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CHAPTER 2. CONVOLUTIONS 3: 3 1003 2003 3003 47 4003 5003 6003 7003 FULL REVBIN_PERMUTE for transposition: 0: 0 1 2 3 1: 4000 4001 4002 4003 2: 2000 2001 2002 2003 3: 6000 6001 6002 6003 4: 1000 1001 1002 1003 5: 5000 5001 5002 5003 6: 3000 3001 3002 3003 7: 7000 7001 7002 7003 CONVOLUTIONS on rows (do not care revbin_permuted sequence), no reordering. e. revbin_permute rows: 0: 0 4000 2000 6000 1000 5000 3000 7000 1: 2 4002 2002 6002 1002 5002 3002 7002 2: 1 4001 2001 6001 1001 5001 3001 7001 3: 3 4003 2003 6003 1003 5003 3003 7003 FULL REVBIN_PERMUTE for transposition: 0: 0 1 2 3 1: 1000 1001 1002 1003 2: 2000 2001 2002 2003 3: 3000 3001 3002 3003 4: 4000 4001 4002 4003 5: 5000 5001 5002 5003 6: 6000 6001 6002 6003 7: 7000 7001 7002 7003 As shown works for sizes that are a power of two, generalizes for sizes a power of some prime.

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. Let Trc be the operator corresponding to the postprocessing in real_complex_fft_by_fht, and Tcr correspond to the preprocessing in complex_real_fft_by_fht.

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. Further one may want to print the current values of the loop variables inside comments at the beginning of a block.

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