I spent most of my vacation (that was mostly in December) working on the not-new PotM: Nabel (a full numeric tower for Janet). Unfortunately, with the end of my vacation, the amount of time and effort I can dedicate to it has dropped dramatically. The good news is that it’s actually mostly done. The current status is summarized as follows:
- Big Integers: Work. Tests being written. Final cleanup prior to publishing being done.
- Big Rationals: Mostly work. No tests yet. Standard library lacking (e.g. no sqrt yet). Many parts need to be ported back to Janet from C (due to new wrapping method). Some rewriting still to do (same style as the final cleanup for Big Integers). I want to finish these (except for the mostly bare stdlib) before publishing.
- Series (all Reals)1: Not written, I’d like to have at least a couple examples before I publish.
- Compex Numbers: Not written.
My original hope was to be able to publish by the end of February. I still hope to be able to do that, but I’m not so certain.
Originally, in relation to the above work, I was planning for this month’s blog to be something along the lines of “how do IEEE floats really work?” I do feel like such a post has a good reason to exist: most online explanations I’ve seen have been pretty flawed. I want to show off the true bitwise representations, talk about how to manipulate them manually, and so on. Sorry you’re reading this and not that!
Anyway, I’m currently and essentially doing two full-time jobs (technically it’s the same one, but I’m currently exercising two separate positions), both of which are in the middle of crunch-time. You’ll see if I’m doing any better by the end of next month, on the basis of whether I post another “Status Update” or an actual article (as well as which article makes it, either the announcement for Nabel’s release, or the floats one).
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This works because of the Riemann Rearrangement Theorem. This would merit a whole post of its own, but I’m writing this on the 29th and I’m out of time! Anyway, the short version is that any real number can be represented as the limit of the terms of a conditionally convergent series, which means that any real number can be represented by a series. It’s a bit of a leap to say that being able to “cut it off” at some given point will give a good enough approximation is a bit of a leap, but that is a sacrifice I am willing to make. ↩︎