alejandro.alvarez5 70bb213259 articulo | 3 роки тому | |
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BigInteger.d.ts | 3 роки тому | |
BigInteger.js | 3 роки тому | |
BigInteger.min.js | 3 роки тому | |
LICENSE | 3 роки тому | |
README.md | 3 роки тому | |
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package.json | 3 роки тому | |
tsconfig.json | 3 роки тому |
BigInteger.js is an arbitrary-length integer library for Javascript, allowing arithmetic operations on integers of unlimited size, notwithstanding memory and time limitations.
Update (December 2, 2018): BigInt
is being added as a native feature of JavaScript. This library now works as a polyfill: if the environment supports the native BigInt
, this library acts as a thin wrapper over the native implementation.
If you are using a browser, you can download BigInteger.js from GitHub or just hotlink to it:
<script src="https://peterolson.github.io/BigInteger.js/BigInteger.min.js"></script>
If you are using node, you can install BigInteger with npm.
npm install big-integer
Then you can include it in your code:
var bigInt = require("big-integer");
bigInt(number, [base], [alphabet], [caseSensitive])
You can create a bigInt by calling the bigInt
function. You can pass in
"Invalid integer"
error if the parsing fails."Invalid integer"
error if the parsing fails.bigInt.zero
.If you provide a second parameter, then it will parse number
as a number in base base
. Note that base
can be any bigInt (even negative or zero). The letters “a-z” and “A-Z” will be interpreted as the numbers 10 to 35. Higher digits can be specified in angle brackets (<
and >
). The default base
is 10
.
You can specify a custom alphabet for base conversion with the third parameter. The default alphabet
is "0123456789abcdefghijklmnopqrstuvwxyz"
.
The fourth parameter specifies whether or not the number string should be case-sensitive, i.e. whether a
and A
should be treated as different digits. By default caseSensitive
is false
.
Examples:
var zero = bigInt();
var ninetyThree = bigInt(93);
var largeNumber = bigInt("75643564363473453456342378564387956906736546456235345");
var googol = bigInt("1e100");
var bigNumber = bigInt(largeNumber);
var maximumByte = bigInt("FF", 16);
var fiftyFiveGoogol = bigInt("<55>0", googol);
Note that Javascript numbers larger than 9007199254740992
and smaller than -9007199254740992
are not precisely represented numbers and will not produce exact results. If you are dealing with numbers outside that range, it is better to pass in strings.
Note that bigInt operations return bigInts, which allows you to chain methods, for example:
var salary = bigInt(dollarsPerHour).times(hoursWorked).plus(randomBonuses)
There are three named constants already stored that you do not have to construct with the bigInt
function yourself:
bigInt.one
, equivalent to bigInt(1)
bigInt.zero
, equivalent to bigInt(0)
bigInt.minusOne
, equivalent to bigInt(-1)
The numbers from -999 to 999 are also already prestored and can be accessed using bigInt[index]
, for example:
bigInt[-999]
, equivalent to bigInt(-999)
bigInt[256]
, equivalent to bigInt(256)
abs()
Returns the absolute value of a bigInt.
bigInt(-45).abs()
=> 45
bigInt(45).abs()
=> 45
add(number)
Performs addition.
bigInt(5).add(7)
=> 12
View benchmarks for this method
and(number)
Performs the bitwise AND operation. The operands are treated as if they were represented using two’s complement representation.
bigInt(6).and(3)
=> 2
bigInt(6).and(-3)
=> 4
bitLength()
Returns the number of digits required to represent a bigInt in binary.
bigInt(5)
=> 3
(since 5 is 101
in binary, which is three digits long)compare(number)
Performs a comparison between two numbers. If the numbers are equal, it returns 0
. If the first number is greater, it returns 1
. If the first number is lesser, it returns -1
.
bigInt(5).compare(5)
=> 0
bigInt(5).compare(4)
=> 1
bigInt(4).compare(5)
=> -1
compareAbs(number)
Performs a comparison between the absolute value of two numbers.
bigInt(5).compareAbs(-5)
=> 0
bigInt(5).compareAbs(4)
=> 1
bigInt(4).compareAbs(-5)
=> -1
compareTo(number)
Alias for the compare
method.
