Comparing Floating Point Values

Comparing Floating Point Values

[markp]

I was wondering if there was a convention for comparing 2 floats
dealing with significant digits. For example, if I had 2 variables (x
and y) and wanted to see if they were equal in an if statement, is
there a standard way to do a compare based on "x" significant digits?

Thank you.

Re: Comparing Floating Point Values

[Adam Beneschan]

markp wrote:
> I was wondering if there was a convention for comparing 2 floats
> dealing with significant digits. For example, if I had 2 variables (x
> and y) and wanted to see if they were equal in an if statement, is
> there a standard way to do a compare based on "x" significant digits?
>
> Thank you.

I don't do a lot of floating-point programming, so I don't know whether
there's a standard.  I would do something like

   if abs(x-y) <= epsilon * x then --- treat x and y as equal...

where epsilon is some suitable small constant or named number.  But
this really isn't my area of knowledge, and if someone else has a
different idea you should trust theirs rather than mine.  And I
wouldn't call this a "convention", which implies that this is sort of
like a "custom" that everyone agrees to follow; the correct value of
epsilon, and the correct way to compare, really depend on a
mathematical analysis of your particular problem.

                           -- Adam

Re: Comparing Floating Point Values

[Ludovic Brenta]

markp writes:
> I was wondering if there was a convention for comparing 2 floats
> dealing with significant digits. For example, if I had 2 variables (x
> and y) and wanted to see if they were equal in an if statement, is
> there a standard way to do a compare based on "x" significant digits?

The way we usually do this is by defining our own floating-point types
and redefine the "=" operator to deal with the precision appropriate
for the type and the application.  For example:

type Kilograms is digits 6 range 0.0 .. 600_000.0;

function "=" (L, R : Kilograms) is
   Epsilon : constant Kilograms := 0.1;
begin
   if L < R then
      return R - L < Epsilon;
   else
      return L - R < Epsilon;
   end if;
end "=";

The above uses an absolute precision; it would be trivial to use a
relative precision instead.

HTH

-- 
Ludovic Brenta.

Re: Comparing Floating Point Values

[Jeffrey R. Carter]

markp wrote:
> I was wondering if there was a convention for comparing 2 floats
> dealing with significant digits. For example, if I had 2 variables (x
> and y) and wanted to see if they were equal in an if statement, is
> there a standard way to do a compare based on "x" significant digits?

You might want to consider the attribute 'Model_Epsilon.

-- 
Jeff Carter
"English bed-wetting types."
Monty Python & the Holy Grail
15

Re: Comparing Floating Point Values

[Gautier]

markp wrote:

> I was wondering if there was a convention for comparing 2 floats
> dealing with significant digits. For example, if I had 2 variables (x
> and y) and wanted to see if they were equal in an if statement, is
> there a standard way to do a compare based on "x" significant digits?
> 
> Thank you.

Probably you are looking at something like abs(x-y) < 10**(-n)
where n is your amount of digits (not "x" !).
This is an absolute test, you may rather be interested by a relative one.

BTW, it's worth to take a look at...
Ada 95 Quality and Style Guide, 7.2.7:
http://www.adaic.com/docs/95style/html/sec_7/7-2-7.html

HTH
______________________________________________________________
Gautier         -- http://www.mysunrise.ch/users/gdm/index.htm
Ada programming -- http://www.mysunrise.ch/users/gdm/gsoft.htm

NB: For a direct answer, e-mail address on the Web site!

Re: Comparing Floating Point Values

[Steve]

"markp" <markwork66@yahoo.com> wrote in message 
news:1166026474.277616.267400@f1g2000cwa.googlegroups.com...
>I was wondering if there was a convention for comparing 2 floats
> dealing with significant digits. For example, if I had 2 variables (x
> and y) and wanted to see if they were equal in an if statement, is
> there a standard way to do a compare based on "x" significant digits?
>
> Thank you.
>

I am not aware of any standard way of doing this in Ada, but I did port some 
code from C to Ada that does the job for 32 bit IEEE 757 floating point 
values if you're interested.

There is a good article on the subject at:

http://www.cygnus-software.com/papers/comparingfloats/comparingfloats.htm

Steve
(The Duck) 

Re: Comparing Floating Point Values

[Martin]

Steve wrote:
[snip]
> http://www.cygnus-software.com/papers/comparingfloats/comparingfloats.htm

I'd second this - I've used the algorithms before and hightlights the
problems using the solutions provided 'above' in this thread.

Another path could be to ask... "Do I /really/ need to use
Floating-Point or would Fixed-Point be better?"...

Cheers
-- Martin