<?php

class LogicUtils
{
    public static function extend(string $num, int $base, int $exnd, bool $comp): string
    {
        $fd = (int)(base_convert($num[0], $base, 10)); // get first digit as a number
        $extd = (string)(($comp && ($fd >= ($base / 2))) ? ($base - 1) : 0); // get the extension digit
        return str_pad((string)($num), $exnd, $extd, STR_PAD_LEFT); // extend to the left
    }

    public static function complement(string $num, int $base): string
    {
        // convert to an integer
        $M = (int)(base_convert($num, $base, 10));

        // check if the highest digit is less than the half of the base, if not, add a zero prefix
        $fd = (int)(base_convert($num[0], $base, 10));

        // create the basis for forming the complement
        $H = (string)($base - 1);
        $K_str = (int)(str_repeat($H, strlen($num)));
        if ($fd >= ($base / 2)) { // if one more digit is needed...
            $K_str = $H . $K_str; // prepend with a zero digit
        }

        // convert to integer
        $K = (int)(base_convert($K_str, $base, 10));

        // form the base's complement
        $C = $K - $M + 1;

        // convert to the final base
        return base_convert((string)$C, 10, $base);
    }

    public static function changeRepresentation(int $num, int $base, string $rep, int $digits): string {
        $neg = $num < 0; // store if the value is negative
        $numa_str = (string)(abs($num)); // create the absolute value as a string
        $numa_str = base_convert($numa_str, 10, $base); // convert to specific base
        if ($neg) {
            if ($rep === "s") {
                $numa_str = self::extend($numa_str, $base, $digits, false);
                $numa_str = "-" . $numa_str;
            } else if ($rep === "c") {
                $numa_str = self::complement($numa_str, $base);
                $numa_str = self::extend($numa_str, $base, $digits, true);
            }
        } else {
            $numa_str = self::extend($numa_str, $base, $digits, false);
            if (($rep === "c") && ($numa_str[0] >= ($base / 2))) {
                $numa_str = "0" . $numa_str;
            }
        }
        return $numa_str;
    }
}