BigInteger Class Reference

An arbitrarily large integer class. More...

Public Member Functions
	BigInteger ()
	Creates an empty BigInteger.
	BigInteger (uint32 value)
	Creates a BigInteger containing an integer value in its low bits.
	BigInteger (int32 value)
	Creates a BigInteger containing an integer value in its low bits.
	BigInteger (int64 value)
	Creates a BigInteger containing an integer value in its low bits.
	BigInteger (const BigInteger &)
	Creates a copy of another BigInteger.
	BigInteger (BigInteger &&) noexcept
	Move constructor.
BigInteger &	operator= (BigInteger &&) noexcept
	Move assignment operator.
	~BigInteger ()
	Destructor.
BigInteger &	operator= (const BigInteger &)
	Copies another BigInteger onto this one.
void	swapWith (BigInteger &) noexcept
	Swaps the internal contents of this with another object.
bool	operator[] (int bit) const noexcept
	Returns the value of a specified bit in the number.
bool	isZero () const noexcept
	Returns true if no bits are set.
bool	isOne () const noexcept
	Returns true if the value is 1.
int	toInteger () const noexcept
	Attempts to get the lowest 32 bits of the value as an integer.
int64	toInt64 () const noexcept
	Attempts to get the lowest 64 bits of the value as an integer.
BigInteger &	clear () noexcept
	Resets the value to 0.
BigInteger &	clearBit (int bitNumber) noexcept
	Clears a particular bit in the number.
BigInteger &	setBit (int bitNumber)
	Sets a specified bit to 1.
BigInteger &	setBit (int bitNumber, bool shouldBeSet)
	Sets or clears a specified bit.
BigInteger &	setRange (int startBit, int numBits, bool shouldBeSet)
	Sets a range of bits to be either on or off.
BigInteger &	insertBit (int bitNumber, bool shouldBeSet)
	Inserts a bit an a given position, shifting up any bits above it.
BigInteger	getBitRange (int startBit, int numBits) const
	Returns a range of bits as a new BigInteger.
uint32	getBitRangeAsInt (int startBit, int numBits) const noexcept
	Returns a range of bits as an integer value.
BigInteger &	setBitRangeAsInt (int startBit, int numBits, uint32 valueToSet)
	Sets a range of bits to an integer value.
BigInteger &	shiftBits (int howManyBitsLeft, int startBit)
	Shifts a section of bits left or right.
int	countNumberOfSetBits () const noexcept
	Returns the total number of set bits in the value.
int	findNextSetBit (int startIndex) const noexcept
	Looks for the index of the next set bit after a given starting point.
int	findNextClearBit (int startIndex) const noexcept
	Looks for the index of the next clear bit after a given starting point.
int	getHighestBit () const noexcept
	Returns the index of the highest set bit in the number.
bool	isNegative () const noexcept
	Returns true if the value is less than zero.
void	setNegative (bool shouldBeNegative) noexcept
	Changes the sign of the number to be positive or negative.
void	negate () noexcept
	Inverts the sign of the number.
BigInteger &	operator+= (const BigInteger &)
BigInteger &	operator-= (const BigInteger &)
BigInteger &	operator*= (const BigInteger &)
BigInteger &	operator/= (const BigInteger &)
BigInteger &	operator|= (const BigInteger &)
BigInteger &	operator&= (const BigInteger &)
BigInteger &	operator^= (const BigInteger &)
BigInteger &	operator%= (const BigInteger &)
BigInteger &	operator<<= (int numBitsToShift)
BigInteger &	operator>>= (int numBitsToShift)
BigInteger &	operator++ ()
BigInteger &	operator-- ()
BigInteger	operator++ (int)
BigInteger	operator-- (int)
BigInteger	operator- () const
BigInteger	operator+ (const BigInteger &) const
BigInteger	operator- (const BigInteger &) const
BigInteger	operator* (const BigInteger &) const
BigInteger	operator/ (const BigInteger &) const
BigInteger	operator| (const BigInteger &) const
BigInteger	operator& (const BigInteger &) const
BigInteger	operator^ (const BigInteger &) const
BigInteger	operator% (const BigInteger &) const
BigInteger	operator<< (int numBitsToShift) const
BigInteger	operator>> (int numBitsToShift) const
bool	operator== (const BigInteger &) const noexcept
bool	operator!= (const BigInteger &) const noexcept
bool	operator< (const BigInteger &) const noexcept
bool	operator<= (const BigInteger &) const noexcept
bool	operator> (const BigInteger &) const noexcept
bool	operator>= (const BigInteger &) const noexcept
int	compare (const BigInteger &other) const noexcept
	Does a signed comparison of two BigIntegers.
int	compareAbsolute (const BigInteger &other) const noexcept
	Compares the magnitudes of two BigIntegers, ignoring their signs.
void	divideBy (const BigInteger &divisor, BigInteger &remainder)
	Divides this value by another one and returns the remainder.
BigInteger	findGreatestCommonDivisor (BigInteger other) const
	Returns the largest value that will divide both this value and the argument.
void	exponentModulo (const BigInteger &exponent, const BigInteger &modulus)
	Performs a combined exponent and modulo operation.
void	inverseModulo (const BigInteger &modulus)
	Performs an inverse modulo on the value.
void	montgomeryMultiplication (const BigInteger &other, const BigInteger &modulus, const BigInteger &modulusp, int k)
	Performs the Montgomery Multiplication with modulo.
void	extendedEuclidean (const BigInteger &a, const BigInteger &b, BigInteger &xOut, BigInteger &yOut)
	Performs the Extended Euclidean algorithm.
String	toString (int base, int minimumNumCharacters=1) const
	Converts the number to a string.
void	parseString (StringRef text, int base)
	Reads the numeric value from a string.
MemoryBlock	toMemoryBlock () const
	Turns the number into a block of binary data.
void	loadFromMemoryBlock (const MemoryBlock &data)
	Converts a block of raw data into a number.

