var testRef = new Firebase('https://*******.firebaseio.com/test');
testRef.push({
  val1: "any object you like",
  val2: 1,
  val3: "as long as it is not undefined or some complex type like a Date object",
  val4: "think of it as JSON"
});

var testRef = new Firebase('https://*******.firebaseio.com/test');
testRef.on('child_added', function(snapshot) {
   var obj = snapshot.val();
   handle(obj); //do what you want with the object
});

var testRef = new Firebase('https://*******.firebaseio.com/test');
testRef.authWithPassword({
  email    : "some@email.com",
  password : "password"
}, function(error, authData) {
  if (error) {
    console.log("Login Failed!", error);
  } else {
    console.log("Authenticated successfully with payload:", authData);
  }
});

{
  "rules": {
    "test": {
      ".read": false,
      ".write": false,
      "$uid": {
        // grants write access to the owner of this user account whose uid must exactly match the key ($uid)
        ".write": "auth !== null && auth.uid === $uid",
        // grants read access to any user who is logged in with an email and password
        ".read": "auth !== null && auth.provider === 'password'"
      }
    }
  }
}

1. It is forbidden to write to test directly, or to read from it
2. It is allowed to write to test/uid (remember the user UID when you created the email/password pair) only by the user with the same uid
3. It is allowed to read from test/uid, as long as you are authenticated in any way

{
  "rules": {
    ".read": false,
    ".write": false,
    "test": {
      ".read": false,
      ".write": false,
      "$uid": {
        // grants write access to the owner of this user account whose uid must exactly match the key ($uid)
        ".write": "auth !== null && auth.uid === $uid",
        // grants read access to any user who is logged in with an email and password
        ".read": "auth !== null && auth.provider === 'password'"
      }
    }
  }
}

{
  "rules": {
    ".read": false,
    ".write": false,
    "test": {
      ".read": "auth.uid == 'MyReadUser'",
      ".write": "auth.uid == 'MyWriteUser'"
    }
  }
}

testRef.authWithCustomToken(token,success,error);

var testRef = new Firebase('https://*****.firebaseio.com/test');
testRef.authWithCustomToken(token, function(err,authData) {
    if (err) alert(err);
    myDataRef.on('child_added', function(snapshot) {
        var message = snapshot.val();
           handle(message);
    });
});

• NOT operator: 1600/51480/1200ms
• === 0 (strong type equality): 1360/47510/2180ms
• === null : 550/45590/510ms
• == with 0: 38700/63030/131940ms
• == with null: 1100/48230/900ms
• === used twice(with 0 and null): 1760/69460/3500ms
• typeof == 'object' (which besides the Dates also catches null): 1360/382980/1380ms
• typeof === 'object' (which besides the Dates also catches null): 1370/407000/1400ms
• instanceof Date: 1060/69200/600ms

var arr=[];
for (var i=0; i<100000; i++) {
    var r=parseInt(Math.random()*5);
    switch(r) {
        case 0: arr.push(null); break;
        case 1: arr.push(undefined); break;
        case 2: arr.push(''); break;
        case 3: arr.push(0); break;
        case 4: arr.push(new Date()); break;
    }
}

var n=0;
var start=performance.now();
for (var j=0; j<1000; j++) {
    for (var i=0; i<100000; i++) {
        if (!arr[i]) n++;
    }
}
var end=performance.now();
console.log('!value                    '+n+': '+(end-start));

n=0;
start=performance.now();
for (var j=0; j<1000; j++) {
    for (var i=0; i<100000; i++) {
        if (arr[i] === 0) n++;
    }
}
end=performance.now();
console.log('value===0                 '+n+': '+(end-start));

n=0;
start=performance.now();
for (var j=0; j<1000; j++) {
    for (var i=0; i<100000; i++) {
        if (arr[i] === null) n++;
    }
}
end=performance.now();
console.log('value===null              '+n+': '+(end-start));

n=0;
start=performance.now();
for (var j=0; j<1000; j++) {
    for (var i=0; i<100000; i++) {
        if (arr[i] == 0) n++;
    }
}
end=performance.now();
console.log('value==0                  '+n+': '+(end-start));

n=0;
start=performance.now();
for (var j=0; j<1000; j++) {
    for (var i=0; i<100000; i++) {
        if (arr[i] == null) n++;
    }
}
end=performance.now();
console.log('value==null               '+n+': '+(end-start));

n=0;
start=performance.now();
for (var j=0; j<1000; j++) {
    for (var i=0; i<100000; i++) {
        if (arr[i] === 0 || arr[i] === null) n++;
    }
}
end=performance.now();
console.log('value===0 || value===null '+n+': '+(end-start));

n=0;
start=performance.now();
for (var j=0; j<1000; j++) {
    for (var i=0; i<100000; i++) {
        if (typeof(arr[i])=='object') n++;
    }
}
end=performance.now();
console.log('typeof(value)==\'object\'   '+n+': '+(end-start));

n=0;
start=performance.now();
for (var j=0; j<1000; j++) {
    for (var i=0; i<100000; i++) {
        if (typeof(arr[i])==='object') n++;
    }
}
end=performance.now();
console.log('typeof(value)===\'object\'  '+n+': '+(end-start));

n=0;
start=performance.now();
for (var j=0; j<1000; j++) {
    for (var i=0; i<100000; i++) {
        if (arr[i] instanceof Date) n++;
    }
}
end=performance.now();
console.log('value instanceof Date     '+n+': '+(end-start));

if (navigator.geolocation) {
    var timeoutInSeconds=1;
    var geotimeout=setTimeout(function() {
        handleNoGeolocation();
    },timeoutInSeconds*1000+500); //plus 500 ms to allow the API to timeout normally
    navigator.geolocation.getCurrentPosition(function (position) {
        clearTimeout(geotimeout);
        var pos = doSomethingWith(position.coords.latitude, position.coords.longitude);
    }, function () {
        clearTimeout(geotimeout);
        handleNoGeolocation();
    },{
        enableHighAccuracy:true,
        timeout: timeoutInSeconds*1000
    });
} else {
    handleNoGeolocation();
}

A blog reader asked me to help him get rid of the ugly effect of a large background image getting loaded. I thought of several solutions, all more complicated than the rest, but in the end settled on one that seems to be working well and doesn't require complicated libraries or difficult implementation: using the img onload event.

Let's assume that the background image is on the body element of the page. The solution involves setting a style on the body to hide it (style="display:none") then adding as child of the body an image that also is hidden and that, when completing loading, shows the body element. Here is the initial code:

<style>
body {
    background: url(bg.jpg) no-repeat center center fixed;
}
</style>
<body>

And after:

<style>
body {
    background: url(bg.jpg) no-repeat center center fixed;
}
</style>
<body style="display:none">
<img src="bg.jpg" onload="document.body.style.display=''" style="display:none;" />

This loads the image in a hidden img element and shows the body element when the image finished loading.

The solution might have some problems with Internet Explorer 9, as it seems the load event is not fired for images retrieved from the cache. In that case, a slightly more complex Javascript solution is needed as detailed in this blog post: How to Fix the IE9 Image Onload Bug. Also, in Internet Explorer 5-7 the load event fires for animated GIFs at every loop. I am sure you know it's a bad idea to have an animated GIF as a page background, though :)

Warning: While this hides the effect of slow loading background images, it also hides the page until the image is loaded. This makes the page appear blank until then. More complex solutions would show some simple html content while the page is loading rather than hiding the entire page, but this post is about the simplest solution for the question asked.

A more comprehensive analysis of image preloading, complete with a very nice Javascript code that covers a lot of cases, can be found at Preloading images using javascript, the right way and without frameworks

function x(arg) {
  if (!arg) {
    arg=[];
  } else if (!arg.length) {
    arg=[];
    for(var i=0; i<arguments.length; i++) arg.push(arguments[i]);
  }
  // do something with arg
}

function x(arg) {
  arg=[];
  console.log(arguments[0]);
}

The algorithm works perfectly well and is better than Sift3, however it's slightly more complex. You might want to start with Sift3 in order to understand where it came from.

Update November 8 2022: I found a bug in the algorithm, relating to maxDistance. I've updated the code. If you didn't use maxDistance, you are unaffected. Basically the fix is to compare temporaryDistance>minDistance (before it was >= ) and to move the calculation of the temporary distance after c1 and c2 are updated to their minimum value when a token was not found (otherwise the temporary distance might become larger than the final distance)

Try the Javascript implementation here:

Algorithm:

• Levenstein
• Sift3
• Sift4  MaxOffset:

String 1:

String 2:

Result: 

Update 28 Mar 2015: I've changed the algorithm significantly. The transpositions are now computed differently and the cost of a transposition in the final result is 1, rather than 0.5. Also, while I think a value of 1 is better conceptually, I noticed that Sift4 approximates Levenshtein a little better when the cost of a transposition is either 2 or a function depending on the offset difference between c2 and c1, especially when maxOffset grows. This can be now changed via the new options function transpositionCostEvaluator. The problem I am having now is more false positives when the letters/tokens of the two strings are the same, but their positions are jumbled differently. With small maxOffset values, like 5 or 10, the result is much better than Sift3, however when maxOffset grows, lots of matches can be found and the cost of transpositions becomes very important.

Update 27 Mar 2015: Thanks to Emanuele Bastianelli who discovered a bug that appeared in an edge case, I've updated the algorithms. Now, at the end of the while loop there is an extra check to prevent the algorithm exiting prematurely, before computing remaining tokens.

Intro

A really long time ago I wrote the third version of Sift, the string distance algorithm. It so happens that I am going to give a small presentation, here in Ispra, about this algorithm, so I had the opportunity to review it. I found some inconsistencies and I actually did some research in the field that gave more more ideas. So before giving the presentation I thought of publishing what I think is the fourth version. What's new:

• 33% more accurate
• three different variants: simple, common and general
• new concepts added
• support for own value and matching functions, different tokenizer functions, etc.
• actually tested with a (slightly more) serious test
• more robust, working better for large values of maxOffset

Before I get into the details, I am publishing the algorithm here for the moment, no Codeplex or PasteBin or GitHub or whatever. Also, it is written in Javascript now, the C# and T-SQL version pending. Of course, it would be great if, as before, the community of people using the algorithm would go into implementing it into various programming languages, however I am a bit apprehensive because more often than not people came with their own improvements or interpretations when translating the algorithm into another language. But support is always welcome!

