Python vs Javascript floating point arithmetic giving very different answers. What am I doing wrong?

Question

Python version | Javascript version | Whitepaper

So, I'm working on a website to calculate Glicko ratings for two player games. It involves a lot of floating point arithmetic (square roots, exponents, division, all the nasty stuff) and I for some reason am getting a completely different answer from the Python implementation of the algorithm I translated line-for-line. The Python version is giving basically the expected answer for the example found in the original whitepaper describing the algorithm, but the Javascript version is quite a bit off.

Have I made an error in translation or is Javascript's floating point math just less accurate?

Expected answer: [1464, 151.4]
Python answer: [1462, 155.5]
Javascript answer: [1470.8, 89.7]

So the rating calculation isn't THAT bad, being 99.6% accurate, but the variance is off by 2/3!

Edit: People have pointed out that the default value of RD in the Pyglicko version is 200. This is a case of the original implementer leaving in test code I believe, as the test case is done on a person with an RD of 200, but clearly default is supposed to be 350. I did, however, specify 200 in my test case in Javascript, so that is not the issue here.

Edit: Changed the algorithm to use map/reduce. Rating is less accurate, variance is more accurate, both for no discernible reason. Wallbanging commence.

Answer 1

typically you get errors like this where you are subtracting two similar numbers - then the normally insignificant differences between values become amplified. for example, if you have two values that are 1.2345 and 1.2346 in python, but 1.2344 and 1.2347 in javascript, then the differences are 1e-4 and 3 e-4 respectively (ie one is 3x the other).

so i would look at where you have subtractions in your code and check those values. you may find that you can either (1) rewrite the maths to avoid the subtraction (often it turns out that you can find an expression that calculates the difference in some other way) or (2) focus on why the values at that particular point differ between the two languages (perhaps the difference in pi that the other answer identified is being amplified in this way).

it's also possible, although less likely here, that you have a difference because something is treated as an integer in python, but as a float in javascript. in python there is a difference between integers and floats, and if you are not careful you can do things like divide two integers to get another integer (eg 3/2 = 1 in python). while in javascript, all numbers are "really" floats, so this does not occur.

finally, it's possible there are small differences in how the calculations are performed. but these are "normal" - to get such drastic differences you need something like what i described above to occur as well.

PS: also note what Daniel Baulig said about the initial value of the parameter rd in the comments above.

Answer 2

My guess is that involves the approximations you're using for some of the constants in the JavaScript version. Your pi2 in particular seems a little.. brief. I believe Python is using doubles for those values.