按索引获取斐波那契数 - PHP

Question

I have a simple PHP function that returns Fibonacci numbers by index and it works:

function fibIndexCalculator($index)
{
    $numbers = [0, 1];
    for ($i = 0; $i < $index; $i++) {
        $lastNumbers = array_slice($numbers, count($numbers) - 2, 2);
        $numbers[] = $lastNumbers[0] + $lastNumbers[1];
    }
    return end($numbers);
}
var_dump(fibIndexCalculator(4));

But if I give the function an index like 200000, then only after 1 hour I can see the result.

Is there any way to change the algorithm for getting the Fibonacci number with a large index in a fast way?

Answer 1

if I give the function an index like 200000, then only after 1 hour I can see the result.

If you do that you'll not see any useful result. The output will be INF. This is because The 64-bit floating point that PHP uses has a maximum value it can represent that is somewhere near 1.797E+308. The Fibonacci number with index 1475 is already around 1E+308...

But up to the limit of floating point, you can use the following direct formula:

function fibIndexCalculator($index) {
    $SQRT5 = sqrt(5);
    return round(((1 + $SQRT5) / 2)**$index / $SQRT5);
}

If you want to stick to the iterative solution, then note how you accumulate an array, where you never use the old values in that array again -- only the last two values. So don't keep an array, but just two variables:

function fibIndexCalculator2($index) {
    if ($index < 2) return $index;
    $b = 1;
    $c = 1;
    while ($index > 2) {
        $a = $b;
        $b = $c;
        $c = $a + $b;
        $index--;
    }
    return $c;
}