Graphe d'héritage de Base:

Fonctions membres publiques statiques
static	isValidEngine ()

Fonctions membres publiques statiques hérités de PHP
static	subtractHelper (array $x_value, $x_negative, array $y_value, $y_negative)

static	scan1divide (PHP $r)

Fonctions membres publiques statiques hérités de Engine
static	setModExpEngine ($engine)

static	minMaxBits ($bits)

Champs de données
const	VARIABLE = 0

const	DATA = 1

Champs de données hérités de PHP
const	VALUE = 0

const	SIGN = 1

const	KARATSUBA_CUTOFF = 25

const	FAST_BITWISE = true

const	ENGINE_DIR = 'PHP'

Champs de données hérités de Engine
const	PRIMES

Fonctions membres protégées statiques
static	powModHelper (PHP $x, PHP $e, PHP $n, $class)

static	prepareReduce (array $x, array $n, $class)

static	multiplyReduce (array $x, array $y, array $n, $class)

static	squareReduce (array $x, array $n, $class)

Fonctions membres protégées statiques hérités de PHP
static	addHelper (array $x_value, $x_negative, array $y_value, $y_negative)

static	multiplyHelper (array $x_value, $x_negative, array $y_value, $y_negative)

static	regularMultiply (array $x_value, array $y_value)

static	compareHelper (array $x_value, $x_negative, array $y_value, $y_negative)

static	trim (array $value)

static	array_repeat ($input, $multiplier)

static	square (array $x)

static	baseSquare (array $value)

static	karatsubaSquare (array $value)

Fonctions membres protégées statiques hérités de Engine
static	setBitmask ($bits)

static	base256_lshift (&$x, $shift)

static	slidingWindow (Engine $x, Engine $e, Engine $n, $class)

static	randomRangePrimeOuter (Engine $min, Engine $max)

static	randomRangeHelper (Engine $min, Engine $max)

static	randomRangePrimeInner (Engine $x, Engine $min, Engine $max)

static	minHelper (array $nums)

static	maxHelper (array $nums)

Membres hérités additionnels
Fonctions membres publiques hérités de PHP
	__construct ($x=0, $base=10)

	toString ()

	toBytes ($twos_compliment=false)

	abs ()

	bitwise_rightShift ($shift)

	bitwise_leftShift ($shift)

	isOdd ()

	testBit ($x)

	isNegative ()

	negate ()

	bitwise_split ($split)

Fonctions membres publiques hérités de Engine
	__construct ($x=0, $base=10)

	toHex ($twos_compliment=false)

	toBits ($twos_compliment=false)

	__sleep ()

	__wakeup ()

	jsonSerialize ()

	__toString ()

	__debugInfo ()

	setPrecision ($bits)

	getPrecision ()

	bitwise_not ()

	bitwise_leftRotate ($shift)

	bitwise_rightRotate ($shift)

	getLength ()

	getLengthInBytes ()

	isPrime ($t=false)

	root ($n=2)

	createRecurringModuloFunction ()

	bitwise_split ($split)

Fonctions membres protégées hérités de PHP
	initialize ($base)

	pad ($str)

	divideHelper (PHP $y)

	convertToObj (array $arr)

	normalize (PHP $result)

	lshift ($shift)

	rshift ($shift)

	powModInner (PHP $e, PHP $n)

	make_odd ()

	testSmallPrimes ()

	powHelper (PHP $n)

Fonctions membres protégées hérités de Engine
	toBytesHelper ()

	powModOuter (Engine $e, Engine $n)

	setupIsPrime ()

	testPrimality ($t)

	rootHelper ($n)

	rootInner ($n)

	extendedGCDHelper (Engine $n)

	bitwiseAndHelper (Engine $x)

	bitwiseOrHelper (Engine $x)

	bitwiseXorHelper (Engine $x)

Attributs protégés hérités de Engine
	$value

	$is_negative

	$precision = -1

	$bitmask = false

	$reduce

	$hex

Attributs protégés statiques hérités de Engine
static	$zero = []

static	$one = []

static	$two = []

static	$modexpEngine

static	$isValidEngine

Documentation des fonctions membres

◆ isValidEngine()

static isValidEngine ( )

static

Test for engine validity

Renvoie: bool

Références class.

◆ multiplyReduce()

static multiplyReduce	(	array	$x,
		array	$y,
		array	$n,
			$class
	)

staticprotected

Modular multiply

Paramètres

array	$x
array	$y
array	$n
string	$class

Voir également: self::slidingWindow()

Renvoie: array

Références $class, $n, et $temp.

◆ powModHelper()

static powModHelper	(	PHP	$x,
		PHP	$e,
		PHP	$n,
			$class
	)

staticprotected

Performs modular exponentiation.

The most naive approach to modular exponentiation has very unreasonable requirements, and and although the approach involving repeated squaring does vastly better, it, too, is impractical for our purposes. The reason being that division - by far the most complicated and time-consuming of the basic operations (eg. +,-,*,/) - occurs multiple times within it.

Modular reductions resolve this issue. Although an individual modular reduction takes more time then an individual division, when performed in succession (with the same modulo), they're a lot faster.

The two most commonly used modular reductions are Barrett and Montgomery reduction. Montgomery reduction, although faster, only works when the gcd of the modulo and of the base being used is 1. In RSA, when the base is a power of two, the modulo - a product of two primes - is always going to have a gcd of 1 (because the product of two odd numbers is odd), but what about when RSA isn't used?

In contrast, Barrett reduction has no such constraint. As such, some bigint implementations perform a Barrett reduction after every operation in the modpow function. Others perform Barrett reductions when the modulo is even and Montgomery reductions when the modulo is odd. BigInteger.java's modPow method, however, uses a trick involving the Chinese Remainder Theorem to factor the even modulo into two numbers - one odd and the other, a power of two - and recombine them, later. This is the method that this modPow function uses. Montgomery Reduction with Even Modulus elaborates.

Paramètres

PHP	$x
PHP	$e
PHP	$n
string	$class

Renvoie: PHP

Références $class, $n, $temp, et PHP\normalize().

Référencé par PHP\powModInner().

◆ prepareReduce()

static prepareReduce	(	array	$x,
		array	$n,
			$class
	)

staticprotected

Modular reduction preparation

Paramètres

array	$x
array	$n
string	$class

Voir également: self::slidingWindow()

Renvoie: array

Références $class, et $n.

◆ squareReduce()

static squareReduce	(	array	$x,
		array	$n,
			$class
	)

staticprotected

Modular square

Paramètres

array	$x
array	$n
string	$class

Voir également: self::slidingWindow()

Renvoie: array

Références $class, et $n.

Documentation des champs

◆ DATA

const DATA = 1

$cache[self::DATA] contains the cached data.

private

◆ VARIABLE

const VARIABLE = 0

Cache constants

$cache[self::VARIABLE] tells us whether or not the cached data is still valid.

private

La documentation de cette classe a été générée à partir du fichier suivant :

Math/BigInteger/Engines/PHP/Base.php

Fonctions membres publiques statiques

Champs de données

Fonctions membres protégées statiques

Membres hérités additionnels

Documentation des fonctions membres

◆ isValidEngine()

◆ multiplyReduce()

◆ powModHelper()

◆ prepareReduce()

◆ squareReduce()

Documentation des champs

◆ DATA

◆ VARIABLE