diff --git a/cayley-dickson.cabal b/cayley-dickson.cabal
--- a/cayley-dickson.cabal
+++ b/cayley-dickson.cabal
@@ -1,5 +1,5 @@
 name:                cayley-dickson
-version:             0.1.2.0
+version:             0.1.3.0
 synopsis:            Complex numbers, quaternions, octonions, sedenions, etc.
 description:         Cayley-Dickson constructions (complex numbers, quaternions,
                      octonions, sedenions, etc.) over general scalars without
@@ -14,6 +14,7 @@
 extra-source-files:  README.md
 cabal-version:       >=1.10
 homepage:            https://github.com/lmj/cayley-dickson
+bug-reports:         https://github.com/lmj/cayley-dickson/issues
 
 source-repository head
   type: git
diff --git a/src/Math/CayleyDickson.hs b/src/Math/CayleyDickson.hs
--- a/src/Math/CayleyDickson.hs
+++ b/src/Math/CayleyDickson.hs
@@ -226,12 +226,16 @@
 ----------------------------------------------------------
 -- polar form and complex function application
 
-polarUsing :: (Conjugable a, Floating a, Ord a) =>
+realPolar :: RealFloat a => Nion n a -> a -> (a, a, Nion n a)
+realPolar sqrtMinus1 r
+  | r >= 0 = (r, 0, sqrtMinus1)
+  | otherwise = (-r, pi, sqrtMinus1)
+
+polarUsing :: (Conjugable a, RealFloat a) =>
               Nion n a -> Nion n a -> (a, a, Nion n a)
+polarUsing sqrtMinus1 (Scalar r) = realPolar sqrtMinus1 r
 polarUsing sqrtMinus1 x
-  | sqnormp == 0 = if r >= 0
-                     then (r, 0, sqrtMinus1)
-                     else (-r, pi, sqrtMinus1)
+  | sqnormp == 0 = realPolar sqrtMinus1 r
   | otherwise = (absx, acos (r / absx), u)
   where
     r = scalarPart x
@@ -239,6 +243,12 @@
     u = purePart x /. (sqrt sqnormp)
     absx = norm x
 
+polar' :: (Tag n, Conjugable a, RealFloat a) =>
+          Proxy n -> Nion n a -> (a, a, Nion n a)
+polar' n x
+  | tagVal n == 0 = error "polar: no polar form in 1 dimension"
+  | otherwise = polarUsing basisElement1 x
+
 -- | Return @(s, t, u)@ such that (approximately)
 --
 --     @x == s .* 'exp' (t .* u)@
@@ -247,10 +257,8 @@
 --
 -- If @x@ has no pure part then @u@ is arbitrarily chosen to be the
 -- first pure basis element.
-polar :: (Tag n, Conjugable a, Floating a, Ord a) =>
-         Nion n a -> (a, a, Nion n a)
-polar (Scalar _) = error "polar: no polar form for scalars"
-polar x = polarUsing basisElement1 x
+polar :: (Tag n, Conjugable a, RealFloat a) => Nion n a -> (a, a, Nion n a)
+polar = polar' Proxy
 
 applyUsing :: (Conjugable a, RealFloat a) =>
               Nion n a -> (a -> a) -> (C.Complex a -> C.Complex a) ->
diff --git a/test/test.hs b/test/test.hs
--- a/test/test.hs
+++ b/test/test.hs
@@ -243,6 +243,11 @@
   assert $ (quaternion 1 2 3 4 :: Quaternion (Ratio Integer)) /. 2 ==
            nion [1 % 2, 1, 3 % 2, 2] 
 
+  forM_ [-2, -1, -0.5, 0, 0.5, 1, 2] $ \r -> do
+    let (s, t, u) = polar $ (fromScalar r :: Quaternion Double)
+    assert $ s >= 0
+    assertClose (fromScalar r) $ s .* exp (t .* u)
+
 checkInverses :: IO ()
 checkInverses = do
   f $ (nion [0.1] :: Nion Tag0 Double)