"Prof Wonmug" wrote:
On Tue, 28 Apr 2009 07:12:12 -0700, Jim Thomlinson
Why calculate a constant?

Accuracy, portability, compatibility?

It should be noted that Jim is referring to the expression 4*Atn(1). That
does not ensure accuracy or compatilibity.

Atn is a transcendental function, which is typically estimated using a
polynomial algorithm. Moreover, VBA sometimes uses different algorithms
than Excel for similar functions. I was pleasantly surprised to learn that
4*Atn(1) has exactly the same binary result as Excel's PI function. There
was certainly no guarantee that would be the case.

On the other hand, Wonmug had used WorksheetFunction.PI(). I do agree that
that is better than a constant for ensuring compatibility with the Excel PI
function with the same accuracy.

Entering a constant with decimal fractions that is not exactly the sum of up
to 53 consecutive powers of 2 might not be portable. I don't know if the
IEEE specifies a standard conversion algorithm. But it is clear that Excel
and VBA treat numbers with more than 15 significant digits differently.

Even within 15 significant digits, I have seen constants where the Excel
conversion could be improved by adding 1 or 2 to the least significant bit.
So I can imagine that different implementations of Excel and VBA could do
the conversion differently. (But I don't know if that would violate a
conversion standard, if any.)