diff --git a/CHANGELOG.md b/CHANGELOG.md
new file mode 100644
--- /dev/null
+++ b/CHANGELOG.md
@@ -0,0 +1,12 @@
+# Changelog
+
+`fib` uses [PVP Versioning][1].
+The changelog is available [on GitHub][2].
+
+0.0.0
+=====
+
+* Initially created.
+
+[1]: https://pvp.haskell.org
+[2]: https://github.com/chessai/fib/releases
diff --git a/LICENSE b/LICENSE
new file mode 100644
--- /dev/null
+++ b/LICENSE
@@ -0,0 +1,29 @@
+BSD 3-Clause License
+
+Copyright (c) 2019, chessai
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are met:
+
+* Redistributions of source code must retain the above copyright notice, this
+  list of conditions and the following disclaimer.
+
+* Redistributions in binary form must reproduce the above copyright notice,
+  this list of conditions and the following disclaimer in the documentation
+  and/or other materials provided with the distribution.
+
+* Neither the name of the copyright holder nor the names of its
+  contributors may be used to endorse or promote products derived from
+  this software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
+FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
+OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
diff --git a/README.md b/README.md
new file mode 100644
--- /dev/null
+++ b/README.md
@@ -0,0 +1,6 @@
+# fib
+
+[![Hackage](https://img.shields.io/hackage/v/fib.svg)](https://hackage.haskell.org/package/fib)
+[![BSD3 license](https://img.shields.io/badge/license-BSD3-blue.svg)](LICENSE)
+
+fibonacci algebra
diff --git a/fib.cabal b/fib.cabal
new file mode 100644
--- /dev/null
+++ b/fib.cabal
@@ -0,0 +1,54 @@
+cabal-version: 2.4
+name:
+  fib
+version:
+  0.1
+synopsis:
+  fibonacci algebra
+description:
+  fibonacci algebra
+homepage:
+  https://github.com/chessai/fib
+bug-reports:
+  https://github.com/chessai/fib/issues
+license:
+  BSD-3-Clause
+license-file:
+  LICENSE
+author:
+  chessai
+maintainer:
+  chessai <chessai1996@gmail.com>
+copyright:
+  2019 chessai
+category:
+  Math
+build-type:
+  Simple
+extra-doc-files:
+    README.md
+  , CHANGELOG.md
+tested-with:
+    GHC == 8.2.2
+  , GHC == 8.4.4
+  , GHC == 8.6.3
+
+library
+  hs-source-dirs:
+    src
+  exposed-modules:
+    Fib
+  other-modules:
+    Prelude
+  build-depends:
+    , base-noprelude >= 4.10.1.0 && < 4.13
+    , semirings >= 0.3
+    , integer-gmp
+  ghc-options:
+    -Wall
+  default-language:
+    Haskell2010
+
+source-repository head
+  type:                git
+  location:            https://github.com/chessai/fib.git
diff --git a/src/Fib.hs b/src/Fib.hs
new file mode 100644
--- /dev/null
+++ b/src/Fib.hs
@@ -0,0 +1,51 @@
+{-# language BangPatterns #-}
+{-# language DeriveFoldable #-}
+{-# language DeriveFunctor #-}
+{-# language DeriveTraversable #-}
+{-# language DerivingStrategies #-}
+
+module Fib
+  ( Fib(..)
+  , phi
+  , fib
+  ) where
+
+data Fib a = Fib a a
+  deriving stock (Show)
+  deriving stock (Functor,Foldable,Traversable)
+
+instance Semiring a => Semiring (Fib a) where
+  zero = Fib zero zero
+  Fib a b `plus` Fib c d = Fib (a `plus` c) (b `plus` d)
+  one = Fib one zero
+  Fib a b `times` Fib c d = Fib (a `times` (c `plus` d) `plus` b `times` c) (a `times` c `plus` b `times` d)
+  {-# inline zero #-}
+  {-# inline one #-}
+  {-# inline plus #-}
+  {-# inline times #-}
+
+instance Ring a => Ring (Fib a) where
+  negate (Fib a b) = Fib (negate a) (negate b)
+  {-# inline negate #-}
+
+instance Applicative Fib where
+  pure x = Fib x x
+  {-# inline pure #-} 
+  Fib fa fb <*> Fib a b = Fib (fa a) (fb b)
+  {-# inline (<*>) #-}
+
+instance Monad Fib where
+  Fib a b >>= f = Fib a' b' where
+    Fib a' _ = f a
+    Fib _ b' = f b
+  {-# inline (>>=) #-}
+
+phi :: Semiring a => Fib a
+phi = one
+{-# inline phi #-}
+
+fib :: Ring a => Integer -> a
+fib n
+  | n >= 0 = case (phi ^ n) of (Fib a _) -> a
+  | otherwise = case (Fib one (negate one) ^ negate n) of (Fib a _) -> a
+{-# inlinable fib #-}
diff --git a/src/Prelude.hs b/src/Prelude.hs
new file mode 100644
--- /dev/null
+++ b/src/Prelude.hs
@@ -0,0 +1,15 @@
+module Prelude
+  ( module P
+  ) where
+
+import GHC.Show as P (Show)
+import Data.Eq as P (Eq(..))
+import Data.Functor as P (Functor(..))
+import Data.Foldable as P (Foldable(..))
+import Data.Traversable as P (Traversable(..))
+import Data.Semiring as P (Semiring(..),Ring(..),(+),(*),(-),(^))
+import Control.Applicative as P (Applicative(..))
+import Control.Monad as P (Monad(..))
+import GHC.Integer as P (Integer)
+import Data.Ord as P (Ord(..))
+import Data.Bool as P (otherwise,Bool)