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Generic number literal

A generic numeral G. It allows writing functions for arbitrary numeric type. The transformation is an efficient one, because it is implemented explicitly for every type. It combines the type classes technique of FsControl (https://github.com/gmpl/FsControl and http://nut-cracker.azurewebsites.net/typeclasses-for-fsharp) with numeric literals. But FsControl is removed to completely avoid unnecessary function calls.

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open System.Numerics
// optional
open MathNet.Numerics

module NumericLiteralG = 
    type GenericNumber = GenericNumber with
        static member instance (GenericNumber, x:int32, _:int8) = fun () -> int8 x
        static member instance (GenericNumber, x:int32, _:uint8) = fun () -> uint8 x
        static member instance (GenericNumber, x:int32, _:int16) = fun () -> int16 x
        static member instance (GenericNumber, x:int32, _:uint16) = fun () -> uint16 x
        static member instance (GenericNumber, x:int32, _:int32) = fun () -> x
        static member instance (GenericNumber, x:int32, _:uint32) = fun () -> uint32 x
        static member instance (GenericNumber, x:int32, _:int64) = fun () -> int64 x
        static member instance (GenericNumber, x:int32, _:uint64) = fun () -> uint64 x
        static member instance (GenericNumber, x:int32, _:float32) = fun () -> float32 x
        static member instance (GenericNumber, x:int32, _:float) = fun () -> float x
        static member instance (GenericNumber, x:int32, _:bigint) = fun () -> bigint x
        static member instance (GenericNumber, x:int32, _:decimal) = fun () -> decimal x
        static member instance (GenericNumber, x:int32, _:Complex) = fun () -> Complex.op_Implicit x
        static member instance (GenericNumber, x:int64, _:int64) = fun () -> int64 x
        static member instance (GenericNumber, x:int64, _:uint64) = fun () -> uint64 x
        static member instance (GenericNumber, x:int64, _:float32) = fun () -> float32 x
        static member instance (GenericNumber, x:int64, _:float) = fun () -> float x
        static member instance (GenericNumber, x:int64, _:bigint) = fun () -> bigint x
        static member instance (GenericNumber, x:int64, _:decimal) = fun () -> decimal x
        static member instance (GenericNumber, x:int64, _:Complex) = fun () -> Complex.op_Implicit x
        static member instance (GenericNumber, x:string, _:float32) = fun () -> float32 x
        static member instance (GenericNumber, x:string, _:float) = fun () -> float x
        static member instance (GenericNumber, x:string, _:bigint) = fun () -> bigint.Parse x
        static member instance (GenericNumber, x:string, _:decimal) = fun () -> decimal x
        static member instance (GenericNumber, x:string, _:Complex) = fun () -> Complex(float x, 0.0)
        // MathNet.Numerics
        static member instance (GenericNumber, x:int32, _:Complex32) = fun () -> Complex32.op_Implicit x
        static member instance (GenericNumber, x:int32, _:bignum) = fun () -> bignum.FromInt x
        static member instance (GenericNumber, x:int64, _:Complex32) = fun () -> Complex32.op_Implicit x
        static member instance (GenericNumber, x:int64, _:bignum) = fun () -> bignum.FromBigInt (bigint x)
        static member instance (GenericNumber, x:string, _:Complex32) = fun () -> Complex32(float32 x, 0.0f)
        static member instance (GenericNumber, x:string, _:bignum) = fun () -> bignum.FromBigInt (bigint.Parse x)

    let inline genericNumber num = Inline.instance (GenericNumber, num) ()

    let inline FromZero () = LanguagePrimitives.GenericZero
    let inline FromOne () = LanguagePrimitives.GenericOne
    let inline FromInt32 n = genericNumber n
    let inline FromInt64 n = genericNumber n
    let inline FromString n = genericNumber n
namespace System
namespace System.Numerics
namespace MathNet
namespace MathNet.Numerics
module NumericLiteralG

