num::spectral Namespace Reference

Classes
class	FFTPlan
	Precomputed plan for repeated complex transforms of a fixed size. More...

Enumerations
enum class	FFTBackend { seq , simd , stdsimd , fftw }
	Selects which backend handles an FFT operation. More...

Functions
void	fft (const CVector &in, CVector &out, FFTBackend b=default_fft_backend)
	Forward complex DFT. out must be pre-allocated to in.size().
void	ifft (const CVector &in, CVector &out, FFTBackend b=default_fft_backend)
	Inverse complex DFT (unnormalised: result = n * true_inverse).
void	rfft (const Vector &in, CVector &out, FFTBackend b=default_fft_backend)
	Real-to-complex forward DFT. out must be pre-allocated to n/2+1.
void	irfft (const CVector &in, int n, Vector &out, FFTBackend b=default_fft_backend)
	Complex-to-real inverse DFT (unnormalised).

Variables
constexpr FFTBackend	seq = FFTBackend::seq
constexpr FFTBackend	fftw = FFTBackend::fftw
constexpr FFTBackend	fft_simd = FFTBackend::simd
constexpr FFTBackend	fft_stdsimd = FFTBackend::stdsimd
constexpr bool	has_fftw
	True when FFTW3 was found at configure time.
constexpr bool	has_fft_simd
	True when handwritten AVX2 or NEON backend is available.
constexpr bool	has_fft_stdsimd
	True when std::experimental::simd is available.
constexpr FFTBackend	default_fft_backend
	Automatically selected at configure time: fftw > simd > seq.

Enumeration Type Documentation

FFTBackend

enum class num::spectral::FFTBackend

strong

Selects which backend handles an FFT operation.

Enumerator
seq	Native Cooley-Tukey radix-2 DIT – always available (power-of-two only)
simd	Handwritten AVX2 / NEON butterfly – falls back to seq if unavailable.
stdsimd	std::experimental::simd butterfly – requires NUMERICS_HAS_STD_SIMD
fftw	FFTW3 (mixed-radix, AVX / NEON optimised) – requires NUMERICS_HAS_FFTW.

Definition at line 26 of file fft.hpp.

Function Documentation

fft()

void num::spectral::fft	(	const CVector &	in,
		CVector &	out,
		FFTBackend	b = default_fft_backend
	)

Forward complex DFT. out must be pre-allocated to in.size().

Definition at line 15 of file fft.cpp.

References backends::opt::fft(), backends::seq::fft(), fftw, num::ipow(), simd, and stdsimd.

ifft()

void num::spectral::ifft	(	const CVector &	in,
		CVector &	out,
		FFTBackend	b = default_fft_backend
	)

Inverse complex DFT (unnormalised: result = n * true_inverse).

Definition at line 31 of file fft.cpp.

References fftw, backends::opt::ifft(), backends::seq::ifft(), num::ipow(), simd, and stdsimd.

irfft()

void num::spectral::irfft	(	const CVector &	in,
		int	n,
		Vector &	out,
		FFTBackend	b = default_fft_backend
	)

Complex-to-real inverse DFT (unnormalised).

Parameters

n	Length of the real output (must satisfy in.size() == n/2+1).

Definition at line 61 of file fft.cpp.

References fftw, num::ipow(), backends::opt::irfft(), backends::seq::irfft(), simd, and stdsimd.

rfft()

void num::spectral::rfft	(	const Vector &	in,
		CVector &	out,
		FFTBackend	b = default_fft_backend
	)

Real-to-complex forward DFT. out must be pre-allocated to n/2+1.

Definition at line 46 of file fft.cpp.

References fftw, num::ipow(), backends::opt::rfft(), backends::seq::rfft(), simd, and stdsimd.

Variable Documentation

default_fft_backend

constexpr FFTBackend num::spectral::default_fft_backend

inlineconstexpr

Initial value:

=
 
 
 
 
 
    FFTBackend::seq

Automatically selected at configure time: fftw > simd > seq.

Definition at line 65 of file fft.hpp.

fft_simd

constexpr FFTBackend num::spectral::fft_simd = FFTBackend::simd

inlineconstexpr

Definition at line 37 of file fft.hpp.

fft_stdsimd

constexpr FFTBackend num::spectral::fft_stdsimd = FFTBackend::stdsimd

inlineconstexpr

Definition at line 38 of file fft.hpp.

fftw

constexpr FFTBackend num::spectral::fftw = FFTBackend::fftw

inlineconstexpr

Definition at line 36 of file fft.hpp.

has_fft_simd

constexpr bool num::spectral::has_fft_simd

inlineconstexpr

Initial value:

=
 
 
 
    false

True when handwritten AVX2 or NEON backend is available.

Definition at line 49 of file fft.hpp.

has_fft_stdsimd

constexpr bool num::spectral::has_fft_stdsimd

inlineconstexpr

Initial value:

=
 
 
 
    false

True when std::experimental::simd is available.

Definition at line 57 of file fft.hpp.

has_fftw

constexpr bool num::spectral::has_fftw

inlineconstexpr

Initial value:

=
 
 
 
    false

True when FFTW3 was found at configure time.

Definition at line 41 of file fft.hpp.

seq

constexpr FFTBackend num::spectral::seq = FFTBackend::seq

inlineconstexpr

Definition at line 35 of file fft.hpp.