New concepts in Sift4

I created a test that used random strings, but also a huge list of commonly used English phrases as well as mutations on these strings, adding or removing small bits and so on. I then implemented Sift3, Levenstein and the new algorithm and computed the error distance between the Levenstein distance and the two Sift variants. This permitted me to see how the error evolves when changing the algorithm and the parameters. One thing I noticed is that when increasing the maxOffset value to large values like 15 or 20, the accuracy of Sift3 was going down. Also, as pointed out by one commenter on the Sift3 post, there are cases when Sift3(a,b) is different from Sift3(b,a). There are edge cases, but this one in particular grated me.

After implementing Sift4, I can now tell you that the simple version is slightly better than Sift3 for small maxOffset values like 5, but it gets better as the value increases. The common version is a bit more complex, but the error decreases with 33% and maintains a low error for large maxOffset values. The extended or general version receives an options object that can change almost everything, but most important is the tokenizer function. Imagine that you want to compute the distance based not on letters, but on n-grams (groups of n characters). Or that you want to compare them by the words in the text, maybe even their synonyms. This can all be achieved just by changing the tokenizer function. The other parameters involve defining what it means for two tokens to match and what is the value of their match, etc.

One of the new concepts implemented is taken from the Jaro distance. Jaro seems a lot like Sift in the way that it considers two characters to match if they are in close proximity. Also, if "the streams cross", like 'ab' vs 'ba', one considers them transpositions and removes some of their value from the distance. Actually, if I look at the implementation, it might be that I have independently discovered the Jaro distance. I will research this further. I don't know if the transposition calculation is the most optimal. At the moment it uses an array of all matches found until a point, clearing it of values as the cursors move along the string. The difference between the simple and the common versions of Sift4 is that the simple version is not computing the transpositions at all and has no concept of maxDistance. In that respect it is a slightly fixed up Sift3.

Another new concept added is the one of local substring. Imagine that the Largest Common Subsequence that Sift is actually trying to find in order to determine the distance is made of substrings, separated by non matching characters. Each of these substrings can be used to improve the distance function. For example one could argue that 'abcdex' is closer to 'abcde' than 'abcxde', because even if the largest common subsequence is 5, the largest common substring is 5 for the first string and only 3 for the second. The extended version of the algorithm allows for changing the value of each substring individually.

Well, here they are, the three versions. The extended version has some examples at the end for possible parameters.

The code

Simplest Sift4:

// Sift4 - simplest version
// online algorithm to compute the distance between two strings in O(n)
// maxOffset is the number of characters to search for matching letters
function sift4(s1, s2, maxOffset) {
    if (!s1 || !s1.length) {
        if (!s2) {
            return 0;
        }
        return s2.length;
    }

    if (!s2 || !s2.length) {
        return s1.length;
    }

    var l1 = s1.length;
    var l2 = s2.length;

    var c1 = 0; //cursor for string 1
    var c2 = 0; //cursor for string 2
    var lcss = 0; //largest common subsequence
    var local_cs = 0; //local common substring
    while ((c1 < l1) && (c2 < l2)) {
        if (s1.charAt(c1) == s2.charAt(c2)) {
            local_cs++;
        } else {
            lcss += local_cs;
            local_cs = 0;
            if (c1 != c2) {
                c1 = c2 = Math.max(c1, c2); //using max to bypass the need for computer transpositions ('ab' vs 'ba')
            }
            for (var i = 0; i < maxOffset && (c1 + i < l1 || c2 + i < l2); i++) {
                if ((c1 + i < l1) && (s1.charAt(c1 + i) == s2.charAt(c2))) {
                    c1 += i;
                    local_cs++;
                    break;
                }
                if ((c2 + i < l2) && (s1.charAt(c1) == s2.charAt(c2 + i))) {
                    c2 += i;
                    local_cs++;
                    break;
                }
            }
        }
        c1++;
        c2++;
    }
    lcss += local_cs;
    return Math.round(Math.max(l1, l2) - lcss);
}

Common Sift4:

// Sift4 - common version
// online algorithm to compute the distance between two strings in O(n)
// maxOffset is the number of characters to search for matching letters
// maxDistance is the distance at which the algorithm should stop computing the value and just exit (the strings are too different anyway)
function sift4(s1, s2, maxOffset, maxDistance) {
    if (!s1 || !s1.length) {
        if (!s2) {
            return 0;
        }
        return s2.length;
    }

    if (!s2 || !s2.length) {
        return s1.length;
    }

    var l1 = s1.length;
    var l2 = s2.length;

    var c1 = 0; //cursor for string 1
    var c2 = 0; //cursor for string 2
    var lcss = 0; //largest common subsequence
    var local_cs = 0; //local common substring
    var trans = 0; //number of transpositions ('ab' vs 'ba')
    var offset_arr = []; //offset pair array, for computing the transpositions
    while ((c1 < l1) && (c2 < l2)) {
        if (s1.charAt(c1) == s2.charAt(c2)) {
            local_cs++;
            var isTrans = false;
            //see if current match is a transposition
            var i = 0;
            while (i < offset_arr.length) {
                var ofs = offset_arr[i];
                if (c1 <= ofs.c1 || c2 <= ofs.c2) {
                    // when two matches cross, the one considered a transposition is the one with the largest difference in offsets
                    isTrans = Math.abs(c2 - c1) >= Math.abs(ofs.c2 - ofs.c1);
                    if (isTrans) {
                        trans++;
                    } else {
                        if (!ofs.trans) {
                            ofs.trans = true;
                            trans++;
                        }
                    }
                    break;
                } else {
                    if (c1 > ofs.c2 && c2 > ofs.c1) {
                        offset_arr.splice(i, 1);
                    } else {
                        i++;
                    }
                }
            }
            offset_arr.push({
                c1: c1,
                c2: c2,
                trans: isTrans
            });
        } else {
            lcss += local_cs;
            local_cs = 0;
            if (c1 != c2) {
                c1 = c2 = Math.min(c1, c2); //using min allows the computation of transpositions
            }
            if (maxDistance) {
                var temporaryDistance = Math.max(c1, c2) - lcss + trans;
                if (temporaryDistance > maxDistance)
                    return temporaryDistance;
            }
            //if matching characters are found, remove 1 from both cursors (they get incremented at the end of the loop)
            //so that we can have only one code block handling matches
            for (var i = 0; i < maxOffset && (c1 + i < l1 || c2 + i < l2); i++) {
                if ((c1 + i < l1) && (s1.charAt(c1 + i) == s2.charAt(c2))) {
                    c1 += i - 1;
                    c2--;
                    break;
                }
                if ((c2 + i < l2) && (s1.charAt(c1) == s2.charAt(c2 + i))) {
                    c1--;
                    c2 += i - 1;
                    break;
                }
            }
        }
        c1++;
        c2++;
        // this covers the case where the last match is on the last token in list, so that it can compute transpositions correctly
        if ((c1 >= l1) || (c2 >= l2)) {
            lcss += local_cs;
            local_cs = 0;
            c1 = c2 = Math.min(c1, c2);
        }
    }
    lcss += local_cs;
    return Math.max(l1, l2) - lcss + trans; //add the cost of transpositions to the final result
}

Extended/General Sift4:

// Sift4 - extended version
// online algorithm to compute the distance between two strings in O(n)
// maxOffset is the number of positions to search for matching tokens
// options: the options for the function, allowing for customization of the scope and algorithm:
//         maxDistance: the distance at which the algorithm should stop computing the value and just exit (the strings are too different anyway)
//         tokenizer: a function to transform strings into vectors of tokens
//        tokenMatcher: a function to determine if two tokens are matching (equal)
//        matchingEvaluator: a function to determine the way a token match should be added to the local_cs. For example a fuzzy match could be implemented.
//        localLengthEvaluator: a function to determine the way the local_cs value is added to the lcss. For example longer continuous substrings could be awarded.
//        transpositionCostEvaluator: a function to determine the value of an individual transposition. For example longer transpositions should have a higher cost.
//        transpositionsEvaluator: a function to determine the way the total cost of transpositions affects the final result
// the options can and should be implemented at a class level, but this is the demo algorithm
function sift4(s1, s2, maxOffset, options) {

    options = extend(options, {
            maxDistance: null,
            tokenizer: function (s) {
                return s ? s.split('') : [];
            },
            tokenMatcher: function (t1, t2) {
                return t1 == t2;
            },
            matchingEvaluator: function (t1, t2) {
                return 1;
            },
            localLengthEvaluator: function (local_cs) {
                return local_cs;
            },
            transpositionCostEvaluator: function (c1, c2) {
                return 1;
            },
            transpositionsEvaluator: function (lcss, trans) {
                return lcss - trans;
            }
        });

    var t1 = options.tokenizer(s1);
    var t2 = options.tokenizer(s2);

    var l1 = t1.length;
    var l2 = t2.length;

    if (l1 == 0)
        return l2;
    if (l2 == 0)
        return l1;

