The type representing a digit inBigUInt‘s underlying number system.

Declaration

publictypealiasWord=UInt

Initializes a new BigUInt with value 0.

Declaration

publicinit()

Initializes a new BigUInt with the specified digits. The digits are ordered from least to most significant.

Declaration

publicinit(words:[Word])

Adda andb together and return the result.

Declaration

publicstaticfunc+(a:BigUInt,b:BigUInt)->BigUInt

Adda andb together, and store the sum ina.

Declaration

publicstaticfunc+=(a:inoutBigUInt,b:BigUInt)

Declaration

publicstaticvarisSigned:Bool{get}

Return true iff this integer is zero.

Declaration

publicvarisZero:Bool{get}

Returns1 if this value is, positive; otherwise,0.

Declaration

publicfuncsignum()->BigUInt

Return Value

The sign of this number, expressed as an integer of the same type.

Return the ones’ complement ofa.

Declaration

publicprefixstaticfunc~(a:BigUInt)->BigUInt

Calculate the bitwise OR ofa andb, and store the result ina.

Declaration

publicstaticfunc|=(a:inoutBigUInt,b:BigUInt)

Calculate the bitwise AND ofa andb and return the result.

Declaration

publicstaticfunc&=(a:inoutBigUInt,b:BigUInt)

Calculate the bitwise XOR ofa andb and return the result.

Declaration

publicstaticfunc^=(a:inoutBigUInt,b:BigUInt)

Declaration

publicinit(fromdecoder:Decoder)throws

Declaration

publicfuncencode(toencoder:Encoder)throws

Comparea tob and return anNSComparisonResult indicating their order.

Declaration

publicstaticfunccompare(_a:BigUInt,_b:BigUInt)->ComparisonResult

Return true iffa is equal tob.

Declaration

publicstaticfunc==(a:BigUInt,b:BigUInt)->Bool

Return true iffa is less thanb.

Declaration

publicstaticfunc<(a:BigUInt,b:BigUInt)->Bool

Initialize a BigInt from bytes accessed from an UnsafeRawBufferPointer

Declaration

publicinit(_buffer:UnsafeRawBufferPointer)

Initializes an integer from the bits stored inside a piece ofData.The data is assumed to be in network (big-endian) byte order.

Declaration

publicinit(_data:Data)

Return aData value that contains the base-256 representation of this integer, in network (big-endian) byte order.

Declaration

publicfuncserialize()->Data

Divide this integer byy and return the resulting quotient and remainder.

Declaration

publicfuncquotientAndRemainder(dividingByy:BigUInt)->(quotient:BigUInt,remainder:BigUInt)

Return Value

(quotient, remainder) wherequotient = floor(self/y),remainder = self - quotient * y

Dividex byy and return the quotient.

Declaration

publicstaticfunc/(x:BigUInt,y:BigUInt)->BigUInt

Dividex byy and return the remainder.

Declaration

publicstaticfunc%(x:BigUInt,y:BigUInt)->BigUInt

Dividex byy and store the quotient inx.

Declaration

publicstaticfunc/=(x:inoutBigUInt,y:BigUInt)

Dividex byy and store the remainder inx.

Declaration

publicstaticfunc%=(x:inoutBigUInt,y:BigUInt)

Returns this integer raised to the powerexponent.

This function calculates the result bysuccessively squaring the base while halving the exponent.

Declaration

publicfuncpower(_exponent:Int)->BigUInt

Return Value

1 ifexponent == 0, otherwiseself raised toexponent. (This implies that0.power(0) == 1.)

Returns the remainder of this integer raised to the powerexponent in modulo arithmetic undermodulus.

Uses theright-to-left binary method.

Declaration

publicfuncpower(_exponent:BigUInt,modulus:BigUInt)->BigUInt

Declaration

publicinit?<T>(exactlysource:T)whereT:BinaryFloatingPoint

Declaration

publicinit<T>(_source:T)whereT:BinaryFloatingPoint

Returns the greatest common divisor ofself andb.

Declaration

publicfuncgreatestCommonDivisor(withb:BigUInt)->BigUInt

Returns themultiplicative inverse of this integer in modulomodulus arithmetic,ornil if there is no such number.

Declaration

publicfuncinverse(_modulus:BigUInt)->BigUInt?

Return Value

Ifgcd(self, modulus) == 1, the value returned is an integera < modulus such that(a * self) % modulus == 1. Ifself andmodulus aren’t coprime, the return value isnil.

