integral competition HP50g vs. DM42

[peacecalc]

Hello folks,

and the winner is....

ahh, I not like to spoiler the result. What was the job of the competitors?

a) Of course numerical, because the hp50g lives in both worlds, the dm42 is only working with numbers.
b) The Fresnel-Integrals have to be calculated.
c) as pair on the stack y-stack has the S(x) result and x-stack contains the result for C(x)
d) hp50g is set in approx. mode and fix 4 (is necessary for accuracy).
dm42 gets 1E-5 for the ACC-variable for controlling accuracy...

e) Definitions of the two Integrals: \[ C(x) = \int_0^x \cos\left(\frac{\pi}{2} \cdot t^2\right) dt \qquad\qquad \hbox{and} \qquad\qquad S(x) = \int_0^x \sin\left(\frac{\pi}{2} \cdot t^2\right) dt \qquad\qquad \qquad\qquad \qquad\qquad \]

f) Maybe a further information, these definite integrals can only calculated numerically. Except for x -> +- infinite.
S(3.9) = 0.4752 and C(3.9) = 0.4223;

DM42 beats the Hp50g in being three times faster by equal accuracy!