Detailed Description

An arbitrarily large integer class.

A BigInteger can be used in a similar way to a normal integer, but has no size limit (except for memory and performance constraints).

Negative values are possible, but the value isn't stored as 2s-complement, so be careful if you use negative values and look at the values of individual bits.

Constructor & Destructor Documentation

BigInteger() [1/6]

BigInteger::BigInteger

(

)

Creates an empty BigInteger.

Referenced by BigInteger(), BigInteger(), clear(), clearBit(), compare(), compareAbsolute(), divideBy(), exponentModulo(), extendedEuclidean(), findGreatestCommonDivisor(), getBitRange(), insertBit(), inverseModulo(), montgomeryMultiplication(), operator!=(), operator%(), operator%=(), operator&(), operator&=(), operator*(), operator*=(), operator+(), operator++(), operator++(), operator+=(), operator-(), operator-(), operator--(), operator--(), operator-=(), operator/(), operator/=(), operator<(), operator<<(), operator<<=(), operator<=(), operator=(), operator=(), operator==(), operator>(), operator>=(), operator>>(), operator>>=(), operator^(), operator^=(), operator|(), operator|=(), setBit(), setBit(), setBitRangeAsInt(), setRange(), shiftBits(), swapWith(), and ~BigInteger().

BigInteger() [2/6]

BigInteger::BigInteger

(

uint32

value

)

Creates a BigInteger containing an integer value in its low bits.

The low 32 bits of the number are initialised with this value.

BigInteger() [3/6]

BigInteger::BigInteger

(

int32

value

)

Creates a BigInteger containing an integer value in its low bits.

The low 32 bits of the number are initialised with the absolute value passed in, and its sign is set to reflect the sign of the number.

BigInteger() [4/6]

BigInteger::BigInteger

(

int64

value

)

Creates a BigInteger containing an integer value in its low bits.

The low 64 bits of the number are initialised with the absolute value passed in, and its sign is set to reflect the sign of the number.

BigInteger() [5/6]

BigInteger::BigInteger

(

const BigInteger &

)

Creates a copy of another BigInteger.

References BigInteger().

BigInteger() [6/6]

BigInteger::BigInteger ( BigInteger && )

noexcept

Move constructor.

References BigInteger().

~BigInteger()

BigInteger::~BigInteger

(

)

Destructor.

References BigInteger().

Member Function Documentation

operator=() [1/2]

BigInteger & BigInteger::operator= ( BigInteger && )

noexcept

Move assignment operator.

References BigInteger().

operator=() [2/2]

BigInteger & BigInteger::operator=

(

const BigInteger &

)

Copies another BigInteger onto this one.

References BigInteger().

swapWith()

void BigInteger::swapWith ( BigInteger & )

noexcept

Swaps the internal contents of this with another object.

