Isn’t a big point of floating point that it can easily have mathematical operators done on them on CPUs? Sure, complex circuitry is no big deal these days, but IIRC, there were very good reasons for what was chosen.
Comment on Repeating of course
Quetzalcutlass@lemmy.world 1 day ago
I feel obligated to post a link to this excellent (albeit incomplete) writeup of posits and unums, which can more accurately represent fractions in memory at the same (or lower) bit size as traditional floating point.
Said page also includes the single best slightly-above-entry-level explanation of how floating point works I’ve ever seen.
LurkingLuddite@piefed.social 1 day ago
Quetzalcutlass@lemmy.world 1 day ago
One of the linked papers makes the claim that the circuitry would be less complex than that needed for floats, but also includes this note:
Floats have one advantage over posits for the hardware designer: the fixed location of bits for the exponent and the fraction mean they can be decoded in parallel. With posits, there is a little serialization in having to determine the regime bits before the other bits can be decoded. There is a simple workaround for this in a processor design, similar to a trick used to speed the exception handling of floats: Some extra register bits can be attached to each value to save the need for extracting size information when decoding instructions.
The proposed system also lacks NaN and separate positive/negative infinities, so it wouldn’t be a drop-in replacement.
terranoid@lemmy.cafe 1 day ago
i have so many schemas to represent the most common fractions perfectly without needing more than just ONE bit. They even work with positive and negative infinity!
Schema 1/2
1 bit, little endian
if one: value is exactly 1/2
If zero: value is NOT one half
Schema 1/3
if one: value is 1/3
Quetzalcutlass@lemmy.world 1 day ago
I’ve managed to create a compression algorithm that reduces files down to a single bit. I call it “is this file ‘loss.png’?”.
It’s guaranteed 100% lossless with any input!
Anafabula@discuss.tchncs.de 1 day ago
Reminds me of MetaGolfScript.