Hacker News new | ask | show | jobs
by mabster 883 days ago
I'm surprised by this, regarding sqrt. The standard stipulates correct rounding for simple arithmetic, including sqrt ever since 754 1985.

Unless of course we are talking about the 80 bit format.

If that's not the case, would be interested to know where they differ.

Unfortunately for the transcendental function the accuracy still hasn't been pinned down, especially since that's still an ongoing research problem.

There's been some great strides in figuring out the worst cases for binary floating point up to doubles so hopefully an upcoming standard will stipulate 0.5 ULP for transcendentals. But decimal floating point still has a long way to go.
1 comments
AshamedCaptain 883 days ago
Because compilers can and have implemented sqrt in terms of rsqrt which is .. fun to work with. This also on SSE.
link
mabster 883 days ago
I spent most of my career working with rsqrt haha. And had my fair share of non-754 architectures too!

Every 754 architecture (including SSE) I've worked on has an accurate sqrt().

I'm assuming you're talking about with "fast math" enabled? In which case all bets are off anyway!

link
AshamedCaptain 882 days ago
No; compilers have done this even without fast-math. Gcc does not seem to do this anymore, but still does plenty of unsafe optimizations by default, like FMA.

Or maybe the library you use...

link
mabster 881 days ago
Argh, sounds really frustrating! It's hard enough to get accuracy when you can control operations never mind when the compiler is doing magic behind the scenes!

FMAs were difficult. The Visual Studio compiler in particular didn't support purposeful FMAs for SSE instructions so you had to rely on the compiler to recognise and replace multiply-additions. Generally I want FMAs because they're more accurate but I want to control where they go.

link
jcranmer 883 days ago
sqrt is a fundamental IEEE 754 operation, required to be correctly rounded, and many architectures implement a dedicated, correctly rounded sqrt instruction.

Now, there is also often an approximate rsqrt and approximate reciprocal, with varying degrees of accuracy, and that can be "fun."

link