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BigInteger

An arbitrarily-large integer.

[BigInteger][1] objects should be considered immutable.  None of the “built-in” methods modify this or their arguments.  All properties should be considered private.

All the methods of [BigInteger][1] instances can be called “statically”.  The static versions are convenient if you don’t already have a [BigInteger][1] object.

As an example, these calls are equivalent.

`` javascript
BigInteger(4).multiply(5); // returns BigIngeger(20);
BigInteger.multiply(4, 5); // returns BigInteger(20);

var a = 42;
var a = BigInteger.toJSValue("0b101010"); // Not completely useless...

``

Summary

[BigInteger][2]
An arbitrarily-large integer.

[Functions][3]

[BigInteger()][1]
Convert a value to a [BigInteger][1].

[Constants][4]

[ZERO][5]
[BigInteger][1] 0.

[ONE][6]
[BigInteger][1] 1.

[M_ONE][7]
[BigInteger][1] -1.

[_0][8]
Shortcut for [ZERO][5].

[_1][9]
Shortcut for [ONE][6].

[small][10]
Array of [BigIntegers][1] from 0 to 36.

[Functions][3]

[toString][11]
Convert a [BigInteger][1] to a string.

[parse][12]
Parse a string into a [BigInteger][1].

[add][13]
Add two [BigIntegers][1].

[negate][14]
Get the additive inverse of a [BigInteger][1].

[abs][15]
Get the absolute value of a [BigInteger][1].

[subtract][16]
Subtract two [BigIntegers][1].

[next][17]
Get the next [BigInteger][1] (add one).

[prev][18]
Get the previous [BigInteger][1] (subtract one).

[compareAbs][19]
Compare the absolute value of two [BigIntegers][1].

[compare][20]
Compare two [BigIntegers][1].

[isUnit][21]
Return true iff this is either 1 or -1.

[multiply][22]
Multiply two [BigIntegers][1].

[square][23]
Multiply a [BigInteger][1] by itself.

[divide][24]
Divide two [BigIntegers][1].

[remainder][25]
Calculate the remainder of two [BigIntegers][1].

[divRem][26]
Calculate the integer quotient and remainder of two [BigIntegers][1].

[isEven][27]
Return true iff this is divisible by two.

[isOdd][28]
Return true iff this is not divisible by two.

[sign][29]
Get the sign of a [BigInteger][1].

[isPositive][30]
Return true iff this > 0.

[isNegative][31]
Return true iff this < 0.

[isZero][32]
Return true iff this == 0.

[exp10][33]
Multiply a [BigInteger][1] by a power of 10.

[pow][34]
Raise a [BigInteger][1] to a power.

[modPow][35]
Raise a [BigInteger][1] to a power (mod m).

[valueOf][36]
Convert a [BigInteger][1] to a native JavaScript integer.

[toJSValue][37]
Convert a [BigInteger][1] to a native JavaScript integer.

[Constants][4]

[MAX_EXP][38]
The largest exponent allowed in [pow][34] and [exp10][33] (0x7FFFFFFF or 2147483647).

$3

$3


function BigInteger(n, s)

Convert a value to a [BigInteger][1].

Although [BigInteger()][1] is the constructor for [BigInteger][1] objects, it is best not to call it as a constructor.  If n is a [BigInteger][1] object, it is simply returned as-is.  Otherwise, [BigInteger()][1] is equivalent to [parse][12] without a radix argument.
` javascript
var n0 = BigInteger(); // Same as
var n1 = BigInteger("123"); // Create a new with value 123
var n2 = BigInteger(123); // Create a new with value 123
var n3 = BigInteger(n2); // Return n2, unchanged
`

The constructor form only takes an array and a sign.  n must be an array of numbers in little-endian order, where each digit is between 0 and 9 inclusive.  A second parameter sets the sign: -1 for negative, +1 for positive, or 0 for zero.  The array is not copied and may be modified.  If the array contains only zeros, the sign parameter is ignored and is forced to zero.

` javascript
new BigInteger([3,2,1], -1): create a new BigInteger with value -123
`

#### Parameters

n
Value to convert to a [BigInteger][1].

#### Returns

A [BigInteger][1] value.

#### See Also

[parse][12], [BigInteger][1]

$3

$3

[BigInteger][1] 0.

$3

[BigInteger][1] 1.

$3

[BigInteger][1] -1.

$3

Shortcut for [ZERO][5].

$3

Shortcut for [ONE][6].

$3

Array of [BigIntegers][1] from 0 to 36.

These are used internally for parsing, but useful when you need a “small” [BigInteger][1].

