I am a common abstract superclass for all Integer implementations. My implementation subclasses are SmallInteger, LargePositiveInteger, and LargeNegativeInteger.

Integer division consists of:
/ exact division, answers a fraction if result is not a whole integer
// answers an Integer, rounded towards negative infinity
\\ is modulo rounded towards negative infinity
quo: truncated division, rounded towards zero

	benchmarks
	benchFib benchmark tinyBenchmarks

	bit manipulation
	<< >> allMask: anyBitOfMagnitudeFrom:to: anyMask: bitAnd: bitClear: bitInvert bitInvert32 bitOr: bitShift: bitShiftMagnitude: bitXor: highBit highBitOfMagnitude lowBit noMask:

	comparing
	< = > hash

	converting
	adaptToFraction:andSend: asCharacter asColorOfDepth: asFloat asFraction asHexDigit asInteger

	enumerating
	timesRepeat:

	mathematical functions
	degreeCos degreeSin factorial gcd: lcm: raisedTo:modulo: take:

	printing
	asStringWithCommas asStringWithCommasSigned asTwoCharacterString asWords byteEncode:base: destinationBuffer: digitBuffer: hex hex8 isLiteral printOn:base: radix: romanString

	private
	copyto: digitAdd: digitCompare: digitDiv:neg: digitLogic:op:length: digitLshift: digitMultiply:neg: digitRshift:bytes:lookfirst: digitSubtract: growby: growto: romanDigits:for:on:

	system primitives
	lastDigit replaceFrom:to:with:startingAt:

	testing
	even isInteger isPowerOfTwo

	tiles
	asPrecedenceName

	truncation and round off
	asLargerPowerOfTwo asPowerOfTwo asSmallerPowerOfTwo atRandom atRandom: ceiling floor normalize rounded truncated

	instance creation
	basicNew byte1:byte2:byte3:byte4: initializedInstance new new:neg: readFrom: readFrom:base: testBitLogic

	prime numbers
	largePrimesUpTo: largePrimesUpTo:do: primesUpTo: primesUpTo:do: verbosePrimesUpTo: verbosePrimesUpTo:do:

	testing
	testTwoComplementRightShift

	arithmetic	top
	* Refer to the comment in Number *
	+ Refer to the comment in Number +
	- Refer to the comment in Number -
	/ Refer to the comment in Number /
	// Integer quotient defined by division with truncation toward negative infinity. 9//4 = 2, -9//4 = -3. -0.9//0.4 = -3. \\ answers the remainder from this division.
	\\\ a modulo method for use in DSA. Be careful if you try to use this elsewhere
	alignedTo: Answer the smallest number not less than receiver that is a multiple of anInteger.
	quo: Refer to the comment in Number quo:

	benchmarks	top
	benchFib Handy send-heavy benchmark
	benchmark Handy bytecode-heavy benchmark
	tinyBenchmarks Report the results of running the two tiny Squeak benchmarks. ar 9/10/1999: Adjusted to run at least 1 sec to get more stable results

