From c3905924154d9a8d56bdc57e2f36fe48b8524eef Mon Sep 17 00:00:00 2001
From: Michael Orlitzky <michael@orlitzky.com>
Date: Mon, 4 Feb 2013 22:17:11 -0500
Subject: [PATCH] Replace (fromRational . toRational) with realToFrac
 everywhere.

---
 src/Integration/Simpson.hs   |  2 +-
 src/Integration/Trapezoid.hs |  2 +-
 src/Normed.hs                | 16 ++++++++--------
 src/ODE/IVP.hs               |  2 +-
 src/Vector.hs                |  4 ++--
 5 files changed, 13 insertions(+), 13 deletions(-)

diff --git a/src/Integration/Simpson.hs b/src/Integration/Simpson.hs
index b700022..2481f85 100644
--- a/src/Integration/Simpson.hs
+++ b/src/Integration/Simpson.hs
@@ -38,7 +38,7 @@ simpson_1 :: (RealFrac a, Fractional b, Num b)
 simpson_1 f a b =
   coefficient * ((f a) + 4*(f midpoint) + (f b))
   where
-    coefficient = (fromRational $ toRational (b - a)) / 6
+    coefficient = (realToFrac (b - a)) / 6
     midpoint = (a + b) / 2
 
 
diff --git a/src/Integration/Trapezoid.hs b/src/Integration/Trapezoid.hs
index 8d4b769..5452a5e 100644
--- a/src/Integration/Trapezoid.hs
+++ b/src/Integration/Trapezoid.hs
@@ -30,7 +30,7 @@ trapezoid_1 :: (RealFrac a, Fractional b, Num b)
             -> a       -- ^ The \"right\" endpoint, @b@
             -> b
 trapezoid_1 f a b =
-  (((f a) + (f b)) / 2) * (fromRational $ toRational (b - a))
+  (((f a) + (f b)) / 2) * (realToFrac (b - a))
 
 
 -- | Use the composite trapezoid rule to numerically integrate @f@
diff --git a/src/Normed.hs b/src/Normed.hs
index 0187df9..9bef763 100644
--- a/src/Normed.hs
+++ b/src/Normed.hs
@@ -25,17 +25,17 @@ instance Normed Integer where
   norm_infty = fromInteger
 
 instance Normed Rational where
-  norm_p _ = fromRational
-  norm_infty = fromRational
+  norm_p _ = realToFrac
+  norm_infty = realToFrac
 
 instance Epsilon e => Normed (BigFloat e) where
-  norm_p _ = fromRational . toRational
-  norm_infty = fromRational . toRational
+  norm_p _ = realToFrac
+  norm_infty = realToFrac
 
 instance Normed Float where
-  norm_p _ = fromRational . toRational
-  norm_infty = fromRational . toRational
+  norm_p _ = realToFrac
+  norm_infty = realToFrac
 
 instance Normed Double where
-  norm_p _ = fromRational . toRational
-  norm_infty = fromRational . toRational
+  norm_p _ = realToFrac
+  norm_infty = realToFrac
diff --git a/src/ODE/IVP.hs b/src/ODE/IVP.hs
index d4876de..6bde763 100644
--- a/src/ODE/IVP.hs
+++ b/src/ODE/IVP.hs
@@ -35,7 +35,7 @@ eulers_method1 :: (RealFrac a, RealFrac b)
 eulers_method1 x0 y0 f h =
   y0 +  h'*y'
   where
-    h' = fromRational $ toRational h
+    h' = realToFrac h
     y' = (f x0 y0)
 
 
diff --git a/src/Vector.hs b/src/Vector.hs
index f55808b..a4d3c13 100644
--- a/src/Vector.hs
+++ b/src/Vector.hs
@@ -143,7 +143,7 @@ instance (RealFloat a, Ord a, Vector v a) => Normed (Vn v a) where
   --   >>> norm_infty v1
   --   5
   --
-  norm_infty (Vn v1) = fromRational $ toRational $ V.foldl max 0 v1
+  norm_infty (Vn v1) = realToFrac $ V.foldl max 0 v1
 
   -- | Generic p-norms. The usual norm in R^n is (norm_p 2).
   --
@@ -156,7 +156,7 @@ instance (RealFloat a, Ord a, Vector v a) => Normed (Vn v a) where
   --   5.0
   --
   norm_p p (Vn v1) =
-    fromRational $ toRational $ root $ V.sum $ V.map (exponentiate . abs) v1
+    realToFrac $ root $ V.sum $ V.map (exponentiate . abs) v1
     where
       exponentiate = (** (fromIntegral p))
       root = (** (recip (fromIntegral p)))
-- 
2.44.2