IntegerTest.class.st

"
SUnit tests for integers
"
Class {
	#name : #IntegerTest,
	#superclass : #TestCase,
	#category : #'Kernel-Tests-Numbers'
}

{ #category : #private }
IntegerTest >> assert: a classAndValueEquals: b [
	self assert: a class = b class.
	self assert: a = b
]

{ #category : #'tests - basic' }
IntegerTest >> testAsLargerPowerOfTwo [
"Invalid input testing"
	"LargeNegativeIntegers"
	self should: [(2 raisedTo: 80) negated asLargerPowerOfTwo] raise: DomainError.
	"Negative SmallIntegers"
	self should: [-1 asLargerPowerOfTwo] raise: DomainError.
	"0"
	self should: [0 asLargerPowerOfTwo] raise: DomainError.
"Valid inputs"
	"Small integers"
	self assert: 1 asLargerPowerOfTwo equals: 1.
	self assert: 2 asLargerPowerOfTwo equals: 2.
	self assert: 3 asLargerPowerOfTwo equals: 4.
	self assert: 4 asLargerPowerOfTwo equals: 4.
	self assert: 5 asLargerPowerOfTwo equals: 8.
	"Large integers"
	self assert: ((2 raisedTo: 80) +1) asLargerPowerOfTwo equals: (2 raisedTo: 80 +1).
	self assert: (2 raisedTo: 80) asLargerPowerOfTwo equals: (2 raisedTo: 80).
	self assert: ((2 raisedTo: 80) - 1) asLargerPowerOfTwo equals: (2 raisedTo: 80)
]

{ #category : #'tests - basic' }
IntegerTest >> testAsSmallerPowerOfTwo [
"Invalid input testing"
	"LargeNegativeIntegers"
	self should: [(2 raisedTo: 80) negated asSmallerPowerOfTwo] raise: DomainError.
	"Negative SmallIntegers"
	self should: [-1 asSmallerPowerOfTwo] raise: DomainError.
	"0"
	self should: [0 asSmallerPowerOfTwo] raise: DomainError.
"Valid inputs"
	"Small integers"
	self assert: 1 asSmallerPowerOfTwo equals: 1.
	self assert: 2 asSmallerPowerOfTwo equals: 2.
	self assert: 3 asSmallerPowerOfTwo equals: 2.
	self assert: 4 asSmallerPowerOfTwo equals: 4.
	self assert: 5 asSmallerPowerOfTwo equals: 4.
	"Large integers"
	self assert: ((2 raisedTo: 80) +1) asSmallerPowerOfTwo equals: (2 raisedTo: 80).
	self assert: (2 raisedTo: 80) asSmallerPowerOfTwo equals: (2 raisedTo: 80).
	self assert: ((2 raisedTo: 80) - 1) asSmallerPowerOfTwo equals: (2 raisedTo: 80 - 1)
]

{ #category : #'tests - printing' }
IntegerTest >> testAsStringWithCommas [
	self assert: 123456789 asStringWithCommas equals: '123,456,789'.
	self assert: -123456789 asStringWithCommas equals: '-123,456,789'
]

{ #category : #'tests - printing' }
IntegerTest >> testBadBase [
	"This used to get into an endless loop.
	See Pharo #114"
	
	self should: [2 printStringBase: 1] raise: Error.
]

{ #category : #'tests - benchmarks' }
IntegerTest >> testBenchFib [

	self assert: (0 benchFib = 1).
	self assert: (1 benchFib = 1).
	self assert: (2 benchFib = 3).
	
]

{ #category : #'tests - mathematical functions' }
IntegerTest >> testBigReceiverInexactNthRoot [
	"
	IntegerTest new testBigReceiverInexactNthRoot
	"

	"Inexact 3rd root (not a whole cube number), so a Float must be answered.
	However, receiver is too big for Float arithmethic."
	| bigNum result |
	bigNum := (100 factorial raisedTo: 3) + 1.		"Add 1 so it is not a whole cube"
	self assert: bigNum asFloat isInfinite.			"Otherwise, we chose a bad sample"
	result := bigNum nthRoot: 3.
	self assert: result isFloat.
	self deny: result isInfinite.
	self assert: result = 100 factorial asFloat.		"No other float is closer. See following line"
	self assert: 100 factorial asFloat = (100 factorial+1) asFloat
]

{ #category : #'tests - mathematical functions' }
IntegerTest >> testBigReceiverInexactSqrt [
	"
	IntegerTest new testBigReceiverInexactSqrt
	"

	"Inexact 3rd root (not a whole cube number), so a Float must be answered.
	However, receiver is too big for Float arithmethic."
	| bigNum result |
	bigNum := 100 factorial squared + 1.		"Add 1 so it is not a whole square"
	self assert: bigNum asFloat isInfinite.			"Otherwise, we chose a bad sample"
	result := bigNum sqrt.
	self assert: result isFloat.
	self deny: result isInfinite.
	self assert: result = 100 factorial asFloat.		"No other float is closer. See following lines"
	self assert: (result successor asFraction squared - bigNum) abs >= (result asFraction squared - bigNum) abs.
	self assert: (result predecessor asFraction squared - bigNum) abs >= (result asFraction squared - bigNum) abs.
]

{ #category : #'tests - bitLogic' }
IntegerTest >> testBitAnd [

	self assert: (2r1100 bitAnd: 2r1010) equals: 2r1000.
	self assert: (2r1100 & 2r1010) equals: 2r1000.
	self assert: (-2 bitAnd: 16rFFFFFFFF) equals: 16rFFFFFFFE.
	self assert: (-2 & 16rFFFFFFFF) equals: 16rFFFFFFFE.
]

{ #category : #'tests - bitLogic' }
IntegerTest >> testBitAt [
	| trials bitSequence2 |

	self assert: (2r10 bitAt: 1) equals: 0.
	self assert: (2r10 bitAt: 2) equals: 1.
	
	self
		assert: ((1 to: 100) allSatisfy: [:i | (0 bitAt: i) = 0])
		description: 'all bits of zero are set to zero'.
	
	self
		assert: ((1 to: 100) allSatisfy: [:i | (-1 bitAt: i) = 1])
		description: 'In two complements, all bits of -1 are set to 1'.
		
	
	trials := #(
		'2r10010011'
		'2r11100100'
		'2r10000000'
		'2r0000101011011001'
		'2r1000101011011001'
		'2r0101010101011000'
		'2r0010011110110010'
		'2r0010011000000000'
		'2r00100111101100101000101011011001'
		'2r01110010011110110010100110101101'
		'2r10101011101011001010000010110110'
		'2r10101000000000000000000000000000'
		'2r0010101110101001110010100000101101100010011110110010100010101100'
		'2r1010101110101100101000001011011000100111101100101000101011011001'
		'2r1010101110101000000000000000000000000000000000000000000000000000').
	trials do: [:bitSequence | | aNumber |
		aNumber := Number readFrom: bitSequence.
		bitSequence2 := (bitSequence size - 2 to: 1 by: -1) inject: '2r' into: [:string :i | string copyWith: (Character digitValue: (aNumber bitAt: i))].
		self assert: bitSequence2 = bitSequence].
	
	trials do: [:bitSequence | | bitInvert |
		bitInvert := -1 - (Number readFrom: bitSequence).
		bitSequence2 := (bitSequence size - 2 to: 1 by: -1) inject: '2r' into: [:string :i | string copyWith: (Character digitValue: 1 - (bitInvert bitAt: i))].
		self assert: bitSequence2 = bitSequence description: '-1-x is similar to a bitInvert operation in two complement']
]

{ #category : #'tests - bitLogic' }
IntegerTest >> testBitClear [

	self assert: (2r1111 bitClear: 2r1000) equals: 2r0111.
	self assert: (2r1111 bitClear: 2r0100) equals: 2r1011.
	self assert: (2r1111 bitClear: 2r0010) equals: 2r1101.
	self assert: (2r1111 bitClear: 2r0001) equals: 2r1110.
]

{ #category : #'tests - bitLogic' }
IntegerTest >> testBitLogic [  
	"This little suite of tests is designed to verify correct operation of most of Pharo's bit manipulation code, including two's complement representation of negative values.  It was written in a hurry and is probably lacking several important checks."
	"self run: #testBitLogic"
	
	| n |
	"Shift 1 bit left then right and test for 1"
	1 to: 100 do: [:i | self assert: ((1 bitShift: i) bitShift: i negated) = 1].

	"Shift -1 left then right and test for 1"
	1 to: 100 do: [:i | self assert: ((-1 bitShift: i) bitShift: i negated) = -1].

	"And a single bit with -1 and test for same value"
	1 to: 100 do: [:i | self assert: ((1 bitShift: i) bitAnd: -1) = (1 bitShift: i)].

	"Verify that (n bitAnd: n negated) = n for single bits"
	1 to: 100 do: [:i |  n := 1 bitShift: i. self assert: (n bitAnd: n negated) = n].

	"Verify that n negated = (n complemented + 1) for single bits"
	1 to: 100 do: [:i | 
					n := 1 bitShift: i. 
					self assert: n negated = ((n bitXor: -1) + 1)].

	"Verify that (n + n complemented) = -1 for single bits"
	1 to: 100 do: [:i | 
					n := 1 bitShift: i.
					self assert: (n + (n bitXor: -1)) = -1].

	"Verify that n negated = (n complemented +1) for single bits"
	1 to: 100 do: [:i | 
					n := 1 bitShift: i.
					self assert: n negated = ((n bitXor: -1) + 1)].
]

{ #category : #'tests - bitLogic' }
IntegerTest >> testBitMask [

	self assert: (2r11 allMask: 2r11).
	self deny: (2r10 allMask: 2r11).
	self deny: (2r01 allMask: 2r11).
	
	self assert: (2r10 anyMask: 2r11).
	self assert: (2r01 anyMask: 2r11).
	self deny: (2r00 anyMask: 2r11).
]

{ #category : #'tests - bitLogic' }
IntegerTest >> testBitOr [

	self assert: (2r0101 | 2r1010) equals: 2r1111.
	self assert: (2r0101 bitOr: 2r1010) equals: 2r1111.
]

{ #category : #'tests - bitLogic' }
IntegerTest >> testBitShift [

	self assert: 2r11 << 2 equals: 2r1100.
	self assert: (2r11 bitShift: 2) equals: 2r1100.
	self assert: 2r1011 >> 2 equals: 2r10.
	self assert: (2r1011 bitShift: -2) equals: 2r10.
]

{ #category : #'tests - bitLogic' }
IntegerTest >> testBitString [
	"self debug: #testBitString"
	
	Smalltalk vm wordSize = 4
		ifTrue: [
			self assert: 2 bitString equals: '0000000000000000000000000000010'.
			self assert: -1 bitString equals: '1111111111111111111111111111111'.
			self assert: -2 bitString equals: '1111111111111111111111111111110'.
			self assert: 2 bitStringLength equals: 31 ]. 
	Smalltalk vm wordSize = 8
		ifTrue: [
			self assert: 2 bitString equals: '0000000000000000000000000000000000000000000000000000000000010'.
			self assert: -1 bitString equals: '1111111111111111111111111111111111111111111111111111111111111'.
			self assert: -2 bitString equals: '1111111111111111111111111111111111111111111111111111111111110'.
			self assert: 2 bitStringLength equals: 61 ]. 
	"32 minus 1 for immediate encoding = 31 = 30 for number + 1 for sign"
	"64 minus 3 for immediate encoding = 61 = 60 for number + 1 for sign"
	self assert: 2 bitStringLength equals: (SmallInteger maxVal highBit + 1).
]

{ #category : #'tests - bitLogic' }
IntegerTest >> testBitXor [

	self assert: (2r1100 bitXor: 2r1010) equals: 2r0110.
]

{ #category : #'tests - instance creation' }
IntegerTest >> testCreationFromBytes1 [
	"self run: #testCreationFromBytes1"
	"it is illegal for a LargeInteger to be less than SmallInteger maxVal." 
	"here we test that Integer>>byte!byte2:byte3:byte4: resconstructs SmallInteger maxVal as an instance of SmallInteger. "
  
	| maxSmallInt hexString byte1 byte2 byte3 byte4 builtInteger |
	Smalltalk vm wordSize = 4 ifFalse: [ ^ self skip ].
	maxSmallInt := SmallInteger maxVal.
	hexString := maxSmallInt printStringHex.
	self assert: hexString size = 8.
	byte4 := Number readFrom: (hexString copyFrom: 1 to: 2) base: 16.
	byte3 := Number readFrom: (hexString copyFrom: 3 to: 4) base: 16.
	byte2 := Number readFrom: (hexString copyFrom: 5 to: 6) base: 16.
	byte1 := Number readFrom: (hexString copyFrom: 7 to: 8) base: 16.
	builtInteger := Integer byte1: byte1 byte2: byte2 byte3: byte3 byte4: byte4.
	self assert: builtInteger = maxSmallInt.
	self assert: builtInteger class = SmallInteger

