Aleph::FFT< Real >::Plan Class Reference

Precomputed FFT plan for repeated transforms of the same size. More...

#include <fft.H>

Collaboration diagram for Aleph::FFT< Real >::Plan:

Public Member Functions
	Plan ()=default
	Constructs an empty plan (size 0).
	Plan (const size_t n)
	Constructs a plan for transforms of size n.
size_t	size () const noexcept
	Returns the transform size this plan was built for.
void	transform (Array< Complex > &a, const bool invert) const
	Computes the FFT or IFFT in-place using precomputed tables.
Array< Complex >	transformed (const Array< Complex > &input, const bool invert=false) const
	Computes the FFT or IFFT returning a new array.
Array< Complex >	inverse_transform (const Array< Complex > &input) const
	Returns the inverse transform as a new array.
Array< Real >	inverse_transform_real (const Array< Complex > &input) const
	Returns the IFFT projected back to real values.
Array< Real >	pinverse_transform_real (ThreadPool &pool, const Array< Complex > &input, const size_t chunk_size=0) const
	Parallel IFFT projected back to real values.
void	ptransform (ThreadPool &pool, Array< Complex > &a, const bool invert, const size_t chunk_size=0) const
	Parallel in-place transform using a thread pool.
Array< Complex >	ptransformed (ThreadPool &pool, const Array< Complex > &input, const bool invert=false, const size_t chunk_size=0) const
	Parallel transform returning a new array.
Array< Complex >	pinverse_transform (ThreadPool &pool, const Array< Complex > &input, const size_t chunk_size=0) const
	Parallel inverse transform returning a new array.
void	transform_batch (Array< Array< Complex > > &batch, const bool invert, const bool prefer_simd=true) const
	In-place batch transform for equal-length complex inputs.
void	ptransform_batch (ThreadPool &pool, Array< Array< Complex > > &batch, const bool invert, const size_t chunk_size=0, const bool prefer_simd=true) const
	Parallel batch transform for equal-length complex inputs.
Array< Array< Complex > >	transformed_batch (const Array< Array< Complex > > &input, const bool invert=false, const bool prefer_simd=true) const
	Returns the batch FFT/IFFT as a new array of arrays.
Array< Array< Complex > >	ptransformed_batch (ThreadPool &pool, const Array< Array< Complex > > &input, const bool invert=false, const size_t chunk_size=0, const bool prefer_simd=true) const
	Returns the parallel batch FFT/IFFT as a new array of arrays.
Array< Array< Complex > >	inverse_transform_batch (const Array< Array< Complex > > &input) const
	Returns the inverse batch transform as a new array of arrays.
Array< Array< Complex > >	pinverse_transform_batch (ThreadPool &pool, const Array< Array< Complex > > &input, const size_t chunk_size=0, const bool prefer_simd=true) const
	Returns the parallel inverse batch transform.
Array< Array< Real > >	inverse_transform_real_batch (const Array< Array< Complex > > &input) const
	Returns the inverse batch transform projected back to real values.
Array< Array< Real > >	pinverse_transform_real_batch (ThreadPool &pool, const Array< Array< Complex > > &input, const size_t chunk_size=0, const bool prefer_simd=true) const
	Returns the parallel inverse batch transform projected back to real values.
Array< Complex >	rfft (const Array< Real > &input) const
	Computes the Real-to-Complex FFT (RFFT).
Array< Complex >	prfft (ThreadPool &pool, const Array< Real > &input, const size_t chunk_size=0) const
	Parallel Real-to-Complex FFT (RFFT).
Array< Real >	irfft (const Array< Complex > &spectrum) const
	Computes the Complex-to-Real Inverse FFT (IRFFT).
Array< Real >	pirfft (ThreadPool &pool, const Array< Complex > &spectrum, const size_t chunk_size=0) const
	Parallel Complex-to-Real Inverse FFT (IRFFT).
Array< Array< Complex > >	rfft_batch (const Array< Array< Real > > &input) const
	Computes a batch of Real-to-Complex FFTs.
Array< Array< Complex > >	prfft_batch (ThreadPool &pool, const Array< Array< Real > > &input, const size_t chunk_size=0) const
	Computes a parallel batch of Real-to-Complex FFTs.
Array< Array< Real > >	irfft_batch (const Array< Array< Complex > > &spectra) const
	Computes a batch of Complex-to-Real Inverse FFTs.
Array< Array< Real > >	pirfft_batch (ThreadPool &pool, const Array< Array< Complex > > &spectra, const size_t chunk_size=0) const
	Computes a parallel batch of Complex-to-Real Inverse FFTs.

Private Types
enum class	Strategy { empty , power_of_two , mixed_radix , bluestein }

Private Member Functions
void	initialize_power_of_two_plan ()
void	initialize_mixed_radix_plan ()
void	initialize_bluestein_plan ()
void	apply_bit_reversal (Array< Complex > &a) const noexcept
bool	automatic_batch_simd_candidate (const size_t batch_size) const noexcept
bool	should_use_avx2 (ThreadPool *pool, const bool prefer_simd) const noexcept
bool	should_use_neon (ThreadPool *pool, const bool prefer_simd) const noexcept
void	apply_butterflies (Array< Complex > &a, const bool invert, ThreadPool *pool, const size_t chunk_size, const bool prefer_simd) const
void	apply_transform (Array< Complex > &a, const bool invert, ThreadPool *pool, const size_t chunk_size, const bool prefer_simd) const
Complex	root_for_length (const size_t length, const size_t exponent, const bool invert) const
Array< Complex >	mixed_radix_transform_recursive (const Array< Complex > &input, const size_t factor_index, const size_t current_size, const bool invert) const
void	apply_mixed_radix_transform (Array< Complex > &a, const bool invert) const
void	apply_bluestein_transform (Array< Complex > &a, const bool invert, ThreadPool *pool, const size_t chunk_size) const
bool	supports_power_of_two_real_optimization () const noexcept

