Re: [boost] RFC: Multiprecision arithmetic library

Subject: Re: [boost] RFC: Multiprecision arithmetic library
From: Paul A. Bristow (pbristow_at_[hidden])
Date: 2011-12-23 12:30:27

> -----Original Message-----
> From: boost-bounces_at_[hidden] [mailto:boost-bounces_at_[hidden]] On Behalf Of John
> Maddock
> Sent: Thursday, December 22, 2011 1:41 PM
> To: boost_at_[hidden]
> Subject: [boost] RFC: Multiprecision arithmetic library
> 
> Folks,
> 
> I'd like to get some feedback on a multiprecision arithmetic library I've been preparing for
possible Boost
> inclusion.  The code is in the sandbox under the "big_number" directory.  Docs can be viewed
online here:
>
http://svn.boost.org/svn/boost/sandbox/big_number/libs/multiprecision/doc/html/boost_multiprecision/
> intro.html
> 
> The main features are:
> 
> * A generic front-end that's capable of wrapping almost any type that's a "number".  The front end
is
> expression template enabled and handles all the expression optimization and code reduction.  For
example
> it's possible to evaluate a polynomial using Horner's rule without a single temporary variable
being
> created.
> * A series of backends that need only provide a reduced interface and set of operations, implement
the
> actual arithmetic, currently supported backends
> are:
> 
> Integer Types
> ~~~~~~~~~
> 1/ GMP (MPZ).
> 2/ libtommath.
> 
> Rational Types
> ~~~~~~~~~~
> 1/ GMP (MPQ).
> [ But note that the integer types can also be used as template aruments to Boost.Rational ]
> 
> Floating Point Types
> ~~~~~~~~~~~~~~
> 1/ GMP (MPF)
> 2/ MPFR
> 3/ cpp_float - an all C++ Boost-licensed backend based on Christopher Kormanyos' e_float code.
> [ Note these three types are fully compatible with Boost.Math Trunk - so you get full standard
library plus
> special function support ]
> 
> There's still a bunch to do, but I'd like to see what folks think, and where the main priorities
should be
> before submission.

This is a really important development, long overdue as a tool in the Boost kit box, made possible
by Christopher Kormanyos  arbitrary precision floating point library which is free of licensing
difficulties, so the whole setup *can* be Boost license.  (Those who can use other restricted
licence packages like GMP can still do so and get a modest improvement in speed).

It should allow user to move seamlessly (well fairly ;-) from the built-in types to much higher
precision types.

This will allow tasks which can only be done now by moving to arbitrary precision like MatLab or
Mathmetica to be done in C++.  
Only those bits of code that need high precision need to use it, leaving most of the code in C++
built-in types. Maximally accurate long double values can be computed and saved.  

The cunning expression template implementation that John has produced offers some useful speedups
(but as he says in the docs, it doesn't give quite the speedup that the over-optimistic might
expect).

The other downside (as he also warns) is that not all existing code can use it without some code
changes.  I fell straight into this pit by trying to use Boost.Test to check cpp_float IO exactly as
I had with Christopher Kormanyos's multiprecision.  I had to use the Boost lightweight test version
instead, not a big problem, and one that can probably be 'cured' by some changes within Boost.Test.

So I see a need for *both* John's expression template enabled version *and* Christopher Kormanyos
version.  So keep at it both of you!

Checks using Boost.Test also show that IO (after some grrrring by both Chris and John - it's a
really, really tiresome task) does as close as is reasonable to expect in matching the IO of
built-ins like double.  This is highly desirable feature IMO.  Boost.Test shows a reassuring number
of decimal digits when displaying failure messages!

As for priority, personally I think that the most important aspect is a Boost-license version of
integer and floating-point (with rational a slightly lower priority).  Of course, for others being
able to use the 'gold-standard' GMP and MPFR may be more important.  

Paul

---
Paul A. Bristow,
Prizet Farmhouse, Kendal LA8 8AB  UK
[phone]  07714330204
pbristow_at_[hidden]