By J. Arndt
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Extra info for Algorithms for Programmers - Ideas, Source Code
A practical compromise is to write a program that, while theoretically not even close to a meta-generator, creates output that, after a little hand editing, is a usable generator code. Further one may want to print the current values of the loop variables inside comments at the beginning of a block. Thereby it is possible to locate the corresponding part (with respect toboth file and temporal location) of a piece of generated code in the original file. In addition one may keep the comments of the original code.
56b) x=0 The inverse transform is again the complex conjugate transform. 57) y=0 which shows that the 2-dimensional FT can be obtained by first applying 1-dimensional transforms on the rows and then applying 1-dimensional transforms on the columns. The same result is obtained when the columns are transformed first and then the rows. This leads us directly to the row-column algorithm for 2-dimensional FFTs. ,R-1][c] // write back column } } Here it is assumed that the rows lie in contiguous memory (as in the C language).
At least for integer sequences one could choose V n (more than two times) bigger than biggest possible value in h(1) and use rounding to nearest integer to isolate h(0) . Alas, even for modest sized arrays numerical overflow and underflow give spurious results. Careful analysis shows that this idea leads to an algorithm far worse than simply using linear convolution. 6 Convolution using the MFA With the weighted convolutions in mind we reformulate the matrix (self-) convolution algorithm given on page 42: 1.
Algorithms for Programmers - Ideas, Source Code by J. Arndt