How to generate random 64-bit value as decimal string in PHP

This was a really interesting problem (how to create the decimal representation of an arbitrary-length random number in PHP, using no optional extensions). Here’s the solution:

Step 1: arbitrary-length random number

// Counts how many bits are needed to represent $value
function count_bits($value) {
    for($count = 0; $value != 0; $value >>= 1) {
        ++$count;
    }
    return $count;
}

// Returns a base16 random string of at least $bits bits
// Actual bits returned will be a multiple of 4 (1 hex digit)
function random_bits($bits) {
    $result="";
    $accumulated_bits = 0;
    $total_bits = count_bits(mt_getrandmax());
    $usable_bits = intval($total_bits / 8) * 8;

    while ($accumulated_bits < $bits) {
        $bits_to_add = min($total_bits - $usable_bits, $bits - $accumulated_bits);
        if ($bits_to_add % 4 != 0) {
            // add bits in whole increments of 4
            $bits_to_add += 4 - $bits_to_add % 4;
        }

        // isolate leftmost $bits_to_add from mt_rand() result
        $more_bits = mt_rand() & ((1 << $bits_to_add) - 1);

        // format as hex (this will be safe)
        $format_string = '%0'.($bits_to_add / 4).'x';
        $result .= sprintf($format_string, $more_bits);
        $accumulated_bits += $bits_to_add;
    }

    return $result;
}

At this point, calling random_bits(2048) will give you 2048 random bits as a hex-encoded string, no problem.

Step 2: arbitrary-precision base conversion

Math is hard, so here’s the code:

function base_convert_arbitrary($number, $fromBase, $toBase) {
    $digits="0123456789abcdefghijklmnopqrstuvwxyz";
    $length = strlen($number);
    $result="";

    $nibbles = array();
    for ($i = 0; $i < $length; ++$i) {
        $nibbles[$i] = strpos($digits, $number[$i]);
    }

    do {
        $value = 0;
        $newlen = 0;
        for ($i = 0; $i < $length; ++$i) {
            $value = $value * $fromBase + $nibbles[$i];
            if ($value >= $toBase) {
                $nibbles[$newlen++] = (int)($value / $toBase);
                $value %= $toBase;
            }
            else if ($newlen > 0) {
                $nibbles[$newlen++] = 0;
            }
        }
        $length = $newlen;
        $result = $digits[$value].$result;
    }
    while ($newlen != 0);
    return $result;
}

This function will work as advertised, for example try base_convert_arbitrary('ffffffffffffffff', 16, 10) == '18446744073709551615' and base_convert_arbitrary('10000000000000000', 16, 10) == '18446744073709551616'.

Putting it together

echo base_convert_arbitrary(random_bits(64), 16, 10);