--- a/Number.st	Thu Jun 22 13:57:19 2017 +0200
+++ b/Number.st	Thu Jun 22 14:33:41 2017 +0200
@@ -1917,6 +1917,21 @@
     "
 !
 
+printfPrintString:formatString
+    "Return a printed representation of the receiver as specified by formatString,
+     which is defined by printf."
+
+    ^ PrintfScanf printf:formatString argument:self
+
+    "
+     2.0 asQDouble printfPrintString:'%10f'
+     2.0 asQDouble printfPrintString:'%10.8f'
+     2.0 printfPrintString:'%10.8f'
+    "
+
+    "Created: / 22-06-2017 / 13:55:22 / cg"
+!
+
 radixPrintStringRadix:radix
     "return a string representation of the receiver in the specified
      base; prepend XXr to the string"
@@ -2407,38 +2422,84 @@
 !
 
 sqrt_withAccuracy:epsilon
-    "compute square root of the receiver using newtom/heron algorithm"
+    "compute square root of the receiver using newton-raphson/heron algorithm"
     "
       Use the Heron algorithm:
 
-		 x_n + (a / x_n)
-	x_n+1 =  ---------------
-		      2
-
-	sqrt(a) = x_n
+                 x_n + (a / x_n)
+        x_n+1 =  ---------------
+                      2
+
+        sqrt(a) = x_n
+    "
+
+    ^ self sqrt_withAccuracy:epsilon fromInitialGuess:(self / 2)
+
+    "
+     2 sqrt                                  1.4142135623731      - computed by CPU/FPU
+     
+     2q sqrt                                 1.414213562373095049 - computed by CPU/FPU
+
+     2q sqrt_withAccuracy:0.01               1.414215686274509804 - computed by Smalltalk
+     2q sqrt_withAccuracy:0.0001             1.414213562374689911
+     2q sqrt_withAccuracy:0.0000001          1.414213562373095049
+     2q sqrt_withAccuracy:0.0000000001       1.414213562373095049
+     2q sqrt_withAccuracy:0.000000000001     1.414213562373095049
+     
+     2q sqrt_withAccuracy:LongFloat epsilon  1.414213562373095049
+
+     (4 sqrt_withAccuracy:Integer epsilon) asFloat
+
+     MessageTally spyOn:[ |arg|
+        arg := 2 asLongFloat.
+        1000000 timesRepeat:[
+             arg sqrt_withAccuracy:0.000000000001
+        ]
+     ]
+     Time millisecondsToRun:[ |arg|
+        arg := 2 asLongFloat.
+        1000000 timesRepeat:[
+             arg sqrt_withAccuracy:0.000000000001
+        ]
+     ]
+    "
+
+    "Modified (comment): / 22-06-2017 / 14:01:16 / cg"
+!
+
+sqrt_withAccuracy:epsilon fromInitialGuess:guess
+    "compute square root of the receiver using newton-raphson/heron algorithm"
+    "
+      Use the Heron algorithm:
+
+                 x_n + (a / x_n)
+        x_n+1 =  ---------------
+                      2
+
+        sqrt(a) = x_n
     "
 
     |approx|
 
     self <= 0 ifTrue:[
-	self = 0 ifTrue:[
-	    ^ self
-	].
-	^ self class
-	    raise:#imaginaryResultSignal
-	    receiver:self
-	    selector:#sqrt
-	    arguments:#()
-	    errorString:'bad (negative) receiver in sqrt'
+        self = 0 ifTrue:[
+            ^ self
+        ].
+        ^ self class
+            raise:#imaginaryResultSignal
+            receiver:self
+            selector:#sqrt
+            arguments:#()
+            errorString:'bad (negative) receiver in sqrt'
     ].
 
-    approx := 1.
+    approx := guess.
     [
-	|lastApprox|
-
-	lastApprox := approx.
-	approx := ((self / approx) + approx) / 2.
-	(approx - lastApprox) abs > epsilon
+        |lastApprox|
+
+        lastApprox := approx.
+        approx := ((self / approx) + approx) / 2.
+        (approx - lastApprox) abs > epsilon
     ] whileTrue.
     ^ approx
 
@@ -2455,18 +2516,20 @@
      (4 sqrt_withAccuracy:Integer epsilon) asFloat
 
      MessageTally spyOn:[ |arg|
-	arg := 2 asLongFloat.
-	1000000 timesRepeat:[
-	     arg sqrt_withAccuracy:0.000000000001
-	]
+        arg := 2 asLongFloat.
+        1000000 timesRepeat:[
+             arg sqrt_withAccuracy:0.000000000001
+        ]
      ]
      Time millisecondsToRun:[ |arg|
-	arg := 2 asLongFloat.
-	1000000 timesRepeat:[
-	     arg sqrt_withAccuracy:0.000000000001
-	]
+        arg := 2 asLongFloat.
+        1000000 timesRepeat:[
+             arg sqrt_withAccuracy:0.000000000001
+        ]
      ]
     "
+
+    "Created: / 22-06-2017 / 13:59:48 / cg"
 !
 
 tan_withAccuracy:epsilon