(34S) Integration (using the double-exponential method)

[Dieter]

(03-24-2017 02:21 PM)emece67 Wrote:  This is my implementation of the double exponential integration method for the wp34s.

Looks like a nice and carefully coded program. Let me ask a few questions:

There is a logic that calculates an epsilon value depending on the display setting. This seems to work fine in FIX mode. But how does this work in SCI/ENG or ALL mode? Note that (unlike RDP) ROUND rounds 1/9 to at most 11 places. Or a certain number of significant digits in SCI/ENG mode.

At LBL 40 the program checks if the integration variable is within the integration limits. This is done by calculating the current x and comparing it to tm in R.06. In such cases I always wonder if roundoff errors might not lead to an error here. Suppose tm is 2 and h*j rounds to 2,000000000000001 so that the test returns false. Can this possibly happen? A simple counter would be a safe solution.

Very small values of the integral, e.g. 1E–16, may be calculated because the actual value is zero, but just as well the correct value of the true integral. Is the program able to distinguish these two cases?

BTW, Pi/2 is directly available as CNST 86. ;-)

Dieter