Sine and Cosine Accuracy

[Scott Robert Ladd]

Morten Welinder wrote:
> If you were to look up a serious math book like Abramowitz&Stegun1965
> you would see a definition like
> 
>     sin z = ((exp(iz)-exp(-iz))/2i                   [4.3.1]

Very true. However, the processor doesn't implement intrinsics for
complex functions -- well, maybe some do, and I've never encountered them!

As such, I was sticking to a discussion specific to reals.


> And there is the answer to your question: if you just think of "sin"
> as something
> with angles and triangles, then sin(2^90) makes very little sense.  But "sin"
> occurs other places where there are no triangles in sight.

That's certainly true; the use of sine and cosine depend on the
application. I don't deny that many applications need to perform sin()
on any double value; however there are also many applications where you
*are* dealing with angles.

I recently wrote a GPS application where using the intrinsics improved
both accuracy and speed (the latter substantially), and using those
intrinsics was only "unsafe" because -funsafe-math-optimizations
includes other transformations.

I am simply lobbying for the separation of hardware intrinsics from
-funsafe-math-optimizations.

..Scott