diff --git a/PRNG.ml b/PRNG.ml
index d66cb40..1ae7622 100644
--- a/PRNG.ml
+++ b/PRNG.ml
@@ -20,6 +20,7 @@ module type STATE = sig
   val make_self_init: unit -> t
   val bool: t -> bool
   val bit: t -> bool
+  val uniform: t -> float
   val float: t -> float -> float
   val byte: t -> int
   val bits8: t -> int
@@ -49,6 +50,7 @@ module type PURE = sig
   val make_self_init: unit -> t
   val bool: t -> bool * t
   val bit: t -> bool * t
+  val uniform: t -> float * t
   val float: float -> t -> float * t
   val byte: t -> int * t
   val bits8: t -> int * t
@@ -143,14 +145,12 @@ let nativeint =
   then fun g bound -> Nativeint.of_int32 (int32 g (Nativeint.to_int32 bound))
   else fun g bound -> Int64.to_nativeint (int64 g (Int64.of_nativeint bound))
 
-let float_64 g bound =
+let rec uniform g =
   let b = X.bits64 g in
-  (Int64.(to_float (shift_right_logical b 11)) *. 0x1.p-53) *. bound
+  let n = Int64.shift_right_logical b 11 in
+  if n <> 0L then Int64.to_float n *. 0x1.p-53 else uniform g
 
-let float_32 g bound =
-  let a = X.bits30 g in
-  let b = X.bits30 g in
-  (float a *. 0x1.p-60 +. float b *. 0x1.p-30) *. bound
+let float g bound = uniform g *. bound
 
 end
 
@@ -218,14 +218,13 @@ let nativeint =
       (Int64.to_nativeint r, g')
   end
 
-let float_64 bound g =
+let rec uniform g =
   let (b, g) = X.bits64 g in
-  ((Int64.(to_float (shift_right_logical b 11)) *. 0x1.p-53) *. bound, g)
+  let n = Int64.shift_right_logical b 11 in
+  if n <> 0L then (Int64.to_float n *. 0x1.p-53, g) else uniform g
 
-let float_32 bound g =
-  let (a, g) = X.bits30 g in
-  let (b, g) = X.bits30 g in
-  ((float a *. 0x1.p-60 +. float b *. 0x1.p-30) *. bound, g)
+let float bound g = 
+  let (f, g) = uniform g in (f *. bound, g)
 
 end
 
@@ -317,8 +316,6 @@ include StateDerived(struct
   let errorprefix = "PRNG.Splitmix.State."
 end)
 
-let float = float_64
-
 let bytes g dst ofs len =
   if ofs < 0 || len < 0 || ofs > Bytes.length dst - len then
     invalid_arg "PRNG.State.bytes"
@@ -401,8 +398,6 @@ include PureDerived(struct
   let errorprefix = "PRNG.Splitmix.Pure."
 end)
 
-let float = float_64
-
 let split g =
   let g1 = next g in
   let g2 = next g1 in
@@ -554,8 +549,6 @@ include StateDerived(struct
   let errorprefix = "PRNG.Chacha.State."
 end)
 
-let float = if Sys.word_size = 64 then float_64 else float_32
-
 let bytes g dst ofs len =
   if ofs < 0 || len < 0 || Bytes.length dst - len > ofs then
     invalid_arg "PRNG.Chacha.State.bytes";
@@ -676,8 +669,6 @@ include PureDerived(struct
   let errorprefix = "PRNG.Chacha.Pure."
 end)
 
-let float = if Sys.word_size = 64 then float_64 else float_32
-
 let bytes g dst ofs len =
   if ofs < 0 || len < 0 || Bytes.length dst - len > ofs then
     invalid_arg "PRNG.Chacha.Pure.bytes";
diff --git a/PRNG.mli b/PRNG.mli
index 39bc329..446f678 100644
--- a/PRNG.mli
+++ b/PRNG.mli
@@ -59,10 +59,19 @@ module type STATE = sig
   val bit: t -> bool
     (** Return a Boolean value in [false,true] with 0.5 probability each. *)
 
+  val uniform: t -> float
+    (** Return a floating-point number evenly distributed between 0.0 and 1.0.
+        0.0 and 1.0 are never returned.
+        The result is of the form [n * 2{^-53}], where [n] is a random integer
+        in [(0, 2{^53})]. *)
+
   val float: t -> float -> float
     (** [float g x] returns a floating-point number evenly distributed
-        between 0.0 and [x].  If [x] is negative, negative numbers 
-        between [x] and 0.0 are returned. *)
+        between 0.0 and [x].  If [x] is negative, negative numbers
+        between [x] and 0.0 are returned.  Implemented as [uniform g *. x].
+        Consequently, the values [0.0] and [x] can be returned
+        (as a result of floating-point rounding), but not if [x] is
+        [1.0], since [float g 1.0] behaves exactly like [uniform g]. *)
 
   val byte: t -> int
   val bits8: t -> int
@@ -90,7 +99,7 @@ module type STATE = sig
         Note that [int32 Int32.max_int] produces numbers between 0 and
         [Int32.max_int] excluded.  To produce numbers between 0 and
         [Int32.max_int] included, use
-        [Int32.logand (bits32 g) Int64.max_int]. *)
+        [Int32.logand (bits32 g) Int32.max_int]. *)
 
   val bits64: t -> int64
     (** Return a 64-bit integer evenly distributed between
@@ -179,6 +188,7 @@ module type PURE = sig
   val bool: t -> bool * t
   val bit: t -> bool * t
 
+  val uniform: t -> float * t
   val float: float -> t -> float * t
 
   val byte: t -> int * t