Back in November of 2016, researchers managed to calculate pi to 22.4 trillion digits. This was done using something called the , which looks a little something like this: Chudnovsky Algorithm Printing out all these digits at a reasonable font size would require a modest . 139 miles of stacked paper Of course, 22 trillion digits is about 22 trillion digits more than necessary for any application. , and 40 can calculate the circumference of the known universe with a precision of the width of a hydrogen atom. Not bad. NASA only uses around 15 What’s good enough for NASA is good enough for me, so I decided to have my program find pi to the 15th decimal place ( ). 3.141592653589793 The Chudnovsky Algorithm scares me with all of those factorials and exponents — I wanted something easier to program. I first turned to a nicer-looking (and much more inefficient) infinite series: the . Here’s what it looks like: Leibniz formula Doubles in Swift generally have a precision of 15 decimal places, which is perfect for my application. In a few minutes, I whipped up the following Swift program in Playgrounds: I left the program to run while I went to grab breakfast, thinking it wouldn’t take more than a few minutes. I came back to find my computer turning itself into a space heater while still working on the 6th decimal place. This was only around the 200,000th iteration of the while loop. I should’ve heeded the warning that this is one of the more inefficient ways of computing digits of pi. If someone reading this has access to a really powerful computer I’d love to see how far you can get before the whole system becomes sluggish. Next I turned to the slightly more efficient Nilakantha series: After spending a few minutes getting Xcode respond (it was still working its way through Leibniz formula), I was eventually able to develop this: Learning from my last trial, this time I expected to wait for hours. Much to my surprise the program finished at 31958 iterations before I was done checking my code for errors. Not bad! Clearly, Swift (and Swift Playgrounds) is not the best language to implement processor-intensive tasks. Lower-level languages such as C++ are better suited. However, I do find it interesting to see how implementations of these various formulas differ from system to system. A great resource for playing with the more efficient algorithms can be found . As you can see, the Chudnovsky algorithm can get 14 digits in one iteration, even if there’s way more math involved per run. here Give these Swift programs a try on your own system and tell me your results! To see more of my writing, follow me and . check out my page on Medium
