Calculating e^x-1 on classic HPs

[Dieter]

(01-14-2016 06:50 PM)Gerson W. Barbosa Wrote:  Here is my plan B for the hyperbolic function approach:
(...)
No additional tests required.

Sorry, Gerson, but I simply could not resist. ;-)
So I ran the 34s test program once again with this method. Here are the results:

Code:

seed = 0,815            n = 100000

ULP    Kahan    alternate   plan B
----------------------------------
 -9        2          -          -
 -8        4          -          -
 -7        7          -          -
 -6       12          -          -
 -5       32          2          2
 -4       60        101        229
 -3      331         58       1852
 -2     4580         74       8025
 -1    22325      16788      20825
 ±0    45193      65769      38405
 +1    22323      16935      20652
 +2     4667         69       7973
 +3      326         78       1792
 +4       64        126        241
 +5       34          -          4
 +6       16          -          -
 +7       12          -          -
 +8        9          -          -
 +9        3          -          -

Kahan = method posted by Pauli, probably due to W. Kahan
alternate = method I suggested in this thread
Plan B = hyperbolic method suggested by Gerson

All results for random arguments in [ln 0.9, ln 2].

Edit: Table extended to show errors up to ±9 ULP. Larger errors were not detected.

Dieter