### Perform a forward FFT with FftPlannerSse

Source: https://docs.rs/rustfft/6.4.1/rustfft/struct.FftPlannerSse.html

Example demonstrating how to initialize a planner, plan a forward FFT, and process a buffer.

```rust
// Perform a forward Fft of size 1234
use std::sync::Arc;
use rustfft::{FftPlannerSse, num_complex::Complex};

if let Ok(mut planner) = FftPlannerSse::new() {
  let fft = planner.plan_fft_forward(1234);

  let mut buffer = vec![Complex{ re: 0.0f32, im: 0.0f32 }; 1234];
  fft.process(&mut buffer);

  // The FFT instance returned by the planner has the type `Arc<dyn Fft<T>>`,
  // where T is the numeric type, ie f32 or f64, so it's cheap to clone
  let fft_clone = Arc::clone(&fft);
}
```

--------------------------------

### Perform a forward FFT with FftPlannerWasmSimd

Source: https://docs.rs/rustfft/6.4.1/rustfft/struct.FftPlannerWasmSimd.html

Example demonstrating how to create a planner, plan a forward FFT, and process a buffer.

```rust
// Perform a forward Fft of size 1234
use std::sync::Arc;
use rustfft::{FftPlannerWasmSimd, num_complex::Complex};

if let Ok(mut planner) = FftPlannerWasmSimd::new() {
  let fft = planner.plan_fft_forward(1234);

  let mut buffer = vec![Complex{ re: 0.0f32, im: 0.0f32 }; 1234];
  fft.process(&mut buffer);

  // The FFT instance returned by the planner has the type `Arc<dyn Fft<T>>`,
  // where T is the numeric type, ie f32 or f64, so it's cheap to clone
  let fft_clone = Arc::clone(&fft);
}
```

--------------------------------

### Perform a forward FFT using FftPlannerNeon

Source: https://docs.rs/rustfft/6.4.1/rustfft/struct.FftPlannerNeon.html

Example demonstrating how to initialize a planner, plan a forward FFT, and process a buffer.

```rust
// Perform a forward Fft of size 1234
use std::sync::Arc;
use rustfft::{FftPlannerNeon, num_complex::Complex};

if let Ok(mut planner) = FftPlannerNeon::new() {
  let fft = planner.plan_fft_forward(1234);

  let mut buffer = vec![Complex{ re: 0.0f32, im: 0.0f32 }; 1234];
  fft.process(&mut buffer);

  // The FFT instance returned by the planner has the type `Arc<dyn Fft<T>>`,
  // where T is the numeric type, ie f32 or f64, so it's cheap to clone
  let fft_clone = Arc::clone(&fft);
}
```

--------------------------------

### Perform an AVX-accelerated FFT

Source: https://docs.rs/rustfft/6.4.1/rustfft/struct.FftPlannerAvx.html

Example demonstrating how to instantiate the planner and perform a forward FFT. The planner returns an error if AVX is not supported or enabled.

```rust
// Perform a forward Fft of size 1234, accelerated by AVX
use std::sync::Arc;
use rustfft::{FftPlannerAvx, num_complex::Complex};

// If FftPlannerAvx::new() returns Ok(), we'll know AVX algorithms are available
// on this machine, and that RustFFT was compiled with the `avx` feature flag
if let Ok(mut planner) = FftPlannerAvx::new() {
    let fft = planner.plan_fft_forward(1234);

    let mut buffer = vec![Complex{ re: 0.0f32, im: 0.0f32 }; 1234];
    fft.process(&mut buffer);

    // The FFT instance returned by the planner has the type `Arc<dyn Fft<T>>`,
    // where T is the numeric type, ie f32 or f64, so it's cheap to clone
    let fft_clone = Arc::clone(&fft);
}
```

--------------------------------

### Perform a forward FFT

Source: https://docs.rs/rustfft/6.4.1/rustfft/struct.FftPlanner.html

Example demonstrating how to use FftPlanner to create a forward FFT instance and process a buffer.

```rust
// Perform a forward Fft of size 1234
use std::sync::Arc;
use rustfft::{FftPlanner, num_complex::Complex};

let mut planner = FftPlanner::new();
let fft = planner.plan_fft_forward(1234);

let mut buffer = vec![Complex{ re: 0.0f32, im: 0.0f32 }; 1234];
fft.process(&mut buffer);

// The FFT instance returned by the planner has the type `Arc<dyn Fft<T>>`,
// where T is the numeric type, ie f32 or f64, so it's cheap to clone
let fft_clone = Arc::clone(&fft);
```

--------------------------------

### Compute FFT with GoodThomasAlgorithmSmall

Source: https://docs.rs/rustfft/6.4.1/rustfft/algorithm/struct.GoodThomasAlgorithmSmall.html

Example demonstrating how to initialize and process a forward FFT of size 56 using GoodThomasAlgorithmSmall with factors 7 and 8.

```rust
// Computes a forward FFT of size 56 using GoodThomasAlgorithmSmall
use std::sync::Arc;
use rustfft::algorithm::GoodThomasAlgorithmSmall;
use rustfft::algorithm::butterflies::{Butterfly7, Butterfly8};
use rustfft::{Fft, FftDirection};
use rustfft::num_complex::Complex;

let mut buffer = vec![Complex{ re: 0.0f32, im: 0.0f32 }; 56];

// we need to find an n1 and n2 such that n1 * n2 == 56 and GCD(n1, n2) == 1
// n1 = 7 and n2 = 8 satisfies this
let inner_fft_n1 = Arc::new(Butterfly7::new(FftDirection::Forward));
let inner_fft_n2 = Arc::new(Butterfly8::new(FftDirection::Forward));

// the good-thomas FFT length will be inner_fft_n1.len() * inner_fft_n2.len() = 56
let fft = GoodThomasAlgorithmSmall::new(inner_fft_n1, inner_fft_n2);
fft.process(&mut buffer);
```

--------------------------------

### Initialize and Process Radix4 FFT

Source: https://docs.rs/rustfft/6.4.1/rustfft/algorithm/struct.Radix4.html

Example showing how to create a Radix4 instance for a specific size and direction, then process a buffer of complex numbers.

```rust
// Computes a forward FFT of size 4096
use rustfft::algorithm::Radix4;
use rustfft::{Fft, FftDirection};
use rustfft::num_complex::Complex;

let mut buffer = vec![Complex{ re: 0.0f32, im: 0.0f32 }; 4096];

let fft = Radix4::new(4096, FftDirection::Forward);
fft.process(&mut buffer);
```

