[RESEARCH] thx to Gabriel Gonzales work n Fibonacci.

src/Gargantext/Prelude.hs

@@ -297,12 +297,6 @@ ma :: [Double] -> [Double]
 ma = movingAverage 3
 
 -----------------------------------------------------------------------
-fib :: Int -> Int
-fib 0 = 0
-fib 1 = 1
-fib n = fib (n-1) + fib (n-2)
-
-
 -----------------------------------------------------------------------
 --- Map in Map = Map2
 -- To avoid Map (a,a) b

src/Gargantext/Prelude/Fibonacci.hs

+{-|
+Module      : Gargantext.Prelude.Utils
+Description : Useful Tools near Prelude of the project
+Copyright   : (c) CNRS, 2017-Present
+License     : AGPL + CECILL v3
+Maintainer  : team@gargantext.org
+Stability   : experimental
+Portability : POSIX
+
+
+Source: 
+Gabriel Gonzales, Blazing fast Fibonacci numbers using Monoids, 2020-04,
+http://www.haskellforall.com/2020/04/blazing-fast-fibonacci-numbers-using.html
+(This post illustrates a nifty application of Haskell’s standard library to solve a numeric problem.)
+
+TODO: quikcheck
+
+-}
+
+
+
+module Gargantext.Prelude.Fibonacci where
+
+import qualified Data.Semigroup as Semigroup
+
+-------------------------------------------------------------
+fib' :: Integer -> Integer
+fib' 0 = 0
+fib' 1 = 1
+fib' n = fib (n-1) + fib (n-2)
+-------------------------------------------------------------
+
+
+data Matrix2x2 = Matrix
+    { x00 :: Integer, x01 :: Integer
+    , x10 :: Integer, x11 :: Integer
+    }
+
+instance Monoid Matrix2x2 where
+    mempty =
+        Matrix
+            { x00 = 1, x01 = 0
+            , x10 = 0, x11 = 1
+            }
+
+instance Semigroup Matrix2x2 where
+    Matrix l00 l01 l10 l11 <> Matrix r00 r01 r10 r11 =
+        Matrix
+            { x00 = l00 * r00 + l01 * r10, x01 = l00 * r01 + l01 * r11
+            , x10 = l10 * r00 + l11 * r10, x11 = l10 * r01 + l11 * r11
+            }
+
+fib :: Integer -> Integer
+fib n = x01 (Semigroup.mtimesDefault n matrix)
+  where
+    matrix =
+        Matrix
+            { x00 = 0, x01 = 1
+            , x10 = 1, x11 = 1
+            }