I think I got it!Xerxes a écrit :...
The differences between MODE10/11 are not obvious sometimes:
The evaluation of "1/23" gives 0.04347826087 but "FRAC(1/23*1E3)" gives
This is the reason for the higher accuracy of the Frolov test using MODE11.
Shortly: MODE11 prevents the CASIO for "cheating" and trying to round-down to display "nice round integers". MODE10 (or switch on/off) resets the unit to "integer cheating".
Don't blame me for using such terminology, here is what I saw yesterday trying to figure out the meaning of these hidden modes:
And just for the test as explained on the above page:
123456789 + .008 - 123456789 -> Mode10: 0.008 mode11: 0.008
123456789 + .007 - 123456789 -> Mode10: 0 mode11: 0.007
... ... for .006 to .001 the default MODE 10 truncates attempting to show "nice integer", and the MODE11 gives the fair result.
I will quote John Meyers:
So this is the meaning of MODE10/11: turning of this truncation. That is why it gives better result for Frolov's test, because the truncation is mostly one direction - down. The cumulative error for the default MODE10 can be significant, but the error of the full mantissa of MODE11 may compensate this accumulation, because in is in the both directions.Here's the scoop: Every time this type of Casio calculates a numeric result,
it looks at the last three digits of the internal "mantissa" (the significant
digits of the truncated result); if these digits are anywhere in the range
001 thru 007, your Casio just lops off these digits, presuming that the
"correct" result *should* have ended with 000; similarly, if the last
three mantissa digits of the truncated result are in the range 993-999,
your helpful FUDGING Casio "fixes up" that result for you by
ROUNDING IT UP until its last three digits are 000 !!!
Correct : 674530.471
Finally, it is not fair from CASIO not to document this feature and the option to control it. Improperly made algorithm where summation occurs may lead to significant final accumulated error.