diff --git a/.travis.yml b/.travis.yml
--- a/.travis.yml
+++ b/.travis.yml
@@ -1,46 +1,92 @@
+# This file has been generated -- see https://github.com/hvr/multi-ghc-travis
+#
+# Modifications: benchmarks disabled, cabal check disabled, IRC notifications
 language: c
 sudo: false
 
+cache:
+  directories:
+    - $HOME/.cabsnap
+    - $HOME/.cabal/packages
+
+before_cache:
+  - rm -fv $HOME/.cabal/packages/hackage.haskell.org/build-reports.log
+  - rm -fv $HOME/.cabal/packages/hackage.haskell.org/00-index.tar
+
 matrix:
   include:
-    - env: CABALVER=1.16 GHCVER=7.4.2 GHCOPTS="-Werror" JOPTS=""
-      addons: {apt: {packages: [cabal-install-1.16, ghc-7.4.2], sources: [hvr-ghc]}}
-    - env: CABALVER=1.18 GHCVER=7.6.3 GHCOPTS="-Werror" JOPTS="-j2"
-      addons: {apt: {packages: [cabal-install-1.18, ghc-7.6.3], sources: [hvr-ghc]}}
-    - env: CABALVER=1.18 GHCVER=7.8.4 GHCOPTS="-Werror" JOPTS="-j2"
-      addons: {apt: {packages: [cabal-install-1.18, ghc-7.8.4], sources: [hvr-ghc]}}
-    - env: CABALVER=1.22 GHCVER=7.10.1 GHCOPTS="" JOPTS="-j2"
-      addons: {apt: {packages: [cabal-install-1.22, ghc-7.10.1],sources: [hvr-ghc]}}
-    - env: CABALVER=head GHCVER=head GHCOPTS="" JOPTS="-j2"
-      addons: {apt: {packages: [cabal-install-head,ghc-head],  sources: [hvr-ghc]}}
-
-  allow_failures:
-   - env: CABALVER=head GHCVER=head GHCOPTS="" JOPTS="-j2"
+    - env: CABALVER=1.16 GHCVER=7.4.2 ALEXVER=3.1.7 HAPPYVER=1.19.5
+      compiler: ": #GHC 7.4.2"
+      addons: {apt: {packages: [cabal-install-1.16,ghc-7.4.2,alex-3.1.7,happy-1.19.5], sources: [hvr-ghc]}}
+    - env: CABALVER=1.16 GHCVER=7.6.3 ALEXVER=3.1.7 HAPPYVER=1.19.5
+      compiler: ": #GHC 7.6.3"
+      addons: {apt: {packages: [cabal-install-1.16,ghc-7.6.3,alex-3.1.7,happy-1.19.5], sources: [hvr-ghc]}}
+    - env: CABALVER=1.18 GHCVER=7.8.4 ALEXVER=3.1.7 HAPPYVER=1.19.5
+      compiler: ": #GHC 7.8.4"
+      addons: {apt: {packages: [cabal-install-1.18,ghc-7.8.4,alex-3.1.7,happy-1.19.5], sources: [hvr-ghc]}}
+    - env: CABALVER=1.22 GHCVER=7.10.3 ALEXVER=3.1.7 HAPPYVER=1.19.5
+      compiler: ": #GHC 7.10.3"
+      addons: {apt: {packages: [cabal-install-1.22,ghc-7.10.3,alex-3.1.7,happy-1.19.5], sources: [hvr-ghc]}}
+    - env: CABALVER=1.24 GHCVER=8.0.1 ALEXVER=3.1.7 HAPPYVER=1.19.5
+      compiler: ": #GHC 8.0.1"
+      addons: {apt: {packages: [cabal-install-1.24,ghc-8.0.1,alex-3.1.7,happy-1.19.5], sources: [hvr-ghc]}}
 
 before_install:
- - export PATH=~/.cabal/bin:/opt/ghc/$GHCVER/bin:/opt/cabal/$CABALVER/bin:$PATH
- - export CABAL=cabal-$CABALVER
- - travis_retry $CABAL update
- - if [ "$CABALVER" = "1.22" ]; then cabal install Cabal-1.22.4.0; fi
- - $CABAL --version
- - echo "$(ghc --version) [$(ghc --print-project-git-commit-id 2> /dev/null || echo '?')]"
+ - unset CC
+ - export PATH=/opt/ghc/$GHCVER/bin:/opt/cabal/$CABALVER/bin:/opt/alex/$ALEXVER/bin:/opt/happy/$HAPPYVER/bin:$PATH
 
