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

[Adam Beneschan <adam@irvine.com>]

On Thursday, January 17, 2013 2:33:28 AM UTC-8, Ada novice wrote:
> Hello,
> 
>      I have been thinking that since with floating-point representation the distribution of model numbers gets worse (more and more wider spacing) with large numbers leading to less accurate representation of a number, is it better to just go for fixed-point types e.g. in
> 
> 
> type Position is delta 1.0**(-12) range 0.0 to 100_000

This must be a typo ... 1.0**(-12) is just 1, isn't it?

> and define every variable similarly so that we have an equally spaced distribution of the model numbers between the lower and upper bounds?
> 
> Why not just fixed-point types in numerical calculations?
> 
> And why not just use decimal fixed point types as in
> 
> type Velocity is delta 1E-10 digits 15 
> 
> for example if we know what magnitudes of the Velocity are to be expected?
> 
> I understand that it is a question of portability as well as the actual delta that would be used would perhaps not be the same for all machines and for all compilers.

I can think of two reasons why using floating-point may be better, but this depends on the application:

(1) Floating-point numbers have a greater range, because the exponent is part of the number.  Thus, an IEEE 64-bit floating-point value can represent positive numbers as large as 1.7*10**308 or as small as 2.2*10**(-308); a fixed-point number that represented all those possible values would have to have a whole lot of bits.  

(2) Many processors have built-in support for mathematical functions on floating-point values (square root, trig functions, log, e**x).  If your program does lots of those, you'll probably want to use floating-point numbers instead of calling library functions to do the computation (slow) or constantly converting back and forth between fixed- and floating-point.

If neither of those is an issue, then it may be better to use fixed point.

                              -- Adam