mp::mpi Class Reference
[Signed integers]

User class that provides an interface to use signed integers with the MP++ library. More...

#include <mpi.h>

Inheritance diagram for mp::mpi:

List of all members.

Pseudo-random number generator
void	prng (size_type n)
	Generate a pseudo-random number.
static void	prng_seed (limb_long_type seed)
	Set the PRNG seed.
static void	prng_seed (const mpn_ &seed)
	Set the PRNG seed.
Public Types
typedef mp::int_type	int_type
	Type for integer conversion.
typedef mp::size_type	size_type
	Type of index registers.
typedef mp::limb_type	limb_type
	Type of normal limbs.
typedef mp::limb_long_type	limb_long_type
	Type of double-long limbs.
typedef mp::radix_type	radix_type
	Type of radix identifier.
Public Member Functions
	mpi (const mpi_ &n)
	mpi ()
	mpi (int_type n, size_type size=0)
	mpi (const mpi &n, size_type size=0)
	mpi (const std::string &s, radix_type b=0)
void	prime (size_type n)
	Set to a random prime number.
bool	isPrime (int n=_MP_RM_TESTS)
	Primality testing.
int_type	toInt () const
	Conversion to standard signed integer type.
int	compare (const mpi_ &n) const
	Compare two MPIs.
void	checkNeg ()
	Makes sure no -0 condition can exist.
void	setUse ()
	Sets the local use_ variable after an operation.
Conversion operators
	operator int_type () const
	operator std::string () const
Assignment overloads
const mpi &	operator= (int_type n)
const mpi &	operator= (const mpi &n)
const mpi &	operator= (const std::string &s)
Bit shifting assignment overloads
const mpi &	operator<<= (size_type y)
const mpi &	operator>>= (size_type y)
Bitwise assignment overloads
const mpi &	operator &= (const mpi &n)
const mpi &	operator|= (const mpi &n)
const mpi &	operator^= (const mpi &n)
mpi	operator~ ()
Increment & decrement overloads
mpi &	operator++ ()
const mpi	operator++ (int)
mpi &	operator-- ()
const mpi	operator-- (int)
Arithmetic assignment overloads
const mpi &	operator+= (const mpi &n)
const mpi &	operator-= (const mpi &n)
const mpi &	operator *= (const mpi &n)
const mpi &	operator/= (const mpi &n)
const mpi &	operator%= (const mpi &n)
Initialization and basic alteration
void	init (int_type n, size_type size=0)
	Initialization to signed integer.
void	init (const mpi_ &n, size_type size=0)
	Initialization to an MPI.
void	clear ()
	Resets the number.
void	resize (size_type size)
	Resizes to size bits.
void	swap (mpi_ &n)
	Swaps this with n.
Initialization and basic alteration
void	init (limb_type n, size_type size=0)
	Initialization to single limb.
void	init (const mpn_ &n, size_type size=0)
	Initialization to MPN.
void	swap (mpn_ &n)
	Swaps this with n.
Information retreval
bool	isNeg () const
	Is the number negative?
size_type	size () const
	Find the number of bits in use.
String conversion
void	setString (const std::string &s, radix_type b=0)
	String input.
std::string	getString (radix_type b=string_base) const
	String output.
Bit shifting
void	shift_l (size_type n)
	Left shift.
void	shift_r (size_type n)
	Right shift.
Debugging output
void	print () const
	Binary dump to stdout.
Algebraic functions
void	add (const mpi_ &n)
	Addition of an MPI.
void	sub (const mpi_ &n)
	Subtraction of an MPI.
void	mul (const mpi_ &n)
	Multiplication by an MPI.
void	div (const mpi_ &n)
	Division by an MPI.
void	mod (const mpi_ &n)
	Modulus by an MPI.
Algebraic functions
void	add (const mpn_ &n)
	Addition of an MPN.
void	sub (const mpn_ &n)
	Subtraction of an MPN.
void	mul (const mpn_ &n)
	Multiplication by an MPN.
void	div_mod (mpn_ &n)
	Division by an MPN.
Additional arithmetic operations
void	negate ()
	Flips the sign register, AKA negates.
void	abs ()
	Clears the sign register, AKA takes the absolute value.
void	sqr ()
	Squares the number efficiantly.
mpi_	pow (int_type e) const
	Exponentation.
mpi_	pow_mod (const mpi_ &e, const mpi_ &m) const
	Performs modular exponentiation.
Comparison
int	compare (const mpn_ &n) const
	Compare two MPNs.
Information retreval
bool	isZero () const
	Is the number zero?
size_type	low_zeros () const
	Returns number of consecutive zero limbs, starting at the lowest limb.
Raw accessors
Data format is
raw_type	getRaw () const
	Raw data output.
void	setRaw (const raw_type &data)
	Raw data input.
Limb retreval overloads
Subscript operator is overloaded to allow users to interact with the individual limbs of a number in a safe way.
const limb_type &	operator[] (size_type i) const
	Const limb retreval.
limb_type &	operator[] (size_type i)
	Limb retreval and writing.
Bitwise functions
size_type	popcount () const
	Population count.
void	bitwise (const mpn_ &y, int type)
	Binary bitwise operations.
void	bitwise_not ()
	Bitwise not operation.
Static Public Member Functions
static const byte	capabilities ()
	A bitmask of this class' numerical and functional capabilities.
static void	setDefaultBase (radix_type b)
	Sets the default base for string conversion.
static radix_type	getDefaultBase ()
	Gets the default base for string conversion.
static void	interrupt ()
	Interrupt the next main (math, string, PRNG) operation that runs.
Static Public Attributes
static const size_type	limb_size_bits = _MP_SIZE / 2
	Size of a single limb (in bits).
static const limb_type	limb_full = (1 << limb_size_bits) - 1
	A limb with all bits set.
static const size_type	size_max = INT_MAX
	The largest positive size_type value.
static const std::string	string_digits = _MP_STR_DIGIT
	The digits used in string conversion.
Protected Member Functions
void	onInterrupt () const
	Activated when interrupt register is set.
Algebraic functions with single limbs
These are much faster than the normal algebraic functions, and are called anyway if the argument fits within a single limb.
void	add_l (limb_type n)
	Addition of a single limb.
void	sub_l (limb_type n)
	Subtraction of a single limb.
void	mul_l (limb_type n)
	Multiplacation by a single limb.
void	div_mod_l (limb_type &n)
	Division by a single limb.
Protected Attributes
bool	neg_
	negativity register (true if negative).
size_type	alloc_
	Number of limbs allocated, pointed to by data.
size_type	use_
	Number of limbs used (always <= alloc).
limb_type *	data_
	Pointer to the data.
Static Protected Attributes
static radix_type	string_base = _MP_STR_BASE
	Default base for string conversion.
static bool	interrupted
	Interrupt register.

