diff --git a/basis/PackReal32Tagged.sml b/basis/PackReal32Tagged.sml
index c79f27fb..66d4bbc0 100644
--- a/basis/PackReal32Tagged.sml
+++ b/basis/PackReal32Tagged.sml
@@ -1,115 +1,124 @@
 (*
     Title:      Standard Basis Library: Pack Real32 structures for 64-bit platforms
     Author:     David Matthews
     Copyright   David Matthews 2021
 
     This library is free software; you can redistribute it and/or
     modify it under the terms of the GNU Lesser General Public
     Licence version 2.1 as published by the Free Software Foundation.
     
     This library is distributed in the hope that it will be useful,
     but WITHOUT ANY WARRANTY; without even the implied warranty of
     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
     Lesser General Public Licence for more details.
     
     You should have received a copy of the GNU Lesser General Public
     License along with this library; if not, write to the Free Software
     Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
 *)
 
 (* On 64-bit platforms Real32.real values are held as tagged values
    with the floating point value in the high-order 32-bits. *)
 
 local
     val r32AsWord: Real32.real -> word = RunCall.unsafeCast
     and wordAsR32: word -> Real32.real = RunCall.unsafeCast
     
     infix << >>
     infix orb
     val op orb = Word.orb
     and op << = Word.<<
     and op >> = Word.>>
 
     val wordToW8 = Word8.fromLarge o Word.toLarge
     and w8ToWord = Word.fromLarge o Word8.toLarge
+    
+    (* Word values are already shifted by one bit so the
+       actual shifts are 31, 39, 47 and 55 bits. *)
+    val shift0 = Word.fromInt Word.wordSize - 0w32
+    and shift1 = Word.fromInt Word.wordSize - 0w24
+    and shift2 = Word.fromInt Word.wordSize - 0w16
+    and shift3 = Word.fromInt Word.wordSize - 0w08
 in
 
     structure PackReal32Little: PACK_REAL =
     struct
         type real = Real32.real
         val bytesPerElem = 4
         val isBigEndian = false
         
         fun toBytes r =
         let
             val w: word = r32AsWord r
         in
-            Word8Vector.fromList[wordToW8(w >> 0w32), wordToW8(w >> 0w40), wordToW8(w >> 0w48), wordToW8(w >> 0w56)]
+            Word8Vector.fromList[wordToW8(w >> shift0), wordToW8(w >> shift1),
+                    wordToW8(w >> shift2), wordToW8(w >> shift3)]
         end
 
         fun subVec(v, i) =
-            wordAsR32((w8ToWord(Word8Vector.sub(v, i)) << 0w32) orb
-                (w8ToWord(Word8Vector.sub(v, i+1)) << 0w40) orb
-                (w8ToWord(Word8Vector.sub(v, i+2)) << 0w48) orb
-                (w8ToWord(Word8Vector.sub(v, i+3)) << 0w56))
+            wordAsR32((w8ToWord(Word8Vector.sub(v, i)) << shift0) orb
+                (w8ToWord(Word8Vector.sub(v, i+1)) << shift1) orb
+                (w8ToWord(Word8Vector.sub(v, i+2)) << shift2) orb
+                (w8ToWord(Word8Vector.sub(v, i+3)) << shift3))
 
         fun fromBytes v = subVec(v, 0)
 
         fun subArr(v, i) =
-            wordAsR32((w8ToWord(Word8Array.sub(v, i)) << 0w32) orb
-                (w8ToWord(Word8Array.sub(v, i+1)) << 0w40) orb
-                (w8ToWord(Word8Array.sub(v, i+2)) << 0w48) orb
-                (w8ToWord(Word8Array.sub(v, i+3)) << 0w56))
+            wordAsR32((w8ToWord(Word8Array.sub(v, i)) << shift0) orb
+                (w8ToWord(Word8Array.sub(v, i+1)) << shift1) orb
+                (w8ToWord(Word8Array.sub(v, i+2)) << shift2) orb
+                (w8ToWord(Word8Array.sub(v, i+3)) << shift3))
 
         fun update(v, i, r) =
         let
             val w: word = r32AsWord r
             open Word8Array
         in
-            Word8Array.update(v, i, wordToW8(w >> 0w32));
-            Word8Array.update(v, i+1, wordToW8(w >> 0w40));
-            Word8Array.update(v, i+2, wordToW8(w >> 0w48));
-            Word8Array.update(v, i+3, wordToW8(w >> 0w56))
+            Word8Array.update(v, i, wordToW8(w >> shift0));
+            Word8Array.update(v, i+1, wordToW8(w >> shift1));
+            Word8Array.update(v, i+2, wordToW8(w >> shift2));
+            Word8Array.update(v, i+3, wordToW8(w >> shift3))
         end
     end
 
     structure PackReal32Big: PACK_REAL =
     struct
         type real = Real32.real
         val bytesPerElem = 4
         val isBigEndian = false
         
         fun toBytes r =
         let
             val w: word = r32AsWord r
         in
-            Word8Vector.fromList[wordToW8(w >> 0w56), wordToW8(w >> 0w48), wordToW8(w >> 0w40), wordToW8(w >> 0w32)]
+            Word8Vector.fromList[wordToW8(w >> shift3), wordToW8(w >> shift2),
+                wordToW8(w >> shift1), wordToW8(w >> shift0)]
         end
 
         fun subVec(v, i) =
-            wordAsR32((w8ToWord(Word8Vector.sub(v, i)) << 0w56) orb
-                (w8ToWord(Word8Vector.sub(v, i+1)) << 0w48) orb
-                (w8ToWord(Word8Vector.sub(v, i+2)) << 0w40) orb
-                (w8ToWord(Word8Vector.sub(v, i+3)) << 0w32))
+            wordAsR32((w8ToWord(Word8Vector.sub(v, i)) << shift3) orb
+                (w8ToWord(Word8Vector.sub(v, i+1)) << shift2) orb
+                (w8ToWord(Word8Vector.sub(v, i+2)) << shift1) orb
+                (w8ToWord(Word8Vector.sub(v, i+3)) << shift0))
 
         fun fromBytes v = subVec(v, 0)
 
         fun subArr(v, i) =
-            wordAsR32((w8ToWord(Word8Array.sub(v, i)) << 0w56) orb
-                (w8ToWord(Word8Array.sub(v, i+1)) << 0w48) orb
-                (w8ToWord(Word8Array.sub(v, i+2)) << 0w40) orb
-                (w8ToWord(Word8Array.sub(v, i+3)) << 0w32))
+            wordAsR32((w8ToWord(Word8Array.sub(v, i)) << shift3) orb
+                (w8ToWord(Word8Array.sub(v, i+1)) << shift2) orb
+                (w8ToWord(Word8Array.sub(v, i+2)) << shift1) orb
+                (w8ToWord(Word8Array.sub(v, i+3)) << shift0))
 
         fun update(v, i, r) =
         let
             val w: word = r32AsWord r
             open Word8Array
         in
-            Word8Array.update(v, i, wordToW8(w >> 0w56));
-            Word8Array.update(v, i+1, wordToW8(w >> 0w48));
-            Word8Array.update(v, i+2, wordToW8(w >> 0w40));
-            Word8Array.update(v, i+3, wordToW8(w >> 0w32))
+            Word8Array.update(v, i, wordToW8(w >> shift3));
+            Word8Array.update(v, i+1, wordToW8(w >> shift2));
+            Word8Array.update(v, i+2, wordToW8(w >> shift1));
+            Word8Array.update(v, i+3, wordToW8(w >> shift0))
         end
     end
 
 end;