    var c1 = 0; //cursor for string 1
    var c2 = 0; //cursor for string 2
    var lcss = 0; //largest common subsequence
    var local_cs = 0; //local common substring
    var trans = 0; //number of transpositions ('ab' vs 'ba')
    var offset_arr = []; //offset pair array, for computing the transpositions
    while ((c1 < l1) && (c2 < l2)) {
        if (options.tokenMatcher(t1[c1], t2[c2])) {
            local_cs += options.matchingEvaluator(t1[c1], t2[c2]);
            var isTrans = false;
            //see if current match is a transposition
            var i = 0;
            while (i < offset_arr.length) {
                var ofs = offset_arr[i];
                if (c1 <= ofs.c1 || c2 <= ofs.c2) {
                    // when two matches cross, the one considered a transposition is the one with the largest difference in offsets
                    isTrans = Math.abs(c2 - c1) >= Math.abs(ofs.c2 - ofs.c1);
                    if (isTrans) {
                        trans += options.transpositionCostEvaluator(c1, c2);
                    } else {
                        if (!ofs.trans) {
                            ofs.trans = true;
                            trans += options.transpositionCostEvaluator(ofs.c1, ofs.c2);
                        }
                    }
                    break;
                } else {
                    if (c1 > ofs.c2 && c2 > ofs.c1) {
                        offset_arr.splice(i, 1);
                    } else {
                        i++;
                    }
                }
            }
            offset_arr.push({
                c1: c1,
                c2: c2,
                trans: isTrans
            });
        } else {
            lcss += options.localLengthEvaluator(local_cs);
            local_cs = 0;
            if (c1 != c2) {
                c1 = c2 = Math.min(c1, c2); //using min allows the computation of transpositions
            }
            if (options.maxDistance) {
                var temporaryDistance = options.localLengthEvaluator(Math.max(c1, c2)) - options.transpositionsEvaluator(lcss, trans);
                if (temporaryDistance > options.maxDistance)
                    return Math.round(temporaryDistance);
            }
            //if matching tokens are found, remove 1 from both cursors (they get incremented at the end of the loop)
            //so that we can have only one code block handling matches
            for (var i = 0; i < maxOffset && (c1 + i < l1 || c2 + i < l2); i++) {
                if ((c1 + i < l1) && options.tokenMatcher(t1[c1 + i], t2[c2])) {
                    c1 += i - 1;
                    c2--;
                    break;
                }
                if ((c2 + i < l2) && options.tokenMatcher(t1[c1], t2[c2 + i])) {
                    c1--;
                    c2 += i - 1;
                    break;
                }
            }
        }
        c1++;
        c2++;
        // this covers the case where the last match is on the last token in list, so that it can compute transpositions correctly
        if ((c1 >= l1) || (c2 >= l2)) {
            lcss += options.localLengthEvaluator(local_cs);
            local_cs = 0;
            c1 = c2 = Math.min(c1, c2);
        }
    }
    lcss += options.localLengthEvaluator(local_cs);
    return Math.round(options.localLengthEvaluator(Math.max(l1, l2)) - options.transpositionsEvaluator(lcss, trans)); //add the cost of found transpositions
}

function extend(obj, def) {
    var result = {};
    for (var prop in def) {
        if (!obj || !obj.hasOwnProperty(prop)) {
            result[prop] = def[prop];
        } else {
            result[prop] = obj[prop];
        }
    }
    return result;
}

// possible values for the options
// tokenizers:
function nGramTokenizer(s, n) { //tokenizer:function(s) { return nGramTokenizer(s,2); }
    var result = [];
    if (!s)
        return result;
    for (var i = 0; i <= s.length - n; i++) {
        result.push(s.substr(i, n));
    }
    return result;
}

function wordSplitTokenizer(s) { //tokenizer:wordSplitTokenizer
    if (!s)
        return [];
    return s.split(/\s+/);
}

function characterFrequencyTokenizer(s) { //tokenizer:characterFrequencyTokenizer (letters only)
    var result = [];
    for (var i = 0; i <= 25; i++) {
        var val = 0;
        if (s) {
            for (j = 0; j < s.length; j++) {
                var code = s.charCodeAt(j);
                if (code == i + 65 || code == i + 97)
                    val++;
            }
        }
        result.push(val);
    }
    return result;
}

//tokenMatchers:
function sift4TokenMatcher(t1, t2) { //tokenMatcher:sift4TokenMatcher
    var similarity = 1 - sift4(t1, t2, 5) / Math.max(t1.length, t2.length);
    return similarity > 0.7;
}

//matchingEvaluators:
function sift4MatchingEvaluator(t1, t2) { //matchingEvaluator:sift4MatchingEvaluator
    var similarity = 1 - sift4(t1, t2, 5) / Math.max(t1.length, t2.length);
    return similarity;
}

//localLengthEvaluators:
function rewardLengthEvaluator(l) {
    if (l < 1)
        return l; //0 -> 0
    return l - 1 / (l + 1); //1 -> 0.5, 2-> 0.66, 9 -> 0.9
}

function rewardLengthEvaluator2(l) {
    return Math.pow(l, 1.5); // 0 -> 0, 1 -> 1, 2 -> 2.83, 10 -> 31.62
}

//transpositionCostEvaluators:
function longerTranspositionsAreMoreCostly(c1, c2) {
    return Math.abs(c2 - c1) / 9 + 1;
}

As always, I will be most happy to know if you used my algorithm and how it performed, as well as receive any suggestion that you might have.

Options explained

Here is some explanation for the options of the general algorithm.

It no longer searches for characters, but for tokens. That is why the default tokenizer function splits the values into characters so that the algorithm would work on an array of one character long tokens. Other options are possible, like splitting the strings by empty spaces so that the comparisons are done on words or transforming a string into an array of strings N characters long, the so called N-grams. The tokenizer can be anything, like the characterFrequencyTokenizer, which turns each word in an array of 25 values representing the number of letters in the word for each letter a-z.

The tokenMatcher function returns true if two tokens are matching. They can be fuzzy matched, for example the sift4tokenMatcher example function uses Sift inside Sift to determine the character distance between two tokens and returns true if they match more than 70%.

The matchingEvaluator is a function that returns the value that will be added to the "common substring" length value when two tokens match. The default is 1, but one can use some other metric, like the similarity, for example. Of course, the common substring length has lost its meaning when these functions change, but the variable local_cs is still used.

The lengthEvaluator is taking the length value of the local common substring and returns a value that will be added to the longest common subsequence value. Usually it returns the same value as the one provided, but some functions could reward longer substrings.

FAQ

Q: Can you make Sift4 to work case insensitive?
A: Just turn the strings to lower or upper case before you compare them. Since this algorithm is more general, the concept of 'case' might not apply. Or implement a case insensitive tokenMatcher.

Q: Can you make Sift4 to compare strings based on their meaning, like using synonyms?
A: Use a tokenizer function that splits the strings into words, then replaces them with the most used of their synonyms. A more complex solution would require to analyze the strings beforehand and turn them into some ordered synonym or equivalent expressions equivalents, then use Sift4 with a word tokenizer (one is provided in the Extended algorithm source)

Q: I need an implementation for this programming language, can you help?
A: I can, but I might not have the time. Ask anyway, maybe I can be persuaded :)

Q: I have been using Sift3 until now, how do I upgrade to Sift4?
A: The best way I can think of is to implement Sift4 Simplest, as it needs only the Sift3 code and some minor changes. Since you never needed tokens before, I doubt you need them now. But if you do, I can help, see the above question.

Q: How can I reward you for this fantastic piece of software engineering?
A: While I did this for free and I don't expect to make any money out of it and while this algorithm is completely free to use and change as you see fit, I don't mind having a beer every now and then ;)

Q: Your algorithm really sucks because... reasons.
A: It may. I would be glad to discuss the reasons, though, and try to fix any problem you encounter.

Q: I compared Sift4 with another algorithm that is much more exact and there are differences.
A: Of course, they are different algorithms. This is a fuzzy distance calculator, it doesn't give you the exact value. There are still edge cases. But the idea of Sift is to be fast and relatively accurate, rather than very accurate. You need more accuracy, try to combine Sift with Levenshtein for example, computing Levenshtein only where Sift says the strings are above a certain similarity.

Q: I want to make maxOffset dependent on the length of the strings compared. Can you do that?
A: That is a perfect example why maxOffset should be a parameter of the function rather than a member of the class. Since this implementation is so far Javascript only, just compute the maxOffset that is convenient to you before you compare.

Q: I want to vary the weight of matches based on the position of the match, for example matches at the beginning of the string could be more valuable than those at the end.
A: The position of the match is indeed not sent to the functions that can be specified in the options object of the Sift4 Extended, but that can be trivially changed in the code. I don't think this particular request is very common, though, and I prefer to keep it out of the published implementation to make the code easier to understand.

Q: I found a bug!
A: Let me know it and I will try and fix it.

Q: If you need to compare large lists of strings, it is better to precompute some things, like specific hashes or suffix trees, etc. This will speed up the comparison tremendously!
A: Sift is what is called an online algorithm. It does not precompute anything, it just gets the two strings and the parameters for its functioning and returns the distance. You are correct in what you are saying, but that kind of solution is not in the scope of Sift, at least not version 4.

Q: What are the edge cases for Sift?
A: Probably there are several, but I didn't really spot them. One of them is that one might find both letters at a position matching letters at other positions, but only one will count. Example 'abxx' and 'bayy'. The algorithm will look at position 0, find no match, then try to find the closest match for each letter. Starting with position 0 in the first string it will find 'a' matched in position 1 in the second. It will increase both counters and lcss will be increase as well. Next check will be 'b', the character at position 1 in the first string matched with position 2 in the second string. No match, therefore both counters will be reset to 1, and starting search again. The 'b' match is lost and distance is 3 instead of 2. Also I think there might be some situations where the counters are not equal and the biggest of them reaches the end of its string, thus terminating the algorithm, but there could have been more matches. Incidentally I tried to fix both these issues and the error from Levenshtein was not really affected, but I am not 100% sure of the implementation.

Q: The algorithm continues to be asymmetric, Sift4(s1,s2) can be different from Sift4(s2,s1).
A: Yes. This is one of the artifacts of the linear nature of the algorithm. There is a function that is symmetric and that is Math.min(Sift4(a,b),Sift4(b,a)), however it is twice as slow, obviously.

