diff --git a/random.cabal b/random.cabal
index d7954b333..8d6e25e6f 100644
--- a/random.cabal
+++ b/random.cabal
@@ -142,7 +142,8 @@ test-suite doctests
         mwc-random >=0.13 && <0.15,
         primitive >=0.6 && <0.8,
         random -any,
-        unliftio >=0.2 && <0.3
+        unliftio >=0.2 && <0.3,
+        vector >= 0.10 && <0.14
 
 test-suite spec
     type:             exitcode-stdio-1.0
diff --git a/src/System/Random/Internal.hs b/src/System/Random/Internal.hs
index 61719988c..554e99fbe 100644
--- a/src/System/Random/Internal.hs
+++ b/src/System/Random/Internal.hs
@@ -897,7 +897,7 @@ boundedExclusiveIntegralM s gen = go
     twoToK = (1 :: a) `shiftL` k
     modTwoToKMask = twoToK - 1
 
-    t = (twoToK - s) `mod` s
+    t = (twoToK - s) `rem` s -- `rem`, instead of `mod` because `twoToK >= s` is guaranteed
     go :: (Bits a, Integral a, StatefulGen g m) => m a
     go = do
       x <- uniformIntegralWords n gen
diff --git a/src/System/Random/Stateful.hs b/src/System/Random/Stateful.hs
index 842c1e081..47bd3e30c 100644
--- a/src/System/Random/Stateful.hs
+++ b/src/System/Random/Stateful.hs
@@ -624,8 +624,7 @@ runSTGen_ g action = fst $ runSTGen g action
 -- $implementmonadrandom
 --
 -- Typically, a monadic pseudo-random number generator has facilities to save
--- and restore its internal state in addition to generating pseudo-random
--- pseudo-random numbers.
+-- and restore its internal state in addition to generating pseudo-random numbers.
 --
 -- Here is an example instance for the monadic pseudo-random number generator
 -- from the @mwc-random@ package:
@@ -642,6 +641,46 @@ runSTGen_ g action = fst $ runSTGen g action
 -- >   thawGen = MWC.restore
 -- >   freezeGen = MWC.save
 --
+-- === @FrozenGen@
+--
+-- `FrozenGen` gives us ability to use any stateful pseudo-random number generator in its
+-- immutable form, if one exists that is. This concept is commonly known as a seed, which
+-- allows us to save and restore the actual mutable state of a pseudo-random number
+-- generator. The biggest benefit that can be drawn from a polymorphic access to a
+-- stateful pseudo-random number generator in a frozen form is the ability to serialize,
+-- deserialize and possibly even use the stateful generator in a pure setting without
+-- knowing the actual type of a generator ahead of time. For example we can write a
+-- function that accepts a frozen state of some pseudo-random number generator and
+-- produces a short list with random even integers.
+--
+-- >>> import Data.Int (Int8)
+-- >>> :{
+-- myCustomRandomList :: FrozenGen f m => f -> m [Int8]
+-- myCustomRandomList f =
+--   withMutableGen_ f $ \gen -> do
+--     len <- uniformRM (5, 10) gen
+--     replicateM len $ do
+--       x <- uniformM gen
+--       pure $ if even x then x else x + 1
+-- :}
+--
+-- and later we can apply it to a frozen version of a stateful generator, such as `STGen`:
+--
+-- >>> print $ runST $ myCustomRandomList (STGen (mkStdGen 217))
+-- [-50,-2,4,-8,-58,-40,24,-32,-110,24]
+--
+-- or a @Seed@ from @mwc-random@:
+--
+-- >>> import Data.Vector.Primitive as P
+-- >>> print $ runST $ myCustomRandomList (MWC.toSeed (P.fromList [1,2,3]))
+-- [24,40,10,40,-8,48,-78,70,-12]
+--
+-- Alternatively, instead of discarding the final state of the generator, as it happens
+-- above, we could have used `withMutableGen`, which together with the result would give
+-- us back its frozen form. This would allow us to store the end state of our generator
+-- somewhere for the later reuse.
+--
+--
 -- $references
 --
 -- 1. Guy L. Steele, Jr., Doug Lea, and Christine H. Flood. 2014. Fast
diff --git a/test/Spec.hs b/test/Spec.hs
index 9cc8b5276..63eb126f3 100644
--- a/test/Spec.hs
+++ b/test/Spec.hs
@@ -69,6 +69,8 @@ main =
     , runSpec
     , floatTests
     , byteStringSpec
+    , SC.testProperty "uniformRangeWithinExcludedF" $ seeded Range.uniformRangeWithinExcludedF
+    , SC.testProperty "uniformRangeWithinExcludedD" $ seeded Range.uniformRangeWithinExcludedD
     ]
 
 floatTests :: TestTree
diff --git a/test/Spec/Range.hs b/test/Spec/Range.hs
index a235f56c1..9a61b59a7 100644
--- a/test/Spec/Range.hs
+++ b/test/Spec/Range.hs
@@ -3,9 +3,11 @@ module Spec.Range
   , bounded
   , singleton
   , uniformRangeWithin
-  , uniformRangeWithinExcluded
+  , uniformRangeWithinExcludedF
+  , uniformRangeWithinExcludedD
   ) where
 
+import System.Random.Internal
 import System.Random.Stateful
 import Data.Proxy
 
@@ -29,8 +31,12 @@ uniformRangeWithin _ gen (l, r) =
   runStateGen_ gen $ \g ->
     (\result -> min l r <= result && result <= max l r) <$> uniformRM (l, r) g
 
-uniformRangeWithinExcluded ::
-     (RandomGen g, UniformRange a, Ord a) => Proxy a -> g -> (a, a) -> Bool
-uniformRangeWithinExcluded _ gen (l, r) =
+uniformRangeWithinExcludedF :: RandomGen g => g -> Bool
+uniformRangeWithinExcludedF gen =
   runStateGen_ gen $ \g ->
-    (\result -> min l r <= result && (l == r || result < max l r)) <$> uniformRM (l, r) g
+    (\result -> 0 < result && result <= 1) <$> uniformFloatPositive01M g
+
+uniformRangeWithinExcludedD :: RandomGen g => g -> Bool
+uniformRangeWithinExcludedD gen =
+  runStateGen_ gen $ \g ->
+    (\result -> 0 < result && result <= 1) <$> uniformDoublePositive01M g