3 ms·

> They likely compared the binnary64 with posit16 using the accumulator (aka quire). As far as I can tell, Klöwer didn't. He mentions around the 13 minute mark

> They likely compared the binnary64 with posit16 using the accumulator (aka quire). As far as I can tell, Klöwer didn't. He mentions around the 13 minute mark (slide 9) that he used the SigmoidNumbers software package for Julia. From the looks of the examples he gives, if he used the quire, it must have happened implicitly. Which IIRC is not how using the quire works. He did rescale all his inputs to minimize rounding errors that way, and he mentions that this has benefits for posits that floats don't have (because of the tapered precision of posits).

piadodjanho 7y ago
Hmm. Their results seems to good to be true without using quire. Look: The two largest/smallest exponent posit16 can represent are: min exp: 2^{ (+14<<es) or 0x01 } * (1+0) = 2^(-28) max exp: 2^{ (-14<<es) or 0x00 } * (1+0) = 2^(+29) Note those numbers only have the implicit bit as significant. They don't have any space left to encode any other information other than the sign and regime. While the double (binary64) can represent a much larger range of exponent: min exp: 2^{ (-1023-2047-1) } * (1+0) = 2^(-1022) max exp: 2^{ (-1023+2047-1) } * (1+0) = 2^(1023) Also, all doubles have 52 bits of precision while the posit have at most 16-1-2-1=12 maximum bits of precision. Their significant are encoded slightly differently though. I'm not sure if this would be enough to achieve such different result without quire. The scaling he mention could be done very easily introducing a parameter bias on FPGA implementation. I might add that to my work. I pinged Klöwer on twitter.
- vanderZwan 7y ago
  You clearly know more about this topic than me, thanks for taking the time to explain your viewpoints. > I pinged Klöwer on twitter. Probably the most sensible, easiest way to clear this up, haha :)
- vanderZwan 7y ago
  Tweet exchange + link, for anyone else stumbling upon this later: > @milankloewer Would mind joining this thread on HN: https://news.ycombinator.com/item?id=20392612 https://news.ycombinator.com/item?id=20392612 We are discussing the results of your work with posit. > Happy to join. In short: I did not use any quires so far. All simulations are entirely based on 16bit posits, but I compare them to Float16 and not Float64. Tricks are: Scaling and rewriting algorithms to avoid very large and very small numbers, that's it. https://twitter.com/milankloewer/status/1148670158883475461 https://twitter.com/milankloewer/status/1148670158883475461

piadodjanho 7y ago

Hmm. Their results seems to good to be true without using quire. Look: The two largest/smallest exponent posit16 can represent are: min exp: 2^{ (+14<<es) or 0x01 } * (1+0) = 2^(-28) max exp: 2^{ (-14<<es) or 0x00 } * (1+0) = 2^(+29) Note those numbers only have the implicit bit as significant. They don't have any space left to encode any other information other than the sign and regime. While the double (binary64) can represent a much larger range of exponent: min exp: 2^{ (-1023-2047-1) } * (1+0) = 2^(-1022) max exp: 2^{ (-1023+2047-1) } * (1+0) = 2^(1023) Also, all doubles have 52 bits of precision while the posit have at most 16-1-2-1=12 maximum bits of precision. Their significant are encoded slightly differently though. I'm not sure if this would be enough to achieve such different result without quire. The scaling he mention could be done very easily introducing a parameter bias on FPGA implementation. I might add that to my work. I pinged Klöwer on twitter.

vanderZwan 7y ago
You clearly know more about this topic than me, thanks for taking the time to explain your viewpoints. > I pinged Klöwer on twitter. Probably the most sensible, easiest way to clear this up, haha :)
vanderZwan 7y ago
Tweet exchange + link, for anyone else stumbling upon this later: > @milankloewer Would mind joining this thread on HN: https://news.ycombinator.com/item?id=20392612 https://news.ycombinator.com/item?id=20392612 We are discussing the results of your work with posit. > Happy to join. In short: I did not use any quires so far. All simulations are entirely based on 16bit posits, but I compare them to Float16 and not Float64. Tricks are: Scaling and rewriting algorithms to avoid very large and very small numbers, that's it. https://twitter.com/milankloewer/status/1148670158883475461 https://twitter.com/milankloewer/status/1148670158883475461