaultMain
+main = defaultMain $ testGroup "crypto-numbers"
     [ testGroup "serialization"
         [ testProperty "unbinary.binary==id" (\(Positive i) -> os2ip (i2osp i) == i)
         , testProperty "length integer" (\(Positive i) -> B.length (i2osp i) == lengthBytes i)
@@ -178,7 +175,9 @@
         [ testProperty "miller-rabin" prop_miller_rabin_valid
         ]
     , testGroup "F2m"
-        [ testProperty "invF2m" prop_invF2m_valid
+        [ testCase "inv2Fm 1" (invF2m 283 566 @?= Nothing)
+        , testCase "inv2Fm 1" (invF2m 283 64800122153546929198091027632453789752394810192663929321789113225485980298851325347397170296259938610151214285229944494947456450203170796566256526607878773803495973593989422 @?= Nothing)
+        , testProperty "invF2m" prop_invF2m_valid
         , testProperty "squareF2m" prop_squareF2m_valid
         ]
     ]
diff --git a/crypto-numbers.cabal b/crypto-numbers.cabal
--- a/crypto-numbers.cabal
+++ b/crypto-numbers.cabal
@@ -1,5 +1,5 @@
 Name:                crypto-numbers
-Version:             0.2.3
+Version:             0.2.4
 Description:         Cryptographic numbers: functions and algorithms
 License:             BSD3
 License-file:        LICENSE
@@ -44,11 +44,9 @@
                    , bytestring
                    , byteable
                    , vector
-                   , QuickCheck >= 2
-                   , HUnit
-                   , test-framework >= 0.3.3
-                   , test-framework-quickcheck2 >= 0.2.9
-                   , test-framework-hunit
+                   , tasty >= 0.10.0.1
+                   , tasty-quickcheck
+                   , tasty-hunit
   ghc-options:       -Wall -O2
 
 Benchmark bench-crypto-numbers