--------------------------------

### Compute forward FFT using MixedRadix

Source: https://docs.rs/rustfft/6.4.1/rustfft/algorithm/struct.MixedRadix.html

Example demonstrating how to factor a size 1200 FFT into 30 and 40 using the MixedRadix algorithm.

```rust
// Computes a forward FFT of size 1200, using the Mixed-Radix Algorithm
use rustfft::algorithm::MixedRadix;
use rustfft::{Fft, FftPlanner};
use rustfft::num_complex::Complex;

let mut buffer = vec![Complex{ re: 0.0f32, im: 0.0f32 }; 1200];

// we need to find an n1 and n2 such that n1 * n2 == 1200
// n1 = 30 and n2 = 40 satisfies this
let mut planner = FftPlanner::new();
let inner_fft_n1 = planner.plan_fft_forward(30);
let inner_fft_n2 = planner.plan_fft_forward(40);

// the mixed radix FFT length will be inner_fft_n1.len() * inner_fft_n2.len() = 1200
let fft = MixedRadix::new(inner_fft_n1, inner_fft_n2);
fft.process(&mut buffer);
```

--------------------------------

### Compute FFT with GoodThomasAlgorithm

Source: https://docs.rs/rustfft/6.4.1/rustfft/algorithm/struct.GoodThomasAlgorithm.html

Example demonstrating how to compute a forward FFT of size 1200 using the Good-Thomas Algorithm by providing two coprime factors.

```rust
// Computes a forward FFT of size 1200, using the Good-Thomas Algorithm
use rustfft::algorithm::GoodThomasAlgorithm;
use rustfft::{Fft, FftPlanner};
use rustfft::num_complex::Complex;
use rustfft::num_traits::Zero;

let mut buffer = vec![Complex{ re: 0.0f32, im: 0.0f32 }; 1200];

// we need to find an n1 and n2 such that n1 * n2 == 1200 and GCD(n1, n2) == 1
// n1 = 48 and n2 = 25 satisfies this
let mut planner = FftPlanner::new();
let inner_fft_n1 = planner.plan_fft_forward(48);
let inner_fft_n2 = planner.plan_fft_forward(25);

// the good-thomas FFT length will be inner_fft_n1.len() * inner_fft_n2.len() = 1200
let fft = GoodThomasAlgorithm::new(inner_fft_n1, inner_fft_n2);
fft.process(&mut buffer);
```

--------------------------------

### FftPlannerNeon::new

Source: https://docs.rs/rustfft/6.4.1/rustfft/struct.FftPlannerNeon.html

Creates a new instance of FftPlannerNeon. Returns Ok if the machine supports the required instruction sets, otherwise returns Err.

```APIDOC
## pub fn new() -> Result<Self, ()>

### Description
Creates a new `FftPlannerNeon` instance. Returns `Ok(planner_instance)` if this machine has the required instruction sets. Returns `Err(())` if some instruction sets are missing.
```

--------------------------------

### FftPlannerSse::new

Source: https://docs.rs/rustfft/6.4.1/rustfft/struct.FftPlannerSse.html

Creates a new instance of FftPlannerSse. Returns Ok if the current CPU supports SSE4.1 and the feature is enabled, otherwise returns Err.

```APIDOC
## pub fn new() -> Result<Self, ()>

### Description
Creates a new `FftPlannerSse` instance. Returns `Ok(planner_instance)` if compiling for X86_64 with SSE support enabled and the CPU supports `sse4.1`. Returns `Err(())` if SSE support is unavailable.
```

--------------------------------

### Initialize and process a Radix3 FFT

Source: https://docs.rs/rustfft/6.4.1/rustfft/algorithm/struct.Radix3.html

Demonstrates how to create a Radix3 instance for a power-of-three size and perform an in-place forward FFT.

```rust
// Computes a forward FFT of size 2187
use rustfft::algorithm::Radix3;
use rustfft::{Fft, FftDirection};
use rustfft::num_complex::Complex;

let mut buffer = vec![Complex{ re: 0.0f32, im: 0.0f32 }; 2187];

let fft = Radix3::new(2187, FftDirection::Forward);
fft.process(&mut buffer);
```

--------------------------------

### Radix4::new

Source: https://docs.rs/rustfft

Directly initializes a Radix4 FFT algorithm instance, bypassing the planner.

```APIDOC
## Radix4::new(len: usize, direction: FftDirection)

### Description
Directly creates an instance of the Radix4 FFT algorithm. This bypasses the planner and disables SIMD optimizations.

### Usage
```rust
use rustfft::{Fft, FftDirection, num_complex::Complex, algorithm::Radix4};

let fft = Radix4::new(4096, FftDirection::Forward);

let mut buffer = vec![Complex{ re: 0.0f32, im: 0.0f32 }; 4096];
fft.process(&mut buffer);
```
```

--------------------------------

### Initialize and process a naive DFT

Source: https://docs.rs/rustfft/6.4.1/rustfft/algorithm/struct.Dft.html

Demonstrates how to create a new Dft instance of a specific size and direction, then process a buffer of complex numbers.

```rust
// Computes a naive DFT of size 123
use rustfft::algorithm::Dft;
use rustfft::{Fft, FftDirection};
use rustfft::num_complex::Complex;

let mut buffer = vec![Complex{ re: 0.0f32, im: 0.0f32 }; 123];

let dft = Dft::new(123, FftDirection::Forward);
dft.process(&mut buffer);
```

--------------------------------

### FftPlanner::new()

Source: https://docs.rs/rustfft/6.4.1/rustfft/struct.FftPlanner.html

Creates a new FftPlanner instance. The planner will automatically detect available CPU features like AVX, SSE, or Neon to optimize FFT planning.

```APIDOC
## pub fn new() -> Self

### Description
Creates a new `FftPlanner` instance. The planner will detect available CPU features and set itself up to plan FFTs with the fastest available instruction set.
```