Implementations in other languages

public class Sift4
{
    private Options _options;

    public Sift4(Options options)
    {
        if (options == null) options = new Options();
        if (options.Tokenizer == null)
        {
            options.Tokenizer = (s) => s == null
            ? new string[0]
            : s.ToCharArray().Select(c => c.ToString()).ToArray();
        }
        if (options.TokenMatcher == null)
        {
            options.TokenMatcher = (t1, t2) => t1 == t2;
        }
        if (options.MatchingEvaluator == null)
        {
            options.MatchingEvaluator = (t1, t2) => 1;
        }
        if (options.LocalLengthEvaluator == null)
        {
            options.LocalLengthEvaluator = (l) => l;
        }
        if (options.TranspositionCostEvaluator == null)
        {
            options.TranspositionCostEvaluator = (c1, c2) => 1;
        }
        if (options.TranspositionsEvaluator == null)
        {
            options.TranspositionsEvaluator = (l, t) => l - t;
        }
        _options = options;
    }

    /// <summary>
    /// General distance algorithm uses all the parameters in the options object and works on tokens
    /// </summary>
    /// <param name="s1"></param>
    /// <param name="s2"></param>
    /// <param name="maxOffset"></param>
    /// <returns></returns>
    public double GeneralDistance(string s1, string s2, int maxOffset)
    {
        var t1 = _options.Tokenizer(s1);
        var t2 = _options.Tokenizer(s2);

        var l1 = t1.Length;
        var l2 = t2.Length;

        if (l1 == 0) return _options.LocalLengthEvaluator(l2);
        if (l2 == 0) return _options.LocalLengthEvaluator(l1);

        var c1 = 0;  //cursor for string 1
        var c2 = 0;  //cursor for string 2
        var lcss = 0.0;  //largest common subsequence
        var local_cs = 0.0; //local common substring
        var trans = 0.0;  //cost of transpositions ('axb' vs 'xba')
        var offset_arr = new LinkedList<OffsetPair>();  //offset pair array, for computing the transpositions

        while ((c1 < l1) && (c2 < l2))
        {
            if (_options.TokenMatcher(t1[c1], t2[c2]))
            {
                local_cs += _options.MatchingEvaluator(t1[c1], t2[c2]);
                var isTransposition = false;
                var op = offset_arr.First;
                while (op != null)
                {  //see if current match is a transposition
                    var ofs = op.Value;
                    if (c1 <= ofs.C1 || c2 <= ofs.C2)
                    {
                        // when two matches cross, the one considered a transposition is the one with the largest difference in offsets
                        isTransposition = Math.Abs(c2 - c1) >= Math.Abs(ofs.C2 - ofs.C1);
                        if (isTransposition)
                        {
                            trans += _options.TranspositionCostEvaluator(c1, c2);
                        }
                        else
                        {
                            if (!ofs.IsTransposition)
                            {
                                ofs.IsTransposition = true;
                                trans += _options.TranspositionCostEvaluator(ofs.C1, ofs.C2);
                            }
                        }
                        break;
                    }
                    else
                    {
                        var next_op = op.Next;
                        if (c1 > ofs.C2 && c2 > ofs.C1)
                        {
                            offset_arr.Remove(op);
                        }
                        op = next_op;
                    }
                }
                offset_arr.AddLast(new OffsetPair(c1, c2)
                {
                    IsTransposition = isTransposition
                });
            }
            else
            {
                lcss += _options.LocalLengthEvaluator(local_cs);
                local_cs = 0;
                if (c1 != c2)
                {
                    c1 = c2 = Math.Min(c1, c2);  //using min allows the computation of transpositions
                }
                if (_options.MaxDistance != null)
                {
                    var temporaryDistance = _options.LocalLengthEvaluator(Math.Max(c1, c2)) - _options.TranspositionsEvaluator(lcss, trans);
                    if (temporaryDistance > _options.MaxDistance) return Math.Round(temporaryDistance, MidpointRounding.AwayFromZero);
                }
                //if matching tokens are found, remove 1 from both cursors (they get incremented at the end of the loop)
                //so that we can have only one code block handling matches 
                for (var i = 0; i < maxOffset && (c1 + i < l1 || c2 + i < l2); i++)
                {
                    if ((c1 + i < l1) && _options.TokenMatcher(t1[c1 + i], t2[c2]))
                    {
                        c1 += i - 1;
                        c2--;
                        break;
                    }
                    if ((c2 + i < l2) && _options.TokenMatcher(t1[c1], t2[c2 + i]))
                    {
                        c1--;
                        c2 += i - 1;
                        break;
                    }
                }
            }
            c1++;
            c2++;
            // this covers the case where the last match is on the last token in list, so that it can compute transpositions correctly
            if ((c1 >= l1) || (c2 >= l2))
            {
                lcss += _options.LocalLengthEvaluator(local_cs);
                local_cs = 0;
                c1 = c2 = Math.Min(c1, c2);
            }
        }
        lcss += _options.LocalLengthEvaluator(local_cs);
        return Math.Round(_options.LocalLengthEvaluator(Math.Max(l1, l2)) - _options.TranspositionsEvaluator(lcss, trans), MidpointRounding.AwayFromZero); //apply transposition cost to the final result
    }

    /// <summary>
    /// Static distance algorithm working on strings, computing transpositions as well as stopping when maxDistance was reached.
    /// </summary>
    /// <param name="s1"></param>
    /// <param name="s2"></param>
    /// <param name="maxOffset"></param>
    /// <param name="maxDistance"></param>
    /// <returns></returns>
    public static double CommonDistance(string s1, string s2, int maxOffset, int maxDistance = 0)
    {
        var l1 = s1 == null ? 0 : s1.Length;
        var l2 = s2 == null ? 0 : s2.Length;

        if (l1 == 0) return l2;
        if (l2 == 0) return l1;

        var c1 = 0;  //cursor for string 1
        var c2 = 0;  //cursor for string 2
        var lcss = 0;  //largest common subsequence
        var local_cs = 0; //local common substring
        var trans = 0;  //number of transpositions ('axb' vs 'xba')
        var offset_arr = new LinkedList<OffsetPair>();  //offset pair array, for computing the transpositions

        while ((c1 < l1) && (c2 < l2))
        {
            if (s1[c1] == s2[c2])
            {
                local_cs++;
                var isTransposition = false;
                var op = offset_arr.First;
                while (op != null)
                {  //see if current match is a transposition
                    var ofs = op.Value;
                    if (c1 <= ofs.C1 || c2 <= ofs.C2)
                    {
                        // when two matches cross, the one considered a transposition is the one with the largest difference in offsets
                        isTransposition = Math.Abs(c2 - c1) >= Math.Abs(ofs.C2 - ofs.C1);
                        if (isTransposition)
                        {
                            trans++;
                        }
                        else
                        {
                            if (!ofs.IsTransposition)
                            {
                                ofs.IsTransposition = true;
                                trans++;
                            }
                        }
                        break;
                    }
                    else
                    {
                        var next_op = op.Next;
                        if (c1 > ofs.C2 && c2 > ofs.C1)
                        {
                            offset_arr.Remove(op);
                        }
                        op = next_op;
                    }
                }
                offset_arr.AddLast(new OffsetPair(c1, c2)
                {
                    IsTransposition = isTransposition
                });
            }
            else
            {
                lcss += local_cs;
                local_cs = 0;
                if (c1 != c2)
                {
                    c1 = c2 = Math.Min(c1, c2);  //using min allows the computation of transpositions
                }
                if (maxDistance > 0)
                {
                    var temporaryDistance = Math.Max(c1, c2) - (lcss - trans);
                    if (temporaryDistance > maxDistance) return temporaryDistance;
                }
                //if matching tokens are found, remove 1 from both cursors (they get incremented at the end of the loop)
                //so that we can have only one code block handling matches 
                for (var i = 0; i < maxOffset && (c1 + i < l1 || c2 + i < l2); i++)
                {
                    if ((c1 + i < l1) && s1[c1 + i] == s2[c2])
                    {
                        c1 += i - 1;
                        c2--;
                        break;
                    }
                    if ((c2 + i < l2) && s1[c1] == s2[c2 + i])
                    {
                        c1--;
                        c2 += i - 1;
                        break;
                    }
                }
            }
            c1++;
            c2++;
            // this covers the case where the last match is on the last token in list, so that it can compute transpositions correctly
            if ((c1 >= l1) || (c2 >= l2))
            {
                lcss += local_cs;
                local_cs = 0;
                c1 = c2 = Math.Min(c1, c2);
            }
        }
        lcss += local_cs;
        return Math.Max(l1, l2) - (lcss - trans); //apply transposition cost to the final result
    }

    /// <summary>
    /// Standard Sift algorithm, using strings and taking only maxOffset as a parameter
    /// </summary>
    /// <param name="s1"></param>
    /// <param name="s2"></param>
    /// <param name="maxOffset"></param>
    /// <returns></returns>
    public static int SimplestDistance(string s1, string s2, int maxOffset)
    {
        var l1 = s1 == null ? 0 : s1.Length;
        var l2 = s2 == null ? 0 : s2.Length;

        if (l1 == 0) return l2;
        if (l2 == 0) return l1;

        var c1 = 0;  //cursor for string 1
        var c2 = 0;  //cursor for string 2
        var lcss = 0;  //largest common subsequence
        var local_cs = 0; //local common substring

        while ((c1 < l1) && (c2 < l2))
        {
            if (s1[c1] == s2[c2])
            {
                local_cs++;
            }
            else
            {
                lcss += local_cs;
                local_cs = 0;
                if (c1 != c2)
                {
                    c1 = c2 = Math.Max(c1, c2);
                }
                //if matching tokens are found, remove 1 from both cursors (they get incremented at the end of the loop)
                //so that we can have only one code block handling matches 
                for (var i = 0; i < maxOffset && (c1 + i < l1 && c2 + i < l2); i++)
                {
                    if ((c1 + i < l1) && s1[c1 + i] == s2[c2])
                    {
                        c1 += i - 1;
                        c2--;
                        break;
                    }
                    if ((c2 + i < l2) && s1[c1] == s2[c2 + i])
                    {
                        c1--;
                        c2 += i - 1;
                        break;
                    }
                }
            }
            c1++;
            c2++;
        }
        lcss += local_cs;
        return Math.Max(l1, l2) - lcss;
    }

    private class OffsetPair
    {
        public int C1 { get; set; }
        public int C2 { get; set; }
        public bool IsTransposition { get; set; }

        public OffsetPair(int c1, int c2)
        {
            this.C1 = c1;
            this.C2 = c2;
            this.IsTransposition = false;
        }
    }

    public class Options
    {
        /// <summary>
        /// If set, the algorithm will stop if the distance reaches this value
        /// </summary>
        public int? MaxDistance { get; set; }