	bit manipulation	top
	<< left shift
	>> right shift
	allMask: Treat the argument as a bit mask. Answer whether all of the bits that are 1 in the argument are 1 in the receiver.
	anyBitOfMagnitudeFrom:to: Tests for any magnitude bits in the interval from start to stopArg.
	anyMask: Treat the argument as a bit mask. Answer whether any of the bits that are 1 in the argument are 1 in the receiver.
	bitAnd: Answer an Integer whose bits are the logical AND of the receiver's bits and those of the argument, n.
	bitClear: Answer an Integer equal to the receiver, except with all bits cleared that are set in aMask.
	bitInvert Answer an Integer whose bits are the logical negation of the receiver's bits. Numbers are interpreted as having 2's-complement representation.
	bitInvert32 Answer the 32-bit complement of the receiver.
	bitOr: Answer an Integer whose bits are the logical OR of the receiver's bits and those of the argument, n.
	bitShift: Answer an Integer whose value (in twos-complement representation) is the receiver's value (in twos-complement representation) shifted left by the number of bits indicated by the argument. Negative arguments shift right. Zeros are shifted in from the right in left shifts.
	bitShiftMagnitude: Answer an Integer whose value (in magnitude representation) is the receiver's value (in magnitude representation) shifted left by the number of bits indicated by the argument. Negative arguments shift right. Zeros are shifted in from the right in left shifts.
	bitXor: Answer an Integer whose bits are the logical XOR of the receiver's bits and those of the argument, n.
	highBit Answer the index of the high order bit of the receiver, or zero if the receiver is zero. Raise an error if the receiver is negative, since negative integers are defined to have an infinite number of leading 1's in 2's-complement arithmetic. Use >>highBitOfMagnitude if you want to get the highest bit of the magnitude.
	highBitOfMagnitude Answer the index of the high order bit of the magnitude of the receiver, or zero if the receiver is zero.
	lowBit Answer the index of the low order bit of this number.
	noMask: Treat the argument as a bit mask. Answer whether none of the bits that are 1 in the argument are 1 in the receiver.

	comparing	top
	< Answer whether the receiver is less than the argument.
	= Compare the receiver with the argument and answer with true if the receiver is equal to the argument. Otherwise answer false.
	> Answer whether the receiver is greater than the argument.
	hash Hash is reimplemented because = is implemented.

	converting	top
	adaptToFraction:andSend: If I am involved in arithmetic with a Fraction, convert me to a Fraction.
	asCharacter Answer the Character whose value is the receiver.
	asColorOfDepth: Return a color value representing the receiver as color of the given depth
	asFloat Answer a Float that represents the value of the receiver. Optimized to process only the significant digits of a LargeInteger. SqR: 11/30/1998 21:11
	asFraction Answer a Fraction that represents value of the the receiver.
	asHexDigit
	asInteger Answer with the receiver itself.

	enumerating	top
	timesRepeat: Evaluate the argument, aBlock, the number of times represented by the receiver.

	mathematical functions	top
	degreeCos Answer the cosine of the receiver taken as an angle in degrees.
	degreeSin Answer the sine of the receiver taken as an angle in degrees.
	factorial Answer the factorial of the receiver.
	gcd: See Knuth, Vol 2, 4.5.2, Algorithm L
	lcm: Answer the least common multiple of the receiver and n.
	raisedTo:modulo: Answer the modular exponential. Code by Jesse Welton.
	take: Return the number of combinations of (self) elements taken kk at a time. For 6 take 3, this is 6*5*4 / (1*2*3). Zero outside of Pascal's triangle. Use a trick to go faster.

	printing	top
	asStringWithCommas 123456789 asStringWithCommas
	asStringWithCommasSigned 123456789 asStringWithCommasSigned
	asTwoCharacterString Answer a two-character string representing the receiver, with leading zero if required. Intended for use with integers in the range 0 to 99, but plausible replies given for other values too
	asWords SmallInteger maxVal asWords
	byteEncode:base: Print a representation of the receiver on the stream, aStream, in base, b, where 2<=b<=16.
	destinationBuffer:
	digitBuffer:
	hex
	hex8 16r3333 hex8
	isLiteral Answer whether the receiver has a literal text form recognized by the compiler.
	printOn:base: Print a representation of the receiver on the stream, aStream, in base, b, where 2<=b<=16.
	radix: Answer a String representing the receiver as a base radix integer.
	romanString 1999 romanString

	private	top
	copyto:
	digitAdd:
	digitCompare: Compare the magnitude of self with that of arg. Return a code of 1, 0, -1 for self >, = , < arg
	digitDiv:neg: Answer with an array of (quotient, remainder).
	digitLogic:op:length:
	digitLshift:
	digitMultiply:neg:
	digitRshift:bytes:lookfirst: Shift right 8*b+anInteger bits, 0<=n<8. Discard all digits beyond a, and all zeroes at or below a.
	digitSubtract:
	growby:
	growto:
	romanDigits:for:on:

	system primitives	top
	lastDigit Answer the last digit of the integer base 256. LargePositiveInteger uses bytes of base two number, and each is a 'digit'.
	replaceFrom:to:with:startingAt: Catches failure if LgInt replace primitive fails

	testing	top
	even Refer to the comment in Number|even.
	isInteger True for all subclasses of Integer.
	isPowerOfTwo Return true if the receiver is an integral power of two.

