4 ms·

Type I and II unums are likely dead ends. Type III (posits) look promising. Facebook AI has developed their own type of "posit" with the terribly undescriptive

by kortex 6y ago

Type I and II unums are likely dead ends. Type III (posits) look promising. Facebook AI has developed their own type of "posit" with the terribly undescriptive name of "(8, 1, alpha, beta, gamma) log". Much less catchy than "posit" or "unum" but have been actually demonstrated to have numerical benefits. https://engineering.fb.com/ai-research/floating-point-math/ https://engineering.fb.com/ai-research/floating-point-math/

bsder 6y ago
The key quote from that paper is as follows: "Against 32-bit IEEE 754 single-precision FMA, ELMA will not be effective, though, as the Kulisch accumulator is massive (increasing adder/shifter sizes and flip-flop power), and the log-to-linear lookup table is prohibitive." So, these things may be effective if you can dial your precision down. Okay. We use domain-specific number representations all the time. Fixed-point binary for DSP. Decimal representations for currency. The Facebook takeaway is that transistors are now so cheap, that we can do <16 bit floating arithmetic with mostly ROM lookup tables if we make some restrictions. That is, however, NOT what Gustafson is proposing. He proposes these for general usage as a panacea to the complications of floating point. Numerics isn't some secret cabal. A new floating point system that allowed the folks doing partial differential equation solvers, computational fluid dynamics, or discrete time simulation to gain even 25% in time or to open up a new simulation field because of extra stability would get a serious look. And while William Kahan (who drove a lot of IEEE-754) generally comes off as an insufferable jerk, he knows his stuff, and he wasn't alone. The numerics folks at IBM and DEC (and others) were mostly converging to the same things with differences at the margins (signed zero, denorms, NaNs, etc.)--mostly because some of the things that IEEE-754 demanded were a huge pain to implement in hardware of the day. As for politics, IEEE-754 was basically a reaction to allowing DEC or IBM to create a de facto definition of the floating point standard.

by kortex 6y ago

bsder 6y ago

The key quote from that paper is as follows: "Against 32-bit IEEE 754 single-precision FMA, ELMA will not be effective, though, as the Kulisch accumulator is massive (increasing adder/shifter sizes and flip-flop power), and the log-to-linear lookup table is prohibitive." So, these things may be effective if you can dial your precision down. Okay. We use domain-specific number representations all the time. Fixed-point binary for DSP. Decimal representations for currency. The Facebook takeaway is that transistors are now so cheap, that we can do <16 bit floating arithmetic with mostly ROM lookup tables if we make some restrictions. That is, however, NOT what Gustafson is proposing. He proposes these for general usage as a panacea to the complications of floating point. Numerics isn't some secret cabal. A new floating point system that allowed the folks doing partial differential equation solvers, computational fluid dynamics, or discrete time simulation to gain even 25% in time or to open up a new simulation field because of extra stability would get a serious look. And while William Kahan (who drove a lot of IEEE-754) generally comes off as an insufferable jerk, he knows his stuff, and he wasn't alone. The numerics folks at IBM and DEC (and others) were mostly converging to the same things with differences at the margins (signed zero, denorms, NaNs, etc.)--mostly because some of the things that IEEE-754 demanded were a huge pain to implement in hardware of the day. As for politics, IEEE-754 was basically a reaction to allowing DEC or IBM to create a de facto definition of the floating point standard.