References BigInteger(), and swapWith().

Referenced by swapWith().

operator[]()

bool BigInteger::operator[] ( int bit ) const

noexcept

Returns the value of a specified bit in the number.

If the index is out-of-range, the result will be false.

isZero()

bool BigInteger::isZero ( ) const

noexcept

Returns true if no bits are set.

References isZero().

Referenced by isZero().

isOne()

bool BigInteger::isOne ( ) const

noexcept

Returns true if the value is 1.

References isOne().

Referenced by isOne().

toInteger()

int BigInteger::toInteger ( ) const

noexcept

Attempts to get the lowest 32 bits of the value as an integer.

If the value is bigger than the integer limits, this will return only the lower bits.

References toInteger().

Referenced by toInteger().

toInt64()

int64 BigInteger::toInt64 ( ) const

noexcept

Attempts to get the lowest 64 bits of the value as an integer.

If the value is bigger than the integer limits, this will return only the lower bits.

References toInt64().

Referenced by toInt64().

clear()

BigInteger & BigInteger::clear ( )

noexcept

Resets the value to 0.

References BigInteger(), and clear().

Referenced by clear().

clearBit()

BigInteger & BigInteger::clearBit ( int bitNumber )

noexcept

Clears a particular bit in the number.

References BigInteger(), and clearBit().

Referenced by clearBit().

setBit() [1/2]

BigInteger & BigInteger::setBit

(

int

bitNumber

)

Sets a specified bit to 1.

References BigInteger(), and setBit().

Referenced by setBit(), and setBit().

setBit() [2/2]

BigInteger & BigInteger::setBit	(	int	bitNumber,
		bool	shouldBeSet )

Sets or clears a specified bit.

References BigInteger(), and setBit().

setRange()

BigInteger & BigInteger::setRange	(	int	startBit,
		int	numBits,
		bool	shouldBeSet )

Sets a range of bits to be either on or off.

Parameters

startBit	the first bit to change
numBits	the number of bits to change
shouldBeSet	whether to turn these bits on or off

References BigInteger(), and setRange().

Referenced by setRange().

insertBit()

BigInteger & BigInteger::insertBit	(	int	bitNumber,
		bool	shouldBeSet )

Inserts a bit an a given position, shifting up any bits above it.

References BigInteger(), and insertBit().

Referenced by insertBit().

getBitRange()

BigInteger BigInteger::getBitRange	(	int	startBit,
		int	numBits ) const

Returns a range of bits as a new BigInteger.

e.g. getBitRangeAsInt (0, 64) would return the lowest 64 bits.

See also

getBitRangeAsInt

References BigInteger(), and getBitRange().

Referenced by getBitRange().

getBitRangeAsInt()

uint32 BigInteger::getBitRangeAsInt ( int startBit, int numBits ) const

noexcept

Returns a range of bits as an integer value.

e.g. getBitRangeAsInt (0, 32) would return the lowest 32 bits.

Asking for more than 32 bits isn't allowed (obviously) - for that, use getBitRange().

References getBitRangeAsInt().

Referenced by getBitRangeAsInt().

setBitRangeAsInt()

BigInteger & BigInteger::setBitRangeAsInt	(	int	startBit,
		int	numBits,
		uint32	valueToSet )

Sets a range of bits to an integer value.

Copies the given integer onto a range of bits, starting at startBit, and using up to numBits of the available bits.

References BigInteger(), and setBitRangeAsInt().

Referenced by setBitRangeAsInt().

shiftBits()

BigInteger & BigInteger::shiftBits	(	int	howManyBitsLeft,
		int	startBit )

Shifts a section of bits left or right.

Parameters

howManyBitsLeft	how far to move the bits (+ve numbers shift it left, -ve numbers shift it right).
startBit	the first bit to affect - if this is > 0, only bits above that index will be affected.

References BigInteger(), and shiftBits().

Referenced by shiftBits().

countNumberOfSetBits()

int BigInteger::countNumberOfSetBits ( ) const

noexcept

Returns the total number of set bits in the value.

References countNumberOfSetBits().

Referenced by countNumberOfSetBits().

findNextSetBit()

int BigInteger::findNextSetBit ( int startIndex ) const

noexcept

Looks for the index of the next set bit after a given starting point.

This searches from startIndex (inclusive) upwards for the first set bit, and returns its index. If no set bits are found, it returns -1.

