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Abstract: The typical subroutines that compute sin(z) and exp(z) bear little resemblance to our mathematical knowledge of these functions: they are composed of concrete arithmetic expressions that include many mysterious numerical constants. Instead of programming these subroutines conventionally, we can express their construction using symbolic ideas such as periodicity and Taylor series. Such an approach has many advantages: the code is closer to the mathematical basis of the function, less... (Update)
Context of citations to this paper: More
.... became interested in numerical applications and in the use of Lisp to generate and transform numerical programs [Sussman, 1988; Roylance, 1988] Sussman also spent a fair amount of time at MIT teaching Lisp to undergraduates. Sussman thought it was absolutely crazy to have...
...into expressions that can be optimized and compiled. 5. 1 Constructing functions from their Defining Properties Gerald Roylance shows [52] how many standard mathematical functions can be constructed from their defining properties, instead of specified as a sequence of obscure...
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BibTeX entry: (Update)
Roylance, Gerald. Expressing mathematical subroutines constructively. In [ACM LFP, 1988], pp. 8--13. http://citeseer.ist.psu.edu/roylance87expressing.html More
@inproceedings{ roylance88expressing,
author = "G. Roylance",
title = "Expressing Mathematical Subroutines Constructively",
booktitle = "Proceedings of the 1988 {ACM} Conference on {LISP} and Functional Programming, Snowbird, {UT}",
publisher = "ACM",
address = "New York, NY",
pages = "8--13",
year = "1988",
url = "citeseer.ist.psu.edu/roylance87expressing.html" }
Citations (may not include all citations):430 Structure and Interpretation of Com- puter Programs (context) - Abelson, Sussman - 1985
230 Handbook of Mathematical Func- tions with Formulas (context) - Abramowitz, Stegun - 1972
25 Digital Press (context) - Jr, Lisp - 1984
5 Numerical Methods That Work (context) - Acton - 1970
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