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.DS_Store
/.build
/Packages
xcuserdata/
DerivedData/
.swiftpm/configuration/registries.json
.swiftpm/xcode/package.xcworkspace/contents.xcworkspacedata
.netrc

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Copyright (c) 2024 John K. Luebs
Copyright (c) 2020 Dario Mambro ( dario.mambro@gmail.com )
Copyright (c) 2019 Hayati Ayguen ( h_ayguen@web.de )
Copyright (c) 2013 Julien Pommier ( pommier@modartt.com )
Copyright (c) 2004 the University Corporation for Atmospheric
Research ("UCAR"). All rights reserved. Developed by NCAR's
Computational and Information Systems Laboratory, UCAR,
www.cisl.ucar.edu.
Redistribution and use of the Software in source and binary forms,
with or without modification, is permitted provided that the
following conditions are met:
- Neither the names of NCAR's Computational and Information Systems
Laboratory, the University Corporation for Atmospheric Research,
nor the names of its sponsors or contributors may be used to
endorse or promote products derived from this Software without
specific prior written permission.
- Redistributions of source code must retain the above copyright
notices, this list of conditions, and the disclaimer below.
- Redistributions in binary form must reproduce the above copyright
notice, this list of conditions, and the disclaimer below in the
documentation and/or other materials provided with the
distribution.
THIS SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING, BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
NONINFRINGEMENT. IN NO EVENT SHALL THE CONTRIBUTORS OR COPYRIGHT
HOLDERS BE LIABLE FOR ANY CLAIM, INDIRECT, INCIDENTAL, SPECIAL,
EXEMPLARY, OR CONSEQUENTIAL DAMAGES OR OTHER LIABILITY, WHETHER IN AN
ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS WITH THE
SOFTWARE.

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{
"originHash" : "d50b9049eb671b1ad14bc8ba592c78735f9e357a6b59835343af6e20e8be4701",
"pins" : [
{
"identity" : "swift-numerics",
"kind" : "remoteSourceControl",
"location" : "https://github.com/apple/swift-numerics",
"state" : {
"revision" : "0a5bc04095a675662cf24757cc0640aa2204253b",
"version" : "1.0.2"
}
}
],
"version" : 3
}

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// swift-tools-version: 6.0
// The swift-tools-version declares the minimum version of Swift required to build this package.
import PackageDescription
let package = Package(
name: "SwiftPFFFT",
products: [
.library(
name: "PFFFT",
targets: ["PFFFT", "PFFFTLib"]
),
],
dependencies: [
.package(url: "https://github.com/apple/swift-numerics", from: "1.0.0"),
],
targets: [
.target(
name: "PFFFTLib",
publicHeadersPath: "include",
cSettings: [
.define("PFFFT_SCALVEC_ENABLED", to: "1"),
.define("_USE_MATH_DEFINES"),
.define("NDEBUG"),
.unsafeFlags(["-O3"]),
]
),
.target(
name: "PFFFT",
dependencies: ["PFFFTLib", .product(name: "Numerics", package: "swift-numerics")]
),
.testTarget(
name: "PFFFTTests",
dependencies: ["PFFFT"]
),
],
cLanguageStandard: .c99
)

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# SwiftPFFFT
Swift package providing a PFFFT (Pretty Fast, Fast Fourier Transform) library with wrapper.
This code is based on the marton78 fork of PFFFT that was forked from the original PFFFT implementation
by Julien Pommier. This fork provides support for doubles in addition to floats and provides additional SIMD implementations:
The origin for the C implementation in this package is https://github.com/marton78/pffft.
PFFFT provides substantial performance improvement over KissFFT. The advantage over FFTW is reasonable
performance with much simpler usage and a permissive 3 clause BSD license.
