mastodon 4.7.3Programmer at Pacific Light & Hologram
New paper on branchless extended precision floating point algorithms. Using the idea of Floating Point Accumulation Networks (FPANs), it defines addition, subtraction, multiplication and division as dataflow diagrams consisting of inputs and TwoSum(), TwoProd() and Addition operations. The goal was to define extended range ops that work on all FP ALUs including GPUs.
https://theory.stanford.edu/~aiken/publications/papers/sc25.pdf
Gifted myself with both editions of Jim Blinn's Corner for $35 delivered from thriftbooks.com
Published in 1996, still wildly relevant today except maybe the "How to attend Siggraph" section. To do that one it really helps to be Jim Blinn.
From @jsiehler@mathstodon.xyz, cartesian grids of points where no three points lie on any gridline. The diagram below was all known solution as of 1997, today there are solutions up to 68 points and many multiples with rotation and reflection rules.
Finally I understand the difference between [Dekker71] FAST-TWO-SUM(a,b) and [Knuth81] TWO-SUM(a,b)
FAST-TWO-SUM requires a>b and both return:
x = a + b + err(a⊕b)
y = -err(a⊕b)
So yes, x+y = a+b but not quite how you might imagine.
Well that only took 30 years to grok.
Mandelbulbs render better when the ray marcher is computed on FPGA using CORDIC.
https://heichips.github.io/presentations-pdf/presentation-15.pdf
Finally, finally sourced the mid-top drivers for my pair of Solana point-source speakers. They've been unavailable for months so now we can go about building a box with a top-hat and 4-channel Speakon.
GossipGoblin has been using AI to build visuals for his cyberpunk stories for a while. Now he's attempted a short film instead of reels. Unapologetic slop for slop's sake.
Gustafson is BACK with a shot across the IEEE754 bows! If you only use a subset of Posit2022 standard it can be 74% better than other Posit implementations!
Also one very specific part of the implementation "...matches or exceeds IEEE compliant 32-bit floating-point performance, offering faster and smaller area implementation, with slight increase in worst-case power due to higher speed."
We're worse only because we're faster!
https://arxiv.org/abs/2603.01615
Takum32 still better in most cases.
