From 29f7502f34bdd54dff446a3a886f0e24b7e44493 Mon Sep 17 00:00:00 2001
From: Michael Orlitzky <michael@orlitzky.com>
Date: Wed, 20 Feb 2013 19:06:10 -0500
Subject: [PATCH] Convert Integration/Simpson.hs and Integration/Trapezoid.hs
 to numeric-prelude.

---
 src/Integration/Simpson.hs   | 19 ++++++++++++++++---
 src/Integration/Trapezoid.hs | 20 +++++++++++++++++---
 2 files changed, 33 insertions(+), 6 deletions(-)

diff --git a/src/Integration/Simpson.hs b/src/Integration/Simpson.hs
index 2481f85..c3d59ff 100644
--- a/src/Integration/Simpson.hs
+++ b/src/Integration/Simpson.hs
@@ -1,8 +1,17 @@
+{-# LANGUAGE RebindableSyntax #-}
+
 module Integration.Simpson
 where
 
 import Misc (partition)
 
+import NumericPrelude hiding (abs)
+import Algebra.Absolute (abs)
+import qualified Algebra.Field as Field
+import qualified Algebra.RealField as RealField
+import qualified Algebra.RealRing as RealRing
+import qualified Algebra.ToInteger as ToInteger
+import qualified Algebra.ToRational as ToRational
 
 -- | Use the Simpson's rule to numerically integrate @f@ over the
 --   interval [@a@, @b@].
@@ -30,7 +39,7 @@ import Misc (partition)
 --   >>> simpson_1 f 0 1
 --   0.25
 --
-simpson_1 :: (RealFrac a, Fractional b, Num b)
+simpson_1 :: (RealField.C a, ToRational.C a, RealField.C b)
             => (a -> b) -- ^ The function @f@
             -> a       -- ^ The \"left\" endpoint, @a@
             -> a       -- ^ The \"right\" endpoint, @b@
@@ -38,7 +47,7 @@ simpson_1 :: (RealFrac a, Fractional b, Num b)
 simpson_1 f a b =
   coefficient * ((f a) + 4*(f midpoint) + (f b))
   where
-    coefficient = (realToFrac (b - a)) / 6
+    coefficient = (fromRational' $ toRational (b - a)) / 6
     midpoint = (a + b) / 2
 
 
@@ -59,7 +68,11 @@ simpson_1 f a b =
 --   >>> abs (area - 2) < 0.00001
 --   True
 --
-simpson :: (RealFrac a, Fractional b, Num b, Integral c)
+simpson :: (RealField.C a,
+            ToRational.C a,
+            RealField.C b,
+            ToInteger.C c,
+            Enum c)
           => c -- ^ The number of subintervals to use, @n@
           -> (a -> b) -- ^ The function @f@
           -> a       -- ^ The \"left\" endpoint, @a@
diff --git a/src/Integration/Trapezoid.hs b/src/Integration/Trapezoid.hs
index 5452a5e..c358fef 100644
--- a/src/Integration/Trapezoid.hs
+++ b/src/Integration/Trapezoid.hs
@@ -1,8 +1,18 @@
+{-# LANGUAGE RebindableSyntax #-}
+
 module Integration.Trapezoid
 where
 
 import Misc (partition)
 
+import NumericPrelude hiding (abs)
+import Algebra.Absolute (abs)
+import qualified Algebra.Field as Field
+import qualified Algebra.RealField as RealField
+import qualified Algebra.RealRing as RealRing
+import qualified Algebra.ToInteger as ToInteger
+import qualified Algebra.ToRational as ToRational
+
 -- | Use the trapezoid rule to numerically integrate @f@ over the
 --   interval [@a@, @b@].
 --
@@ -24,13 +34,13 @@ import Misc (partition)
 --   >>> trapezoid_1 f (-1) 1
 --   2.0
 --
-trapezoid_1 :: (RealFrac a, Fractional b, Num b)
+trapezoid_1 :: (Field.C a, ToRational.C a, Field.C b)
             => (a -> b) -- ^ The function @f@
             -> a       -- ^ The \"left\" endpoint, @a@
             -> a       -- ^ The \"right\" endpoint, @b@
             -> b
 trapezoid_1 f a b =
-  (((f a) + (f b)) / 2) * (realToFrac (b - a))
+  (((f a) + (f b)) / 2) * (fromRational' $ toRational (b - a))
 
 
 -- | Use the composite trapezoid rule to numerically integrate @f@
@@ -47,7 +57,11 @@ trapezoid_1 f a b =
 --   >>> abs (area - 2) < 0.0001
 --   True
 --
-trapezoid :: (RealFrac a, Fractional b, Num b, Integral c)
+trapezoid :: (RealField.C a,
+              ToRational.C a,
+              RealField.C b,
+              ToInteger.C c,
+              Enum c)
           => c -- ^ The number of subintervals to use, @n@
           -> (a -> b) -- ^ The function @f@
           -> a       -- ^ The \"left\" endpoint, @a@
-- 
2.43.2