accuracy of fp division

Accelerated Computing CUDA CUDA Programming and Performance
1

Hi,

I’m running into problem that seemingly shows that the accuracy of single precision floating-point
division on CUDA is lower than that of CPU…

Is this really true ? and if yes are there any means to deal with that ?

thanks

2

Yes, this is documented in the programming guide (P86) - single precision division is only accurate to 2 ulp (this is because the GPU implements division using reciprocal).

One work-around is to use double precision (if you GPU supports it), which is fully compliant.

3

Hmmmm…
This could explain why my gpu gmres solver converges in more iterations than the cpu version. Loss of orthogonality due to lower precision…

I have no idea how to test the hypothesis, though…

Maybe compare to emu mode?

4

ok thanks for reply. I have G200 but double precision div should be real slow since it does not have hardware support,

so i have to look for other options…

5

Hi,

What would be the other work-arounds beside doubles?

thanks

eyal

6

One step of Newton iteration might polish the final bits. This is certainly possible for computing 1/Z , but I imagine it could be extended for Y/Z.

The iteration

x2= x1*(2.0-Z*x1)

polishes the computation of X, converging to 1.0/Z.

7

FYI, in CUDA 2.2 we are planning on adding some new device functions that will provide IEEE-compliant single precision reciprocal, square-root, and division.

Note that these will be much slower than the built-in operations, but may be useful for developers who need to match CPU results exactly.

8

Hi Simon,

Thanks for the information, can you please suggest a workaround for now for sqrt accuracy?

9

I would try using some kind of iterative method to improve the accuracy of sqrt, as SPWorley suggested:
[url=“Methods of computing square roots - Wikipedia”]http://en.wikipedia.org/wiki/Methods_of_co...ng_square_roots[/url]