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+--- Thread: WP34s: Domain Error in RMDR and MOD (/thread-4982.html)
WP34s: Domain Error in RMDR and MOD - Dieter - 10-21-2015 12:13 PM
I just noticed a strange behaviour of the RMDR and MOD functions. For large arguments they may return a "Domain Error". Some further investigation showed that these functions seem to work for y < 1E820 · x, and as soon as y gets larger the error occurs:
Code:
[DBLON]
[EEX] 820 [ENTER] 360 [x] => 3,6 E+822
360 [RMDR] => Domain Error
[MOD] => Domain Error
[x<>y] [ENTER] [ULP] [-] => 3,599999999999999999999999999999999 E+822
360 [RMDR] => 80Since the arguments are out of range in single precision mode, all this happens only after switching to double precision.
Any idea what's going on here?
Dieter
RE: WP34s: Domain Error in RMDR and MOD - Paul Dale - 10-21-2015 09:39 PM
The decNumber mod function isn't efficient and requires enough digits to represent the source numbers and the result (i.e. 2*384 + 16). I increase the number of carried digits for these operations to a little above this so that single precision never fails. I didn't go as far as supporting double precision -- there isn't sufficient RAM to do this directly.
Making double precision inputs work across the entire range will require a different algorithm and since we don't guarantee any results in double precision I didn't bother
- Pauli
RE: WP34s: Domain Error in RMDR and MOD - Dieter - 10-22-2015 01:00 PM
(10-21-2015 09:39 PM)Paul Dale Wrote: The decNumber mod function isn't efficient and requires enough digits to represent the source numbers and the result (i.e. 2*384 + 16). I increase the number of carried digits for these operations to a little above this so that single precision never fails.
Wait... does this mean that RMDR and MOD internally use 400+ digits?
(10-21-2015 09:39 PM)Paul Dale Wrote: Making double precision inputs work across the entire range will require a different algorithm and since we don't guarantee any results in double precision I didn't bother
OK. Maybe a table with such restrictions would be helpful. I am also thinking of the distributions, Gamma and Beta with extreme cases of their parameters.
Dieter
RE: WP34s: Domain Error in RMDR and MOD - Paul Dale - 10-22-2015 09:57 PM
Mod uses 450 digits internally.
Modulo reduction by two pi for the trig functions uses 820.
So in double precision, neither is adequate to support the entire range.
Pauli