Gist a fast Fibonacci

FastFibonacci.ps1

filter Get-Fibonacci {
    <#
    .SYNOPSIS
        Gets the fibonacci sequence
    .DESCRIPTION
        Gets the fibonacci sequence or ratio sequence using a bit of function state magic.
    .NOTES
        Stores the fibonacci sequence in the function definition.
        
        By keeping state between calls, we perform a very fast iterative implementation of the fibonacci sequence.

        This was inspired by the advanced generator example for JavaScript on MDN.

        Since PowerShell yields values rather than returns them, all PowerShell functions are effectively generators.
    .EXAMPLE
        # Get the next 3 fibonacci numbers
        fibonacci
        fibonacci
        fibonacci
    .EXAMPLE
        # See how long it takes to get the first 1kb of fibonacci numbers
        Measure-Command { fibonacci 1kb }
    .EXAMPLE
        # Get the fibonacci sequence so far
        fibonacci -Sequence
    .LINK
        https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Iterators_and_generators#advanced_generators
    #>
    [alias('Fibonacci')]
    param(
    # If we want, we can ask for the Nth number.
    [int]
    $N = -1,

    # If set, will output all numbers in the sequence
    [Alias('Sequence')] 
    [switch]
    $All,

    # If set, will get the ratio between numbers
    [switch]
    $Ratio
    )

    # If we are piped in a number greater than zero, use it
    if ($_ -is [int] -and $_ -ge 0) {
        $n = $_
    }

    # Get myself
    $my = $MyInvocation.MyCommand    

    # Initialize my state
    if (-not $my.Current) {        
        $my | 
            Add-Member NoteProperty Current (0) -Force -PassThru |
            Add-Member NoteProperty Next (1) -Force -PassThru |
            Add-Member NoteProperty Sequence @() -Force
    }

    # If we ask for the Nth number
    if ($n -ge 0) {
        # we just make sure we have called ourself that many times.
        while ($my.Sequence.Length -le $n) {
            $null = & $my                            
        }
        # If we want the ratio
        if ($ratio) {
            # divide by the previous number if there is one.
            if ($my.Sequence[$n - 1]) {
                return $my.Sequence[$n] / $my.Sequence[$n -1]
            } else {
                return $my.Sequence[$n]
            }            
        }
        # otherwise, return the Nth number in the sequence.
        return $my.Sequence[$n]
    }

    # If we want all of the sequence
    if ($all) {
        # and don't want the ratio
        if (-not $ratio) {
            # return the sequence
            return $my.Sequence            
        } else {
            # otherwise return all the ratios
            for ($n = 2; $n -lt $my.Sequence.Length; $n++) {
                $my.Sequence[$n]/$my.Sequence[$n-1]
            }
            return
        }        
    }
    
    # add the current number to the sequence    
    $my.Sequence += $my.Current

    # If we want the ratio, get current over next
    if ($Ratio) {
        $my.Current/$my.Next
    } else {
        $my.Current    
    }
    
    # Set current and next to next and next + current
    $my.Current, $my.Next = $my.Next, ($my.Next + $my.Current)
}

Measure-Command { Fibonacci 2kb }

$goldenRatio = (1 + [Math]::Sqrt(5))/2

(Fibonacci 42) / (Fibonacci 41) -eq $goldenRatio