diff --git a/ChangeLog.md b/ChangeLog.md
--- a/ChangeLog.md
+++ b/ChangeLog.md
@@ -1,5 +1,9 @@
 # Change log for galois-field
 
+## 0.4.1
+
+* Add compilation optimisations with `INLINABLE`.
+
 ## 0.4.0
 
 * Add `Vector` implementation of extension fields.
diff --git a/galois-field.cabal b/galois-field.cabal
--- a/galois-field.cabal
+++ b/galois-field.cabal
@@ -1,11 +1,13 @@
--- This file has been generated from package.yaml by hpack version 0.28.2.
+cabal-version: 1.12
+
+-- This file has been generated from package.yaml by hpack version 0.31.2.
 --
 -- see: https://github.com/sol/hpack
 --
--- hash: 033214ea0f37604de3c3e831efac36ce0278f2f57df82216bf93635ec31dc830
+-- hash: 4e436d9365d8254a628fd2f0a1ce476eb6073af326050f22b8aac993adf97375
 
 name:           galois-field
-version:        0.4.0
+version:        0.4.1
 synopsis:       Galois field library
 description:    An efficient implementation of Galois fields used in cryptography research
 category:       Cryptography
@@ -15,10 +17,9 @@
 license:        MIT
 license-file:   LICENSE
 build-type:     Simple
-cabal-version:  >= 1.10
 extra-source-files:
-    ChangeLog.md
     README.md
+    ChangeLog.md
 
 source-repository head
   type: git
@@ -35,7 +36,7 @@
   hs-source-dirs:
       src
   default-extensions: LambdaCase RecordWildCards OverloadedStrings NoImplicitPrelude FlexibleInstances FlexibleContexts ScopedTypeVariables RankNTypes DataKinds DeriveGeneric GeneralizedNewtypeDeriving KindSignatures MultiParamTypeClasses PatternSynonyms
-  ghc-options: -O2 -Wall
+  ghc-options: -Wall
   build-depends:
       MonadRandom
     , base >=4.10 && <5
@@ -65,7 +66,7 @@
       tests
       src
   default-extensions: LambdaCase RecordWildCards OverloadedStrings NoImplicitPrelude FlexibleInstances FlexibleContexts ScopedTypeVariables RankNTypes DataKinds DeriveGeneric GeneralizedNewtypeDeriving KindSignatures MultiParamTypeClasses PatternSynonyms
-  ghc-options: -O2 -Wall -main-is Main
+  ghc-options: -Wall -main-is Main
   build-depends:
       MonadRandom
     , base >=4.10 && <5
@@ -96,7 +97,7 @@
       benchmarks
       src
   default-extensions: LambdaCase RecordWildCards OverloadedStrings NoImplicitPrelude FlexibleInstances FlexibleContexts ScopedTypeVariables RankNTypes DataKinds DeriveGeneric GeneralizedNewtypeDeriving KindSignatures MultiParamTypeClasses PatternSynonyms
-  ghc-options: -O2 -Wall -main-is Main
+  ghc-options: -Wall -main-is Main
   build-depends:
       MonadRandom
     , base >=4.10 && <5
diff --git a/src/BinaryField.hs b/src/BinaryField.hs
--- a/src/BinaryField.hs
+++ b/src/BinaryField.hs
@@ -23,12 +23,12 @@
 
 -- Binary fields are Galois fields.
 instance KnownNat im => GaloisField (BinaryField im) where
-  char          = const 2
-  {-# INLINE char #-}
-  deg           = binLog . natVal
-  {-# INLINE deg #-}
-  frob          = flip pow 2
-  {-# INLINE frob #-}
+  char = const 2
+  {-# INLINABLE char #-}
+  deg  = binLog . natVal
+  {-# INLINABLE deg #-}
+  frob = flip pow 2
+  {-# INLINABLE frob #-}
 
 {-# RULES "BinaryField/pow"
   forall (k :: KnownNat im => BinaryField im) n . (^) k n = pow k n
@@ -69,7 +69,6 @@
   quotRem = (flip (,) 0 .) . (/)
   {-# INLINE quotRem #-}
   degree  = panic "not implemented."
-  {-# INLINE degree #-}
 
