The following is an implementation of a binary search for arrays which gives you the ability to do fuzzy matches (default), exact matches, or specify your own comparison function:

(function() {
// Use this if the search isn't called with a 2nd param or it
// is false.
function fnFuzzy(a, b) {
return a < b ? -1 : a > b ? 1 : a == b ? 0 : null;
}
// Use this if the search is called with a 2nd param of true.
function fnExact(a, b) {
return a < b ? -1 : a > b ? 1 : a === b ? 0 : null;
}
// Recursively does a binary search.
function binarySearch(arr, item, min, max, fnCmp) {
if(min > max) {
return -1;
}
var mid = parseInt((min + max) / 2);
var ret = fnCmp(item, arr[mid]);
if(ret) {
return binarySearch(arr, item,
ret > 0 ? mid + 1 : min,
ret < 0 ? mid - 1 : max, fnCmp);
}
else if(ret == 0) {
return mid;
}
}
// Define the prototypal function.
Array.prototype.binarySearch = function(item, extactMatch) {
return binarySearch(this, item, 0, this.length - 1,
extactMatch
? typeof extactMatch == "function"
? extactMatch
: fnExact
: fnFuzzy);
};
})();

I used the following to test the normal execution of this binary function:

// Create a pre-sorted array of distinct random numbers ranging
// from 0 to 9999 and keep a reverse index to validate what is
// being returned by the binarySearch() function:
var arr = [], reverseIndex = {"-1" : -1};
for(var limit = 10000, i = 0; i < limit; i++) {
if(Math.random() < 0.5) {
reverseIndex[i] = arr.length;
arr.push(i);
}
else {
reverseIndex[i] = -1;
}
}
reverseIndex[limit] = -1;
// Run through all numbers from -1 to 10000, using the reverse
// index making sure that the binarySearch() function works
// properly:
for(var v1, v2, i = -1; i <= limit; i++) {
// If the binary search doesn't return the correct thing,
// let the user know.
if((v1 = arr.binarySearch(i)) != (v2 = reverseIndex[i])) {
alert("The search for " + i + " returned an index of "
+ v1 + " when it should have returned " + v2
+ ".");
break;
}
}
// If all of the tests were successfully run, tell the user.
if(i == limit + 1) {
alert("All " + arr.length
+ " numbers that should have been found were found.");
}