divide(number)
Performs integer division, disregarding the remainder.
bigInt(59).divide(5)
=> 11
View benchmarks for this method
divmod(number)
Performs division and returns an object with two properties: quotient
and remainder
. The sign of the remainder will match the sign of the dividend.
bigInt(59).divmod(5)
=> {quotient: bigInt(11), remainder: bigInt(4) }
bigInt(-5).divmod(2)
=> {quotient: bigInt(-2), remainder: bigInt(-1) }
View benchmarks for this method
eq(number)
Alias for the equals
method.
equals(number)
Checks if two numbers are equal.
bigInt(5).equals(5)
=> true
bigInt(4).equals(7)
=> false
geq(number)
Alias for the greaterOrEquals
method.
greater(number)
Checks if the first number is greater than the second.
bigInt(5).greater(6)
=> false
bigInt(5).greater(5)
=> false
bigInt(5).greater(4)
=> true
greaterOrEquals(number)
Checks if the first number is greater than or equal to the second.
bigInt(5).greaterOrEquals(6)
=> false
bigInt(5).greaterOrEquals(5)
=> true
bigInt(5).greaterOrEquals(4)
=> true
gt(number)
Alias for the greater
method.
isDivisibleBy(number)
Returns true
if the first number is divisible by the second number, false
otherwise.
bigInt(999).isDivisibleBy(333)
=> true
bigInt(99).isDivisibleBy(5)
=> false
isEven()
Returns true
if the number is even, false
otherwise.
bigInt(6).isEven()
=> true
bigInt(3).isEven()
=> false
isNegative()
Returns true
if the number is negative, false
otherwise.
Returns false
for 0
and -0
.
bigInt(-23).isNegative()
=> true
bigInt(50).isNegative()
=> false
isOdd()
Returns true
if the number is odd, false
otherwise.
bigInt(13).isOdd()
=> true
bigInt(40).isOdd()
=> false
isPositive()
Return true
if the number is positive, false
otherwise.
Returns false
for 0
and -0
.
bigInt(54).isPositive()
=> true
bigInt(-1).isPositive()
=> false
isPrime(strict?)
Returns true
if the number is prime, false
otherwise.
Set “strict” boolean to true to force GRH-supported lower bound of 2*log(N)^2.
bigInt(5).isPrime()
=> true
bigInt(6).isPrime()
=> false
isProbablePrime([iterations], [rng])
Returns true
if the number is very likely to be prime, false
otherwise.
Supplying iterations
is optional - it determines the number of iterations of the test (default: 5
). The more iterations, the lower chance of getting a false positive.
This uses the Miller Rabin test.
bigInt(5).isProbablePrime()
=> true
bigInt(49).isProbablePrime()
=> false
bigInt(1729).isProbablePrime()
=> false
Note that this function is not deterministic, since it relies on random sampling of factors, so the result for some numbers is not always the same - unless you pass a predictable random number generator as rng
. The behavior and requirements are the same as with randBetween
.
bigInt(1729).isProbablePrime(1, () => 0.1)
=> false
bigInt(1729).isProbablePrime(1, () => 0.2)
=> true
If the number is composite then the Miller–Rabin primality test declares the number probably prime with a probability at most 4
to the power −iterations
.
If the number is prime, this function always returns true
.
isUnit()
Returns true
if the number is 1
or -1
, false
otherwise.
bigInt.one.isUnit()
=> true
bigInt.minusOne.isUnit()
=> true
bigInt(5).isUnit()
=> false
isZero()
Return true
if the number is 0
or -0
, false
otherwise.
bigInt.zero.isZero()
=> true
bigInt("-0").isZero()
=> true
bigInt(50).isZero()
=> false
leq(number)
Alias for the lesserOrEquals
method.
lesser(number)
Checks if the first number is lesser than the second.
bigInt(5).lesser(6)
=> true
bigInt(5).lesser(5)
=> false
bigInt(5).lesser(4)
=> false
lesserOrEquals(number)
Checks if the first number is less than or equal to the second.
