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Compression, encryption, and data codecs are all related fields that most programmers will use ready-made solutions for. This recipe is a shallow adventure into the writing of original code and algorithms that explores a combination of those topics. Based on the work of recipe 577433, the code here is compliant with JavaScript and will run a test of itself when executed. From the program's report, one can gather that the novel procedures compress the source and accurately decompress it again. For those who wish to experiment further with the concept, note that fewer unique characters will yield higher compression ratios.

To get a copy of biginteger.js for the program to run and compression algorithm to operator, please go to http://silentmatt.com/biginteger/ and use the latest version of Matthew Crumley's excellent JavaScript big integer library.

JavaScript, 179 lines
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# /* ================== */
# /* text_compressor.js */
# /* ================== */

function compress(string)
{
	// Get the unique characters and numeric base.
	var unique = create_set(string);
	var base = unique.length;
	// Create a key that will encode data properly.
	shuffle(unique);
	var mapping = create_dict(unique);
	while (!mapping[string[string.length - 1]])
	{
		shuffle(unique);
		mapping = create_dict(unique);
	}
	// Create a compressed numeric representation.
	var value = BigInteger();
	for (var place = 0; place < string.length; place++)
	{
		var multiple = BigInteger(base).pow(place);
		var product = BigInteger(mapping[string[place]]).multiply(multiple);
		value = value.add(product);
	}
	// Return the number as a string with the table.
	return [array_to_string(decode(value)), unique.join("")];
}

function create_set(string)
{
	var set = new Object();
	for (var index = 0; index < string.length; index++)
	{
		set[string[index]] = 0;
	}
	var array = new Array();
	for (var value in set)
	{
		array.push(value);
	}
	return array;
}

function shuffle(array)
{
	var range = array.length - 1;
	for (var index = 0; index < array.length; index++)
	{
		var destination = Math.floor(Math.random() * range);
		if (destination >= index)
		{
			destination++;
		}
		var temporary = array[destination];
		array[destination] = array[index];
		array[index] = temporary;
	}
}

function create_dict(array)
{
	var dict = new Object();
	for (var index = 0; index < array.length; index++)
	{
		dict[array[index]] = index;
	}
	return dict;
}

function decode(number)
{
	// Change a number into a string.
	var array = new Array();
	while (!number.isZero())
	{
		var answer = number.divRem(256);
		number = answer[0];
		array.push(answer[1]);
	}
	return array;
}

function array_to_string(array)
{
	for (var index = 0; index < array.length; index++)
	{
		array[index] = String.fromCharCode(array[index]);
	}
	return array.join("");
}

function decompress(string, key)
{
	// Get the numeric value of the string.
	var number = encode(string);
	// Find the numeric base and prepare storage.
	var base = key.length;
	var array = new Array();
	// Decode the value into the original string.
	while (!number.isZero())
	{
		var answer = number.divRem(base);
		number = answer[0];
		array.push(key[answer[1]]);
	}
	// Return the "string" as a bytes object.
	return array.join("");
}

function encode(string)
{
	// Change a string into a number.
	assert(string.length > 0 && string[string.length - 1] != String.fromCharCode(0), "String has ambiguous value!");
	var value = BigInteger();
	for (var shift = 0; shift < string.length; shift++)
	{
		var multiple = BigInteger(256).pow(shift);
		var product = BigInteger(string[shift].charCodeAt()).multiply(multiple);
		value = value.add(product);
	}
	return value;
}

function assert(okay, error)
{
	if (!okay)
	{
		alert(error);
		throw new Error(error);
	}
}