Private Attributes
size_t	n_ = 0
Strategy	strategy_ = Strategy::empty
size_t	log_n_ = 0
Array< size_t >	bit_rev_
Array< Complex >	twiddles_
std::shared_ptr< const Plan >	half_plan_
Array< size_t >	factors_
Array< Complex >	roots_
size_t	bluestein_size_ = 0
Array< Complex >	bluestein_chirp_
Array< Complex >	bluestein_kernel_forward_
Array< Complex >	bluestein_kernel_inverse_
std::shared_ptr< const Plan >	bluestein_plan_

Detailed Description

template<std::floating_point Real = double>
class Aleph::FFT< Real >::Plan

Precomputed FFT plan for repeated transforms of the same size.

A Plan precomputes the state needed for a given transform size N. Power-of-two sizes cache the bit-reversal permutation and radix-2/radix-4 twiddle tables. Other sizes cache either a mixed-radix factorization or the Bluestein convolution kernel. Subsequent calls to transform reuse these tables instead of rebuilding them.

This is beneficial when multiple transforms of the same size are performed (e.g., streaming audio, sliding-window spectral analysis).

Note

Construction cost is O(N). Each transform execution is O(N log N).

FFT<double>::Plan plan(1024);
plan.transform(signal_a, false);  // forward, in-place
plan.transform(signal_b, false);  // reuses precomputed tables
auto spectrum = plan.transformed(signal_c);  // functional variant

Definition at line 6293 of file fft.H.

Member Enumeration Documentation

Strategy

template<std::floating_point Real = double>

enum class Aleph::FFT::Plan::Strategy

strongprivate

Enumerator
empty
power_of_two
mixed_radix
bluestein

Definition at line 6295 of file fft.H.

Constructor & Destructor Documentation

Plan() [1/2]

template<std::floating_point Real = double>

Aleph::FFT< Real >::Plan::Plan ( )

default

Constructs an empty plan (size 0).

Plan() [2/2]

template<std::floating_point Real = double>

Aleph::FFT< Real >::Plan::Plan ( const size_t  n )

inlineexplicit

Constructs a plan for transforms of size n.

Precomputes the bit-reversal permutation and all twiddle factors. Construction cost is O(N).

Parameters

n	Transform size (must be positive).

Exceptions

std::invalid_argument

if n is zero.

Definition at line 7256 of file fft.H.

References ah_invalid_argument_if, Aleph::blossom_maximum_cardinality_matching(), Aleph::FFT< Real >::Plan::empty, Aleph::FFT< Real >::factor_small_radices(), Aleph::FFT< Real >::Plan::factors_, Aleph::FFT< Real >::Plan::initialize_bluestein_plan(), Aleph::FFT< Real >::Plan::initialize_mixed_radix_plan(), Aleph::FFT< Real >::Plan::initialize_power_of_two_plan(), Aleph::Array< T >::is_empty(), Aleph::FFT< Real >::is_power_of_two(), Aleph::FFT< Real >::Plan::n_, and Aleph::FFT< Real >::Plan::strategy_.

Member Function Documentation

apply_bit_reversal()

template<std::floating_point Real = double>

void Aleph::FFT< Real >::Plan::apply_bit_reversal ( Array< Complex > &  a ) const

inlineprivatenoexcept

Definition at line 6406 of file fft.H.

References Aleph::FFT< Real >::Plan::bit_rev_, and Aleph::FFT< Real >::Plan::n_.

Referenced by Aleph::FFT< Real >::Plan::apply_transform().

apply_bluestein_transform()

template<std::floating_point Real = double>

void Aleph::FFT< Real >::Plan::apply_bluestein_transform ( Array< Complex > &  a, const bool  invert, ThreadPool *  pool, const size_t  chunk_size  ) const

inlineprivate

Definition at line 7173 of file fft.H.

References Aleph::and, Aleph::blossom_maximum_cardinality_matching(), Aleph::FFT< Real >::Plan::bluestein_chirp_, Aleph::FFT< Real >::Plan::bluestein_kernel_forward_, Aleph::FFT< Real >::Plan::bluestein_kernel_inverse_, Aleph::FFT< Real >::Plan::bluestein_plan_, Aleph::FFT< Real >::Plan::bluestein_size_, Aleph::Array< T >::create(), Aleph::FFT< Real >::Plan::n_, Aleph::ThreadPool::num_threads(), and Aleph::parallel_for_index().

Referenced by Aleph::FFT< Real >::Plan::apply_transform().

apply_butterflies()

template<std::floating_point Real = double>

void Aleph::FFT< Real >::Plan::apply_butterflies ( Array< Complex > &  a, const bool  invert, ThreadPool *  pool, const size_t  chunk_size, const bool  prefer_simd  ) const

inlineprivate

Definition at line 6900 of file fft.H.

References Aleph::and, Aleph::blossom_maximum_cardinality_matching(), Aleph::FFT< Real >::Plan::log_n_, Aleph::FFT< Real >::Plan::n_, Aleph::ThreadPool::num_threads(), Aleph::parallel_for_index(), r, Aleph::FFT< Real >::Plan::should_use_avx2(), Aleph::FFT< Real >::Plan::should_use_neon(), and Aleph::FFT< Real >::Plan::twiddles_.

Referenced by Aleph::FFT< Real >::Plan::apply_transform().

apply_mixed_radix_transform()

template<std::floating_point Real = double>

void Aleph::FFT< Real >::Plan::apply_mixed_radix_transform ( Array< Complex > &  a, const bool  invert  ) const

inlineprivate

Definition at line 7160 of file fft.H.

