Stanford Seminar: Beyond Floating Point: Next Generation Computer Arithmetic

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Recommends espeed · 2017-02 · on “Why does e to pi i equal -1? (2015) [video]”

Have you seen "Stanford Seminar: Beyond Floating Point: Next Generation Computer Arithmetic"? [this video]

Recommends trsohmers · 2017-02 · on “The “high-level CPU” challenge (2008)”

Well unums in particular (especially the new type 3 "posits" ones) are very interesting and practical for hardware implementation. John Gustafson, the creator of unums, gave the first talk on type 3 unums at Stanford earlier this month, and there are already multiple hardware implementation efforts (one of which I am indirectly overseeing). While many people have recently hyped up low precision floating point for things like machine learning, Posits provide greater dynamic range AND greater accuracy for very few bits (as low as four, but with good ML starting 8 to 10 bits). On top of all of that, it costs less area and power in silicon than IEEE hardware. Check out the talk: [this video]

Recommends vanderZwan · 2017-02 · on “GCC optimized code gives strange floating point results”

I'm very surprised nobody has brought up John Gustafson's Unum work. His latest iteration is the posit, which he presented at Stanford earlier this month[0][1] EDIT: apologies to CalChris[2]. What I should have said is discussed Gustafson's Unum work. [0] [this video] (relevant question at 1h22m37s) [1] [LINK] [2] [LINK]

Recommends dnautics · 2017-09 · on “Floating Point Visually Explained”

You may like: [this video] It turns out the math is slightly harder but it's faster than IEEE FP in hardware, probably because of less conditionals in the spec. There is better performance in terms of numerical accuracy at the cost of substantially more difficult error analysis. Disclaimer: I'm in the video.

Recommends gbrown_ · 2018-06 · on “Floating-Point Determinism (2013)”

For anyone interested in this sort of thing you'd probably also be interested in John Gustafson's work on unums/posits. Here's a nice introductory presentation [this video]

Cites espeed · 2017-02 · on “Intel Gets Serious About Neuromorphic, Cognitive Computing Future”

Are these the Neuromorphic chips [1] Jeff Hawkins of Numenta [2] has been talking about? [1] Neuromorphic Chips [LINK] [2] Numenta papers/videos [LINK] It would also be good to see a major chip manufacturer or cloud provider that makes its own chips (Google/IBM) get serious about graph processing chips [3,4] and moving beyond floating point [5]. [3] Novel Graph Processor Architecture [LINK] [4] Novel Graph Processor Architecture, Prototype System, and Results [LINK] [5] Stanford Seminar: Beyond Floating Point: Next Generation Computer Arithmetic [this video]

Cites vanderZwan · 2017-02 · on “The Fundamental Theorem of Algebra: A Visual Approach (2015) [pdf]”

> Points near the origin have dark colors, with the color assigned to a complex number z approaching black as z approaches 0. Points far from the origin are light, with the color of z approaching white as |z| approaches infinity. Every complex number has a different color in this picture, so a complex number can be uniquely specified by giving its color. So I was wondering if this approach could also be useful in the context of floats and integers. The implementation becomes simpler in many ways (we only have a finite number of possible values to consider). For example, start with a unique mapping of 8-bit integers to a continuous colour ramp. I suppose the easiest option would be to start i

Cites dnautics · 2017-03 · on “How many floating-point numbers are in the interval [0,1]?”

so I'm the author of one of the first usable unum implementations. We're actually moving to something called sigmoid numbers which are even better. The lecture doesn't cover "valid mode" but that's more like the "unum". At the end of the video, there's a demonstration where I show some very interesting results concerning machine learning. [this video] You can try out sigmoid numbers in julia here: [LINK] Also, I am working on some verilog implementations, so we may have this in hardware rather soon. A few things about sigmoid numbers: 1) they have fixed sizes, so you don't have to worry about keeping track of things (which was a pain). 2) they have a property I call "isomorphic structure" - which