bases/bases.js

Utility for converting numbers to/from different bases/alphabets.

// bases.js
// Utility for converting numbers to/from different bases/alphabets.
// See README.md for details.

var bases = (typeof exports !== 'undefined' ? exports : (window.Bases = {}));

// Returns a string representation of the given number for the given alphabet:
bases.toAlphabet = function (num, alphabet) {
    var base = alphabet.length;
    var digits = [];    // these will be in reverse order since arrays are stacks

    // execute at least once, even if num is 0, since we should return the '0':
    do {
        digits.push(num % base);    // TODO handle negatives properly?
        num = Math.floor(num / base);
    } while (num > 0);

    var chars = [];
    while (digits.length) {
        chars.push(alphabet[digits.pop()]);
    }
    return chars.join('');
};

// Returns an integer representation of the given string for the given alphabet:
bases.fromAlphabet = function (str, alphabet) {
    var base = alphabet.length;
    var pos = 0;
    var num = 0;
    var c;

    while (str.length) {
        c = str[str.length - 1];
        str = str.substr(0, str.length - 1);
        num += Math.pow(base, pos) * alphabet.indexOf(c);
        pos++;
    }

    return num;
};

// Known alphabets:
bases.NUMERALS = '0123456789';
bases.LETTERS_LOWERCASE = 'abcdefghijklmnopqrstuvwxyz';
bases.LETTERS_UPPERCASE = bases.LETTERS_LOWERCASE.toUpperCase();
bases.KNOWN_ALPHABETS = {};

// Each of the number ones, starting from base-2 (base-1 doesn't make sense?):
for (var i = 2; i <= 10; i++) {
    bases.KNOWN_ALPHABETS[i] = bases.NUMERALS.substr(0, i);
}

// Node's native hex is 0-9 followed by *lowercase* a-f, so we'll take that
// approach for everything from base-11 to base-16:
for (var i = 11; i <= 16; i++) {
    bases.KNOWN_ALPHABETS[i] = bases.NUMERALS + bases.LETTERS_LOWERCASE.substr(0, i - 10);
}

// We also model base-36 off of that, just using the full letter alphabet:
bases.KNOWN_ALPHABETS[36] = bases.NUMERALS + bases.LETTERS_LOWERCASE;

// And base-62 will be the uppercase letters added:
bases.KNOWN_ALPHABETS[62] = bases.NUMERALS + bases.LETTERS_LOWERCASE + bases.LETTERS_UPPERCASE;

// For base-26, we'll assume the user wants just the letter alphabet:
bases.KNOWN_ALPHABETS[26] = bases.LETTERS_LOWERCASE;

// We'll also add a similar base-52, just letters, lowercase then uppercase:
bases.KNOWN_ALPHABETS[52] = bases.LETTERS_LOWERCASE + bases.LETTERS_UPPERCASE;

// Base-64 is a formally-specified alphabet that has a particular order:
// http://en.wikipedia.org/wiki/Base64 (and Node.js follows this too)
// TODO FIXME But our code above doesn't add padding! Don't use this yet...
bases.KNOWN_ALPHABETS[64] = bases.LETTERS_UPPERCASE + bases.LETTERS_LOWERCASE + bases.NUMERALS + '+/';

// Flickr and others also have a base-58 that removes confusing characters, but
// there isn't consensus on the order of lowercase vs. uppercase... =/
// http://www.flickr.com/groups/api/discuss/72157616713786392/
// https://en.bitcoin.it/wiki/Base58Check_encoding#Base58_symbol_chart
// https://github.com/dougal/base58/blob/master/lib/base58.rb
// http://icoloma.blogspot.com/2010/03/create-your-own-bitly-using-base58.html
// We'll arbitrarily stay consistent with the above and using lowercase first:
bases.KNOWN_ALPHABETS[58] = bases.KNOWN_ALPHABETS[62].replace(/[0OlI]/g, '');

// And Douglas Crockford shared a similar base-32 from base-36:
// http://www.crockford.com/wrmg/base32.html
// Unlike our base-36, he explicitly specifies uppercase letters
bases.KNOWN_ALPHABETS[32] = bases.NUMERALS + bases.LETTERS_UPPERCASE.replace(/[ILOU]/g, '');

// Closure helper for convenience aliases like bases.toBase36():
function makeAlias (base, alphabet) {
    bases['toBase' + base] = function (num) {
        return bases.toAlphabet(num, alphabet);
    };
    bases['fromBase' + base] = function (str) {
        return bases.fromAlphabet(str, alphabet);
    };
}

// Do this for all known alphabets:
for (var base in bases.KNOWN_ALPHABETS) {
    if (bases.KNOWN_ALPHABETS.hasOwnProperty(base)) {
        makeAlias(base, bases.KNOWN_ALPHABETS[base]);
    }
}

// And a generic alias too:
bases.toBase = function (num, base) {
    return bases.toAlphabet(num, bases.KNOWN_ALPHABETS[base]);
};

bases.fromBase = function (str, base) {
    return bases.fromAlphabet(str, bases.KNOWN_ALPHABETS[base]);
};