It refers to "unit in the last place", essentially the size of smallest
change for a floating point number of a given magnitude. The Wikipedia page
explains more: https://en.wikipedia.org/wiki/Unit_in_the_last_place
Now, there is also this famous paper, which discusses this in great detail:
https:
Hi,
and what is ulps?
/// Jürgen
On 08/15/2015 01:15 PM, Elias Mårtenson
wrote:
Arguably ⎕CT should be specified in terms of ulps,
since GNU APL uses double precision floating point for all
numeric ope
Hi Mike,
page 58 merely says that ⌈ and ⌊ use comparison
tolerance, but not in which way.
And page 133 (floor) says: "using comparison" tolerance and not
"using RFUZZ".
I read page 58 like this:
a) ⎕CT is the same as comparison tol
Arguably ⎕CT should be specified in terms of ulps, since GNU APL uses
double precision floating point for all numeric operations.
On 15 August 2015 at 02:54, Mike Duvos wrote:
> Hi Jürgen,
>
> > Z← R For real numbers, yields the largest integer that does not exceed R
> (within the comparison tol
Hi Jürgen,
> Z← R For real numbers, yields the largest integer that does not exceed R
(within the comparison tolerance).
> That is essentially what ISO says and what GNU APL has implemented. The
observed behavior
> of the IBM APL2 implementation seems to be (within R times the comparison
toleranc
Hi Mike,
the problem with relative ⎕CT is that when the N gets
large, say > ÷⎕CT then N×⎕CT becomes >
1 so the
interval around N where you would round up (for ⌊)
contains one integer or even several. The ISO intention
seems to be that only num
Hi Juergen,
You write...
"Summary: For *⌈* and *⌊* GNU APL follows the ISO standard while IBM APL2
does not."
While this may be the case, I would argue that the APL2 approach is much
more numerically robust than the ISO approach.
Within the range of contiguous integers exactly representable as
Hi,
I have analyzed this issue a little and the following was my
conclusion.
1. when looking at the GNU APL code I found that it could be
simplified a little and I did that, SVN
2. It is perfectly correct that, as Jay pointed out, ⎕CT
Hi Jay,
Thanks. That's an interesting bit of info.
IBM APL2 returns 5. According to the APL2 manual, the system uses relative
tolerance.
With absolute tolerance, as long as they are still using a closed interval
around the number, it should still return 5.
If I fudge 5 by half the comparison
I don't know anything about the GNU APL implementation, but I can tell
you that the definition of tolerant-floor changed between standard APL
(ISO 8485) and Extended APL (ISO 13751). In ISO 8485 the tolerance is
relative, so both your examples should definitely return 5. In
Extended APL the toleran
⌊5-⎕CT
4
⌈5+⎕CT
6
Unless something has drastically changed since I last read the APL spec,
both of these should return 5.
11 matches
Mail list logo