        /// <summary>
        /// The function that turns strings into a list of tokens (also strings)
        /// </summary>
        public Func<string, string[]> Tokenizer { get; set; }

        /// <summary>
        /// The function that determines if two tokens are matching (similar to characters being the same in the simple algorithm)
        /// </summary>
        public Func<string, string, bool> TokenMatcher { get; set; }

        /// <summary>
        /// The function that determines the value of a match of two tokens (the equivalent of adding 1 to the lcss when two characters match)
        /// This assumes that the TokenMatcher function is a lot less expensive than this evaluator. If that is not the case, 
        /// you can optimize the speed of the algorithm by using only the matching evaluator and then calculating if two tokens match on the returned value.
        /// </summary>
        public Func<string, string, double> MatchingEvaluator { get; set; }

        /// <summary>
        /// Determines if the local value (computed on subsequent matched tokens) must be modified.
        /// In case one wants to reward longer matched substrings, for example, this is what you need to change.
        /// </summary>
        public Func<double, double> LocalLengthEvaluator { get; set; }

        /// <summary>
        /// The function determining the cost of an individual transposition, based on its counter positions.
        /// </summary>
        public Func<int, int, double> TranspositionCostEvaluator { get; set; }

        /// <summary>
        /// The function determining how the cost of transpositions affects the final result
        /// Change it if it doesn't suit you.
        /// </summary>
        public Func<double, double, double> TranspositionsEvaluator { get; set; }
    }
}

// Sift4 - common version
// online algorithm to compute the distance between two strings in O(n)
// $maxOffset is the number of characters to search for matching letters
// $maxDistance is the distance at which the algorithm should stop computing the value and just exit (the strings are too different anyway)
function sift4($s1, $s2, $maxOffset, $maxDistance = 0) {
    if (!$s1 || !strlen($s1)) {
        if (!$s2) {
            return 0;
        }
        return strlen($s2);
    }
    if (!$s2 || !strlen($s2)) {
        return strlen($s1);
    }
    $l1 = strlen($s1);
    $l2 = strlen($s2);
    $c1 = 0; //cursor for string 1
    $c2 = 0; //cursor for string 2
    $lcss = 0; //largest common subsequence
    $local_cs = 0; //local common substring
    $trans = 0; //number of transpositions ('ab' vs 'ba')
    $offset_arr = array(); //offset pair array, for computing the transpositions
    while (($c1 < $l1) && ($c2 < $l2)) {
        if (substr($s1, $c1, 1) == substr($s2, $c2, 1)) {
            $local_cs++;
            $isTrans = false;
            $i = 0;
            while ($i < sizeof($offset_arr)) { //see if current match is a transposition
                $ofs = $offset_arr[$i];
                if ($c1 <= $ofs['c1'] || $c2 <= $ofs['c2']) {
                    $isTrans = abs($c2 - $c1) >= abs($ofs['c2'] - $ofs['c1']);
                    if ($isTrans) {
                        $trans++;
                    } else {
                        if (!$ofs['trans']) {
                            $ofs['trans'] = true;
                            $trans++;
                        }
                    }
                    break;
                } else {
                    if ($c1 > $ofs['c2'] && $c2 > $ofs['c1']) {
                        array_splice($offset_arr, $i, 1);
                    } else {
                        $i++;
                    }
                }
            }
            array_push($offset_arr, array('c1' = > $c1, 'c2' = > $c2, 'trans' = > $isTrans));
        } else {
            $lcss+= $local_cs;
            $local_cs = 0;
            if ($c1 != $c2) {
                $c1 = $c2 = min($c1, $c2); //using min allows the computation of transpositions
            }
            if ($maxDistance) {
                $temporaryDistance = max($c1, $c2) - $lcss + $trans;
                if ($temporaryDistance > $maxDistance) return $temporaryDistance;
            }

            //if matching characters are found, remove 1 from both cursors (they get incremented at the end of the loop)
            //so that we can have only one code block handling matches
            for ($i = 0;$i < $maxOffset && ($c1 + $i < $l1 || $c2 + $i < $l2);$i++) {
                if (($c1 + $i < $l1) && (substr($s1, $c1 + $i, 1) == substr($s2, $c2, 1))) {
                    $c1+= $i - 1;
                    $c2--;
                    break;
                }
                if (($c2 + $i < $l2) && (substr($s1, $c1, 1) == substr($s2, $c2 + $i, 1))) {
                    $c1--;
                    $c2+= $i - 1;
                    break;
                }
            }
        }
        $c1++;
        $c2++;
        // this covers the case where the last match is on the last token in list, so that it can compute transpositions correctly
        if (($c1 >= $l1) || ($c2 >= $l2)) {
            $lcss+= $local_cs;
            $local_cs = 0;
            $c1 = $c2 = min($c1, $c2);
        }
    }
    $lcss+= $local_cs;
    return max($l1, $l2) - $lcss + $trans; //apply transposition cost to final result
    
}

---<summary>
---Static distance algorithm working on strings, computing transpositions as well as stopping when maxDistance was reached.
---</summary>
---<param name="s1"></param>
---<param name="s2"></param>
---<param name="maxOffset"></param>
---<param name="maxDistance"></param>
---<returns></returns>
CREATE FUNCTION Sift4common(@s1          NVARCHAR(max), 
                            @s2          NVARCHAR(max), 
                            @maxOffset   INT, 
                            @maxDistance INT) 
returns INT 
AS 
  BEGIN 
      DECLARE @l1 INT = Len(Isnull(@s1, '')); 
      DECLARE @l2 INT = Len(Isnull(@s2, '')); 

      IF ( @l1 = 0 ) 
        RETURN @l2; 

      IF ( @l2 = 0 ) 
        RETURN @l1; 

      DECLARE @c1 INT = 0; 
      DECLARE @c2 INT = 0; 
      DECLARE @lcss INT = 0; 
      DECLARE @local_cs INT = 0; 
      DECLARE @trans INT = 0; 
      DECLARE @offset_arr TABLE 
        ( 
           C1    INT, 
           C2    INT, 
           Trans BIT 
        ) 
      DECLARE @i INT 
      DECLARE @temporaryDistance FLOAT 
      DECLARE @result INT 
      DECLARE @oc1 INT, 
              @oc2 INT, 
              @otr BIT 
      DECLARE @isTrans BIT 

      WHILE ( ( @c1 < @l1 ) 
              AND ( @c2 < @l2 ) ) 
        BEGIN 
            IF ( Substring(@s1, @c1 + 1, 1) = Substring(@s2, @c2 + 1, 1) ) 
              BEGIN 
                  SET @local_cs=@local_cs + 1; 
                  SET @isTrans=0 
                  SET @oc1=NULL; 

                  SELECT TOP 1 @oc1 = o.C1, 
                               @oc2 = o.C2, 
                               @otr = o.Trans 
                  FROM   @offset_arr o 
                  WHERE  @c1 <= o.C1 
                          OR @c2 <= o.C2 

                  IF ( @oc1 IS NOT NULL ) 
                    BEGIN 
                        SET @isTrans=CASE 
                                       WHEN Abs(@c2 - @c1) >= Abs(@oc2 - @oc1) 
                                     THEN 1 
                                       ELSE 0 
                                     END 

                        IF ( @isTrans = 1 ) 
                          BEGIN 
                              SET @trans=@trans + 1 
                          END 
                        ELSE IF ( @otr = 0 ) 
                          BEGIN 
                              SET @trans=@trans + 1 

                              UPDATE @offset_arr 
                              SET    Trans = 1 
                              WHERE  C1 = @oc1 
                                     AND C2 = @oc2 
                          END 
                    END 

                  DELETE FROM @offset_arr 
                  WHERE  @c1 > C1 
                         AND @c1 > C2 
                         AND @c2 > C1 
                         AND @c2 > C2; 

                  INSERT INTO @offset_arr 
                  VALUES      (@c1, 
                               @c2, 
                               @isTrans); 
              END 
            ELSE 
              BEGIN 
                  SET @lcss = @lcss + @local_cs; 
                  SET @local_cs = 0; 

                  IF ( @c1 != @c2 ) 
                    -- using min allows the computation of transpositions  
                    BEGIN 
                        IF ( @c1 < @c2 ) 
                          BEGIN 
                              SET @c2=@c1; 
                          END 
                        ELSE 
                          BEGIN 
                              SET @c1=@c2; 
                          END 
                    END 
                IF ( @maxDistance > 0 ) 
                  BEGIN 
                    IF ( @c1 > @c2 ) 
                    BEGIN 
                      SET @temporaryDistance = @c1 - ( @lcss - @trans / 2.0 ); 
                    END 
                    ELSE 
                    BEGIN 
                      SET @temporaryDistance = @c2 - ( @lcss - @trans / 2.0 ); 
                    END 

                  IF ( @temporaryDistance > @maxDistance ) 
                    RETURN Round(@temporaryDistance, 0); 
              END 


                  --if matching tokens are found, remove 1 from both cursors (they get incremented at the end of the loop)
                  --so that we can have only one code block handling matches   
                  SET @i=0; 

                  WHILE ( @i < @maxOffset 
                          AND ( @c1 + @i < @l1 
                                 OR @c2 + @i < @l2 ) ) 
                    BEGIN 
                        IF ( ( @c1 + @i < @l1 ) 
                             AND Substring(@s1, @c1 + @i + 1, 1) = 
                                 Substring(@s2, @c2 + 1, 1) 
                           ) 
                          BEGIN 
                              SET @c1 = @c1 + @i - 1; 
                              SET @c2=@c2 - 1; 

                              BREAK; 
                          END 

                        IF ( ( @c2 + @i < @l2 ) 
                             AND Substring(@s1, @c1 + 1, 1) = Substring(@s2, 
                                                              @c2 + @i + 1, 1 
                                                              ) 
                           ) 
                          BEGIN 
                              SET @c1 = @c1 - 1; 
                              SET @c2=@c2 + @i - 1; 