]

{ #category : #'tests - instance creation' }
IntegerTest >> testCreationFromBytes2 [
 	"self run: #testCreationFromBytes2"

	"it is illegal for a LargeInteger to be less than SmallInteger maxVal." 
	"here we test that Integer>>byte!byte2:byte3:byte4: resconstructs (SmallInteger maxVal + 1) as an instance of LargePositiveInteger. "
	| maxSmallInt hexString byte1 byte2 byte3 byte4 builtInteger |
	Smalltalk vm wordSize = 4 ifFalse: [ ^ self skip ].
	maxSmallInt := SmallInteger maxVal.
	hexString := (maxSmallInt + 1) printStringHex.
	self assert: hexString size = 8.
	byte4 := Number readFrom: (hexString copyFrom: 1 to: 2) base: 16.
	byte3 := Number readFrom: (hexString copyFrom: 3 to: 4) base: 16.
	byte2 := Number readFrom: (hexString copyFrom: 5 to: 6) base: 16.
	byte1 := Number readFrom: (hexString copyFrom: 7 to: 8) base: 16.
	builtInteger := Integer byte1: byte1 byte2: byte2 byte3: byte3 byte4: byte4.
	self assert: builtInteger = (maxSmallInt + 1).
	self deny: builtInteger class = SmallInteger

]

{ #category : #'tests - instance creation' }
IntegerTest >> testCreationFromBytes3 [
	"self run: #testCreationFromBytes3"

	"it is illegal for a LargeInteger to be less than SmallInteger maxVal." 
	"here we test that Integer>>byte!byte2:byte3:byte4: resconstructs (SmallInteger maxVal - 1) as an instance of SmallInteger. "
	| maxSmallInt hexString byte1 byte2 byte3 byte4 builtInteger |
	Smalltalk vm wordSize = 4 ifFalse: [ ^ self skip ].
	maxSmallInt := SmallInteger maxVal.
	hexString := (maxSmallInt - 1) printStringHex.
	self assert: hexString size = 8.
	byte4 := Number readFrom: (hexString copyFrom: 1 to: 2) base: 16.
	byte3 := Number readFrom: (hexString copyFrom: 3 to: 4) base: 16.
	byte2 := Number readFrom: (hexString copyFrom: 5 to: 6) base: 16.
	byte1 := Number readFrom: (hexString copyFrom: 7 to: 8) base: 16.
	builtInteger := Integer byte1: byte1 byte2: byte2 byte3: byte3 byte4: byte4.
	self assert: builtInteger = (maxSmallInt - 1).
	self assert: builtInteger class = SmallInteger

]

{ #category : #'tests - arithmetic' }
IntegerTest >> testCrossSumBase [
	"self run: #testCrossSumBase"

	self assert: (
		((-20 to: 20) collect: [:each | each crossSumBase: 10]) asArray = 
		#(2 10 9 8 7 6 5 4 3 2 1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 10 2)).
	self assert: (
		((-20 to: 20) collect: [:each | each crossSumBase: 2]) asArray = 
		#(2 3 2 2 1 4 3 3 2 3 2 2 1 3 2 2 1 2 1 1 0 1 1 2 1 2 2 3 1 2 2 3 2 3 3 4 1 2 2 3 2)).
	self should: [10 crossSumBase: 1] raise: AssertionFailure
]

{ #category : #'tests - mathematical functions' }
IntegerTest >> testDegreeCos [
	"self run: #testDegreeCos"

	45 degreeCos.	"Following tests use approximate equality, because cosine are generally evaluated using inexact Floating point arithmetic"
	self assert: (45 degreeCos squared - (1 / 2)) abs <= Float epsilon.
	self assert: (60 degreeCos - (1 / 2)) abs <= Float epsilon.
	self assert: (120 degreeCos + (1 / 2)) abs <= Float epsilon.
	-360 to: 360 do: [ :i | self assert: (i degreeCos closeTo: i degreesToRadians cos) ].	"Following tests use strict equality which is a requested property of degreeCos"
	-10 to: 10 do: [ :k | 
		self assert: (k * 360 + 90) degreeCos = 0.
		self assert: (k * 360 - 90) degreeCos = 0.
		self assert: (k * 360 + 180) degreeCos + 1 = 0.
		self assert: (k * 360) degreeCos - 1 = 0 ]
]

{ #category : #'tests - mathematical functions' }
IntegerTest >> testDegreeSin [
	"self run: #testDegreeSin"

	45 degreeSin.	"Following tests use approximate equality, because sine are generally evaluated using inexact Floating point arithmetic"
	self assert: (45 degreeSin squared - (1 / 2)) abs <= Float epsilon.
	self assert: (30 degreeSin - (1 / 2)) abs <= Float epsilon.
	self assert: (-30 degreeSin + (1 / 2)) abs <= Float epsilon.
	-360 to: 360 do: [ :i | self assert: (i degreeSin closeTo: i degreesToRadians sin) ].	"Following tests use strict equality which is a requested property of degreeSin"
	-10 to: 10 do: [ :k | 
		self assert: (k * 360 + 90) degreeSin - 1 = 0.
		self assert: (k * 360 - 90) degreeSin + 1 = 0.
		self assert: (k * 360 + 180) degreeSin = 0.
		self assert: (k * 360) degreeSin = 0 ]
]

{ #category : #'tests - instance creation' }
IntegerTest >> testDifferentBases [
	"self run: #testDifferentBases"
	"| value |
	2 to: 36 do: [:each|
		value := 0.
		1 to: each-1 do: [:n| value := value + (n * (each raisedToInteger: n))].
		value := value negated.
		Transcript tab; show: 'self assert: (', value printString, ' printStringBase: ', each printString, ') = ''', (value printStringBase: each), '''.'; cr.
		Transcript tab; show: 'self assert: (', value printString, ' radix: ', each printString, ') = ''', (value radix: each), '''.'; cr.
		Transcript tab; show: 'self assert: ', value printString, ' printStringHex = ''', (value printStringBase: 16), '''.'; cr.
		Transcript tab; show: 'self assert: (', value printString, ' storeStringBase: ', each printString, ') = ''', (value storeStringBase: each), '''.'; cr.
		Transcript tab; show: 'self assert: ', value printString, ' storeStringHex = ''', (value storeStringBase: 16), '''.'; cr.


].
	"

	self assert: 2r10 = 2.
	self assert: 3r210 = 21.
	self assert: 4r3210 = 228.
	self assert: 5r43210 = 2930.
	self assert: 6r543210 = 44790.
	self assert: 7r6543210 = 800667.
	self assert: 8r76543210 = 16434824.
	self assert: 9r876543210 = 381367044.
	self assert: 10r9876543210 = 9876543210.
	self assert: 11rA9876543210 = 282458553905.
	self assert: 12rBA9876543210 = 8842413667692.
	self assert: 13rCBA9876543210 = 300771807240918.
	self assert: 14rDCBA9876543210 = 11046255305880158.
	self assert: 15rEDCBA9876543210 = 435659737878916215.
	self assert: 16rFEDCBA9876543210 = 18364758544493064720.
	self assert: 17rGFEDCBA9876543210 = 824008854613343261192.
	self assert: 18rHGFEDCBA9876543210 = 39210261334551566857170.
	self assert: 19rIHGFEDCBA9876543210 = 1972313422155189164466189.
	self assert: 20rJIHGFEDCBA9876543210 = 104567135734072022160664820.
	self assert: 21rKJIHGFEDCBA9876543210 = 5827980550840017565077671610.
	self assert: 22rLKJIHGFEDCBA9876543210 = 340653664490377789692799452102.
	self assert: 23rMLKJIHGFEDCBA9876543210 = 20837326537038308910317109288851.
	self assert: 24rNMLKJIHGFEDCBA9876543210 = 1331214537196502869015340298036888.
	self assert: 25rONMLKJIHGFEDCBA9876543210 = 88663644327703473714387251271141900.
	self assert: 26rPONMLKJIHGFEDCBA9876543210 = 6146269788878825859099399609538763450.
	self assert: 27rQPONMLKJIHGFEDCBA9876543210 = 442770531899482980347734468443677777577.
	self assert: 28rRQPONMLKJIHGFEDCBA9876543210 = 33100056003358651440264672384704297711484.
	self assert: 29rSRQPONMLKJIHGFEDCBA9876543210 = 2564411043271974895869785066497940850811934.
	self assert: 30rTSRQPONMLKJIHGFEDCBA9876543210 = 205646315052919334126040428061831153388822830.
	self assert: 31rUTSRQPONMLKJIHGFEDCBA9876543210 = 17050208381689099029767742314582582184093573615.
	self assert: 32rVUTSRQPONMLKJIHGFEDCBA9876543210 = 1459980823972598128486511383358617792788444579872.
	self assert: 33rWVUTSRQPONMLKJIHGFEDCBA9876543210 = 128983956064237823710866404905431464703849549412368.
	self assert: 34rXWVUTSRQPONMLKJIHGFEDCBA9876543210 = 11745843093701610854378775891116314824081102660800418.
	self assert: 35rYXWVUTSRQPONMLKJIHGFEDCBA9876543210 = 1101553773143634726491620528194292510495517905608180485.
	self assert: 36rZYXWVUTSRQPONMLKJIHGFEDCBA9876543210 = 106300512100105327644605138221229898724869759421181854980.

	self assert: -2r10 = -2.
	self assert: -3r210 = -21.
	self assert: -4r3210 = -228.
	self assert: -5r43210 = -2930.
	self assert: -6r543210 = -44790.
	self assert: -7r6543210 = -800667.
	self assert: -8r76543210 = -16434824.
	self assert: -9r876543210 = -381367044.
	self assert: -10r9876543210 = -9876543210.
	self assert: -11rA9876543210 = -282458553905.
	self assert: -12rBA9876543210 = -8842413667692.
	self assert: -13rCBA9876543210 = -300771807240918.
	self assert: -14rDCBA9876543210 = -11046255305880158.
	self assert: -15rEDCBA9876543210 = -435659737878916215.
	self assert: -16rFEDCBA9876543210 = -18364758544493064720.
	self assert: -17rGFEDCBA9876543210 = -824008854613343261192.
	self assert: -18rHGFEDCBA9876543210 = -39210261334551566857170.
	self assert: -19rIHGFEDCBA9876543210 = -1972313422155189164466189.
	self assert: -20rJIHGFEDCBA9876543210 = -104567135734072022160664820.
	self assert: -21rKJIHGFEDCBA9876543210 = -5827980550840017565077671610.
	self assert: -22rLKJIHGFEDCBA9876543210 = -340653664490377789692799452102.
	self assert: -23rMLKJIHGFEDCBA9876543210 = -20837326537038308910317109288851.
	self assert: -24rNMLKJIHGFEDCBA9876543210 = -1331214537196502869015340298036888.
	self assert: -25rONMLKJIHGFEDCBA9876543210 = -88663644327703473714387251271141900.
	self assert: -26rPONMLKJIHGFEDCBA9876543210 = -6146269788878825859099399609538763450.
	self assert: -27rQPONMLKJIHGFEDCBA9876543210 = -442770531899482980347734468443677777577.
	self assert: -28rRQPONMLKJIHGFEDCBA9876543210 = -33100056003358651440264672384704297711484.
	self assert: -29rSRQPONMLKJIHGFEDCBA9876543210 = -2564411043271974895869785066497940850811934.
	self assert: -30rTSRQPONMLKJIHGFEDCBA9876543210 = -205646315052919334126040428061831153388822830.
	self assert: -31rUTSRQPONMLKJIHGFEDCBA9876543210 = -17050208381689099029767742314582582184093573615.
	self assert: -32rVUTSRQPONMLKJIHGFEDCBA9876543210 = -1459980823972598128486511383358617792788444579872.
	self assert: -33rWVUTSRQPONMLKJIHGFEDCBA9876543210 = -128983956064237823710866404905431464703849549412368.
	self assert: -34rXWVUTSRQPONMLKJIHGFEDCBA9876543210 = -11745843093701610854378775891116314824081102660800418.
	self assert: -35rYXWVUTSRQPONMLKJIHGFEDCBA9876543210 = -1101553773143634726491620528194292510495517905608180485.
	self assert: -36rZYXWVUTSRQPONMLKJIHGFEDCBA9876543210 = -106300512100105327644605138221229898724869759421181854980.
]

{ #category : #'tests - basic' }
IntegerTest >> testDigitsAccess [

	self assert: (42 digitAt: 2 base: 10) equals: 4.
	self assert: (42 digitAt: 1 base: 10) equals: 2.
	self assert: (1 digitAt: 2 base: 10) equals: 0.
	self assert: (16rFF digitAt: 1 base: 16) equals: 15.

	self assert: (42 decimalDigitAt: 2) equals: 4.
	self assert: (42 decimalDigitAt: 1) equals: 2.
	
	self assert: (42 decimalDigitLength) equals: 2.
	self assert: (0 decimalDigitLength) equals: 1.
	self assert: (100000000000 decimalDigitLength) equals: 12. "large integer"

	"last digit of the integer base 256"
	self assert: (255 lastDigit) equals: 255.
	self assert: (256 lastDigit) equals: 1.
	self assert: ((256*256-1) lastDigit) equals: 255.
	self assert: ((256*256) lastDigit) equals: 1.

