By Arndt J.

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Implementing such a metagenerator of course is highly nontrivial. It actually is equivalent to writing an interpreter for the language used plus the necessary data flow analysis11 . A practical compromise is to write a program that, while theoretically not even close to a metagenerator, creates output that, after a little hand editing, is a usable generator code. pl] is capable of converting a (highly pedantically formatted) piece of C++ code12 into something that is reasonable close to a generator.

8) Same for B. Then 2 n−1 hτ := Ax Bτ −x τ = 0, 1, 2, . . 10) n≤x<2n where the right sum is zero because ax = 0 for n ≤ x < 2n. 11) x>τ where the rhs. sums are silently understood as restricted to 0 ≤ x < n. For 0 ≤ τ < n the sum Sτ is always zero because b2n+τ −x is zero (n ≤ 2n + τ − x < 2n for 0 ≤ τ − x < n); (0) the sum Rτ is already equal to hτ . For n ≤ τ < 2n the sum Sτ is again zero, this time because it (1) extends over nothing (simultaneous conditions x < n and x > τ ≥ n); Rτ can be identified with hτ (0 ≤ τ < n) by setting τ = n + τ .

E. the way array data is stored in the C language, as opposed to the Fortran language convention. Further let α ≥ 2 be the number of times the data set exceeds the RAM size. 5 one reads from disk (row by row, involving R seeks) the number of colums that just fit into RAM, does the (many, short) column-FFTs3 , writes back (again R seeks) and proceeds to the next block; this happens for α of these blocks, giving a total of 4 α R seeks for steps 1 and 3. In step 2 one has to read (α times) blocks of one or more rows, which lie in contiguous portions of the disk, perform the FFT on the rows and write back to disk, leading to a total of 2 α seeks.

### Algorithms for programmers.Ideas and source code by Arndt J.

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