It’s 1979 – What Exactly Did That ∫ Key Do?

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[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 elegant at certain types of problem, but fall apart when applied to others. The Romberg-Kahan algorithm is the only one that never throws up its hands in failure; ideal for a general-purpose scientific calculator that knows only what its operator keys in, and not a lick more.

It’s a pretty neat fact about classic HP calculators, and an interesting bit of historical context for these machines. Should you wish for something a bit more tactile and don’t mind some DIY, it’s entirely possible to re-create old HP calculators as handhelds driven by modern microcontrollers, complete with 3D-printed cases.

Thanks to [Stephen Walters] for the tip!



from Blog – Hackaday https://ift.tt/gBkKur1

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