Yeppp! High performance mathematical library

[Gunther]

Dave,

I guess with a math paper, the translation would probably be accurate in any case.

Dave.

I think no one would read it if it were not written in English. It is the lingua franca in science.

Gunther

[Adamanteus]

Good idea. We can try to make our own HPC library. Why not? Any ideas?

Gunther

That's possible to join entusiasts on Math DLL Project, on old site version there is it.

[Gunther]

That's possible to join entusiasts on Math DLL Project, on old site version there is it.

Couldn't find a HPC approach.

Gunther

[Marat Dukhan]

Yeppp! author here and ready to answer your questions!

[jj2007]

Yeppp! author here and ready to answer your questions!

Yeppp, that's an excellent service!

Welcome to the Forum. We have some looooong threads aiming at beating the best C compilers with even better hand-crafted assembler. If you have a frequently-used Yeppp! algo that needs a speedup, this is your chance

But of course, some of us will also be interested to produce an interface Yeppp! - Masm. GSL has already one.

[Marat Dukhan]

If you have a frequently-used Yeppp! algo that needs a speedup, this is your chance

All of Yeppp! is a collection of algos which need speedups. Contributors are welcome! :icon14:

But of course, some of us will also be interested to produce an interface Yeppp! - Masm.

This is easy. Most of Yeppp! is auto-generated, so one would only need to patch the code-generator.

[dedndave]

welcome to the forum   :t

i haven't used the library yet, but i have looked it over
looks very interesting   

[Gunther]

Marat,

first things first: Welcome to the forum.

It's good to know that another experienced programmer is floating around here. I hope you'll have fun.

Gunther

[Adamanteus]

Couldn't find a HPC approach.

Gunther

YES - there only algos, but using threads or standalone MPI-like libraries is deal for it - or, "two in one" only modern 

[qWord]

Marat Dukhan,

is there any documentation (or literature) on the used methods for approximation? What precision-reference did you use to test the math functions (the folder unit-test/source/math is empty).

regards, qWord

[Marat Dukhan]

is there any documentation (or literature) on the used methods for approximation? What precision-reference did you use to test the math functions (the folder unit-test/source/math is empty).

The framework I developed for testing performance & accuracy is open sourced at bitbucket.org/MDukhan/hysteria. For accuracy testing it computes functions to 160-bit precision with GMP, and then converts the result to double-double. I also work on mathematical proofs of error bounds, and plan to release a tech report on that.

[Gunther]

Marat,

The framework I developed for testing performance & accuracy is open sourced at bitbucket.org/MDukhan/hysteria. For accuracy testing it computes functions to 160-bit precision with GMP, and then converts the result to double-double. I also work on mathematical proofs of error bounds, and plan to release a tech report on that.

Thank you for your fast reply. Your test framework looks impressive. Is double-double 128 bit? Which kind of error analysis do you use?

Gunther

[Marat Dukhan]

Is double-double 128 bit?

Yes, double-double is an unevaluated sum of two doubles. From high-level perspective you can imagine it as double with 106-bit mantissa.

Which kind of error analysis do you use?

To analyse error of interpolating polynomial, I split function domain into intervals of constant ULP, bound the absolute error of approximation (with Sollya) and evaluation (with Gappa), compute the total ULP error on each interval, and choose the maximum of all intervals. Other kinds of errors (range reduction and reconstruction) are analysed on case-by-case basis.

[Gunther]

To analyse error of interpolating polynomial, I split function domain into intervals of constant ULP, bound the absolute error of approximation (with Sollya) and evaluation (with Gappa), compute the total ULP error on each interval, and choose the maximum of all intervals. Other kinds of errors (range reduction and reconstruction) are analysed on case-by-case basis.

That's the approximation error, of course. My question has two directions. The other is: What's with the numerical stability? Do you use some backward error analysis (introduced by Wilkinson) or an error interval (see my PM)?

Gunther

[qWord]

Yes, double-double is an unevaluated sum of two doubles. From high-level perspective you can imagine it as double with 106-bit mantissa.

I'm right in when assuming the method described by T.J. Dekker^[1]?

All of Yeppp! is a collection of algos which need speedups. Contributors are welcome! :icon14:

For the polynomials, it might be possible to reformulate them in such a way that the packed instructions (SSE2, add/mulpd) can be used.

[1]T.J. Dekker, "A Floating-Point Technique for Extending the Available Precision", Springer