References Aleph::blossom_maximum_cardinality_matching(), Aleph::FFT< Real >::Plan::mixed_radix_transform_recursive(), Aleph::FFT< Real >::Plan::n_, and output.

Referenced by Aleph::FFT< Real >::Plan::apply_transform().

apply_transform()

template<std::floating_point Real = double>

void Aleph::FFT< Real >::Plan::apply_transform ( Array< Complex > &  a, const bool  invert, ThreadPool *  pool, const size_t  chunk_size, const bool  prefer_simd  ) const

inlineprivate

Definition at line 7074 of file fft.H.

References ah_invalid_argument_if, Aleph::FFT< Real >::Plan::apply_bit_reversal(), Aleph::FFT< Real >::Plan::apply_bluestein_transform(), Aleph::FFT< Real >::Plan::apply_butterflies(), Aleph::FFT< Real >::Plan::apply_mixed_radix_transform(), Aleph::blossom_maximum_cardinality_matching(), Aleph::FFT< Real >::Plan::bluestein, Aleph::FFT< Real >::Plan::empty, Aleph::FFT< Real >::Plan::mixed_radix, Aleph::FFT< Real >::Plan::n_, Aleph::FFT< Real >::Plan::power_of_two, Aleph::Array< T >::size(), and Aleph::FFT< Real >::Plan::strategy_.

Referenced by Aleph::FFT< Real >::Plan::ptransform(), Aleph::FFT< Real >::Plan::ptransform_batch(), Aleph::FFT< Real >::Plan::transform(), and Aleph::FFT< Real >::Plan::transform_batch().

automatic_batch_simd_candidate()

template<std::floating_point Real = double>

bool Aleph::FFT< Real >::Plan::automatic_batch_simd_candidate ( const size_t  batch_size ) const

inlineprivatenoexcept

Definition at line 6832 of file fft.H.

References Aleph::and, Aleph::blossom_maximum_cardinality_matching(), Aleph::FFT< Real >::Plan::log_n_, Aleph::FFT< Real >::Plan::n_, Aleph::FFT< Real >::Plan::power_of_two, and Aleph::FFT< Real >::Plan::strategy_.

Referenced by Aleph::FFT< Real >::Plan::ptransform_batch(), and Aleph::FFT< Real >::Plan::transform_batch().

initialize_bluestein_plan()

template<std::floating_point Real = double>

void Aleph::FFT< Real >::Plan::initialize_bluestein_plan ( )

inlineprivate

Definition at line 6366 of file fft.H.

References Aleph::blossom_maximum_cardinality_matching(), Aleph::FFT< Real >::Plan::bluestein, Aleph::FFT< Real >::Plan::bluestein_chirp_, Aleph::FFT< Real >::Plan::bluestein_kernel_forward_, Aleph::FFT< Real >::Plan::bluestein_kernel_inverse_, Aleph::FFT< Real >::Plan::bluestein_plan_, Aleph::FFT< Real >::Plan::bluestein_size_, Aleph::Array< T >::create(), Aleph::FFT< Real >::Plan::n_, Aleph::FFT< Real >::next_power_of_two(), Aleph::FFT< Real >::Plan::strategy_, and value.

Referenced by Aleph::FFT< Real >::Plan::Plan().

initialize_mixed_radix_plan()

template<std::floating_point Real = double>

void Aleph::FFT< Real >::Plan::initialize_mixed_radix_plan ( )

inlineprivate

Definition at line 6354 of file fft.H.

References Aleph::blossom_maximum_cardinality_matching(), Aleph::Array< T >::create(), Aleph::FFT< Real >::Plan::mixed_radix, Aleph::FFT< Real >::Plan::n_, Aleph::FFT< Real >::Plan::roots_, and Aleph::FFT< Real >::Plan::strategy_.

Referenced by Aleph::FFT< Real >::Plan::Plan().

initialize_power_of_two_plan()

template<std::floating_point Real = double>

void Aleph::FFT< Real >::Plan::initialize_power_of_two_plan ( )

inlineprivate

Definition at line 6318 of file fft.H.

References Aleph::FFT< Real >::Plan::bit_rev_, Aleph::blossom_maximum_cardinality_matching(), Aleph::Array< T >::create(), Aleph::FFT< Real >::Plan::half_plan_, Aleph::FFT< Real >::Plan::log_n_, Aleph::FFT< Real >::Plan::n_, offset, Aleph::FFT< Real >::Plan::power_of_two, Aleph::FFT< Real >::Plan::strategy_, and Aleph::FFT< Real >::Plan::twiddles_.

Referenced by Aleph::FFT< Real >::Plan::Plan().

inverse_transform()

template<std::floating_point Real = double>

Array< Complex > Aleph::FFT< Real >::Plan::inverse_transform ( const Array< Complex > &  input ) const

inline

Returns the inverse transform as a new array.

Definition at line 7314 of file fft.H.

References Aleph::blossom_maximum_cardinality_matching(), and Aleph::FFT< Real >::Plan::transformed().

inverse_transform_batch()

template<std::floating_point Real = double>

Array< Array< Complex > > Aleph::FFT< Real >::Plan::inverse_transform_batch ( const Array< Array< Complex > > &  input ) const

inline

Returns the inverse batch transform as a new array of arrays.

Definition at line 7499 of file fft.H.

References Aleph::blossom_maximum_cardinality_matching(), and Aleph::FFT< Real >::Plan::transformed_batch().

inverse_transform_real()

template<std::floating_point Real = double>

Array< Real > Aleph::FFT< Real >::Plan::inverse_transform_real ( const Array< Complex > &  input ) const

inline

Returns the IFFT projected back to real values.