--------------------------------

### Initialize and execute a forward FFT with FftPlannerScalar

Source: https://docs.rs/rustfft/6.4.1/rustfft/struct.FftPlannerScalar.html

Demonstrates creating a planner, planning a forward FFT of a specific size, and processing a buffer. The returned FFT instance is an Arc, making it safe to clone.

```rust
// Perform a forward Fft of size 1234
use std::sync::Arc;
use rustfft::{FftPlannerScalar, num_complex::Complex};

let mut planner = FftPlannerScalar::new();
let fft = planner.plan_fft_forward(1234);

let mut buffer = vec![Complex{ re: 0.0f32, im: 0.0f32 }; 1234];
fft.process(&mut buffer);

// The FFT instance returned by the planner has the type `Arc<dyn Fft<T>>`,
// where T is the numeric type, ie f32 or f64, so it's cheap to clone
let fft_clone = Arc::clone(&fft);
```

--------------------------------

### FftPlannerWasmSimd::new

Source: https://docs.rs/rustfft/6.4.1/rustfft/struct.FftPlannerWasmSimd.html

Creates a new instance of the FftPlannerWasmSimd. Returns Ok if the machine supports the required instruction sets, otherwise returns Err.

```APIDOC
### pub fn new() -> Result<Self, ()>

Creates a new `FftPlannerWasmSimd` instance. Returns `Ok(planner_instance)` if this machine has the required instruction sets. Returns `Err(())` if some instruction sets are missing.
```

--------------------------------

### Compute a prime-sized FFT using Rader's Algorithm

Source: https://docs.rs/rustfft/6.4.1/rustfft/algorithm/struct.RadersAlgorithm.html

Demonstrates initializing and executing a prime-sized FFT by wrapping an inner FFT of size N-1.

```rust
// Computes a forward FFT of size 1201 (prime number), using Rader's Algorithm
use rustfft::algorithm::RadersAlgorithm;
use rustfft::{Fft, FftPlanner};
use rustfft::num_complex::Complex;

let mut buffer = vec![Complex{ re: 0.0f32, im: 0.0f32 }; 1201];

// plan a FFT of size n - 1 = 1200
let mut planner = FftPlanner::new();
let inner_fft = planner.plan_fft_forward(1200);

let fft = RadersAlgorithm::new(inner_fft);
fft.process(&mut buffer);
```

--------------------------------

### Compute a forward FFT using Bluestein's Algorithm

Source: https://docs.rs/rustfft/6.4.1/rustfft/algorithm/struct.BluesteinsAlgorithm.html

Demonstrates initializing and executing a forward FFT of size 1201 using an inner FFT of size 2401.

```rust
// Computes a forward FFT of size 1201, using Bluestein's Algorithm
use rustfft::algorithm::BluesteinsAlgorithm;
use rustfft::{Fft, FftPlanner};
use rustfft::num_complex::Complex;

let mut buffer = vec![Complex{ re: 0.0f32, im: 0.0f32 }; 1201];

// We need to find an inner FFT whose size is greater than 1201*2 - 1.
// The size 2401 (7^4) satisfies this requirement, while also being relatively fast.
let mut planner = FftPlanner::new();
let inner_fft = planner.plan_fft_forward(2401);

let fft = BluesteinsAlgorithm::new(1201, inner_fft);
fft.process(&mut buffer);
```

--------------------------------

### Perform a forward FFT using Radix4 algorithm

Source: https://docs.rs/rustfft/6.4.1/rustfft/index.html

Directly instantiate a specific algorithm to avoid planner overhead. Note that bypassing the planner disables all SIMD optimizations.

```rust
// Computes a forward FFT of size 4096
use rustfft::{Fft, FftDirection, num_complex::Complex, algorithm::Radix4};

let fft = Radix4::new(4096, FftDirection::Forward);

let mut buffer = vec![Complex{ re: 0.0f32, im: 0.0f32 }; 4096];
fft.process(&mut buffer);
```

--------------------------------

### Compute a forward FFT of size 40

Source: https://docs.rs/rustfft/6.4.1/rustfft/algorithm/struct.MixedRadixSmall.html

Demonstrates initializing and executing a MixedRadixSmall FFT by combining two smaller butterfly FFTs.

```rust
// Computes a forward FFT of size 40 using MixedRadixSmall
use std::sync::Arc;
use rustfft::algorithm::MixedRadixSmall;
use rustfft::algorithm::butterflies::{Butterfly5, Butterfly8};
use rustfft::{Fft, FftDirection};
use rustfft::num_complex::Complex;

let len = 40;

let mut buffer = vec![Complex{ re: 0.0f32, im: 0.0f32 }; len];

// we need to find an n1 and n2 such that n1 * n2 == 40
// n1 = 5 and n2 = 8 satisfies this
let inner_fft_n1 = Arc::new(Butterfly5::new(FftDirection::Forward));
let inner_fft_n2 = Arc::new(Butterfly8::new(FftDirection::Forward));

// the mixed radix FFT length will be inner_fft_n1.len() * inner_fft_n2.len() = 40
let fft = MixedRadixSmall::new(inner_fft_n1, inner_fft_n2);
fft.process(&mut buffer);
```

--------------------------------

### FftPlanner::plan_fft_forward

Source: https://docs.rs/rustfft/6.4.1/rustfft/index.html

The FftPlanner is the recommended way to perform FFTs. It automatically selects the best algorithm for a given size and enables SIMD optimizations if supported by the hardware.

```APIDOC
## FftPlanner::plan_fft_forward(size)

### Description
Creates a plan for a forward FFT of the specified size. The planner automatically chooses the most efficient algorithm and initializes necessary buffers.

### Parameters
- **size** (usize) - Required - The length of the FFT to perform.

### Example
```rust
use rustfft::{FftPlanner, num_complex::Complex};

let mut planner = FftPlanner::new();
let fft = planner.plan_fft_forward(1234);

let mut buffer = vec![Complex{ re: 0.0f32, im: 0.0f32 }; 1234];
fft.process(&mut buffer);
```
```

--------------------------------

### FftPlannerScalar::new

Source: https://docs.rs/rustfft/6.4.1/rustfft/struct.FftPlannerScalar.html

Creates a new instance of FftPlannerScalar.

```APIDOC
## pub fn new() -> Self

### Description
Creates a new `FftPlannerScalar` instance.
```

