Boost logo

Boost Users :

Subject: Re: [Boost-users] [Review] Polynomial library review begins today
From: John Maddock (john_at_[hidden])
Date: 2009-03-17 14:29:58

A little later than planned, here is my review of the polynomial library:

Documentation and Design

As previously noted by others the Introduction doesn't adequately describe
the library - some sort of simple tutorial at this point would be useful
too. The "Background" section doesn't really describe the "background" as
such either.

This constructor:

template<typename U>
polynomial(const U& v);

had me a little confused at first - is there any advantage to making this a
template rather than simply accepting a const FieldType& as the single

This constructor:

polynomial(std::vector<FieldType>& c);

should *not* modify the original vector IMO, a construct-with-move should be
a separate constructor - I'm sure we have a move/rvalue reference emulation
library available somewhere? Likewise for the assignment operator
polynomial<FieldType>& operator=(std::vector<FieldType>& c);

It's not clear from the documentation what this constructor does:

polynomial(InputIterator first1, InputIterator last1, InputIterator first2);

It needs to clearly state the degree of the resulting polynomial and whether
it passes through all/any of the points - in fact maybe the constructor
should have a final parameter for the degree of the polynomial and use
least-squares fitting when required? Likewise for the member function
template<typename InputIterator> void interpolate(InputIterator first1,
InputIterator last1, InputIterator first2);

Operators: the / and % operators need good descriptions of what they do,
given that no exact division is possible. As someone else has already
noted, a function to calculate divide and remainder in one step would be
useful too.

GCD: presumably this is restricted to polynomials with integer coefficients?
If so it should say so.

Evaluation: The docs should say what method is used for the
evaluate_faithfully method and give a reference. Renaming as someone else
suggested may be better too, but personally I'm easy either way on that.
I'm not sure whether there should be an evaluate_by_preconditioning method,
shouldn't the polynomial "know" that it has been preconditioned and react
accordingly. I haven't looked/checked but do the usual arithmetic operators
still work if the polynomial has been preconditioned? I assume probably
not, but if that's the case there should be a stern warning to that effect,
*and* checks in code to prevent us from doing something stupid :-) BTW,
preconditioning can be applied to polynomials of any degree I believe it's
just that it gets hard to implement in the generic case.

In addition I'd like to see the evaluation functions templated, so that the
type being evaluated can differ from FieldType - it would surely be quite
common for example to create and manipulate polynomials with integer
coefficients, but then want to evaluate on a floating point type. There is
machinery in Boost.Math BTW to handle the mixed argument-promotion and
calculation of the result type, let me know if you need help in using this.

Special Forms: the functions provided do *not* generate polynomials in the
alternative forms, but rather generate the named polynomial of order N,
which is rather less useful, but at the very least the docs need updating to
reflect this.


I haven't spent a great deal of time on this, but I note that:

test_arithmetics.cpp fails on cygwin: or at least it did once I added a

    using std::pow;

to start of operator*= to get things compiling.

None of the code builds with msvc: there are a couple of issues here:

    friend polynomial<FieldType>
boost::math::tools::gcd<>(polynomial<FieldType> u, polynomial<FieldType> v);

Needs to be changed to:

    friend polynomial<FieldType>
boost::math::tools::gcd<FieldType>(polynomial<FieldType> u,
polynomial<FieldType> v);

to get msvc to Grok the code.

After that there are a bunch of failures due to the use of log2 which msvc
doesn't support (and since it's not part of the std other compilers are
likely to complain too).

I haven't looked too hard at the implementation, except to echo the comments
posted previously that the Conceptual requirements for FieldType need
documenting and *testing*. There are concept checking classes and
archetypes in Boost.Math which may be of use here. Again, shout if you need
help in figuring out how to use these. I did notice that operator*= for
example uses std::complex<double> internally which effectively limits the
precision that can be achieved - to be useful to me - and to replace the
existing "implementation detail" polynomial class in Boost.Math - I would
need the polynomial class to be usable with arbitrary precision types such
as NTL::RR or mpfr_class. Also as previously noted, multiplication of small
polynomials may well be more efficient with the "naive" algorithm, so some
performance tests and experimenting is required here. Related to this, use
of "round" should be restricted to types that are known to be integers?

* What is your evaluation of the potential usefulness of the library?

As noted by others it's a niche library but potentially quite useful within
that niche.

* Do you think the library should be accepted as a Boost library? Be
sure to say this explicitly so that your other comments don't obscure your
overall opinion.

I think that the library could be accepted into Boost, but not it's it's
current form, so I would vote no for now: please note this is my personal
review of the library and should not be confused with my role as review
manager for this library.

Regards, John Maddock.

Boost-users list run by williamkempf at, kalb at, bjorn.karlsson at, gregod at, wekempf at