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Could you elaborate on how these points not apply to the IEEE standard for decimal floating-point? From what I can grasp, also the IEEE standard has multiple re

Could you elaborate on how these points not apply to the IEEE standard for decimal floating-point? From what I can grasp, also the IEEE standard has multiple representations for the same values. > For most comparisons (no, comparing numbers with the same exponent is not the norm) I'd say that exponent 0 is the norm, meaning precise numbers in a really wide range, isn't it?

StefanKarpinski 13y ago
That is not the case – there is exactly one representation for every single IEEE 754 value besides NaN – and checking if something is NaN or not is easy (two instructions). Not only that, but negative and positive values are in integer order, meaning that you can compare same-signed values using integer comparisons. What I meant by exponent zero not being the norm is that most numbers you work with won't have exponent zero. Specifically only one in 2^16 of the possibly representable values and only one in 2^24 of the possible representations. If you're using the "natural" representation, then only the integers -9 through 9 have zero exponent.
- JonahBraun 13y ago
  I'm not an expert but you seem to be wrong on this. The wikipedia article you linked to for the IEEE 754 decimal64 format says: "Because the significand is not normalized, most values with less than 16 significant digits have multiple possible representations; 1×102=0.1×103=0.01×104, etc. Zero has 768 possible representations (1536 if you include both signed zeros)."
  - bsder 13y ago
    Denorms basically don't occur except in very specific numerical cirumstances, so everybody treats these things as unique. This actually had a significant impact on the implementation of IEEE754 on the DEC Alpha chips. The DEC Alpha microprocessors used a software trap whenever a denormal was encountered. This was a fine idea--until you start emulating an x86 and discover that one of the big programs you want to support--AutoCAD--buries things into denormals and your performance is dog-slow.
  - StefanKarpinski 13y ago
    I meant the IEEE 754 binary32/64 standard that has been implemented in hardware everywhere since the early 1980s and is what we all actually use on a day to day basis – the usage of which is what Crockford thinks is the biggest mistake in JavaScript. I now see that the above post was asking specifically about "IEEE 754 decimal", which I missed. Yes, there are multiple representations of many numbers in that too. This is why non-binary floating-point representations kind of suck.

StefanKarpinski 13y ago

That is not the case – there is exactly one representation for every single IEEE 754 value besides NaN – and checking if something is NaN or not is easy (two instructions). Not only that, but negative and positive values are in integer order, meaning that you can compare same-signed values using integer comparisons. What I meant by exponent zero not being the norm is that most numbers you work with won't have exponent zero. Specifically only one in 2^16 of the possibly representable values and only one in 2^24 of the possible representations. If you're using the "natural" representation, then only the integers -9 through 9 have zero exponent.

JonahBraun 13y ago
I'm not an expert but you seem to be wrong on this. The wikipedia article you linked to for the IEEE 754 decimal64 format says: "Because the significand is not normalized, most values with less than 16 significant digits have multiple possible representations; 1×102=0.1×103=0.01×104, etc. Zero has 768 possible representations (1536 if you include both signed zeros)."
- bsder 13y ago
  Denorms basically don't occur except in very specific numerical cirumstances, so everybody treats these things as unique. This actually had a significant impact on the implementation of IEEE754 on the DEC Alpha chips. The DEC Alpha microprocessors used a software trap whenever a denormal was encountered. This was a fine idea--until you start emulating an x86 and discover that one of the big programs you want to support--AutoCAD--buries things into denormals and your performance is dog-slow.
- StefanKarpinski 13y ago
  I meant the IEEE 754 binary32/64 standard that has been implemented in hardware everywhere since the early 1980s and is what we all actually use on a day to day basis – the usage of which is what Crockford thinks is the biggest mistake in JavaScript. I now see that the above post was asking specifically about "IEEE 754 decimal", which I missed. Yes, there are multiple representations of many numbers in that too. This is why non-binary floating-point representations kind of suck.