The following program calculates the value of the series of the Basel Problem. The result is a number that starts with 1.644934. Like π, this sequence can go on forever, which means the program never exits. Without proper design, such a program runs into the maximum call stack size exceeded error, which is designed to prevent a program from using too much memory.
var cr = 1;
var total = 0;
var x = function() {
total = total + (1/(cr*cr));
if(! (cr % 20000)) {
$('#t1').val(total);
$('#t2').val(cr);
setTimeout(x,0);
}
else {
x();
}
cr++;
};
x(); //initial call to x().
The solution is to add a setTimeout call somewhere in the program before things get too close to exceeding the call stack. In the above program, cr is a counter variable that starts with 1 and increases by 1 for every iteration of the x function. Using the conditional if(! (cr % 20000)) allows the program to catch its breath every 20,000 iterations and empties the call stack. It checks whether cr is divisible by 20,000 without a remainder. If it is not, we do nothing and let the program run its course. But if is divisible without a remainer, it means we have reached the end of a 20,000 iteration run. When this happens, we output the value of the total and the cr variables to two textboxes, t1 and t2.
Next, instead of calling x() the normal way, we call it via setTimeout(x,0);. As you know, setTimeout is genearlly used to run a function after a certain amount of time has passed, which is why usually the second argument is non-zero. But in this case, we do not need any wait time. The fact that we are calling x() via setTimeout is what matters, as this breaks the flow of the program, allowing proper screen output of the variables and the infinite continuation of the program.
The program is extremely fast, doing 1 million iterations about every 2.4 seconds on my computer. The result (the value of total) is not perfectly accurate due to the limitations of JavaScript numbers. More accuracy can be had using an extended numbers library.
You may wonder why we cannot put all calls to x() inside a setTimeout(). The reason is that doing so prevents the JavaScript interpreter from optimizing the program, causing it to run extremely slowly (about 1000 iterations per second on my computer). Using the method above, we run the program in optimized blocks of 20,000 iterations (the first block is actually 19,999 iterations since cr starts from 1, but for simplicity I have said 20,000 throughout the article).