private function doMul(string $a, string $b) : string
    {
        $x = \strlen($a);
        $y = \strlen($b);

        $maxDigits = \intdiv($this->maxDigits, 2);
        $complement = 10 ** $maxDigits;

        $result = '0';

        for ($i = $x - $maxDigits;; $i -= $maxDigits) {
            $blockALength = $maxDigits;

            if ($i < 0) {
                $blockALength += $i;
                $i = 0;
            }

            $blockA = (int) \substr($a, $i, $blockALength);

            $line = '';
            $carry = 0;

            for ($j = $y - $maxDigits;; $j -= $maxDigits) {
                $blockBLength = $maxDigits;

                if ($j < 0) {
                    $blockBLength += $j;
                    $j = 0;
                }

                $blockB = (int) \substr($b, $j, $blockBLength);

                $mul = $blockA * $blockB + $carry;
                $value = $mul % $complement;
                $carry = ($mul - $value) / $complement;

                $value = (string) $value;
                $value = \str_pad($value, $maxDigits, '0', STR_PAD_LEFT);

                $line = $value . $line;

                if ($j === 0) {
                    break;
                }
            }

            if ($carry !== 0) {
                $line = $carry . $line;
            }

            $line = \ltrim($line, '0');

            if ($line !== '') {
                $line .= \str_repeat('0', $x - $blockALength - $i);
                $result = $this->add($result, $line);
            }

            if ($i === 0) {
                break;
            }
        }

        return $result;
    }