Append thisBigUInt to the specified hasher.

Declaration

publicfunchash(intohasher:inoutHasher)

Declaration

publicinit?<T>(exactlysource:T)whereT:BinaryInteger

Declaration

publicinit<T>(_source:T)whereT:BinaryInteger

Declaration

publicinit<T>(truncatingIfNeededsource:T)whereT:BinaryInteger

Declaration

publicinit<T>(clampingsource:T)whereT:BinaryInteger

Initialize a new big integer from an integer literal.

Declaration

publicinit(integerLiteralvalue:UInt64)

Multiply this big integer by a single word, and store the result in place of the original big integer.

Declaration

publicmutatingfuncmultiply(byWordy:Word)

Multiply this big integer by a single Word, and return the result.

Declaration

publicfuncmultiplied(byWordy:Word)->BigUInt

Multiplyx byy, and add the result to this integer, optionally shiftedshift words to the left.

Declaration

publicmutatingfuncmultiplyAndAdd(_x:BigUInt,_y:Word,shiftedByshift:Int=0)

Return Value

self is set toself + (x * y) << (shift * 2^Word.bitWidth)

Multiply this integer byy and return the result.

Declaration

publicfuncmultiplied(byy:BigUInt)->BigUInt

Multiplication switches to an asymptotically better recursive algorithm when arguments have more words than this limit.

Declaration

publicstaticvardirectMultiplicationLimit:Int

Multiplya byb and return the result.

Declaration

publicstaticfunc*(x:BigUInt,y:BigUInt)->BigUInt

Multiplya byb and store the result ina.

Declaration

publicstaticfunc*=(a:inoutBigUInt,b:BigUInt)

Returns true iff this integer passes thestrong probable prime test for the specified base.

Declaration

publicfuncisStrongProbablePrime(_base:BigUInt)->Bool

Returns true if this integer is probably prime. Returns false if this integer is definitely not prime.

This function performs a probabilisticMiller-Rabin Primality Test, consisting ofrounds iterations, each calculating the strong probable prime test for a random base. The number of rounds is 10 by default,but you may specify your own choice.

To speed things up, the function checks ifself is divisible by the first few prime numbers beforediving into (slower) Miller-Rabin testing.

Also, whenself is less than 82 bits wide,isPrime does a deterministic test that is guaranteed to return a correct result.

Declaration

publicfuncisPrime(rounds:Int=10)->Bool

Create a big unsigned integer consisting ofwidth uniformly distributed random bits.

Declaration

publicstaticfuncrandomInteger<RNG>(withMaximumWidthwidth:Int,usinggenerator:inoutRNG)->BigUIntwhereRNG:RandomNumberGenerator

Parameters

Return Value

A big unsigned integer less than1 << width.

Create a big unsigned integer consisting ofwidth uniformly distributed random bits.

Declaration

publicstaticfuncrandomInteger(withMaximumWidthwidth:Int)->BigUInt

Parameters

Return Value

A big unsigned integer less than1 << width.

Create a big unsigned integer consisting ofwidth-1 uniformly distributed random bits followed by a one bit.

Declaration

publicstaticfuncrandomInteger<RNG>(withExactWidthwidth:Int,usinggenerator:inoutRNG)->BigUIntwhereRNG:RandomNumberGenerator

Parameters

Return Value

A random big unsigned integer whose width iswidth.

Create a big unsigned integer consisting ofwidth-1 uniformly distributed random bits followed by a one bit.

Declaration

publicstaticfuncrandomInteger(withExactWidthwidth:Int)->BigUInt

Return Value

A random big unsigned integer whose width iswidth.

Create a uniformly distributed random unsigned integer that’s less than the specified limit.

Declaration

publicstaticfuncrandomInteger<RNG>(lessThanlimit:BigUInt,usinggenerator:inoutRNG)->BigUIntwhereRNG:RandomNumberGenerator

Parameters

Return Value

A random big unsigned integer that is less thanlimit.

Create a uniformly distributed random unsigned integer that’s less than the specified limit.

Declaration

publicstaticfuncrandomInteger(lessThanlimit:BigUInt)->BigUInt

Parameters

Return Value

A random big unsigned integer that is less thanlimit.

