Various formulas

adjust values linear, so that sum is 1

/// <summary>Takes a list of values and scales the values, so that the sum of the result is always 1 (100%).</summary>
/// <param name="values">A list of values that need to be scaled.</param>
/// <returns>Scaled values, from which the sum is 1.</returns>
let scaleSoThatSumIsOne (values:seq<decimal>) = 
    let Σ = Seq.sum values
    match Σ with
    | 0.0m -> 
        let n = decimal (Seq.length values)
        seq { 
            for p in values do 
                yield p + (1m / n)
        }
    | _ -> 
        let ΔΣ = 1m - Σ
        seq { 
            for p in values do 
                yield p + (p * ΔΣ/Σ)
        }

[<EntryPoint>]
let main argv = 
    for p in scaleSoThatSumIsOne [ 0.0m; -0.0m ] do 
        printfn "%M" p
    0

calculate epsilon of step in float datatypes

let ε = 
    let rec δ λ = 
        match λ+1.0 with 
        | 1.0 -> λ
        | _ -> δ(λ/2.0)
    δ(1.0)
 
[<EntryPoint>]
let main argv = 
    printfn "ε = %e" ε
    0