Modified with changes proposed in #184 (comment) (inverseBinomialCoefficient)

Author: Hernán Morales Durand

src/Math-Numerical/Integer.extension.st

@@ -1,59 +1,41 @@
 Extension { #name : #Integer }
 
 { #category : #'*Math-Numerical' }
-Integer >> findNK [
-	" Reverse binomial coefficient. Answer a <Collection> with all n and k such that n take: k = self. Elements in the answered Collection should be read as paired. Each pair represents (n,k) in the binomial coefficient formula. 
-	See https://math.stackexchange.com/a/103385/205 for details. "
-
-	| k |
-	[ self > 1 ] assert.
-    k := 0.
-	^ Array streamContents: [ : stream | 
-	    [ true ] whileTrue: [ 
-			| nmin nmax choose |
-			k := k + 1.
-			((2 * k + 1) * self) <= (4 ** k)
-				ifTrue: [ ^ stream contents ].
-			nmin := k firstOver: (k factorial * self).
-			nmax := nmin + k + 1.
-			nmin := nmin max: (2 * k).
-	      choose := nmin asInteger take: k.
-			nmin to: nmax do: [ : n |
-				choose = self
-					ifTrue: [  
-						stream nextPutAll: { n asInteger . k asInteger }.
-						k < (n - k)
-							ifTrue: [ stream nextPutAll: { n asInteger . (n - k) asInteger } ] ].
-	            choose := choose * (n + 1).
-	            choose := (choose / (n + 1 - k)) ceiling ] ] ]
-
+Integer >> gamma [
+	self > 0
+		ifFalse: [^ self error: 'Attempt to compute the Gamma function of a non-positive integer'].
+	^ (self - 1) factorial.
 ]
 
 { #category : #'*Math-Numerical' }
-Integer >> firstOver: c [
-    " Binary search to find smallest value of n for which n ** self >= c "
-	| n lo hi mid |
-
-    n := 1.
-    [ (n ** self) < c ] whileTrue: [ n := n * 2 ].
-    lo := 1.
-    hi := n.
-    [ (hi - lo) > 1 ] whileTrue: [ 
-		mid := lo + ((hi - lo) / 2) ceiling.
-		(mid ** self) < c
-			ifTrue: [ lo := mid ]
-			ifFalse: [ hi := mid ] ].
-	[ (hi ** self) >= c ] assert.
-	[ ((hi - 1) ** self) < c ] assert.
-   ^ hi
+Integer >> inverseBinomialCoefficient [
 
-]
+	" Reverse binomial coefficient. Answer a <Collection> with all n and k such that n take: k = self. Elements in the answered Collection should be read as paired. Each pair represents (n,k) in the binomial coefficient formula. 
+	See https://math.stackexchange.com/a/103385/205 for details. "
 
-{ #category : #'*Math-Numerical' }
-Integer >> gamma [
-	self > 0
-		ifFalse: [^ self error: 'Attempt to compute the Gamma function of a non-positive integer'].
-	^ (self - 1) factorial.
+	| k |
+	[ self > 1 ] assert.
+	k := 0.
+	^ Array streamContents: [ :stream | 
+		  [ true ] whileTrue: [ 
+			  | nmin nmax choose |
+			  k := k + 1.
+			  2 * k + 1 * self <= (4 ** k) ifTrue: [ ^ stream contents ].
+			  nmin := ((k factorial * self) nthRoot: k) ceiling.
+			  nmax := nmin + k + 1.
+			  nmin := nmin max: 2 * k.
+			  choose := nmin asInteger numberOfCombinationsTaken: k.
+			  nmin to: nmax do: [ :n | 
+				  choose = self ifTrue: [ 
+					  stream nextPutAll: { 
+							  n asInteger.
+							  k asInteger }.
+					  k < (n - k) ifTrue: [ 
+						  stream nextPutAll: { 
+								  n asInteger.
+								  (n - k) asInteger } ] ].
+				  choose := choose * (n + 1).
+				  choose := (choose / (n + 1 - k)) ceiling ] ] ]
 ]
 
 { #category : #'*Math-Numerical' }

src/Math-Tests-Numerical/IntegerTest.extension.st

@@ -3,40 +3,15 @@ Extension { #name : #IntegerTest }
 { #category : #'*Math-Tests-Numerical' }
 IntegerTest >> testFindNK [
 
