[boost] Re: [Ann] Proposed Math library additions (complex number inverse trig functions).

From: Hubert Holin (Hubert.Holin_at_[hidden])
Date: 2005-04-05 09:24:13

Somewhere in the E.U., le 05/04/2005

   Bonjour

In article <007601c537a0$696a8210$51eb1b52_at_fuji>,
 "John Maddock" <john_at_[hidden]> wrote:

> As part of the project to produce a Boost TR1 implementation I've 
> implemented the additional algorithms in <complex> that are part of the TR:
> 
> fabs
> asin asinh
> acos acosh
> atan atanh
> 
> It occurs to me that maybe these should really be spun out as a separate 
> library rather than "slipped in" as part of another submission (comments 
> welcome on that).

      FWIW, asinh, acosh and atanh are already in Boost! If you wish, I 
can retire them (though I planed to add valarray support, I even printed 
a few days ago the discussion which had taken place on this two years 
(ahem) ago...).

> In the mean time these algorithms can be downloaded as part of the TR1 
> library here: 
> http://boost-sandbox.sourceforge.net/vault/index.php?&direction=0&order=&direc
> tory=tr1

(not showing up yet...)

> All the inverse trig functions are defined for the full complex plain, and 
> do the right thing even for exceptional input (no overflow or underflow 
> during the computation if the result is actually representable).  They also 
> do the right thing for infinities and nan's, as specified by C99.
> 
> The asin/asinh/acos/acosh algorithms have a theoretical max error bound of 
> 9.5e (experimental bounds are much lower, about 4e), there is no theoretical 
> work on atan/atanh that I know of, but experimentally the error bound seems 
> lower than for asin/acos.  This is some of the most heavily commented code 
> I've written, so refer to the header for more information on the literature 
> sources used etc.
> 
> During the implementation I found that I needed a few other things that 
> might make useful Boost components (part implemented, part wish list as 
> noted below):
> 
> log1p:
> ~~~~
> 
> This algorithm is part of C99, but by no means all compilers support it yet, 
> I used a Taylor series expansion for small x: I'm aware that there are much 
> more efficient methods, but optimizing compilers completely trash the logic 
> of these (Intel C++ proved to be particularly bad).

      I had planed to work on it (and a few related such as expm1...) 
something liketwo years ago and had planed to add it to the same special 
functions library. They really are important.

> Series Summation (Kahan Method):
> ~~~~~~~~~~~~~~~~~~~~~~~~
> 
> I wrote a small routine to apply the Kahan summation method to a 
> nullary-functor that generates successive terms in a series.  Summation 
> stops when the next term is below a particular threshold.  I've found the 
> Kahan method to be significantly more accurate for certain series, but again 
> some highly optimizing compilers can cause small errors to creep in (I 
> believe that the issue is double-rounding of intermediate terms on machines 
> with extended-double registers).  Probably my current interface to this one 
> needs some more thought before it could be anything other than a detail, and 
> if we're talking about wish lists, infinite product, and continued fraction 
> evaluation would be useful additions too....
> 
> Floating point testing:
> ~~~~~~~~~~~~~~
> 
> Currently just a version of C99's isnan, and only works for quiet nan's with 
> IEEE-conforming compilers.  More of a wish list really, I could really use 
> all the C99 fp-testing macros (as C++ functions obviously).
> 
> Numeric constants:
> ~~~~~~~~~~~~~
> 
> Currently I've embedded the numeric constants used inside the 
> implementation, a numeric constants library really would have simplified 
> things... just a pity we could never agree on an interface last time this 
> came up.
> 
> Whew, I think that's all, thanks for reading this far!
> 
> Regards,
> 
> John.

      Thanks for the work! I'll look into details when they show up.

   Merci

         Hubert Holin