Re: fixed point vs floating point

[Geert Bosch <geert@gonzo.sun3.iaf.nl>]

Matthew Heaney <mheaney@ni.net> wrote:
 ``If my abstraction calls for a real type having an absolute error and not a
   relative error, then clearly a fixed point type is called for, even if it's
   less efficient, right?  Isn't it always true that we should code for
   correctness first, by using a type that directly models the abstraction,
   and then optimize only if necessary?  Are you making an exception to this
   rule for fixed point types?

   You seem to be suggesting - in the name of efficiency - that we convert a
   fixed point number into a floating point, calculate the sine, and then
   convert the result back into fixed point.  OK, fair enough, but what is the
   accuracy of the result?  ''

The fixed point type is the abstraction that you do calculations with
when you are calculating with currencies for example. The heading of a ship
is of course a real value. So any difference between this real value and
the calculated one (whether fixed or float) is error for you.

When converting a real value between 0.0 and 360.0 to a value in radians and
then taking the sine using floating pt you will have a result that has
a certain relative error. Since you also know that the result
interval is in -1.0 .. 1.0, you have a result with a known absolute
precision. 

On typical hardware this absolute error will be much smaller than 1.0E-12.

Regards,
   Geert

Disclaimer: I'm not a numerical analyst!