An oddity if not a bug

A1:
=FACT(9)/FACT(6)/FACT(3) returns 84, as it should

A2:
=COMBIN(9,3) returns 84, as it should

A3:
=A1=A2 returns TRUE

A4:
=A1-A2 returns 0

A5:
=MOD(A4,1) returns 0

A6:
=MOD(A1,1) returns 0

A7:
=MOD(A2,1) returns -1.42109E-14

So the @#$% fudge factor strikes again, or does it? Shouldn't it affect
the evaluated value of cell A2 with the final result for A2 an integer?
This shouldn't be. If cell A4 is zero with no remainder in A5, why
should A7 have a remainder?

Same results in 2003 and 2007.

Don't know the reason but I've read posts by Jerry Lewis that cover this:

=A1-A2 = 0

But:

=(A1-A2)=0 returns FALSE

So you'd think that A5: =MOD(A4,1) should have a remainder. Or is that the
fudge factor in effect?

Biff

"Harlan Grove" wrote in message
oups.com...
A1:
=FACT(9)/FACT(6)/FACT(3) returns 84, as it should

A2:
=COMBIN(9,3) returns 84, as it should

A3:
=A1=A2 returns TRUE

A4:
=A1-A2 returns 0

A5:
=MOD(A4,1) returns 0

A6:
=MOD(A1,1) returns 0

A7:
=MOD(A2,1) returns -1.42109E-14

So the @#$% fudge factor strikes again, or does it? Shouldn't it affect
the evaluated value of cell A2 with the final result for A2 an integer?
This shouldn't be. If cell A4 is zero with no remainder in A5, why
should A7 have a remainder?

Same results in 2003 and 2007.

So you'd think that A5: =MOD(A4,1) should have a remainder. Or is that the
fudge factor in effect?

There it is:

=MOD((A1-A2),1)

1.4210854715202E-14

Biff

"Biff" wrote in message
...
Don't know the reason but I've read posts by Jerry Lewis that cover this:

=A1-A2 = 0

But:

=(A1-A2)=0 returns FALSE

So you'd think that A5: =MOD(A4,1) should have a remainder. Or is that the
fudge factor in effect?

Biff

"Harlan Grove" wrote in message
oups.com...
A1:
=FACT(9)/FACT(6)/FACT(3) returns 84, as it should

A2:
=COMBIN(9,3) returns 84, as it should

A3:
=A1=A2 returns TRUE

A4:
=A1-A2 returns 0

A5:
=MOD(A4,1) returns 0

A6:
=MOD(A1,1) returns 0

A7:
=MOD(A2,1) returns -1.42109E-14

So the @#$% fudge factor strikes again, or does it? Shouldn't it affect
the evaluated value of cell A2 with the final result for A2 an integer?
This shouldn't be. If cell A4 is zero with no remainder in A5, why
should A7 have a remainder?

Same results in 2003 and 2007.

Biff wrote...
So you'd think that A5: =MOD(A4,1) should have a remainder. Or is that the
fudge factor in effect?

There it is:

=MOD((A1-A2),1)

1.4210854715202E-14
....

I hadn't thought of that, but this is still a bug. COMBIN should *only*
return integers or error values. If both its arguments are numbers,
it'll truncate them to integers, e.g., COMBIN(7.2,2.9) returns the same
result as COMBIN(5,2). If its arguments are integers, then numerically
it can only return integers.

If its result would be beyond Excel's capacity, e.g., COMBIN(1030,515),
no problem having it return #NUM!. If its result would take more than
15 decimal digits, no problem that it'd be only approximately correct
to 15 decimal digits (and it'd also be an integer). But when it could
easily be represented in 15 or fewer decimal digits, there's no excuse
for it not to be an integer.

FWIW, the standard approach when N gets large enough that FACT(N)
exceeds 15 decimal digits is to use
EXP(GAMMALN(N+1)-GAMMALN(k+1)-GAMMALN(N-k+1)), but in the case of N=9
and k=3, this returns 84.0000000106965, while (COMBIN(9,3)-84) is
negative. Leaves me wondering how Microsoft is calculating this.

this is still a bug. COMBIN should *only*
return integers or error values.

I agree and had always assumed as much. This little exercise proves
otherwise.

=MOD((COMBIN(9,3)-84),1)

Returns 1.

Biff

"Harlan Grove" wrote in message
oups.com...
Biff wrote...
So you'd think that A5: =MOD(A4,1) should have a remainder. Or is that
the
fudge factor in effect?

There it is:

=MOD((A1-A2),1)

1.4210854715202E-14
...

I hadn't thought of that, but this is still a bug. COMBIN should *only*
return integers or error values. If both its arguments are numbers,
it'll truncate them to integers, e.g., COMBIN(7.2,2.9) returns the same
result as COMBIN(5,2). If its arguments are integers, then numerically
it can only return integers.