	
]

{ #category : #'tests - basic' }
IntegerTest >> testEven [
	
	self deny: (1073741825 even).
	self assert: (1073741824  even).
	
]

{ #category : #'tests - mathematical functions' }
IntegerTest >> testExactRaisedTo [
	"
	IntegerTest new testExactRaisedTo
	"
	self assert: (4 raisedTo: 1/2) classAndValueEquals: 2.
	self assert: (9 raisedTo: 1/2) classAndValueEquals: 3.
	self assert: (9 raisedTo: -1/2) classAndValueEquals: 1/3.
	self assert: (-1 raisedTo: 1/3) classAndValueEquals: -1.
	#( 1 5 29 135 1234 567890 123123123 456456456456 98765432109876543210987654321 987123987123987123987123987123987123987123987123) do: [ :i |
		self assert: (i squared raisedTo: 1/2) classAndValueEquals: i.
		self assert: (i negated squared raisedTo: 1/2) classAndValueEquals: i ].

	self assert: (8 raisedTo: 1/3) classAndValueEquals: 2.
	self assert: (27 raisedTo: 1/3) classAndValueEquals: 3.
	#( 1 5 29 135 1234 567890 123123123 456456456456 98765432109876543210987654321 987123987123987123987123987123987123987123987123) do: [ :i |
		self assert: ((i raisedTo: 3) raisedTo: 1/3) classAndValueEquals: i.
		self assert: ((i negated raisedTo: 3) raisedTo: 1/3) classAndValueEquals: i negated ].

	self assert: (4 raisedTo: 3/2) classAndValueEquals: 8.
	self assert: (8 raisedTo: 2/3) classAndValueEquals: 4.
	self assert: (8 raisedTo: -2/3) classAndValueEquals: 1/4.
	#( 1 5 29 135 1234 567890 123123123 456456456456 98765432109876543210987654321 987123987123987123987123987123987123987123987123) do: [ :i |
		self assert: ((i raisedTo: 3) raisedTo: 2/3) classAndValueEquals: i*i.
		self assert: ((i raisedTo: 2) raisedTo: 3/2) classAndValueEquals: i*i*i.
		self assert: ((i negated raisedTo: 3) raisedTo: 2/3) classAndValueEquals: i*i.
		self assert: ((i negated raisedTo: 2) raisedTo: 3/2) classAndValueEquals: i*i*i ].

	self assert: (32 raisedTo: 3/5) classAndValueEquals: 8.
	self assert: (8 raisedTo: 5/3) classAndValueEquals: 32.
	#( 1 5 29 135 1234 567890 123123123 456456456456 98765432109876543210987654321 987123987123987123987123987123987123987123987123) do: [ :i |
		self assert: ((i raisedTo: 5) raisedTo: 3/5) classAndValueEquals: i*i*i.
		self assert: ((i raisedTo: 3) raisedTo: 5/3) classAndValueEquals: i*i*i*i*i.
		self assert: ((i negated raisedTo: 5) raisedTo: 3/5) classAndValueEquals: (i*i*i) negated.
		self assert: ((i negated raisedTo: 3) raisedTo: 5/3) classAndValueEquals: (i*i*i*i*i) negated.

		self assert: ((i raisedTo: -5) raisedTo: 3/5) classAndValueEquals: 1/(i*i*i).
		self assert: ((i raisedTo: -3) raisedTo: 5/3) classAndValueEquals: 1/(i*i*i*i*i).
		self assert: ((i negated raisedTo: -5) raisedTo: 3/5) classAndValueEquals: -1/(i*i*i).
		self assert: ((i negated raisedTo: -3) raisedTo: 5/3) classAndValueEquals: -1/(i*i*i*i*i).

		self assert: ((i raisedTo: 5) raisedTo: -3/5) classAndValueEquals: 1/(i*i*i).
		self assert: ((i raisedTo: 3) raisedTo: -5/3) classAndValueEquals: 1/(i*i*i*i*i).
		self assert: ((i negated raisedTo: 5) raisedTo: -3/5) classAndValueEquals: -1/(i*i*i).
		self assert: ((i negated raisedTo: 3) raisedTo: -5/3) classAndValueEquals: -1/(i*i*i*i*i).

		"No exact result => Float result"
		self assert: ((i raisedTo: 3) +1 raisedTo: 5/3) isFloat.
		self assert: ((i negated raisedTo: 3) -1 raisedTo: 5/3) isFloat ].
]

{ #category : #'tests - mathematical functions' }
IntegerTest >> testExactSqrt [
	"
	IntegerTest new testExactSqrt
	"
	self assert: 4 sqrt classAndValueEquals: 2.
	self assert: 9 sqrt classAndValueEquals: 3.
	self assert: Float maxExactInteger squared sqrt classAndValueEquals: Float maxExactInteger.
	self assert: (Float maxExactInteger+1) squared sqrt classAndValueEquals: Float maxExactInteger+1.
	#( 1 5 29 135 1234 567890 123123123 456456456456 98765432109876543210987654321 987123987123987123987123987123987123987123987123) do: [ :i |
		self assert: i squared sqrt classAndValueEquals: i ]
]

{ #category : #'tests - mathematical functions' }
IntegerTest >> testFloorLog [
	self assert: (100 floorLog: 10) = 2.
	self assert: (((2 raisedTo: Float emax + 3) floorLog: 10) = (2 log*(Float emax + 3)) floor) description: 'Integer>>floorLog: should not overflow'
]

{ #category : #'tests - printing' }
IntegerTest >> testHex [
	self assert: 0 hex =  '16r0'.
	self assert: 12 hex =  '16rC'.
	self assert: 1234 hex =  '16r4D2'.
]

{ #category : #'tests - bitLogic' }
IntegerTest >> testHighBit [

	| suite |
	self assert: (2r1110 highBit) equals: 4.
	self assert: (2r0110 highBit) equals: 3.
	self assert: (2r0000 highBit) equals: 0.
	
	suite := (0 to: 1024) asArray , #(16rFDFD 16rFFFF 16r1000 16r1000000 16r1000001 16r70000000 16r7AFAFAFA ) , {SmallInteger maxVal . SmallInteger maxVal+1}.
	suite := suite , (suite collect: [:e | e raisedTo: 20]).
	
	suite do: [:anInteger |
		| highBit shifted |
		highBit := 0.
		shifted := 1.
		[shifted > anInteger] whileFalse: [highBit := highBit+1. shifted := shifted bitShift: 1].
		self assert: anInteger highBit = highBit].
]

{ #category : #'tests - bitLogic' }
IntegerTest >> testHighBitOfMagnitude [
	| suite |

	suite := (0 to: 1024) asArray , #(16rFDFD 16rFFFF 16r1000 16r1000000 16r1000001 16r70000000 16r7AFAFAFA ) , {SmallInteger maxVal . SmallInteger maxVal+1}.
	suite := suite , (suite collect: [:e | e raisedTo: 20]).
	
	suite do: [:anInteger |
		| highBit shifted |
		highBit := 0.
		shifted := 1.
		[shifted > anInteger] whileFalse: [highBit := highBit+1. shifted := shifted bitShift: 1].
		self assert: anInteger highBitOfMagnitude = highBit.
		self assert: anInteger negated highBitOfMagnitude = highBit].
]

{ #category : #'tests - printing' }
IntegerTest >> testIntegerHex [
	| result |
	result := 15 asInteger hex.
	self assert: result = '16rF'.
	result := 0 asInteger hex.
	self assert: result = '16r0'.
	result := 255 asInteger hex.
	self assert: result = '16rFF'.
	result := 90 asInteger hex.
	self assert: result = '16r5A'
]

{ #category : #'tests - printing' }
IntegerTest >> testIntegerPadding [
	"self run: #testIntegerPadding"

	self assert: (1 printStringBase: 10 length: 0 padded: false) = '1'.
	self assert: (1 printStringBase: 10 length: 1 padded: false) = '1'.
	self assert: (1 printStringBase: 10 length: 2 padded: false) = ' 1'.
	self assert: (1024 printStringBase: 10 length: 19 padded: false) = '               1024'.
	self assert: (1024 printStringBase: 10 length: -1 padded: false) = '1024'.
	self assert: (1024 printStringBase: 10 length: 5 padded: false) =  ' 1024'.
	self assert: (-1024 printStringBase: 10 length: 5 padded: false) =   '-1024'.
	self assert: (-1024 printStringBase: 10 length: 19 padded: false) =  '              -1024'.

	self assert: (1 printStringBase: 10 length: 0 padded: true) = '1'.
	self assert: (1 printStringBase: 10 length: 1 padded: true) = '1'.
	self assert: (1 printStringBase: 10 length: 2 padded: true) = '01'.
	self assert: (1024 printStringBase: 10 length: 19 padded: true) = '0000000000000001024'.
	self assert: (1024 printStringBase: 10 length: -1 padded: true) = '1024'.
	self assert: (1024 printStringBase: 10 length: 5 padded: true) =  '01024'.
	self assert: (-1024 printStringBase: 10 length: 5 padded: true) =   '-1024'.
	self assert: (-1024 printStringBase: 10 length: 19 padded: true) =  '-000000000000001024'.

	self assert: (1 printStringBase: 16 length: 0 padded: false) = '1'.
	self assert: (1 printStringBase: 16 length: 1 padded: false) = '1'.
	self assert: (1 printStringBase: 16 length: 2 padded: false) = ' 1'.
	self assert: (2047 printStringBase: 16 length: 19 padded: false) =  '                7FF'.
	self assert: (2047 printStringBase: 16 length: -1 padded: false) =  '7FF'.
	self assert: (2047 printStringBase: 16 length: 4 padded: false) =  ' 7FF'.
	self assert: (-2047 printStringBase: 16 length: 4 padded: false) = '-7FF'.
	self assert: (-2047 printStringBase: 16 length: 19 padded: false) =  '               -7FF'.

	self assert: (1 printStringBase: 16 length: 0 padded: true) = '1'.
	self assert: (1 printStringBase: 16 length: 1 padded: true) = '1'.
	self assert: (1 printStringBase: 16 length: 2 padded: true) = '01'.
	self assert: (2047 printStringBase: 16 length: 19 padded: true) =  '00000000000000007FF'.
	self assert: (2047 printStringBase: 16 length: -1 padded: true) =  '7FF'.
	self assert: (2047 printStringBase: 16 length: 4 padded: true) =  '07FF'.
	self assert: (-2047 printStringBase: 16 length: 4 padded: true) = '-7FF'.
	self assert: (-2047 printStringBase: 16 length: 19 padded: true) =  '-0000000000000007FF'.

	self assert: (1 storeStringBase: 10 length: 0 padded: false) = '1'.
	self assert: (1 storeStringBase: 10 length: 1 padded: false) = '1'.
	self assert: (1 storeStringBase: 10 length: 2 padded: false) = ' 1'.
	self assert: (1024 storeStringBase: 10 length: 19 padded: false) = '               1024'.
	self assert: (1024 storeStringBase: 10 length: -1 padded: false) = '1024'.
	self assert: (1024 storeStringBase: 10 length: 5 padded: false) =  ' 1024'.
	self assert: (-1024 storeStringBase: 10 length: 5 padded: false) =   '-1024'.
	self assert: (-1024 storeStringBase: 10 length: 19 padded: false) =  '              -1024'.

	self assert: (1 storeStringBase: 10 length: 0 padded: true) = '1'.
	self assert: (1 storeStringBase: 10 length: 1 padded: true) = '1'.
	self assert: (1 storeStringBase: 10 length: 2 padded: true) = '01'.
	self assert: (1024 storeStringBase: 10 length: 19 padded: true) = '0000000000000001024'.
	self assert: (1024 storeStringBase: 10 length: -1 padded: true) = '1024'.
	self assert: (1024 storeStringBase: 10 length: 5 padded: true) =  '01024'.
	self assert: (-1024 storeStringBase: 10 length: 5 padded: true) =   '-1024'.
	self assert: (-1024 storeStringBase: 10 length: 19 padded: true) =  '-000000000000001024'.

