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Back in the days that I used to devour everything to do with HP calculators, I remember one of the HP Notes issues which contained a summary explanation of how the Solve and Integrate algorithms worked. If I remember correctly, they were (justifiably) proud of the Integrate feature wherein the function could be undefined at the endpoints of integration.

I'm wondering now, seeing a number of emulators available, whether these algorithms have ever been published in a more detailed form? If an emulator uses a ROM, then I guess there's no coding needed. But if it is a non-ROM emulator, then what would the author do to emulate these functions?

In the PPC-ROM manual is a good description of the Romberg integration. AFAIK there is a PDF/scann of the manual out there somewhere.

Hope this helps


There are several sources for the details of the algorithm:

- the HP-34C Owner's Handbook discusses it at lenght,
giving a lot of useful information

- the HP-15C Advanced Functions manual also discusses it
very thoroughly

- the HP-71B Math ROM manual, ditto

and for the most comprehensive, detailed exposition,
look at this article, written by the very creator
of the algorithm:

"Handheld Calculator Evaluates Integrals"
by William M. Kahan

Hewlett-Packard Journal, August 1980

All those manuals and article are available in the CD set
you can obtain from this Museum of HP Calculators, follow
this link:


The exact reference for the article is:

HP Journal, August 1980 Vol. 31 No. 8


pages 23-32
Handheld Calculator Evaluates Integrals

- The HP-34C is the first handheld calculator to have a key that performs numerical integration almost automatically. It may change your attitude towards what used to be regarded as a dreary tedious task.

by William M. Kahan

reference taken from Craig Finseth's site