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Subject: [boost] [Polynomial] Review Result
From: John Maddock (john_at_[hidden])
Date: 2009-04-09 12:19:17

Apologies for the delay in putting this together...

First off I'd like to thank the author for submitting this for review - I
wish all our SOC students were similarly diligent! :-)

We received a number of reviews of this library, but none were in favor of
acceptance in its current form, and most thought that there was still a fair
bit of work to do to get the library into shape. However, most thought that
the library could be accepted into Boost given sufficient

Therefore the library is not accepted into Boost at this time, but I would
like to encourage the author to continue to work on the library and resubmit
at a future time.

In no particular order the main review comments are summarized below:

Principal comments:

* Documentation, especially the background is inadequate and needs a good
  a) From the examples are nothing that a competent programmer couldn't
figure out from the declarations. Some more interesting or useful examples
would be nice, particularly for things like the special forms.
  It's not exactly clear what I would do with those functions.
  b) There is no documentation or references to the various algorithms used.
Those, too, would be nice.
  c) Doc.html appear to have been created 'the Hard Way'. Would be much
more useful and look nicer if produced with the Quickbook, Doxygen...
toolchain. And make it maintainable by other people.

* Use of constructors and assignment operators that modify their arguments
isn't acceptable - best to find another interface for this.

* Several reviewers noted that the code didn't build for them, in particular
log2 isn't available on all platforms/compilers.

* evaluate_polynomial() and evaluate_polynomial_faithfully() take their
coefficient arguments in the opposite order of all the other
functions/constructors in the library, without providing any reason for that
choice. That's seems somewhat surprising. I'd suggest fixing that, or at
the very least providing an argument in the documentation why this makes
some sense.
* Rename evaluate() to horner() and provide evaluate() as an inline call
to horner().

* Rename evaluate_faithfully() to compensated_horner().

* Things that say "Be careful about this" generally need fixing.

* It would be nice to have operator* and operator/ as well as *= and /=.

* Considering they share the same core algorithm, it might be nice to have
a function that could do division and return the remainder at the same time.
Something like
  poly::divide(P &divisor, P &quotient, P &remainer)

* FFTs are good for multiplying polynomials above a certain size, but they
are rather heavy for small polynomials and can lead to unexpected crosstalk
between terms. There should be an option for * that doesn't use the FFT,
and it should be the default for small polynomials.

* operator/= has a hardcoded "std::vector<double> new_coefficients" that
later gets rounded?? This should be fixed to work with any type that
fulfills the necessary
  conceptual requirements (and tested and documented what those requirements
are - it would be nice if they were the same as the rest of Boost.Math).

* The name FieldType is mathematically misleading since the instantiating
type is very likely not to be a field (e.g. int or a multiple precision
integer type).

* the Polynomial class provides a fairly minimalist set of supported
functions. This may well be deliberate (if so, apologies), but I would like
to see a richer interface including such things as
            - content (gcd of coefficients, where that makes sense)
            - polynomial discriminant
            - resultant of 2 polynomials
            - evaluation of homogeneous polynomial ( f(x) = sum c_i
x^i,f(a,b) = sum c_i a^i b^(d-i) )
            - evaluation at a polynomial (f(g(x)))
            - Pseudo-division of polynomials
            - finding roots over C
            - finding roots over F_p
            - factorisation over Z
            - factorisation over F_p

* We had one feature request for extending support to finite fields.

* 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

* It's not clear from the documentation what this constructor does:
     polynomial(InputIterator first1, InputIterator last1, InputIterator
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.

* 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?

John Maddock
Review Manager for Polynomial Library.

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