@Fabian Giesen
Abstraction maker, abstraction breaker. FUN FACT: things I prefix with FUN FACT are sometimes fun and sometimes factual, but very rarely both.
Relays (1)
- wss://relay.ditto.pub – read & write
Recent Notes
"ugly as sin" please, it's not ugly, just odd. But sure, if traditional, even symmetry is more your thing, there's always cos.
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@nprofile1q... @nprofile1q... I thought you ran in those circles. Oh well, guess I inadvertently put you into a box there. I'll make a point to avoid that in the future.
Healers deal in health. Stealers deal in stealth.
There's this observation that the volume of unit-radius hyperspheres gets tiny as dimension increases, and also the famous example where you place unit spheres at the vertices (+-1, +-1, ..., +1) of a d-dimensional hypercube, put a sphere at the origin and see how big you can make it until it touches the corner spheres. (Spoiler: as d increases, very big indeed.)
Sometimes this is framed as "d-dim hyperspheres are just weird". They're not.
Hypercubes are the weird ones.
Sometimes this is framed as "d-dim hyperspheres are just weird". They're not.
Hypercubes are the weird ones.
Pivco-Huffman https://marcinzukowski.github.io/pivco-huffman/paper-1.0/ph.html IMO, very interesting.
(Marcin contacted me asking to get a version of Oodle's Huffman and TANS coders for testing and we had a long email exchange over the last several weeks.)
(Marcin contacted me asking to get a version of Oodle's Huffman and TANS coders for testing and we had a long email exchange over the last several weeks.)
nostr:nprofile1qy2hwumn8ghj7un9d3shjtnyd968gmewwp6kyqpq6qmlxsjk0mwtch4sq6wkstgnsmat86dxzw2l4lp7t073z0sfpfes6nlwq4 Now I want to play MHRD again. https://store.steampowered.com/app/576030/MHRD/
@nprofile1q... @nprofile1q... don't love MHRD. Turing Complete is a much better version of that, although I have my gripes with TC as well. :)
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Although the original thing never got published, a different paper analyzing the algorithm (and confirming it gives correctly rounded results) was, in 1992: https://bpb-us-e1.wpmucdn.com/websites.uta....
Anyway, if the idea of a floating-point computation ultimately unwrapping the float bits and doing a bunch of integer shifts and adds on them blows your mind, buckle up! You're not gonna believe how your FPU does FP additions, subtractions, multiplications and divisions either!
(and, yes, square roots)
This is not meant in a condescending way. I heartily recommend everyone with an interest in the topic check out how FP works under the hood. There's too much "a wizard did it!!!" going around
(and, yes, square roots)
This is not meant in a condescending way. I heartily recommend everyone with an interest in the topic check out how FP works under the hood. There's too much "a wizard did it!!!" going around
That paper was concerned with doubles and getting the initial approximation to slightly under 8 bits was sufficient to get a correctly rounded double sqrt within 3 iterations.
Tweaking the magic valu...
Although the original thing never got published, a different paper analyzing the algorithm (and confirming it gives correctly rounded results) was, in 1992: https://bpb-us-e1.wpmucdn.com/websites.uta.edu/dist/7/5059/files/2021/06/csd-94-850.pdf
it also gives more of an explanation why it works, the original Kahan/Ng paper just assumes you're familiar with how IEEE floats are constructed and expects you to keep up. :)
it also gives more of an explanation why it works, the original Kahan/Ng paper just assumes you're familiar with how IEEE floats are constructed and expects you to keep up. :)
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That paper was never formally published (that I can track down anyhow) but note it has both regular and reciprocal square root versions (the latter on the way to computing a square root) as well as in...
That paper was concerned with doubles and getting the initial approximation to slightly under 8 bits was sufficient to get a correctly rounded double sqrt within 3 iterations.
Tweaking the magic value to get rid of the initial LUT altogether is reasonable for float32, for the correctly rounded float64 sqrt-from-rsqrt they cared about it would've needed an extra iter which they tried to avoid.
Tweaking the magic value to get rid of the initial LUT altogether is reasonable for float32, for the correctly rounded float64 sqrt-from-rsqrt they cared about it would've needed an extra iter which they tried to avoid.
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OK everyone on here and following me probably already knows this but I want to get it off my chest anyway:
*please* stop attributing reciprocal-square-root-by-IEEE-bit-twiddling to John Carmack/Quake...
That paper was never formally published (that I can track down anyhow) but note it has both regular and reciprocal square root versions (the latter on the way to computing a square root) as well as instructions for getting correctly rounded (=equivalent to doing the calculation exactly then rounding in active rounding mode) results.
That paper was 1986.
The only thing that ever changes is the exact choice of magic number constant; the paper didn't sweat it because it used a 64-entry LUT.
That paper was 1986.
The only thing that ever changes is the exact choice of magic number constant; the paper didn't sweat it because it used a 64-entry LUT.
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OK everyone on here and following me probably already knows this but I want to get it off my chest anyway:
*please* stop attributing reciprocal-square-root-by-IEEE-bit-twiddling to John Carmack/Quake 3.
John has a lot of "firsts" under his belt but this is not one of them.
This trick is _old_. The magic constant changes, but the trick itself is _old_.
1993 versions of Sun's fdlibm already included this reproduction of W. Kahan and K. C. Ng's paper on the subject: https://github.com/freemint/fdlibm/blob/master/e_sqrt.c#L215
*please* stop attributing reciprocal-square-root-by-IEEE-bit-twiddling to John Carmack/Quake 3.
John has a lot of "firsts" under his belt but this is not one of them.
This trick is _old_. The magic constant changes, but the trick itself is _old_.
1993 versions of Sun's fdlibm already included this reproduction of W. Kahan and K. C. Ng's paper on the subject: https://github.com/freemint/fdlibm/blob/master/e_sqrt.c#L215
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