 install:
- - |    
-   if [ $GHCVER = "head" ] || [ $GHCVER = "7.8.4" ] || [ $GHCVER = "7.10.1" ]; then
-     $CABAL install --constraint=transformers\ installed happy alex
-     export PATH=$HOME/.cabal/bin:$PATH
+ - cabal --version
+ - echo "$(ghc --version) [$(ghc --print-project-git-commit-id 2> /dev/null || echo '?')]"
+ - if [ -f $HOME/.cabal/packages/hackage.haskell.org/00-index.tar.gz ];
+   then
+     zcat $HOME/.cabal/packages/hackage.haskell.org/00-index.tar.gz >
+          $HOME/.cabal/packages/hackage.haskell.org/00-index.tar;
    fi
- - $CABAL install $JOPTS --enable-tests --only-dependencies --force
+ - travis_retry cabal update -v
+ - sed -i 's/^jobs:/-- jobs:/' ${HOME}/.cabal/config
+ - cabal install --only-dependencies --enable-tests --dry -v > installplan.txt
+ - sed -i -e '1,/^Resolving /d' installplan.txt; cat installplan.txt
 
-script:
- - $CABAL configure -v2 --enable-tests
- - $CABAL build $JOPTS --ghc-options=$GHCOPTS
- - |
-   if [ $GHCVER != "head" ]; then
-     $CABAL test
+# check whether current requested install-plan matches cached package-db snapshot
+ - if diff -u installplan.txt $HOME/.cabsnap/installplan.txt;
+   then
+     echo "cabal build-cache HIT";
+     rm -rfv .ghc;
+     cp -a $HOME/.cabsnap/ghc $HOME/.ghc;
+     cp -a $HOME/.cabsnap/lib $HOME/.cabsnap/share $HOME/.cabsnap/bin $HOME/.cabal/;
+   else
+     echo "cabal build-cache MISS";
+     rm -rf $HOME/.cabsnap;
+     mkdir -p $HOME/.ghc $HOME/.cabal/lib $HOME/.cabal/share $HOME/.cabal/bin;
+     cabal install --only-dependencies --enable-tests;
    fi
 
+# snapshot package-db on cache miss
+ - if [ ! -d $HOME/.cabsnap ];
+   then
+      echo "snapshotting package-db to build-cache";
+      mkdir $HOME/.cabsnap;
+      cp -a $HOME/.ghc $HOME/.cabsnap/ghc;
+      cp -a $HOME/.cabal/lib $HOME/.cabal/share $HOME/.cabal/bin installplan.txt $HOME/.cabsnap/;
+   fi
+
+# Here starts the actual work to be performed for the package under test;
+# any command which exits with a non-zero exit code causes the build to fail.
+script:
+ - if [ -f configure.ac ]; then autoreconf -i; fi
+ - cabal configure --enable-tests -v2  # -v2 provides useful information for debugging
+ - cabal build   # this builds all libraries and executables (including tests)
+ - cabal test
+ - cabal sdist   # tests that a source-distribution can be generated
+                 # - cabal check disabled due to spurious -O2 warning
+
+# Check that the resulting source distribution can be built & installed.
+# If there are no other `.tar.gz` files in `dist`, this can be even simpler:
+# `cabal install --force-reinstalls dist/*-*.tar.gz`
+ - SRC_TGZ=$(cabal info . | awk '{print $2;exit}').tar.gz &&
+   (cd dist && cabal install --force-reinstalls "$SRC_TGZ")
+
 notifications:
   irc:
     channels:
@@ -48,3 +94,4 @@
     skip_join: true
     template:
       - "\x0313ad\x0f/\x0306%{branch}\x0f \x0314%{commit}\x0f %{message} \x0302\x1f%{build_url}\x0f"
+# EOF
diff --git a/CHANGELOG.markdown b/CHANGELOG.markdown
--- a/CHANGELOG.markdown
+++ b/CHANGELOG.markdown
@@ -1,3 +1,9 @@
+4.3.2.1
+-----
+* GHC 8 support
+* Fix Kahn mode's `**` implementation
+* Fix multiple problems in Erf and InvErf methods
+
 4.3.2
 -----
 * Added `NoEq` versions of several combinators that can be used when `Eq` isn't available on the numeric type involved.
diff --git a/Setup.lhs b/Setup.lhs
--- a/Setup.lhs
+++ b/Setup.lhs
@@ -30,6 +30,10 @@
     withTestLBI pkg lbi $ \suite suitecfg -> do
       rewriteFile (dir </> "Build_" ++ testName suite ++ ".hs") $ unlines
         [ "module Build_" ++ testName suite ++ " where"
+        , ""
+        , "autogen_dir :: String"
+        , "autogen_dir = " ++ show dir
+        , ""
         , "deps :: [String]"
         , "deps = " ++ (show $ formatdeps (testDeps libcfg suitecfg))
         ]
diff --git a/ad.cabal b/ad.cabal
--- a/ad.cabal
+++ b/ad.cabal
@@ -1,5 +1,5 @@
 name:          ad
-version:       4.3.2
+version:       4.3.2.1
 license:       BSD3
 license-File:  LICENSE
 copyright:     (c) Edward Kmett 2010-2015,
@@ -12,7 +12,7 @@
 bug-reports:   http://github.com/ekmett/ad/issues
 build-type:    Custom
 cabal-version: >= 1.10
-tested-with:   GHC==7.0.1, GHC == 7.0.4, GHC == 7.2.2, GHC == 7.4.2, GHC == 7.6.3, GHC == 7.8.4, GHC == 7.10.1, GHC == 7.10.2
+tested-with:   GHC == 7.4.2, GHC == 7.6.3, GHC == 7.8.4, GHC == 7.10.3, GHC == 8.0.1
 synopsis:      Automatic Differentiation
 extra-source-files:
   .ghci
@@ -105,14 +105,14 @@
   build-depends:
     array            >= 0.2   && < 0.6,
     base             >= 4.3   && < 5,
-    comonad          >= 4     && < 5,
+    comonad          >= 4     && < 6,
     containers       >= 0.2   && < 0.6,
     data-reify       >= 0.6   && < 0.7,
     erf              >= 2.0   && < 2.1,
     free             >= 4.6.1 && < 5,
     nats             >= 0.1.2 && < 2,
     reflection       >= 1.4   && < 3,
-    transformers     >= 0.3   && < 0.5
+    transformers     >= 0.3   && < 0.6
 
