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0 pointsStefanKarpinski12y ago0 comments

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.

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JonahBraun12y ago· 2 in thread

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)."

StefanKarpinskiOP12y 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.

bsder12y 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.

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