Arbitrary-precision arithmetic Explanation

Question

I\'m trying to learn C and have come across the inability to work with REALLY big numbers (i.e., 100 digits, 1000 digits, etc.). I am aware that there exist libraries to do

Answer 1

One of the ultimate references (IMHO) is Knuth's TAOCP Volume II. It explains lots of algorithms for representing numbers and arithmetic operations on these representations.

@Book{Knuth:taocp:2,
   author    = {Knuth, Donald E.},
   title     = {The Art of Computer Programming},
   volume    = {2: Seminumerical Algorithms, second edition},
   year      = {1981},
   publisher = {\Range{Addison}{Wesley}},
   isbn      = {0-201-03822-6},
}

Answer 2

Here's a simple ( naive ) example I did in PHP.

I implemented "Add" and "Multiply" and used that for an exponent example.

http://adevsoft.com/simple-php-arbitrary-precision-integer-big-num-example/

Code snip

// Add two big integers
function ba($a, $b)
{
    if( $a === "0" ) return $b;
    else if( $b === "0") return $a;

    $aa = str_split(strrev(strlen($a)>1?ltrim($a,"0"):$a), 9);
    $bb = str_split(strrev(strlen($b)>1?ltrim($b,"0"):$b), 9);
    $rr = Array();

    $maxC = max(Array(count($aa), count($bb)));
    $aa = array_pad(array_map("strrev", $aa),$maxC+1,"0");
    $bb = array_pad(array_map("strrev", $bb),$maxC+1,"0");

    for( $i=0; $i<=$maxC; $i++ )
    {
        $t = str_pad((string) ($aa[$i] + $bb[$i]), 9, "0", STR_PAD_LEFT);

        if( strlen($t) > 9 )
        {
            $aa[$i+1] = ba($aa[$i+1], substr($t,0,1));
            $t = substr($t, 1);
        }

        array_unshift($rr, $t);
     }

     return implode($rr);
}