A quick precision test

[Gerson W. Barbosa]

(06-02-2014 10:37 PM)pito Wrote:  A friend of mine has advised me today there is following quick precision test when testing better calculators in the shop:

Take 1.0000001 and do x^2 27times..

This is from an old Scientific American article, "How to handle numbers with thousands of digits, and why one might want to", by Fred Gruenberger (Computer Recreations, April 1984). ( "Come e perché trattare numeri con migliaia di cifre", in Le Scienze )

In double precision the WP 34S return:

674530,4707410845593826891847277722

Comparing this result with

674530,4707410845593826891780297468 ( 1,0000001 ENTER 27 f 2^x f y^x )

we get

Percent error = 9,92990782557e-25 ( excellent! )

As a comparison, Hewlett-Packard 33, 67, 41C returns

"674494,0561"

Percent error = 0,00540 ( not so bad in 1984 )

Regards,

Gerson.

Note: "DECIMAL-POINT IS COMMA"