standards , range , accuracy trigonometric functions

[RBato]

Dear Intel Community

How is standards , range , accuracy trigonometric functions in Intel C++ Compiler ? How is Your advise ?

[Bernard]

I used only once minimax polynomial where I tried  approximate Gamma function on problematic interval [0.01 <x< 1.0]. For  calculation  Stirling approximation was used. It converged  very well on the interval lying above abscissa point 1.0 , but for the abscissa values below that point it was divergent. In such a case Mathematica 8 calculated minima approximation for problematic range.

[Jeff_Arnold]

Re: #21. "I've never found an easily accessible documentation of the practical side of this stuff..."

You might consider looking at these two books by Jean-Michel Muller and some members of the group at ENS Lyon. (The name of the research team changes aperiodically.) One of the best collections of floating-point experts anywhere, including some of the major contributors to mpfr. Also look for various journal and conference publications from the group.

Handbook of Floating-Point Arithmetic

Birkhauser Boston, dec. 2009. 572 p. 62 illus., ISBN: 978-0-8176-4704-9

@Book{MullerEtAl2010,
  title = {Handbook of Floating-Point Arithmetic},
  author = {Muller, Jean-Michel and Brisebarre, Nicolas and de Dinechin, Florent and Jeannerod, Claude-Pierre and Lef{\`e}vre, Vincent and Melquiond, Guillaume and Revol, Nathalie and Stehl{\'e}, Damien and Torres, Serge},
  publisher = {{B}irkh\"auser {B}oston },
  pages = {572 },
  note = {{ACM} {G}.1.0; {G}.1.2; {G}.4; {B}.2.0; {B}.2.4; {F}.2.1.,
  ISBN 978-0-8176-4704-9}, year = {2010}, }

Elementary Functions: Algorithms and Implementaton

Springer Science & Business Media, 2006. 288 p, ISBN: 0817644083, 9780817644086

@book{muller2006elementary,
  title={Elementary Functions: Algorithms and Implementation},
  author={Muller, J.M.},
  isbn={9780817644086},
  lccn={2005048094},
  series={Computer Science},
  url={http://books.google.com/books?id=Mx-\_kaANJBEC},
  year={2006},
  publisher={Birkhauser Boston}
}

[TimP]

Thanks. Muller's Elementary Functions is good background. I took the 3 hour free android browse.

[Bernard]

Those books are very good , but there is another book related to functions approximation "Computer Approximations" by Hart and Cheney.

[Jeff_Arnold]

Computer Approximations by Cheney, Hart et al is a classic text in the field.  It presents much information about the theoretical unpinnings of many of the mathematical techniques which can be used to generate approximations for various functions (e.g, Remez' algorithm).  But it was first published in 1968.  It is completely out of date with respect to software implementation techniques for math libraries on modern processors.

[Bernard]

>>>But it was first published in 1968.  It is completely out of date with respect to software implementation techniques for math libraries on modern processors.>>>

Yes that is true if you are judging this book in the context of modern math libraries implementations.

[TimP]

I posted my white paper on Horner polynomial and related topics at

https://docs.google.com/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnx0cHJpbmNlc2l0ZXxneDo3ODhmMTc5ODFmOTdkMzE0

[Bernard]

Thanks Tim.

[TimP]

Someone notified me that they are blocked from reading google sites (not surprisingly) so I am trying t attach a copy here.

[Bernard]

Very interesting and informative white paper.

[RBato]

Where x87 were correct ( jobs , industry ) ?

[Bernard]

Rafał B. wrote:

Where x87 were correct ( jobs , industry ) ?

Are you asking about the specific programming field which used x87 code?

[RBato]

Thank You for Your answer .
Yes my question is about this . I'm interesting where were used x87 incorrect and why too .

[Bernard]

I think that x87 code was part of some libraries which targeted older CPUs  before the introduction of SSE SIMD unit.

One place where you can see actually source code of such a library is in MASM,  that one specific floating point library is fully written in x87 assembly.

[TimP]

Intel continues to support x87 libraries and code generation for 32-bit CPUs prior to Pentium 4.  Separate support for Pentium-III features and performance was discontinued a few years ago.

[RBato]

How is relation between x87 and SEE SIMD ?

[TimP]

Rafał B. wrote:

How is relation between x87 and SEE SIMD ?

You should read some references on this topic, so as to ask more specific questions (if you have any questions pertaining to C or C++ compiler).

[RBato]

thank You for Your answer .

Please indicate information source .

[RBato]

How is smoothing function x87 by AVX 256 / AVX 512 ? 
- errors calculation
- methods
- example
- sources

[TimP]

Even this one http://en.wikipedia.org/wiki/SSE2 is a starting point if you don't know what aspect of the topic you are interested in.

[Bernard]

Rafał B. wrote:

How is smoothing function x87 by AVX 256 / AVX 512 ? 

- errors calculation

- methods

- example

- sources

What do you mean? 

Are you referring to this function http://en.wikipedia.org/wiki/Smoothing