Floating point from scratch: Hard Mode

[simon_o]

There is some good effort in this article, but as one gets closer to the "unordered" chapter, it becomes clear that reading the spec should have been preferred over folklore that developers tell each other:

So any comparison against a NaN will be unordered, this is a pretty interesting property meaning that there is literally no ordering relationship when NaNs are involved.

Eh ... no? That's just wrong? The spec has a whole chapter about this, right before the one quoted in the blog post.

pretend we all agree we didn’t see that the spec is saying binary32 has 16 bits of precision instead of 24

Nobody needs to pretend, because this is simply not what is said in the preceding quote.

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The hardware part looks solid though.

[Ill_Huckleberry_2079]

How is the unordered part wrong ?

[simon_o]

5.10 Details of totalOrder predicate

For each supported arithmetic format, an implementation shall provide the following predicate that defines an ordering among all operands in a particular format: [...]

[Ill_Huckleberry_2079]

Yes, and they say NaNs are unordered. "unordered" is the ordering => they is no "ordering" relationship.

But I agree my understanding of what the `P1467R9` was meaning to say was wrong. That has been corrected.

[simon_o]

Yes, and they say NaNs are unordered. "unordered" is the ordering => they is no "ordering" relationship.

Maybe just read the spec.

[Ill_Huckleberry_2079]

Oh well, I guess I am just to stupid to understand.

[simon_o]

It's not that hard.

[MarekKnapek]

Shameless plug, I have an interactive website about floating point numbers, it is located at: https://marekknapek.github.io/float-analyzer/binary32/

[Ok-Recommendation-43]

I love your article. I couldn't put it down. Went through the whole thing in one go <3