Exceptions

std::domain_error

if the result has non-negligible imaginary parts.

Definition at line 7325 of file fft.H.

References ah_invalid_argument_if, Aleph::blossom_maximum_cardinality_matching(), Aleph::FFT< Real >::Plan::half_plan_, Aleph::FFT< Real >::inverse_transform_real_optimized_impl(), Aleph::FFT< Real >::Plan::n_, output, Aleph::FFT< Real >::project_real_output(), Aleph::Array< T >::size(), Aleph::FFT< Real >::Plan::supports_power_of_two_real_optimization(), Aleph::FFT< Real >::Plan::transform(), and Aleph::FFT< Real >::validate_real_spectrum().

Referenced by Aleph::FFT< Real >::OverlapAdd::convolve_impl(), Aleph::FFT< Real >::Plan::inverse_transform_real_batch(), Aleph::FFT< Real >::Plan::irfft(), Aleph::FFT< Real >::Plan::pinverse_transform_real_batch(), Aleph::FFT< Real >::OverlapAdd::process_chunk_impl(), Aleph::FFT< Real >::OverlapSave::process_chunk_impl(), Aleph::FFT< Real >::ISTFTProcessor::process_frame_impl(), and Aleph::FFT< Real >::PartitionedConvolver::process_partition_impl().

inverse_transform_real_batch()

template<std::floating_point Real = double>

Array< Array< Real > > Aleph::FFT< Real >::Plan::inverse_transform_real_batch ( const Array< Array< Complex > > &  input ) const

inline

Returns the inverse batch transform projected back to real values.

Definition at line 7518 of file fft.H.

References ah_invalid_argument_if, Aleph::blossom_maximum_cardinality_matching(), Aleph::FFT< Real >::Plan::inverse_transform_real(), Aleph::FFT< Real >::Plan::n_, output, and Aleph::FFT< Real >::Plan::size().

Referenced by Aleph::FFT< Real >::OverlapAddBank::convolve_impl(), Aleph::FFT< Real >::Plan::irfft_batch(), and Aleph::FFT< Real >::OverlapAddBank::process_chunk_batch_impl().

irfft()

template<std::floating_point Real = double>

Array< Real > Aleph::FFT< Real >::Plan::irfft ( const Array< Complex > &  spectrum ) const

inline

Computes the Complex-to-Real Inverse FFT (IRFFT).

Parameters

spectrum

Compact complex spectrum (size N/2 + 1).

Returns

Real signal of size N.

Definition at line 7602 of file fft.H.

References Aleph::FFT< Real >::expand_real_spectrum(), Aleph::FFT< Real >::Plan::inverse_transform_real(), Aleph::FFT< Real >::Plan::n_, and Aleph::FFT< Real >::spectrum().

irfft_batch()

template<std::floating_point Real = double>

Array< Array< Real > > Aleph::FFT< Real >::Plan::irfft_batch ( const Array< Array< Complex > > &  spectra ) const

inline

Computes a batch of Complex-to-Real Inverse FFTs.

Definition at line 7641 of file fft.H.

References Aleph::blossom_maximum_cardinality_matching(), Aleph::FFT< Real >::expand_real_batch_spectra(), Aleph::FFT< Real >::Plan::inverse_transform_real_batch(), and Aleph::FFT< Real >::Plan::n_.

mixed_radix_transform_recursive()

template<std::floating_point Real = double>

Array< Complex > Aleph::FFT< Real >::Plan::mixed_radix_transform_recursive ( const Array< Complex > &  input, const size_t  factor_index, const size_t  current_size, const bool  invert  ) const

inlineprivate

Definition at line 7119 of file fft.H.

References Aleph::Array< T >::append(), Aleph::blossom_maximum_cardinality_matching(), Aleph::Array< T >::create(), Aleph::FFT< Real >::Plan::factors_, Aleph::FFT< Real >::Plan::mixed_radix_transform_recursive(), output, Aleph::Array< T >::reserve(), Aleph::FFT< Real >::Plan::root_for_length(), and Aleph::sum().

Referenced by Aleph::FFT< Real >::Plan::apply_mixed_radix_transform(), and Aleph::FFT< Real >::Plan::mixed_radix_transform_recursive().

pinverse_transform()

template<std::floating_point Real = double>

Array< Complex > Aleph::FFT< Real >::Plan::pinverse_transform ( ThreadPool &  pool, const Array< Complex > &  input, const size_t  chunk_size = 0  ) const

inline

Parallel inverse transform returning a new array.

Definition at line 7407 of file fft.H.

References Aleph::blossom_maximum_cardinality_matching(), and Aleph::FFT< Real >::Plan::ptransformed().

pinverse_transform_batch()

template<std::floating_point Real = double>

Array< Array< Complex > > Aleph::FFT< Real >::Plan::pinverse_transform_batch ( ThreadPool &  pool, const Array< Array< Complex > > &  input, const size_t  chunk_size = 0, const bool  prefer_simd = true  ) const

inline

Returns the parallel inverse batch transform.

Definition at line 7506 of file fft.H.

References Aleph::blossom_maximum_cardinality_matching(), and Aleph::FFT< Real >::Plan::ptransformed_batch().

pinverse_transform_real()

template<std::floating_point Real = double>

Array< Real > Aleph::FFT< Real >::Plan::pinverse_transform_real ( ThreadPool &  pool, const Array< Complex > &  input, const size_t  chunk_size = 0  ) const

inline

Parallel IFFT projected back to real values.

Definition at line 7350 of file fft.H.