	tiles	top
	asPrecedenceName

	truncation and round off	top
	asLargerPowerOfTwo Convert the receiver into a power of two which is not less than the receiver
	asPowerOfTwo Convert the receiver into a power of two
	asSmallerPowerOfTwo Convert the receiver into a power of two which is not larger than the receiver
	atRandom Answer a random integer from 1 to self. This implementation uses a shared generator. Heavy users should their own implementation or use Interval>atRandom: directly.
	atRandom: Answer a random integer from 1 to self picked from aGenerator.
	ceiling Refer to the comment in Number|ceiling.
	floor Refer to the comment in Number|floor.
	normalize SmallInts OK; LgInts override
	rounded Refer to the comment in Number|rounded.
	truncated Refer to the comment in Number|truncated.

	examples	top
	exampleFor: Provide a MethodCall with a valid example of aSelector, ready to run. If 'all', provide all tests we know about for SUnit tests. When 'all', each will be a Verifier, with an expected answer. Returns a list of MethodCalls, Verifiers, or VerifierOfPropertys.

	instance creation	top
	basicNew Primitive. Answer an instance of the receiver (which is a class) with no indexable variables. Fail if the class is indexable. Essential. See Object documentation whatIsAPrimitive.
	byte1:byte2:byte3:byte4: Depending on high-order byte copy directly into a LargeInteger, or build up a SmallInteger by shifting
	initializedInstance Answer an instance of the receiver which in some sense is initialized. In the case of Morphs, this will yield an instance that can be attached to the Hand after having received the same kind of basic initialization that would be obtained from an instance chosen from the 'new morph' menu. Return nil if the receiver is reluctant for some reason to return such a thing
	new Answer a new instance of the receiver (which is a class) with no indexable variables. Fail if the class is indexable.
	new:neg: Answer an instance of a large integer whose size is length. neg is a flag determining whether the integer is negative or not.
	readFrom: Answer a new Integer as described on the stream, aStream. Embedded radix specifiers not allowed - use Number readFrom: for that.
	readFrom:base: Answer an instance of one of my concrete subclasses. Initial minus sign accepted, and bases > 10 use letters A-Z. Embedded radix specifiers not allowed--use Number readFrom: for that. Answer zero (not an error) if there are no digits.
	testBitLogic Integer testBitLogic

	prime numbers	top
	largePrimesUpTo: Compute and return all the prime numbers up to maxValue
	largePrimesUpTo:do: Evaluate aBlock with all primes up to maxValue. The Algorithm is adapted from http://www.rsok.com/~jrm/printprimes.html It encodes prime numbers much more compactly than #primesUpTo: 38.5 integer per byte (2310 numbers per 60 byte) allow for some fun large primes. (all primes up to SmallInteger maxVal can be computed within ~27MB of memory; the regular #primesUpTo: would require 4 *GIGA*bytes). Note: The algorithm could be re-written to produce the first primes (which require the longest time to sieve) faster but only at the cost of clarity.
	primesUpTo: Return a list of prime integers up to the given integer.
	primesUpTo:do: Compute aBlock with all prime integers up to the given integer.
	verbosePrimesUpTo: Integer verbosePrimesUpTo: SmallInteger maxVal
	verbosePrimesUpTo:do: Integer verbosePrimesUpTo: SmallInteger maxVal

	testing	top
	testTwoComplementRightShift self testTwoComplementRightShift