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Detailed Description

User class that provides an interface to use signed integers with the MP++ library.

All standard arithmetic, logical, conversion, and comparison operators are overloaded, so no knowledge of the underlying functions is required.

Most overloads function just as if operating on standard signed integer types, except that there is no chance (within the available heap) of overflow.

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Member Typedef Documentation

typedef mp::int_type mp::mpi_::int_type [inherited]

Type for integer conversion.

typedef mp::limb_long_type mp::mpn_::limb_long_type [inherited]

Type of double-long limbs.

typedef mp::limb_type mp::mpn_::limb_type [inherited]

Type of normal limbs.

typedef mp::radix_type mp::mpn_::radix_type [inherited]

Type of radix identifier.

typedef mp::size_type mp::mpn_::size_type [inherited]

Type of index registers.

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Constructor & Destructor Documentation

mp::mpi::mpi (  const mpi_ &  n  )  [inline]

mp::mpi::mpi (   )  [inline]

mp::mpi::mpi (  int_type  n, size_type  size = 0 )  [inline]

mp::mpi::mpi (  const mpi &  n, size_type  size = 0 )  [inline]

mp::mpi::mpi (  const std::string &  s, radix_type  b = 0 )  [inline]

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Member Function Documentation

void mp::mpi_::abs (   )  [inherited]

Clears the sign register, AKA takes the absolute value.

void mp::mpn_::add (  const mpn_ &  n  )  [inherited]

Addition of an MPN. Parameters: n  Number to add

void mp::mpi_::add (  const mpi_ &  n  )  [inherited]

Addition of an MPI. Parameters: n  Number to add

void mp::mpn_::add_l (  limb_type  n  )  [protected, inherited]