                              BREAK; 
                          END 

                        SET @i=@i + 1; 
                    END 
              END 

            SET @c1=@c1 + 1; 
            SET @c2=@c2 + 1; 

            IF ( ( @c1 >= @l1 ) 
                  OR ( @c2 >= @l2 ) ) 
              BEGIN 
                  SET @lcss = @lcss + @local_cs; 
                  SET @local_cs = 0; 

                  IF ( @c1 < @c2 ) 
                    BEGIN 
                        SET @c2=@c1; 
                    END 
                  ELSE 
                    BEGIN 
                        SET @c1=@c2; 
                    END 
              END 
        END 

      SET @lcss = @lcss + @local_cs; 

      --apply the transposition cost to the final result 
      IF ( @l1 > @l2 ) 
        BEGIN 
            SET @result = @l1 - ( @lcss - @trans ); 
        END 
      ELSE 
        BEGIN 
            SET @result = @l2 - ( @lcss - @trans ); 
        END 

      RETURN @result; 
  END 

BEGIN 
DECLARE l1 INT DEFAULT Length(IFNULL(s1, '')); 
DECLARE l2 INT DEFAULT Length(IFNULL(s2, '')); 


DECLARE c1 INT Default 0; 
DECLARE c2 INT default 0; 
DECLARE lcss INT default 0; 
DECLARE local_cs INT default 0; 
DECLARE trans INT default 0; 
DECLARE i INT;
DECLARE temporaryDistance FLOAT;
DECLARE result INT;
DECLARE oc1 INT;
DECLARE oc2 INT;
DECLARE otr smallint;
DECLARE isTrans smallint;

drop temporary table if exists offset_arr;
CREATE TEMPORARY TABLE IF not EXISTS offset_arr
( 
C1 INT, 
C2 INT,
Trans BIT
)engine=memory;


/*      delete from offset_arr;*/


IF l1 = 0 THEN
RETURN l2; 
END IF;
IF l2 = 0 THEN 
RETURN l1; 
END IF;  






WHILE ( ( c1 < l1 ) AND ( c2 < l2 ) ) 
DO 
IF ( Substring(s1, c1 + 1, 1) = Substring(s2, c2 + 1, 1) ) THEN

SET local_cs=local_cs + 1; 
SET isTrans=0;
SET oc1=NULL;
SELECT  o.C1, o.C2,o.Trans  into oc1, oc2, otr
FROM offset_arr o 
WHERE c1 <= o.C1 OR c2 <= o.C2
LIMIT 1;
IF oc1 IS NOT NULL THEN

SET isTrans=CASE WHEN ABS(c2-c1)>=ABS(oc2-oc1) THEN 1 ELSE 0 END;
IF (isTrans=1) THEN
SET trans=trans+1;
ELSE
IF (otr=0) THEN


SET trans=trans+1;
UPDATE offset_arr SET Trans=1 WHERE C1=oc1 AND C2=oc2;
END IF;
END IF;  
END IF;


DELETE FROM offset_arr 
WHERE  c1 > C1 
AND c1 > C2
AND c2 > C1 
AND c2 > C2; 


INSERT INTO offset_arr 
VALUES (c1, c2, isTrans); 

ELSE 

SET lcss = lcss + local_cs; 
SET local_cs = 0; 


IF ( c1 != c2 ) THEN
-- using min allows the computation of transpositions 


IF ( c1 < c2 ) THEN
SET c2=c1; 
ELSE 
SET c1=c2; 
END IF;

IF ( maxDistance > 0 ) THEN


IF ( c1 > c2 ) THEN
SET temporaryDistance = c1 - ( lcss - trans / 2.0 ); 
ELSE 
SET temporaryDistance = c2 - ( lcss - trans / 2.0 ); 
END IF;


IF ( temporaryDistance > maxDistance ) THEN
RETURN Round(temporaryDistance, 0); 
END IF;  
END IF;

END IF;


/*if matching tokens are found, remove 1 from both cursors (they get incremented at the end of the loop)
--so that we can have only one code block handling matches  */
SET i=0; 


label : WHILE ( i < maxOffset AND (c1 + i < l1 OR c2 + i < l2) ) do


IF ( ( c1 + i < l1 ) 
AND Substring(s1, c1 + i + 1, 1) = Substring(s2, c2 + 1, 1) 
) THEN


SET c1 = c1 + i - 1; 
SET c2=c2 - 1; 


leave label; 
END IF; 


IF ( ( c2 + i < l2 ) 
AND Substring(s1, c1 + 1, 1) = Substring(s2, c2 + i + 1, 1) 
)THEN 


SET c1 = c1 - 1; 
SET c2=c2 + i - 1; 


leave label;  
END IF;


SET i=i + 1; 
END WHILE;
END IF; 


SET c1=c1 + 1; 
SET c2=c2 + 1; 


IF ( ( c1 >= l1 ) OR ( c2 >= l2 ) ) THEN
SET lcss = lcss + local_cs; 
SET local_cs = 0; 


IF ( c1 < c2 ) THEN
SET c2=c1; 
ELSE 
SET c1=c2; 
END IF;
END IF;
END while;


SET lcss = lcss + local_cs; 


/*apply the transposition cost to the final result*/
IF ( l1 > l2 ) THEN
SET result = l1 - (lcss - trans);
ELSE 
SET result = l2 - (lcss - trans);
END IF;
RETURN result; 
END

/**
 * Sift4 - common version
 * online algorithm to compute the distance between two strings in O(n)
 * Algorithm by siderite, java port by Nathan Fischer 2016
 * /blog/super-fast-and-accurate-string-distance.html
 * @param s1
 * @param s2
 * @param maxOffset the number of characters to search for matching letters
 * @return
 */
public static double sift4(String s1, String s2, int maxOffset) {
    class Offset {
        int c1;
        int c2;
        boolean trans;

        Offset(int c1, int c2, boolean trans) {
            this.c1 = c1;
            this.c2 = c2;
            this.trans = trans;
        }
    }

    if (s1 == null || s1.isEmpty())
        return s2 == null ? 0 : s2.length();

    if (s2 == null || s2.isEmpty())
        return s1.length();

    int l1 = s1.length();
    int l2 = s2.length();

    int c1 = 0; //cursor for string 1
    int c2 = 0; //cursor for string 2
    int lcss = 0; //largest common subsequence
    int local_cs = 0; //local common substring
    int trans = 0; //number of transpositions ('ab' vs 'ba')
    LinkedList < Offset > offset_arr = new LinkedList < > (); //offset pair array, for computing the transpositions

    while ((c1 < l1) && (c2 < l2)) {
        if (s1.charAt(c1) == s2.charAt(c2)) {
            local_cs++;
            boolean isTrans = false;
            //see if current match is a transposition
            int i = 0;
            while (i < offset_arr.size()) {
                Offset ofs = offset_arr.get(i);
                if (c1 <= ofs.c1 || c2 <= ofs.c2) {
                    // when two matches cross, the one considered a transposition is the one with the largest difference in offsets
                    isTrans = Math.abs(c2 - c1) >= Math.abs(ofs.c2 - ofs.c1);
                    if (isTrans) {
                        trans++;
                    } else {
                        if (!ofs.trans) {
                            ofs.trans = true;
                            trans++;
                        }
                    }
                    break;
                } else {
                    if (c1 > ofs.c2 && c2 > ofs.c1) {
                        offset_arr.remove(i);
                    } else {
                        i++;
                    }
                }
            }
            offset_arr.add(new Offset(c1, c2, isTrans));
        } else {
            lcss += local_cs;
            local_cs = 0;
            if (c1 != c2) {
                c1 = c2 = Math.min(c1, c2); //using min allows the computation of transpositions
            }
            //if matching characters are found, remove 1 from both cursors (they get incremented at the end of the loop)
            //so that we can have only one code block handling matches
            for (int i = 0; i < maxOffset && (c1 + i < l1 || c2 + i < l2); i++) {
                if ((c1 + i < l1) && (s1.charAt(c1 + i) == s2.charAt(c2))) {
                    c1 += i - 1;
                    c2--;
                    break;
                }
                if ((c2 + i < l2) && (s1.charAt(c1) == s2.charAt(c2 + i))) {
                    c1--;
                    c2 += i - 1;
                    break;
                }
            }
        }
        c1++;
        c2++;
        // this covers the case where the last match is on the last token in list, so that it can compute transpositions correctly
        if ((c1 >= l1) || (c2 >= l2)) {
            lcss += local_cs;
            local_cs = 0;
            c1 = c2 = Math.min(c1, c2);
        }
    }
    lcss += local_cs;
    return Math.round(Math.max(l1, l2) - lcss + trans); //add the cost of transpositions to the final result
}

function Calc-Sift4Distance 
{
  <# 
      .SYNOPSIS 

      Compute the edit distance between 2 strings using the sift4 string
      edit distance algorithm.

      .PARAMETER s1

      The 1st string

      .PARAMETER s2

      The 2nd string

      .PARAMETER maxOffset

      The maximum common substring length for which to search. The default
      is 10.

      .RETURN

      The # of edits needed to make the given 2 strings equal.
  #>

  Param(
    [Parameter(Mandatory = $True, ValueFromPipelineByPropertyName = $True)]
    [String]
    $s1,

    [Parameter(Mandatory = $True, ValueFromPipelineByPropertyName = $True)]
    [String]
    $s2,

    [Parameter(ValueFromPipelineByPropertyName = $True)]
    [Int]
    $maxOffset = 10
  )

  # Handle null or empty strings.
  if ((-not $s1) -or ($s1.length -eq 0)) 
  {
    if (-not $s2) 
    {
      return 0
    }
    return $s2.length
  }

  if ((-not $s2) -or ($s2.length -eq 0)) 
  {
    return $s1.length
  }

  # Initialization.
  $l1 = $s1.length
  $l2 = $s2.length
  $c1 = 0 # Cursor for string 1.
  $c2 = 0 # Cursor for string 2.
  $lcss = 0 # Largest common subsequence.
  $local_cs = 0 # Local common substring.