 -- Binary fields are fields.
 instance KnownNat im => Field (BinaryField im) where
@@ -97,7 +96,7 @@
   times       = (*)
   {-# INLINE times #-}
   fromNatural = fromIntegral
-  {-# INLINE fromNatural #-}
+  {-# INLINABLE fromNatural #-}
 
 -------------------------------------------------------------------------------
 -- Other instances
@@ -106,6 +105,7 @@
 -- Binary fields are arbitrary.
 instance KnownNat im => Arbitrary (BinaryField im) where
   arbitrary = BF <$> choose (0, order (witness :: BinaryField im) - 1)
+  {-# INLINABLE arbitrary #-}
 
 -- Binary fields are pretty.
 instance KnownNat im => Pretty (BinaryField im) where
@@ -114,7 +114,7 @@
 -- Binary fields are random.
 instance KnownNat im => Random (BinaryField im) where
   random  = first BF . randomR (0, order (witness :: BinaryField im) - 1)
-  {-# INLINE random #-}
+  {-# INLINABLE random #-}
   randomR = panic "not implemented."
 
 -------------------------------------------------------------------------------
diff --git a/src/ExtensionField.hs b/src/ExtensionField.hs
--- a/src/ExtensionField.hs
+++ b/src/ExtensionField.hs
@@ -39,18 +39,19 @@
   {-# MINIMAL split #-}
   -- | Splitting polynomial @f(X)@.
   split :: ExtensionField k im -> VPoly k
-  -- | Splitting polynomial degree.
+  -- Splitting polynomial degree.
   deg' :: ExtensionField k im -> Int
   deg' = pred . fromIntegral . degree . split
+  {-# INLINABLE deg' #-}
 
 -- Extension fields are Galois fields.
 instance IrreducibleMonic k im => GaloisField (ExtensionField k im) where
-  char          = const (char (witness :: k))
-  {-# INLINE char #-}
-  deg           = (deg (witness :: k) *) . deg'
-  {-# INLINE deg #-}
-  frob          = pow <*> char
-  {-# INLINE frob #-}
+  char = const (char (witness :: k))
+  {-# INLINABLE char #-}
+  deg  = (deg (witness :: k) *) . deg'
+  {-# INLINABLE deg #-}
+  frob = pow <*> char
+  {-# INLINABLE frob #-}
 
 {-# RULES "ExtensionField/pow"
   forall (k :: IrreducibleMonic k im => ExtensionField k im) n . (^) k n = pow k n
@@ -63,7 +64,7 @@
 -- Extension fields are fractional.
 instance IrreducibleMonic k im => Fractional (ExtensionField k im) where
   recip (EF x)        = EF (polyInv x (split (witness :: ExtensionField k im)))
-  {-# INLINE recip #-}
+  {-# INLINABLE recip #-}
   fromRational (x:%y) = fromInteger x / fromInteger y
   {-# INLINABLE fromRational #-}
 
@@ -72,7 +73,7 @@
   EF x + EF y   = EF (plus x y)
   {-# INLINE (+) #-}
   EF x * EF y   = EF (rem (times x y) (split (witness :: ExtensionField k im)))
-  {-# INLINE (*) #-}
+  {-# INLINABLE (*) #-}
   EF x - EF y   = EF (x - y)
   {-# INLINE (-) #-}
   negate (EF x) = EF (S.negate x)
@@ -91,7 +92,6 @@
   quotRem = (flip (,) 0 .) . (/)
   {-# INLINE quotRem #-}
   degree  = panic "not implemented."
-  {-# INLINE degree #-}
 
 -- Extension fields are fields.
 instance IrreducibleMonic k im => Field (ExtensionField k im) where
@@ -119,7 +119,7 @@
   times       = (*)
   {-# INLINE times #-}
   fromNatural = fromIntegral
-  {-# INLINE fromNatural #-}
+  {-# INLINABLE fromNatural #-}
 
