#probit

China banning Bitcoin for the Nth time =))

Coding is a balancing act. When it comes to quantiles for non uniform RNG the balance is between accuracy and execution speed. My focus has been on achieving a standard normal distribution RNG.

Because of the goal of the project, I'm doing in a this in a C++ environment where I can not use C++11 or the boost libraries. As a result I must implement a solution myself. At first I used the Box Muller transform, but its an unwieldy beast. It employs both square root and log functions and requires dual random values (which isn't so bad as it produces two values as well). Its output is not ideal as it doesn't handle symmetry well and produces data ranges with peculiar holes. All in all it's not great.

There's another popular algorithm for large sets which is the Ziggurat algorithm. It's good, but I have reasons for not using it that largely boil down to the fact that one of my goals is to create an easy-to-use library; Ziggurat is not easy to use.

At this point in my reading I encountered probit; a quantile function for the normal distribution that works well with semi-random numbers. The equation for it is pretty straight forward, except.

Except that it relies on an inverse error function. Can that be implemented? Sure. But this is where I get in my own way; erfinv is ugly. Every implementation I've seen uses tables and long equations mediated by multiple conditionals. It's not inefficient, it's not unreasonably imprecise, it's just ugly. I don't like writing ugly code in my personal projects.

But probit has an interesting counterpart; logit is the equivalent quantile for the logistic distribution. Overlay logistic and normal curves and you can see a lot of similarities. This, I felt, could suffice if needs must. Best of all, it's a graceful little function. It does use a log, but only one. It's gorgeous!

But it's not right, really. Trying to pass off logit as though it gave you a normal distribution. I needed a solution. It needn't be perfect, just good enough for the target use (which is in games). So I resolved to modify logit, to introduce what I think might be called a coefficient.

I started with a plot of probit, logit, and the different between them. Then I stated tinkering, trying to match another curve - with a simple equation - to that product. What I've achieved so far isn't perfect, but it's probably close enough for my purpose and I think that it could be tweaked further, with minimal added complexity.

It does introduce a trigonometric function to the mix, but it feels graceful. Best of all it produces output that, in my opinion, is superior to the Box Muller algorithm. It's more naturally balanced and doesn't seem to have the troubling gaps.

I'll probably find time to compare the computational efficiency and might yet try for a better fit to the target curve, but for now I'm happy.

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HUMAN Protocol Foundation Announce HMT Now Listed on Probit

PRESS RELEASE. The HUMAN Protocol Foundation is delighted to announce that HMT is now listed on Probit. Probit joins other exchanges, Bitfinex, FTX and Gate.io in offering our community the opportunity to buy, sell, and trade HMT. About HMT HMT is the native cryptocurrency of HUMAN Protocol. In practice, Requesters – who want to launch a job – must first purchase HMT, with which they pre-fund a…