If its result would be beyond Excel's capacity, e.g., COMBIN(1030,515),
no problem having it return #NUM!. If its result would take more than
15 decimal digits, no problem that it'd be only approximately correct
to 15 decimal digits (and it'd also be an integer). But when it could
easily be represented in 15 or fewer decimal digits, there's no excuse
for it not to be an integer.

FWIW, the standard approach when N gets large enough that FACT(N)
exceeds 15 decimal digits is to use
EXP(GAMMALN(N+1)-GAMMALN(k+1)-GAMMALN(N-k+1)), but in the case of N=9
and k=3, this returns 84.0000000106965, while (COMBIN(9,3)-84) is
negative. Leaves me wondering how Microsoft is calculating this.

Biff wrote...
this is still a bug. COMBIN should *only*
return integers or error values.

I agree and had always assumed as much. This little exercise proves
otherwise.

=MOD((COMBIN(9,3)-84),1)

Returns 1.
....

Actually, it returns 0.999999999999986. And don't get me started on
MOD.

With all boils in need of lancing in Excel, what does Microsoft do?
Give it a nose job.

With all boils in need of lancing in Excel, what does Microsoft do?

Enhance the charting "experience" ?

Did you see that post at http://blogs.msdn.com/excel/default.aspx ?

A "user experience designer" ? WTF is that?

That's what MS is interested in. Zen fluff!

Biff

"Harlan Grove" wrote in message
ups.com...
Biff wrote...
this is still a bug. COMBIN should *only*
return integers or error values.

I agree and had always assumed as much. This little exercise proves
otherwise.

=MOD((COMBIN(9,3)-84),1)

Returns 1.
...

Actually, it returns 0.999999999999986. And don't get me started on
MOD.

With all boils in need of lancing in Excel, what does Microsoft do?
Give it a nose job.

But if A8 = COMBIN(9,3)-84 it appears to properly return 0
and if A9 = MOD(A8,1)

it also appears to properly return 0.

"Harlan Grove" wrote:

Biff wrote...
this is still a bug. COMBIN should *only*
return integers or error values.

I agree and had always assumed as much. This little exercise proves
otherwise.

=MOD((COMBIN(9,3)-84),1)

Returns 1.
....

Actually, it returns 0.999999999999986. And don't get me started on
MOD.

With all boils in need of lancing in Excel, what does Microsoft do?
Give it a nose job.

That's the "fudge factor" Harlan was talking about.

The result is not EXACTLY zero but the difference is so extremely small that
Excel "fudges" the result to be 0.

But if A8 = COMBIN(9,3)-84 it appears to properly return 0

Try this:

=(COMBIN(9,3)-84)=0

Jerry Lewis has explained that a test for true equality must be done this
way. Look for some of his posts where he gets into great detail about this.
It's really complex and quite educational.

Biff

"JMB" wrote in message
...
But if A8 = COMBIN(9,3)-84 it appears to properly return 0
and if A9 = MOD(A8,1)

it also appears to properly return 0.

"Harlan Grove" wrote:

Biff wrote...
this is still a bug. COMBIN should *only*
return integers or error values.

I agree and had always assumed as much. This little exercise proves
otherwise.

=MOD((COMBIN(9,3)-84),1)

Returns 1.
....

Actually, it returns 0.999999999999986. And don't get me started on
MOD.

With all boils in need of lancing in Excel, what does Microsoft do?
Give it a nose job.

Thanks for the suggestion, it is educational.

From one of Jerry's posts, it seems that excel may/may not apply a fudge
factor when nesting functions -or am I misunderstanding?

I was aware of the 15 digit limits and the binary fraction issue, but, as
Harlan stated, there's no apparent reason for Combin to apply the fudge
factor in this case.



"Biff" wrote:

That's the "fudge factor" Harlan was talking about.

The result is not EXACTLY zero but the difference is so extremely small that
Excel "fudges" the result to be 0.

But if A8 = COMBIN(9,3)-84 it appears to properly return 0

Try this:

=(COMBIN(9,3)-84)=0

Jerry Lewis has explained that a test for true equality must be done this
way. Look for some of his posts where he gets into great detail about this.
It's really complex and quite educational.

Biff

"JMB" wrote in message
...
But if A8 = COMBIN(9,3)-84 it appears to properly return 0
and if A9 = MOD(A8,1)

it also appears to properly return 0.

"Harlan Grove" wrote:

Biff wrote...
this is still a bug. COMBIN should *only*
return integers or error values.

I agree and had always assumed as much. This little exercise proves
otherwise.

=MOD((COMBIN(9,3)-84),1)

Returns 1.
....

Actually, it returns 0.999999999999986. And don't get me started on
MOD.

With all boils in need of lancing in Excel, what does Microsoft do?
Give it a nose job.