PHP - How to base_convert() up to base 62

Question

I need a base_convert() function that works from base 2 up to base 62 but I'm missing the math I need to use, I know that due to the limitations of PHP I need to make use of bcmath, which is fine.

Functions like these convert a number to and from base 10 to another base up to 62, but I want to implement the same functionality of base_convert(), e.g.: a only one function that can convert between arbitrary bases.

I've found a function that seems to do this, but it gives me the feeling of having some redundant and slow code and I would like to tweak it a little bit if I knew German, which I don't. =(

Here is a more readable version of the function:

function bc_base_convert($value, $quellformat, $zielformat)
{
    $vorrat = '0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ';

    if (min($quellformat, $zielformat) < 2)
    {
        trigger_error('Bad Format min: 2', E_USER_ERROR);
    }

    if (max($quellformat, $zielformat) > strlen($vorrat))
    {
        trigger_error('Bad Format max: ' . strlen($vorrat), E_USER_ERROR);
    }

    $dezi = '0';
    $level = 0;
    $result = '';
    $value = trim(strval($value), "\r\n\t +");
    $vorzeichen = '-' === $value{0} ? '-' : '';
    $value = ltrim($value, "-0");
    $len = strlen($value);

    for ($i = 0; $i < $len; $i++)
    {
        $wert = strpos($vorrat, $value{$len - 1 - $i});

        if (FALSE === $wert)
        {
            trigger_error('Bad Char in input 1', E_USER_ERROR);
        }

        if ($wert >= $quellformat)
        {
            trigger_error('Bad Char in input 2', E_USER_ERROR);
        }

        $dezi = bcadd($dezi, bcmul(bcpow($quellformat, $i), $wert));
    }

    if (10 == $zielformat)
    {
        return $vorzeichen . $dezi; // abkürzung
    }

    while (1 !== bccomp(bcpow($zielformat, $level++), $dezi));

    for ($i = $level - 2; $i >= 0; $i--)
    {
        $factor = bcpow($zielformat, $i);
        $zahl = bcdiv($dezi, $factor, 0);
        $dezi = bcmod($dezi, $factor);
        $result .= $vorrat{$zahl};
    }

    $result = empty($result) ? '0' : $result;

    return $vorzeichen . $result;
}

Can anyone explain me the above function or give me some lights on the process of direct conversion between arbitrary bases?

Answer 1

As of PHP 5.3.2 both bc_math and gmp now support bases up to 62, so you can just do:

echo gmp_strval(gmp_init($mynumber, $srcbase), $destbase);

or the bc_math equivalent.

Answer 2

Please dont ask me where i got it from, i just remeber that its based of some examples i found on the web...

  function charset_base_convert ($numstring, $fromcharset, $tocharset) {
     $frombase=strlen($fromcharset);
     $tobase=strlen($tocharset);
     $chars = $fromcharset;
     $tostring = $tocharset;

     $length = strlen($numstring);
     $result = '';
     for ($i = 0; $i < $length; $i++) {
         $number[$i] = strpos($chars, $numstring{$i});
     }
     do {
         $divide = 0;
         $newlen = 0;
         for ($i = 0; $i < $length; $i++) {
             $divide = $divide * $frombase + $number[$i];
             if ($divide >= $tobase) {
                 $number[$newlen++] = (int)($divide / $tobase);
                 $divide = $divide % $tobase;
             } elseif ($newlen > 0) {
                 $number[$newlen++] = 0;
             }
         }
         $length = $newlen;
         $result = $tostring{$divide} . $result;
     }
     while ($newlen != 0);
     return $result;
  }

Answer 3

The easiest approach for any translation problems, from numeric base to human languages, is to translate via an intermediate format.

function bc_base_convert($num, $from, $to) {
    return bc_convert_to(bc_parse_num($num, $from), $to);
}

Now all you need to write are bc_convert_to and bc_parse_num. If the platform distinguishes numeric types, you'll need to take this in to account. Also, floating point numbers require special consideration because a number may have a finite representation in one base, but not another (e.g. 1/3 is 0.1₃ but 0.333...₁₀, and 1/10₁₀ is .0001100110011...₂).

As for a generalized explanation of how conversion works, consider how positional base systems work. A numeral of the form "a_na_n-1...a₁a₀" in a base b represents the number "a_n*bⁿ + a_n-1*b^n-1 + ... + a₁*b¹ + a₀*b⁰". Conversion basically works by evaluating the expression in the context of another base β.

Answer 4

Most of the examples I found on the internet and in this answers use BC Math functions. If you do not want to use use BC Math functions, you can have a look at this library: http://www.lalit.org/lab/base62-php-convert-number-to-base-62-for-short-urls/

• It doesn’t use BC Math functions so works without the use of BC Math library.
• It uses the native base_convert functions when the base is below 36 for faster execution.
• The output number is backward compatible with the native base_convert function.
• Can be used to convert to and from arbitrary bases between 2-64.