Re: [Boost-users] Re: C++ Template Metaprogramming - factorial exampl e

From: Aleksey Gurtovoy (agurtovoy_at_[hidden])
Date: 2005-01-24 18:40:46

Brad Austin writes:
> I wrote:
>> I recently purchased David Abrahams' and Aleksey Gurtovoy's new
>> book on the MPL, "C++ Template Metaprogramming" (obviously recently
>> since it's only been out a couple of weeks), and am working through
>> some of the examples.  I'm having trouble with the factorial
>> example in section 8.3.1, page 160:
>>
>>     #include <boost/mpl/int.hpp>
>>     #include <boost/mpl/multiplies.hpp>
>>     #include <boost/mpl/equal.hpp>
>>     #include <boost/mpl/eval_if.hpp>
>>     #include <boost/mpl/prior.hpp>
>>     #include <boost/static_assert.hpp>
>>
>>     namespace mpl = boost::mpl;
>>
>>     template <class N>
>>     struct factorial
>>       : mpl::eval_if<
>>             mpl::equal_to<N,mpl::int_<0> >  // check N == 0
>>           , mpl::int_<1>                    // 0! == 1
>>           , mpl::multiplies<                // N! == N * (N-1)!
>>                 N
>>               , factorial<typename mpl::prior<N>::type>
>>             >
>>         >
>>     {
>>         BOOST_STATIC_ASSERT(N::value >= 0); // for nonnegative N
>>     };
>>
>> There's a minor issue in that equal.hpp is (apparently) mistakenly
>> included instead of equal_to.hpp, but even after fixing that, I can't
>> get this to compile in the form in which it's written.  Should it, or
>> is it broken?
>
> After spending some more time on this I now believe the code is
> broken.

You are right.

> There's some uncertainty because mpl::multiplies<> has apparently been
> either renamed or replaced with mpl::times<>, and only the latter is
> documented in the MPL Reference Manual, so I'm not certain whether or
> not the two behave identically.

They do. 'multiplies' is simply a synonym for 'times'.

> However changing "multiplies" to
> "times" didn't seem to make any difference in terms of the compilation
> errors, so in the analysis that follows I'm making the assumption that
> if there is any difference, it isn't doesn't change anything relevant
> to the problem at hand.
>
> According to the MPL Reference Manual, in an expression of the form
> mpl::times<T1,T2>, T1 and T2 must meet the requirements of an
> integral constant, not merely the weaker requirements of a nullary
> metafunction.  

Correct.

> In this case T2 is an expression of the form
> factorial<T3>, so for this to be vaild factorial<> must model an
> integral constant, not merely a metafunction *returning* an integral
> constant.  

Ditto.

> However factorial<> derives from an expression of the
> form mpl::eval_if<T4,T5,T6>, and doesn't add any nested types or a
> value of its own.  Therefore factorial<> only models an integral
> constant if mpl::eval_if<T4,T5,T6> does, which it doesn't.

More precisely, it doesn't in the "official" 1.32.0 codebase. In the
Boost distribution on the CD 'eval_if' _derives_ from the result
metafunction, and that's probably how this and may be a few other
factorial examples slipped through our tests.  Removal of the
inheritance for GCC (as an implementation detail) was a last-minute
fix just before 1.32 was officially released.

> mpl::eval_if<T4,T5,T6>::type models an integral constant (provided
> T5:type and T6::type do), but mpl::eval_if<T4,T5,T6> is merely a
> metafunction returning that constant.
>
> Also, the first argument to eval_if is supposed to be an integral
> constant, and T4 is an expression of the form mpl::equal_to<T7,T8>,
> which again is just a nullary function, not an integral constant. 

Not if T7 and T8 are Integral Constants, see
http://www.boost.org/libs/mpl/doc/refmanual/equal-to.html.

-- 
Aleksey Gurtovoy
MetaCommunications Engineering