PHP: Negative Base Conversion from Base 10 Decimal

negabase.php

<?php

/**
 * Negabase
 * To convert a decimal to negative base.
 * Divide the number by the negative base.
 * Acquire the whole number quotient and remainder.
 * If the remainder is negative, add 1 to the quotient and add the absolute value of the base to the remainder.
 * Divide the quotient by the negative base... rinse and repeat until the quotient is 0.
 * Aggregate the remainders in reverse (as a stack), and you have your negative base representation.
 */

function negative_base ($decimal, $base) {

    // initialise a digit stack
    $digits = [];

    // divide the decimal by the base repeatedly until the quotient is 0
    while ($decimal != 0) {

        // how many of the base exist in the quotient?
        $quotient = intval($decimal / $base);
        // modulus can return negative numbers
        $remainder = $decimal % $base;

        // negative base numbers do not have negative digits
        // if we get a negative remainder from the modulus
        // all we have to do is increment the quotient
        // and add the absolute value of the base to the remainder
        // This works because:
        //     (a/b = q r) -> (b*q + r = a) where 
        //         a => numerator, 
        //         b => denominator, 
        //         q => quotient, 
        //         r => remainder
        // If we get a negative remainder, we can just increment the quotient multiplying the denominator
        // giving us a number greater than the numerator
        // Subtracting this number from the numerator gives us a positive remainder
        // For example: (-5 / -2) => (2 r:-1) => (3 r:1) because [3 * -2 = -6 -> -6 + 1 -5 -> r:1]
        if ($remainder < 0) {
            $quotient += 1;
            $remainder += (-1 * $base);
        }

        // repeat the division using the new quotient
        $decimal = $quotient;

        // push the current number onto the stack
        array_unshift($digits, $remainder);

    }

    return $digits;

}

$number = 42;
$base = -2;
$negative_base_number = negative_base($number, $base);