Pure-PHP 32-bit Engine.
Uses 64-bit floats if int size is 4 bits
author | Jim Wigginton terrafrost@php.net |
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package | Default |
__construct(integer|\phpseclib3\Math\BigInteger\Engines\numeric-string $x,integer $base = 10)
integer|\phpseclib3\Math\BigInteger\Engines\numeric-string
integer Base-10 number or base-$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\PHP32 $y): \phpseclib3\Math\BigInteger\Engines\PHP32
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\PHP32 $min,\phpseclib3\Math\BigInteger\Engines\PHP32 $max): boolean
boolean
bitwise_and(\phpseclib3\Math\BigInteger\Engines\PHP32 $x): \phpseclib3\Math\BigInteger\Engines\PHP32
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\PHP32 $x): \phpseclib3\Math\BigInteger\Engines\PHP32
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\PHP32 $x): \phpseclib3\Math\BigInteger\Engines\PHP32
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\PHP32 $y): integer
Although one might think !$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\PHP32::equals() |
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integer
in 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() |
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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\PHP32 $y): \phpseclib3\Math\BigInteger\Engines\array{PHP32,
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{PHP32,
PHP32}
divide_digit(array $dividend,integer $divisor): array
abc / x = a00 / x + b0 / x + c / x
array
integer
array
equals(\phpseclib3\Math\BigInteger\Engines\PHP32 $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\PHP32 $n): array<mixed,\phpseclib3\Math\BigInteger\Engines\PHP32>
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\PHP32>
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\PHP32 $n): \phpseclib3\Math\BigInteger\Engines\PHP32
Say you have 693 and 609. The GCD is 21.
\phpseclib3\Math\BigInteger\Engines\PHP32
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() |
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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() |
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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() |
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max(\phpseclib3\Math\BigInteger\Engines\PHP32 $nums): \phpseclib3\Math\BigInteger\Engines\PHP32
maxHelper(array $nums): \phpseclib3\Math\BigInteger\Engines\Engine
min(\phpseclib3\Math\BigInteger\Engines\PHP32 $nums): \phpseclib3\Math\BigInteger\Engines\PHP32
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\PHP32 $n): false|\phpseclib3\Math\BigInteger\Engines\PHP32
Say you have (30 mod 17 * x mod 17) mod 17 == 1. x can be found using modular inverses.
false|\phpseclib3\Math\BigInteger\Engines\PHP32
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\PHP32 $e,\phpseclib3\Math\BigInteger\Engines\PHP32 $n): \phpseclib3\Math\BigInteger\Engines\PHP32
multiply(\phpseclib3\Math\BigInteger\Engines\PHP32 $y): \phpseclib3\Math\BigInteger\Engines\PHP32
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\PHP32 $n): \phpseclib3\Math\BigInteger\Engines\PHP32
powHelper(\phpseclib3\Math\BigInteger\Engines\PHP $n): \phpseclib3\Math\BigInteger\Engines\PHP
powMod(\phpseclib3\Math\BigInteger\Engines\PHP32 $e,\phpseclib3\Math\BigInteger\Engines\PHP32 $n): \phpseclib3\Math\BigInteger\Engines\PHP32
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\PHP32 $min,\phpseclib3\Math\BigInteger\Engines\PHP32 $max): \phpseclib3\Math\BigInteger\Engines\PHP32
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\PHP32
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\PHP32 $min,\phpseclib3\Math\BigInteger\Engines\PHP32 $max): false|\phpseclib3\Math\BigInteger\Engines\PHP32
If there's not a prime within the given range, false will be returned.
false|\phpseclib3\Math\BigInteger\Engines\PHP32
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() |
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integer
setBitmask(integer $bits): static
see | \phpseclib3\Math\BigInteger\Engines\Engine::setPrecision() |
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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 |
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\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\PHP32 $y): \phpseclib3\Math\BigInteger\Engines\PHP32
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() |
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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 | |
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ENGINE_DIR
see | |
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PRIMES
zero :\phpseclib3\Math\BigInteger\Engines\array<class-string<static>,
var | static> |
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\phpseclib3\Math\BigInteger\Engines\array,
one :\phpseclib3\Math\BigInteger\Engines\array<class-string<static>,
var | static> |
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\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 | |
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var |
integer
bitmask :static|false
see | |
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var |
static|false
reduce :callable
var |
---|
callable
hex :string
see | |
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var |
string