from Script
Multiple items
union case GenericNumber.GenericNumber: GenericNumber

--------------------
type GenericNumber =
  | GenericNumber
  static member instance : GenericNumber:GenericNumber * x:int32 * int8 -> (unit -> sbyte)
  static member instance : GenericNumber:GenericNumber * x:int32 * uint8 -> (unit -> byte)
  static member instance : GenericNumber:GenericNumber * x:int32 * int16 -> (unit -> int16)
  static member instance : GenericNumber:GenericNumber * x:int32 * uint16 -> (unit -> uint16)
  static member instance : GenericNumber:GenericNumber * x:int32 * int32 -> (unit -> int32)
  static member instance : GenericNumber:GenericNumber * x:int32 * uint32 -> (unit -> uint32)
  static member instance : GenericNumber:GenericNumber * x:int32 * int64 -> (unit -> int64)
  static member instance : GenericNumber:GenericNumber * x:int32 * uint64 -> (unit -> uint64)
  static member instance : GenericNumber:GenericNumber * x:int32 * float32 -> (unit -> float32)
  static member instance : GenericNumber:GenericNumber * x:int32 * float -> (unit -> float)
  static member instance : GenericNumber:GenericNumber * x:int32 * bigint -> (unit -> BigInteger)
  static member instance : GenericNumber:GenericNumber * x:int32 * decimal -> (unit -> decimal)
  static member instance : GenericNumber:GenericNumber * x:int32 * Complex -> (unit -> Complex)
  static member instance : GenericNumber:GenericNumber * x:int64 * int64 -> (unit -> int64)
  static member instance : GenericNumber:GenericNumber * x:int64 * uint64 -> (unit -> uint64)
  static member instance : GenericNumber:GenericNumber * x:int64 * float32 -> (unit -> float32)
  static member instance : GenericNumber:GenericNumber * x:int64 * float -> (unit -> float)
  static member instance : GenericNumber:GenericNumber * x:int64 * bigint -> (unit -> BigInteger)
  static member instance : GenericNumber:GenericNumber * x:int64 * decimal -> (unit -> decimal)
  static member instance : GenericNumber:GenericNumber * x:int64 * Complex -> (unit -> Complex)
  static member instance : GenericNumber:GenericNumber * x:string * float32 -> (unit -> float32)
  static member instance : GenericNumber:GenericNumber * x:string * float -> (unit -> float)
  static member instance : GenericNumber:GenericNumber * x:string * bigint -> (unit -> BigInteger)
  static member instance : GenericNumber:GenericNumber * x:string * decimal -> (unit -> decimal)
  static member instance : GenericNumber:GenericNumber * x:string * Complex -> (unit -> Complex)
  static member instance : GenericNumber:GenericNumber * x:int32 * Complex32 -> (unit -> Complex32)
  static member instance : GenericNumber:GenericNumber * x:int32 * bignum -> (unit -> BigRational)
  static member instance : GenericNumber:GenericNumber * x:int64 * Complex32 -> (unit -> Complex32)
  static member instance : GenericNumber:GenericNumber * x:int64 * bignum -> (unit -> BigRational)
  static member instance : GenericNumber:GenericNumber * x:string * Complex32 -> (unit -> Complex32)
  static member instance : GenericNumber:GenericNumber * x:string * bignum -> (unit -> BigRational)

Full name: Script.NumericLiteralG.GenericNumber
static member GenericNumber.instance : GenericNumber:GenericNumber * x:int32 * int8 -> (unit -> sbyte)

Full name: Script.NumericLiteralG.GenericNumber.instance
val x : int32
Multiple items
val int32 : value:'T -> int32 (requires member op_Explicit)

Full name: Microsoft.FSharp.Core.Operators.int32

--------------------
type int32 = System.Int32

Full name: Microsoft.FSharp.Core.int32
Multiple items
val int8 : value:'T -> sbyte (requires member op_Explicit)

Full name: Microsoft.FSharp.Core.ExtraTopLevelOperators.int8

--------------------
type int8 = System.SByte

Full name: Microsoft.FSharp.Core.int8
static member GenericNumber.instance : GenericNumber:GenericNumber * x:int32 * uint8 -> (unit -> byte)

Full name: Script.NumericLiteralG.GenericNumber.instance
Multiple items
val uint8 : value:'T -> byte (requires member op_Explicit)

