Pure-PHP 64-bit Engine.
Uses 64-bit integers if int size is 8 bits
| author | Jim Wigginton terrafrost@php.net |
|---|---|
| package | Default |
__construct(integer|\phpseclib3\Math\BigInteger\Engines\numeric-string $x,integer $base = 10)
integer|\phpseclib3\Math\BigInteger\Engines\numeric-stringinteger Base-10 number or base-$base number if $base set.
integer
__debugInfo(): array
Will be called, automatically, when print_r() or var_dump() are called
array __sleep(): array
Will be called, automatically, when serialize() is called on a BigInteger object.
array __toString(): string
string __wakeup(): void
Will be called, automatically, when unserialize() is called on a BigInteger object.
abs(): \phpseclib3\Math\BigInteger\Engines\PHP
add(\phpseclib3\Math\BigInteger\Engines\PHP64 $y): \phpseclib3\Math\BigInteger\Engines\PHP64
addHelper(array $x_value,boolean $x_negative,array $y_value,boolean $y_negative): array
array
boolean
array
boolean
array array_repeat(integer $input,integer $multiplier): array
integer
integer
array base256_lshift(string &$x,integer $shift): void
Shifts binary strings $shift bits, essentially multiplying by 2**$shift.
string
integer
baseSquare(array $value): array
Squaring can be done faster than multiplying a number by itself can be. See HAC 14.2.4 / MPM 5.3 for more information.
array
array between(\phpseclib3\Math\BigInteger\Engines\PHP64 $min,\phpseclib3\Math\BigInteger\Engines\PHP64 $max): boolean
boolean bitwise_and(\phpseclib3\Math\BigInteger\Engines\PHP64 $x): \phpseclib3\Math\BigInteger\Engines\PHP64
bitwise_leftRotate(integer $shift): \phpseclib3\Math\BigInteger\Engines\Engine
Instead of the top x bits being dropped they're appended to the shifted bit string.
integer
\phpseclib3\Math\BigInteger\Engines\Engine bitwise_leftShift(integer $shift): \phpseclib3\Math\BigInteger\Engines\PHP
Shifts BigInteger's by $shift bits, effectively multiplying by 2**$shift.
integer
\phpseclib3\Math\BigInteger\Engines\PHP bitwise_not(): \phpseclib3\Math\BigInteger\Engines\Engine|string
bitwise_or(\phpseclib3\Math\BigInteger\Engines\PHP64 $x): \phpseclib3\Math\BigInteger\Engines\PHP64
bitwise_rightRotate(integer $shift): \phpseclib3\Math\BigInteger\Engines\Engine
Instead of the bottom x bits being dropped they're prepended to the shifted bit string.
integer
\phpseclib3\Math\BigInteger\Engines\Engine bitwise_rightShift(integer $shift): \phpseclib3\Math\BigInteger\Engines\PHP
Shifts BigInteger's by $shift bits, effectively dividing by 2**$shift.
integer
\phpseclib3\Math\BigInteger\Engines\PHP bitwise_small_split(integer $split): \phpseclib3\Math\BigInteger\Engines\list<int>
integer
\phpseclib3\Math\BigInteger\Engines\list bitwise_split(integer $split): array<mixed,\phpseclib3\Math\BigInteger\Engines\Engine>
Splits BigInteger's into chunks of $split bits
integer
array<mixed,\phpseclib3\Math\BigInteger\Engines\Engine> bitwise_xor(\phpseclib3\Math\BigInteger\Engines\PHP64 $x): \phpseclib3\Math\BigInteger\Engines\PHP64
bitwiseAndHelper(\phpseclib3\Math\BigInteger\Engines\Engine $x): \phpseclib3\Math\BigInteger\Engines\Engine
bitwiseOrHelper(\phpseclib3\Math\BigInteger\Engines\Engine $x): \phpseclib3\Math\BigInteger\Engines\Engine
bitwiseXorHelper(\phpseclib3\Math\BigInteger\Engines\Engine $x): \phpseclib3\Math\BigInteger\Engines\Engine
compare(\phpseclib3\Math\BigInteger\Engines\PHP64 $y): integer
Although one might think !$x->compare($y) means $x != $y, it, in fact, means the opposite. The reason for this is demonstrated thusly:
$x > $y: $x->compare($y) > 0 $x < $y: $x->compare($y) < 0 $x == $y: $x->compare($y) == 0
Note how the same comparison operator is used. If you want to test for equality, use $x->equals($y).
