Re: [Boost-users] proto: analytical-only math functions

Subject: Re: [Boost-users] proto: analytical-only math functions
From: Hicham Mouline (hicham_at_[hidden])
Date: 2009-03-14 08:55:36

-----Original Message-----
From: boost-users-bounces_at_[hidden]
[mailto:boost-users-bounces_at_[hidden]] On Behalf Of Eric Niebler
Sent: 07 March 2009 02:32
To: boost-users_at_[hidden]
Subject: Re: [Boost-users] proto: analytical-only math functions

Hicham Mouline wrote:
> 
> Step1 is to have a derivative metafunction which computers the nth
> derivative of a function at compile time.
> 
> In order to do that, I need a mathematical language to write my
> functions.
> 
> so I have constants, variables, basic_functions and user-defined
> functions that are terminals of my language
> 
> f(x) = log(x);
> 
> g(x) = derivative(1, f, x);
> 
> g(x) will be 1/x;
> 
> I should manage to run derivative purely in compile time.

>You won't be able to do it this way with exactly this syntax. The object 
>"f" will not carry the compile-time information that derivative() would 
>need to do its job. You might need something like this:

>   BOOST_PROTO_AUTO( _f, f(x) = log(x) );
>   BOOST_PROTO_AUTO( _g, g(x) = derivative(1, _f, x) );

>Or, you could do it all in one big expression, like:

>   let( f(x) = log(x) )[ g(x) = derivative(1, f, x) ];

>or something. And if I'm right in assuming that the first parameter of 
>derivative is which derivative to take, you'll need to make that 
>information available at compile-time as well, so:
>   let( f(x) = log(x) )[ g(x) = derivative<1>(f, x) ];

I am thinking about user friendliness.
I think I will have the user define this:

typedef   proto::terminal<  function_tag< mpl::size_t<3> > >::type
function3;
function3 f( x1, x2, x3,  x1+ x2+ x3+ c6 );  // after all, store the
expression tree at runtime

1. Can I define a constructor for the terminal like this?
2. Can I store the expression tree somewhere? Inside the function_tag
template?

Regards,