Undocumented

Declaration

publicstaticfunc>>=<Other>(lhs:inoutBigUInt,rhs:Other)whereOther:BinaryInteger

Undocumented

Declaration

publicstaticfunc<<=<Other>(lhs:inoutBigUInt,rhs:Other)whereOther:BinaryInteger

Undocumented

Declaration

publicstaticfunc>><Other>(lhs:BigUInt,rhs:Other)->BigUIntwhereOther:BinaryInteger

Undocumented

Declaration

publicstaticfunc<<<Other>(lhs:BigUInt,rhs:Other)->BigUIntwhereOther:BinaryInteger

Returns the integer square root of a big integer; i.e., the largest integer whose square isn’t greater thanvalue.

Declaration

publicfuncsquareRoot()->BigUInt

Return Value

floor(sqrt(self))

A type that can represent the distance between two values ofaBigUInt.

Declaration

publictypealiasStride=BigInt

Addsn toself and returns the result. Traps if the result would be less than zero.

Declaration

publicfuncadvanced(byn:BigInt)->BigUInt

Returns the (potentially negative) difference betweenself andother as aBigInt. Never traps.

Declaration

publicfuncdistance(toother:BigUInt)->BigInt

Initialize a big integer from an ASCII representation in a given radix. Numerals above9 are represented byletters from the English alphabet.

Declaration

publicinit?<S>(_text:S,radix:Int=10)whereS:StringProtocol

Return Value

The integer represented bytext, or nil iftext contains a character that does not represent a numeral inradix.

Initialize a new big integer from a Unicode scalar.The scalar must represent a decimal digit.

Declaration

publicinit(unicodeScalarLiteralvalue:UnicodeScalar)

Initialize a new big integer from an extended grapheme cluster.The cluster must consist of a decimal digit.

Declaration

publicinit(extendedGraphemeClusterLiteralvalue:String)

Initialize a new big integer from a decimal number represented by a string literal of arbitrary length.The string must contain only decimal digits.

Declaration

publicinit(stringLiteralvalue:StringLiteralType)

Return the decimal representation of this integer.

Declaration

publicvardescription:String{get}

Return the playground quick look representation of this integer.

Declaration

publicvarplaygroundDescription:Any{get}

Subtractother from this integer in place, and return a flag indicating if the operation caused anarithmetic overflow.other is shiftedshift digits to the left before being subtracted.

Declaration

publicmutatingfuncsubtractReportingOverflow(_b:BigUInt,shiftedByshift:Int=0)->Bool

Subtractother from this integer, returning the difference and a flag indicating arithmetic overflow.other is shiftedshift digits to the left before being subtracted.

Declaration

publicfuncsubtractingReportingOverflow(_other:BigUInt,shiftedByshift:Int)->(partialValue:BigUInt,overflow:Bool)

Subtractsother fromself, returning the result and a flag indicating arithmetic overflow.

Declaration

publicfuncsubtractingReportingOverflow(_other:BigUInt)->(partialValue:BigUInt,overflow:Bool)

Subtractother from this integer in place.other is shiftedshift digits to the left before being subtracted.

Declaration

publicmutatingfuncsubtract(_other:BigUInt,shiftedByshift:Int=0)

Subtractb from this integer, and return the difference.b is shiftedshift digits to the left before being subtracted.

Declaration

publicfuncsubtracting(_other:BigUInt,shiftedByshift:Int=0)->BigUInt

Decrement this integer by one.

Declaration

publicmutatingfuncdecrement(shiftedByshift:Int=0)

Subtractb froma and return the result.

Declaration

publicstaticfunc-(a:BigUInt,b:BigUInt)->BigUInt

Subtractb froma and store the result ina.

Declaration

publicstaticfunc-=(a:inoutBigUInt,b:BigUInt)

Undocumented

Declaration

publicsubscript(bitAtindex:Int)->Bool{getset}

The minimum number of bits required to represent this integer in binary.

Declaration

publicvarbitWidth:Int{get}

Return Value

floor(log2(2 * self + 1))

The number of leading zero bits in the binary representation of this integer in base2^(Word.bitWidth).This is useful when you need to normalize aBigUInt such that the top bit of its most significant word is 1.

Declaration

publicvarleadingZeroBitCount:Int{get}

Return Value

A value in0...(Word.bitWidth - 1).

The number of trailing zero bits in the binary representation of this integer.

Declaration

publicvartrailingZeroBitCount:Int{get}

Return Value

A value in0...width.

Declaration

publicstructWords:RandomAccessCollection

Declaration

publicvarwords:Words{get}

Undocumented

Declaration

publicinit<Words>(words:Words)whereWords:Sequence,Words.Element==BigUInt.Word