	self assert: (1 storeStringBase: 16 length: 0 padded: false) = '16r1'.
	self assert: (1 storeStringBase: 16 length: 4 padded: false) = '16r1'.
	self assert: (1 storeStringBase: 16 length: 5 padded: false) = ' 16r1'.
	self assert: (2047 storeStringBase: 16 length: 19 padded: false) =  '             16r7FF'.
	self assert: (2047 storeStringBase: 16 length: -1 padded: false) =  '16r7FF'.
	self assert: (2047 storeStringBase: 16 length: 7 padded: false) =  ' 16r7FF'.
	self assert: (-2047 storeStringBase: 16 length: 7 padded: false) = '-16r7FF'.
	self assert: (-2047 storeStringBase: 16 length: 19 padded: false) =  '            -16r7FF'.

	self assert: (1 storeStringBase: 16 length: 0 padded: true) = '16r1'.
	self assert: (1 storeStringBase: 16 length: 4 padded: true) = '16r1'.
	self assert: (1 storeStringBase: 16 length: 5 padded: true) = '16r01'.
	self assert: (2047 storeStringBase: 16 length: 19 padded: true) =  '16r00000000000007FF'.
	self assert: (2047 storeStringBase: 16 length: -1 padded: true) =  '16r7FF'.
	self assert: (2047 storeStringBase: 16 length: 7 padded: true) =  '16r07FF'.
	self assert: (-2047 storeStringBase: 16 length: 7 padded: true) = '-16r7FF'.
	self assert: (-2047 storeStringBase: 16 length: 19 padded: true) =  '-16r0000000000007FF'.

]

{ #category : #'tests - instance creation' }
IntegerTest >> testIntegerReadsNotOkFromStream [
	self should: [Integer readFrom: 'a23' readStream] raise: Error.
	self should: [Integer readFrom: '-a23' readStream] raise: Error.
	self should: [Integer readFrom: 'a3' readStream base: 8] raise: Error.
	self should: [Integer readFrom: '-a3' readStream base: 8] raise: Error.
]

{ #category : #'tests - instance creation' }
IntegerTest >> testIntegerReadsNotOkFromString [
	self should: [Integer readFrom: 'aaa'] raise: Error.
	self should: [Integer readFrom: '-aaa'] raise: Error.
	self should: [Integer readFrom: 'a3' base: 8] raise: Error.
]

{ #category : #'tests - instance creation' }
IntegerTest >> testIntegerReadsOkFromStream [
	self assert: (Integer readFrom: '123' readStream) = 123.
	self assert: (Integer readFrom: '-123' readStream) = -123.
	self assert: (Integer readFrom: 'a3' readStream base: 16) = 163.
	self assert: (Integer readFrom: '-a3' readStream base: 16) = -163.
	
	self assert: (Integer readFrom: '3a' readStream base: 10) = 3.
]

{ #category : #'tests - instance creation' }
IntegerTest >> testIntegerReadsOkFromString [
	self assert: (Integer readFrom: '123') = 123.
	self assert: (Integer readFrom: '-123') = -123.
	self assert: (Integer readFrom: 'a3' base: 16) = 163.
	self assert: (Integer readFrom: '-a3' base: 16) = -163.
]

{ #category : #'tests - basic' }
IntegerTest >> testIsInteger [

	self assert: (0 isInteger).
	
]

{ #category : #'tests - basic' }
IntegerTest >> testIsPowerOfTwo [
	"LargeNegativeIntegers"
	self deny: (2 raisedTo: 80) negated isPowerOfTwo.
	"Negative SmallIntegers"
	self deny: (-1 isPowerOfTwo).
	" 0, incase implementation has forgotten edge case"
	self deny: (0 isPowerOfTwo).
	"Positive SmallIntegers"
	self assert: (1 isPowerOfTwo).
	self assert: (2 isPowerOfTwo).
	self deny:  (3 isPowerOfTwo).
	self assert: (4 isPowerOfTwo).
	self deny: (5 isPowerOfTwo).
	" LargePositiveIntegers"
	self deny: ((2 raisedTo: 80) - 1) isPowerOfTwo.
	self assert: (2 raisedTo: 80) isPowerOfTwo.
	self deny: ((2 raisedTo: 80) + 1) isPowerOfTwo
]

{ #category : #'tests - basic' }
IntegerTest >> testIsPowerOfTwoM6873 [
	"This is a non regression test for http://bugs.squeak.org/view.php?id=6873"

	self deny: ((1 to: 80) anySatisfy: [:n | (2 raisedTo: n) negated isPowerOfTwo])
		description: 'A negative integer cannot be a power of two'.
]

{ #category : #'tests - basic' }
IntegerTest >> testIsPrime [

	"The following tests should return 'true'"
	self assert: 17 isPrime.
	self assert: 78901 isPrime.
	self assert: 104729 isPrime.
	self assert: 15485863 isPrime.
	self assert: 2038074743 isPrime.
	self assert: 29996224275833 isPrime.
	
	"The following tests should return 'false' (first 5 are Carmichael integers)"
	self deny: 561 isPrime.
	self deny: 2821 isPrime.
	self deny: 6601 isPrime.
	self deny: 10585 isPrime.
	self deny: 15841 isPrime.
	self deny: 256 isPrime.
	self deny: 29996224275831 isPrime.
]

{ #category : #'tests - basic' }
IntegerTest >> testIsPrime2 [

	"Not primes:"
	#(-100 -5 -3 -2 -1 0 1) do: [ :each |
		self deny: each isPrime ].

	"The following tests should return 'true'"
	#(17 78901 104729 15485863 2038074743) do: [ :each |
		self assert: each isPrime ].
	
	"The following tests should return 'false' (first 5 are Carmichael integers)"
	#(561 2821 6601 10585 15841 256 29996224275831) do: [ :each |
		self deny: each isPrime ].
]

{ #category : #'tests - basic' }
IntegerTest >> testIsProbablyPrime [

	"Not primes:"
	#(-100 -5 -3 -2 -1 0 1) do: [ :each |
		self deny: each isProbablyPrime ].

	"The following tests should return 'true'"
	#(17 78901 104729 15485863 2038074743 29996224275833) do: [ :each |
		self assert: each isProbablyPrime ].
	
	"The following tests should return 'false' (first 5 are Carmichael integers)"
	#(561 2821 6601 10585 15841 256 29996224275831) do: [ :each |
		self deny: each isProbablyPrime ].
]

{ #category : #'tests - basic' }
IntegerTest >> testLargePrimesUpTo [

	| nn | 
	nn := (2 raisedTo: 17) - 1. 
	self deny: (Integer primesUpTo: nn) last = nn.
	self assert: (Integer primesUpTo: nn + 1) last  = nn.
	
	

]

{ #category : #'tests - mathematical functions' }
IntegerTest >> testLn [
	self assert: (100 ln closeTo: 10 ln*2).
	self assert: ((2 raisedTo: Float emax + 3) ln closeTo: 2 ln*(Float emax + 3)) description: 'Integer>>ln should not overflow'
]

{ #category : #'tests - mathematical functions' }
IntegerTest >> testLog [
	self assert: (100 log closeTo: 2).
	self assert: ((2 raisedTo: Float emax + 3) log closeTo: 2 log*(Float emax + 3)) description: 'Integer>>log should not overflow'
]

{ #category : #'tests - bitLogic' }
IntegerTest >> testLowBit [

	| suite |
	"Simple examples"
	self assert: (2r1011 lowBit) equals: 1.
	self assert: (2r1010 lowBit) equals: 2.
	self assert: (2r000000 lowBit) equals: 0.
	
	suite := (0 to: 1024) asArray , #(16rFDFD 16rFFFF 16r1000 16r1000000 16r1000001 16r70000000 16r7AFAFAFA ) , {SmallInteger maxVal . SmallInteger maxVal+1}.
	suite := suite , (suite collect: [:e | e raisedTo: 20]).
	
	suite do: [:anInteger |
		| lowBit |
		lowBit := (anInteger respondsTo: #bitAt:)
			ifTrue: [(1 to: anInteger highBit) detect: [:bitIndex | (anInteger bitAt: bitIndex) ~= 0] ifNone: [0]]
			ifFalse: [(1 to: anInteger highBit) detect: [:bitIndex | (anInteger bitAnd: (1 bitShift: bitIndex-1)) ~= 0] ifNone: [0]].
		self assert: anInteger lowBit = lowBit.
		self assert: anInteger negated lowBit = lowBit].
]

{ #category : #'tests - printing' }
IntegerTest >> testNegativeIntegerPrinting [
	"self run: #testnegativeIntegerPrinting"