-	self assert: 6 findNK equals:  #(6 1 6 5 4 2).
-	self assert: 10 findNK equals: #(10 1 10 9 5 2 5 3).
-	self assert: 20 findNK equals: #(20 1 20 19 6 3).	
-	self assert: 21 findNK equals: #(21 1 21 20 7 2 7 5).
-	self assert: 55 findNK equals: #(55 1 55 54 11 2 11 9).
-	self assert: 120 findNK equals: #(120 1 120 119 16 2 16 14 10 3 10 7).
-	self assert: 3003 findNK equals: #(3003 1 3003 3002 78 2 78 76 15 5 15 10 14 6 14 8).
-	self assert: 8966473191018617158916954970192684 findNK equals: #(8966473191018617158916954970192684 1 8966473191018617158916954970192684 8966473191018617158916954970192683 123 45 123 78).
-	self assert: 116682544286207712305570174244760883486876241791210077037133735047856714594324355733933738740204795317223528882568337264611289789138133946725471443924278812277695432803500115699090641248357468388106131543801393801287657125117557432072695477147403395443757359171876874010770591355653882772562301453205472707597435095925666815012707478996454360460481159339802667334477440 findNK equals: #(116682544286207712305570174244760883486876241791210077037133735047856714594324355733933738740204795317223528882568337264611289789138133946725471443924278812277695432803500115699090641248357468388106131543801393801287657125117557432072695477147403395443757359171876874010770591355653882772562301453205472707597435095925666815012707478996454360460481159339802667334477440 1 116682544286207712305570174244760883486876241791210077037133735047856714594324355733933738740204795317223528882568337264611289789138133946725471443924278812277695432803500115699090641248357468388106131543801393801287657125117557432072695477147403395443757359171876874010770591355653882772562301453205472707597435095925666815012707478996454360460481159339802667334477440 116682544286207712305570174244760883486876241791210077037133735047856714594324355733933738740204795317223528882568337264611289789138133946725471443924278812277695432803500115699090641248357468388106131543801393801287657125117557432072695477147403395443757359171876874010770591355653882772562301453205472707597435095925666815012707478996454360460481159339802667334477439 1234 567 1234 667).
-	self should: [ 1 findNK ] raise: Error.
-	self should: [ 0 findNK ] raise: Error.
-]
-
-{ #category : #'*Math-Tests-Numerical' }
-IntegerTest >> testFirstOver [
-
-	self assert: (2 firstOver: 3) equals: 2.
-	self assert: (2 firstOver: 4) equals: 2.
-	self assert: (2 firstOver: 5) equals: 3.
-	self assert: (2 firstOver: 6) equals: 3.
-	
-	self assert: (3 firstOver: 3) equals: 2.
-	self assert: (3 firstOver: 4) equals: 2.
-	self assert: (3 firstOver: 5) equals: 2.
-	self assert: (3 firstOver: 6) equals: 2.
-
-	self assert: (4 firstOver: 2) equals: 2.
-	self assert: (4 firstOver: 3) equals: 2.
-	self assert: (4 firstOver: 4) equals: 2.
-	self assert: (4 firstOver: 5) equals: 2.
-	
-	self assert: (4 firstOver: "SmallInteger maxVal"1152921504606846975) equals: 32768.
-	self assert: (3 firstOver: 1152921504606846975) equals: 1048576.
-	self assert: (2 firstOver: 1152921504606846975) equals: 1073741824.	
-	self assert: (1 firstOver: 1152921504606846975) equals: 1152921504606846975.			
+	self assert: 6 inverseBinomialCoefficient equals:  #(6 1 6 5 4 2).
+	self assert: 10 inverseBinomialCoefficient equals: #(10 1 10 9 5 2 5 3).
+	self assert: 20 inverseBinomialCoefficient equals: #(20 1 20 19 6 3).	
+	self assert: 21 inverseBinomialCoefficient equals: #(21 1 21 20 7 2 7 5).
+	self assert: 55 inverseBinomialCoefficient equals: #(55 1 55 54 11 2 11 9).
+	self assert: 120 inverseBinomialCoefficient equals: #(120 1 120 119 16 2 16 14 10 3 10 7).
+	self assert: 3003 inverseBinomialCoefficient equals: #(3003 1 3003 3002 78 2 78 76 15 5 15 10 14 6 14 8).
+	self assert: 8966473191018617158916954970192684 inverseBinomialCoefficient equals: #(8966473191018617158916954970192684 1 8966473191018617158916954970192684 8966473191018617158916954970192683 123 45 123 78).
 
+	self should: [ 1 inverseBinomialCoefficient ] raise: Error.
+	self should: [ 0 inverseBinomialCoefficient ] raise: Error.
 ]