{@internal Could return $this->subtract($x), but that's not as fast as what we do do.}
| see | \phpseclib3\Math\BigInteger\Engines\PHP64::equals() |
|---|
integerin case < 0 if $this is less than $y; > 0 if $this is greater than $y, and 0 if they are equal.
compareHelper(array $x_value,boolean $x_negative,array $y_value,boolean $y_negative): integer
| see | static::compare() |
|---|
array
boolean
array
boolean
integer convertToObj(array $arr): static
array
static createRecurringModuloFunction(): callable
Sometimes it may be desirable to do repeated modulos with the same number outside of modular exponentiation
callable divide(\phpseclib3\Math\BigInteger\Engines\PHP64 $y): \phpseclib3\Math\BigInteger\Engines\array{PHP64,
Returns an array whose first element contains the quotient and whose second element contains the "common residue". If the remainder would be positive, the "common residue" and the remainder are the same. If the remainder would be negative, the "common residue" is equal to the sum of the remainder and the divisor (basically, the "common residue" is the first positive modulo).
\phpseclib3\Math\BigInteger\Engines\array{PHP64,PHP64}
divide_digit(array $dividend,integer $divisor): array
abc / x = a00 / x + b0 / x + c / x
array
integer
array equals(\phpseclib3\Math\BigInteger\Engines\PHP64 $x): boolean
If you need to see if one number is greater than or less than another number, use BigInteger::compare()
boolean extendedGCD(\phpseclib3\Math\BigInteger\Engines\PHP64 $n): array<mixed,\phpseclib3\Math\BigInteger\Engines\PHP64>
Say you have (30 mod 17 * x mod 17) mod 17 == 1. x can be found using modular inverses.
array<mixed,\phpseclib3\Math\BigInteger\Engines\PHP64> extendedGCDHelper(\phpseclib3\Math\BigInteger\Engines\Engine $n): \phpseclib3\Math\BigInteger\Engines\array{gcd:
\phpseclib3\Math\BigInteger\Engines\array{gcd:Engine, x: Engine, y: Engine}
gcd(\phpseclib3\Math\BigInteger\Engines\PHP64 $n): \phpseclib3\Math\BigInteger\Engines\PHP64
Say you have 693 and 609. The GCD is 21.
\phpseclib3\Math\BigInteger\Engines\PHP64 getLength(): integer
integer getLengthInBytes(): integer
integer getPrecision(): integer
Returns the precision if it exists, -1 if it doesn't
integer initialize(integer $base)
| see | \phpseclib3\Math\BigInteger\Engines\parent::__construct() |
|---|---|
integer
int2bytes(integer $x): string
integer
string isNegative(): boolean
boolean isOdd(): boolean
boolean isPrime(integer|boolean $t = false): boolean
Assuming the $t parameter is not set, this function has an error rate of 2**-80. The main motivation for the $t parameter is distributability. BigInteger::randomPrime() can be distributed across multiple pageloads on a website instead of just one.
integer|boolean
boolean isValidEngine(): boolean
| see | \phpseclib3\Math\BigInteger\Engines\parent::__construct() |
|---|---|
boolean jsonSerialize()
karatsuba(array $x_value,array $y_value): array
karatsubaSquare(array $value): array
lshift(integer $shift)
Shifts BigInteger's by $shift bits.
integer
make_odd()
If the current number is odd it'll be unchanged. If it's even, one will be added to it.
| see | self::randomPrime() |
|---|---|
max(\phpseclib3\Math\BigInteger\Engines\PHP64 $nums): \phpseclib3\Math\BigInteger\Engines\PHP64
maxHelper(array $nums): \phpseclib3\Math\BigInteger\Engines\Engine
min(\phpseclib3\Math\BigInteger\Engines\PHP64 $nums): \phpseclib3\Math\BigInteger\Engines\PHP64
minHelper(array $nums): \phpseclib3\Math\BigInteger\Engines\Engine
minMaxBits(integer $bits): \phpseclib3\Math\BigInteger\Engines\array{min:
integer
\phpseclib3\Math\BigInteger\Engines\array{min:static, max: static}
modInverse(\phpseclib3\Math\BigInteger\Engines\PHP64 $n): false|\phpseclib3\Math\BigInteger\Engines\PHP64
Say you have (30 mod 17 * x mod 17) mod 17 == 1. x can be found using modular inverses.
false|\phpseclib3\Math\BigInteger\Engines\PHP64 modInverseHelper(\phpseclib3\Math\BigInteger\Engines\Engine $n): static|false
Say you have (30 mod 17 * x mod 17) mod 17 == 1. x can be found using modular inverses.