Addition of a single limb. Parameters: n  Limb to add

void mp::mpn_::bitwise (  const mpn_ &  y, int  type )  [inherited]

Binary bitwise operations. Parameters: y  Second parameter of the operation type  Type of bitwise operation to perform 1: AND 2: OR 3: XOR

void mp::mpn_::bitwise_not (   )  [inherited]

Bitwise not operation. Operates on chunks of bytes, so that a not of a not is equal to the origional.

const byte mp::mpi_::capabilities (   )  [static, inherited]

A bitmask of this class' numerical and functional capabilities. Reimplemented from mp::mpn_. Reimplemented in mp::mpf_.

void mp::mpi_::checkNeg (   )  [inherited]

Makes sure no -0 condition can exist.

void mp::mpi_::clear (   )  [inherited]

Resets the number. Reimplemented from mp::mpn_. Reimplemented in mp::mpf_.

int mp::mpn_::compare (  const mpn_ &  n  )  const [inherited]

Compare two MPNs. Parameters: n  Number to compare with Returns: sign(this - n)

int mp::mpi_::compare (  const mpi_ &  n  )  const [inherited]

Compare two MPIs. Parameters: n  Number to compare with Returns: sign(this - n)

void mp::mpi_::div (  const mpi_ &  n  )  [inherited]

Division by an MPI. Parameters: n  Number to divide by. If 0, a range_error exception is thrown.

void mp::mpn_::div_mod (  mpn_ &  n  )  [inherited]

Division by an MPN. Parameters: n  Divisor and remainder storage. If less than 0, a range_error is thrown.

void mp::mpn_::div_mod_l (  limb_type &  n  )  [protected, inherited]

Division by a single limb. Parameters: n  Divisor and remainder storage. If less than 0, a range_error is thrown.

radix_type mp::mpi_::getDefaultBase (   )  [static, inherited]

Gets the default base for string conversion. Returns: Current default string base

raw_type mp::mpn_::getRaw (   )  const [inherited]

Raw data output.

string mp::mpi_::getString (  radix_type  b = string_base  )  const [inherited]

String output. Converts number to a string in base b. Parameters: b  Base of the output string. If less than 2 or greater than the number of available conversion digits, an out_of_range exception is thrown. Returns: Output string Reimplemented from mp::mpn_. Reimplemented in mp::mpf_.

void mp::mpn_::init (  const mpn_ &  n, size_type  size = 0 )  [inherited]

Initialization to MPN. MPN is truncated or padded with zeros in the to fit the size. Parameters: n  Number to which this is initialized size  Size of the result, in limbs. If 0, size is set to 1. If less than 0, an out_of_range exception is thrown.

void mp::mpn_::init (  limb_type  n, size_type  size = 0 )  [inherited]

Initialization to single limb. MPN is padded with zeros to fit the size. Parameters: n  Number to which this is initialized size  Size of the result, in limbs. If 0, size is set to 1. If less than 0, an out_of_range exception is thrown.

void mp::mpi_::init (  const mpi_ &  n, size_type  size = 0 )  [inherited]

Initialization to an MPI. MPI is truncated or padded with zeros to fit the size. Parameters: n  Number to which this is initialized. If self is argument, a runtime_error is thrown. size  Minimum size of the result, in bits. If 0, size is set to the input's size. If less than 0, an out_of_range exception is thrown. Reimplemented in mp::mpf_.

void mp::mpi_::init (  int_type  n, size_type  size = 0 )  [inherited]

Initialization to signed integer. MPI is padded with zeros to fit the size. Parameters: n  Number to which this is initialized size  Minimum size of the result, in bits. If 0, size is set to mpi_::limb_size. If less than 0, an out_of_range exception is thrown. Reimplemented in mp::mpf_.

void mp::mpn_::interrupt (   )  [static, inherited]

Interrupt the next main (math, string, PRNG) operation that runs.

bool mp::mpi_::isNeg (   )  const [inherited]

Is the number negative? Returns: True if the number is negative

bool mp::mpi::isPrime (  int  n = _MP_RM_TESTS  )

Primality testing. Uses the Rabin-Miller probabilistic test to determine if a number is likely prime or not. Parameters: n  Number of iterations of the probabilistic test. If less than 1, an out_of_range exception is thrown. Returns: True if the number is likely prime

bool mp::mpn_::isZero (   )  const [inherited]