  # Scan strings.
  while (($c1 -lt $l1) -and ($c2 -lt $l2)) 
  {
    if ($s1[$c1] -eq $s2[$c2]) 
    {
      $local_cs++
    }
    else 
    {
      $lcss += $local_cs
      $local_cs = 0
      if ($c1 -ne $c2) 
      {
        # Using max to bypass the need for computer transpositions ('ab' vs 'ba').
        $c1 = $c2 = (@($c1, $c2) | Measure-Object -Maximum).Maximum
      }

      for ($i = 0; (($i -lt $maxOffset) -and ((($c1 + $i) -lt $l1) -or (($c2 + $i) -lt $l2))); $i++) 
      {
        if ((($c1 + $i) -lt $l1) -and ($s1[$c1 + $i] -eq $s2[$c2])) 
        {
          $c1 += $i
          $local_cs++
          break
        }

        if ((($c1 + $i) -lt $l2) -and ($s1[$c1] -eq $s2[$c2 + $i])) 
        {
          $c2 += $i
          $local_cs++
          break
        }
      }
    }
    $c1++
    $c2++
  }
  $lcss += $local_cs
  return [math]::Round((@($l1, $l2) | Measure-Object -Maximum).Maximum - $lcss)
}

struct sift_offset {
  int c1;
  int c2;
  bool trans;
};

template < typename T >
  int sift4(T * s1, int s1_size, T * s2, int s2_size, int maxOffset, int maxDistance) {
    if (!s1 || !s1_size) {
      if (!s2) {
        return 0;
      }
      return s2_size;
    }

    if (!s2 || !s2_size) {
      return s1_size;
    }

    int l1 = s1_size;
    int l2 = s2_size;

    int c1 = 0; //cursor for string 1
    int c2 = 0; //cursor for string 2
    int lcss = 0; //largest common subsequence
    int local_cs = 0; //local common substring
    int trans = 0; //number of transpositions ('ab' vs 'ba')
    std::vector < sift_offset > offset_arr; //offset pair array, for computing the transpositions

    while ((c1 < l1) && (c2 < l2)) {
      if (s1[c1] == s2[c2]) {
        local_cs++;
        bool isTrans = false;
        //see if current match is a transposition
        int i = 0;
        while (i < offset_arr.size()) {
          sift_offset ofs = offset_arr[i];
          if (c1 <= ofs.c1 || c2 <= ofs.c2) {
            // when two matches cross, the one considered a transposition is the one with the largest difference in offsets
            isTrans = std::abs(c2 - c1) >= std::abs(ofs.c2 - ofs.c1);

            if (isTrans) {
              trans++;
            } else {
              if (!ofs.trans) {
                ofs.trans = true;
                trans++;
              }
            }
            break;
          } else {
            if (c1 > ofs.c2 && c2 > ofs.c1) {
              offset_arr.erase(offset_arr.begin() + i);

            } else {
              i++;
            }
          }
        }
        offset_arr.push_back({
          c1,
          c2,
          isTrans
        });
      } else {
        lcss += local_cs;
        local_cs = 0;
        if (c1 != c2) {
          c1 = c2 = (int) min(c1, c2); //using min allows the computation of transpositions
        }
        //if matching characters are found, remove 1 from both cursors (they get incremented at the end of the loop)
        //so that we can have only one code block handling matches 
        for (int i = 0; i < maxOffset && (c1 + i < l1 || c2 + i < l2); i++) {
          if ((c1 + i < l1) && (s1[c1 + i] == s2[c2])) {
            c1 += i - 1;
            c2--;
            break;
          }
          if ((c2 + i < l2) && (s1[c1] == s2[c2 + i])) {
            c1--;
            c2 += i - 1;
            break;
          }
        }
      }
      c1++;
      c2++;
      if (maxDistance) {
        int temporaryDistance = (int) max(c1, c2) - lcss + trans;
        if (temporaryDistance >= maxDistance) return std: round(temporaryDistance);
      }

    }
    // this covers the case where the last match is on the last token in list, so that it can compute transpositions correctly
    if ((c1 >= l1) || (c2 >= l2)) {
      lcss += local_cs;
      local_cs = 0;
      c1 = c2 = (int) min(c1, c2);
    }
  }
lcss += local_cs;
return std::round((int) max(l1, l2) - lcss + trans); //add the cost of transpositions to the final result
}

You can find a Go implementation here, written by Jason W. Hutchinson.
There is also a Swift implementation here.
A Perl 6 (now called Raku) implementation can be found here.

<div ng-click="row.toggleExpand()" ng-style="rowStyle(row)" class="ngAggregate">
    <span class="ngAggregateText">{{row.label CUSTOM_FILTERS}} ({{row.totalChildren()}} {{AggItemsLabel}})</span>
    <div class="{{row.aggClass()}}"></div>
</div>

ngAggregate.prototype.totalChildren = function () {
    if (this.aggChildren.length > 0) {
        var i = 0;
        var recurse = function (cur) {
            if (cur.aggChildren.length > 0) {
                angular.forEach(cur.aggChildren, function (a) {
                    recurse(a);
                });
            } else {
                i += cur.children.length;
            }
        };
        recurse(this);
        return i;
    } else {
        return this.children.length;
    }
};

• Define the options for the grid. I am sure you already have it defined somewhere, if not, it is advisable you would. Sooner or later you will want to customize the output and functionality.
• Add a new property to the options called aggregateTemplate. This will look probably like the default template, but with another function instead of totalChildren.
• Define the function that will aggregate the items.

$scope.gridOptions = {
        data: 'Data.Units',
        enableColumnResize: true,
        showColumnMenu: false,
        showFilter: true,
        multiSelect: false,
        showGroupPanel: true,
        enablePaging: false,
        showFooter: true,
        columnDefs: [
            { field: 'Country', displayName: 'Country', width: 190 },
            { field: 'Type', displayName: 'Unit Type' },
            { field: 'Count', displayName: 'Count', width: 180}
        ],
        aggregateTemplate: "<div ng-click=\"row.toggleExpand()\" ng-style=\"rowStyle(row)\" class=\"ngAggregate\">" +
    "    <span class=\"ngAggregateText\">{{row.label CUSTOM_FILTERS}} ({{aggFunc(row)}} {{AggItemsLabel}})</span>" +
    "    <div class=\"{{row.aggClass()}}\"></div>" +
    "</div>"
    };

$scope.aggFunc = function (row) {
        var sumColumn='Count';
        var total = 0;
        angular.forEach(row.children, function(entry) {
            total+=entry.entity[sumColumn];
        });
        angular.forEach(row.aggChildren, function(entry) {
            total+=$scope.aggFunc(entry);
        });
        return total;
    };

module.run(["$templateCache", function($templateCache) {

  $templateCache.put("aggregateCountTemplate.html",
    "<div ng-click=\"row.toggleExpand()\" ng-style=\"rowStyle(row)\" class=\"ngAggregate\">" +
    "    <span class=\"ngAggregateText\">{{row.label CUSTOM_FILTERS}} ({{aggFunc(row)}} {{AggItemsLabel}})</span>" +
    "    <div class=\"{{row.aggClass()}}\"></div>" +
    "</div>"
  );

}]);

$scope.gridOptions = {
        [...]
        aggregateTemplate: "aggregateCountTemplate.html"
    };

$scope.gridOptions = {
        [...]
        aggregateTemplate: "/templates/aggregateCountTemplate.html"
    };

var module = angular.module('app', ['ngResource', 'ui.bootstrap', 'ui', 'ngGrid', 'importTreeFilter', 'ui.date', 'SharedServices', 'ui.autocomplete']);

module.run(["$templateCache","$rootScope", function($templateCache,$rootScope) {

  $rootScope.aggregateCountFunc = function (row) {
        var total = 0;
        angular.forEach(row.children, function(entry) {
            total+=entry.entity.Count;
        });
        angular.forEach(row.aggChildren, function(entry) {
            total+=$rootScope.aggregateCountFunc(entry);
        });
        return total;
    };

  $templateCache.put("aggregateCountTemplate.html",
    "<div ng-click=\"row.toggleExpand()\" ng-style=\"rowStyle(row)\" class=\"ngAggregate\">" +
    "    <span class=\"ngAggregateText\">{{row.label CUSTOM_FILTERS}} ({{aggregateCountFunc(row)}}{{AggItemsLabel}})</span>" +
    "    <div class=\"{{row.aggClass()}}\"></div>" +
    "</div>"
  );

}]);

var j=jQuery(elem);
if (j.is('img[alt]')) {
   j.attr('alt',translate(j.attr('alt')));
}

if (/^img$/i.test(elem.tagName)) {
  var alt=elem.getAttribute('alt');
  if (alt) {
    elem.setAttribute('alt',translate(alt));
  }
}

function angularCompile(elem, data) {
    // create an injector
    var $injector = angular.injector(['ng','app']);
            
    // use the type inference to auto inject arguments, or use implicit injection
    $injector.invoke(function($rootScope, $compile, $document){
        var compiled = $compile(elem || $document);
        compiled($rootScope);
        if (data) {
            for (var k in data) {
                if (data.hasOwnProperty(k)) {
                    $rootScope[k]=data[k];
                }
            }
        }
           $rootScope.$digest();
    });
}

angularCompile(dialog[0],{editedObject: obj}); // will take the jQuery dialog element, compile it, and add to the scope the editedObject property with the value of obj.