References ah_invalid_argument_if, Aleph::blossom_maximum_cardinality_matching(), Aleph::FFT< Real >::Plan::half_plan_, Aleph::FFT< Real >::inverse_transform_real_optimized_impl(), Aleph::FFT< Real >::Plan::n_, output, Aleph::FFT< Real >::project_real_output(), Aleph::FFT< Real >::Plan::ptransform(), Aleph::Array< T >::size(), Aleph::FFT< Real >::Plan::supports_power_of_two_real_optimization(), and Aleph::FFT< Real >::validate_real_spectrum().

Referenced by Aleph::FFT< Real >::OverlapAdd::convolve_impl(), Aleph::FFT< Real >::Plan::pinverse_transform_real_batch(), Aleph::FFT< Real >::Plan::pirfft(), Aleph::FFT< Real >::OverlapAdd::process_chunk_impl(), and Aleph::FFT< Real >::ISTFTProcessor::process_frame_impl().

pinverse_transform_real_batch()

template<std::floating_point Real = double>

Array< Array< Real > > Aleph::FFT< Real >::Plan::pinverse_transform_real_batch ( ThreadPool &  pool, const Array< Array< Complex > > &  input, const size_t  chunk_size = 0, const bool  prefer_simd = true  ) const

inline

Returns the parallel inverse batch transform projected back to real values.

Definition at line 7536 of file fft.H.

References ah_invalid_argument_if, Aleph::blossom_maximum_cardinality_matching(), Aleph::FFT< Real >::Plan::inverse_transform_real(), Aleph::FFT< Real >::Plan::n_, Aleph::ThreadPool::num_threads(), output, Aleph::parallel_for_index(), Aleph::FFT< Real >::Plan::pinverse_transform_real(), and Aleph::FFT< Real >::Plan::size().

Referenced by Aleph::FFT< Real >::OverlapAddBank::convolve_impl(), Aleph::FFT< Real >::Plan::pirfft_batch(), and Aleph::FFT< Real >::OverlapAddBank::process_chunk_batch_impl().

pirfft()

template<std::floating_point Real = double>

Array< Real > Aleph::FFT< Real >::Plan::pirfft ( ThreadPool &  pool, const Array< Complex > &  spectrum, const size_t  chunk_size = 0  ) const

inline

Parallel Complex-to-Real Inverse FFT (IRFFT).

Definition at line 7611 of file fft.H.

References Aleph::FFT< Real >::expand_real_spectrum(), Aleph::FFT< Real >::Plan::n_, Aleph::FFT< Real >::Plan::pinverse_transform_real(), and Aleph::FFT< Real >::spectrum().

pirfft_batch()

template<std::floating_point Real = double>

Array< Array< Real > > Aleph::FFT< Real >::Plan::pirfft_batch ( ThreadPool &  pool, const Array< Array< Complex > > &  spectra, const size_t  chunk_size = 0  ) const

inline

Computes a parallel batch of Complex-to-Real Inverse FFTs.

Definition at line 7649 of file fft.H.

References Aleph::blossom_maximum_cardinality_matching(), Aleph::FFT< Real >::expand_real_batch_spectra(), Aleph::FFT< Real >::Plan::n_, and Aleph::FFT< Real >::Plan::pinverse_transform_real_batch().

prfft()

template<std::floating_point Real = double>

Array< Complex > Aleph::FFT< Real >::Plan::prfft ( ThreadPool &  pool, const Array< Real > &  input, const size_t  chunk_size = 0  ) const

inline

Parallel Real-to-Complex FFT (RFFT).

Definition at line 7584 of file fft.H.

References ah_invalid_argument_if, Aleph::blossom_maximum_cardinality_matching(), Aleph::FFT< Real >::compact_real_spectrum(), Aleph::FFT< Real >::Plan::n_, Aleph::FFT< Real >::project_to_plan_spectrum(), and Aleph::Array< T >::size().

prfft_batch()

template<std::floating_point Real = double>

Array< Array< Complex > > Aleph::FFT< Real >::Plan::prfft_batch ( ThreadPool &  pool, const Array< Array< Real > > &  input, const size_t  chunk_size = 0  ) const

inline

Computes a parallel batch of Real-to-Complex FFTs.

Definition at line 7631 of file fft.H.

References Aleph::blossom_maximum_cardinality_matching(), Aleph::FFT< Real >::compact_real_batch_spectra(), and Aleph::FFT< Real >::project_to_plan_batch_spectra().

ptransform()

template<std::floating_point Real = double>

void Aleph::FFT< Real >::Plan::ptransform ( ThreadPool &  pool, Array< Complex > &  a, const bool  invert, const size_t  chunk_size = 0  ) const

inline

Parallel in-place transform using a thread pool.

Parameters

pool	Thread pool for parallel butterfly stages.
a	Array of complex values (size must equal plan size).
invert	If true, compute the inverse transform.
chunk_size	Minimum iterations per parallel chunk (0 = auto).

Definition at line 7387 of file fft.H.

References Aleph::FFT< Real >::Plan::apply_transform().

Referenced by Aleph::FFT< Real >::OverlapAdd::convolve_impl(), Aleph::FFT< Real >::Plan::pinverse_transform_real(), Aleph::FFT< Real >::OverlapAdd::process_chunk_impl(), and Aleph::FFT< Real >::Plan::ptransformed().

ptransform_batch()

template<std::floating_point Real = double>

void Aleph::FFT< Real >::Plan::ptransform_batch ( ThreadPool &  pool, Array< Array< Complex > > &  batch, const bool  invert, const size_t  chunk_size = 0, const bool  prefer_simd = true  ) const

inline

Parallel batch transform for equal-length complex inputs.

