# Fraction

Arbitrary precision fraction in Swift.

## Usage

Fraction can be converted from `BinaryInteger`, `BinaryFloatingPoint` or `String`.
It supports nearly all the methods and members that a `BinaryFloatingPoint` should have. But it is not binary as it uses `Int10` as its numerator and denominator type.
`Int10` is an arbitrary precision floating point created by the same author.

## Example

Basic arithmetic.

```let a: Fraction = 1/2
let b: Fraction = 3/2
print(pow(a, b)) //prints 7997214/22619537```

Inverse trigonometric functions.

```let a: Fraction = 1/2
print(artanh(a)) //prints 241031271779/438792236834```

## Precision

By default, `Double` is used to calculate in events like `sqrt(_:)`. In these circumstances, precision will be lost, the result return is only an approximation. This is reasonable as it is impossible to find the exact result of, for example, `sqrt(2)`.

## Converting from `String`

```print(Fraction("1/2")!) // 1/2
print(Fraction("0.5")!) // 1/2
print(Fraction("1")!)   // 1```

## Converting from `BinaryFloatingPoint`

If the length of decimal part the float is less or equal to 10 or it is a recruiting decimal, a precise fraction would be produced.

Otherwise, approximate x by

``````                   1
d1 + ----------------------
1
d2 + -------------------
1
d3 + ----------------
1
d4 + -------------
1
d5 + ----------
1
d6 + ------
1
d7 + ---
d8
``````

## Install

Source code could be found in releases.
Please make sure you copy all three files of /Fraction/Fraction.swift, /Fraction/Int10.swift and /Fraction/Arithmetical.swift.

## Speed

If you need the process to be fast while rarely encounter large values, it is suggested to change line 19 in Fraction.swift to `typealias Integer = Int`. After modifying a few things, `Int` is used to represent the numerator and denominator.

## About `Int10`.

It is a structure of arbitrary-precise Signed Integer of radix 10.

```let a = Int10("12345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890")!
print(a) // prints 12345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890```

```let a = Int10("1000")!
print(a.factorial) // prints 402387260077093773543702433923003985719374864210714632543799910429938512398629020592044208486969404800479988610197196058631666872994808558901323829669944590997424504087073759918823627727188732519779505950995276120874975462497043601418278094646496291056393887437886487337119181045825783647849977012476632889835955735432513185323958463075557409114262417474349347553428646576611667797396668820291207379143853719588249808126867838374559731746136085379534524221586593201928090878297308431392844403281231558611036976801357304216168747609675871348312025478589320767169132448426236131412508780208000261683151027341827977704784635868170164365024153691398281264810213092761244896359928705114964975419909342221566832572080821333186116811553615836546984046708975602900950537616475847728421889679646244945160765353408198901385442487984959953319101723355556602139450399736280750137837615307127761926849034352625200015888535147331611702103968175921510907788019393178114194545257223865541461062892187960223838971476088506276862967146674697562911234082439208160153780889893964518263243671616762179168909779911903754031274622289988005195444414282012187361745992642956581746628302955570299024324153181617210465832036786906117260158783520751516284225540265170483304226143974286933061690897968482590125458327168226458066526769958652682272807075781391858178889652208164348344825993266043367660176999612831860788386150279465955131156552036093988180612138558600301435694527224206344631797460594682573103790084024432438465657245014402821885252470935190620929023136493273497565513958720559654228749774011413346962715422845862377387538230483865688976461927383814900140767310446640259899490222221765904339901886018566526485061799702356193897017860040811889729918311021171229845901641921068884387121855646124960798722908519296819372388642614839657382291123125024186649353143970137428531926649875337218940694281434118520158014123344828015051399694290153483077644569099073152433278288269864602789864321139083506217095002597389863554277196742822248757586765752344220207573630569498825087968928162753848863396909959826280956121450994871701244516461260379029309120889086942028510640182154399457156805941872748998094254742173582401063677404595741785160829230135358081840096996372524230560855903700624271243416909004153690105933983835777939410970027753472000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000```

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