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Public Member Functions | List of all members
BigInteger Class Reference
juce_core » maths

An arbitrarily large integer class. More...

`#include <juce_BigInteger.h>`

## 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.

## ◆ 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.

## ◆ BigInteger() [6/6]

BigInteger::BigInteger | ( | BigInteger && |  | ) |
| noexcept

Move constructor.

## ◆ ~BigInteger()

BigInteger::~BigInteger | ( |  | ) |

Destructor.

## Member Function Documentation

## ◆ operator=() [1/2]

BigInteger & BigInteger::operator= | ( | BigInteger && |  | ) |
| noexcept

Move assignment operator.

## ◆ operator=() [2/2]

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

Copies another BigInteger onto this one.

## ◆ swapWith()

void BigInteger::swapWith | ( | BigInteger & |  | ) |
| noexcept

Swaps the internal contents of this with another object.

## ◆ 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.

## ◆ isOne()

bool BigInteger::isOne | ( |  | ) | const
| noexcept

Returns true if the value is 1.

## ◆ 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.

## ◆ 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.

## ◆ clear()

BigInteger & BigInteger::clear | ( |  | ) |
| noexcept

Resets the value to 0.

## ◆ clearBit()

BigInteger & BigInteger::clearBit | ( | int | bitNumber | ) |
| noexcept

Clears a particular bit in the number.

## ◆ setBit() [1/2]

BigInteger & BigInteger::setBit | ( | int | bitNumber | ) |

Sets a specified bit to 1.

## ◆ setBit() [2/2]

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

Sets or clears a specified bit.

## ◆ 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

## ◆ insertBit()

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

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

## ◆ 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

## ◆ 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().

## ◆ 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.

## ◆ 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.

## ◆ countNumberOfSetBits()

int BigInteger::countNumberOfSetBits | ( |  | ) | const
| noexcept

Returns the total number of set bits in the value.

## ◆ 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.

## ◆ 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.

## ◆ 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.

## ◆ isNegative()

bool BigInteger::isNegative | ( |  | ) | const
| noexcept

Returns true if the value is less than zero.

See also
  setNegative, negate

## ◆ setNegative()

void BigInteger::setNegative | ( | bool | shouldBeNegative | ) |
| noexcept

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

See also
  isNegative, negate

## ◆ negate()

void BigInteger::negate | ( |  | ) |
| noexcept

Inverts the sign of the number.

See also
  isNegative, setNegative

## ◆ operator+=()

BigInteger & BigInteger::operator+= | ( | const BigInteger & |  | ) |

## ◆ operator-=()

BigInteger & BigInteger::operator-= | ( | const BigInteger & |  | ) |

## ◆ operator*=()

BigInteger & BigInteger::operator*= | ( | const BigInteger & |  | ) |

## ◆ operator/=()

BigInteger & BigInteger::operator/= | ( | const BigInteger & |  | ) |

## ◆ operator|=()

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

## ◆ operator&=()

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

## ◆ operator^=()

BigInteger & BigInteger::operator^= | ( | const BigInteger & |  | ) |

## ◆ operator%=()

BigInteger & BigInteger::operator%= | ( | const BigInteger & |  | ) |

## ◆ operator<<=()

BigInteger & BigInteger::operator<<= | ( | int | numBitsToShift | ) |

## ◆ operator>>=()

BigInteger & BigInteger::operator>>= | ( | int | numBitsToShift | ) |

## ◆ operator++() [1/2]

BigInteger & BigInteger::operator++ | ( |  | ) |

## ◆ operator--() [1/2]

BigInteger & BigInteger::operator-- | ( |  | ) |

## ◆ operator++() [2/2]

BigInteger BigInteger::operator++ | ( | int |  | ) |

## ◆ operator--() [2/2]

BigInteger BigInteger::operator-- | ( | int |  | ) |

## ◆ operator-() [1/2]

BigInteger BigInteger::operator- | ( |  | ) | const

## ◆ operator+()

BigInteger BigInteger::operator+ | ( | const BigInteger & |  | ) | const

## ◆ operator-() [2/2]

BigInteger BigInteger::operator- | ( | const BigInteger & |  | ) | const

## ◆ operator*()

BigInteger BigInteger::operator* | ( | const BigInteger & |  | ) | const

## ◆ operator/()

BigInteger BigInteger::operator/ | ( | const BigInteger & |  | ) | const

## ◆ operator|()

BigInteger BigInteger::operator| | ( | const BigInteger & |  | ) | const

## ◆ operator&()

BigInteger BigInteger::operator& | ( | const BigInteger & |  | ) | const

## ◆ operator^()

BigInteger BigInteger::operator^ | ( | const BigInteger & |  | ) | const

## ◆ operator%()

BigInteger BigInteger::operator% | ( | const BigInteger & |  | ) | const

## ◆ operator<<()

BigInteger BigInteger::operator<< | ( | int | numBitsToShift | ) | const

## ◆ operator>>()

BigInteger BigInteger::operator>> | ( | int | numBitsToShift | ) | const

## ◆ operator==()

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

## ◆ operator!=()

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

## ◆ operator<()

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

## ◆ operator<=()

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

## ◆ operator>()

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

## ◆ operator>=()

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

## ◆ 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

## ◆ 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

## ◆ 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.

## ◆ findGreatestCommonDivisor()

BigInteger BigInteger::findGreatestCommonDivisor | ( | BigInteger | other | ) | const

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

## ◆ 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.

## ◆ inverseModulo()

void BigInteger::inverseModulo | ( | const BigInteger & | modulus | ) |

Performs an inverse modulo on the value.

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

## ◆ 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

## ◆ 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.

## ◆ 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.

## ◆ 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.

## ◆ 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

## ◆ 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

The documentation for this class was generated from the following file:

- juce_BigInteger.h