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By Arndt J.

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16) CHAPTER 3. n-1] input,result { fft(c[], n) fht_fft_conversion(c[], n, is) } or the same thing with swapped lines. Of course the same ideas also work for separate real- and imaginaryparts. n-1] input,result { fht(a[], n) for i:=1 to n/2-1 { t := n - i u := a[i] v := a[t] a[i] := 1/2 * (u+v) a[t] := 1/2 * (u-v) } } At the end of this procedure the ordering of the output data c ∈ C is a[0] a[1] a[2] = = = c0 c1 c2 a[n/2] a[n/2 + 1] a[n/2 + 2] a[n/2 + 3] ... = = = = ... 20) CHAPTER 3. cc] Vice versa: same line of thought as for complex versions.

31) looks like: +-| 0: 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: 15: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 .

In fact the thoughts here a not at all restricted to FFT codes, but FFTs and several unrollable routines like matrix multiplications and convolutions are prime candidates for automated generation. Writing such a program is easy: Take an existing FFT and change all computations into print statements that emit the necesary code. The process, however, is less than delightful and errorprone. It would be much better to have another program that takes the existing FFT code as input and emit the code for the generator.

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