OpenTranslationDialog=function(Rule, onProceed, onCancel) {
  jQuery.ajax({
          type: 'GET',
          url: '/Content/ng-templates/dialogs/Translation.html',
          data: Rule,
          success: function(data) {
            var dialog=jQuery('<div></div>')
              .html(data)
              .dialog({
                resizable:true,
                width:700,
                modal:true,
                    buttons: {
                      "Save": function() {
                    var url='/some/api/url';
                    jQuery.ajax({
                        type:'PUT',
                        url:url,
                        data:Rule,
                        success:function() {
                          if (onProceed) onProceed();
                              $(this).dialog( "close" );
                        },
                        error:function() {
                          alert('There was an error saving the rule');
                        }
                      });
                      },
                      Cancel: function() {
                    if (onCancel) onCancel();
                          $(this).dialog( "close" );
                      }
                    }
              });

            angularCompile(dialog[0],{Rule:Rule});
          },
          error:function() {
              alert('There was an error getting the dialog template');
                  }
      });
}

function FindProxyForURL(url, host) {

var defProxy="10.20.30.40:50"; // the misbehaving or incomplete proxy

var domains=[
   ".mysite.com",
   ".xxx",
   "localhost"
];
var ipClasses=[
   "11.22.33.0",
   "55.0.0.0",
   "127.0.0.0"
];

for (var i=0; i<domains.length; i++) {
  if (dnsDomainIs(host,domains[i])) return "DIRECT";
}

var MYHOST = dnsResolve(host);

for (var i=0; i<ipClasses.length; i++) {
  var mask=getMask(ipClasses[i]);
  if (isInNet(MYHOST, ipClasses[i],mask)) return "DIRECT";
}

return "PROXY "+defProxy;

function getMask(ip) {
 var splits=ip.split('.');
 for (var i=0; i<splits.length; i++) {
  if (splits[i]!='0') splits[i]='255';
 }
    return splits.join('.');
}

}

SELECT v.Val,Count(1) as Nr
FROM #Values v
INNER JOIN Ranges r
ON r.Start<=v AND r.[End]>=v

SELECT DISTINCT Val
INTO #Values
FROM (
  SELECT 0 as Val
    UNION ALL
  SELECT Start FROM Ranges
    UNION ALL
  SELECT [End]-1 FROM Ranges
) x
ORDER BY Val

SELECT v.Val,
       Count(r.Start) as Nr
FROM #Values v
LEFT JOIN Ranges r
  ON r.Start<=v.Val AND r.[End]>v.Val
GROUP BY v.Val

<div ol-map controls="zoom,navigation,layerSwitcher,attribution,mousePosition" control-opts="{navigation:{handleRightClicks:true}}">
    <az-layer name="Street" lyr-type="tiles"></az-layer>
    <az-layer name="Airports" lyr-type="geojson" lyr-url="examples/data/airports.json" projection="EPSG:4326"></az-layer>
</div>

OpenLayers.Format.RSI = OpenLayers.Class(OpenLayers.Format.JSON, {

    read: function(json, type, filter) {
        type = (type) ? type : "FeatureCollection";
        var results = null;
        var obj = null;
        if (typeof json == "string") {
            obj = OpenLayers.Format.JSON.prototype.read.apply(this,
                                                              [json, filter]);
        } else { 
            obj = json;
        }    
        if(!obj) {
            OpenLayers.Console.error("Bad JSON: " + json);
        }

        var features=[];
        for (var i=0; i<obj.length; i++) {
            var item=obj[i];
            var point=new OpenLayers.Geometry.Point(item.Lon,item.Lat).transform('EPSG:4326', 'EPSG:3857');
            if (!isNaN(point.x)&&!isNaN(point.y)) {
                var feature=new OpenLayers.Feature.Vector(point,item);
                features.push(feature);
            }
        }
        
        return features;
    },
    

    CLASS_NAME: "OpenLayers.Format.RSI" 

});

        var bounds={
            minLon:1000000000,
            minLat:1000000000,
            maxLon:-1000000000,
            maxLat:-1000000000
        };
    
        for (var i=0; i<layer.features.length; i++) {
            var feature=layer.features[i];
            var point=feature.geometry;
            if (!isNaN(point.x)&&!isNaN(point.y)) {
                bounds.minLon=Math.min(bounds.minLon,point.x);
                bounds.maxLon=Math.max(bounds.maxLon,point.x);
                bounds.minLat=Math.min(bounds.minLat,point.y);
                bounds.maxLat=Math.max(bounds.maxLat,point.y);
            }
        }
        map.updateSize();
        var extent=new OpenLayers.Bounds(bounds.minLon,bounds.minLat,bounds.maxLon,bounds.maxLat);
        map.zoomToExtent(extent,true);

        layer.styleMap=new OpenLayers.StyleMap({
                "default": defaultStyle,
                "select": selectStyle
            });

        layer.events.on({
            "featureselected": clickFeature
        });

        var map=layer.map;

        var hover = new OpenLayers.Control.SelectFeature(
            layer, {hover: true, highlightOnly: true}
        );
        map.addControl(hover);
        hover.events.on({"featurehighlighted": displayFeature});
           hover.events.on({"featureunhighlighted": hideFeature});
        hover.activate();

        var click = new OpenLayers.Control.SelectFeature(
            layer, {hover: false}
        );
        map.addControl(click);
        click.activate();

        var defaultStyle = new OpenLayers.Style({
            pointRadius: "${radius}",
            strokeWidth: "${width}",
            externalGraphic: "${icon}",
            strokeColor: "rgba(55, 55, 28, 0.5)",
            fillColor: "rgba(55, 55, 28, 0.2)"
        }, {
            context: {
                width: function(feature) {
                    return (feature.cluster) ? 2 : 1;
                },
                radius: function(feature) {
                    return feature.cluster&&feature.cluster.length>1
                        ? Math.min(feature.attributes.count, 7) + 2
                        : 7;
                }
            }
        });

        function fIcon(feature,type) {
                    var iconKey=type+'icon';
                    if (feature[iconKey]) return feature[iconKey];
                    if(feature.cluster&&feature.cluster.length>1) {
                        var canvas = document.createElement("canvas");
                        var radius=Math.min(feature.cluster.length, 7) + 2;
                        canvas.width = radius*2;
                        canvas.height = radius*2;
                        var ctx = canvas.getContext("2d");
                            ctx.fillStyle = this.defaultStyle.fillColor;
                        ctx.strokeStyle = this.defaultStyle.strokeColor;
                        //ctx.fillRect(0,0,canvas.width,canvas.height);
                        ctx.beginPath();
                        ctx.arc(radius,radius,radius,0,Math.PI*2);
                        ctx.fill();
                        ctx.stroke();
                            ctx.fillStyle = this.defaultStyle.strokeColor;
                        var bounds={
                            minX:1000000000,
                            minY:1000000000,
                            maxX:-1000000000,
                            maxY:-1000000000
                        };
                        for(var c = 0; c < feature.cluster.length; c++) {
                              var child=feature.cluster[c];
                            var x=feature.geometry.x-child.geometry.x;
                            var y=feature.geometry.y-child.geometry.y;
                                bounds.minX=Math.min(bounds.minX,x);
                                bounds.minY=Math.min(bounds.minY,y);
                                bounds.maxX=Math.max(bounds.maxX,x);
                                bounds.maxY=Math.max(bounds.maxY,y);
                        }
                        var q=0;
                        q=Math.max(Math.abs(bounds.maxX),q);
                        q=Math.max(Math.abs(bounds.maxY),q);
                        q=Math.max(Math.abs(bounds.minX),q);
                        q=Math.max(Math.abs(bounds.minY),q);
                        q=radius/q;
                        var zoom=2;
                        for(var c = 0; c < feature.cluster.length; c++) {
                              var child=feature.cluster[c];
                            var x=-(feature.geometry.x-child.geometry.x)*q+radius;
                            var y=(feature.geometry.y-child.geometry.y)*q+radius;
                                ctx.fillRect(parseInt(x-zoom/2), parseInt(y-zoom/2), zoom, zoom);
                        }
                        feature[iconKey] = canvas.toDataURL("image/png");
                    } else {
                        feature[iconKey] = OpenLayers.Marker.defaultIcon().url;
                    }
                    return feature[iconKey];
                };

        defaultStyle.context.icon=function(feature) {
            return fIcon.call(defaultStyle,feature,'default');
        }
        selectStyle.context.icon=function(feature) {
            return fIcon.call(selectStyle,feature,'select');
        }

var Result={
    CouldNotLoadUrl:1,
    UrlLoadedButContentCannotBeAccessed:2,
    UrlLoadedContentCanBeAccessed:3
};


function isAvailable(url, callback, timeout) {
    if (!+(timeout)||+(timeout)<0) {
        timeout=5000;
    }
    var timer=setTimeout(function() {
        ifr.remove();
        callback(Result.CouldNotLoadUrl,url);
    },timeout);
    var ifr=$('<iframe></iframe>')
        .hide()
        .appendTo('body');
    ifr.on('load',function() {
        if (timer) clearTimeout(timer);
        var result;
        try {
            var iframe=ifr[0];
            var doc=(iframe.contentWindow||iframe.contentDocument).location.href;
            result=Result.UrlLoadedContentCanBeAccessed;
        } catch(ex) {
            result=Result.UrlLoadedButContentCannotBeAccessed;
            alt=ex;
        }
        ifr.remove();
        callback(result,url,alt);
    });
    ifr.attr('src',url);
}

isAvailable('https://siderite.dev',function(result,url,alt) {
    switch(result) {
        case Result.CouldNotLoadUrl:
            alert('Could not load '+url+' in an iframe (timeout after '+alt+' milliseconds)');
            break;
        case Result.UrlLoadedButContentCannotBeAccessed:
            alert(url+' loaded in an iframe, but content is innaccessible ('+alt+')');
            break;
        case Result.UrlLoadedContentCanBeAccessed:
            alert(url+' loaded in an iframe and content is accessible');
            break;
    }
},10000);

<style>
div {
   width:100px;
   height:100px;
   background-color:blue !important;
}
</style>
<div style="background-color:red;"></div>

<style>
div {
   width:100px !important;
   height:100px;
   background-color:blue !important;
}
</style>
<div style="background-color:red;"></div>
<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.7.2/jquery.min.js"></script>
<script>
$(function() {
//  $('div').width(200); // the width remains 100!
//  $('div').width('200px'); // the width remains 100!
//  $('div')[0].style.width='200px'; // the width remains 100!

//  $('div').width('200px !important'); //this is not a valid value for the width parameter! in IE it will even show an error
//  $('div').css('width','200px !important'); //this is not a valid value for the width parameter! in IE it will even show an error
//  $('div')[0].style.width='200px !important'; //this is not a valid value for the width parameter! in IE it will even show an error

var oldStyle=$('div').attr('style')||'';
$('div').attr('style',oldStyle+';width: 200px !important'); // this is the only thing I found to be working!

});
</script>