--------------------------------

### fn process(&self, buffer: &mut [Complex<T>])

Source: https://docs.rs/rustfft/6.4.1/rustfft/trait.Fft.html

Computes a Fast Fourier Transform (FFT) in-place on the provided buffer. This is a convenience method that automatically allocates the necessary scratch space.

```APIDOC
## fn process(&self, buffer: &mut [Complex<T>])

### Description
Computes a FFT in-place. This is a convenience method that allocates a `Vec` with the required scratch space and performs the computation.

### Parameters
- **buffer** (&mut [Complex<T>]) - Required - The buffer containing the complex numbers to transform.

### Panics
This method panics if:
- `buffer.len() % self.len() > 0`
- `buffer.len() < self.len()`
```

--------------------------------

### FftPlannerAvx::new()

Source: https://docs.rs/rustfft/6.4.1/rustfft/struct.FftPlannerAvx.html

Constructs a new FftPlannerAvx instance. Returns Ok if the current CPU supports AVX and FMA and the library was compiled with the avx feature flag, otherwise returns Err.

```APIDOC
### pub fn new() -> Result<Self, ()>

Constructs a new `FftPlannerAvx` instance. Returns `Ok(planner_instance)` if the environment supports AVX/FMA and the feature is enabled, otherwise returns `Err(())`.
```

--------------------------------

### FftPlannerSse::plan_fft

Source: https://docs.rs/rustfft/6.4.1/rustfft/struct.FftPlannerSse.html

Returns an FFT instance for a specified length and direction using SSE4.1 instructions.

```APIDOC
## pub fn plan_fft(&mut self, len: usize, direction: FftDirection) -> Arc<dyn Fft<T>>

### Description
Returns an `Fft` instance configured to compute FFTs of size `len` using SSE4.1 instructions. The `direction` parameter determines whether to compute a forward or inverse FFT.
```

--------------------------------

### RadersAlgorithm::new

Source: https://docs.rs/rustfft/6.4.1/rustfft/algorithm/struct.RadersAlgorithm.html

Creates a new instance of RadersAlgorithm. This constructor is computationally expensive as it performs an internal FFT calculation.

```APIDOC
## pub fn new(inner_fft: Arc<dyn Fft<T>>) -> Self

### Description
Creates a FFT instance which will process inputs/outputs of size `inner_fft.len() + 1`. Note that this constructor is quite expensive to run as it must compute a FFT using `inner_fft` within the constructor.

### Parameters
- **inner_fft** (Arc<dyn Fft<T>>) - Required - The inner FFT instance to use, which must have a length of N-1 where N is the desired prime size.

### Panics
Panics if `inner_fft.len() + 1` is not a prime number.
```

--------------------------------

### FftPlannerNeon::plan_fft

Source: https://docs.rs/rustfft/6.4.1/rustfft/struct.FftPlannerNeon.html

Returns an FFT instance configured for a specific size and direction using Neon instructions.

```APIDOC
## pub fn plan_fft(&mut self, len: usize, direction: FftDirection) -> Arc<dyn Fft<T>>

### Description
Returns a `Fft` instance which uses Neon instructions to compute FFTs of size `len`. If the provided `direction` is `FftDirection::Forward`, the returned instance will compute forward FFTs. If it’s `FftDirection::Inverse`, it will compute inverse FFTs.
```

--------------------------------

### FftPlanner::plan_fft_forward()

Source: https://docs.rs/rustfft/6.4.1/rustfft/struct.FftPlanner.html

Returns an FFT instance specifically for forward FFT computations.

```APIDOC
## pub fn plan_fft_forward(&mut self, len: usize) -> Arc<dyn Fft<T>>

### Description
Returns a `Fft` instance which computes forward FFTs of size `len`. The planner attempts to re-use internal data between calls to reduce memory usage and initialization time.
```

--------------------------------

### FftPlannerNeon::plan_fft_forward

Source: https://docs.rs/rustfft/6.4.1/rustfft/struct.FftPlannerNeon.html

Returns an FFT instance configured for forward FFTs of a specific size using Neon instructions.

```APIDOC
## pub fn plan_fft_forward(&mut self, len: usize) -> Arc<dyn Fft<T>>

### Description
Returns a `Fft` instance which uses Neon instructions to compute forward FFTs of size `len`.
```

--------------------------------

### FftPlanner::plan_fft()

Source: https://docs.rs/rustfft/6.4.1/rustfft/struct.FftPlanner.html

Returns an FFT instance for a specified length and direction. Reusing the planner for multiple calls allows for internal data reuse.

```APIDOC
## pub fn plan_fft(&mut self, len: usize, direction: FftDirection) -> Arc<dyn Fft<T>>

### Description
Returns a `Fft` instance which computes FFTs of size `len`. If the provided `direction` is `FftDirection::Forward`, the returned instance will compute forward FFTs; if `FftDirection::Inverse`, it will compute inverse FFTs.
```

--------------------------------

### FftPlannerAvx::plan_fft()

Source: https://docs.rs/rustfft/6.4.1/rustfft/struct.FftPlannerAvx.html

Returns an FFT instance configured for the specified length and direction using AVX instructions.

```APIDOC
### pub fn plan_fft(&mut self, len: usize, direction: FftDirection) -> Arc<dyn Fft<T>>

Returns an `Fft` instance that uses AVX instructions to compute FFTs of size `len` in the specified `direction` (Forward or Inverse).
```

--------------------------------

### GoodThomasAlgorithmSmall::new

Source: https://docs.rs/rustfft/6.4.1/rustfft/algorithm/struct.GoodThomasAlgorithmSmall.html

Creates a new instance of GoodThomasAlgorithmSmall. The total FFT size is the product of the lengths of the provided width_fft and height_fft, which must be coprime.

```APIDOC
## pub fn new(width_fft: Arc<dyn Fft<T>>, height_fft: Arc<dyn Fft<T>>) -> Self

### Description
Creates a FFT instance which will process inputs/outputs of size `width_fft.len() * height_fft.len()`. Note that `GCD(width_fft.len(), height_fft.len())` must be equal to 1.
```