{@internal See HAC 14.64 for more information.}
static|false modPow(\phpseclib3\Math\BigInteger\Engines\PHP64 $e,\phpseclib3\Math\BigInteger\Engines\PHP64 $n): \phpseclib3\Math\BigInteger\Engines\PHP64
multiply(\phpseclib3\Math\BigInteger\Engines\PHP64 $y): \phpseclib3\Math\BigInteger\Engines\PHP64
multiplyHelper(array $x_value,boolean $x_negative,array $y_value,boolean $y_negative): array
array
boolean
array
boolean
array negate(): static
Given $k, returns -$k
static normalize(\phpseclib3\Math\BigInteger\Engines\PHP $result): static
Removes leading zeros and truncates (if necessary) to maintain the appropriate precision
static pad(string $str): string
string
string pow(\phpseclib3\Math\BigInteger\Engines\PHP64 $n): \phpseclib3\Math\BigInteger\Engines\PHP64
powHelper(\phpseclib3\Math\BigInteger\Engines\PHP $n): \phpseclib3\Math\BigInteger\Engines\PHP
powMod(\phpseclib3\Math\BigInteger\Engines\PHP64 $e,\phpseclib3\Math\BigInteger\Engines\PHP64 $n): \phpseclib3\Math\BigInteger\Engines\PHP64|false
powModInner(\phpseclib3\Math\BigInteger\Engines\PHP $e,\phpseclib3\Math\BigInteger\Engines\PHP $n): \phpseclib3\Math\BigInteger\Engines\PHP
powModOuter(\phpseclib3\Math\BigInteger\Engines\Engine $e,\phpseclib3\Math\BigInteger\Engines\Engine $n): static|false
static|false random(integer $size): \phpseclib3\Math\BigInteger\Engines\Engine
Bit length is equal to $size
integer
\phpseclib3\Math\BigInteger\Engines\Engine randomPrime(integer $size): \phpseclib3\Math\BigInteger\Engines\Engine
Bit length is equal to $size
integer
\phpseclib3\Math\BigInteger\Engines\Engine randomRange(\phpseclib3\Math\BigInteger\Engines\PHP64 $min,\phpseclib3\Math\BigInteger\Engines\PHP64 $max): \phpseclib3\Math\BigInteger\Engines\PHP64
Returns a random number between $min and $max where $min and $max can be defined using one of the two methods:
BigInteger::randomRange($min, $max) BigInteger::randomRange($max, $min)
\phpseclib3\Math\BigInteger\Engines\PHP64 randomRangeHelper(\phpseclib3\Math\BigInteger\Engines\Engine $min,\phpseclib3\Math\BigInteger\Engines\Engine $max): \phpseclib3\Math\BigInteger\Engines\Engine
Returns a random number between $min and $max where $min and $max can be defined using one of the two methods:
BigInteger::randomRange($min, $max) BigInteger::randomRange($max, $min)
\phpseclib3\Math\BigInteger\Engines\Engine randomRangePrime(\phpseclib3\Math\BigInteger\Engines\PHP64 $min,\phpseclib3\Math\BigInteger\Engines\PHP64 $max): false|\phpseclib3\Math\BigInteger\Engines\PHP64
If there's not a prime within the given range, false will be returned.
false|\phpseclib3\Math\BigInteger\Engines\PHP64 randomRangePrimeInner(\phpseclib3\Math\BigInteger\Engines\Engine $x,\phpseclib3\Math\BigInteger\Engines\Engine $min,\phpseclib3\Math\BigInteger\Engines\Engine $max): static|false
static|false randomRangePrimeOuter(\phpseclib3\Math\BigInteger\Engines\Engine $min,\phpseclib3\Math\BigInteger\Engines\Engine $max): static|false
static|false regularMultiply(array $x_value,array $y_value): array
Modeled after 'multiply' in MutableBigInteger.java.
array
array
array root(integer $n = 2): \phpseclib3\Math\BigInteger\Engines\Engine
rootHelper(integer $n): \phpseclib3\Math\BigInteger\Engines\Engine
rootInner(integer $n): \phpseclib3\Math\BigInteger\Engines\Engine
Returns the nth root of a positive biginteger, where n defaults to 2
{@internal This function is based off of this page and this stackoverflow question.}
integer
\phpseclib3\Math\BigInteger\Engines\Engine rshift(integer $shift)
Shifts BigInteger's by $shift bits.
integer
safe_divide(integer $x,integer $y): integer
Even if int64 is being used the division operator will return a float64 value if the dividend is not evenly divisible by the divisor. Since a float64 doesn't have the precision of int64 this is a problem so, when int64 is being used, we'll guarantee that the dividend is divisible by first subtracting the remainder.