bigInt(5).lesserOrEquals(6)
=> true
bigInt(5).lesserOrEquals(5)
=> true
bigInt(5).lesserOrEquals(4)
=> false
lt(number)
Alias for the lesser
method.
minus(number)
Alias for the subtract
method.
bigInt(3).minus(5)
=> -2
View benchmarks for this method
mod(number)
Performs division and returns the remainder, disregarding the quotient. The sign of the remainder will match the sign of the dividend.
bigInt(59).mod(5)
=> 4
bigInt(-5).mod(2)
=> -1
View benchmarks for this method
modInv(mod)
Finds the multiplicative inverse of the number modulo mod
.
bigInt(3).modInv(11)
=> 4
bigInt(42).modInv(2017)
=> 1969
modPow(exp, mod)
Takes the number to the power exp
modulo mod
.
bigInt(10).modPow(3, 30)
=> 10
multiply(number)
Performs multiplication.
bigInt(111).multiply(111)
=> 12321
View benchmarks for this method
neq(number)
Alias for the notEquals
method.
next()
Adds one to the number.
bigInt(6).next()
=> 7
not()
Performs the bitwise NOT operation. The operands are treated as if they were represented using two’s complement representation.
bigInt(10).not()
=> -11
bigInt(0).not()
=> -1
notEquals(number)
Checks if two numbers are not equal.
bigInt(5).notEquals(5)
=> false
bigInt(4).notEquals(7)
=> true
or(number)
Performs the bitwise OR operation. The operands are treated as if they were represented using two’s complement representation.
bigInt(13).or(10)
=> 15
bigInt(13).or(-8)
=> -3
over(number)
Alias for the divide
method.
bigInt(59).over(5)
=> 11
View benchmarks for this method
plus(number)
Alias for the add
method.
bigInt(5).plus(7)
=> 12
View benchmarks for this method
pow(number)
Performs exponentiation. If the exponent is less than 0
, pow
returns 0
. bigInt.zero.pow(0)
returns 1
.
bigInt(16).pow(16)
=> 18446744073709551616
View benchmarks for this method
prev(number)
Subtracts one from the number.
bigInt(6).prev()
=> 5
remainder(number)
Alias for the mod
method.
View benchmarks for this method
shiftLeft(n)
Shifts the number left by n
places in its binary representation. If a negative number is provided, it will shift right. Throws an error if n
is outside of the range [-9007199254740992, 9007199254740992]
.
bigInt(8).shiftLeft(2)
=> 32
bigInt(8).shiftLeft(-2)
=> 2
shiftRight(n)
Shifts the number right by n
places in its binary representation. If a negative number is provided, it will shift left. Throws an error if n
is outside of the range [-9007199254740992, 9007199254740992]
.
bigInt(8).shiftRight(2)
=> 2
bigInt(8).shiftRight(-2)
=> 32
square()
Squares the number
bigInt(3).square()
=> 9
View benchmarks for this method
subtract(number)
Performs subtraction.
bigInt(3).subtract(5)
=> -2
View benchmarks for this method
times(number)
Alias for the multiply
method.
bigInt(111).times(111)
=> 12321
View benchmarks for this method
toArray(radix)
Converts a bigInt into an object with the properties “value” and “isNegative.” “Value” is an array of integers modulo the given radix. “isNegative” is a boolean that represents the sign of the result.
bigInt("1e9").toArray(10)
=> {
value: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0],
isNegative: false
}bigInt("1e9").toArray(16)
=> {
value: [3, 11, 9, 10, 12, 10, 0, 0],
isNegative: false
}bigInt(567890).toArray(100)
=> {
value: [56, 78, 90],
isNegative: false
}Negative bases are supported.
bigInt(12345).toArray(-10)
=> {
value: [2, 8, 4, 6, 5],
isNegative: false
}Base 1 and base -1 are also supported.
bigInt(-15).toArray(1)
=> {
value: [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
isNegative: true
}bigInt(-15).toArray(-1)
=> {
value: [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1,
0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0],
isNegative: false
}Base 0 is only allowed for the number zero.
bigInt(0).toArray(0)
=> {
value: [0],
isNegative: false
}bigInt(1).toArray(0)
=> Error: Cannot convert nonzero numbers to base 0.
toJSNumber()
Converts a bigInt into a native Javascript number. Loses precision for numbers outside the range [-9007199254740992, 9007199254740992]
.
bigInt("18446744073709551616").toJSNumber()
=> 18446744073709552000
xor(number)
Performs the bitwise XOR operation. The operands are treated as if they were represented using two’s complement representation.
bigInt(12).xor(5)
=> 9
bigInt(12).xor(-5)
=> -9
fromArray(digits, base = 10, isNegative?)
