Code of the Day: Javascript Decimal Expansion a.k.a Division

Posted by on May 16, 2012 No comments


Today’s Code of the Day is about decimal expansion, which is just division.

So you might be asking yourself, “if decimal expansion is divsion. Then why not use a/b?”.
Well the problem is that Javascript has a ton of problems when dealing with floating point operations because of the way they are stored.

Examples:

var a = 1/3;
a.toString()     // returns  "0.3333333333333333"
a.toFixed(25);   // returns "0.3333333333333333148296163"
0.1 + 0.2;       // returns 0.30000000000000004

Source for decimalExpansion()

// borrowed from jQuery 1.7.2
var isNumeric = function(val){
	return !isNaN(parseFloat(val)) && isFinite(val);
};
/**
* @author Larry Battle <http://bateru.com/news/contact-me>
* @date May 16, 2012
* @license MIT and GPLv3
*/
//decimalExpansion returns a string representation of a divided by b to a fixed length.
// All the paramaters must be whole numbers.
// Example: decimalExpansion( 1, 3, 3 ) === "0.333"
var decimalExpansion = function( a, b, decLength){
	if( !isNumeric(a) || !isNumeric(b) || !a || !isNumeric(decLength) ){
		return null;
	}
	var arr = [], tmp="", val, aLen = a.toString().length, i = 0, maxDecimal = 100;
	decLength = Math.min( Math.max( 0, decLength||0 ), maxDecimal) + aLen;
 
	while( i < decLength ){
		if( i===aLen){
			arr.push('.');
		}
		tmp += a.toString().charAt(i) || "0";
		val = Math.floor( (+tmp)/+b );
		arr.push( val );
		tmp %= b;
		i++;
	}
	if (tmp > 4) {
		arr[arr.length - 1]++;
	}	
	return arr.join('').replace( /^(-)?0+(?=\d)/, '');
};

Test cases:

Demo:

Here are excellent links over the topic.
Wolfram MathWorld: Decimal Expansion
Wikipedia.org: Fraction (mathematics)
Oracle: What Every Computer Scientist Should Know About Floating-Point Arithmetic

Code of the Day: Javascript, Fix for isNaN

Posted by on May 14, 2012 No comments

Javascript is a dynamically typed langauges. This feature causes for Arrays, Booleans, and other types to be converted to a numeric values depending on usage.
However this feature can cause headarches when trying to detect numbers.

For example, isNaN() detects if a value is a non-number. That’s what NaN stands for, “Not a number”.
So you might think that the opposite result from isNaN() would indicate if a value is a number.

// Works for most cases but not for strict comparisons.
var isNumber = function(val){
	return !isNaN( val );
};

Example:
Note: Click the “result” tab to run the test cases in jsfiddle.net.

Solution:
So here’s a simple fix for isNaN and isNumber.

// isNaN2 returns a boolean for if a value is not a number or +-Infinity
var isNaN2 = (function (global) {
    var _isNaN = global.isNaN;
    return function (val) {
        return _isNaN("" + val) || (typeof val === "object" && !(val || "").hasOwnProperty('push'));
    };
}(this));
// isNumeric returns a boolean for if a value is a number or +-Infinity
var isNumeric = (function (global) {
    var _isNaN = global.isNaN;
    return function (val) {
        return !_isNaN("" + val)&&(typeof val !== "object" || (val || "").hasOwnProperty('push'));
    };
}(this));


isNaN vs isNaN2

Testcases for isNaN2 and isNumeric

*Update*
Well it turns out that jQuery has a better implementation. The only difference is that infinity is not a number, which is correct.

$.isNumeric = function( obj ){
    return !isNaN( parseFloat( obj ) ) && isFinite( obj );
};


api.jquery.com/jQuery.isNumeric

Code of the Day: Javascript, Prime Factors of a Number

Posted by on May 11, 2012 No comments

Javascript: Prime Factorization

Today’s code is a enhancement of Code Renaissance‘s version of “Finding Prime Numbers in Javascript”.
Main difference are the following.

  1. Faster performance by eliminating recursion and caching Math.sqrt.
  2. Whole numbers bigger than 1 return an empty array, since they’re not prime numbers.
  3. Decimal values are converted to whole numbers.

/**
* @author Larry Battle - http://bateru.com/news/contact-me
* @date May 11, 2012
* @license MIT and GPL v3
* @purpose Return the prime factors of a number.
* @info - http://bateru.com/news/?s=prime+factors
*/
var getPrimeFactors = function(num) {
    num = Math.floor(num);
    var root, factors = [], x, sqrt = Math.sqrt, doLoop = 1 < num;
    while( doLoop ){
        root = sqrt(num);
        x = 2;
        if (num % x) {
            x = 3;
            while ((num % x) && ((x += 2) < root));
        }
        x = (x > root) ? num : x;
        factors.push(x);
        doLoop = ( x != num );
        num /= x;
    }
    return factors;
}

Example:
getPrimeFactors(15120) // returns [2, 2, 2, 3, 3, 3, 7]

Demo:

Code of the Day: Javascript, Convert decimal to a simplified fraction

Posted by on May 8, 2012 No comments

Inspired from a stackoverflow.com question.
Convert decimal amount to text string fraction in Javascript?

