Build symbolic R2HC expressions for all k in 0..=n/2. Y[k].re = Σ_{j=0..n-1} x[j] · cos(-2π·j·k/N) = Σ x[j]·cos(2π·j·k/N) Y[k].im = Σ_{j=0..n-1} x[j

Synthesize a frame from spectrum. # Arguments `spectrum` - Complex spectrum (must have length = fft_size) # Returns Time-domain frame of length ff

Convert to dense representation.

Topologically sort assignments so that each temp is defined before use.

Transpose a 3D array along specified axes. Useful for optimizing 3D FFTs with better cache access patterns. Swaps axes 1 and 2 (middle and inner dime

reason: matrix index arithmetic 'i * cols + j' and 'j * rows + i' are standard and correct, not suspicious

Cache-friendly blocked matrix transpose. Transposes an N1×N2 row-major matrix in-place using blocking to improve cache utilization. The result is the

In-place square matrix transpose with cache blocking. Uses cache-blocked algorithm for better locality on large matrices.

Try to factor `n` as a product of supported radices {2, 3, 4, 5, 7, 8, 16}. Returns `Some(factors)` ordered innermost-first (the first element is the

Radix-2 DIT twiddle butterfly, backward.

Radix-3 DIT twiddle butterfly, backward direction (exp(+2πi k/N)).

Radix-4 DIT twiddle butterfly, backward.

Radix-5 DIT twiddle butterfly, backward direction.

Radix-8 DIT twiddle butterfly, backward.

Radix-8 DIT twiddle butterfly, forward. Layout: twiddles[(j-1)*stride + s] for j=1..7.

Compute the largest power of 2 dividing `n`. Returns the exponent `k` such that `2^k | n` but `2^(k+1)` does not. Returns 0 if `n` is odd, and `None`

Map a `u64` PRNG output to `f32` in `[-1.0, 1.0]` without precision-loss casts. Constructs an IEEE 754 f32 in `[1.0, 2.0)` from the top 23 mantissa b

Unpack SoA output for transform `t` into `(re_out[0..n], im_out[0..n])`.

Verify singleton detection against other stages.

Store wisdom entry.

Execute `f` with a thread-local scratch buffer of at least `n` elements. The buffer is zero-initialized on each call. It grows lazily but never shrin

Write the JSON report and emit the Markdown table.