 -------------------------------------------------------------------------------
 -- Other instances
@@ -128,6 +128,7 @@
 -- Extension fields are arbitrary.
 instance IrreducibleMonic k im => Arbitrary (ExtensionField k im) where
   arbitrary = toField <$> vector (deg' (witness :: ExtensionField k im))
+  {-# INLINABLE arbitrary #-}
 
 -- Extension fields are pretty.
 instance IrreducibleMonic k im => Pretty (ExtensionField k im) where
@@ -141,7 +142,7 @@
         | n <= 0    = (xs, g)
         | otherwise = case random g of
         (x, g') -> unfold (n - 1) (x : xs) g'
-  {-# INLINE random #-}
+  {-# INLINABLE random #-}
   randomR = panic "not implemented."
 
 -------------------------------------------------------------------------------
@@ -179,7 +180,7 @@
 polyInv xs ps = case first leading (polyGCD xs ps) of
   (Just (0, x), ys) -> scale 0 (recip x) ys
   _                 -> panic "no multiplicative inverse."
-{-# INLINE polyInv #-}
+{-# INLINABLE polyInv #-}
 
 -- Polynomial extended greatest common divisor algorithm.
 polyGCD :: forall k . GaloisField k => VPoly k -> VPoly k -> (VPoly k, VPoly k)
@@ -189,4 +190,4 @@
     polyGCD' s _  r 0  = (r, s)
     polyGCD' s s' r r' = case quot r r' of
       q -> polyGCD' s' (s - times q s') r' (r - times q r')
-{-# INLINE polyGCD #-}
+{-# INLINABLE polyGCD #-}
diff --git a/src/GaloisField.hs b/src/GaloisField.hs
--- a/src/GaloisField.hs
+++ b/src/GaloisField.hs
@@ -24,17 +24,17 @@
   -- | Division.
   divide :: k -> k -> k
   divide = quot
-  {-# INLINE divide #-}
+  {-# INLINABLE divide #-}
 
   -- | Inversion.
   invert :: k -> k
   invert = quot one
-  {-# INLINE invert #-}
+  {-# INLINABLE invert #-}
 
   -- | Subtraction.
   minus :: k -> k -> k
   minus = (-)
-  {-# INLINE minus #-}
+  {-# INLINABLE minus #-}
 
 -- | Galois fields @GF(p^q)@ for @p@ prime and @q@ non-negative.
 class (Arbitrary k, Field k, Fractional k,
@@ -52,9 +52,9 @@
   -- | Order @p^q@ of field.
   order :: k -> Integer
   order = (^) <$> char <*> deg
-  {-# INLINE order #-}
+  {-# INLINABLE order #-}
 
-  -- | Frobenius endomorphism @x->x^p@ of prime subfield.
+  -- | Frobenius endomorphism @x -> x^p@ of prime subfield.
   frob :: k -> k
 
   -- Functions
@@ -74,32 +74,32 @@
           z' = z * y
           y' = y * y
           m' = div m 2
-  {-# INLINE pow #-}
+  {-# INLINABLE pow #-}
 
   -- | Get randomised quadratic nonresidue.
   qnr :: k
   qnr = getQNR
-  {-# INLINE qnr #-}
+  {-# INLINABLE qnr #-}
 
   -- | Check if quadratic residue.
   qr :: k -> Bool
   qr = not . isQNR
-  {-# INLINE qr #-}
+  {-# INLINABLE qr #-}
 
   -- | Solve quadratic @ax^2 + bx + c = 0@ over field.
   quad :: k -> k -> k -> Maybe k
   quad = solveQuadratic
-  {-# INLINE quad #-}
+  {-# INLINABLE quad #-}
 
   -- | Randomised field element.
   rnd :: MonadRandom m => m k
   rnd = getRandom
-  {-# INLINE rnd #-}
+  {-# INLINABLE rnd #-}
 
   -- | Square root of field element.
   sr :: k -> Maybe k
   sr = squareRoot
-  {-# INLINE sr #-}
+  {-# INLINABLE sr #-}
 