#### See Also

[ZERO][5], [ONE][6], [_0][8], [_1][9]

Functions

$3

BigInteger.prototype.toString = function(base)

Convert a [BigInteger][1] to a string.

When base is greater than 10, letters are upper case.

#### Parameters

base
Optional base to represent the number in (default is base 10).  Must be between 2 and 36 inclusive, or an Error will be thrown.

#### Returns

The string representation of the [BigInteger][1].

$3

BigInteger.parse = function(s, base)

Parse a string into a [BigInteger][1].

base is optional but, if provided, must be from 2 to 36 inclusive.  If base is not provided, it will be guessed based on the leading characters of s as follows:

* ”0x” or “0X”: base = 16
* ”0b” or “0B”: base = 2
* ”0”: base = 8
* else: base = 10

If no base is provided, or base is 10, the number can be in exponential form.  For example, these are all valid:

` javascript
BigInteger.parse("1e9"); // Same as "1000000000"
BigInteger.parse("1.234*10^3"); // Same as 1234
BigInteger.parse("56789 10 * -2"); // Same as 567
`

If any characters fall outside the range defined by the radix, an exception will be thrown.

#### Parameters

s
The string to parse.

base
Optional radix (default is to guess based on s).

#### Returns

a [BigInteger][1] instance.

$3

BigInteger.prototype.add = function(n)


Add two [BigIntegers][1].

#### Parameters

n
The number to add to this.  Will be converted to a [BigInteger][1].

#### Returns

The numbers added together.

#### See Also

[subtract][16], [multiply][22], [divide][24], [next][17]

$3

> BigInteger.prototype.negate = function()

Get the additive inverse of a [BigInteger][1].

#### Returns

A [BigInteger][1] with the same magnatude, but with the opposite sign.

#### See Also

[abs][15]

$3

> BigInteger.prototype.abs = function()

Get the absolute value of a [BigInteger][1].

#### Returns

A [BigInteger][1] with the same magnatude, but always positive (or zero).

#### See Also

[negate][14]

$3

BigInteger.prototype.negate = function()

Subtract two [BigIntegers][1].

#### Parameters

n
The number to subtract from this.  Will be converted to a [BigInteger][1].

#### Returns

The n subtracted from this.

#### See Also

[add][13], [multiply][22], [divide][24], [prev][18]

$3

BigInteger.prototype.next = function()

Get the next [BigInteger][1] (add one).

#### Returns

this + 1.

#### See Also

[add][13], [prev][18]

$3

BigInteger.prototype.prev = function()

Get the previous [BigInteger][1] (subtract one).

#### Returns

this
1.

#### See Also

[next][17], [subtract][16]

$3

BigInteger.prototype.compareAbs = function(n)

Compare the absolute value of two [BigIntegers][1].

Calling [compareAbs][19] is faster than calling [abs][15] twice, then [compare][20].

#### Parameters

n
The number to compare to this.  Will be converted to a [BigInteger][1].

#### Returns

-1, 0, or +1 if |this| is less than, equal to, or greater than |n|.

#### See Also

[compare][20], [abs][15]

$3

BigInteger.prototype.compare = function(n)


Compare two [BigIntegers][1].

#### Parameters

n
The number to compare to this.  Will be converted to a [BigInteger][1].

#### Returns

-1, 0, or +1 if this is less than, equal to, or greater than n.

#### See Also

[compareAbs][19], [isPositive][30], [isNegative][31], [isUnit][21]

$3

BigInteger.prototype.isUnit = function()

Return true iff this is either 1 or -1.

#### Returns

true if this compares equal to [BigInteger.ONE][6] or [BigInteger.M_ONE][7].

#### See Also

[isZero][32], [isNegative][31], [isPositive][30], [compareAbs][19], [compare][20], [BigInteger.ONE][6], [BigInteger.M_ONE][7]

$3

BigInteger.prototype.multiply = function(n)

Multiply two [BigIntegers][1].

#### Parameters

n
The number to multiply this by.  Will be converted to a [BigInteger][1].

#### Returns

The numbers multiplied together.

#### See Also

[add][13], [subtract][16], [divide][24], [square][23]

$3

BigInteger.prototype.square = function()

Multiply a [BigInteger][1] by itself.

This is slightly faster than regular multiplication, since it removes the duplicated multiplcations.

#### Returns

this.multiply(this)

#### See Also

[multiply][22]

$3

BigInteger.prototype.divide = function(n)

Divide two [BigIntegers][1].

[divide][24] throws an exception if n is zero.

#### Parameters

n
The number to divide this by.  Will be converted to a [BigInteger][1].

#### Returns

The this / n, truncated to an integer.

