Converting large numbers into letters (and back again) - php

Question

Is there a term for the idea of storing large numbers as letters? For example let's say I have the (relatively small) number 138201162401719 and I want to shrink the number of characters (I know this does not help with saving disk space) to the fewest possible number of characters. There are 26 letters in the English alphabet (but i count them as 25 since we need a zero letter). If I start splitting up my large number into pieces that are each 25 or less I get:
13, 8, 20, 11, 6, 24, 0, 17, 19
If I then count the numbers of the alphabet a=0, b=1, c=2, d=3... I can convert this to:
NIULGYART
So I went from 15 digits long (138201162401719) to 9 characters long (NIULGYART). This could of course be easily converted back to the original number as well.
So...my first question is "Does this have a name" and my second "Does anyone have PHP code that will do the conversion (in both directions)?"
I am looking for proper terminology so that I can do my own research in Google...though working code examples are cool too.

Answer 1

This only possible if you're considering to store your number before processing as a string. Because you can't store huge number as integers. You will lost the precision (13820116240171986468445 will be stored as 1.3820116240172E+22) so the alot of digits are lost.
If you're considering storing the number as a string this will be your answer:
Functions used: intval, chr and preg_match_all.
<?php
$regex = '/(2[0-5])|(1[0-9])|([0-9])/';
$numberString = '138201162401719';
preg_match_all($regex, $numberString, $numberArray, PREG_SET_ORDER);
echo($numberString . " -> ");
foreach($numberArray as $value){
$character = chr (intval($value[0]) + 65);
echo($character);
}
?>
Demo
This is the result:
138201162401719 -> NIULGYART

Answer 2

Here's how I would do it:
Store the big number as a string and split it into an array of numbers containing one digit each
Loop through the array extract 2-digit chunks using substr()
Check if the number is less than 26 (in which case, it is an alphabet) and add them to an array
Use array_map() with chr() to create a new array of characters from the above array
Implode the resulting array to get the cipher
In code:
$str = '138201162401719';
$arr = str_split($str);
$i = 0; // starting from the left
while ($i < count($arr)) {
$n = substr($str, $i, 2);
$firstchar = substr($n, 0, 1);
if ($n < 26 && $firstchar != 0) {
$result[] = substr($str, $i, 2);
$i += 2; // advance two characters
} else {
$result[] = substr($str, $i, 1);
$i++; // advance one character
}
}
$output = array_map(function($n) {
return chr($n+65);
}, $result);
echo implode($output); // => NIULGYART
Demo.

Answer 3

As an alternative, you could convert the input integer to express it in base 26, instead of base 10. Something like (pseudocode):
func convertBase26(num)
if (num < 0)
return "-" & convertBase26(-num) // '&' is concatenate.
else if (num = 0)
return "A"
endif
output = "";
while (num > 0)
output <- ('A' + num MOD 26) & output // Modulus operator.
num <- num DIV 26 // Integer division.
endwhile
return output
endfunc
This uses A = 0, B = 1, up to Z = 25 and standard place notation: 26 = BA. Obviously a base conversion is easily reversible.

Answer 4

strtr() is a magnificent tool for this task! It replaces the longest match as is traverses the string.
Code: (Demo)
function toAlpha ($num) {
return strtr($num, range("A", "Z"));
}
$string = toAlpha("138201162401719");
echo "$string\n";
$string = toAlpha("123456789012345");
echo "$string\n";
$string = toAlpha("101112131415161");
echo "$string\n";
$string = toAlpha("2625242322212019");
echo "$string";
Output:
NIULGYART
MDEFGHIJAMDEF
KLMNOPQB
CGZYXWVUT
Just flip the lookup array to reverse the conversion: https://3v4l.org/YsFZu
Merged: https://3v4l.org/u3NQ5
Of course, I must mention that there is a vulnerability with converting a sequence of letters to numbers and back to letters. Consider BB becomes 11 then is mistaken for eleven which would traslate to L when converted again.
There are ways to mitigate this by adjusting the lookup array, but that may not be necessary/favorable depending on program requirements.
And here is another consideration from CodeReview.

Answer 5

I have been trying to do the same thing in PHP without success.
Assuming I'm using the 26 letters of the English alphabet, starting with A = 0 down to Z as 25:
I find the highest power of 26 lower than the number I am encoding. I divide it by the best power of 26 I found. Of the result I take away the integer, convert it to a letter and multiply the decimals by 26. I keep doing that until I get a whole number. It's ok to get a zero as it's an A, but if it has decimals it must be multiplied.
For 1 billion which is DGEHTYM and it's done in 6 loops obviously. Although my answer demonstrates how to encode, I'm afraid it does not help doing so on PHP which is what I'm trying to do myself. I hope the algorithm helps people out there though.