 -------------------------------------------------------------------------------
 -- Square roots
@@ -108,7 +108,7 @@
 -- Check if an element is a quadratic nonresidue.
 isQNR :: GaloisField k => k -> Bool
 isQNR n = pow n (shiftR (order n) 1) /= 1
-{-# INLINE isQNR #-}
+{-# INLINABLE isQNR #-}
 
 -- Factor the order @p - 1@ to get @q@ and @s@ such that @p - 1 = q2^s@.
 factorOrder :: GaloisField k => k -> (Integer, Int)
@@ -118,7 +118,7 @@
     factorOrder' qs@(q, s)
       | testBit q 0 = qs
       | otherwise   = factorOrder' (shiftR q 1, s + 1)
-{-# INLINE factorOrder #-}
+{-# INLINABLE factorOrder #-}
 
 -- Get a random quadratic nonresidue.
 getQNR :: forall k . GaloisField k => k
@@ -128,7 +128,7 @@
     getQNR' (x, g)
       | x /= 0 && isQNR x = x
       | otherwise         = getQNR' (runRand rnd g)
-{-# INLINE getQNR #-}
+{-# INLINABLE getQNR #-}
 
 -- Get a square root of @n@ with the Tonelli-Shanks algorithm.
 squareRoot :: forall k . GaloisField k => k -> Maybe k
@@ -159,7 +159,7 @@
         least :: k -> Int -> Int
         least 1  j = j
         least ti j = least (ti * ti) (j + 1)
-{-# INLINE squareRoot #-}
+{-# INLINABLE squareRoot #-}
 
 -- Solve a quadratic equation @ax^2 + bx + c = 0@.
 solveQuadratic :: forall k . GaloisField k => k -> k -> k -> Maybe k
@@ -181,4 +181,4 @@
         m  = deg x
         xs = take m (iterate (join (*)) x)
         h  = zipWith ($) (cycle [identity, const 0]) xs
-{-# INLINE solveQuadratic #-}
+{-# INLINABLE solveQuadratic #-}
diff --git a/src/PrimeField.hs b/src/PrimeField.hs
--- a/src/PrimeField.hs
+++ b/src/PrimeField.hs
@@ -25,11 +25,11 @@
 -- Prime fields are Galois fields.
 instance KnownNat p => GaloisField (PrimeField p) where
   char         = natVal
-  {-# INLINE char #-}
+  {-# INLINABLE char #-}
   deg          = const 1
-  {-# INLINE deg #-}
+  {-# INLINABLE deg #-}
   frob         = identity
-  {-# INLINE frob #-}
+  {-# INLINABLE frob #-}
   pow (PF x) n = PF (powModInteger x n (natVal (witness :: PrimeField p)))
   {-# INLINE pow #-}
 
@@ -82,7 +82,6 @@
   quotRem = (flip (,) 0 .) . (/)
   {-# INLINE quotRem #-}
   degree  = panic "not implemented."
-  {-# INLINE degree #-}
 
 -- Prime fields are fields.
 instance KnownNat p => Field (PrimeField p) where
@@ -110,7 +109,7 @@
   times       = (*)
   {-# INLINE times #-}
   fromNatural = fromIntegral
-  {-# INLINE fromNatural #-}
+  {-# INLINABLE fromNatural #-}
 
 -------------------------------------------------------------------------------
 -- Other instances
@@ -119,6 +118,7 @@
 -- Prime fields are arbitrary.
 instance KnownNat p => Arbitrary (PrimeField p) where
   arbitrary = PF <$> choose (0, natVal (witness :: PrimeField p) - 1)
+  {-# INLINABLE arbitrary #-}
 
 -- Prime fields are pretty.
 instance KnownNat p => Pretty (PrimeField p) where
@@ -127,7 +127,7 @@
 -- Prime fields are random.
 instance KnownNat p => Random (PrimeField p) where
   random  = first PF . randomR (0, natVal (witness :: PrimeField p) - 1)
-  {-# INLINE random #-}
+  {-# INLINABLE random #-}
   randomR = panic "not implemented."
 
 -------------------------------------------------------------------------------