	self assert: (-2 printStringBase: 2) = '-10'.
	self assert: (-2 radix: 2) = '-10'.
	self assert: -2 printStringHex = '-2'.
	self assert: (-2 storeStringBase: 2) = '-2r10'.
	self assert: -2 storeStringHex = '-16r2'.
	self assert: (-21 printStringBase: 3) = '-210'.
	self assert: (-21 radix: 3) = '-210'.
	self assert: -21 printStringHex = '-15'.
	self assert: (-21 storeStringBase: 3) = '-3r210'.
	self assert: -21 storeStringHex = '-16r15'.
	self assert: (-228 printStringBase: 4) = '-3210'.
	self assert: (-228 radix: 4) = '-3210'.
	self assert: -228 printStringHex = '-E4'.
	self assert: (-228 storeStringBase: 4) = '-4r3210'.
	self assert: -228 storeStringHex = '-16rE4'.
	self assert: (-2930 printStringBase: 5) = '-43210'.
	self assert: (-2930 radix: 5) = '-43210'.
	self assert: -2930 printStringHex = '-B72'.
	self assert: (-2930 storeStringBase: 5) = '-5r43210'.
	self assert: -2930 storeStringHex = '-16rB72'.
	self assert: (-44790 printStringBase: 6) = '-543210'.
	self assert: (-44790 radix: 6) = '-543210'.
	self assert: -44790 printStringHex = '-AEF6'.
	self assert: (-44790 storeStringBase: 6) = '-6r543210'.
	self assert: -44790 storeStringHex = '-16rAEF6'.
	self assert: (-800667 printStringBase: 7) = '-6543210'.
	self assert: (-800667 radix: 7) = '-6543210'.
	self assert: -800667 printStringHex = '-C379B'.
	self assert: (-800667 storeStringBase: 7) = '-7r6543210'.
	self assert: -800667 storeStringHex = '-16rC379B'.
	self assert: (-16434824 printStringBase: 8) = '-76543210'.
	self assert: (-16434824 radix: 8) = '-76543210'.
	self assert: -16434824 printStringHex = '-FAC688'.
	self assert: (-16434824 storeStringBase: 8) = '-8r76543210'.
	self assert: -16434824 storeStringHex = '-16rFAC688'.
	self assert: (-381367044 printStringBase: 9) = '-876543210'.
	self assert: (-381367044 radix: 9) = '-876543210'.
	self assert: -381367044 printStringHex = '-16BB3304'.
	self assert: (-381367044 storeStringBase: 9) = '-9r876543210'.
	self assert: -381367044 storeStringHex = '-16r16BB3304'.
	self assert: (-9876543210 printStringBase: 10) = '-9876543210'.
	self assert: (-9876543210 radix: 10) = '-9876543210'.
	self assert: -9876543210 printStringHex = '-24CB016EA'.
	self assert: (-9876543210 storeStringBase: 10) = '-9876543210'.
	self assert: -9876543210 storeStringHex = '-16r24CB016EA'.
	self assert: (-282458553905 printStringBase: 11) = '-A9876543210'.
	self assert: (-282458553905 radix: 11) = '-A9876543210'.
	self assert: -282458553905 printStringHex = '-41C3D77E31'.
	self assert: (-282458553905 storeStringBase: 11) = '-11rA9876543210'.
	self assert: -282458553905 storeStringHex = '-16r41C3D77E31'.
	self assert: (-8842413667692 printStringBase: 12) = '-BA9876543210'.
	self assert: (-8842413667692 radix: 12) = '-BA9876543210'.
	self assert: -8842413667692 printStringHex = '-80AC8ECF56C'.
	self assert: (-8842413667692 storeStringBase: 12) = '-12rBA9876543210'.
	self assert: -8842413667692 storeStringHex = '-16r80AC8ECF56C'.
	self assert: (-300771807240918 printStringBase: 13) = '-CBA9876543210'.
	self assert: (-300771807240918 radix: 13) = '-CBA9876543210'.
	self assert: -300771807240918 printStringHex = '-1118CE4BAA2D6'.
	self assert: (-300771807240918 storeStringBase: 13) = '-13rCBA9876543210'.
	self assert: -300771807240918 storeStringHex = '-16r1118CE4BAA2D6'.
	self assert: (-11046255305880158 printStringBase: 14) = '-DCBA9876543210'.
	self assert: (-11046255305880158 radix: 14) = '-DCBA9876543210'.
	self assert: -11046255305880158 printStringHex = '-273E82BB9AF25E'.
	self assert: (-11046255305880158 storeStringBase: 14) = '-14rDCBA9876543210'.
	self assert: -11046255305880158 storeStringHex = '-16r273E82BB9AF25E'.
	self assert: (-435659737878916215 printStringBase: 15) = '-EDCBA9876543210'.
	self assert: (-435659737878916215 radix: 15) = '-EDCBA9876543210'.
	self assert: -435659737878916215 printStringHex = '-60BC6392F366C77'.
	self assert: (-435659737878916215 storeStringBase: 15) = '-15rEDCBA9876543210'.
	self assert: -435659737878916215 storeStringHex = '-16r60BC6392F366C77'.
	self assert: (-18364758544493064720 printStringBase: 16) = '-FEDCBA9876543210'.
	self assert: (-18364758544493064720 radix: 16) = '-FEDCBA9876543210'.
	self assert: -18364758544493064720 printStringHex = '-FEDCBA9876543210'.
	self assert: (-18364758544493064720 storeStringBase: 16) = '-16rFEDCBA9876543210'.
	self assert: -18364758544493064720 storeStringHex = '-16rFEDCBA9876543210'.
	self assert: (-824008854613343261192 printStringBase: 17) = '-GFEDCBA9876543210'.
	self assert: (-824008854613343261192 radix: 17) = '-GFEDCBA9876543210'.
	self assert: -824008854613343261192 printStringHex = '-2CAB6B877C1CD2D208'.
	self assert: (-824008854613343261192 storeStringBase: 17) = '-17rGFEDCBA9876543210'.
	self assert: -824008854613343261192 storeStringHex = '-16r2CAB6B877C1CD2D208'.
	self assert: (-39210261334551566857170 printStringBase: 18) = '-HGFEDCBA9876543210'.
	self assert: (-39210261334551566857170 radix: 18) = '-HGFEDCBA9876543210'.
	self assert: -39210261334551566857170 printStringHex = '-84D97AFCAE81415B3D2'.
	self assert: (-39210261334551566857170 storeStringBase: 18) = '-18rHGFEDCBA9876543210'.
	self assert: -39210261334551566857170 storeStringHex = '-16r84D97AFCAE81415B3D2'.
	self assert: (-1972313422155189164466189 printStringBase: 19) = '-IHGFEDCBA9876543210'.
	self assert: (-1972313422155189164466189 radix: 19) = '-IHGFEDCBA9876543210'.
	self assert: -1972313422155189164466189 printStringHex = '-1A1A75329C5C6FC00600D'.
	self assert: (-1972313422155189164466189 storeStringBase: 19) = '-19rIHGFEDCBA9876543210'.
	self assert: -1972313422155189164466189 storeStringHex = '-16r1A1A75329C5C6FC00600D'.
	self assert: (-104567135734072022160664820 printStringBase: 20) = '-JIHGFEDCBA9876543210'.
	self assert: (-104567135734072022160664820 radix: 20) = '-JIHGFEDCBA9876543210'.
	self assert: -104567135734072022160664820 printStringHex = '-567EF3C9636D242A8C68F4'.
	self assert: (-104567135734072022160664820 storeStringBase: 20) = '-20rJIHGFEDCBA9876543210'.
	self assert: -104567135734072022160664820 storeStringHex = '-16r567EF3C9636D242A8C68F4'.
	self assert: (-5827980550840017565077671610 printStringBase: 21) = '-KJIHGFEDCBA9876543210'.
	self assert: (-5827980550840017565077671610 radix: 21) = '-KJIHGFEDCBA9876543210'.
	self assert: -5827980550840017565077671610 printStringHex = '-12D4CAE2B8A09BCFDBE30EBA'.
	self assert: (-5827980550840017565077671610 storeStringBase: 21) = '-21rKJIHGFEDCBA9876543210'.
	self assert: -5827980550840017565077671610 storeStringHex = '-16r12D4CAE2B8A09BCFDBE30EBA'.
	self assert: (-340653664490377789692799452102 printStringBase: 22) = '-LKJIHGFEDCBA9876543210'.
	self assert: (-340653664490377789692799452102 radix: 22) = '-LKJIHGFEDCBA9876543210'.
	self assert: -340653664490377789692799452102 printStringHex = '-44CB61B5B47E1A5D8F88583C6'.
	self assert: (-340653664490377789692799452102 storeStringBase: 22) = '-22rLKJIHGFEDCBA9876543210'.
	self assert: -340653664490377789692799452102 storeStringHex = '-16r44CB61B5B47E1A5D8F88583C6'.
	self assert: (-20837326537038308910317109288851 printStringBase: 23) = '-MLKJIHGFEDCBA9876543210'.
	self assert: (-20837326537038308910317109288851 radix: 23) = '-MLKJIHGFEDCBA9876543210'.
	self assert: -20837326537038308910317109288851 printStringHex = '-1070108876456E0EF115B389F93'.
	self assert: (-20837326537038308910317109288851 storeStringBase: 23) = '-23rMLKJIHGFEDCBA9876543210'.
	self assert: -20837326537038308910317109288851 storeStringHex = '-16r1070108876456E0EF115B389F93'.
	self assert: (-1331214537196502869015340298036888 printStringBase: 24) = '-NMLKJIHGFEDCBA9876543210'.
	self assert: (-1331214537196502869015340298036888 radix: 24) = '-NMLKJIHGFEDCBA9876543210'.
	self assert: -1331214537196502869015340298036888 printStringHex = '-41A24A285154B026B6ED206C6698'.
	self assert: (-1331214537196502869015340298036888 storeStringBase: 24) = '-24rNMLKJIHGFEDCBA9876543210'.
	self assert: -1331214537196502869015340298036888 storeStringHex = '-16r41A24A285154B026B6ED206C6698'.
	self assert: (-88663644327703473714387251271141900 printStringBase: 25) = '-ONMLKJIHGFEDCBA9876543210'.
	self assert: (-88663644327703473714387251271141900 radix: 25) = '-ONMLKJIHGFEDCBA9876543210'.
	self assert: -88663644327703473714387251271141900 printStringHex = '-111374860A2C6CEBE5999630398A0C'.
	self assert: (-88663644327703473714387251271141900 storeStringBase: 25) = '-25rONMLKJIHGFEDCBA9876543210'.
	self assert: -88663644327703473714387251271141900 storeStringHex = '-16r111374860A2C6CEBE5999630398A0C'.
	self assert: (-6146269788878825859099399609538763450 printStringBase: 26) = '-PONMLKJIHGFEDCBA9876543210'.
	self assert: (-6146269788878825859099399609538763450 radix: 26) = '-PONMLKJIHGFEDCBA9876543210'.
	self assert: -6146269788878825859099399609538763450 printStringHex = '-49FBA7F30B0F48BD14E6A99BD8ADABA'.
	self assert: (-6146269788878825859099399609538763450 storeStringBase: 26) = '-26rPONMLKJIHGFEDCBA9876543210'.
	self assert: -6146269788878825859099399609538763450 storeStringHex = '-16r49FBA7F30B0F48BD14E6A99BD8ADABA'.
	self assert: (-442770531899482980347734468443677777577 printStringBase: 27) = '-QPONMLKJIHGFEDCBA9876543210'.
	self assert: (-442770531899482980347734468443677777577 radix: 27) = '-QPONMLKJIHGFEDCBA9876543210'.
	self assert: -442770531899482980347734468443677777577 printStringHex = '-14D1A80A997343640C1145A073731DEA9'.
	self assert: (-442770531899482980347734468443677777577 storeStringBase: 27) = '-27rQPONMLKJIHGFEDCBA9876543210'.
	self assert: -442770531899482980347734468443677777577 storeStringHex = '-16r14D1A80A997343640C1145A073731DEA9'.
	self assert: (-33100056003358651440264672384704297711484 printStringBase: 28) = '-RQPONMLKJIHGFEDCBA9876543210'.
	self assert: (-33100056003358651440264672384704297711484 radix: 28) = '-RQPONMLKJIHGFEDCBA9876543210'.
	self assert: -33100056003358651440264672384704297711484 printStringHex = '-6145B6E6DACFA25D0E936F51D25932377C'.
	self assert: (-33100056003358651440264672384704297711484 storeStringBase: 28) = '-28rRQPONMLKJIHGFEDCBA9876543210'.
	self assert: -33100056003358651440264672384704297711484 storeStringHex = '-16r6145B6E6DACFA25D0E936F51D25932377C'.
	self assert: (-2564411043271974895869785066497940850811934 printStringBase: 29) = '-SRQPONMLKJIHGFEDCBA9876543210'.
	self assert: (-2564411043271974895869785066497940850811934 radix: 29) = '-SRQPONMLKJIHGFEDCBA9876543210'.
	self assert: -2564411043271974895869785066497940850811934 printStringHex = '-1D702071CBA4A1597D4DD37E95EFAC79241E'.
	self assert: (-2564411043271974895869785066497940850811934 storeStringBase: 29) = '-29rSRQPONMLKJIHGFEDCBA9876543210'.
	self assert: -2564411043271974895869785066497940850811934 storeStringHex = '-16r1D702071CBA4A1597D4DD37E95EFAC79241E'.
	self assert: (-205646315052919334126040428061831153388822830 printStringBase: 30) = '-TSRQPONMLKJIHGFEDCBA9876543210'.
	self assert: (-205646315052919334126040428061831153388822830 radix: 30) = '-TSRQPONMLKJIHGFEDCBA9876543210'.
	self assert: -205646315052919334126040428061831153388822830 printStringHex = '-938B4343B54B550989989D02998718FFB212E'.
	self assert: (-205646315052919334126040428061831153388822830 storeStringBase: 30) = '-30rTSRQPONMLKJIHGFEDCBA9876543210'.
	self assert: -205646315052919334126040428061831153388822830 storeStringHex = '-16r938B4343B54B550989989D02998718FFB212E'.
	self assert: (-17050208381689099029767742314582582184093573615 printStringBase: 31) = '-UTSRQPONMLKJIHGFEDCBA9876543210'.
	self assert: (-17050208381689099029767742314582582184093573615 radix: 31) = '-UTSRQPONMLKJIHGFEDCBA9876543210'.
	self assert: -17050208381689099029767742314582582184093573615 printStringHex = '-2FC8ECB1521BA16D24A69E976D53873E2C661EF'.
	self assert: (-17050208381689099029767742314582582184093573615 storeStringBase: 31) = '-31rUTSRQPONMLKJIHGFEDCBA9876543210'.
	self assert: -17050208381689099029767742314582582184093573615 storeStringHex = '-16r2FC8ECB1521BA16D24A69E976D53873E2C661EF'.
	self assert: (-1459980823972598128486511383358617792788444579872 printStringBase: 32) = '-VUTSRQPONMLKJIHGFEDCBA9876543210'.
	self assert: (-1459980823972598128486511383358617792788444579872 radix: 32) = '-VUTSRQPONMLKJIHGFEDCBA9876543210'.
	self assert: -1459980823972598128486511383358617792788444579872 printStringHex = '-FFBBCDEB38BDAB49CA307B9AC5A928398A418820'.
	self assert: (-1459980823972598128486511383358617792788444579872 storeStringBase: 32) = '-32rVUTSRQPONMLKJIHGFEDCBA9876543210'.
	self assert: -1459980823972598128486511383358617792788444579872 storeStringHex = '-16rFFBBCDEB38BDAB49CA307B9AC5A928398A418820'.
	self assert: (-128983956064237823710866404905431464703849549412368 printStringBase: 33) = '-WVUTSRQPONMLKJIHGFEDCBA9876543210'.
	self assert: (-128983956064237823710866404905431464703849549412368 radix: 33) = '-WVUTSRQPONMLKJIHGFEDCBA9876543210'.
	self assert: -128983956064237823710866404905431464703849549412368 printStringHex = '-584120A0328DE272AB055A8AA003CE4A559F223810'.
	self assert: (-128983956064237823710866404905431464703849549412368 storeStringBase: 33) = '-33rWVUTSRQPONMLKJIHGFEDCBA9876543210'.
	self assert: -128983956064237823710866404905431464703849549412368 storeStringHex = '-16r584120A0328DE272AB055A8AA003CE4A559F223810'.
	self assert: (-11745843093701610854378775891116314824081102660800418 printStringBase: 34) = '-XWVUTSRQPONMLKJIHGFEDCBA9876543210'.
	self assert: (-11745843093701610854378775891116314824081102660800418 radix: 34) = '-XWVUTSRQPONMLKJIHGFEDCBA9876543210'.
	self assert: -11745843093701610854378775891116314824081102660800418 printStringHex = '-1F64D4FC76000F7B92CF0CD5D0F350139AB9F25D8FA2'.
	self assert: (-11745843093701610854378775891116314824081102660800418 storeStringBase: 34) = '-34rXWVUTSRQPONMLKJIHGFEDCBA9876543210'.
	self assert: -11745843093701610854378775891116314824081102660800418 storeStringHex = '-16r1F64D4FC76000F7B92CF0CD5D0F350139AB9F25D8FA2'.
	self assert: (-1101553773143634726491620528194292510495517905608180485 printStringBase: 35) = '-YXWVUTSRQPONMLKJIHGFEDCBA9876543210'.
	self assert: (-1101553773143634726491620528194292510495517905608180485 radix: 35) = '-YXWVUTSRQPONMLKJIHGFEDCBA9876543210'.
	self assert: -1101553773143634726491620528194292510495517905608180485 printStringHex = '-B8031AD55AD1FAA89E07A271CA1ED2F420415D1570305'.
	self assert: (-1101553773143634726491620528194292510495517905608180485 storeStringBase: 35) = '-35rYXWVUTSRQPONMLKJIHGFEDCBA9876543210'.
	self assert: -1101553773143634726491620528194292510495517905608180485 storeStringHex = '-16rB8031AD55AD1FAA89E07A271CA1ED2F420415D1570305'.
	self assert: (-106300512100105327644605138221229898724869759421181854980 printStringBase: 36) = '-ZYXWVUTSRQPONMLKJIHGFEDCBA9876543210'.
	self assert: (-106300512100105327644605138221229898724869759421181854980 radix: 36) = '-ZYXWVUTSRQPONMLKJIHGFEDCBA9876543210'.
	self assert: -106300512100105327644605138221229898724869759421181854980 printStringHex = '-455D441E55A37239AB4C303189576071AF5578FFCA80504'.
	self assert: (-106300512100105327644605138221229898724869759421181854980 storeStringBase: 36) = '-36rZYXWVUTSRQPONMLKJIHGFEDCBA9876543210'.
	self assert: -106300512100105327644605138221229898724869759421181854980 storeStringHex = '-16r455D441E55A37239AB4C303189576071AF5578FFCA80504'.
]