When the batch has more than one item, parallelism is applied across batch elements and each individual transform runs sequentially to avoid nested thread-pool oversubscription.

Definition at line 7438 of file fft.H.

References ah_invalid_argument_if, Aleph::and, Aleph::FFT< Real >::Plan::apply_transform(), Aleph::FFT< Real >::Plan::automatic_batch_simd_candidate(), Aleph::blossom_maximum_cardinality_matching(), Aleph::FFT< Real >::Plan::n_, Aleph::ThreadPool::num_threads(), Aleph::parallel_for_index(), and Aleph::FFT< Real >::Plan::size().

Referenced by Aleph::FFT< Real >::OverlapAddBank::convolve_impl(), Aleph::FFT< Real >::OverlapAddBank::process_chunk_batch_impl(), and Aleph::FFT< Real >::Plan::ptransformed_batch().

ptransformed()

template<std::floating_point Real = double>

Array< Complex > Aleph::FFT< Real >::Plan::ptransformed ( ThreadPool &  pool, const Array< Complex > &  input, const bool  invert = false, const size_t  chunk_size = 0  ) const

inline

Parallel transform returning a new array.

Definition at line 7396 of file fft.H.

References Aleph::blossom_maximum_cardinality_matching(), output, and Aleph::FFT< Real >::Plan::ptransform().

Referenced by Aleph::FFT< Real >::Plan::pinverse_transform().

ptransformed_batch()

template<std::floating_point Real = double>

Array< Array< Complex > > Aleph::FFT< Real >::Plan::ptransformed_batch ( ThreadPool &  pool, const Array< Array< Complex > > &  input, const bool  invert = false, const size_t  chunk_size = 0, const bool  prefer_simd = true  ) const

inline

Returns the parallel batch FFT/IFFT as a new array of arrays.

Definition at line 7486 of file fft.H.

References Aleph::blossom_maximum_cardinality_matching(), output, and Aleph::FFT< Real >::Plan::ptransform_batch().

Referenced by Aleph::FFT< Real >::Plan::pinverse_transform_batch().

rfft()

template<std::floating_point Real = double>

Array< Complex > Aleph::FFT< Real >::Plan::rfft ( const Array< Real > &  input ) const

inline

Computes the Real-to-Complex FFT (RFFT).

Returns the compact spectrum (size N/2 + 1) for a real input.

Parameters

input

Real input array (size must equal plan size).

Returns

Compact complex spectrum.

Definition at line 7574 of file fft.H.

References ah_invalid_argument_if, Aleph::blossom_maximum_cardinality_matching(), Aleph::FFT< Real >::compact_real_spectrum(), Aleph::FFT< Real >::Plan::n_, Aleph::FFT< Real >::project_to_plan_spectrum(), and Aleph::Array< T >::size().

rfft_batch()

template<std::floating_point Real = double>

Array< Array< Complex > > Aleph::FFT< Real >::Plan::rfft_batch ( const Array< Array< Real > > &  input ) const

inline

Computes a batch of Real-to-Complex FFTs.

Definition at line 7623 of file fft.H.

References Aleph::blossom_maximum_cardinality_matching(), Aleph::FFT< Real >::compact_real_batch_spectra(), and Aleph::FFT< Real >::project_to_plan_batch_spectra().

root_for_length()

template<std::floating_point Real = double>

Complex Aleph::FFT< Real >::Plan::root_for_length ( const size_t  length, const size_t  exponent, const bool  invert  ) const

inlineprivate

Definition at line 7105 of file fft.H.

References Aleph::blossom_maximum_cardinality_matching(), Aleph::FFT< Real >::Plan::n_, root(), and Aleph::FFT< Real >::Plan::roots_.

Referenced by Aleph::FFT< Real >::Plan::mixed_radix_transform_recursive().

should_use_avx2()

template<std::floating_point Real = double>

bool Aleph::FFT< Real >::Plan::should_use_avx2 ( ThreadPool *  pool, const bool  prefer_simd  ) const

inlineprivatenoexcept

Definition at line 6841 of file fft.H.

References Aleph::and, Aleph::FFT< Real >::automatic, Aleph::FFT< Real >::avx2, Aleph::FFT< Real >::avx2_only, Aleph::blossom_maximum_cardinality_matching(), Aleph::FFT< Real >::detected_simd_backend(), Aleph::FFT< Real >::Plan::log_n_, Aleph::FFT< Real >::neon_only, Aleph::FFT< Real >::Plan::power_of_two, Aleph::FFT< Real >::scalar_only, Aleph::FFT< Real >::simd_preference(), and Aleph::FFT< Real >::Plan::strategy_.

Referenced by Aleph::FFT< Real >::Plan::apply_butterflies().

should_use_neon()

template<std::floating_point Real = double>

bool Aleph::FFT< Real >::Plan::should_use_neon ( ThreadPool *  pool, const bool  prefer_simd  ) const

inlineprivatenoexcept

Definition at line 6870 of file fft.H.

References Aleph::and, Aleph::FFT< Real >::automatic, Aleph::FFT< Real >::avx2_only, Aleph::blossom_maximum_cardinality_matching(), Aleph::FFT< Real >::detected_simd_backend(), Aleph::FFT< Real >::Plan::log_n_, Aleph::FFT< Real >::neon, Aleph::FFT< Real >::neon_only, Aleph::FFT< Real >::Plan::power_of_two, Aleph::FFT< Real >::scalar_only, Aleph::FFT< Real >::simd_preference(), and Aleph::FFT< Real >::Plan::strategy_.

Referenced by Aleph::FFT< Real >::Plan::apply_butterflies().

size()

template<std::floating_point Real = double>

size_t Aleph::FFT< Real >::Plan::size ( ) const

inlinenoexcept

Returns the transform size this plan was built for.

