Clean up imports everywhere.

[numerical-analysis.git] / src / Misc.hs

diff --git a/src/Misc.hs b/src/Misc.hs
index 24fd5b756febd19bd512cf9a7b06682f2aba9f7d..c81d3594fad218bd6d76d224e3aa942071c0a1cf 100644 (file)
--- a/src/Misc.hs
+++ b/src/Misc.hs
@@ -1,12 +1,14 @@
 {-# LANGUAGE RebindableSyntax #-}
+{-# LANGUAGE ScopedTypeVariables #-}
 
 -- | Stuff for which I'm too lazy to come up with a decent name.
 module Misc
 where
 
 import NumericPrelude
-import Algebra.Field
-import Algebra.ToInteger
+import Algebra.Field ( C )
+import Algebra.RealRing ( C )
+import Algebra.ToInteger ( C )
 
 -- | Partition the interval [@a@, @b@] into @n@ subintervals, which we
 --   then return as a list of pairs.
@@ -34,4 +36,15 @@ partition n a b
                  let xi = a + k'*h,
                  let xj = a + (k'+1)*h ]
     where
-      h = (b-a)/(fromIntegral $ toInteger n)
+      coerced_n = fromIntegral $ toInteger n
+      h = (b-a)/coerced_n
+
+
+-- | Compute the unit roundoff (machine epsilon) for this machine. We
+--   find the largest number epsilon such that 1+epsilon <= 1. If you
+--   request anything other than a Float or Double from this, expect
+--   to wait a while.
+--
+unit_roundoff :: forall a. (Algebra.RealRing.C a, Algebra.Field.C a) => a
+unit_roundoff =
+  head [ 1/2^(k-1) | k <- [0..], 1 + 1/(2^k) <= (1::a) ]