Full name: Microsoft.FSharp.Core.ExtraTopLevelOperators.uint8

--------------------
type uint8 = System.Byte

Full name: Microsoft.FSharp.Core.uint8
static member GenericNumber.instance : GenericNumber:GenericNumber * x:int32 * int16 -> (unit -> int16)

Full name: Script.NumericLiteralG.GenericNumber.instance
Multiple items
val int16 : value:'T -> int16 (requires member op_Explicit)

Full name: Microsoft.FSharp.Core.Operators.int16

--------------------
type int16 = System.Int16

Full name: Microsoft.FSharp.Core.int16

--------------------
type int16<'Measure> = int16

Full name: Microsoft.FSharp.Core.int16<_>
static member GenericNumber.instance : GenericNumber:GenericNumber * x:int32 * uint16 -> (unit -> uint16)

Full name: Script.NumericLiteralG.GenericNumber.instance
Multiple items
val uint16 : value:'T -> uint16 (requires member op_Explicit)

Full name: Microsoft.FSharp.Core.Operators.uint16

--------------------
type uint16 = System.UInt16

Full name: Microsoft.FSharp.Core.uint16
static member GenericNumber.instance : GenericNumber:GenericNumber * x:int32 * int32 -> (unit -> int32)

Full name: Script.NumericLiteralG.GenericNumber.instance
static member GenericNumber.instance : GenericNumber:GenericNumber * x:int32 * uint32 -> (unit -> uint32)

Full name: Script.NumericLiteralG.GenericNumber.instance
Multiple items
val uint32 : value:'T -> uint32 (requires member op_Explicit)

Full name: Microsoft.FSharp.Core.Operators.uint32

--------------------
type uint32 = System.UInt32

Full name: Microsoft.FSharp.Core.uint32
static member GenericNumber.instance : GenericNumber:GenericNumber * x:int32 * int64 -> (unit -> int64)

Full name: Script.NumericLiteralG.GenericNumber.instance
Multiple items
val int64 : value:'T -> int64 (requires member op_Explicit)

Full name: Microsoft.FSharp.Core.Operators.int64

--------------------
type int64 = System.Int64

Full name: Microsoft.FSharp.Core.int64

--------------------
type int64<'Measure> = int64

Full name: Microsoft.FSharp.Core.int64<_>
static member GenericNumber.instance : GenericNumber:GenericNumber * x:int32 * uint64 -> (unit -> uint64)

Full name: Script.NumericLiteralG.GenericNumber.instance
Multiple items
val uint64 : value:'T -> uint64 (requires member op_Explicit)

Full name: Microsoft.FSharp.Core.Operators.uint64

--------------------
type uint64 = System.UInt64

Full name: Microsoft.FSharp.Core.uint64
static member GenericNumber.instance : GenericNumber:GenericNumber * x:int32 * float32 -> (unit -> float32)

Full name: Script.NumericLiteralG.GenericNumber.instance
Multiple items
val float32 : value:'T -> float32 (requires member op_Explicit)

Full name: Microsoft.FSharp.Core.Operators.float32

--------------------
type float32 = System.Single

Full name: Microsoft.FSharp.Core.float32

--------------------
type float32<'Measure> = float32

Full name: Microsoft.FSharp.Core.float32<_>
static member GenericNumber.instance : GenericNumber:GenericNumber * x:int32 * float -> (unit -> float)

Full name: Script.NumericLiteralG.GenericNumber.instance
Multiple items
val float : value:'T -> float (requires member op_Explicit)

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

--------------------
type float = System.Double

Full name: Microsoft.FSharp.Core.float

--------------------
type float<'Measure> = float

Full name: Microsoft.FSharp.Core.float<_>
static member GenericNumber.instance : GenericNumber:GenericNumber * x:int32 * bigint -> (unit -> BigInteger)

Full name: Script.NumericLiteralG.GenericNumber.instance
type bigint = BigInteger

Full name: Microsoft.FSharp.Core.bigint
static member GenericNumber.instance : GenericNumber:GenericNumber * x:int32 * decimal -> (unit -> decimal)