--------------------------------

### FftPlannerAvx::plan_fft_forward()

Source: https://docs.rs/rustfft/6.4.1/rustfft/struct.FftPlannerAvx.html

Returns an FFT instance configured for forward FFTs of the specified length using AVX instructions.

```APIDOC
### pub fn plan_fft_forward(&mut self, len: usize) -> Arc<dyn Fft<T>>

Returns an `Fft` instance optimized for forward FFTs of size `len` using AVX instructions.
```

--------------------------------

### Fft Trait Methods

Source: https://docs.rs/rustfft/6.4.1/rustfft/algorithm/struct.GoodThomasAlgorithmSmall.html

Methods for performing FFT computations and querying scratch buffer requirements.

```APIDOC
## Fft Trait Methods

### process_immutable_with_scratch(&self, input: &[Complex<T>], output: &mut [Complex<T>], scratch: &mut [Complex<T>])
Computes a FFT on chunks of size `self.len()` while keeping the input buffer untouched.

### process_outofplace_with_scratch(&self, input: &mut [Complex<T>], output: &mut [Complex<T>], scratch: &mut [Complex<T>])
Computes a FFT on chunks of size `self.len()` using separate input and output buffers.

### process_with_scratch(&self, buffer: &mut [Complex<T>], scratch: &mut [Complex<T>])
Computes a FFT in-place on chunks of size `self.len()`.

### get_inplace_scratch_len(&self) -> usize
Returns the required size of the scratch buffer for in-place processing.

### get_outofplace_scratch_len(&self) -> usize
Returns the required size of the scratch buffer for out-of-place processing.

### get_immutable_scratch_len(&self) -> usize
Returns the required size of the scratch buffer for immutable processing.

### process(&self, buffer: &mut [Complex<T>])
Computes a FFT in-place.
```

--------------------------------

### FftPlannerNeon::plan_fft_inverse

Source: https://docs.rs/rustfft/6.4.1/rustfft/struct.FftPlannerNeon.html

Returns an FFT instance configured for inverse FFTs of a specific size using Neon instructions.

```APIDOC
## pub fn plan_fft_inverse(&mut self, len: usize) -> Arc<dyn Fft<T>>

### Description
Returns a `Fft` instance which uses Neon instructions to compute inverse FFTs of size `len`.
```

--------------------------------

### FftPlanner::plan_fft_inverse()

Source: https://docs.rs/rustfft/6.4.1/rustfft/struct.FftPlanner.html

Returns an FFT instance specifically for inverse FFT computations.

```APIDOC
## pub fn plan_fft_inverse(&mut self, len: usize) -> Arc<dyn Fft<T>>

### Description
Returns a `Fft` instance which computes inverse FFTs of size `len`. The planner attempts to re-use internal data between calls to reduce memory usage and initialization time.
```

--------------------------------

### Radix4::new

Source: https://docs.rs/rustfft/6.4.1/rustfft/index.html

Advanced users can bypass the planner to use specific FFT algorithms directly, though this disables automatic SIMD optimizations.

```APIDOC
## Radix4::new(size, direction)

### Description
Directly instantiates a Radix4 FFT algorithm instance. This is useful for specific performance requirements when the FFT size is known.

### Parameters
- **size** (usize) - Required - The length of the FFT.
- **direction** (FftDirection) - Required - The direction of the FFT (Forward or Inverse).

### Example
```rust
use rustfft::{Fft, FftDirection, num_complex::Complex, algorithm::Radix4};

let fft = Radix4::new(4096, FftDirection::Forward);

let mut buffer = vec![Complex{ re: 0.0f32, im: 0.0f32 }; 4096];
fft.process(&mut buffer);
```
```

--------------------------------

### FftPlannerAvx::plan_fft_inverse()

Source: https://docs.rs/rustfft/6.4.1/rustfft/struct.FftPlannerAvx.html

Returns an FFT instance configured for inverse FFTs of the specified length using AVX instructions.

```APIDOC
### pub fn plan_fft_inverse(&mut self, len: usize) -> Arc<dyn Fft<T>>

Returns an `Fft` instance optimized for inverse FFTs of size `len` using AVX instructions.
```

--------------------------------

### FftPlannerSse::plan_fft_forward

Source: https://docs.rs/rustfft/6.4.1/rustfft/struct.FftPlannerSse.html

Returns an FFT instance for computing forward FFTs of a specified length.

```APIDOC
## pub fn plan_fft_forward(&mut self, len: usize) -> Arc<dyn Fft<T>>

### Description
Returns an `Fft` instance that uses SSE4.1 instructions to compute forward FFTs of size `len`.
```

--------------------------------

### Radix4::new

Source: https://docs.rs/rustfft/6.4.1/rustfft/algorithm/struct.Radix4.html

Constructs a new Radix4 instance for a specified length and direction.

```APIDOC
## Radix4::new(len: usize, direction: FftDirection) -> Self

### Description
Preallocates necessary arrays and precomputes data to efficiently compute a power-of-two FFT.

### Parameters
- **len** (usize) - The size of the FFT to compute.
- **direction** (FftDirection) - The direction of the FFT (Forward or Inverse).
```

--------------------------------

### Butterfly23::new

Source: https://docs.rs/rustfft/6.4.1/rustfft/algorithm/butterflies/struct.Butterfly23.html

Creates a new instance of the Butterfly23 FFT algorithm with the specified direction.

```APIDOC
## pub fn new(direction: FftDirection) -> Self

### Description
Creates a new instance of the Butterfly23 algorithm configured for either forward or inverse FFT operations.

### Parameters
- **direction** (FftDirection) - Required - The direction of the FFT (Forward or Inverse).
```

--------------------------------

### Butterfly4::new

Source: https://docs.rs/rustfft/6.4.1/rustfft/algorithm/butterflies/struct.Butterfly4.html

Creates a new instance of the Butterfly4 algorithm for the specified FFT direction.

```APIDOC
## Butterfly4::new

### Description
Creates a new instance of the Butterfly4 algorithm, configured to perform either forward or inverse FFTs based on the provided direction.

### Signature
`pub fn new(direction: FftDirection) -> Self`
```

--------------------------------

### Dft::process

Source: https://docs.rs/rustfft/6.4.1/rustfft/algorithm/struct.Dft.html

Computes a FFT in-place on the provided buffer.

```APIDOC
## pub fn process(&self, buffer: &mut [Complex<T>])

### Description
Computes the FFT in-place on the provided buffer of complex numbers.

### Parameters
- **buffer** (&mut [Complex<T>]) - The data buffer to process.
```

