namespace math
{
// Generic base class for all constants
template< typename T, template< class > class F > struct constant
{
[snip]
};
I like this idea, especially how it allows the constant to be transparent within an expression.
// And their relationship:
// The user can now write 'pi / two' and needn't remember
// whether it was 'half_pi' or 'pi_by_2' or whatever...
half_pi_t operator/( const pi_t&, const two_t& ) { return half_pi_t(); }
minus_one_t operator-( const one_t& ) { return minus_one_t(); }
one_t operator-( const minus_one_t& ) { return one_t(); }
one_t sin( const half_pi_t& ) { return one_t(); }
This is a very powerful concept, allowing the compiler to simplify certain expressions.
long double r = 0;
for( int i = 0; i < 10000000; ++i )
r = d * -sin( pi / 2. ); // try replacing the "2." by "two" - makes this test program 100x faster!
This is strange, but shows compiler optimization in action:
r = d * -sin( pi_t / two_t ) ==> r = d * -sin( half_pi_t ) ==> r = d * -one_t ==> r = d * minus_one_t
This could be further optimized by adding the rules
T operator*( T val, one_t ){ return( val ); }
T operator*( T val, minus_one_t ){ return( -val ); }
T operator+( T val, zero_t ){ return( val ); }-----
Some general comments:
[1] I agree that custom types should be supported in the constant framework.
[2] The 40 decimal places should be used for irrational numbers (i.e. most mathematical constants like pi, e, sqrt(2)).
[3] Physics-based constants should be definable within the constants framework and should be set to their current accuracy (possibly making use of intervals).
[4] Other types beyond real numbers should be supportable within the constant framework (intervals, matrices, complex numbers, etc), e.g.
matrix2x2 identity( 1, 0, 0, 1 );
Regards, Reece
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