Add some numeric_traits?

From: Daryle Walker (darylew_at_[hidden])
Date: 2001-05-24 16:16:29

With the discussion over quaternions, I'm wondering if we should have a
header describing numeric type properties.  Maybe like:

template < typename T >
class boost::numeric_traits
{
    static const bool is_specialized = false;

    static const bool has_real = false;
    static const bool is_scalar = false;

    static const bool has_magnitude = false;

    typedef T  component_type;
    typedef component_type magnitude_type;

    //...
};

Specializations of the template should define "is_specialized" to be TRUE,
of course.  Only types that are real and scalar would have
std::numeric_limits specializations.  Vector-like types that include the
real numbers, like complex and quaternion numbers, would have "has_real"
TRUE but "is_scalar" FALSE.  Category types, like modulo arithmetic, would
have "has_real" FALSE but "is_scalar" TRUE.  Matrices and true-vectors would
have both "has_real" and "is_scalar" FALSE.  The types of the components is
described as "component_type."  (What would happen with heterogeneous number
types?  Can they exist?)  If the number can be collapsed to a scalar
describing its relative size (indicated with "has_magnitude"), the type of
that size (from an "abs" function) is "magnitude_type."

-- 
Daryle Walker
Mac, Internet, and Video Game Junkie
darylew AT mac DOT com