Full name: Script.NumericLiteralG.GenericNumber.instance
Multiple items
val decimal : value:'T -> decimal (requires member op_Explicit)

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

--------------------
type decimal = System.Decimal

Full name: Microsoft.FSharp.Core.decimal

--------------------
type decimal<'Measure> = decimal

Full name: Microsoft.FSharp.Core.decimal<_>
static member GenericNumber.instance : GenericNumber:GenericNumber * x:int32 * Complex -> (unit -> Complex)

Full name: Script.NumericLiteralG.GenericNumber.instance
Multiple items
type Complex =
  struct
    new : real:float * imaginary:float -> Complex
    member Equals : obj:obj -> bool + 1 overload
    member GetHashCode : unit -> int
    member Imaginary : float
    member Magnitude : float
    member Phase : float
    member Real : float
    member ToString : unit -> string + 3 overloads
    static val Zero : Complex
    static val One : Complex
    ...
  end

Full name: System.Numerics.Complex

--------------------
Complex()
Complex(real: float, imaginary: float) : unit
Complex.op_Implicit(value: float) : Complex
Complex.op_Implicit(value: float32) : Complex
Complex.op_Implicit(value: byte) : Complex
Complex.op_Implicit(value: sbyte) : Complex
Complex.op_Implicit(value: uint64) : Complex
Complex.op_Implicit(value: uint32) : Complex
Complex.op_Implicit(value: uint16) : Complex
Complex.op_Implicit(value: int64) : Complex
Complex.op_Implicit(value: int) : Complex
Complex.op_Implicit(value: int16) : Complex
static member GenericNumber.instance : GenericNumber:GenericNumber * x:int64 * int64 -> (unit -> int64)

Full name: Script.NumericLiteralG.GenericNumber.instance
val x : int64
static member GenericNumber.instance : GenericNumber:GenericNumber * x:int64 * uint64 -> (unit -> uint64)

Full name: Script.NumericLiteralG.GenericNumber.instance
static member GenericNumber.instance : GenericNumber:GenericNumber * x:int64 * float32 -> (unit -> float32)

Full name: Script.NumericLiteralG.GenericNumber.instance
static member GenericNumber.instance : GenericNumber:GenericNumber * x:int64 * float -> (unit -> float)

Full name: Script.NumericLiteralG.GenericNumber.instance
static member GenericNumber.instance : GenericNumber:GenericNumber * x:int64 * bigint -> (unit -> BigInteger)

Full name: Script.NumericLiteralG.GenericNumber.instance
static member GenericNumber.instance : GenericNumber:GenericNumber * x:int64 * decimal -> (unit -> decimal)

Full name: Script.NumericLiteralG.GenericNumber.instance
static member GenericNumber.instance : GenericNumber:GenericNumber * x:int64 * Complex -> (unit -> Complex)

Full name: Script.NumericLiteralG.GenericNumber.instance
static member GenericNumber.instance : GenericNumber:GenericNumber * x:string * float32 -> (unit -> float32)

Full name: Script.NumericLiteralG.GenericNumber.instance
val x : string
Multiple items
val string : value:'T -> string

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

--------------------
type string = System.String

Full name: Microsoft.FSharp.Core.string
static member GenericNumber.instance : GenericNumber:GenericNumber * x:string * float -> (unit -> float)

Full name: Script.NumericLiteralG.GenericNumber.instance
static member GenericNumber.instance : GenericNumber:GenericNumber * x:string * bigint -> (unit -> BigInteger)

Full name: Script.NumericLiteralG.GenericNumber.instance
BigInteger.Parse(value: string) : BigInteger
BigInteger.Parse(value: string, provider: System.IFormatProvider) : BigInteger
BigInteger.Parse(value: string, style: System.Globalization.NumberStyles) : BigInteger
BigInteger.Parse(value: string, style: System.Globalization.NumberStyles, provider: System.IFormatProvider) : BigInteger
static member GenericNumber.instance : GenericNumber:GenericNumber * x:string * decimal -> (unit -> decimal)

Full name: Script.NumericLiteralG.GenericNumber.instance
static member GenericNumber.instance : GenericNumber:GenericNumber * x:string * Complex -> (unit -> Complex)