## Example
``` swift
// construct an interface for FFT, IFFT and convolutions. The interface is parameterized on the
// type of element in the signal (time) domain. The spectrum (frequency) domain type will always be
// complex. For a real valued signal the spectrum size will be `n / 2`, with the packing convention
//
let fft = try FFT<Complex<Float>>(n: 16)
let signal = fft.makeSignalBuffer()
signal.mutateEach { (i, v) in
v = Complex(Float(i) + 1.0, Float(i) - 2.0)
}
let spectrum = fft.makeSpectrumBuffer()
fft.forward(signal: signal, spectrum: spectrum)
fft.inverse(spectrum: spectrum, signal: signal)
```

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import ComplexModule
import RealModule
let bufferAlignment = 32
@frozen
public struct Buffer<T>: ~Copyable {
public let buffer: UnsafeMutableBufferPointer<T>
var count: Int { buffer.count }
var baseAddress: UnsafeMutablePointer<T> { buffer.baseAddress! }
public init(capacity: Int) {
buffer = UnsafeMutableRawBufferPointer.allocate(
byteCount: MemoryLayout<T>.stride * capacity,
alignment: bufferAlignment
).bindMemory(to: T.self)
}
deinit {
buffer.deallocate()
}
@inlinable public func withUnsafeMutableBufferPointer<R>(_ body: (UnsafeMutableBufferPointer<T>) throws -> R) rethrows -> R {
try body(buffer)
}
@inlinable public func withUnsafeBufferPointer<R>(_ body: (UnsafeBufferPointer<T>) throws -> R) rethrows -> R {
try body(UnsafeBufferPointer(buffer))
}
@inlinable public func withUnsafeMutableBytes<R>(_ body: (UnsafeMutableRawBufferPointer) throws -> R) rethrows -> R {
try body(UnsafeMutableRawBufferPointer(buffer))
}
@inlinable public func map<U>(_ transform: (T) throws -> U) rethrows -> [U] {
try buffer.map(transform)
}
@inlinable public func mutateEach(_ body: (Int, inout T) throws -> Void) rethrows {
for i in 0 ..< buffer.count {
try body(i, &buffer[i])
}
}
}
public protocol ComplexType {
associatedtype RealType: Real
var real: RealType { get set }
var imaginary: RealType { get set }
}
extension Complex: ComplexType {}
public extension Buffer where T: ComplexType {
@inlinable public func mutateEachSwapLast(_ body: (Int, inout T) throws -> Void) rethrows {
for i in 0 ..< buffer.count {
try body(i, &buffer[i])
}
buffer[0].imaginary = buffer[buffer.count - 1].real
}
}

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internal import PFFFTLib
import ComplexModule
import RealModule
@frozen
public enum FFTType {
case real
case complex
}
@frozen
public enum FFTSign {
case forward
case backward
}
public enum FFTError: Error {
case invalidSize
}
public protocol FFTElement {
associatedtype FFTScalarType: FFTScalar
associatedtype FFTComplexType = Complex<FFTScalarType>
static func pffftSetup(_ n: Int, _ type: FFTType) throws -> OpaquePointer
static func pffftMinFftSize(_ type: FFTType) -> Int
static func pffftIsValidSize(_ n: Int, _ type: FFTType) -> Bool
static func pffftNearestValidSize(_ n: Int, _ type: FFTType, _ higher: Bool) -> Int
}
public protocol FFTScalar: Real {
static func pffftTransformOrdered(_ ptr: OpaquePointer, _ input: UnsafeMutablePointer<Self>, _ output: UnsafeMutablePointer<Self>, _ work: UnsafeMutablePointer<Self>?, _ dir: FFTSign)
static func pffftTransform(_ ptr: OpaquePointer, _ input: UnsafeMutablePointer<Self>, _ output: UnsafeMutablePointer<Self>, _ work: UnsafeMutablePointer<Self>?, _ dir: FFTSign)
