Re: [boost] Numeric constants

Subject: Re: [boost] Numeric constants
From: John Maddock (john_at_[hidden])
Date: 2009-01-30 11:42:48

>> template <class T> T pi();
>
> I have a fixed-point class.  What actually happens when I call
> pi<fixed>() ?  Presumably the implementation just does "return
> 3.1415...", so fixed::fixed(double) gets called.  Yes my fixed class
> has a constructor that takes a double, and if I'm really lucky it may
> do the conversion at compile time - but more likely it will happen at
> run time.  I would get the same code if you just declared "const double
> pi = 3.1415" (or #defined it).
>
> My 64-bit fixed point type can store more digits of PI than a 64-bit
> floating point value.  But I'm not aware of any way of filling those
> extra digits [ignoring the existence of long double].  Similarly if I
> had an arbitrary precision (i.e. variable length) type, how would it be
> constructed from the 100-digit constants that you mention without
> support from the language (or maybe macros)?
>
> (As for the actual constants, the only ones I find myself using are pi
> and the approximate radius of the earth.)

Currently with Boost.Math if you call:

pi<my_UDT>()

then internally it does a lexical_cast from a string containing ~100 decimal 
digits to my_UDT.  The resulting value is cached for performance reasons, 
but of course that's not thread safe, although it could be made so (still on 
the TODO list though).  So unless my_UDT supports an unfeasably large number 
of digits, you should get pi to the full precision of your type.  We 
currently use this with both NTL::RR and mpfr_class (2 arbitrary precision 
types), and it works very well.  Obviously there are float/double/long 
double specialisations that just return the numeric constant directly (with 
appropriate suffix).  And finally don't forget that you could add 
user-defined full specialisations of the templates for my_UDT if my_UDT 
provides it's own interfaces to various constants.

John.