Re: Question about best practices with numerical functions

["Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de>]

On 06/07/2020 19:02, Shark8 wrote:

> One way to do this would be to use fixed-point types:
> (1) Convert your input to the fixed-point that has a "good enough" delta for the precision you want.
> (2) Run the algorithm.
> (3) Convert back to your normal value-type.
> This assumes you're using floating-point or integers, but one nice thing about fixed-point is that it has a bounded error when dealing with operations, unlike floating-point. -- I remember some years ago seeing a bug report dealing with floating-point, where the particular error simply couldn't have happened with fixed-point.

Rounding error is bounded in both cases. Fixed-point has same error 
regardless the values involved in the operations. Floating-point has 
error depending on the values.

I would say that floating-point error would be roughly same for 
addition, subtraction and multiplication, provided fixed-point does not 
overflow. It will be hugely better for division.

Using fixed-point arithmetic has only sense for a few marginal cases of 
rounding.

Furthermore converting many algorithms to fixed-point might turn quite 
non-trivial as you will have to ensure absence of overflows and 
underflows. Where floating-point computation just would lose some 
precision, fixed-point will catastrophically fail.

-- 
Regards,
Dmitry A. Kazakov
http://www.dmitry-kazakov.de