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by yeputons 8 hours ago
> On the contrary, IEEE floating point results are precisely specified to produce the closest representable value to the mathematically exact result.

Not sure about Rust, but C++ only guarantees that for four arithmetic operations and `sqrt`. Not `pow`, not `log`. Not even when when all inputs/outputs are integers. Sometimes you can even get `(int)pow(10, 2) == 99`, which I believe is fully standard-compliant.
1 comments
kaathewise 7 hours ago
Yeah, those operations (+fma) are the only ones for which IEEE 754 mandates correct rounding.

Calculating correct rounding for other functions without hardware support is both challenging to implement and is often really slow. And that's before one gets into special functions. Or, even worse, inverses of special functions. Sometimes you might be lucky when those don't over/underflow around the edges of the domain

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inigyou 5 hours ago
It's still challenging to implement with hardware support but you don't notice because it challenges Intel instead of you. There is a reason that no instruction set since x87 implements transcendentals - and x87 did them in microcode.
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kaathewise 5 hours ago
True!

Older numerical libraries such as cephes had to work with heterogeneous non-IEEE floating point implementations: you can still see remnants of VAX tests in the docs, for example. That, too, must've been quite a struggle

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