HP 15C and INT(1/√(1-x),0,1)

[Dieter]

(01-11-2018 10:25 PM)salvomic Wrote:  See [url=http://www.hpmuseum.org/cgi-sys/cgiwrap/hpmuseum
Advanced Pac should use Romberg method as HP 15C,

Romberg is not the same as Romberg. ;-) The implementations are different. The IG code is a (slightly modified) "classic" Romberg approach. The HP Integrate code however seems to be a bit more sophisticated as it uses a different sampling method to avoid problems with periodic functions. This was explained in the respective HP Journal Kahan article, cf. August 1980 issue, p. 26: "What method underlies the ∫xy key?":

Quote:The HP-34C uses a Romberg method; for details consult reference 2. Several refinements were found necessary. In stead of uniformly spaced nodes, which can induce a kind of resonance or aliasing that produces misleading results when the integrand is periodic, the ∫xy key's nodes are spaced nonuniformly. (...)

The article continues with further details.

(01-11-2018 10:25 PM)salvomic Wrote:  and timing are comparable, actually (I mean with classic 15, not LE).

The 41C is much faster than the 15C so I'd expect significantly shorter execution times.

(01-11-2018 10:25 PM)salvomic Wrote:  I've both Math and Advantage. The manual of Advantage warns that some functions (complex...) are the same in the module and that would be better not to use both together,

Why? Do they have the same function names so that a calling them can be ambiguous?

(01-11-2018 10:25 PM)salvomic Wrote:  however some functions in Math aren't in Advantage (Fourier, hyperbolic...), some other are in Advantage and not in Math (Vectors, TVM...),

And some are neither in the one nor the other. I would have expected a complete set of complex trig and hyperbolic functions along with their inverses in full precision 13-digit MCode routines.

(01-11-2018 10:25 PM)salvomic Wrote:  However, the integration is more easy in Advantage and not in Math, IMHO.

The Math and Math/Stat ROMs include an integration program (INTG) but, as usual, both the chosen algorithm and the implementation leave significant room for improvement: it's simply the standard Simpson method without any improvements (e.g. as in this example) and the program is not coded particularly well. So on the '41 the Advantage ROM's INTEG seems to be the best choice.

Dieter