Thread

1. rf15 · 1789732795 · focus · HN ↗

   ...Is this running extra micro code to fix some hardware bug/unreliability? How can this happen? Doesn't look like a normal design decision.

   1. Sharlin · 1789733432 · focus · HN ↗

      Subnormal numbers have a different, basically fixed-point, representation. They exist in order to bridge the large (relatively speaking; indeed "infinite" in a sense) gap between the least positive normal number, zero, and the greatest negative normal number, caused by the usual significand-exponent representation.

      Most "mundane" uses of floating point have no need for subnormal numbers, and results that underflow could just be flushed to zero. But they’re sometimes important in scientific computing to ensure sufficient smoothness around zero, avoiding precision issues.

      1. adrian_b · 1789830623 · focus · HN ↗

         On early computers, any underflow generated an exception that would crash the program if not handled.

         This was very good, because underflows completely break the assumptions about floating-point arithmetic on which numeric algorithms are based, so the errors in the final results become unpredictable.

         Subnormal numbers have been introduced as a means to avoid handling every underflow exception, because typically the use of subnormals eliminates the errors that would otherwise be caused by underflows.

         The flush-to-zero and denormals-of-zero options must be strictly forbidden for any general-purpose applications. They should be permitted only in applications where there is no doubt that regardless how big the errors will be they will not have any really harmful effect, which is true for games and perhaps for AI, but for little else.

         This is another great misfeature promoted by Intel, in order to win meaningless benchmarks. It would have been much better if these standard-breaking features would not have existed, because they are much more often used when they should not be used, than when they are harmless.

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