Re: Numerical calculations: Why not use fixed point types for everything?

[Adam Beneschan <adam@irvine.com>]

On Friday, January 18, 2013 10:15:06 AM UTC-8, Dennis Lee Bieber wrote:

> 	Integer operations may be faster than floating point... But fixed
> point with a non-zero decimal place add in the overhead of having to
> track where the point is and shifting results to match the declared data
> type.
> 
> 25 * 25 => 725
> 
> 2.5 * 2.5 => 7.25 -- but if the data type is only one decimal place this
> now has to be rounded and shifted to become 7.3.

Perhaps.  But I tend to assume my computer is going to return correct arithmetical results, which none of the above are.  :(

In general, of course you're right that if your values aren't represented with enough precision, or with a scale factor that will require rounding, you're going to run into problems.  But of course that's a problem with floating-point as well as with fixed-point.  If the range of values is small enough, you can actually declare fixed-point types that have greater precision than the available floating-point types.  And how much precision is necessary depends on the problem domain.  And there's no reason to assume that all values in your program have to have the same scale factor--in fact, Ada's definition of fixed-point multiplication and division operations supports cases where an intermediate result may have more precision than the operands, and rounding can wait until the final expression result is computed.

                        -- Adam