Re:Why does e to pi i equal -1? (2015) [video]
by dnautics on Tuesday February 14, 2017 @05:10AM
(#13642483)
I don't think it can be made that efficient in software. Is there a particular reason why you need 16 bits? A 32-bit float is going to be better than a 16-bit posit almost always (posits are better their equivalently sized float, but they're not that good) and once it's in posit representation do you have a way of doing mathematical operations on them?
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Re:Why does e to pi i equal -1? (2015) [video]
by jacobolus on Tuesday February 14, 2017 @06:03AM
(#13642666)
This is just for data compression, not for computation directly. 32 bits is often overkill for transmission/storage of rotations, unit vectors, geographical locations, unit quaternions, and the like. Depending on the use case 8 bits might be enough, or 12, or 16.
To actually do computation I would convert the posits back into 32-bit floats (or e.g. in the Javascript case, 64-bit floats), and then take the inverse stereographic projection.
[Stereographic projection is extremely cheap; for each data point only requires one division and some additions and multiplications.]
I’ll do some experimenting at some point.