WP 34S solve an integral

[Dieter]

(04-25-2015 06:59 PM)BarryMead Wrote:  Thanks Dieter: By testing convergence precision far away from zero you were able to preserve the relationship between displayed digits and error significance. Normally as a number approaches zero Scientific Notation display modes just reduce the power of 10 and keep the number of significant digits constant. So typically in these modes rounding near zero doesn't help. But by comparing the target value with the integral away from zero you were able to still use rounding to shorten the run time even in SCI, ENG, and ALL display modes. Nice work!

All this works with up to 12 digits – both ROUND and the x≈? commands are limited by the number of displayable digits. Which is perfectly fine for cases like this one where 4 or 5 digits will do since we want to get a fast result.

BTW the Integrate routine uses the same x≈? test, so again 12 safe digits is the best we can get. OK, the actual result usually is more precise since convergence is better than linear and the "exit logic" may add one more iteration "just to be sure". But let's not forget there is another similar test that allows comparing two values in 14, 24 or even 32 digits: the CNVG? test. It's especially useful in DP mode. For instance, replacing x≈? Y with CNVG? 01 would check whether X and Y agree in 24 significant digits.

BTW2: I would love to have a CNVG? test where the number of compared digits can be specified by the user instead of being limited to the three mentioned cases. So that e.g. CNVG? 20 would compare 20 significant digits. Yes, I know the current CNVG? can do a bit more (compare the absolute or relative error, handle NaNs etc), but still...

Dieter