3 ms·

posits can be also projected to m*2^e, just with larger m and e.

whatshisface 5y ago
Converting to floats, computing and converting back would hardly result in a smaller FPU, unless I am missing something about it. Edit: a dead comment replies with, > I'm the implementor for posits (deactivated my primary hn account) -- I built circuit diagrams for computation with posits. So, we have them -- and they are smaller. There is also a key insight into the representation of posits (negative numbers have a "hidden -2" instead of a "hidden 1") that I cracked early on in my fiddling with circuits that was completely missed by all other implementers until earlier this year, even after I communicated it to them through email correspondence several times.
- throwaway_posit 5y ago
  I'm the implementor for posits (deactivated my primary hn account) -- I built circuit diagrams for computation with posits. So, we have them -- and they are smaller. There is also a key insight into the representation of posits (negative numbers have a "hidden -2" instead of a "hidden 1") that I cracked early on in my fiddling with circuits that was completely missed by all other implementers until earlier this year, even after I communicated it to them through email correspondence several times.
  - FullyFunctional 5y ago
    I don't know how you can claim to be "the" implementor as there are many implementations. However, your explanation doesn't have enough context. Do you have a paper describing this in better detail?
    - throwaway_posit 5y ago
      Sorry, should have specified: I'm the original implementor. I'm on the paper with John Gustafson, and presenter/live-demoer of the second half the Stanford video. There is a paper coming out with details on the yonemoto -2 hidden bit method... I don't know if it's still preprint or embargoed or what but it is recent. I'm really not involved in the project anymore so my knowledge of the existence of this paper is only due to the courtesy of the authors.
      - FullyFunctional 5y ago
        Is the source code available? It would be amazing to the best possible implementation available as Verilog. There are quite a few pretty good IEEE 754 implementations.
  - adrian_b 5y ago
    I can believe that for not too large number sizes a posit implementation might be smaller than for the traditional FP format. However "smaller" must be qualified, because the size of a FPU varies enormously depending on the speed target. A completely different size results when the target is to do a fused multiply-add in 4 cycles at 5 GHz than when the target is to do it in 100 cycles at 200 MHz. So unless you give more information about what you have compared, we cannot know whether it is true that a posit implementation can be smaller.
  - a1369209993 5y ago
    > negative numbers have a "hidden -2" instead of a "hidden 1" Isn't this just (what I assumed was) the standard implementation technique for FPUs that aren't[0] stuck with IBM/Intel's braindead sign-magnitude junk? 0: so (eg, for a 1.7.8 float) -1.996..-1.000 would be 3F00-3FFF, and +1.000..+1.996 would be C000-C0FF, making 0x[-2].00-0x[-2].FF and 0x[+1].00-0x[+1].FF (with implicit -2/+1 corresponding to 3F/C0)
- adgjlsfhk1 5y ago
  I don't mean converting to floats, I mean treating the exponent and mantissa separately. Processors already do something similar for floats. For addition, (for example), you de-normalize the smaller input by an amount to make the exponents line up, add and re-normalize. The steps would be pretty much exactly the same for posits, the only difference is how you calculate the difference in exponents (which just boils down to a few shifts based on the useed value).

Converting to floats, computing and converting back would hardly result in a smaller FPU, unless I am missing something about it. Edit: a dead comment replies with, > I'm the implementor for posits (deactivated my primary hn account) -- I built circuit diagrams for computation with posits. So, we have them -- and they are smaller. There is also a key insight into the representation of posits (negative numbers have a "hidden -2" instead of a "hidden 1") that I cracked early on in my fiddling with circuits that was completely missed by all other implementers until earlier this year, even after I communicated it to them through email correspondence several times.

throwaway_posit 5y ago
I'm the implementor for posits (deactivated my primary hn account) -- I built circuit diagrams for computation with posits. So, we have them -- and they are smaller. There is also a key insight into the representation of posits (negative numbers have a "hidden -2" instead of a "hidden 1") that I cracked early on in my fiddling with circuits that was completely missed by all other implementers until earlier this year, even after I communicated it to them through email correspondence several times.
- FullyFunctional 5y ago
  I don't know how you can claim to be "the" implementor as there are many implementations. However, your explanation doesn't have enough context. Do you have a paper describing this in better detail?
  - throwaway_posit 5y ago
    Sorry, should have specified: I'm the original implementor. I'm on the paper with John Gustafson, and presenter/live-demoer of the second half the Stanford video. There is a paper coming out with details on the yonemoto -2 hidden bit method... I don't know if it's still preprint or embargoed or what but it is recent. I'm really not involved in the project anymore so my knowledge of the existence of this paper is only due to the courtesy of the authors.
    - FullyFunctional 5y ago
      Is the source code available? It would be amazing to the best possible implementation available as Verilog. There are quite a few pretty good IEEE 754 implementations.
- adrian_b 5y ago
  I can believe that for not too large number sizes a posit implementation might be smaller than for the traditional FP format. However "smaller" must be qualified, because the size of a FPU varies enormously depending on the speed target. A completely different size results when the target is to do a fused multiply-add in 4 cycles at 5 GHz than when the target is to do it in 100 cycles at 200 MHz. So unless you give more information about what you have compared, we cannot know whether it is true that a posit implementation can be smaller.
- a1369209993 5y ago
  > negative numbers have a "hidden -2" instead of a "hidden 1" Isn't this just (what I assumed was) the standard implementation technique for FPUs that aren't[0] stuck with IBM/Intel's braindead sign-magnitude junk? 0: so (eg, for a 1.7.8 float) -1.996..-1.000 would be 3F00-3FFF, and +1.000..+1.996 would be C000-C0FF, making 0x[-2].00-0x[-2].FF and 0x[+1].00-0x[+1].FF (with implicit -2/+1 corresponding to 3F/C0)
adgjlsfhk1 5y ago
I don't mean converting to floats, I mean treating the exponent and mantissa separately. Processors already do something similar for floats. For addition, (for example), you de-normalize the smaller input by an amount to make the exponents line up, add and re-normalize. The steps would be pretty much exactly the same for posits, the only difference is how you calculate the difference in exponents (which just boils down to a few shifts based on the useed value).