static func pffftZreorder(_ ptr: OpaquePointer, _ input: UnsafeMutablePointer<Self>, _ output: UnsafeMutablePointer<Self>, _ dir: FFTSign)
static func pffftZconvolveAccumulate(_ ptr: OpaquePointer, _ dftA: UnsafeMutablePointer<Self>, _ dftB: UnsafeMutablePointer<Self>, _ dftAB: UnsafeMutablePointer<Self>, _ scaling: Self)
static func pffftZconvolveNoAccu(_ ptr: OpaquePointer, _ dftA: UnsafeMutablePointer<Self>, _ dftB: UnsafeMutablePointer<Self>, _ dftAB: UnsafeMutablePointer<Self>, _ scaling: Self)
static func pffftSimdArch() -> String
}
extension Float: FFTScalar {
public static func pffftTransformOrdered(_ ptr: OpaquePointer, _ input: UnsafeMutablePointer<Self>, _ output: UnsafeMutablePointer<Self>, _ work: UnsafeMutablePointer<Self>?, _ dir: FFTSign) {
pffft_transform_ordered(ptr, input, output, work, pffft_direction_t(dir))
}
public static func pffftTransform(_ ptr: OpaquePointer, _ input: UnsafeMutablePointer<Self>, _ output: UnsafeMutablePointer<Self>, _ work: UnsafeMutablePointer<Self>?, _ dir: FFTSign) {
pffft_transform(ptr, input, output, work, pffft_direction_t(dir))
}
public static func pffftZreorder(_ ptr: OpaquePointer, _ input: UnsafeMutablePointer<Self>, _ output: UnsafeMutablePointer<Self>, _ dir: FFTSign) {
pffft_zreorder(ptr, input, output, pffft_direction_t(dir))
}
public static func pffftZconvolveAccumulate(_ ptr: OpaquePointer, _ dftA: UnsafeMutablePointer<Self>, _ dftB: UnsafeMutablePointer<Self>, _ dftAB: UnsafeMutablePointer<Self>, _ scaling: Self) {
pffft_zconvolve_accumulate(ptr, dftA, dftB, dftAB, scaling)
}
public static func pffftZconvolveNoAccu(_ ptr: OpaquePointer, _ dftA: UnsafeMutablePointer<Self>, _ dftB: UnsafeMutablePointer<Self>, _ dftAB: UnsafeMutablePointer<Self>, _ scaling: Self) {
pffft_zconvolve_no_accu(ptr, dftA, dftB, dftAB, scaling)
}
public static func pffftSimdArch() -> String {
String(cString: pffft_simd_arch())
}
}
extension Double: FFTScalar {
public static func pffftTransformOrdered(_ ptr: OpaquePointer, _ input: UnsafeMutablePointer<Double>, _ output: UnsafeMutablePointer<Double>, _ work: UnsafeMutablePointer<Double>?, _ dir: FFTSign) {
pffftd_transform_ordered(ptr, input, output, work, pffft_direction_t(dir))
}
public static func pffftTransform(_ ptr: OpaquePointer, _ input: UnsafeMutablePointer<Double>, _ output: UnsafeMutablePointer<Double>, _ work: UnsafeMutablePointer<Double>?, _ dir: FFTSign) {
pffftd_transform(ptr, input, output, work, pffft_direction_t(dir))
}
public static func pffftZreorder(_ ptr: OpaquePointer, _ input: UnsafeMutablePointer<Double>, _ output: UnsafeMutablePointer<Double>, _ dir: FFTSign) {
pffftd_zreorder(ptr, input, output, pffft_direction_t(dir))
}
public static func pffftZconvolveAccumulate(_ ptr: OpaquePointer, _ dftA: UnsafeMutablePointer<Double>, _ dftB: UnsafeMutablePointer<Double>, _ dftAB: UnsafeMutablePointer<Double>, _ scaling: Double) {
pffftd_zconvolve_accumulate(ptr, dftA, dftB, dftAB, scaling)
}
public static func pffftZconvolveNoAccu(_ ptr: OpaquePointer, _ dftA: UnsafeMutablePointer<Double>, _ dftB: UnsafeMutablePointer<Double>, _ dftAB: UnsafeMutablePointer<Double>, _ scaling: Double) {
pffftd_zconvolve_no_accu(ptr, dftA, dftB, dftAB, scaling)
}
public static func pffftSimdArch() -> String {
String(cString: pffftd_simd_arch())
}
}
extension Complex: FFTElement where RealType: FFTElement & FFTScalar {
public typealias FFTScalarType = RealType