{ #category : #'tests - instance creation' }
IntegerTest >> testNew [
	self should: [Integer new] raise: self defaultTestError. 
]

{ #category : #'tests - mathematical functions' }
IntegerTest >> testNthRoot [
	1 << 2000 nthRoot: 100.
	self assert: (1 << 2000 nthRoot: 100) equals: 1 << 20
]

{ #category : #'tests - mathematical functions' }
IntegerTest >> testNthRootErrorConditions [
	"
	IntegerTest new testExactRaisedToErrorConditions
	"

	self should: [ -2 nthRoot: 1/4 ] raise: ArithmeticError.
	self should: [ -2 nthRoot: 1.24 ] raise: ArithmeticError.
]

{ #category : #'tests - mathematical functions' }
IntegerTest >> testNthRootExactness [
	| inexactRoots largeExactPowersOf6 |
	largeExactPowersOf6 := (2 to: 100) collect: [:k | k raisedTo: 66].
	inexactRoots := largeExactPowersOf6 reject: [:e | (e nthRoot: 6) isInteger].
	self assert: inexactRoots isEmpty description: 'Failed to find the exact 6th root of these numbers'
]

{ #category : #'tests - mathematical functions' }
IntegerTest >> testNthRootTruncated [
	<timeout:  5 "seconds">
	| tooBigToBeAFloat large |
	tooBigToBeAFloat := 1 << 2000.
	self assert: (tooBigToBeAFloat nthRootTruncated: 100) equals: 1 << 20.
	self assert: (tooBigToBeAFloat + 1 nthRootTruncated: 100) equals: 1 << 20.
	self assert: (tooBigToBeAFloat - 1 nthRootTruncated: 100) equals: 1 << 20 - 1.
	
	large := -3 raisedTo: 255.
	self assert: (large nthRootTruncated: 17) equals: (-3 raisedTo: 15).
	self assert: (large + 11 nthRootTruncated: 17) equals: (-3 raisedTo: 15) + 1.
	self assert: (large - 11 nthRootTruncated: 17) equals: (-3 raisedTo: 15).
	
	2 to: 10 do: [:thePower |
		1 to: 10000 do: [:n |
			| theTruncatedRoot |
			theTruncatedRoot := n nthRootTruncated: thePower.
			self assert: (theTruncatedRoot raisedTo: thePower) <= n.
			self assert: (theTruncatedRoot + 1 raisedTo: thePower) > n]]
]

{ #category : #'tests - printing' }
IntegerTest >> testNumberOfDigits [
	
	2 to: 32 do: [:b |
		1 to: 1000//b do: [:n |
			| bRaisedToN |
			bRaisedToN := b raisedTo: n.
			self assert: (bRaisedToN - 1 numberOfDigitsInBase: b) = n.
			self assert: (bRaisedToN numberOfDigitsInBase: b) = (n+1).
			self assert: (bRaisedToN + 1 numberOfDigitsInBase: b) = (n+1).
			
			self assert: (bRaisedToN negated + 1 numberOfDigitsInBase: b) = n.
			self assert: (bRaisedToN negated numberOfDigitsInBase: b) = (n+1).
			self assert: (bRaisedToN negated - 1 numberOfDigitsInBase: b) = (n+1).]].

]

{ #category : #'tests - printing' }
IntegerTest >> testPositiveIntegerPrinting [
	"self run: #testPositiveIntegerPrinting"

	self assert: 0 printString = '0'.
	self assert: 0 printStringHex = '0'.
	self assert: 0 storeStringHex = '16r0'.

