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

[Robin Vowels <robin.vowels@gmail.com>]

On Jan 19, 5:15 am, Dennis Lee Bieber <wlfr...@ix.netcom.com> wrote:
> On Fri, 18 Jan 2013 01:17:37 -0800 (PST), Ada novice <shai.l...@gmx.com>
> declaimed the following in comp.lang.ada:
>
>
>
> > I have read (John Mc Cormick: Building parallel...with Ada's book) that fixed point arithmetic is faster than floating-point arithmetic since integer instructions are faster so I would ask about the second point put by Adam that mathematical functions are slow with fixed-point numbers. Can you please elaborate on that?
>
>         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.
>
>         All these adjustments and tracking are being done at the high-level
> instruction set, not in the processor hardware. In contrast, a floating
> point processor does all the mantissa and exponent adjustments in the
> hardware, which may be faster than having to do things like --
>
> ld i1, 25
> mult i1, 25
> add i1, 5
> div i1, 10

It may not be like that at all.
In the first place, 25 is a constant.
In the second place, adjusting the value (scaling) is achieved
with a shift, not an actual division by 10.
Thus, multiplication is simply
multiply a,b
shift.rounded a

> -- the sequence to treat integer registers as fixed 1-decimal place data
> compared to (the add/div would be added by the compiler based upon the
> number of decimal places to be kept in the result, based upon the number
> of places that were in the source
>
> ld f1, 2.5E0
> mult f1, 2.5E0