Structure and Interpretation of Computer Programs
Structure and Interpretation of Computer Programs
Intelligence in scientific computing
Communications of the ACM
Partial evaluation applied to numerical computation
LFP '90 Proceedings of the 1990 ACM conference on LISP and functional programming
HOPL-II The second ACM SIGPLAN conference on History of programming languages
History of programming languages---II
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The typical subroutines that compute sin(x) and exp(x) 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, Taylor series, and economization. Such an approach has many advantages: the code is closer to the mathematical basis of the function, is less vulnerable to errors, and is trivially adaptable to various precisions.