Re: [boost] [Review][PQS] Review deadline

From: Leland Brown (lelandbrown_at_[hidden])
Date: 2006-06-09 17:40:43

Paul A Bristow <pbristow <at> hetp.u-net.com> writes:

> |   (And BTW, it did find several bugs in my 
> |  computations by flagging dimensions problems!)
> 
> Can you elaborate a little on the value of using a dimensional analysis by
> sharing some of these with us?

One example I was able to dig up was in approximating a function's derivatives 
using finite differences.  In simplified form, my code had looked something 
like this:

   length f( time t );
   ...
   t3_quantity t  = // some time value
   t3_quantity dt = // some time value
   ...
   t3_quantity x    = f(t);
   t3_quantity xdot = f(t+dt) - x;  // incorrect!
   ...
   velocity v = xdot;  // runtime error caught here!

The erroneous line should have been:

   t3_quantity ydot = ( f(t+dt) - x ) / dt;

I had left out the division, which changes the units.

Incidentally, when using t1_quantity or t2_quantity types, the error would be 
caught at compile-time, and on the line actually containing the error:

   time t  = // some time value
   time dt = // some time value
   ...
   length   x    = f(t);
   velocity xdot = f(t+dt) - x;  // error here - caught by compiler!

(Because these errors are caught at compile-time, and thus usually before the 
code is checked in, the fixes don't appear in the change history, so I can't 
produce actual examples I've encountered for those cases.)

Another example is my mistake in an earlier post, where I tried to show code 
taking sqrt(acceleration/length) to get a time value.  But actually it gives a 
frequency, so if the error were not corrected I'd get the reciprocal of the 
value I want.  Dimensional analysis would prevent the invalid assignment from 
occurring.

-- Leland