	self assert: (2 printStringBase: 2) = '10'.
	self assert: (2 radix: 2) = '10'.
	self assert: 2 printStringHex = '2'.
	self assert: (2 storeStringBase: 2) = '2r10'.
	self assert: 2 storeStringHex = '16r2'.
	self assert: (21 printStringBase: 3) = '210'.
	self assert: (21 radix: 3) = '210'.
	self assert: 21 printStringHex = '15'.
	self assert: (21 storeStringBase: 3) = '3r210'.
	self assert: 21 storeStringHex = '16r15'.
	self assert: (228 printStringBase: 4) = '3210'.
	self assert: (228 radix: 4) = '3210'.
	self assert: 228 printStringHex = 'E4'.
	self assert: (228 storeStringBase: 4) = '4r3210'.
	self assert: 228 storeStringHex = '16rE4'.
	self assert: (2930 printStringBase: 5) = '43210'.
	self assert: (2930 radix: 5) = '43210'.
	self assert: 2930 printStringHex = 'B72'.
	self assert: (2930 storeStringBase: 5) = '5r43210'.
	self assert: 2930 storeStringHex = '16rB72'.
	self assert: (44790 printStringBase: 6) = '543210'.
	self assert: (44790 radix: 6) = '543210'.
	self assert: 44790 printStringHex = 'AEF6'.
	self assert: (44790 storeStringBase: 6) = '6r543210'.
	self assert: 44790 storeStringHex = '16rAEF6'.
	self assert: (800667 printStringBase: 7) = '6543210'.
	self assert: (800667 radix: 7) = '6543210'.
	self assert: 800667 printStringHex = 'C379B'.
	self assert: (800667 storeStringBase: 7) = '7r6543210'.
	self assert: 800667 storeStringHex = '16rC379B'.
	self assert: (16434824 printStringBase: 8) = '76543210'.
	self assert: (16434824 radix: 8) = '76543210'.
	self assert: 16434824 printStringHex = 'FAC688'.
	self assert: (16434824 storeStringBase: 8) = '8r76543210'.
	self assert: 16434824 storeStringHex = '16rFAC688'.
	self assert: (381367044 printStringBase: 9) = '876543210'.
	self assert: (381367044 radix: 9) = '876543210'.
	self assert: 381367044 printStringHex = '16BB3304'.
	self assert: (381367044 storeStringBase: 9) = '9r876543210'.
	self assert: 381367044 storeStringHex = '16r16BB3304'.
	self assert: (9876543210 printStringBase: 10) = '9876543210'.
	self assert: (9876543210 radix: 10) = '9876543210'.
	self assert: 9876543210 printStringHex = '24CB016EA'.
	self assert: (9876543210 storeStringBase: 10) = '9876543210'.
	self assert: 9876543210 storeStringHex = '16r24CB016EA'.
	self assert: (282458553905 printStringBase: 11) = 'A9876543210'.
	self assert: (282458553905 radix: 11) = 'A9876543210'.
	self assert: 282458553905 printStringHex = '41C3D77E31'.
	self assert: (282458553905 storeStringBase: 11) = '11rA9876543210'.
	self assert: 282458553905 storeStringHex = '16r41C3D77E31'.
	self assert: (8842413667692 printStringBase: 12) = 'BA9876543210'.
	self assert: (8842413667692 radix: 12) = 'BA9876543210'.
	self assert: 8842413667692 printStringHex = '80AC8ECF56C'.
	self assert: (8842413667692 storeStringBase: 12) = '12rBA9876543210'.
	self assert: 8842413667692 storeStringHex = '16r80AC8ECF56C'.
	self assert: (300771807240918 printStringBase: 13) = 'CBA9876543210'.
	self assert: (300771807240918 radix: 13) = 'CBA9876543210'.
	self assert: 300771807240918 printStringHex = '1118CE4BAA2D6'.
	self assert: (300771807240918 storeStringBase: 13) = '13rCBA9876543210'.
	self assert: 300771807240918 storeStringHex = '16r1118CE4BAA2D6'.
	self assert: (11046255305880158 printStringBase: 14) = 'DCBA9876543210'.
	self assert: (11046255305880158 radix: 14) = 'DCBA9876543210'.
	self assert: 11046255305880158 printStringHex = '273E82BB9AF25E'.
	self assert: (11046255305880158 storeStringBase: 14) = '14rDCBA9876543210'.
	self assert: 11046255305880158 storeStringHex = '16r273E82BB9AF25E'.
	self assert: (435659737878916215 printStringBase: 15) = 'EDCBA9876543210'.
	self assert: (435659737878916215 radix: 15) = 'EDCBA9876543210'.
	self assert: 435659737878916215 printStringHex = '60BC6392F366C77'.
	self assert: (435659737878916215 storeStringBase: 15) = '15rEDCBA9876543210'.
	self assert: 435659737878916215 storeStringHex = '16r60BC6392F366C77'.
	self assert: (18364758544493064720 printStringBase: 16) = 'FEDCBA9876543210'.
	self assert: (18364758544493064720 radix: 16) = 'FEDCBA9876543210'.
	self assert: 18364758544493064720 printStringHex = 'FEDCBA9876543210'.
	self assert: (18364758544493064720 storeStringBase: 16) = '16rFEDCBA9876543210'.
	self assert: 18364758544493064720 storeStringHex = '16rFEDCBA9876543210'.
	self assert: (824008854613343261192 printStringBase: 17) = 'GFEDCBA9876543210'.
	self assert: (824008854613343261192 radix: 17) = 'GFEDCBA9876543210'.
	self assert: 824008854613343261192 printStringHex = '2CAB6B877C1CD2D208'.
	self assert: (824008854613343261192 storeStringBase: 17) = '17rGFEDCBA9876543210'.
	self assert: 824008854613343261192 storeStringHex = '16r2CAB6B877C1CD2D208'.
	self assert: (39210261334551566857170 printStringBase: 18) = 'HGFEDCBA9876543210'.
	self assert: (39210261334551566857170 radix: 18) = 'HGFEDCBA9876543210'.
	self assert: 39210261334551566857170 printStringHex = '84D97AFCAE81415B3D2'.
	self assert: (39210261334551566857170 storeStringBase: 18) = '18rHGFEDCBA9876543210'.
	self assert: 39210261334551566857170 storeStringHex = '16r84D97AFCAE81415B3D2'.
	self assert: (1972313422155189164466189 printStringBase: 19) = 'IHGFEDCBA9876543210'.
	self assert: (1972313422155189164466189 radix: 19) = 'IHGFEDCBA9876543210'.
	self assert: 1972313422155189164466189 printStringHex = '1A1A75329C5C6FC00600D'.
	self assert: (1972313422155189164466189 storeStringBase: 19) = '19rIHGFEDCBA9876543210'.
	self assert: 1972313422155189164466189 storeStringHex = '16r1A1A75329C5C6FC00600D'.
	self assert: (104567135734072022160664820 printStringBase: 20) = 'JIHGFEDCBA9876543210'.
	self assert: (104567135734072022160664820 radix: 20) = 'JIHGFEDCBA9876543210'.
	self assert: 104567135734072022160664820 printStringHex = '567EF3C9636D242A8C68F4'.
	self assert: (104567135734072022160664820 storeStringBase: 20) = '20rJIHGFEDCBA9876543210'.
	self assert: 104567135734072022160664820 storeStringHex = '16r567EF3C9636D242A8C68F4'.
	self assert: (5827980550840017565077671610 printStringBase: 21) = 'KJIHGFEDCBA9876543210'.
	self assert: (5827980550840017565077671610 radix: 21) = 'KJIHGFEDCBA9876543210'.
	self assert: 5827980550840017565077671610 printStringHex = '12D4CAE2B8A09BCFDBE30EBA'.
	self assert: (5827980550840017565077671610 storeStringBase: 21) = '21rKJIHGFEDCBA9876543210'.
	self assert: 5827980550840017565077671610 storeStringHex = '16r12D4CAE2B8A09BCFDBE30EBA'.
	self assert: (340653664490377789692799452102 printStringBase: 22) = 'LKJIHGFEDCBA9876543210'.
	self assert: (340653664490377789692799452102 radix: 22) = 'LKJIHGFEDCBA9876543210'.
	self assert: 340653664490377789692799452102 printStringHex = '44CB61B5B47E1A5D8F88583C6'.
	self assert: (340653664490377789692799452102 storeStringBase: 22) = '22rLKJIHGFEDCBA9876543210'.
	self assert: 340653664490377789692799452102 storeStringHex = '16r44CB61B5B47E1A5D8F88583C6'.
	self assert: (20837326537038308910317109288851 printStringBase: 23) = 'MLKJIHGFEDCBA9876543210'.
	self assert: (20837326537038308910317109288851 radix: 23) = 'MLKJIHGFEDCBA9876543210'.
	self assert: 20837326537038308910317109288851 printStringHex = '1070108876456E0EF115B389F93'.
	self assert: (20837326537038308910317109288851 storeStringBase: 23) = '23rMLKJIHGFEDCBA9876543210'.
	self assert: 20837326537038308910317109288851 storeStringHex = '16r1070108876456E0EF115B389F93'.
	self assert: (1331214537196502869015340298036888 printStringBase: 24) = 'NMLKJIHGFEDCBA9876543210'.
	self assert: (1331214537196502869015340298036888 radix: 24) = 'NMLKJIHGFEDCBA9876543210'.
	self assert: 1331214537196502869015340298036888 printStringHex = '41A24A285154B026B6ED206C6698'.
	self assert: (1331214537196502869015340298036888 storeStringBase: 24) = '24rNMLKJIHGFEDCBA9876543210'.
	self assert: 1331214537196502869015340298036888 storeStringHex = '16r41A24A285154B026B6ED206C6698'.
	self assert: (88663644327703473714387251271141900 printStringBase: 25) = 'ONMLKJIHGFEDCBA9876543210'.
	self assert: (88663644327703473714387251271141900 radix: 25) = 'ONMLKJIHGFEDCBA9876543210'.
	self assert: 88663644327703473714387251271141900 printStringHex = '111374860A2C6CEBE5999630398A0C'.
	self assert: (88663644327703473714387251271141900 storeStringBase: 25) = '25rONMLKJIHGFEDCBA9876543210'.
	self assert: 88663644327703473714387251271141900 storeStringHex = '16r111374860A2C6CEBE5999630398A0C'.
	self assert: (6146269788878825859099399609538763450 printStringBase: 26) = 'PONMLKJIHGFEDCBA9876543210'.
	self assert: (6146269788878825859099399609538763450 radix: 26) = 'PONMLKJIHGFEDCBA9876543210'.
	self assert: 6146269788878825859099399609538763450 printStringHex = '49FBA7F30B0F48BD14E6A99BD8ADABA'.
	self assert: (6146269788878825859099399609538763450 storeStringBase: 26) = '26rPONMLKJIHGFEDCBA9876543210'.
	self assert: 6146269788878825859099399609538763450 storeStringHex = '16r49FBA7F30B0F48BD14E6A99BD8ADABA'.
	self assert: (442770531899482980347734468443677777577 printStringBase: 27) = 'QPONMLKJIHGFEDCBA9876543210'.
	self assert: (442770531899482980347734468443677777577 radix: 27) = 'QPONMLKJIHGFEDCBA9876543210'.
	self assert: 442770531899482980347734468443677777577 printStringHex = '14D1A80A997343640C1145A073731DEA9'.
	self assert: (442770531899482980347734468443677777577 storeStringBase: 27) = '27rQPONMLKJIHGFEDCBA9876543210'.
	self assert: 442770531899482980347734468443677777577 storeStringHex = '16r14D1A80A997343640C1145A073731DEA9'.
	self assert: (33100056003358651440264672384704297711484 printStringBase: 28) = 'RQPONMLKJIHGFEDCBA9876543210'.
	self assert: (33100056003358651440264672384704297711484 radix: 28) = 'RQPONMLKJIHGFEDCBA9876543210'.
	self assert: 33100056003358651440264672384704297711484 printStringHex = '6145B6E6DACFA25D0E936F51D25932377C'.
	self assert: (33100056003358651440264672384704297711484 storeStringBase: 28) = '28rRQPONMLKJIHGFEDCBA9876543210'.
	self assert: 33100056003358651440264672384704297711484 storeStringHex = '16r6145B6E6DACFA25D0E936F51D25932377C'.
	self assert: (2564411043271974895869785066497940850811934 printStringBase: 29) = 'SRQPONMLKJIHGFEDCBA9876543210'.
	self assert: (2564411043271974895869785066497940850811934 radix: 29) = 'SRQPONMLKJIHGFEDCBA9876543210'.
	self assert: 2564411043271974895869785066497940850811934 printStringHex = '1D702071CBA4A1597D4DD37E95EFAC79241E'.
	self assert: (2564411043271974895869785066497940850811934 storeStringBase: 29) = '29rSRQPONMLKJIHGFEDCBA9876543210'.
	self assert: 2564411043271974895869785066497940850811934 storeStringHex = '16r1D702071CBA4A1597D4DD37E95EFAC79241E'.
	self assert: (205646315052919334126040428061831153388822830 printStringBase: 30) = 'TSRQPONMLKJIHGFEDCBA9876543210'.
	self assert: (205646315052919334126040428061831153388822830 radix: 30) = 'TSRQPONMLKJIHGFEDCBA9876543210'.
	self assert: 205646315052919334126040428061831153388822830 printStringHex = '938B4343B54B550989989D02998718FFB212E'.
	self assert: (205646315052919334126040428061831153388822830 storeStringBase: 30) = '30rTSRQPONMLKJIHGFEDCBA9876543210'.
	self assert: 205646315052919334126040428061831153388822830 storeStringHex = '16r938B4343B54B550989989D02998718FFB212E'.
	self assert: (17050208381689099029767742314582582184093573615 printStringBase: 31) = 'UTSRQPONMLKJIHGFEDCBA9876543210'.
	self assert: (17050208381689099029767742314582582184093573615 radix: 31) = 'UTSRQPONMLKJIHGFEDCBA9876543210'.
	self assert: 17050208381689099029767742314582582184093573615 printStringHex = '2FC8ECB1521BA16D24A69E976D53873E2C661EF'.
	self assert: (17050208381689099029767742314582582184093573615 storeStringBase: 31) = '31rUTSRQPONMLKJIHGFEDCBA9876543210'.
	self assert: 17050208381689099029767742314582582184093573615 storeStringHex = '16r2FC8ECB1521BA16D24A69E976D53873E2C661EF'.
	self assert: (1459980823972598128486511383358617792788444579872 printStringBase: 32) = 'VUTSRQPONMLKJIHGFEDCBA9876543210'.
	self assert: (1459980823972598128486511383358617792788444579872 radix: 32) = 'VUTSRQPONMLKJIHGFEDCBA9876543210'.
	self assert: 1459980823972598128486511383358617792788444579872 printStringHex = 'FFBBCDEB38BDAB49CA307B9AC5A928398A418820'.
	self assert: (1459980823972598128486511383358617792788444579872 storeStringBase: 32) = '32rVUTSRQPONMLKJIHGFEDCBA9876543210'.
	self assert: 1459980823972598128486511383358617792788444579872 storeStringHex = '16rFFBBCDEB38BDAB49CA307B9AC5A928398A418820'.
	self assert: (128983956064237823710866404905431464703849549412368 printStringBase: 33) = 'WVUTSRQPONMLKJIHGFEDCBA9876543210'.
	self assert: (128983956064237823710866404905431464703849549412368 radix: 33) = 'WVUTSRQPONMLKJIHGFEDCBA9876543210'.
	self assert: 128983956064237823710866404905431464703849549412368 printStringHex = '584120A0328DE272AB055A8AA003CE4A559F223810'.
	self assert: (128983956064237823710866404905431464703849549412368 storeStringBase: 33) = '33rWVUTSRQPONMLKJIHGFEDCBA9876543210'.
	self assert: 128983956064237823710866404905431464703849549412368 storeStringHex = '16r584120A0328DE272AB055A8AA003CE4A559F223810'.
	self assert: (11745843093701610854378775891116314824081102660800418 printStringBase: 34) = 'XWVUTSRQPONMLKJIHGFEDCBA9876543210'.
	self assert: (11745843093701610854378775891116314824081102660800418 radix: 34) = 'XWVUTSRQPONMLKJIHGFEDCBA9876543210'.
	self assert: 11745843093701610854378775891116314824081102660800418 printStringHex = '1F64D4FC76000F7B92CF0CD5D0F350139AB9F25D8FA2'.
	self assert: (11745843093701610854378775891116314824081102660800418 storeStringBase: 34) = '34rXWVUTSRQPONMLKJIHGFEDCBA9876543210'.
	self assert: 11745843093701610854378775891116314824081102660800418 storeStringHex = '16r1F64D4FC76000F7B92CF0CD5D0F350139AB9F25D8FA2'.
	self assert: (1101553773143634726491620528194292510495517905608180485 printStringBase: 35) = 'YXWVUTSRQPONMLKJIHGFEDCBA9876543210'.
	self assert: (1101553773143634726491620528194292510495517905608180485 radix: 35) = 'YXWVUTSRQPONMLKJIHGFEDCBA9876543210'.
	self assert: 1101553773143634726491620528194292510495517905608180485 printStringHex = 'B8031AD55AD1FAA89E07A271CA1ED2F420415D1570305'.
	self assert: (1101553773143634726491620528194292510495517905608180485 storeStringBase: 35) = '35rYXWVUTSRQPONMLKJIHGFEDCBA9876543210'.
	self assert: 1101553773143634726491620528194292510495517905608180485 storeStringHex = '16rB8031AD55AD1FAA89E07A271CA1ED2F420415D1570305'.
	self assert: (106300512100105327644605138221229898724869759421181854980 printStringBase: 36) = 'ZYXWVUTSRQPONMLKJIHGFEDCBA9876543210'.
	self assert: (106300512100105327644605138221229898724869759421181854980 radix: 36) = 'ZYXWVUTSRQPONMLKJIHGFEDCBA9876543210'.
	self assert: 106300512100105327644605138221229898724869759421181854980 printStringHex = '455D441E55A37239AB4C303189576071AF5578FFCA80504'.
	self assert: (106300512100105327644605138221229898724869759421181854980 storeStringBase: 36) = '36rZYXWVUTSRQPONMLKJIHGFEDCBA9876543210'.
	self assert: 106300512100105327644605138221229898724869759421181854980 storeStringHex = '16r455D441E55A37239AB4C303189576071AF5578FFCA80504'.
]

{ #category : #'tests - basic' }
IntegerTest >> testPrimesUpTo [

	| primes nn|
	primes := Integer primesUpTo: 100.
	self assert: primes = #(2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97).
	
	"upTo: semantics means 'non-inclusive'"
	primes := Integer primesUpTo: 5.
	self assert: primes = #(2 3).
	
