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Subject: RE: [office-comment] Error in FLOOR function specification

I don't understand the statement that the result is undefined when x and p have opposite signs.  Since we're talking about *integer* multiples, it is completely well-defined to say that


is the largest multiple of p not greater than x so long as p is not zero.  It may be that the multiplier has different sign than p to make this happen, and that is already the case for floor(-12.5,1) which I have not seen any objection to.

It may be that some library functions are defined with that case undefined, but there is no mathematical reason for it.

 - Dennis

PS: It does not matter whether I believe the statement in the OpenFormula text is in error or not. I am not on the ODF TC and not the one to make any repairs to the specification (although sometimes my advice is useful to the TC).  The way to see what the ODF TC is making of this is to see what happens when a JIRA issue on your comment is created.  The JIRA is viewable by the public at <https://issues.oasis-open.org/browse/OFFICE/>.

-----Original Message-----
From: cowan@ccil.org [mailto:cowan@ccil.org] 
Sent: Tuesday, February 24, 2015 06:38
To: dennis.hamilton@acm.org
Cc: 'Joel'; office-comment@lists.oasis-open.org
Subject: RE: [office-comment] Error in FLOOR function specification

Dennis Hamilton scripsit:
[ ... ]

> In particular, floor(x) is the largest integer not greater than x,
> ceiling(x) is the smallest integer not less than x.  Similarly, floor(x,p)
> is the largest integer multiple of p not greater than x and ceiling(x,p)
> is the smallest integer multiple of p not less than x.

That's the way it should be defined, yes.  But when x and p have
opposite signs, the result is undefined, and the standard needs
to take that into account.

[ ... ]

Now arguably it would be better to rewrite floor and ceiling completely
to provide the mathematical definition, and then provide exception
clauses for the p = 0 (same as p = 1 for positive x and p = -1 for
negative x) and opposite-sign cases.

But in the meantime, the existing definition of floor is wrong
as written, and that can be fixed by replacing "away from zero"
with "toward zero".  Please take the time to convince yourself
that this is true.

John Cowan          http://www.ccil.org/~cowan        cowan@ccil.org
In computer science, we stand on each other's feet.  --Brian K. Reid

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