#### See Also

[add][13], [subtract][16], [multiply][22], [divRem][26], [remainder][25]

$3

BigInteger.prototype.remainder = function(n)


Calculate the remainder of two [BigIntegers][1].

[remainder][25] throws an exception if n is zero.

#### Parameters

n
The remainder after this is divided this by n.  Will be converted to a [BigInteger][1].

#### Returns

this % n.

#### See Also

[divRem][26], [divide][24]

$3

BigInteger.prototype.divRem = function(n)

Calculate the integer quotient and remainder of two [BigIntegers][1].

[divRem][26] throws an exception if n is zero.

#### Parameters

n
The number to divide this by.  Will be converted to a [BigInteger][1].

#### Returns

A two-element array containing the quotient and the remainder.

a.divRem(b)

is exactly equivalent to

[a.divide(b), a.remainder(b)]

except it is faster, because they are calculated at the same time.

#### See Also

[divide][24], [remainder][25]

$3

BigInteger.prototype.isEven = function()

Return true iff this is divisible by two.

Note that [BigInteger.ZERO][5] is even.

#### Returns

true if this is even, false otherwise.

#### See Also

[isOdd][28]

$3

BigInteger.prototype.isOdd = function()

Return true iff this is not divisible by two.

#### Returns

true if this is odd, false otherwise.

#### See Also

[isEven][27]

$3

BigInteger.prototype.sign = function()

Get the sign of a [BigInteger][1].

#### Returns

* -1 if this < 0
* 0 if this == 0
* +1 if this > 0

#### See Also

[isZero][32], [isPositive][30], [isNegative][31], [compare][20], [BigInteger.ZERO][5]

$3

BigInteger.prototype.isPositive = function()

Return true iff this > 0.

#### Returns

true if this.compare([BigInteger.ZERO][5]) == 1.

#### See Also

[sign][29], [isZero][32], [isNegative][31], [isUnit][21], [compare][20], [BigInteger.ZERO][5]

$3

BigInteger.prototype.isNegative = function()

Return true iff this < 0.

#### Returns

true if this.compare([BigInteger.ZERO][5]) == -1.

#### See Also

[sign][29], [isPositive][30], [isZero][32], [isUnit][21], [compare][20], [BigInteger.ZERO][5]

$3

BigInteger.prototype.isZero = function()

Return true iff this == 0.

#### Returns

true if this.compare([BigInteger.ZERO][5]) == 0.

#### See Also

[sign][29], [isPositive][30], [isNegative][31], [isUnit][21], [BigInteger.ZERO][5]

$3

BigInteger.prototype.exp10 = function(n)

Multiply a [BigInteger][1] by a power of 10.

This is equivalent to, but faster than

` javascript
if (n >= 0) {
return this.multiply(BigInteger("1e" + n));
} else { // n
return this.divide(BigInteger("1e" + -n));
}
`

#### Parameters

n
The power of 10 to multiply this by.  n is converted to a javascipt number and must be no greater than [BigInteger.MAX_EXP][38] (0x7FFFFFFF), or an exception will be thrown.

#### Returns

this (10 n*), truncated to an integer if necessary.

#### See Also

[pow][34], [multiply][22]

$3

BigInteger.prototype.pow = function(n)


Raise a [BigInteger][1] to a power.

In this implementation, 0**0 is 1.

#### Parameters

n
The exponent to raise this by.  n must be no greater than [BigInteger.MAX_EXP][38] (0x7FFFFFFF), or an exception will be thrown.

#### Returns

this raised to the nth power.

#### See Also

[modPow][35]

$3

BigInteger.prototype.modPow = function(exponent, modulus)

Raise a [BigInteger][1] to a power (mod m).

Because it is reduced by a modulus, [modPow][35] is not limited by [BigInteger.MAX_EXP][38] like [pow][34].

#### Parameters

exponent
The exponent to raise this by.  Must be positive.

modulus
The modulus.

#### Returns

this ^ exponent (mod modulus).

#### See Also

[pow][34],

$3

BigInteger.prototype.valueOf = function()

Convert a [BigInteger][1] to a native JavaScript integer.

This is called automatically by JavaScipt to convert a [BigInteger][1] to a native value.

#### Returns

parseInt(this.toString(), 10)

#### See Also

[toString][11], [toJSValue][37]

$3

BigInteger.prototype.toJSValue = function()

Convert a [BigInteger][1] to a native JavaScript integer.

This is the same as valueOf, but more explicitly named.

#### Returns

parseInt(this.toString(), 10)`

#### See Also

[toString][11], [valueOf][36]

$3

$3

The largest exponent allowed in [pow][34] and [exp10][33] (0x7FFFFFFF or 2147483647).

