Re:Posits, a New Kind of Number, Improves the Math of AI
by themerone on Wednesday September 28, 2022 @09:30AM
(#33007669)
Floating point bitmaps are a lot more common than you think. A lot of consumers don't see them, but their software will internally use floats. Floating point bitmaps are standard practice in visual effects and animation. The OpenEXR format exists for the exchange of images with floating point bit depths up to 32.
Re:Posits, a New Kind of Number, Improves the Math of AI
by bXVsbGVy on Wednesday September 28, 2022 @12:11PM
(#33009650)
Posit always have more precision than a IEEE floating with same number of bits because it has more bits for the mantissa.
Posit would likely enable to better compression with Huffman encoding.
Re:Posits, a New Kind of Number, Improves the Math of AI
by CSSer on Wednesday September 28, 2022 @08:55AM
(#33007316)
If point 1 is true then why is 0.1 + 0.2 = 30000000000000004? Is that not close enough to zero?
Edit: It seems I’m conflating “precision” with “accuracy”, which is a separate concept in math.
Re:Posits, a New Kind of Number, Improves the Math of AI
by jcranmer on Wednesday September 28, 2022 @09:05AM
(#33007415)
That result happens for the same reason that 1 / 3 * 3 != 1, if you use decimal: 1 / 3 = .333, .333 * 3 = .999, which is different from 1.00.
0.1 is the same as 1 / 10, which does not have a finite representation in binary notation, just as 1 / 3 does not have a finite representation in binary or decimal notation.
Re:Posits, a New Kind of Number, Improves the Math of AI
by throwawaymaths on Wednesday September 28, 2022 @09:01AM
(#33007383)
This is a problem for all number systems. The true issue here is not a precision in the underlying bit representation of IEEE-754, it's that 0.1 and 0.2 aren't actually a valid IEEE-754 numbers, and so they get casted to their best approximations.
2. Bitmap images are not using floating-point values, except in some super niche use cases like GIS data, so “posits” are irrelevant for the use case you’ve posited. (ba-dum-ts)
3. Non-linear gamma is completely unnecessary for bit depths >= 16.