References findNextSetBit().

Referenced by findNextSetBit().

findNextClearBit()

int BigInteger::findNextClearBit ( int startIndex ) const

noexcept

Looks for the index of the next clear bit after a given starting point.

This searches from startIndex (inclusive) upwards for the first clear bit, and returns its index.

References findNextClearBit().

Referenced by findNextClearBit().

getHighestBit()

int BigInteger::getHighestBit ( ) const

noexcept

Returns the index of the highest set bit in the number.

If the value is zero, this will return -1.

References getHighestBit().

Referenced by getHighestBit().

isNegative()

bool BigInteger::isNegative ( ) const

noexcept

Returns true if the value is less than zero.

See also

setNegative, negate

References isNegative().

Referenced by isNegative().

setNegative()

void BigInteger::setNegative ( bool shouldBeNegative )

noexcept

Changes the sign of the number to be positive or negative.

See also

isNegative, negate

References setNegative().

Referenced by setNegative().

negate()

void BigInteger::negate ( )

noexcept

Inverts the sign of the number.

See also

isNegative, setNegative

References negate().

Referenced by negate().

operator+=()

BigInteger & BigInteger::operator+=

(

const BigInteger &

)

References BigInteger().

operator-=()

BigInteger & BigInteger::operator-=

(

const BigInteger &

)

References BigInteger().

operator*=()

BigInteger & BigInteger::operator*=

(

const BigInteger &

)

References BigInteger().

operator/=()

BigInteger & BigInteger::operator/=

(

const BigInteger &

)

References BigInteger().

operator|=()

BigInteger & BigInteger::operator|=

(

const BigInteger &

)

References BigInteger().

operator&=()

BigInteger & BigInteger::operator&=

(

const BigInteger &

)

References BigInteger().

operator^=()

BigInteger & BigInteger::operator^=

(

const BigInteger &

)

References BigInteger().

operator%=()

BigInteger & BigInteger::operator%=

(

const BigInteger &

)

References BigInteger().

operator<<=()

BigInteger & BigInteger::operator<<=

(

int

numBitsToShift

)

References BigInteger().

operator>>=()

BigInteger & BigInteger::operator>>=

(

int

numBitsToShift

)

References BigInteger().

operator++() [1/2]

BigInteger & BigInteger::operator++

(

)

References BigInteger().

operator--() [1/2]

BigInteger & BigInteger::operator--

(

)

References BigInteger().

operator++() [2/2]

BigInteger BigInteger::operator++

(

int

)

References BigInteger().

operator--() [2/2]

BigInteger BigInteger::operator--

(

int

)

References BigInteger().

operator-() [1/2]

BigInteger BigInteger::operator-

(

)

const

References BigInteger().

operator+()

BigInteger BigInteger::operator+

(

const BigInteger &

)

const

References BigInteger().

operator-() [2/2]

BigInteger BigInteger::operator-

(

const BigInteger &

)

const

References BigInteger().

operator*()

BigInteger BigInteger::operator*

(

const BigInteger &

)

const

References BigInteger().

operator/()

BigInteger BigInteger::operator/

(

const BigInteger &

)

const

References BigInteger().

operator|()

BigInteger BigInteger::operator|

(

const BigInteger &

)

const

References BigInteger().

operator&()

BigInteger BigInteger::operator&

(

const BigInteger &

)

const

References BigInteger().

operator^()

BigInteger BigInteger::operator^

(

const BigInteger &

)

const

References BigInteger().

operator%()

BigInteger BigInteger::operator%

(

const BigInteger &

)

const

References BigInteger().

operator<<()

BigInteger BigInteger::operator<<

(

int

numBitsToShift

)

const

References BigInteger().

operator>>()

BigInteger BigInteger::operator>>

(

int

numBitsToShift

)

const

References BigInteger().

operator==()

bool BigInteger::operator== ( const BigInteger & ) const

noexcept

References BigInteger().

operator!=()

bool BigInteger::operator!= ( const BigInteger & ) const

noexcept

References BigInteger().

operator<()

bool BigInteger::operator< ( const BigInteger & ) const

noexcept

References BigInteger().

operator<=()

bool BigInteger::operator<= ( const BigInteger & ) const

noexcept

References BigInteger().

operator>()

bool BigInteger::operator> ( const BigInteger & ) const

noexcept

References BigInteger().

operator>=()

bool BigInteger::operator>= ( const BigInteger & ) const

noexcept

References BigInteger().

compare()

int BigInteger::compare ( const BigInteger & other ) const

noexcept

Does a signed comparison of two BigIntegers.

