Re: [boost] Re: Math Constants Library formal review results

From: James Dennett (jdennett_at_[hidden])
Date: 2001-05-15 07:08:42

Corwin Joy wrote:
> 
> --- In boost_at_y..., "Paul A. Bristow" <pbristow_at_h...> wrote:
> > There has been a lot of dissention about the format of my proposed
> > mathematical constants.
> >  <..snip..> e.g.
> > a collection of
> > namespace math_double_constants
> > {
> >   const double pi = 31459;
> > }
> 
> Not to rain on your parade, but as a mathematician I can tell you
> that what you are doing here is a *bad* idea anyway. 

As a methematician and a programmer, I can tell you that it's
not :)

> If you want to
> do serious numerical work, then I would *strongly* recommend not
> defining PI as a fixed sequence of digits like you do above because
> then you will never be able to take advantage of the full numerical
> accuracy of the machine you are working on. 

Unless you give enough digits, in which case you may well be
able to.

> (Plus, it is less
> portable.)

If compiler problems turning digit strings into numbers are
taken into account, that may be true.

>  Better, is to use constants that are calculated to the
> precision of the machine you are working on e.g.
> const double pi = 4.0 *(atan(0.5) + atan(0.2) + atan(0.125));

It is unlikely that your definition of pi will give the best
accuracy because of errors during the calculation.  A constant
should have an error in (at most) the last binary digit, if
the compiler isn't completely useless.

> If you do something like above
> double pi = 3.15; // (rounded to 2 dp)
> 
> the numerical analysts will likely be displeased.

But if you put enough digits there, they'll be happy.

-- James Dennett