5 ms·

Hardware support for UNUM floating point arithmetic [pdf]

50 points by gbrown_ 9y ago

screeny05 9y ago
please add a [PDF] to the header
- gjem97 9y ago
  Just wondering: why is it useful to know it's a PDF before clicking?
  - dEnigma 9y ago
    In my case, while I'm on my phone, the pdf is automatically downloaded and opened in a different app; so it is nice to have a warning.
    - pasbesoin 9y ago
      It's also something of a legacy convention (though one I prefer to maintain), from when PDF files were a leading vector for malware. Though even back then, malware concerns aside, people would curse when a link caused Acrobat Reader (or, depending on one's system, the full Acrobat program) to unexpectedly fire up. Once upon a time, browsers didn't have integrated PDF handling. And, even now, with integrated PDF handling, said handling is not proof against exploits.
noahdesu 9y ago
Woah, really cool. My understanding is that Posit, the successor to unum versions 1 and 2, is the future and is much easier to implement in hardware [0]. [0]: https://posithub.org/about https://posithub.org/about
- j_s 9y ago
  There is a Posit BoF at SC17 (supercomputing) Nov 14 DEN: http://sc17.supercomputing.org/presentation/?id=bof135&sess=sess333 http://sc17.supercomputing.org/presentation/?id=bof135&sess=... Posit Paper: http://johngustafson.net/pdfs/BeatingFloatingPoint.pdf http://johngustafson.net/pdfs/BeatingFloatingPoint.pdf A new data type called a posit is designed as a direct drop-in replacement for IEEE Standard 754 floating-point numbers (floats). Unlike earlier forms of universal number (unum) arithmetic, posits do not require interval arithmetic or variable size operands; like floats, they round if an answer is inexact. However, they provide compelling advantages over floats, including larger dynamic range, higher accuracy, better closure, bitwise identical results across systems, simpler hardware, and simpler exception handling. source: https://twitter.com/daniel_bilar/status/920252363159539712 https://twitter.com/daniel_bilar/status/920252363159539712
deleted 9y ago
[deleted]
petermonsson 9y ago
I am confused. I see half the performance and 3-5x the area of IEEE754, but the conclusion is that UNUM is comparable. That would not be my conclusion. What am I missing?
- fdej 9y ago
  The idea is that computers spend much more energy moving data between the processor and memory than actually processing the data. Unums use a variable length encoding which makes processing more costly but reduces the amount of data transfer. At least in theory; whether this is a net benefit remains to be proven.
  - deleted 9y ago
    [deleted]
- iainmerrick 9y ago
  If it's exactly reproducible on different hardware and software configurations, as seems to be one of the goals, that alone would be a useful improvement on IEEE754.
  - wolfgke 9y ago
    > If it's exactly reproducible on different hardware and software configurations, as seems to be one of the goals, that alone would be a useful improvement on IEEE754. IEEE754 already supports that (except for the minor fact that the NaN types can in theory be represented by different bit sequences - in practise all the same are used). The problem rather is that typical programming languages (such as C, C++) have no proper support for IEEE754. And you have to be very precise in your intentions: For each of the operations defined in IEEE754 you have to define which of the four (+ one optional one in the 2008 revision) rounding modes is to be used. Or you have to be precise whether a MAC or and multiply (then round) and add (then round again) is to be used. This of course has again implications that depending on what the compiler makes out of it either the program will not run on processors with no MAC support or the code has to use a software emulation (slow).

50 points by gbrown_ 9y ago

screeny05 9y ago

please add a [PDF] to the header

gjem97 9y ago
Just wondering: why is it useful to know it's a PDF before clicking?
- dEnigma 9y ago
  In my case, while I'm on my phone, the pdf is automatically downloaded and opened in a different app; so it is nice to have a warning.
  - pasbesoin 9y ago
    It's also something of a legacy convention (though one I prefer to maintain), from when PDF files were a leading vector for malware. Though even back then, malware concerns aside, people would curse when a link caused Acrobat Reader (or, depending on one's system, the full Acrobat program) to unexpectedly fire up. Once upon a time, browsers didn't have integrated PDF handling. And, even now, with integrated PDF handling, said handling is not proof against exploits.

noahdesu 9y ago

Woah, really cool. My understanding is that Posit, the successor to unum versions 1 and 2, is the future and is much easier to implement in hardware [0]. [0]: https://posithub.org/about https://posithub.org/about

j_s 9y ago
There is a Posit BoF at SC17 (supercomputing) Nov 14 DEN: http://sc17.supercomputing.org/presentation/?id=bof135&sess=sess333 http://sc17.supercomputing.org/presentation/?id=bof135&sess=... Posit Paper: http://johngustafson.net/pdfs/BeatingFloatingPoint.pdf http://johngustafson.net/pdfs/BeatingFloatingPoint.pdf A new data type called a posit is designed as a direct drop-in replacement for IEEE Standard 754 floating-point numbers (floats). Unlike earlier forms of universal number (unum) arithmetic, posits do not require interval arithmetic or variable size operands; like floats, they round if an answer is inexact. However, they provide compelling advantages over floats, including larger dynamic range, higher accuracy, better closure, bitwise identical results across systems, simpler hardware, and simpler exception handling. source: https://twitter.com/daniel_bilar/status/920252363159539712 https://twitter.com/daniel_bilar/status/920252363159539712

deleted 9y ago

[deleted]

petermonsson 9y ago

I am confused. I see half the performance and 3-5x the area of IEEE754, but the conclusion is that UNUM is comparable. That would not be my conclusion. What am I missing?

fdej 9y ago
The idea is that computers spend much more energy moving data between the processor and memory than actually processing the data. Unums use a variable length encoding which makes processing more costly but reduces the amount of data transfer. At least in theory; whether this is a net benefit remains to be proven.
- deleted 9y ago
  [deleted]
iainmerrick 9y ago
If it's exactly reproducible on different hardware and software configurations, as seems to be one of the goals, that alone would be a useful improvement on IEEE754.
- wolfgke 9y ago
  > If it's exactly reproducible on different hardware and software configurations, as seems to be one of the goals, that alone would be a useful improvement on IEEE754. IEEE754 already supports that (except for the minor fact that the NaN types can in theory be represented by different bit sequences - in practise all the same are used). The problem rather is that typical programming languages (such as C, C++) have no proper support for IEEE754. And you have to be very precise in your intentions: For each of the operations defined in IEEE754 you have to define which of the four (+ one optional one in the 2008 revision) rounding modes is to be used. Or you have to be precise whether a MAC or and multiply (then round) and add (then round again) is to be used. This of course has again implications that depending on what the compiler makes out of it either the program will not run on processors with no MAC support or the code has to use a software emulation (slow).