OpenEuphoria

Re: Remainder

• Posted by Robert Craig <rds at RapidEuphoria.com> Nov 08, 2003
• 792 views

kbochert at copper.net wrote:
> A solution is to observe the bit pattern of the double generated by X/Y
> and correct the case where it is a single bit less than a whole number.
> 
> In C: (and without sign stuff)
>    double rem( double X, double Y)
>        struct {
>            double d;
>            long L[2];
>            } z;
>        z.d = X / Y;
>        if (L[0] == -1) {
>            L[0] = 0;
>            ++L[1];
>            } ;
>         return X - floor (z) * Y
>      }
> 
> (Basically, if X is a multiple of Y, then the error case division produces
> a double whose bit pattern looks something like:
> 0x0048FFFFFFFFFFFF  )
> 
> This works very nicely on all cases I have tried where X is a multiple
> of Y, and at worst, decreases the accuracy of a very few remainders()
> ( 1 in 65k?) by a single bit.
> 
> 
> How do you do this in EU??

You have my source. In runtime.c, Dremainder(),
you can see that I just call the C fmod() function,
which I assume executes an Intel instruction.
I also have a cryptic comment "for now". I don't remember
why I said that. Maybe I thought there was a speed optimization
I could do.

I never attempt to "fix" problems due to finite
floating-point accuracy. Most languages that I'm aware of
leave it to the programmer to handle situations like this.

One exception is APL, which has a concept called
"comparison tolerance" or "fuzz".
In APL if two numbers are the same to about
13 digits (as I recall) then APL considers them to be exactly equal.
The programmer can adjust this value up or down if he wants.
This fuzz value pervades the whole APL system.
I believe it also affects operations like floor and remainder,
just like your idea above, but the differences
can be much more than 1 bit.

The fuzz factor idea solves a lot of problems,
but you can have weird cases where for example
   A = B and B = C but A != C

I don't think computer science types
are happy with the idea.

Regards,
    Rob Craig
    Rapid Deployment Software
    http://www.RapidEuphoria.com