# /* ======== */
# /* Test.htm */
# /* ======== */

<html>
    <head>
        <title>Text Compressor</title>
        <script type="text/javascript" src="biginteger.js"></script>
        <script type="text/javascript" src="text_compressor.js"></script>
        <script type="text/javascript">
//<![CDATA[
            var example = "Hello, world! This is a simple test. What do you think of it so far? It probably needs more text. The key was 26 characters long, the data was 40 characters long, and the original string was 68 characters long. Having a longer string should allow for greater compression at the expense of (most likely) a longer key and lower compression ratio. The approximation was off so much after adding the length of the data and table (key) together along with one (1) for the value of a length field; I decided to make this string much longer in the hope of decreasing the error. Since this program is not very dynamic and only needs to be run once, having a long run time is not much of a problem. It certainly takes much longer to run now, and the ratios are considerably closer as well. Hopefully, anyone who might run this experiment will have the patience to let it run to completion. Well, that ends it.";
            
            function start()
            {
                document.getElementById("output").innerHTML = "Running compression test ...";
                setTimeout("test();", 10);
            }

            function test()
            {
                var lines = new Array();
                lines.push("Uncompressed size = " + example.length);
                var data = compress(example);
                lines.push("Compressed size = " + data[0].length);
                lines.push("Table size = " + data[1].length);
                lines.push("Approximate compression ratio = log(" + data[1].length + ") / log(256) = " +(100 * Math.log(data[1].length) / Math.log(256)) + "%");
                lines.push("Real compression ratio (data) = " + data[0].length + " / " + example.length + " = " + (100 * data[0].length / example.length) + "%");
                var total_length = data[0].length + data[1].length + 1;
                lines.push("Real compression ratio (total) = " + total_length + " / " + example.length + " = " + (100 * total_length / example.length) + "%");
                var original = decompress(data[0], data[1]);
                lines.push("Decompression of the data was " + (original == example ? "" : "not ") + "successful.");
                lines.push("The original text is displayed below:");
                lines.push("<hr />");
                lines.push(original);
                document.getElementById("output").innerHTML = lines.join("<br />");
            }
//]]>
        </script>
    </head>
    <body onload="setTimeout('start();', 1000);">
        <h1>Results</h1>
        <hr />
        <div id="output" />
    </body>
</html>

2 comments

Stephen Chappell (author) 10 years, 10 months ago  # | flag

To follow the algorithm's operation, it helps to understand that an array of 8-bit bytes can be treated as a base-256 number. As such, any array of bytes can be translated into an actual number for manipulation purposes. Doing this in JavaScript is slightly challenging since the language does not have built-in support for big integers: an extra library must be used. The encode and decode functions up above make great use of this fact and can be used solely on their own for the purpose of turning strings into big integer objects.

The text compressor takes advantage of the fact that written communications usually have less than 256 unique bytes in them. Such text could be more efficient if it were written in a lower base, one that used fewer bits than the 8 required for base-256. So that is just what the compression algorithm does in its second phase of operation (the first phase creates a base mapping for the characters). Once the text has been converted into a number where the base is unspecified, the data is reconstructed as an array of base-256 bytes.

Decompression follows the reverse operations of the compression algorithm in order to reconstitute the original text. The base-256 array of bytes are changed back into the number formed in the second phase of compression. The base that the original data was encoded into is determined by the size of the compression table, and the number is divided by that base to form indexes into that table. The bytes resulting from that operation are appended together to form the original character array that had been passed to compression.

Compression rates can be approximated with the formula log(N) / log(256), where N is the number of unique bytes in the data. For example: if using only the characters A-Z, the ratio of compressed to uncompressed data sizes would be about 58.75%. Compressing bytes expressed as two hexadecimal digits would lead to a ratio of exactly 100% (neither losing nor gaining any size). Since the text compressor is primarily meant for data encoded in 7-bit ASCII, the lowest percentage in size reduction should be expected to be about 12.5%.

It is not advisable to use the text compression on binary data since there could be a wide range of values present in such an array. Trying to compress encrypted or already-compressed data would most likely be a futile attempt. Furthermore, the performance of the algorithm will degrade given larger and larger arrays for processing. The compression algorithm in recipe 502202 compensated for this by splitting its text into manageable chunks joined on null bytes. As a result, any serious usage of this recipe would require optimizations.

tonytong 5 years, 11 months ago  # | flag

i find a free online javascript minifier to compress your js code, so it will reduce the size of web page.