public typealias FFTComplexType = Self
public static func pffftSetup(_ n: Int, _: FFTType) throws -> OpaquePointer {
return try FFTScalarType.pffftSetup(n, .complex)
}
public static func pffftMinFftSize(_: FFTType) -> Int {
return FFTScalarType.pffftMinFftSize(.complex)
}
public static func pffftIsValidSize(_ n: Int, _: FFTType) -> Bool {
return FFTScalarType.pffftIsValidSize(n, .complex)
}
public static func pffftNearestValidSize(_ n: Int, _: FFTType, _ higher: Bool) -> Int {
return FFTScalarType.pffftNearestValidSize(n, .complex, higher)
}
}
extension Double: FFTElement {
public typealias FFTScalarType = Double
public static func pffftSetup(_ n: Int, _ type: FFTType) throws -> OpaquePointer {
guard let ptr = pffftd_new_setup(Int32(n), pffft_transform_t(type)) else { throw FFTError.invalidSize }
return ptr
}
public static func pffftMinFftSize(_ type: FFTType) -> Int {
Int(pffftd_min_fft_size(pffft_transform_t(type)))
}
public static func pffftIsValidSize(_ n: Int, _ type: FFTType) -> Bool {
pffftd_is_valid_size(Int32(n), pffft_transform_t(type)) != 0
}
public static func pffftNearestValidSize(_ n: Int, _ type: FFTType, _ higher: Bool) -> Int {
Int(pffftd_nearest_transform_size(Int32(n), pffft_transform_t(type), higher ? 1 : 0))
}
}
extension Float: FFTElement {
public typealias FFTScalarType = Float
public static func pffftSetup(_ n: Int, _ type: FFTType) throws -> OpaquePointer {
guard let ptr = pffft_new_setup(Int32(n), pffft_transform_t(type)) else { throw FFTError.invalidSize }
return ptr
}
public static func pffftMinFftSize(_ type: FFTType) -> Int {
Int(pffft_min_fft_size(pffft_transform_t(type)))
}
public static func pffftIsValidSize(_ n: Int, _ type: FFTType) -> Bool {
pffft_is_valid_size(Int32(n), pffft_transform_t(type)) != 0
}
public static func pffftNearestValidSize(_ n: Int, _ type: FFTType, _ higher: Bool) -> Int {
Int(pffft_nearest_transform_size(Int32(n), pffft_transform_t(type), higher ? 1 : 0))
}
}
@frozen
public struct FFT<T: FFTElement>: ~Copyable {
public typealias ComplexType = T.FFTComplexType
public typealias ScalarType = T.FFTScalarType
let ptr: OpaquePointer
let n: Int
let work: Buffer<ScalarType>?
let setup: Setup
public init(setup: Setup) {
self.setup = setup
ptr = setup.ptr
n = setup.n
work = n > 4096 ? Buffer<ScalarType>(capacity: T.self == ComplexType.self ? 2 * n : n) : nil
}
/// Initialize the FFT implementation with the given size and type.
/// Since an FFT setup for a given size and element type is expensive to create but consists
/// of read only data, a global cache is used to reuse setups.
/// - Parameters:
/// - n: The size of the FFT.
/// - Throws: `FFTError.invalidSize` if the size is invalid.
public init(n: Int) throws {
try self.init(setup: SetupCache.shared.get(n: n, type: T.self))
}
/// Make a buffer for the FFT (time-domain) signal.
/// - Parameters:
/// - extra: An extra number of elements to allocate.
public func makeSignalBuffer(extra: Int = 0) -> Buffer<T> {
Buffer(capacity: n + extra)
}
/// Make a buffer for the FFT (frequency-domain) spectrum.
/// - Parameters:
/// - extra: An extra number of elements to allocate.
public func makeSpectrumBuffer(extra: Int = 0) -> Buffer<ComplexType> {
Buffer(capacity: T.self == ComplexType.self ? (n + extra) : n / 2 + extra)
}
/// Make a buffer for the internal layout of the FFT (frequency-domain) spectrum.
