It’s 1979 – What Exactly Did That ∫ Key Do?
[Michel Jean] asked a question few others might: what exactly is going on under the hood of a classic HP scientific calculator when one presses the ∫ key ? A numerical integration, sure, but how exactly? There are a number of useful algorithms that could be firing up when the integral button is pressed, and like any curious hacker [Michel] decided to personally verify what was happening. [Michel] implemented different integration algorithms in C++ and experimentally compared them against HP calculator results. By setting up rigorous tests, [Michel] was able to conclude that the calculators definitely use Romberg-Kahan, developed by HP Mathematician William Kahan. Selected by HP in 1979 for use in their scientific calculators, the Romberg-Kahan algorithm was kept in service for nearly a decade. Was it because the algorithm was fast and efficient? Not really. The reason it was chosen over others was on account of its robustness. Some methods are ridiculously fast and tremendously e...