Constructs a bigInt from an array of digits in base base
. The optional isNegative
flag will make the number negative.
bigInt.fromArray([1, 2, 3, 4, 5], 10)
=> 12345
bigInt.fromArray([1, 0, 0], 2, true)
=> -4
gcd(a, b)
Finds the greatest common denominator of a
and b
.
bigInt.gcd(42,56)
=> 14
isInstance(x)
Returns true
if x
is a BigInteger, false
otherwise.
bigInt.isInstance(bigInt(14))
=> true
bigInt.isInstance(14)
=> false
lcm(a,b)
Finds the least common multiple of a
and b
.
bigInt.lcm(21, 6)
=> 42
max(a,b)
Returns the largest of a
and b
.
bigInt.max(77, 432)
=> 432
min(a,b)
Returns the smallest of a
and b
.
bigInt.min(77, 432)
=> 77
randBetween(min, max, [rng])
Returns a random number between min
and max
, optionally using rng
to generate randomness.
bigInt.randBetween("-1e100", "1e100")
=> (for example) 8494907165436643479673097939554427056789510374838494147955756275846226209006506706784609314471378745
rng
should take no arguments and return a number
between 0 and 1. It defaults to Math.random
.
bigInt.randBetween("-1e100", "1e100", () => 0.5)
=> (always) 50000005000000500000050000005000000500000050000005000000500000050000005000000500000050000005000000
toString(radix = 10, [alphabet])
Converts a bigInt to a string. There is an optional radix parameter (which defaults to 10) that converts the number to the given radix. Digits in the range 10-35
will use the letters a-z
.
bigInt("1e9").toString()
=> "1000000000"
bigInt("1e9").toString(16)
=> "3b9aca00"
You can use a custom base alphabet with the second parameter. The default alphabet
is "0123456789abcdefghijklmnopqrstuvwxyz"
.
bigInt("5").toString(2, "aA")
=> "AaA"
Note that arithmetical operators will trigger the valueOf
function rather than the toString
function. When converting a bigInteger to a string, you should use the toString
method or the String
function instead of adding the empty string.
bigInt("999999999999999999").toString()
=> "999999999999999999"
String(bigInt("999999999999999999"))
=> "999999999999999999"
bigInt("999999999999999999") + ""
=> 1000000000000000000
Bases larger than 36 are supported. If a digit is greater than or equal to 36, it will be enclosed in angle brackets.
bigInt(567890).toString(100)
=> "<56><78><90>"
Negative bases are also supported.
bigInt(12345).toString(-10)
=> "28465"
Base 1 and base -1 are also supported.
bigInt(-15).toString(1)
=> "-111111111111111"
bigInt(-15).toString(-1)
=> "101010101010101010101010101010"
Base 0 is only allowed for the number zero.
bigInt(0).toString(0)
=> 0
bigInt(1).toString(0)
=> Error: Cannot convert nonzero numbers to base 0.
View benchmarks for this method
valueOf()
Converts a bigInt to a native Javascript number. This override allows you to use native arithmetic operators without explicit conversion:
bigInt("100") + bigInt("200") === 300; //true
To contribute, just fork the project, make some changes, and submit a pull request. Please verify that the unit tests pass before submitting.
The unit tests are contained in the spec/spec.js
file. You can run them locally by opening the spec/SpecRunner.html
or file or running npm test
. You can also run the tests online from GitHub.
There are performance benchmarks that can be viewed from the benchmarks/index.html
page. You can run them online from GitHub.
This project is public domain. For more details, read about the Unlicense.