--------------------------------

### FftPlannerWasmSimd::plan_fft_forward

Source: https://docs.rs/rustfft/6.4.1/rustfft/struct.FftPlannerWasmSimd.html

Returns an FFT instance configured for forward FFTs of a specific size using WASM SIMD instructions.

```APIDOC
### pub fn plan_fft_forward(&mut self, len: usize) -> Arc<dyn Fft<T>>

Returns a `Fft` instance which uses WebAssembly SIMD instructions to compute forward FFTs of size `len`.
```

--------------------------------

### FftPlannerWasmSimd::plan_fft

Source: https://docs.rs/rustfft/6.4.1/rustfft/struct.FftPlannerWasmSimd.html

Returns an FFT instance configured for a specific size and direction using WASM SIMD instructions.

```APIDOC
### pub fn plan_fft(&mut self, len: usize, direction: FftDirection) -> Arc<dyn Fft<T>>

Returns a `Fft` instance which uses WebAssembly SIMD instructions to compute FFTs of size `len`. If the provided `direction` is `FftDirection::Forward`, the returned instance will compute forward FFTs. If it’s `FftDirection::Inverse`, it will compute inverse FFTs.
```

--------------------------------

### FftPlannerSse::plan_fft_inverse

Source: https://docs.rs/rustfft/6.4.1/rustfft/struct.FftPlannerSse.html

Returns an FFT instance for computing inverse FFTs of a specified length.

```APIDOC
## pub fn plan_fft_inverse(&mut self, len: usize) -> Arc<dyn Fft<T>>

### Description
Returns an `Fft` instance that uses SSE4.1 instructions to compute inverse FFTs of size `len`.
```

--------------------------------

### Dft::new

Source: https://docs.rs/rustfft/6.4.1/rustfft/algorithm/struct.Dft.html

Creates a new instance of the Dft struct with a specified length and direction.

```APIDOC
## pub fn new(len: usize, direction: FftDirection) -> Self

### Description
Preallocates necessary arrays and precomputes data to efficiently compute a Discrete Fourier Transform of the specified length.

### Parameters
- **len** (usize) - The size of the DFT.
- **direction** (FftDirection) - The direction of the transform (Forward or Inverse).
```

--------------------------------

### FftPlannerScalar::plan_fft_forward

Source: https://docs.rs/rustfft/6.4.1/rustfft/struct.FftPlannerScalar.html

Returns an FFT instance for computing forward FFTs.

```APIDOC
## pub fn plan_fft_forward(&mut self, len: usize) -> Arc<dyn Fft<T>>

### Description
Returns a `Fft` instance which computes forward FFTs of size `len`.
```

--------------------------------

### Radix4::process

Source: https://docs.rs/rustfft/6.4.1/rustfft/algorithm/struct.Radix4.html

Computes an in-place FFT on the provided buffer.

```APIDOC
## Radix4::process(&self, buffer: &mut [Complex<T>])

### Description
Computes a Fast Fourier Transform in-place on the provided buffer.

### Parameters
- **buffer** (&mut [Complex<T>]) - The data buffer to process.
```

--------------------------------

### MixedRadix::new

Source: https://docs.rs/rustfft/6.4.1/rustfft/algorithm/struct.MixedRadix.html

Creates a new FFT instance that processes inputs and outputs of size width_fft.len() * height_fft.len().

```APIDOC
## MixedRadix::new

### Description
Creates a new FFT instance which will process inputs/outputs of size `width_fft.len() * height_fft.len()`.

### Signature
`pub fn new(width_fft: Arc<dyn Fft<T>>, height_fft: Arc<dyn Fft<T>>) -> Self`
```

--------------------------------

### MixedRadixSmall::new

Source: https://docs.rs/rustfft/6.4.1/rustfft/algorithm/struct.MixedRadixSmall.html

Creates a new instance of the MixedRadixSmall FFT algorithm, which processes inputs and outputs of size width_fft.len() * height_fft.len().

```APIDOC
## pub fn new(width_fft: Arc<dyn Fft<T>>, height_fft: Arc<dyn Fft<T>>) -> Self

### Description
Creates a FFT instance which will process inputs/outputs of size `width_fft.len() * height_fft.len()`.

### Parameters
- **width_fft** (Arc<dyn Fft<T>>) - Required - The first inner FFT instance.
- **height_fft** (Arc<dyn Fft<T>>) - Required - The second inner FFT instance.
```

--------------------------------

### GoodThomasAlgorithm Structure Definition

Source: https://docs.rs/rustfft/6.4.1/rustfft/algorithm/struct.GoodThomasAlgorithm.html

The internal structure definition for the GoodThomasAlgorithm.

```rust
pub struct GoodThomasAlgorithm<T> { /* private fields */ }
```

--------------------------------

### Define FftPlanner struct

Source: https://docs.rs/rustfft/6.4.1/rustfft/struct.FftPlanner.html

The definition of the FftPlanner struct.

```rust
pub struct FftPlanner<T: FftNum> { /* private fields */ }
```

--------------------------------

### FftPlannerWasmSimd::plan_fft_inverse

Source: https://docs.rs/rustfft/6.4.1/rustfft/struct.FftPlannerWasmSimd.html

Returns an FFT instance configured for inverse FFTs of a specific size using WASM SIMD instructions.

```APIDOC
### pub fn plan_fft_inverse(&mut self, len: usize) -> Arc<dyn Fft<T>>

Returns a `Fft` instance which uses WebAssembly SIMD instructions to compute inverse FFTs of size `len`.
```

--------------------------------

### MixedRadixSmall::process

Source: https://docs.rs/rustfft/6.4.1/rustfft/algorithm/struct.MixedRadixSmall.html

Computes a Fast Fourier Transform (FFT) in-place on the provided buffer.

```APIDOC
## pub fn process(&self, buffer: &mut [Complex<T>])

### Description
Computes a FFT in-place on the provided buffer.

### Parameters
- **buffer** (&mut [Complex<T>]) - Required - The data buffer to process.
```