integer
integer
integer scan1divide(\phpseclib3\Math\BigInteger\Engines\PHP $r): integer
ie. $s = gmp_scan1($n, 0) and $r = gmp_div_q($n, gmp_pow(gmp_init('2'), $s));
| see | self::isPrime() |
|---|
integer setBitmask(integer $bits): static
| see | \phpseclib3\Math\BigInteger\Engines\Engine::setPrecision() |
|---|
integer
static setModExpEngine(\phpseclib3\Math\BigInteger\Engines\class-string<Engine> $engine)
Throws an exception if the type is invalid
\phpseclib3\Math\BigInteger\Engines\class-string
setPrecision(integer $bits)
Some bitwise operations give different results depending on the precision being used. Examples include left shift, not, and rotates.
integer
setupIsPrime(): integer
integer slidingWindow(\phpseclib3\Math\BigInteger\Engines\Engine $x,\phpseclib3\Math\BigInteger\Engines\Engine $e,\phpseclib3\Math\BigInteger\Engines\Engine $n,\phpseclib3\Math\BigInteger\Engines\class-string<T> $class): \phpseclib3\Math\BigInteger\Engines\T
Based on HAC 14.85 / MPM 7.7. In a departure from those algorithims, however, this function performs a modular reduction after every multiplication and squaring operation. As such, this function has the same preconditions that the reductions being used do.
| template | T of Engine |
|---|
\phpseclib3\Math\BigInteger\Engines\class-string
\phpseclib3\Math\BigInteger\Engines\T square(\phpseclib3\Math\BigInteger\Engines\list<static> $x): \phpseclib3\Math\BigInteger\Engines\list<static>
\phpseclib3\Math\BigInteger\Engines\list
\phpseclib3\Math\BigInteger\Engines\list subtract(\phpseclib3\Math\BigInteger\Engines\PHP64 $y): \phpseclib3\Math\BigInteger\Engines\PHP64
subtractHelper(array $x_value,boolean $x_negative,array $y_value,boolean $y_negative): array
array
boolean
array
boolean
array testBit( $x): boolean
boolean testPrimality(integer $t): boolean
Uses the Miller-Rabin primality test. See HAC 4.24 for more info.
integer
boolean testSmallPrimes()
| see | self::isPrime() |
|---|---|
toBits(boolean $twos_compliment = false): string
Negative numbers are saved as positive numbers, unless $twos_compliment is set to true, at which point, they're saved as two's compliment.
boolean
string toBytes(boolean $twos_compliment = false): string
boolean
string toBytesHelper(): string
Negative numbers are saved as positive numbers, unless $twos_compliment is set to true, at which point, they're saved as two's compliment.
string toHex(boolean $twos_compliment = false): string
boolean
string toString(): string
string trim(\phpseclib3\Math\BigInteger\Engines\list<static> $value): \phpseclib3\Math\BigInteger\Engines\list<static>
Removes leading zeros
\phpseclib3\Math\BigInteger\Engines\list
\phpseclib3\Math\BigInteger\Engines\list BASE
BASE_FULL
MAX_DIGIT
MSB
MAX10
MAX10LEN
MAX_DIGIT2
VALUE
SIGN
KARATSUBA_CUTOFF
At what point do we switch between Karatsuba multiplication and schoolbook long multiplication?
FAST_BITWISE
| see | |
|---|---|
ENGINE_DIR
| see | |
|---|---|
PRIMES
zero :\phpseclib3\Math\BigInteger\Engines\array<class-string<static>,
| var | static> |
|---|
\phpseclib3\Math\BigInteger\Engines\array, one :\phpseclib3\Math\BigInteger\Engines\array<class-string<static>,
| var | static> |
|---|
\phpseclib3\Math\BigInteger\Engines\array, two :\phpseclib3\Math\BigInteger\Engines\array<class-string<static>,
| var | static> |
|---|
\phpseclib3\Math\BigInteger\Engines\array, modexpEngine :\phpseclib3\Math\BigInteger\Engines\array<class-string<static>,
| var | class-string |
|---|
\phpseclib3\Math\BigInteger\Engines\array, isValidEngine :\phpseclib3\Math\BigInteger\Engines\array<class-string<static>,
| var | bool> |
|---|
\phpseclib3\Math\BigInteger\Engines\array, value :\GMP|string|array|integer
| var |
|---|
\GMP|string|array|integer is_negative :boolean
| var |
|---|
boolean precision :integer
| see | |
|---|---|
| var |
integer bitmask :static|false
| see | |
|---|---|
| var |
static|false reduce :callable
| var |
|---|
callable hex :string
| see | |
|---|---|
| var |
string