/// - Parameters:
/// - extra: An extra number of points to allocate. For complex FFTs, 2 * extra
/// additional elements will be allocated.
public func makeInternalLayoutBuffer(extra: Int = 0) -> Buffer<ScalarType> {
Buffer(capacity: (T.self == ComplexType.self ? 2 : 1) * (n + extra))
}
@inline(__always)
func toAddress(_ work: borrowing Buffer<ScalarType>?) -> UnsafeMutablePointer<ScalarType>? {
switch work {
case let .some(b): return b.baseAddress
case .none: return nil
}
}
@inline(__always)
func rebind<I>(_ buffer: borrowing Buffer<I>) -> UnsafeMutablePointer<ScalarType>! {
UnsafeMutableRawBufferPointer(buffer.buffer).bindMemory(to: ScalarType.self).baseAddress
}
@inline(__always)
func checkFftBufferCounts(signal: borrowing Buffer<T>, spectrum: borrowing Buffer<ComplexType>) {
guard signal.count >= n else {
fatalError("signal buffer too small")
}
guard spectrum.count >= (T.self == ComplexType.self ? n : n / 2) else {
fatalError("spectrum buffer too small")
}
}
@inline(__always)
func checkFftInternalLayoutBufferCounts(signal: borrowing Buffer<T>, spectrum: borrowing Buffer<ScalarType>) {
guard signal.count >= n else {
fatalError("signal buffer too small")
}
guard spectrum.count >= (T.self == ComplexType.self ? 2 * n : n) else {
fatalError("spectrum buffer too small")
}
}
@inline(__always)
func checkConvolveBufferCounts(a: borrowing Buffer<ScalarType>, b: borrowing Buffer<ScalarType>, ab: borrowing Buffer<ScalarType>) {
let minCount = T.self == ComplexType.self ? 2 * n : n
guard a.count >= minCount else {
fatalError("a buffer too small")
}
guard b.count >= minCount else {
fatalError("b buffer too small")
}
guard ab.count >= minCount else {
fatalError("ab buffer too small")
}
}
/// Perform a forward FFT on the input buffer.
///
/// The input and output buffers may be the same.
/// The data is stores in order as expected (interleaved complex components ordered by frequency).
/// The input and output buffer must have a capacity of at least `n` for real FFTs and `2 * n` for complex FFTs.
/// A fatal error will occur if any buffer is too small.
///
/// For a real forward transform with real input, the output array is organized as follows:
/// index k > 2 where k is even is the real part of the k/2-th complex coefficient.
/// index k > 2 where k is odd is the imaginary part of the k/2-th complex coefficient.
/// index k = 0 is the real part of the 0 frequency (DC) coefficient.
/// index k = 1 is the real part of the Nyquist coefficient.
///
/// Transforms are not scaled. fft_backward(fft_forward(x)) == n * x.
///
/// - Parameters:
/// - input: The input buffer.
/// - output: The output buffer.
/// - work: An optional work buffer. Must have capacity of at least `n` for real FFTs and `2 * n` for complex FFTs.
/// - sign: The direction of the FFT.
public func forward(signal: borrowing Buffer<T>, spectrum: borrowing Buffer<ComplexType>) {
checkFftBufferCounts(signal: signal, spectrum: spectrum)
ScalarType.pffftTransformOrdered(ptr, rebind(signal), rebind(spectrum), toAddress(work), .forward)
}
public func inverse(spectrum: borrowing Buffer<ComplexType>, signal: borrowing Buffer<T>) {
checkFftBufferCounts(signal: signal, spectrum: spectrum)
ScalarType.pffftTransformOrdered(ptr, rebind(spectrum), rebind(signal), toAddress(work), .backward)
}
/// Perform a forward FFT on the input buffer, with implementation defined order.
///
/// This function behaves similarly to `fft` however the z-domain data is stored in most efficient ordering,
/// which is suitable for transforming back with this function, or for convolution.
/// - Parameters:
/// - input: The input buffer.
/// - output: The output buffer.
/// - work: An optional work buffer. Must have capacity of at least `n` for real FFTs and `2 * n` for complex FFTs.
