Rational type for units of measure

A more idiomatic definition of a Rational type with custom operators.

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// This is an alternative version of the type defined in the F# PR:
// https://visualfsharp.codeplex.com/SourceControl/network/forks/andrewjkennedy/fsharpcontrib/contribution/7632

let rec gcd a (b: int) =
  if b = 0 then a else
    gcd b (a % b)

let lcm a b = 
  (a * b) / gcd a b

type Rational = 
  { numerator: int
    denominator: int }
  static member Create(p, q) = 
    let p, q =
      if q = 0 then raise(System.DivideByZeroException())
      let g = gcd q p in
      p/g, q/g
 
    let p, q =
      if q > 0 then p, q else -p, -q
    
    { numerator = p
      denominator = q }

  static member (+) (m, n) =
    Rational.Create(m.numerator*n.denominator + n.numerator*m.denominator, m.denominator*n.denominator)

  static member (~-) m = 
    Rational.Create(-m.numerator, m.denominator)
 
  static member (*) (m, n) =
    Rational.Create(m.numerator*n.numerator, m.denominator*n.denominator)
 
  static member (/) (m, n) =
    Rational.Create(m.numerator*n.denominator, m.denominator*n.numerator)
 
  static member Abs(m) = 
    Rational.Create(abs m.numerator, m.denominator)
 
  override this.ToString() =
    if this.denominator = 1 then this.numerator.ToString() 
    else sprintf "(%A/%A)" this.numerator this.denominator

val gcd : a:int -> b:int -> int

Full name: Script.gcd

val a : int

val b : int

Multiple items
val int : value:'T -> int (requires member op_Explicit)

Full name: Microsoft.FSharp.Core.Operators.int

--------------------
type int = int32

Full name: Microsoft.FSharp.Core.int

--------------------
type int<'Measure> = int

Full name: Microsoft.FSharp.Core.int<_>

val lcm : a:int -> b:int -> int

Full name: Script.lcm

type Rational =
  {numerator: int;
   denominator: int;}
  override ToString : unit -> string
  static member Abs : m:Rational -> Rational
  static member Create : p:int * q:int -> Rational
  static member ( + ) : m:Rational * n:Rational -> Rational
  static member ( / ) : m:Rational * n:Rational -> Rational
  static member ( * ) : m:Rational * n:Rational -> Rational
  static member ( ~- ) : m:Rational -> Rational

Full name: Script.Rational

Rational.numerator: int

Rational.denominator: int

static member Rational.Create : p:int * q:int -> Rational

Full name: Script.Rational.Create

val p : int

val q : int

val raise : exn:System.Exception -> 'T

Full name: Microsoft.FSharp.Core.Operators.raise

namespace System

Multiple items
type DivideByZeroException =
inherit ArithmeticException
new : unit -> DivideByZeroException + 2 overloads

Full name: System.DivideByZeroException

--------------------
System.DivideByZeroException() : unit
System.DivideByZeroException(message: string) : unit
System.DivideByZeroException(message: string, innerException: exn) : unit

val g : int

val m : Rational

val n : Rational

static member Rational.Create : p:int * q:int -> Rational

static member Rational.Abs : m:Rational -> Rational

Full name: Script.Rational.Abs

val abs : value:'T -> 'T (requires member Abs)

Full name: Microsoft.FSharp.Core.Operators.abs

val this : Rational

override Rational.ToString : unit -> string

Full name: Script.Rational.ToString

System.Int32.ToString() : string
System.Int32.ToString(provider: System.IFormatProvider) : string
System.Int32.ToString(format: string) : string
System.Int32.ToString(format: string, provider: System.IFormatProvider) : string

val sprintf : format:Printf.StringFormat<'T> -> 'T

Full name: Microsoft.FSharp.Core.ExtraTopLevelOperators.sprintf

Raw view Test code New version

More information

Link:	http://fssnip.net/oC
Posted:	10 years ago
Author:	Tomas Petricek
Tags:	rational , math