Return values are:

• 0 if the numbers are the same
• < 0 if this number is smaller than the other
• > 0 if this number is bigger than the other

References BigInteger(), and compare().

Referenced by compare().

compareAbsolute()

int BigInteger::compareAbsolute ( const BigInteger & other ) const

noexcept

Compares the magnitudes of two BigIntegers, ignoring their signs.

Return values are:

• 0 if the numbers are the same
• < 0 if this number is smaller than the other
• > 0 if this number is bigger than the other

References BigInteger(), and compareAbsolute().

Referenced by compareAbsolute().

divideBy()

void BigInteger::divideBy	(	const BigInteger &	divisor,
		BigInteger &	remainder )

Divides this value by another one and returns the remainder.

This number is divided by other, leaving the quotient in this number, with the remainder being copied to the other BigInteger passed in.

References BigInteger(), and divideBy().

Referenced by divideBy().

findGreatestCommonDivisor()

BigInteger BigInteger::findGreatestCommonDivisor

(

BigInteger

other

)

const

Returns the largest value that will divide both this value and the argument.

References BigInteger(), and findGreatestCommonDivisor().

Referenced by findGreatestCommonDivisor().

exponentModulo()

void BigInteger::exponentModulo	(	const BigInteger &	exponent,
		const BigInteger &	modulus )

Performs a combined exponent and modulo operation.

This BigInteger's value becomes (this ^ exponent) % modulus.

References BigInteger(), and exponentModulo().

Referenced by exponentModulo().

inverseModulo()

void BigInteger::inverseModulo

(

const BigInteger &

modulus

)

Performs an inverse modulo on the value.

i.e. the result is (this ^ -1) mod (modulus).

References BigInteger(), and inverseModulo().

Referenced by inverseModulo().

montgomeryMultiplication()

void BigInteger::montgomeryMultiplication	(	const BigInteger &	other,
		const BigInteger &	modulus,
		const BigInteger &	modulusp,
		int	k )

Performs the Montgomery Multiplication with modulo.

This object is left containing the result value: ((this * other) * R1) % modulus. To get this result, we need modulus, modulusp and k such as R = 2^k, with modulus * modulusp - R * R1 = GCD(modulus, R) = 1

References BigInteger(), and montgomeryMultiplication().

Referenced by montgomeryMultiplication().

extendedEuclidean()

void BigInteger::extendedEuclidean	(	const BigInteger &	a,
		const BigInteger &	b,
		BigInteger &	xOut,
		BigInteger &	yOut )

Performs the Extended Euclidean algorithm.

This method will set the xOut and yOut arguments such that (a * xOut) - (b * yOut) = GCD (a, b). On return, this object is left containing the value of the GCD.

References BigInteger(), and extendedEuclidean().

Referenced by extendedEuclidean().

toString()

String BigInteger::toString	(	int	base,
		int	minimumNumCharacters = 1 ) const

Converts the number to a string.

Specify a base such as 2 (binary), 8 (octal), 10 (decimal), 16 (hex). If minimumNumCharacters is greater than 0, the returned string will be padded with leading zeros to reach at least that length.

References toString().

Referenced by toString().

parseString()

void BigInteger::parseString	(	StringRef	text,
		int	base )

Reads the numeric value from a string.

Specify a base such as 2 (binary), 8 (octal), 10 (decimal), 16 (hex). Any invalid characters will be ignored.

References parseString().

Referenced by parseString().

toMemoryBlock()

MemoryBlock BigInteger::toMemoryBlock

(

)

const

Turns the number into a block of binary data.

The data is arranged as little-endian, so the first byte of data is the low 8 bits of the number, and so on.

See also

loadFromMemoryBlock

References toMemoryBlock().

Referenced by toMemoryBlock().

loadFromMemoryBlock()

void BigInteger::loadFromMemoryBlock

(

const MemoryBlock &

data

)

Converts a block of raw data into a number.

The data is arranged as little-endian, so the first byte of data is the low 8 bits of the number, and so on.

See also

toMemoryBlock

References loadFromMemoryBlock().

Referenced by loadFromMemoryBlock().