Code

/**
 * @author Larry Battle <http://bateru.com/news/contact-me>
 * @license MIT
 * @version 1.0
 * @date May 08, 2012
 * @purpose To provide a function that converts a decimal to a simplified fraction.
 * @info <http://bateru.com/news/2012/05/code-of-the-day-javascript-convert-decimal-to-a-simplified-fraction/>
 */
var mixin = {};
mixin.getKeys = function (obj) {
    var props = [];
    for (var prop in obj) {
        if (obj.hasOwnProperty(prop)) {
            props.push(prop);
        }
    }
    return props;
};
mixin.getFractionObject = (function () {
    var obj = {
        0 : '0',
        1 : '1'
    },
    num = 10,
    den = 11,
    value;
    while (--num) {
        while (--den > 1) {
            value = (num / den).toFixed(3);
            if (value < 1) {
                obj[value] = num + "/" + den;
            }
        }
        den = 11;
    }
    obj.keys = mixin.getKeys(obj);
    return function () {
        return obj;
    };
}
    ());
mixin.getClosestNum = function (arr, val) {
    if (typeof arr !== "object" || !(arr.hasOwnProperty('length')) || isNaN(val)) {
        return false;
    }
    var i = arr.length,
    j = i - 1,
    minDiff = Math.abs(+val - arr[j]),
    diff;
    while (i--) {
        diff = Math.abs(+val - arr[i]);
        if (diff < minDiff) {
            minDiff = diff;
            j = i;
        }
    }
    return arr[j];
};
mixin.getFractionFromDecimal = function (dec) {
    if (isNaN(dec) || !isFinite(dec)) {
        return false;
    }
    if (!/\./.test(dec)) {
        return dec;
    }
    var fracs = mixin.getFractionObject(),
    matches = dec.toString().match(/(\d+)(\.\d+)/),
    fraction = fracs[mixin.getClosestNum(fracs.keys, Math.abs(+matches[2]))],
    sign = ( 0 < dec || (fraction == "0" && Math.abs(dec) < 1) ) ? '' : '-';
    if (1 < Math.abs(dec)) {
        if (isNaN(fraction)) {
            fraction = +matches[1] + " " + fraction;
        } else {
            fraction = +matches[1] + (+fraction);
        }
    }
    return sign + fraction;
};

Testcases and Demo

// Qunit Testcases
$(document).ready(function(){
	var runAllTests = function () {
		test("Test getKeys()", function () {
			var obj = {};
			deepEqual([], getKeys(obj), "Empty objects should have no props.");
			obj.a = 1;
			deepEqual(['a'], getKeys(obj), "a should be returned as a property.");
			obj = {
				1 : 1,
				2 : 1,
				3 : 1
			}
			deepEqual(['1', '2', '3'], getKeys(obj), "1,2,3 should be properties.");
		});
		test("Test getClosestNum()", function () {
			var arr = [0, 1, 2, 3, 10, 99, 1000];
			equal(false, getClosestNum({}, 1), "First argument must be an array.");
			equal(false, getClosestNum(arr), "Second argument must be an defined.");
			equal(false, getClosestNum(arr, {}), "Second argument must be an number.");
			var runThisTest = function (nums, expect) {
				var i = expect.length;
				while (i--) {
					equal(getClosestNum(nums, expect[i][0]), expect[i][1], expect[i][0] + " is the closest to " + expect[i][1]);
				}
			};
			runThisTest(arr, [
					[-10, 0],
					[0.3, 0],
					[0.5, 1],
					[2.1, 2],
					[10.1, 10],
					[100, 99],
					[600, 1000]
				]);
		});
		test("Test getFractionObject()", function () {
			var fracs = getFractionObject();
			var props = getKeys( fracs );
 
			areAllNumbers = true;
			var i = props.length;
			while( i-- ){
				if( isNaN( props[ i ] ) ){
					areAllNumbers = false;
				}
			}
			ok( areAllNumbers, "getFractionObject() returns an object with all properties as a number." );
			equal( fracs[ 0 ], "0", "0.500 should be 0" );
			equal( fracs[ '0.333' ], "1/3", "0.333 should be 1/3" );
			equal( fracs[ '0.500' ], "1/2", "0.500 should be 1/2" );
			equal( fracs[ '0.900' ], "9/10", "0.900 should be 9/10" );
			equal( fracs[ 1 ], "1", "0.500 should be 1" );
		});
		test("Test getFractionFromDecimal() with invalid inputs", function(){
			equal(getFractionFromDecimal( "ten" ), false );
			equal(getFractionFromDecimal( NaN ),  false );
			equal(getFractionFromDecimal( undefined ),  false );
			equal(getFractionFromDecimal( Infinity ),  false );
		});
		test("Test getFractionFromDecimal() with only decimal values <= 1", function(){
			equal(getFractionFromDecimal(0.001), "0" );
			equal(getFractionFromDecimal(0.23), "2/9" );
			equal(getFractionFromDecimal(0.335), "1/3" );
			equal(getFractionFromDecimal(0.756), "3/4" );
			equal(getFractionFromDecimal(0.995), "1" );
		});
		test("Test getFractionFromDecimal() with integers", function(){
			equal(getFractionFromDecimal(12), "12" );
			equal(getFractionFromDecimal(3), "3" );
		});
		test("Test getFractionFromDecimal() with negative values", function(){
			equal(getFractionFromDecimal(-0.001), "0" );
			equal(getFractionFromDecimal(-0.23), "-2/9" );
			equal(getFractionFromDecimal(-0.335), "-1/3" );
			equal(getFractionFromDecimal(-0.756), "-3/4" );
			equal(getFractionFromDecimal(-0.995), "-1" );
		});
		test("Test getFractionFromDecimal() with numbers bigger than 1.", function(){
			equal(getFractionFromDecimal(10.001), "10" );
			equal(getFractionFromDecimal(-10.001), "-10" );
			equal(getFractionFromDecimal(12.23), "12 2/9" );
			equal(getFractionFromDecimal(3.335), "3 1/3" );
			equal(getFractionFromDecimal(99.756), "99 3/4" );
			equal(getFractionFromDecimal(34.995), "35" );
		});
	};
	runAllTests();
});

Example
mixin.getFractionFromDecimal(-99.756); // returns “-99 3/4″

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