diff --git a/CHANGELOG.md b/CHANGELOG.md
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,5 +1,9 @@
 # Changelog for the [`ghc-typelits-natnormalise`](http://hackage.haskell.org/package/ghc-typelits-natnormalise) package
 
+## 0.4.4 *July 19th 2016*
+* Fixes bugs:
+  * Rounding error in `logBase` calculation
+
 ## 0.4.3 *July 18th 2016*
 * Fixes bugs:
   * False positive: "f :: (CLog 2 (2 ^ n) ~ n, (1 <=? n) ~ True) => Proxy n -> Proxy (n+d)"
diff --git a/ghc-typelits-natnormalise.cabal b/ghc-typelits-natnormalise.cabal
--- a/ghc-typelits-natnormalise.cabal
+++ b/ghc-typelits-natnormalise.cabal
@@ -1,5 +1,5 @@
 name:                ghc-typelits-natnormalise
-version:             0.4.3
+version:             0.4.4
 synopsis:            GHC typechecker plugin for types of kind GHC.TypeLits.Nat
 description:
   A type checker plugin for GHC that can solve /equalities/ of types of kind
@@ -65,7 +65,8 @@
   Other-Modules:       GHC.Extra.Instances
   build-depends:       base >=4.8  && <5,
                        ghc  >=7.10 && <8.2,
-                       ghc-tcplugins-extra >= 0.2
+                       ghc-tcplugins-extra >= 0.2,
+                       integer-gmp >= 1.0 && < 1.1
   hs-source-dirs:      src
   default-language:    Haskell2010
   other-extensions:    CPP
diff --git a/src/GHC/TypeLits/Normalise/Unify.hs b/src/GHC/TypeLits/Normalise/Unify.hs
--- a/src/GHC/TypeLits/Normalise/Unify.hs
+++ b/src/GHC/TypeLits/Normalise/Unify.hs
@@ -5,6 +5,7 @@
 -}
 
 {-# LANGUAGE CPP             #-}
+{-# LANGUAGE MagicHash       #-}
 {-# LANGUAGE RecordWildCards #-}
 
 {-# OPTIONS_GHC -fno-warn-unused-imports #-}
@@ -33,6 +34,10 @@
 import Data.Function (on)
 import Data.List     ((\\), intersect, mapAccumL)
 
+import GHC.Base               (isTrue#,(==#))
+import GHC.Integer            (smallInteger)
+import GHC.Integer.Logarithms (integerLogBase#)
+
 -- GHC API
 import Outputable    (Outputable (..), (<+>), ($$), text)
 import TcPluginM     (TcPluginM, tcPluginTrace)
@@ -280,22 +285,14 @@
 -- (i ^ a) ~ j ==> [a := round (logBase i j)], when `i` and `j` are integers,
 -- and `ceiling (logBase i j) == floor (logBase i j)`
 unifiers' ct (S [P [E (S [P [I i]]) p]]) (S [P [I j]])
-    = if kC == kF
-         then unifiers' ct (S [p]) (S [P [I kC]])
-         else []
-  where
-    k  = logBase (fromInteger i :: Double) (fromInteger j)
-    kC = ceiling k :: Integer
-    kF = floor k :: Integer
+  = case integerLogBase i j of
+      Just k  -> unifiers' ct (S [p]) (S [P [I k]])
+      Nothing -> []
 
 unifiers' ct (S [P [I j]]) (S [P [E (S [P [I i]]) p]])
-    = if kC == kF
-         then unifiers' ct (S [p]) (S [P [I kC]])
-         else []
-  where
-    k  = logBase (fromInteger i :: Double) (fromInteger j)
-    kC = ceiling k :: Integer
-    kF = floor k :: Integer
+  = case integerLogBase i j of
+      Just k  -> unifiers' ct (S [p]) (S [P [I k]])
+      Nothing -> []
 
 -- a^d * a^e ~ a^c ==> [c := d + e]
 unifiers' ct (S [P [E s1 p1]]) (S [p2]) = case collectBases p2 of
@@ -392,3 +389,15 @@
   | otherwise = case divMod i j of
                   (k,0) -> Just k
                   _     -> Nothing
+
+-- | Given `x` and `y`, return `Just n` when
+--
+-- `ceiling (logBase x y) == floor (logBase x y)`
+integerLogBase :: Integer -> Integer -> Maybe Integer
+integerLogBase x y | x > 1 && y > 0 =
+  let z1 = integerLogBase# x y
+      z2 = integerLogBase# x (y-1)
+  in  if isTrue# (z1 ==# z2)
+         then Nothing
+         else Just (smallInteger z1)
+integerLogBase _ _ = Nothing