Is the number zero? Returns: True if the number is zero

mpn_::size_type mp::mpn_::low_zeros (   )  const [inherited]

Returns number of consecutive zero limbs, starting at the lowest limb.

void mp::mpi_::mod (  const mpi_ &  n  )  [inherited]

Modulus by an MPI. Parameters: n  Number to divide by. If 0, a range_error exception is thrown.

void mp::mpn_::mul (  const mpn_ &  n  )  [inherited]

Multiplication by an MPN. Parameters: n  Number to multiply by

void mp::mpi_::mul (  const mpi_ &  n  )  [inherited]

Multiplication by an MPI. Parameters: n  Number to multiply by

void mp::mpn_::mul_l (  limb_type  n  )  [protected, inherited]

Multiplacation by a single limb. Parameters: n  Limb to multiply by

void mp::mpi_::negate (   )  [inherited]

Flips the sign register, AKA negates.

void mp::mpn_::onInterrupt (   )  const [protected, inherited]

Activated when interrupt register is set. Throws a runtime_error to break the execution of a main (math, string handling, PRNG) function.

const mpi & mp::mpi::operator &= (  const mpi &  n  )

const mpi & mp::mpi::operator *= (  const mpi &  n  )

mp::mpi::operator int_type (   )  const [inline]

mp::mpi::operator std::string (   )  const [inline]

const mpi & mp::mpi::operator%= (  const mpi &  n  )

const mpi mp::mpi::operator++ (  int   )

mpi & mp::mpi::operator++ (   )

const mpi & mp::mpi::operator+= (  const mpi &  n  )

const mpi mp::mpi::operator-- (  int   )

mpi & mp::mpi::operator-- (   )

const mpi & mp::mpi::operator-= (  const mpi &  n  )

const mpi & mp::mpi::operator/= (  const mpi &  n  )

const mpi & mp::mpi::operator<<= (  size_type  y  )

const mpi & mp::mpi::operator= (  const std::string &  s  )

const mpi & mp::mpi::operator= (  const mpi &  n  )

const mpi & mp::mpi::operator= (  int_type  n  )

const mpi & mp::mpi::operator>>= (  size_type  y  )

mpn_::limb_type & mp::mpn_::operator[] (  size_type  i  )  [inherited]

Limb retreval and writing. Parameters: i  Index of limb. If less than 0, an out_of_range exception is thrown.

const mpn_::limb_type & mp::mpn_::operator[] (  size_type  i  )  const [inherited]

Const limb retreval. Parameters: i  Index of limb. If less than 0, an out_of_range exception is thrown.

const mpi & mp::mpi::operator^= (  const mpi &  n  )

const mpi & mp::mpi::operator|= (  const mpi &  n  )

mpi mp::mpi::operator~ (   )

mpn_::size_type mp::mpn_::popcount (   )  const [inherited]

Population count. Returns: Number of set bits

mpi_ mp::mpi_::pow (  int_type  e  )  const [inherited]

Exponentation. Takes the number to a basic signed integer power. The exponant is limited because the number would overflow if allowed to be any larger. Parameters: e  Exponant in powering operation

mpi_ mp::mpi_::pow_mod (  const mpi_ &  e, const mpi_ &  m )  const [inherited]

Performs modular exponentiation. The result is equivalent to the expression: (this ^ p) m Parameters: e  Exponant in powering operation m  Divisor in modulus operation

void mp::mpi::prime (  size_type  n  )

Set to a random prime number. Parameters: n  Minimum size, in bits, of result

void mp::mpi_::print (   )  const [inherited]

Binary dump to stdout. Includes sign and size information. Reimplemented from mp::mpn_. Reimplemented in mp::mpf_.

void mp::mpn_::prng (  size_type  n  )  [inherited]

Generate a pseudo-random number. Parameters: n  Number of random bits to generate

void mp::mpn_::prng_seed (  const mpn_ &  seed  )  [static, inherited]

Set the PRNG seed. Parameters: seed  Seed for the PRNG

void mp::mpn_::prng_seed (  limb_long_type  seed  )  [static, inherited]

Set the PRNG seed. Parameters: seed  Seed for the PRNG

void mp::mpi_::resize (  size_type  size  )  [inherited]

