diff --git a/System/Random.hs b/System/Random.hs
--- a/System/Random.hs
+++ b/System/Random.hs
@@ -6,7 +6,7 @@
 -- |
 -- Module      :  System.Random
 -- Copyright   :  (c) The University of Glasgow 2001
--- License     :  BSD-style (see the file libraries/base/LICENSE)
+-- License     :  BSD-style (see the file LICENSE in the 'random' repository)
 -- 
 -- Maintainer  :  libraries@haskell.org
 -- Stability   :  stable
@@ -114,7 +114,11 @@
 -- | The class 'RandomGen' provides a common interface to random number
 -- generators.
 --
+#ifdef ENABLE_SPLITTABLEGEN
 -- Minimal complete definition: 'next'.
+#else
+-- Minimal complete definition: 'next' and 'split'.
+#endif
 
 class RandomGen g where
 
@@ -147,7 +151,7 @@
 
 #ifdef ENABLE_SPLITTABLEGEN
 -- | The class 'SplittableGen' proivides a way to specify a random number
--- generator that can be split into two new generators.
+--   generator that can be split into two new generators.
 class SplittableGen g where
 #endif
    -- |The 'split' operation allows one to obtain two distinct random number
@@ -355,11 +359,11 @@
   random g	  = randomR (minBound,maxBound) g
 
 {-# INLINE randomRFloating #-}
-randomRFloating :: (Num a, Ord a, Random a, RandomGen g) => (a, a) -> g -> (a, g)
+randomRFloating :: (Fractional a, Num a, Ord a, Random a, RandomGen g) => (a, a) -> g -> (a, g)
 randomRFloating (l,h) g 
     | l>h       = randomRFloating (h,l) g
     | otherwise = let (coef,g') = random g in 
-		  (l + coef * (h-l), g')
+		  (2.0 * (0.5*l + coef * (0.5*h - 0.5*l)), g')  -- avoid overflow
 
 instance Random Double where
   randomR = randomRFloating
@@ -423,14 +427,17 @@
  | otherwise = case (f n 1 rng) of (v, rng') -> (fromInteger (l + v `mod` k), rng')
      where
        k = h - l + 1
+       -- ERROR: b here (2^31-87) represents a baked-in assumption about genRange:
        b = 2147483561
        n = iLogBase b k
 
+       -- Here we loop until we've generated enough randomness to cover the range:
        f 0 acc g = (acc, g)
        f n' acc g =
           let
 	   (x,g')   = next g
 	  in
+          -- We shift over the random bits generated thusfar (* b) and add in the new ones.
 	  f (n' - 1) (fromIntegral x + acc * b) g'
 
 -- The continuous functions on the other hand take an [inclusive,exclusive) range.
@@ -445,8 +452,8 @@
          (x, rng') -> 
 	    let
 	     scaled_x = 
-		fromDouble ((l+h)/2) + 
-                fromDouble ((h-l) / realToFrac int32Count) *
+		fromDouble (0.5*l + 0.5*h) +                   -- previously (l+h)/2, overflowed
+                fromDouble ((0.5*h - 0.5*l) / (0.5 * realToFrac int32Count)) *  -- avoid overflow
 		fromIntegral (x::Int32)
 	    in
 	    (scaled_x, rng')
@@ -454,6 +461,10 @@
 int32Count :: Integer
 int32Count = toInteger (maxBound::Int32) - toInteger (minBound::Int32) + 1
 
+-- Perform an expensive logarithm on arbitrary-size integers by repeated division.
+-- 
+-- (NOTE: This actually returns ceiling(log(i) base b) except with an
+--  incorrect result at iLogBase b b = 2.)
 iLogBase :: Integer -> Integer -> Integer
 iLogBase b i = if i < b then 1 else 1 + iLogBase b (i `div` b)
 
diff --git a/random.cabal b/random.cabal
--- a/random.cabal
+++ b/random.cabal
@@ -1,7 +1,8 @@
 name:		random
-version:	1.0.1.0
+version:	1.0.1.1
 
 -- 1.0.1.0 -- bump for bug fixes, but no SplittableGen yet
+-- 1.0.1.1 -- bump for overflow bug fixes
 
 license:	BSD3
 license-file:	LICENSE
@@ -10,7 +11,9 @@
 synopsis:	random number library
 category:       System
 description:
-	This package provides a random number library.
+	This package provides a basic random number generation
+	library, including the ability to split random number
+	generators.
 build-type: Simple
 Cabal-Version: >= 1.6