diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/ndarray/generic/cffti/README.md b/lib/node_modules/@stdlib/fft/base/fftpack/ndarray/generic/cffti/README.md index dfa513b40eea..7a7aa91ec270 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/ndarray/generic/cffti/README.md +++ b/lib/node_modules/@stdlib/fft/base/fftpack/ndarray/generic/cffti/README.md @@ -81,6 +81,30 @@ The function has the following parameters: ## Notes +- Let `N` equal the number of elements in the input ndarray. The input ndarray is divided into three sections: + + ```text + size = 2N 2N 2+ceil(log2(N)/2) + ↓ ↓ ↓ + | scratch / workspace | twiddle factors | radix factor table | + ↑ ↑ ↑ + i = 0 ... 2N ... 4N ... + ``` + + - **scratch/workspace**: used as a scratch space when performing transforms. This section is not updated during initialization. + - **twiddle factors**: a table of reusable complex-exponential constants stored as cosine/sine pairs. + - **radix factor table**: a table containing the sequence length `N`, the number of factors into which `N` was decomposed, and the individual integer radix factors. + +- In general, an input ndarray should have `4N + 34` indexed elements (as `log2(N)/2 ≤ 32` for all `2^64`). During initialization, only the sections for storing twiddle factors and the factorization of `N` are updated. + +- The radix factor table is comprised as follows: + + ```text + | sequence_length | number_of_factors | integer_factors | + ``` + +- If `N` equals `1`, the function returns early without modifying the input ndarray, as a single data point is its own Fourier transform. + - If provided an empty one-dimensional input ndarray, the function returns the input ndarray unchanged. diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/ndarray/generic/rffti/README.md b/lib/node_modules/@stdlib/fft/base/fftpack/ndarray/generic/rffti/README.md index 89ad36ee51fb..6d18bdf4aab5 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/ndarray/generic/rffti/README.md +++ b/lib/node_modules/@stdlib/fft/base/fftpack/ndarray/generic/rffti/README.md @@ -81,6 +81,30 @@ The function has the following parameters: ## Notes +- Let `N` equal the number of elements in the input ndarray. The input ndarray is divided into three sections: + + ```text + size = N N 2+ceil(log2(N)/2) + ↓ ↓ ↓ + | scratch / workspace | twiddle factors | radix factor table | + ↑ ↑ ↑ + i = 0 ... N ... 2N ... + ``` + + - **scratch/workspace**: used as a scratch space when performing transforms. This section is not updated during initialization. + - **twiddle factors**: a table of reusable complex-exponential constants stored as cosine/sine pairs. + - **radix factor table**: a table containing the sequence length `N`, the number of factors into which `N` was decomposed, and the individual integer radix factors. + +- In general, an input ndarray should have `2N + 34` indexed elements (as `log2(N)/2 ≤ 32` for all `2^64`). During initialization, only the sections for storing twiddle factors and the factorization of `N` are updated. + +- The radix factor table is comprised as follows: + + ```text + | sequence_length | number_of_factors | integer_factors | + ``` + +- If `N` equals `1`, the function returns early without modifying the input ndarray, as a single data point is its own Fourier transform. + - If provided an empty one-dimensional input ndarray, the function returns the input ndarray unchanged.