	"this test is green for nn>25000, see #testLargePrimesUpTo"
	nn := 5. 
	self deny: (Integer primesUpTo: nn) last = nn.
	self assert: (Integer primesUpTo: nn + 1) last  = nn.
]

{ #category : #'tests - printing' }
IntegerTest >> testPrintOnBaseShowRadix [
	self assert: (String streamContents: [ :str | 123 printOn: str base: 10 showRadix: false ]) equals: '123'.
	self assert: (String streamContents: [ :str | 123 printOn: str base: 10 showRadix: true ]) equals: '10r123'.
	self assert: (String streamContents: [ :str | 123 printOn: str base: 8 showRadix: false ]) equals: '173'.
	self assert: (String streamContents: [ :str | 123 printOn: str base: 8 showRadix: true ]) equals: '8r173'
]

{ #category : #'tests - printing' }
IntegerTest >> testPrintSeparatedByEverySignedOn [
	| printer |
	printer := [ :integer :printSigned | 
		String streamContents: [ :stream | 
			integer
				printSeparatedBy: $.
				every: 3
				signed: printSigned
				on: stream ] ].
	self assert: (printer value: 123456789 value: false) equals: '123.456.789'.
	self assert: (printer value: -123456789 value: false) equals: '-123.456.789'.
	self assert: (printer value: 123456789 value: true) equals: '+123.456.789'.
	self assert: (printer value: -123456789 value: true) equals: '-123.456.789'
]

{ #category : #'tests - printing' }
IntegerTest >> testPrintStringBase [
	
	2 to: 32 do: [:b |
		1 to: 1000//b do: [:n |
			| bRaisedToN |
			bRaisedToN := b raisedTo: n.
			self assert: (bRaisedToN - 1 printStringBase: b) = (String new: n withAll: (Character digitValue: b-1)).
			self assert: (bRaisedToN printStringBase: b) = ('1' , (String new: n withAll: $0)).
			
			self assert: (bRaisedToN negated + 1 printStringBase: b) = ('-' , (String new: n withAll: (Character digitValue: b-1))).
			self assert: (bRaisedToN negated printStringBase: b) = ('-1' , (String new: n withAll: $0))]].

]

{ #category : #'tests - printing' }
IntegerTest >> testPrintStringHex [
	"self run: #testPrintStringHex"
	self assert: 0 printStringHex = '0'.
	self assert: 12 printStringHex = 'C'.
	self assert: 1234 printStringHex = '4D2'.
]

{ #category : #'tests - mathematical functions' }
IntegerTest >> testRaisedToErrorConditions [
	"
	IntegerTest new testRaisedToErrorConditions
	"

	self should: [ -2 raisedTo: 1/4 ] raise: ArithmeticError.
	self should: [ -2 raisedTo: 1.24 ] raise: ArithmeticError.
]

{ #category : #'tests - instance creation' }
IntegerTest >> testReadFrom [
	"Ensure remaining characters in a stream are not lost when parsing an integer."
	| rs i s |
	rs := '123s could be confused with a ScaledDecimal' readStream.
	i := Integer readFrom: rs.
	self assert: i = 123.
	s := rs upToEnd.
	self assert: 's could be confused with a ScaledDecimal' = s.
	rs := '123.s could be confused with a ScaledDecimal' readStream.
	i := Integer readFrom: rs.
	self assert: i = 123.
	s := rs upToEnd.
	self assert: '.s could be confused with a ScaledDecimal' = s
]

{ #category : #'tests - instance creation' }
IntegerTest >> testReadFromWithError [
	"Ensure that a string that does not represent an integer raises an error."
	
	self should: [Integer readFrom: 'invalid'] raise: Error

]

{ #category : #'tests - arithmetic' }
IntegerTest >> testReciprocalModulo [
	1 to: 512 do: [:a |
		a + 1 to: 512 do: [:b |
			| c |
			(a gcd: b) = 1
				ifTrue:
					[c := a reciprocalModulo: b.
					self assert: (a * c) \\ b = 1]
				ifFalse: [self should: [ a reciprocalModulo: b ] raise: Error]]].
]

{ #category : #'tests - printing' }
IntegerTest >> testRomanPrinting [
	self assert: 0 printStringRoman = ''. "No symbol for zero"
	self assert: 1 printStringRoman = 'I'.
	self assert: 2 printStringRoman = 'II'.
	self assert: 3 printStringRoman = 'III'.
	self assert: 4 printStringRoman = 'IV'.
	self assert: 5 printStringRoman = 'V'.
	self assert: 6 printStringRoman = 'VI'.
	self assert: 7 printStringRoman = 'VII'.
	self assert: 8 printStringRoman = 'VIII'.
	self assert: 9 printStringRoman = 'IX'.
	self assert: 10 printStringRoman = 'X'.
	self assert: 23 printStringRoman = 'XXIII'.
	self assert: 36 printStringRoman = 'XXXVI'.
	self assert: 49 printStringRoman = 'XLIX'.
	self assert: 62 printStringRoman = 'LXII'.
	self assert: 75 printStringRoman = 'LXXV'.
	self assert: 88 printStringRoman = 'LXXXVIII'.
	self assert: 99 printStringRoman = 'XCIX'.
	self assert: 100 printStringRoman = 'C'.
	self assert: 101 printStringRoman = 'CI'.
	self assert: 196 printStringRoman = 'CXCVI'.
	self assert: 197 printStringRoman = 'CXCVII'.
	self assert: 198 printStringRoman = 'CXCVIII'.
	self assert: 293 printStringRoman = 'CCXCIII'.
	self assert: 294 printStringRoman = 'CCXCIV'.
	self assert: 295 printStringRoman = 'CCXCV'.
	self assert: 390 printStringRoman = 'CCCXC'.
	self assert: 391 printStringRoman = 'CCCXCI'.
	self assert: 392 printStringRoman = 'CCCXCII'.
	self assert: 487 printStringRoman = 'CDLXXXVII'.
	self assert: 488 printStringRoman = 'CDLXXXVIII'.
	self assert: 489 printStringRoman = 'CDLXXXIX'.
	self assert: 584 printStringRoman = 'DLXXXIV'.
	self assert: 585 printStringRoman = 'DLXXXV'.
	self assert: 586 printStringRoman = 'DLXXXVI'.
	self assert: 681 printStringRoman = 'DCLXXXI'.
	self assert: 682 printStringRoman = 'DCLXXXII'.
	self assert: 683 printStringRoman = 'DCLXXXIII'.
	self assert: 778 printStringRoman = 'DCCLXXVIII'.
	self assert: 779 printStringRoman = 'DCCLXXIX'.
	self assert: 780 printStringRoman = 'DCCLXXX'.
	self assert: 875 printStringRoman = 'DCCCLXXV'.
	self assert: 876 printStringRoman = 'DCCCLXXVI'.
	self assert: 877 printStringRoman = 'DCCCLXXVII'.
	self assert: 972 printStringRoman = 'CMLXXII'.
	self assert: 973 printStringRoman = 'CMLXXIII'.
	self assert: 974 printStringRoman = 'CMLXXIV'.
	self assert: 1069 printStringRoman = 'MLXIX'.
	self assert: 1070 printStringRoman = 'MLXX'.
	self assert: 1071 printStringRoman = 'MLXXI'.
	self assert: 1166 printStringRoman = 'MCLXVI'.
	self assert: 1167 printStringRoman = 'MCLXVII'.
	self assert: 1168 printStringRoman = 'MCLXVIII'.
	self assert: 1263 printStringRoman = 'MCCLXIII'.
	self assert: 1264 printStringRoman = 'MCCLXIV'.
	self assert: 1265 printStringRoman = 'MCCLXV'.
	self assert: 1360 printStringRoman = 'MCCCLX'.
	self assert: 1361 printStringRoman = 'MCCCLXI'.
	self assert: 1362 printStringRoman = 'MCCCLXII'.
	self assert: 1457 printStringRoman = 'MCDLVII'.
	self assert: 1458 printStringRoman = 'MCDLVIII'.
	self assert: 1459 printStringRoman = 'MCDLIX'.
	self assert: 1554 printStringRoman = 'MDLIV'.
	self assert: 1555 printStringRoman = 'MDLV'.
	self assert: 1556 printStringRoman = 'MDLVI'.
	self assert: 1651 printStringRoman = 'MDCLI'.
	self assert: 1652 printStringRoman = 'MDCLII'.
	self assert: 1653 printStringRoman = 'MDCLIII'.
	self assert: 1748 printStringRoman = 'MDCCXLVIII'.
	self assert: 1749 printStringRoman = 'MDCCXLIX'.
	self assert: 1750 printStringRoman = 'MDCCL'.
	self assert: 1845 printStringRoman = 'MDCCCXLV'.
	self assert: 1846 printStringRoman = 'MDCCCXLVI'.
	self assert: 1847 printStringRoman = 'MDCCCXLVII'.
	self assert: 1942 printStringRoman = 'MCMXLII'.
	self assert: 1943 printStringRoman = 'MCMXLIII'.
	self assert: 1944 printStringRoman = 'MCMXLIV'.
	self assert: 2004 printStringRoman = 'MMIV'.

	self assert: -1 printStringRoman = '-I'.
	self assert: -2 printStringRoman = '-II'.
	self assert: -3 printStringRoman = '-III'.
	self assert: -4 printStringRoman = '-IV'.
	self assert: -5 printStringRoman = '-V'.
	self assert: -6 printStringRoman = '-VI'.
	self assert: -7 printStringRoman = '-VII'.
	self assert: -8 printStringRoman = '-VIII'.
	self assert: -9 printStringRoman = '-IX'.
	self assert: -10 printStringRoman = '-X'.

]

{ #category : #'tests - rounding' }
IntegerTest >> testRounding [
        "
        self debug: #testRounding
        "

        self assert: (5 round: 2) equals: 5
]

{ #category : #'tests - mathematical functions' }
IntegerTest >> testSqrtErrorConditions [
	"
	IntegerTest new testSqrtErrorConditions
	"

	self should: [ -1 sqrt ] raise: ArithmeticError
]

{ #category : #'tests - mathematical functions' }
IntegerTest >> testSqrtFloor [

	#(-1234567890123 -10 -5 -1) do: [ :each |
		self should: [ each sqrtFloor ] raise: Error ].
	#(
		0 1 2 3 4 5 10 16 30 160479924 386234481 501619156 524723498 580855366 766098594 834165249 1020363860 1042083924 1049218924
		1459774772895569 3050005981408238 4856589481837079 5650488387708463 7831037396100244) do: [ :each |
			self assert: each asFloat sqrt floor = each sqrtFloor ]
		
]

{ #category : #'tests - printing' }
IntegerTest >> testStoreOn [
	| integer |
	integer := 42.
	
	self assert: (String streamContents: [ :s | integer storeOn: s ]) equals: '42'.
	
	integer := -42.
	
	self assert: (String streamContents: [ :s | integer storeOn: s ]) equals: ' -42'.
]

{ #category : #'tests - instance creation' }
IntegerTest >> testStringAsNumber [
	"This covers parsing in Number>>readFrom:
	Trailing decimal points should be ignored."

	self assert: ('123' asNumber = 123).
	self assert: ('-123' asNumber = -123).
	self assert: ('123.' asNumber = 123).
	self assert: ('-123.' asNumber = -123).
	self assert: ('123This is not to be read' asNumber = 123).
	self assert: ('123s could be confused with a ScaledDecimal' asNumber = 123).
	self assert: ('123e could be confused with a Float' asNumber = 123).

]

{ #category : #'tests - bitLogic' }
IntegerTest >> testTwoComplementBitLogicWithCarry [
	"This is non regression test for http://bugs.squeak.org/view.php?id=6874"
	
	"By property of two complement, following operation is:
	...111110000 this is -16
	...111101111 this is -16-1
	...111100000 this is -32, the result of bitAnd: on two complement
	
	This test used to fail with n=31 39 47.... because of bug 6874"
	
	self assert: ((2 to: 80) allSatisfy: [:n | ((2 raisedTo: n) negated bitAnd: (2 raisedTo: n) negated - 1) = (2 raisedTo: n + 1) negated]).
]

{ #category : #'tests - bitLogic' }
IntegerTest >> testTwoComplementRightShift [
	"self run: #testTwoComplementRightShift"

	| large small |
	small := 2 << 16.
	large := 2 << 32.	
	self assert: ((small negated bitShift: -1) ~= ((small + 1) negated bitShift: -1)
		== ((large negated bitShift: -1) ~= ((large + 1) negated bitShift: -1))).
		
     self assert: ((small bitShift: -1) ~= (small + 1 bitShift: -1)
		== ((large bitShift: -1) ~= (large + 1 bitShift: -1))).
]