--- a/LargeInteger.st	Mon Dec 02 12:36:27 2019 +0100
+++ b/LargeInteger.st	Mon Dec 02 13:20:25 2019 +0100
@@ -5547,10 +5547,34 @@
     "Modified: 5.11.1996 / 16:12:56 / cg"
 !
 
+isPerfectSquare
+    self mightBeASquare ifFalse:[^ false].
+    ^ super isPerfectSquare.
+
+    "
+     2r1010101101010110101010101010101010101010101010101010 isPerfectSquare
+     123456789012345678901234567890 isPerfectSquare
+     123456789012345678901234567890 squared isPerfectSquare 
+     100 factorial isPerfectSquare 
+     100 factorial squared isPerfectSquare 
+     1000 factorial isPerfectSquare         
+     1000 factorial squared isPerfectSquare
+
+     Time millisecondsToRun:[
+        |n|
+        n := 100 factorial squared.
+        1000 timesRepeat:[
+            n isPerfectSquare
+        ]
+     ]      
+    "
+!
+
 mightBeASquare
     "a quick (and cheap) check if the receiver is possibly a square"
 
-    | lsb |
+    | lsb "{ Class: SmallInteger}" 
+      lHdigit|
 
     self negative ifTrue:[ ^ false ].
 
@@ -5570,6 +5594,20 @@
     Also, the receiver must be an aven power of two."
 
     lsb := self byteAt: 1.
+    lHdigit := lsb bitAnd:16r0F.
+    lHdigit > 9 ifTrue:[^ false].
+    "/ 0..9
+    lHdigit > 1 ifTrue:[
+        "/ 2..9
+        lHdigit == 4 ifFalse:[
+            "/ 2,3,5..9
+            lHdigit == 9 ifFalse:[
+                "/ 2,3,5..8
+                ^ false
+            ]
+        ]
+    ].
+
     ^ (lsb == 0 and: [ self lowBit odd ])     "00 (and even power of 2)"
             or: [ lsb = 16r40                       "40"
             or: [ (lsb bitAnd: 16r7) = 1            "any|1 or any|9"
@@ -5578,8 +5616,21 @@
 
 
     "
+     2r1010101101010110101010101010101010101010101010101010 mightBeASquare
      123456789012345678901234567890 mightBeASquare
-     123456789012345678901234567890 squared mightBeASquare 
+     123456789012345678901234567890 squared mightBeASquare
+    "
+    "
+     |n s1 s2|
+     n := 100000.
+     [n <= 200000] whileTrue:[
+        s1 := n squared.
+        s2 := (n+1) squared.
+        self assert:s1 isPerfectSquare.
+        s1+1 to:s2-1 do:[:nonSquares |
+            self assert:(nonSquares isPerfectSquare not)
+        ].
+     ]
     "
 !