   if impl(ghc < 7.8)
     build-depends: tagged >= 0.7 && < 1
@@ -171,7 +171,7 @@
   build-depends:
     base,
     directory,
-    doctest >= 0.9.0.1 && <= 0.11,
+    doctest >= 0.9.0.1 && <= 0.12,
     filepath
   ghc-options: -Wall -threaded
   hs-source-dirs: tests
diff --git a/include/instances.h b/include/instances.h
--- a/include/instances.h
+++ b/include/instances.h
@@ -97,9 +97,9 @@
 instance BODY1(Erf a) => Erf (HEAD) where
   erf = lift1 erf $ \x -> (2 / sqrt pi) * exp (negate x * x)
   erfc = lift1 erfc $ \x -> ((-2) / sqrt pi) * exp (negate x * x)
-  normcdf = lift1 normcdf $ \x -> ((-1) / sqrt pi) * exp (x * x * fromRational (- recip 2) / sqrt (2))
+  normcdf = lift1 normcdf $ \x -> (recip $ sqrt (2 * pi)) * exp (- x * x / 2)
 
 instance BODY1(InvErf a) => InvErf (HEAD) where
-  inverf = lift1 inverfc $ \x -> recip $ (2 / sqrt pi) * exp (negate x * x)
-  inverfc = lift1 inverfc $ \x -> recip $ negate (2 / sqrt pi) * exp (negate x * x)
-  invnormcdf = lift1 invnormcdf $ \x -> recip $ ((-1) / sqrt pi) * exp (x * x * fromRational (- recip 2) / sqrt 2)
+  inverf = lift1_ inverf $ \x _ -> sqrt pi / 2 * exp (x * x)
+  inverfc = lift1_ inverfc $ \x _ -> negate (sqrt pi / 2) * exp (x * x)
+  invnormcdf = lift1_ invnormcdf $ \x _ -> sqrt (2 * pi) * exp (x * x / 2)
diff --git a/src/Numeric/AD/Internal/Kahn.hs b/src/Numeric/AD/Internal/Kahn.hs
--- a/src/Numeric/AD/Internal/Kahn.hs
+++ b/src/Numeric/AD/Internal/Kahn.hs
@@ -116,7 +116,7 @@
 Kahn Zero <**> y             = auto (0 ** primal y)
 _         <**> Kahn Zero     = auto 1
 x         <**> Kahn (Lift y) = lift1 (**y) (\z -> y *^ z ** Id (y-1)) x
-x         <**> y             = lift2_ (**) (\z xi yi -> (yi * z / xi, z * xi)) x y
+x         <**> y             = lift2_ (**) (\z xi yi -> (yi * z / xi, z * log xi)) x y
 
 primal :: Num a => Kahn a -> a
 primal (Kahn Zero) = 0
diff --git a/tests/doctests.hs b/tests/doctests.hs
--- a/tests/doctests.hs
+++ b/tests/doctests.hs
@@ -1,10 +1,7 @@
-{-# LANGUAGE CPP #-}
 module Main where
 
-import Build_doctests (deps)
-#if __GLASGOW_HASKELL__ < 710
+import Build_doctests (autogen_dir, deps)
 import Control.Applicative
-#endif
 import Control.Monad
 import Data.List
 import System.Directory
@@ -14,9 +11,9 @@
 main :: IO ()
 main = getSources >>= \sources -> doctest $
     "-isrc"
-  : "-idist/build/autogen"
+  : ("-i" ++ autogen_dir)
   : "-optP-include"
-  : "-optPdist/build/autogen/cabal_macros.h"
+  : ("-optP" ++ autogen_dir ++ "/cabal_macros.h")
   : "-optP-I"
   : "-optPinclude"
   : "-hide-all-packages"