Definition at line 7284 of file fft.H.

References Aleph::FFT< Real >::Plan::n_.

Referenced by Aleph::FFT< Real >::Plan::inverse_transform_real_batch(), Aleph::FFT< Real >::Plan::pinverse_transform_real_batch(), Aleph::FFT< Real >::Plan::ptransform_batch(), and Aleph::FFT< Real >::Plan::transform_batch().

supports_power_of_two_real_optimization()

template<std::floating_point Real = double>

bool Aleph::FFT< Real >::Plan::supports_power_of_two_real_optimization ( ) const

inlineprivatenoexcept

Definition at line 7237 of file fft.H.

References Aleph::and, Aleph::FFT< Real >::Plan::half_plan_, Aleph::FFT< Real >::Plan::n_, Aleph::FFT< Real >::Plan::power_of_two, and Aleph::FFT< Real >::Plan::strategy_.

Referenced by Aleph::FFT< Real >::Plan::inverse_transform_real(), and Aleph::FFT< Real >::Plan::pinverse_transform_real().

transform()

template<std::floating_point Real = double>

void Aleph::FFT< Real >::Plan::transform ( Array< Complex > &  a, const bool  invert  ) const

inline

Computes the FFT or IFFT in-place using precomputed tables.

Parameters

a	Array of complex values (size must equal plan size).
invert	If true, compute the inverse transform (with 1/N scaling).

Exceptions

std::invalid_argument

if a.size() differs from plan size.

Definition at line 7292 of file fft.H.

References Aleph::FFT< Real >::Plan::apply_transform().

Referenced by Aleph::FFT< Real >::OverlapAdd::OverlapAdd(), Aleph::FFT< Real >::OverlapAddBank::OverlapAddBank(), Aleph::FFT< Real >::OverlapSave::OverlapSave(), Aleph::FFT< Real >::PartitionedConvolver::PartitionedConvolver(), Aleph::FFT< Real >::OverlapAdd::convolve_impl(), Aleph::FFT< Real >::Plan::inverse_transform_real(), Aleph::FFT< Real >::OverlapAdd::process_chunk_impl(), Aleph::FFT< Real >::OverlapSave::process_chunk_impl(), Aleph::FFT< Real >::PartitionedConvolver::process_partition_impl(), and Aleph::FFT< Real >::Plan::transformed().

transform_batch()

template<std::floating_point Real = double>

void Aleph::FFT< Real >::Plan::transform_batch ( Array< Array< Complex > > &  batch, const bool  invert, const bool  prefer_simd = true  ) const

inline

In-place batch transform for equal-length complex inputs.

Definition at line 7415 of file fft.H.

References ah_invalid_argument_if, Aleph::and, Aleph::FFT< Real >::Plan::apply_transform(), Aleph::FFT< Real >::Plan::automatic_batch_simd_candidate(), Aleph::blossom_maximum_cardinality_matching(), Aleph::FFT< Real >::Plan::n_, and Aleph::FFT< Real >::Plan::size().

Referenced by Aleph::FFT< Real >::OverlapAddBank::convolve_impl(), Aleph::FFT< Real >::OverlapAddBank::process_chunk_batch_impl(), and Aleph::FFT< Real >::Plan::transformed_batch().

transformed()

template<std::floating_point Real = double>

Array< Complex > Aleph::FFT< Real >::Plan::transformed ( const Array< Complex > &  input, const bool  invert = false  ) const

inline

Computes the FFT or IFFT returning a new array.

Parameters

input	Input array (size must equal plan size).
invert	If true, compute the inverse transform.

Returns

A new array containing the transformed values.

Definition at line 7304 of file fft.H.

References Aleph::blossom_maximum_cardinality_matching(), output, and Aleph::FFT< Real >::Plan::transform().

Referenced by Aleph::FFT< Real >::Plan::inverse_transform().

transformed_batch()

template<std::floating_point Real = double>

Array< Array< Complex > > Aleph::FFT< Real >::Plan::transformed_batch ( const Array< Array< Complex > > &  input, const bool  invert = false, const bool  prefer_simd = true  ) const

inline

Returns the batch FFT/IFFT as a new array of arrays.

Definition at line 7475 of file fft.H.

References Aleph::blossom_maximum_cardinality_matching(), output, and Aleph::FFT< Real >::Plan::transform_batch().

Referenced by Aleph::FFT< Real >::Plan::inverse_transform_batch().

Member Data Documentation

bit_rev_

template<std::floating_point Real = double>

Array<size_t> Aleph::FFT< Real >::Plan::bit_rev_

private

Definition at line 6306 of file fft.H.

Referenced by Aleph::FFT< Real >::Plan::apply_bit_reversal(), and Aleph::FFT< Real >::Plan::initialize_power_of_two_plan().

bluestein_chirp_

template<std::floating_point Real = double>

Array<Complex> Aleph::FFT< Real >::Plan::bluestein_chirp_

private

Definition at line 6312 of file fft.H.

Referenced by Aleph::FFT< Real >::Plan::apply_bluestein_transform(), and Aleph::FFT< Real >::Plan::initialize_bluestein_plan().

bluestein_kernel_forward_

template<std::floating_point Real = double>

Array<Complex> Aleph::FFT< Real >::Plan::bluestein_kernel_forward_

private

Definition at line 6313 of file fft.H.

Referenced by Aleph::FFT< Real >::Plan::apply_bluestein_transform(), and Aleph::FFT< Real >::Plan::initialize_bluestein_plan().

bluestein_kernel_inverse_

template<std::floating_point Real = double>

Array<Complex> Aleph::FFT< Real >::Plan::bluestein_kernel_inverse_

private

Definition at line 6314 of file fft.H.