--------------------------------

### FftPlannerScalar::plan_fft_inverse

Source: https://docs.rs/rustfft/6.4.1/rustfft/struct.FftPlannerScalar.html

Returns an FFT instance for computing inverse FFTs.

```APIDOC
## pub fn plan_fft_inverse(&mut self, len: usize) -> Arc<dyn Fft<T>>

### Description
Returns a `Fft` instance which computes inverse FFTs of size `len`.
```

--------------------------------

### FftPlannerScalar::plan_fft

Source: https://docs.rs/rustfft/6.4.1/rustfft/struct.FftPlannerScalar.html

Returns an FFT instance for a specified length and direction.

```APIDOC
## pub fn plan_fft(&mut self, len: usize, direction: FftDirection) -> Arc<dyn Fft<T>>

### Description
Returns a `Fft` instance which computes FFTs of size `len`. If `direction` is `FftDirection::Forward`, it computes forward FFTs; if `FftDirection::Inverse`, it computes inverse FFTs.
```

--------------------------------

### Define FftPlannerSse struct

Source: https://docs.rs/rustfft/6.4.1/rustfft/struct.FftPlannerSse.html

The definition of the FftPlannerSse struct.

```rust
pub struct FftPlannerSse<T: FftNum> { /* private fields */ }
```

--------------------------------

### MixedRadix::process

Source: https://docs.rs/rustfft/6.4.1/rustfft/algorithm/struct.MixedRadix.html

Computes a FFT in-place on the provided buffer.

```APIDOC
## MixedRadix::process

### Description
Computes a FFT in-place on the provided buffer.

### Signature
`fn process(&self, buffer: &mut [Complex<T>])`
```

--------------------------------

### Define Butterfly13 struct

Source: https://docs.rs/rustfft/6.4.1/rustfft/algorithm/butterflies/struct.Butterfly13.html

The structure definition for the Butterfly13 algorithm.

```rust
pub struct Butterfly13<T> { /* private fields */ }
```

--------------------------------

### Define FftPlannerAvx struct

Source: https://docs.rs/rustfft/6.4.1/rustfft/struct.FftPlannerAvx.html

The definition of the FftPlannerAvx struct.

```rust
pub struct FftPlannerAvx<T: FftNum> { /* private fields */ }
```

--------------------------------

### Butterfly23 FFT Processing Methods

Source: https://docs.rs/rustfft/6.4.1/rustfft/algorithm/butterflies/struct.Butterfly23.html

Methods for performing FFT computations using the Butterfly23 algorithm.

```APIDOC
## FFT Processing Methods

### process(buffer: &mut [Complex<T>])
Computes an in-place FFT on the provided buffer.

### process_with_scratch(buffer: &mut [Complex<T>], _scratch: &mut [Complex<T>])
Divides the buffer into chunks of size self.len() and computes an FFT on each chunk using a scratch buffer.

### process_outofplace_with_scratch(input: &mut [Complex<T>], output: &mut [Complex<T>], _scratch: &mut [Complex<T>])
Computes an out-of-place FFT, dividing input and output into chunks of size self.len().

### process_immutable_with_scratch(input: &[Complex<T>], output: &mut [Complex<T>], _scratch: &mut [Complex<T>])
Computes an FFT on chunks of the input while keeping the original input buffer untouched.
```

--------------------------------

### Length and Direction Traits

Source: https://docs.rs/rustfft/6.4.1/rustfft/algorithm/struct.GoodThomasAlgorithmSmall.html

Utility methods to retrieve the FFT size and the processing direction.

```APIDOC
## Trait Methods

### len(&self) -> usize
Returns the FFT size that this algorithm can process.

### fft_direction(&self) -> FftDirection
Returns `FftDirection::Forward` if this instance computes forward FFTs, or `FftDirection::Inverse` for inverse FFTs.
```

--------------------------------

### Define FftPlannerWasmSimd struct

Source: https://docs.rs/rustfft/6.4.1/rustfft/struct.FftPlannerWasmSimd.html

The definition of the FftPlannerWasmSimd struct.

```rust
pub struct FftPlannerWasmSimd<T: FftNum> { /* private fields */ }
```

--------------------------------

### Define FftPlannerNeon struct

Source: https://docs.rs/rustfft/6.4.1/rustfft/struct.FftPlannerNeon.html

The definition of the FftPlannerNeon struct.

```rust
pub struct FftPlannerNeon<T: FftNum> { /* private fields */ }
```

--------------------------------

### Define Radix3 struct

Source: https://docs.rs/rustfft/6.4.1/rustfft/algorithm/struct.Radix3.html

The internal structure definition for the Radix3 algorithm.

```rust
pub struct Radix3<T> { /* private fields */ }
```

--------------------------------

### GoodThomasAlgorithmSmall Struct Definition

Source: https://docs.rs/rustfft/6.4.1/rustfft/algorithm/struct.GoodThomasAlgorithmSmall.html

The internal structure definition for GoodThomasAlgorithmSmall.

```rust
pub struct GoodThomasAlgorithmSmall<T> { /* private fields */ }
```

--------------------------------

### Fft Trait Definition

Source: https://docs.rs/rustfft/6.4.1/rustfft/trait.Fft.html

The core trait definition for FFT algorithms, requiring implementation of processing methods and scratch buffer size queries.

```rust
pub trait Fft<T: FftNum>:
    Length
    + Direction
    + Sync
    + Send {
    // Required methods
    fn process_with_scratch(
        &self,
        buffer: &mut [Complex<T>],
        scratch: &mut [Complex<T>],
    );
    fn process_outofplace_with_scratch(
        &self,
        input: &mut [Complex<T>],
        output: &mut [Complex<T>],
        scratch: &mut [Complex<T>],
    );
    fn process_immutable_with_scratch(
        &self,
        input: &[Complex<T>],
        output: &mut [Complex<T>],
        scratch: &mut [Complex<T>],
    );
    fn get_inplace_scratch_len(&self) -> usize;
    fn get_outofplace_scratch_len(&self) -> usize;
    fn get_immutable_scratch_len(&self) -> usize;

    // Provided method
    fn process(&self, buffer: &mut [Complex<T>]) { ... }
}
```

--------------------------------

### Radix4 Struct Definition

Source: https://docs.rs/rustfft/6.4.1/rustfft/algorithm/struct.Radix4.html

The internal structure definition for the Radix4 algorithm.

```rust
pub struct Radix4<T> { /* private fields */ }
```

