HP-34C Integrate Memory Usage

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Two publications with regard to the topic at hand:

a) Remarks on Some Modified Romberg Algorithms for Numerical Integration, Numerical Mathematics and Applications (google books), page 57

" SUMMARY. it is shown that the algorithm for numerical integration used in the pocket calculators HP-34C and HP-15C may be regarded as an element in a class of extrapolation algorithm derived from Romberg's classical algorithm by a nonlinear transformation. Some properties of this class are discussed. "


b) Problems and Methodologies in Mathematical Software Production, Lecture Notes in Computer Science 142, ISBN 0-38741603-6 Springer-Verlag New York, 1982, 276 pages

"                                             Preface
     In November, 1980 a week-long International Seminar on Problems and
Methodologies in Mathematical Software Production was held in Sorrento, Italy.
     The Seminar was organized and supported by the National Committee for the
Mathematical Sciences and the National Group for Mathematical Informatics,
both of which are part of Italy's National Council for Research.
Additional Sponsors for the seminar were University di Napoli, AICA, Informatica
Campania (Italsiel).
     The Seminar was intended for university and industrial researchers …
     Their presentations are collected in this book.
…
This paper is a survey of those concepts that are fundamental to the task
of implementing numerical algorithms. In the next section we define computational
software and describe its relation to algorithms and activities in numerical
analysis. In Section 3 we introduce important details of the hardware
environment in which computational software is written and used. In section 4
we define and discuss the concepts of reliability, robustness and transportability.
In the last section we show how all these things affect the design
of an algorithm and its implementation into software. Throughout the paper,
simple examples involving elementary functions and hand calculators illustrate
the ideas discussed. An additional example is presented in an Appendix …
…
     We motivate our concerns for the environment and for the design and imple-
mentation of algorithms by experimenting with some simple programs. Consider
the evaluation of the magnitude of a complex number …
By definition …
This definition corresponds to the theoretical method for determining Izl, and
suggests the obvious algorithm of squaring the components, summing them, and
extracting the square root. Suppose we implement that algorithm on a programmable
hand calculator, a TI 59, say, and run it …
…
     When we try the same experiment on an HP 34C calculator, we obtain … "
etc.

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