Referenced by Aleph::FFT< Real >::Plan::apply_bluestein_transform(), and Aleph::FFT< Real >::Plan::initialize_bluestein_plan().

bluestein_plan_

template<std::floating_point Real = double>

std::shared_ptr<const Plan> Aleph::FFT< Real >::Plan::bluestein_plan_

private

Definition at line 6315 of file fft.H.

Referenced by Aleph::FFT< Real >::Plan::apply_bluestein_transform(), and Aleph::FFT< Real >::Plan::initialize_bluestein_plan().

bluestein_size_

template<std::floating_point Real = double>

size_t Aleph::FFT< Real >::Plan::bluestein_size_ = 0

private

Definition at line 6311 of file fft.H.

Referenced by Aleph::FFT< Real >::Plan::apply_bluestein_transform(), and Aleph::FFT< Real >::Plan::initialize_bluestein_plan().

factors_

template<std::floating_point Real = double>

Array<size_t> Aleph::FFT< Real >::Plan::factors_

private

Definition at line 6309 of file fft.H.

Referenced by Aleph::FFT< Real >::Plan::Plan(), and Aleph::FFT< Real >::Plan::mixed_radix_transform_recursive().

half_plan_

template<std::floating_point Real = double>

std::shared_ptr<const Plan> Aleph::FFT< Real >::Plan::half_plan_

private

Definition at line 6308 of file fft.H.

Referenced by Aleph::FFT< Real >::Plan::initialize_power_of_two_plan(), Aleph::FFT< Real >::Plan::inverse_transform_real(), Aleph::FFT< Real >::Plan::pinverse_transform_real(), and Aleph::FFT< Real >::Plan::supports_power_of_two_real_optimization().

log_n_

template<std::floating_point Real = double>

size_t Aleph::FFT< Real >::Plan::log_n_ = 0

private

Definition at line 6305 of file fft.H.

Referenced by Aleph::FFT< Real >::Plan::apply_butterflies(), Aleph::FFT< Real >::Plan::automatic_batch_simd_candidate(), Aleph::FFT< Real >::Plan::initialize_power_of_two_plan(), Aleph::FFT< Real >::Plan::should_use_avx2(), and Aleph::FFT< Real >::Plan::should_use_neon().

n_

template<std::floating_point Real = double>

size_t Aleph::FFT< Real >::Plan::n_ = 0

private

Definition at line 6303 of file fft.H.

Referenced by Aleph::FFT< Real >::Plan::Plan(), Aleph::FFT< Real >::Plan::apply_bit_reversal(), Aleph::FFT< Real >::Plan::apply_bluestein_transform(), Aleph::FFT< Real >::Plan::apply_butterflies(), Aleph::FFT< Real >::Plan::apply_mixed_radix_transform(), Aleph::FFT< Real >::Plan::apply_transform(), Aleph::FFT< Real >::Plan::automatic_batch_simd_candidate(), Aleph::FFT< Real >::Plan::initialize_bluestein_plan(), Aleph::FFT< Real >::Plan::initialize_mixed_radix_plan(), Aleph::FFT< Real >::Plan::initialize_power_of_two_plan(), Aleph::FFT< Real >::Plan::inverse_transform_real(), Aleph::FFT< Real >::Plan::inverse_transform_real_batch(), Aleph::FFT< Real >::Plan::irfft(), Aleph::FFT< Real >::Plan::irfft_batch(), Aleph::FFT< Real >::Plan::pinverse_transform_real(), Aleph::FFT< Real >::Plan::pinverse_transform_real_batch(), Aleph::FFT< Real >::Plan::pirfft(), Aleph::FFT< Real >::Plan::pirfft_batch(), Aleph::FFT< Real >::Plan::prfft(), Aleph::FFT< Real >::Plan::ptransform_batch(), Aleph::FFT< Real >::Plan::rfft(), Aleph::FFT< Real >::Plan::root_for_length(), Aleph::FFT< Real >::Plan::size(), Aleph::FFT< Real >::Plan::supports_power_of_two_real_optimization(), and Aleph::FFT< Real >::Plan::transform_batch().

roots_

template<std::floating_point Real = double>

Array<Complex> Aleph::FFT< Real >::Plan::roots_

private

Definition at line 6310 of file fft.H.

Referenced by Aleph::FFT< Real >::Plan::initialize_mixed_radix_plan(), and Aleph::FFT< Real >::Plan::root_for_length().

strategy_

template<std::floating_point Real = double>

Strategy Aleph::FFT< Real >::Plan::strategy_ = Strategy::empty

private

Definition at line 6304 of file fft.H.

Referenced by Aleph::FFT< Real >::Plan::Plan(), Aleph::FFT< Real >::Plan::apply_transform(), Aleph::FFT< Real >::Plan::automatic_batch_simd_candidate(), Aleph::FFT< Real >::Plan::initialize_bluestein_plan(), Aleph::FFT< Real >::Plan::initialize_mixed_radix_plan(), Aleph::FFT< Real >::Plan::initialize_power_of_two_plan(), Aleph::FFT< Real >::Plan::should_use_avx2(), Aleph::FFT< Real >::Plan::should_use_neon(), and Aleph::FFT< Real >::Plan::supports_power_of_two_real_optimization().

twiddles_

template<std::floating_point Real = double>

Array<Complex> Aleph::FFT< Real >::Plan::twiddles_

private

Definition at line 6307 of file fft.H.

Referenced by Aleph::FFT< Real >::Plan::apply_butterflies(), and Aleph::FFT< Real >::Plan::initialize_power_of_two_plan().

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The documentation for this class was generated from the following file:

• fft.H