integral competition HP50g vs. DM42

[peacecalc]

Hello Didier Lachieze,

thank for answering my last question. And very much thanks about showing the sources. Now i know the meaning of 41Z.

@Stevetuc
It is as I supposed: of course it is not possible to integrate a complex value in one step.
The Solution that Jean-Marc Baillard used to calculate the fresnel integrals is a function which is expressed as a finite serie (for |x| < 1) and a approximation |x| < 2. It isn't an numerical integration.

So all calculations with complex numbers are implented as a kind of vector calculus. You have a dual vector space with a special "cross product" rule:

\[ \left(\array{e \\ f}\right) = \left(\array{a \\ b}\right) \cdot \left(\array{c \\ d}\right) = \left(\array{ac - bd \\ bc + ad}\right)\]

So every addition, subtraction and so on doubles the computational costs.
And if you have one processor with one kernel, you have to do one step after the other.

@Thomas Okken: for the estimation of accuracy of complex integrals, why there are problems? It would be enough to show that the |R(z)| < epsilon or is there something I not see? R(z) could be a kind of circle which can small enough?