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Square root for integral types

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module NumericLiteralG =
    let inline FromZero () = LanguagePrimitives.GenericZero
    let inline FromOne () = LanguagePrimitives.GenericOne

let inline isqrt num =
    if num > 0G then
        let two = 1G + 1G
        let inline reduce n = (num / n + n) / two
        let rec impl n = function
            | n' when n' <= n -> n'
            | _               -> impl (reduce n) n
        let n = num / two + 1G
        impl (reduce n) n
    elif num = 0G then num
    else invalidArg "num" "negative numbers are not supported"

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 isqrt : num:'a -> 'a (requires member ( + ) and member get_Zero and member ( / ) and member ( / ) and comparison and member ( / ) and member get_One and member ( + ) and member get_One and member ( + ) and member get_One)

Full name: Script.isqrt

val num : 'a (requires member ( + ) and member get_Zero and member ( / ) and member ( / ) and comparison and member ( / ) and member get_One and member ( + ) and member get_One and member ( + ) and member get_One)

val two : 'd (requires member ( / ) and member ( / ) and member get_One and member ( + ) and member get_One and member ( + ) and member get_Zero and member ( / ) and comparison and member ( + ) and member get_One)

val reduce : ('a -> 'a) (requires member ( + ) and member get_Zero and member ( / ) and member ( / ) and comparison and member ( / ) and member get_One and member ( + ) and member get_One and member ( + ) and member get_One)

val n : 'a (requires member ( + ) and member get_Zero and member ( / ) and member ( / ) and comparison and member ( / ) and member get_One and member ( + ) and member get_One and member ( + ) and member get_One)

val impl : ('a -> 'a -> 'a) (requires member ( + ) and member get_Zero and member ( / ) and member ( / ) and comparison and member ( / ) and member get_One and member ( + ) and member get_One and member ( + ) and member get_One)

val n' : 'a (requires member ( + ) and member get_Zero and member ( / ) and member ( / ) and comparison and member ( / ) and member get_One and member ( + ) and member get_One and member ( + ) and member get_One)

val invalidArg : argumentName:string -> message:string -> 'T

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

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More information

Link:	http://fssnip.net/dR
Posted:	12 years ago
Author:	ildjarn
Tags:	math , square root , sqrt