A quick precision test

[Claudio L.]

(06-06-2014 11:16 AM)pito Wrote:  

(06-06-2014 12:57 AM)Claudio L. Wrote:  ..
I used to trust the results from Alpha blindly (and from the past few posts, I can tell you too). Now I just don't know what to believe, and neither should you from now on.

Claudio

This is with N trailing zeros after the last "4":

Code:

Block[{$MinPrecision = 120}, N[Cos[1.57079632679489661923132169163975144], 130]]

none
0.*10^-35

0
2.09858469968759412260293728493047158318234204531375910645959950911100\
455087648653787132935200077099580084905028343200684*10^-36

00
2.09858469968759412260293728493047158318234204531375910645959950911100\
455087648653787132935200077099580084905028343200684*10^-36

000
2.09858469968759412260293728493047158318234204531375910645959950911100\
455087648653787132935200077099580084905028343200684*10^-36

0000
2.09858469968755291048739331660132323148430199128683081113869140777373\
772224262464875860587211945559288771556897645713391*10^-36

00000
2.09858469968755291048739331660132323148430199128683081113869140777373\
772224262464875860587211945559288771556897645713391*10^-36
..
000000000000000
2.09858469968755291048747229615389016692898991768376891330235232863694\
116237367172368967960981143453674385805543780051439*10^-36


I put the "good" digits in BOLD.
The last one seems to give good 33 digits (well, the last one off by 1 per rounding, but let's not start on that subject again...)

I think it was Paul's error: he asked Alpha "with 120 decimal digits", he should've written "with 120 decimal correctly calculated and correctly rounded digits". See? it was human error, not Alpha.

Claudio