Hi Jerry
Thanks for your reply, which is a useful correction to my remark.

I agree that this is a round-off issue. For example,
in computing 1+x-x with x=1E-8 I obtain 9.999999939225290E-09, which is in
error by only the last figure if I round off at 7 decimal places, or eight
figures. If I use x=1E-14, I get 9.9920072E-15, and at x=1E-15 I get zero. So
I conclude that due to round-off 1+x-1 will exhibit increasing inaccuracy as
x shrinks to values where 1+x to only 15 figures is simply 1. That results
in 8 figure accuracy in 1+x-1 for x in approximately the range 1E-8 to 1E-10.

I suppose the merit in calling round-off issues not an "error in basic
arithmetic", but a "finite precision issue" is that it means Excel is no
worse than other software with the same finite precision issues? Isn't there
other software, however, with different precision issues?



"Jerry W. Lewis" wrote:

You are not thinking in terms of finite precision mathematics. Consider
x=1/3/10^8. With 15 figure accuracy, your calculation would be

1.00000000000000
.00000000333333333333333
-----------------------------------
1.00000000333333
-1.00000000000000
-----------------------------------
0.00000000333333

The final result only caries 6 figures, not because any operation involved
less than 15 figures, but because most of those 15 figures were wasted on
accurate representation of the 1 in 1+x, with the result that most of the
accuracy for x was lost.

On top of the basic issues of finite mathemetics, you also must consider
that most terminating decimal fractions (such as 1E-1) are non-terminating
binary fractions that can only be approximated (just as 1/3 can only be
approximated as a decimal fraction), and hence you will see some of these
finite precision issues in "simple" calculations where you don't expect them
to be relevant.

I am not aware of any instance where Excel performs basic arithmetic
incorrectly.

Jerry

"engineer" wrote:

I don't know if you count it as an error exactly, but try calculating the
formula y= 1+x-1, which should result in the value x. If x is small, say
1E-8, and you display the result of the calculation to say 12 figures, you
will find the result is not x, but may be more or less than x depending on
the value chosen. Accuracy exists only to 8 sig figs, despite claims that
Excel has 15 figure accuracy.

"Clarkinson" wrote:

Hi,
We had this guy in the office today making out that it was easy to find
faults in Computer software.
He claimed it was easy to show and prove that Excel calculates eroneously.
He didn't specify how or under what cirmstances and didn't have time to do a
demonstration.

Anyone else heard of this?

I check "Excel makes mistakes" on Google and found a few articles dated 2003
dealing with a statistical covariance problem .

Apart from that, nothing much. Is there something I've been missing ?

TIA,
EJC