/// - sign: The direction of the FFT.
public func forwardToInternalLayout(signal: borrowing Buffer<T>, spectrum: borrowing Buffer<ScalarType>) {
checkFftInternalLayoutBufferCounts(signal: signal, spectrum: spectrum)
ScalarType.pffftTransform(ptr, rebind(signal), spectrum.baseAddress, toAddress(work), .forward)
}
public func inverseFromInternalLayout(spectrum: borrowing Buffer<ScalarType>, signal: borrowing Buffer<T>) {
checkFftInternalLayoutBufferCounts(signal: signal, spectrum: spectrum)
ScalarType.pffftTransform(ptr, spectrum.baseAddress, rebind(signal), toAddress(work), .backward)
}
public func reorder(spectrum: borrowing Buffer<ScalarType>, output: borrowing Buffer<ComplexType>) {
guard spectrum.count >= (T.self == ComplexType.self ? 2 * n : n) else {
fatalError("signal buffer too small")
}
guard output.count >= n else {
fatalError("outputbuffer too small")
}
ScalarType.pffftZreorder(ptr, spectrum.baseAddress, rebind(output), .forward)
}
/// Perform a convolution of two complex signals in the frequency domain.
///
/// Multiplies frequency domain components of `dftA` and `dftB` and stores the result in `dftAB`.
/// The operation performed is `dftAB = (dftA * dftB) * scaling`.
/// - Parameters:
/// - dftA: The first input buffer of frequency domain data.
/// - dftB: The second input buffer of frequency domain data.
/// - dftAB: The output buffer of frequency domain data.
/// - scaling: The scaling factor to apply to the result.
public func convolve(dftA: borrowing Buffer<ScalarType>, dftB: borrowing Buffer<ScalarType>, dftAB: borrowing Buffer<ScalarType>, scaling: ScalarType) {
checkConvolveBufferCounts(a: dftA, b: dftB, ab: dftAB)
ScalarType.pffftZconvolveNoAccu(ptr, dftA.baseAddress, dftB.baseAddress, dftAB.baseAddress, scaling)
}
/// Perform a convolution of two complex signals in the frequency domain.
///
/// Multiplies frequency domain components of `dftA` and `dftB` and accumulates the result in `dftAB`.
/// The operation performed is `dftAB += (dftA * dftB) * scaling`.
/// - Parameters:
/// - dftA: The first input buffer of frequency domain data.
/// - dftB: The second input buffer of frequency domain data.
/// - dftAB: The output buffer of frequency domain data.
/// - scaling: The scaling factor to apply to the result.
public func convolveAccumulate(dftA: borrowing Buffer<ScalarType>, dftB: borrowing Buffer<ScalarType>, dftAB: borrowing Buffer<ScalarType>, scaling: ScalarType) {
checkConvolveBufferCounts(a: dftA, b: dftB, ab: dftAB)
ScalarType.pffftZconvolveAccumulate(ptr, dftA.baseAddress, dftB.baseAddress, dftAB.baseAddress, scaling)
}
/// Returns whether the given size is valid for the given type.
///
/// The PFFFT library requires `n` to be factorizable to `minFftSize` with factors of 2, 3, 5.
/// - Parameters:
/// - n: The size to check.
/// - Returns: Whether the size is valid.
public static func isValidSize(_ n: Int) -> Bool {
T.pffftIsValidSize(n, .real)
}
/// Returns the nearest valid size for the given type.
/// - Parameters:
/// - n: The size to check.
/// - higher: Whether to return the next higher size if `n` is invalid.
/// - Returns: The nearest valid size.
public static func nearestValidSize(_ n: Int, higher: Bool) -> Int {
T.pffftNearestValidSize(n, .real, higher)
}
/// The minimum FFT size for this type of setup.
