Add reverse binomial with tests. See https://math.stackexchange.com/a/103385/205 for details.

Author: hernanmd

src/Math-Numerical/Integer.extension.st

@@ -1,5 +1,54 @@
 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 isInteger and: [ 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 ] ] ]
+
+]
+
+{ #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
+
+]
+
 { #category : #'*Math-Numerical' }
 Integer >> gamma [
 	self > 0

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

@@ -0,0 +1,42 @@
+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) equals: 32768.
+	self assert: (3 firstOver: SmallInteger maxVal) equals: 1048576.
+	self assert: (2 firstOver: SmallInteger maxVal) equals: 1073741824.	
+	self assert: (1 firstOver: SmallInteger maxVal) equals: 1152921504606846975.			
+
+]