Resizes to size bits. Adds upper zeros or destroys upper bits as necessary. Parameters: size  Size of the result, in bits Reimplemented from mp::mpn_.

void mp::mpi_::setDefaultBase (  radix_type  b  )  [static, inherited]

Sets the default base for string conversion. Parameters: b  Base to set as default. If less than 2 or greater than the number of available conversion digits, an out_of_range exception is thrown.

void mp::mpn_::setRaw (  const raw_type &  data  )  [inherited]

Raw data input.

void mp::mpi_::setString (  const std::string &  s, radix_type  b = 0 )  [inherited]

String input. Converts the input string in base b to an MPI. Parameters: s  Input string b  Base of the input string. If zero, base is guessed using the first few digits of the input string. If less than 2 or greater than the number of available conversion digits, an out_of_range exception is thrown. Reimplemented from mp::mpn_. Reimplemented in mp::mpf_.

void mp::mpn_::setUse (   )  [inherited]

Sets the local use_ variable after an operation. Not necessary for users unless twiddling with individual limbs.

void mp::mpi_::shift_l (  size_type  n  )  [inherited]

Left shift. Non-destructively shifts left n bits, AKA "multiplication by 2 ^\a n". Parameters: n  Number of bits to shift. If less than 0, right shift. Reimplemented from mp::mpn_.

void mp::mpi_::shift_r (  size_type  n  )  [inherited]

Right shift. Destructively shifts right n bits, AKA "integer division by 2 ^\a n". Parameters: n  Number of bits to shift. If less than 0, left shift. Reimplemented from mp::mpn_.

mpi_::size_type mp::mpi_::size (   )  const [inherited]

Find the number of bits in use. Returns: The minimum number of bits required to store the number Reimplemented from mp::mpn_.

void mp::mpi_::sqr (   )  [inherited]

Squares the number efficiantly. Reimplemented from mp::mpn_. Reimplemented in mp::mpf_.

void mp::mpn_::sub (  const mpn_ &  n  )  [inherited]

Subtraction of an MPN. Parameters: n  Number to subtract

void mp::mpi_::sub (  const mpi_ &  n  )  [inherited]

Subtraction of an MPI. Parameters: n  Number to subtract

void mp::mpn_::sub_l (  limb_type  n  )  [protected, inherited]

Subtraction of a single limb. Parameters: n  Limb to subtract

void mp::mpn_::swap (  mpn_ &  n  )  [inherited]

Swaps this with n. This swaps the internals of the number, so it is very fast. A fast move can be done by clear()ing the destination before swap()ing. Parameters: n  Number to swap with

void mp::mpi_::swap (  mpi_ &  n  )  [inherited]

Swaps this with n. Function swaps the internals of the number, so it is very fast. A fast move can be done by clear()ing the destination before swap()ing. Parameters: n  Number to swap with

int_type mp::mpi_::toInt (   )  const [inherited]

Conversion to standard signed integer type. If number is too large to fit in standard integer an overflow_error exception is thrown. Returns: Standard signed integer representation of the number Reimplemented in mp::mpf_.

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Member Data Documentation

size_type mp::mpn_::alloc_ [protected, inherited]

Number of limbs allocated, pointed to by data.

limb_type* mp::mpn_::data_ [protected, inherited]

Pointer to the data.

bool mp::mpn_::interrupted [static, protected, inherited]

Interrupt register.

const mpn_::limb_type mp::mpn_::limb_full = (1 << limb_size_bits) - 1 [static, inherited]

A limb with all bits set.

const mpn_::size_type mp::mpn_::limb_size_bits = _MP_SIZE / 2 [static, inherited]

Size of a single limb (in bits).

bool mp::mpi_::neg_ [protected, inherited]

negativity register (true if negative).

const mpn_::size_type mp::mpn_::size_max = INT_MAX [static, inherited]

The largest positive size_type value.

radix_type mp::mpi_::string_base = _MP_STR_BASE [static, protected, inherited]

Default base for string conversion.

const string mp::mpn_::string_digits = _MP_STR_DIGIT [static, inherited]

The digits used in string conversion.

size_type mp::mpn_::use_ [protected, inherited]

Number of limbs used (always <= alloc).

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

• mpi.h
• mpi/user_math.cpp
• mpi/user_mpi.cpp
• mpi/user_prime.cpp
• mpi/user_str.cpp

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