public static var minFftSize: Int {
T.pffftMinFftSize(.real)
}
public static var simdArch: String {
ScalarType.pffftSimdArch()
}
}

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internal import PFFFTLib
extension pffft_transform_t {
@inline(__always)
init(_ type: FFTType) {
switch type {
case .real: self = PFFFT_REAL
case .complex: self = PFFFT_COMPLEX
}
}
}
extension pffft_direction_t {
@inline(__always)
init(_ sign: FFTSign) {
switch sign {
case .forward: self = PFFFT_FORWARD
case .backward: self = PFFFT_BACKWARD
}
}
}

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internal import PFFFTLib
public class Setup {
let ptr: OpaquePointer
let n: Int
init<T: FFTElement>(n: Int, type: T.Type) throws {
ptr = try type.pffftSetup(n, .real)
self.n = n
}
deinit {
pffft_destroy_setup(ptr)
}
}

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import Foundation
public class SetupCache: @unchecked Sendable {
struct CacheKey: Hashable {
let n: Int
let type: ObjectIdentifier
init(n: Int, type: any FFTElement.Type) {
self.n = n
self.type = ObjectIdentifier(type)
}
}
var cache: [CacheKey: Setup?] = [:]
let queue = DispatchQueue(label: String(describing: SetupCache.self), attributes: .concurrent)
public init() {}
public func get<T: FFTElement>(n: Int, type: T.Type) throws -> Setup {
var setup: Setup??
queue.sync {
setup = cache[CacheKey(n: n, type: type)]
}
if setup == nil {
queue.sync(flags: .barrier) {
let key = CacheKey(n: n, type: type)
setup = cache[key]
if setup == nil {
let entry = try? Setup(n: n, type: type)
cache[key] = entry
setup = entry
}
}
}
guard let s = setup! else { throw FFTError.invalidSize }
return s
}
public func clear() {
queue.sync(flags: .barrier) {
cache.removeAll()
}
}
public static let shared = SetupCache()
}

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/* Copyright (c) 2013 Julien Pommier ( pommier@modartt.com )
Based on original fortran 77 code from FFTPACKv4 from NETLIB,
authored by Dr Paul Swarztrauber of NCAR, in 1985.
As confirmed by the NCAR fftpack software curators, the following
FFTPACKv5 license applies to FFTPACKv4 sources. My changes are
released under the same terms.
FFTPACK license:
http://www.cisl.ucar.edu/css/software/fftpack5/ftpk.html
Copyright (c) 2004 the University Corporation for Atmospheric
Research ("UCAR"). All rights reserved. Developed by NCAR's
Computational and Information Systems Laboratory, UCAR,
www.cisl.ucar.edu.
Redistribution and use of the Software in source and binary forms,
with or without modification, is permitted provided that the
following conditions are met:
- Neither the names of NCAR's Computational and Information Systems
Laboratory, the University Corporation for Atmospheric Research,
nor the names of its sponsors or contributors may be used to
endorse or promote products derived from this Software without
specific prior written permission.
- Redistributions of source code must retain the above copyright
notices, this list of conditions, and the disclaimer below.
- Redistributions in binary form must reproduce the above copyright
notice, this list of conditions, and the disclaimer below in the
documentation and/or other materials provided with the
distribution.
THIS SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING, BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
NONINFRINGEMENT. IN NO EVENT SHALL THE CONTRIBUTORS OR COPYRIGHT
HOLDERS BE LIABLE FOR ANY CLAIM, INDIRECT, INCIDENTAL, SPECIAL,
EXEMPLARY, OR CONSEQUENTIAL DAMAGES OR OTHER LIABILITY, WHETHER IN AN
ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS WITH THE
SOFTWARE.
*/
/*
PFFFT : a Pretty Fast FFT.
This is basically an adaptation of the single precision fftpack
(v4) as found on netlib taking advantage of SIMD instruction found
on cpus such as intel x86 (SSE1), powerpc (Altivec), and arm (NEON).
For architectures where no SIMD instruction is available, the code
falls back to a scalar version.
Restrictions:
- 1D transforms only, with 32-bit single precision.
- supports only transforms for inputs of length N of the form
N=(2^a)*(3^b)*(5^c), a >= 5, b >=0, c >= 0 (32, 48, 64, 96, 128,
144, 160, etc are all acceptable lengths). Performance is best for
128<=N<=8192.
- all (float*) pointers in the functions below are expected to
have an "simd-compatible" alignment, that is 16 bytes on x86 and
powerpc CPUs.
