Accuracy and the power function

[Joe Horn]

(02-16-2014 02:43 PM)Dieter Wrote:  Let's assume \(2\large\pi\) = 6,28318530718, i.e. the best possible 12-digit value. Now evaluate some powers of this:

\(6,28318530718^{-76}  =  2,179 3651 6466 35... · 10^{-61}\)
\(6,28318530718^{ 200}  =  4,324 8761 1401 74... · 10^{ 159}\)
\(6,28318530718^{ 372}  =  8,373 5772 1132 00... · 10^{ 296}\)

The middle example contains an extraneous digit near the end. It should read:
\(6,28318530718^{ 200} = 4,324\ 8761\ 1407\ 46... · 10^{ 159}\)

Quote:Please try this with your 12-digit HP and see what you get.

On the HP 50g, the errors on these calculations are 1 ULP, -1 ULP, and -4 ULP, respectively.