[1]: http://silentmatt.com/biginteger-docs/files/biginteger-js.html#BigInteger.BigInteger
[2]: http://silentmatt.com/biginteger-docs/files/biginteger-js.html#BigInteger
[3]: http://silentmatt.com/biginteger-docs/files/biginteger-js.html#BigInteger.Functions
[4]: http://silentmatt.com/biginteger-docs/files/biginteger-js.html#BigInteger.Constants
[5]: http://silentmatt.com/biginteger-docs/files/biginteger-js.html#BigInteger.ZERO
[6]: http://silentmatt.com/biginteger-docs/files/biginteger-js.html#BigInteger.ONE
[7]: http://silentmatt.com/biginteger-docs/files/biginteger-js.html#BigInteger.M_ONE
[8]: http://silentmatt.com/biginteger-docs/files/biginteger-js.html#BigInteger._0
[9]: http://silentmatt.com/biginteger-docs/files/biginteger-js.html#BigInteger._1
[10]: http://silentmatt.com/biginteger-docs/files/biginteger-js.html#BigInteger.small
[11]: http://silentmatt.com/biginteger-docs/files/biginteger-js.html#BigInteger.toString
[12]: http://silentmatt.com/biginteger-docs/files/biginteger-js.html#BigInteger.parse
[13]: http://silentmatt.com/biginteger-docs/files/biginteger-js.html#BigInteger.add
[14]: http://silentmatt.com/biginteger-docs/files/biginteger-js.html#BigInteger.negate
[15]: http://silentmatt.com/biginteger-docs/files/biginteger-js.html#BigInteger.abs
[16]: http://silentmatt.com/biginteger-docs/files/biginteger-js.html#BigInteger.subtract
[17]: http://silentmatt.com/biginteger-docs/files/biginteger-js.html#BigInteger.next
[18]: http://silentmatt.com/biginteger-docs/files/biginteger-js.html#BigInteger.prev
[19]: http://silentmatt.com/biginteger-docs/files/biginteger-js.html#BigInteger.compareAbs
[20]: http://silentmatt.com/biginteger-docs/files/biginteger-js.html#BigInteger.compare
[21]: http://silentmatt.com/biginteger-docs/files/biginteger-js.html#BigInteger.isUnit
[22]: http://silentmatt.com/biginteger-docs/files/biginteger-js.html#BigInteger.multiply
[23]: http://silentmatt.com/biginteger-docs/files/biginteger-js.html#BigInteger.square
[24]: http://silentmatt.com/biginteger-docs/files/biginteger-js.html#BigInteger.divide
[25]: http://silentmatt.com/biginteger-docs/files/biginteger-js.html#BigInteger.remainder
[26]: http://silentmatt.com/biginteger-docs/files/biginteger-js.html#BigInteger.divRem
[27]: http://silentmatt.com/biginteger-docs/files/biginteger-js.html#BigInteger.isEven
[28]: http://silentmatt.com/biginteger-docs/files/biginteger-js.html#BigInteger.isOdd
[29]: http://silentmatt.com/biginteger-docs/files/biginteger-js.html#BigInteger.sign
[30]: http://silentmatt.com/biginteger-docs/files/biginteger-js.html#BigInteger.isPositive
[31]: http://silentmatt.com/biginteger-docs/files/biginteger-js.html#BigInteger.isNegative
[32]: http://silentmatt.com/biginteger-docs/files/biginteger-js.html#BigInteger.isZero
[33]: http://silentmatt.com/biginteger-docs/files/biginteger-js.html#BigInteger.exp10
[34]: http://silentmatt.com/biginteger-docs/files/biginteger-js.html#BigInteger.pow
[35]: http://silentmatt.com/biginteger-docs/files/biginteger-js.html#BigInteger.modPow
[36]: http://silentmatt.com/biginteger-docs/files/biginteger-js.html#BigInteger.valueOf
[37]: http://silentmatt.com/biginteger-docs/files/biginteger-js.html#BigInteger.toJSValue
[38]: http://silentmatt.com/biginteger-docs/files/biginteger-js.html#BigInteger.MAX_EXP
[39]: http://www.naturaldocs.org
[40]: http://silentmatt.com/biginteger-docs/files/biginteger-js.html/index/General.html
[41]: http://silentmatt.com/biginteger-docs/files/biginteger-js.html/index/Classes.html
[42]: http://silentmatt.com/biginteger-docs/files/biginteger-js.html/index/Constants.html
[43]: http://silentmatt.com/biginteger-docs/files/biginteger-js.html/index/Functions.html