Full name: Script.NumericLiteralG.GenericNumber.instance
static member GenericNumber.instance : GenericNumber:GenericNumber * x:int32 * Complex32 -> (unit -> Complex32)

Full name: Script.NumericLiteralG.GenericNumber.instance
Multiple items
type Complex32 =
  struct
    new : real:float32 * imaginary:float32 -> Complex32
    member CommonLogarithm : unit -> Complex32
    member Conjugate : unit -> Complex32
    member CubicRoots : unit -> Tuple<Complex32, Complex32, Complex32>
    member Equals : other:Complex32 -> bool + 1 overload
    member Exponential : unit -> Complex32
    member GetHashCode : unit -> int
    member Imaginary : float32
    member IsImaginaryOne : unit -> bool
    member IsInfinity : unit -> bool
    ...
  end

Full name: MathNet.Numerics.Complex32

--------------------
Complex32()
Complex32(real: float32, imaginary: float32) : unit
Complex32.op_Implicit(value: float32) : Complex32
Complex32.op_Implicit(value: uint64) : Complex32
Complex32.op_Implicit(value: uint32) : Complex32
Complex32.op_Implicit(value: int64) : Complex32
Complex32.op_Implicit(value: BigInteger) : Complex32
Complex32.op_Implicit(value: int) : Complex32
Complex32.op_Implicit(value: uint16) : Complex32
Complex32.op_Implicit(value: sbyte) : Complex32
Complex32.op_Implicit(value: int16) : Complex32
Complex32.op_Implicit(value: byte) : Complex32
static member GenericNumber.instance : GenericNumber:GenericNumber * x:int32 * bignum -> (unit -> BigRational)

Full name: Script.NumericLiteralG.GenericNumber.instance
type bignum = BigRational

Full name: MathNet.Numerics.bignum
static member BigRational.FromInt : int -> BigRational
static member GenericNumber.instance : GenericNumber:GenericNumber * x:int64 * Complex32 -> (unit -> Complex32)

Full name: Script.NumericLiteralG.GenericNumber.instance
static member GenericNumber.instance : GenericNumber:GenericNumber * x:int64 * bignum -> (unit -> BigRational)

Full name: Script.NumericLiteralG.GenericNumber.instance
static member BigRational.FromBigInt : BigInteger -> BigRational
static member GenericNumber.instance : GenericNumber:GenericNumber * x:string * Complex32 -> (unit -> Complex32)

Full name: Script.NumericLiteralG.GenericNumber.instance
static member GenericNumber.instance : GenericNumber:GenericNumber * x:string * bignum -> (unit -> BigRational)

Full name: Script.NumericLiteralG.GenericNumber.instance
val genericNumber : num:'a -> 'b

Full name: Script.NumericLiteralG.genericNumber
val num : 'a
val FromZero : unit -> 'a (requires member get_Zero)

Full name: Script.NumericLiteralG.FromZero
module LanguagePrimitives

from Microsoft.FSharp.Core
val GenericZero<'T (requires member get_Zero)> : 'T (requires member get_Zero)

Full name: Microsoft.FSharp.Core.LanguagePrimitives.GenericZero
val FromOne : unit -> 'a (requires member get_One)

Full name: Script.NumericLiteralG.FromOne
val GenericOne<'T (requires member get_One)> : 'T (requires member get_One)

Full name: Microsoft.FSharp.Core.LanguagePrimitives.GenericOne
val FromInt32 : n:'a -> 'b

Full name: Script.NumericLiteralG.FromInt32
val n : 'a
val FromInt64 : n:'a -> 'b

Full name: Script.NumericLiteralG.FromInt64
val FromString : n:'a -> 'b

Full name: Script.NumericLiteralG.FromString
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More information

Link:http://fssnip.net/mv
Posted:10 years ago
Author:Daniel Fabian (@iceypoi)
Tags: math , numerics , generics , type classes

This web site is created using F# and Suave web server. It is hosted on Azure and the source code is on GitHub. Contributions are welcome!

The first version of fssnip.net has been created by @tomaspetricek back in 2010. This web site is a new, open-source and contribution-friendly version.