In a recent article 2, it was shown that function samples for all functions composed of the elementary functions can be computed using two operators, By and Times, which deliver samples of the maximum possible order for linear combinations and products of functions. The article highlighted the simplicity of the exposition, but made no attempt to modify algorithms to improve the speed of calculations. In particular, it was noted that the APL functions took around three seconds to obtain the values of the first ten derivatives of the test function ( x csc x )/ log arctan exp x while Mathematica 2.0 obtained the same results in about a second. The APL functions, however, were also able to obtain these derivatives at any number of points, and the calculation for 100 points took approximately 18 seconds. This article will show how a simple adjustment can significantly reduce these execution times.
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Speeding times
Spunde, Walter G.
Follow ACM SIGAPL APL Quote Quad
, Volume 24 (3)
Association for Computing Machinery – Mar 1, 1994
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