Fibonacci number

 0, 1, 1, 2, 3, 5, 8, 13, 21, ???

type
    /// domain for Fibonacci function
    /// where result is within nativeUInt
    // You can not name it fibonacciDomain,
    // since the Fibonacci function itself
    // is defined for all whole numbers
    // but the result beyond F(n) exceeds high(nativeUInt).
    fibonacciLeftInverseRange =
        {$ifdef CPU64} 0..93 {$else} 0..47 {$endif};

{**
    implements Fibonacci sequence recursively
    
    \param n the index of the Fibonacci number to retrieve
    \returns the Fibonacci value at n
}
function fibonacci(const n: fibonacciLeftInverseRange): nativeUInt;
begin
    // optimization: then part gets executed most of the time
    if n > 1 then
    begin
        fibonacci := fibonacci(n - 2) + fibonacci(n - 1);
    end
    else
    begin
        // since the domain is restricted to non-negative integers
        // we can bluntly assign the result to n
        fibonacci := n;
    end;
end;

{**
    implements Fibonacci sequence iteratively
    
    \param n the index of the Fibonacci number to calculate
    \returns the Fibonacci value at n
}
function fibonacci(const n: fibonacciLeftInverseRange): nativeUInt;
type
    /// more meaningful identifiers than simple integers
    relativePosition = (previous, current, next);
var
    /// temporary iterator variable
    i: longword;
    /// holds preceding fibonacci values
    f: array[relativePosition] of nativeUInt;
begin
    f[previous] := 0;
    f[current] := 1;
    
    // note, in Pascal for-loop-limits are inclusive
    for i := 1 to n do
    begin
        f[next] := f[previous] + f[current];
        f[previous] := f[current];
        f[current] := f[next];
    end;
    
    // assign to previous, bc f[current] = f[next] for next iteration
    fibonacci := f[previous];
end;