--------------------------------

### Dft struct definition

Source: https://docs.rs/rustfft/6.4.1/rustfft/algorithm/struct.Dft.html

The definition of the Dft struct.

```rust
pub struct Dft<T> { /* private fields */ }
```

--------------------------------

### Butterfly17 Struct Definition

Source: https://docs.rs/rustfft/6.4.1/rustfft/algorithm/butterflies/struct.Butterfly17.html

The internal structure definition for the Butterfly17 algorithm.

```rust
pub struct Butterfly17<T> { /* private fields */ }
```

--------------------------------

### Dft::len

Source: https://docs.rs/rustfft/6.4.1/rustfft/algorithm/struct.Dft.html

Returns the FFT size that this algorithm instance is configured to process.

```APIDOC
## pub fn len(&self) -> usize

### Description
Returns the FFT size that this algorithm can process.
```

--------------------------------

### Define the Length trait

Source: https://docs.rs/rustfft/6.4.1/rustfft/trait.Length.html

The trait requires implementing the len method to return the FFT size as a usize.

```rust
pub trait Length {
    // Required method
    fn len(&self) -> usize;
}
```

--------------------------------

### Butterfly12 struct definition

Source: https://docs.rs/rustfft/6.4.1/rustfft/algorithm/butterflies/struct.Butterfly12.html

The definition of the Butterfly12 struct.

```rust
pub struct Butterfly12<T> { /* private fields */ }
```

--------------------------------

### Butterfly24 Struct Definition

Source: https://docs.rs/rustfft/6.4.1/rustfft/algorithm/butterflies/struct.Butterfly24.html

The definition of the Butterfly24 struct.

```rust
pub struct Butterfly24<T> { /* private fields */ }
```

--------------------------------

### FftNum Implementor Blanket Implementation

Source: https://docs.rs/rustfft/6.4.1/rustfft/trait.FftNum.html

The blanket implementation for any type T that satisfies the trait bounds.

```rust
impl<T> FftNum for T
where T: Copy + FromPrimitive + Signed + Sync + Send + Debug + 'static,
```

--------------------------------

### Define Butterfly7 struct

Source: https://docs.rs/rustfft/6.4.1/rustfft/algorithm/butterflies/struct.Butterfly7.html

The definition of the Butterfly7 struct with private fields.

```rust
pub struct Butterfly7<T> { /* private fields */ }
```

--------------------------------

### Butterfly1 struct definition

Source: https://docs.rs/rustfft/6.4.1/rustfft/algorithm/butterflies/struct.Butterfly1.html

The definition of the Butterfly1 struct.

```rust
pub struct Butterfly1<T> { /* private fields */ }
```

--------------------------------

### Define Butterfly29 struct

Source: https://docs.rs/rustfft/6.4.1/rustfft/algorithm/butterflies/struct.Butterfly29.html

The definition of the Butterfly29 struct.

```rust
pub struct Butterfly29<T> { /* private fields */ }
```

--------------------------------

### Define MixedRadix struct

Source: https://docs.rs/rustfft/6.4.1/rustfft/algorithm/struct.MixedRadix.html

The internal structure definition for the MixedRadix algorithm.

```rust
pub struct MixedRadix<T> { /* private fields */ }
```

--------------------------------

### FftPlannerScalar struct definition

Source: https://docs.rs/rustfft/6.4.1/rustfft/struct.FftPlannerScalar.html

The definition of the FftPlannerScalar struct.

```rust
pub struct FftPlannerScalar<T: FftNum> { /* private fields */ }
```

--------------------------------

### Butterfly27 Struct Definition

Source: https://docs.rs/rustfft/6.4.1/rustfft/algorithm/butterflies/struct.Butterfly27.html

The definition of the Butterfly27 struct.

```rust
pub struct Butterfly27<T> { /* private fields */ }
```

--------------------------------

### opposite_direction

Source: https://docs.rs/rustfft/6.4.1/rustfft/enum.FftDirection.html

Returns the opposite direction of the current FftDirection instance. If the current direction is Forward, it returns Inverse, and vice versa.

```APIDOC
## pub fn opposite_direction(&self) -> FftDirection

### Description
Returns the opposite direction of the current `FftDirection` instance.

### Signature
`pub fn opposite_direction(&self) -> FftDirection`

### Returns
- **FftDirection** - The opposite direction (Forward becomes Inverse, Inverse becomes Forward).
```

--------------------------------

### Define the Direction trait

Source: https://docs.rs/rustfft/6.4.1/rustfft/trait.Direction.html

The trait requires implementation of the fft_direction method to return the current FftDirection.

```rust
pub trait Direction {
    // Required method
    fn fft_direction(&self) -> FftDirection;
}
```

--------------------------------

### Butterfly19 Struct Definition

Source: https://docs.rs/rustfft/6.4.1/rustfft/algorithm/butterflies/struct.Butterfly19.html

The definition of the Butterfly19 struct.

```rust
pub struct Butterfly19<T> { /* private fields */ }
```

--------------------------------

### Butterfly23 Struct Definition

Source: https://docs.rs/rustfft/6.4.1/rustfft/algorithm/butterflies/struct.Butterfly23.html

The definition of the Butterfly23 struct.

```rust
pub struct Butterfly23<T> { /* private fields */ }
```

--------------------------------

### FftNum Trait Definition

Source: https://docs.rs/rustfft/6.4.1/rustfft/trait.FftNum.html

The trait definition specifying the required supertraits for any type implementing FftNum.

```rust
pub trait FftNum:
    Copy
    + FromPrimitive
    + Signed
    + Sync
    + Send
    + Debug
    + 'static { }
```

--------------------------------

### MixedRadix::len

Source: https://docs.rs/rustfft/6.4.1/rustfft/algorithm/struct.MixedRadix.html

Returns the FFT size that this algorithm can process.

```APIDOC
## MixedRadix::len

### Description
Returns the FFT size that this algorithm can process.

### Signature
`fn len(&self) -> usize`
```

--------------------------------

### Butterfly8 Struct Definition

Source: https://docs.rs/rustfft/6.4.1/rustfft/algorithm/butterflies/struct.Butterfly8.html

The definition of the Butterfly8 struct, which is generic over type T.

```rust
pub struct Butterfly8<T> { /* private fields */ }
```

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