You can allocate such buffers with the functions
pffft_aligned_malloc / pffft_aligned_free (or with stuff like
posix_memalign..)
*/
#ifndef PFFFT_H
#define PFFFT_H
#include <stddef.h> /* for size_t */
#ifdef __cplusplus
extern "C" {
#endif
/* opaque struct holding internal stuff (precomputed twiddle factors)
this struct can be shared by many threads as it contains only
read-only data.
*/
typedef struct PFFFT_Setup PFFFT_Setup;
#ifndef PFFFT_COMMON_ENUMS
#define PFFFT_COMMON_ENUMS
/* direction of the transform */
typedef enum { PFFFT_FORWARD, PFFFT_BACKWARD } pffft_direction_t;
/* type of transform */
typedef enum { PFFFT_REAL, PFFFT_COMPLEX } pffft_transform_t;
#endif
/*
prepare for performing transforms of size N -- the returned
PFFFT_Setup structure is read-only so it can safely be shared by
multiple concurrent threads.
*/
PFFFT_Setup *pffft_new_setup(int N, pffft_transform_t transform);
void pffft_destroy_setup(PFFFT_Setup *);
/*
Perform a Fourier transform , The z-domain data is stored in the
most efficient order for transforming it back, or using it for
convolution. If you need to have its content sorted in the
"usual" way, that is as an array of interleaved complex numbers,
either use pffft_transform_ordered , or call pffft_zreorder after
the forward fft, and before the backward fft.
Transforms are not scaled: PFFFT_BACKWARD(PFFFT_FORWARD(x)) = N*x.
Typically you will want to scale the backward transform by 1/N.
The 'work' pointer should point to an area of N (2*N for complex
fft) floats, properly aligned. If 'work' is NULL, then stack will
be used instead (this is probably the best strategy for small
FFTs, say for N < 16384). Threads usually have a small stack, that
there's no sufficient amount of memory, usually leading to a crash!
Use the heap with pffft_aligned_malloc() in this case.
For a real forward transform (PFFFT_REAL | PFFFT_FORWARD) with real
input with input(=transformation) length N, the output array is
'mostly' complex:
index k in 1 .. N/2 -1 corresponds to frequency k * Samplerate / N
index k == 0 is a special case:
the real() part contains the result for the DC frequency 0,
the imag() part contains the result for the Nyquist frequency Samplerate/2
both 0-frequency and half frequency components, which are real,
are assembled in the first entry as F(0)+i*F(N/2).
With the output size N/2 complex values (=N real/imag values), it is
obvious, that the result for negative frequencies are not output,
cause of symmetry.
input and output may alias.
*/
void pffft_transform(PFFFT_Setup *setup, const float *input, float *output, float *work, pffft_direction_t direction);
/*
Similar to pffft_transform, but makes sure that the output is
ordered as expected (interleaved complex numbers). This is
similar to calling pffft_transform and then pffft_zreorder.
input and output may alias.
*/
void pffft_transform_ordered(PFFFT_Setup *setup, const float *input, float *output, float *work, pffft_direction_t direction);
/*
call pffft_zreorder(.., PFFFT_FORWARD) after pffft_transform(...,
PFFFT_FORWARD) if you want to have the frequency components in
the correct "canonical" order, as interleaved complex numbers.
(for real transforms, both 0-frequency and half frequency
components, which are real, are assembled in the first entry as
F(0)+i*F(n/2+1). Note that the original fftpack did place
F(n/2+1) at the end of the arrays).
input and output should not alias.
*/
void pffft_zreorder(PFFFT_Setup *setup, const float *input, float *output, pffft_direction_t direction);
/*
Perform a multiplication of the frequency components of dft_a and
dft_b and accumulate them into dft_ab. The arrays should have
been obtained with pffft_transform(.., PFFFT_FORWARD) and should
*not* have been reordered with pffft_zreorder (otherwise just
perform the operation yourself as the dft coefs are stored as
interleaved complex numbers).
the operation performed is: dft_ab += (dft_a * fdt_b)*scaling
The dft_a, dft_b and dft_ab pointers may alias.
*/
void pffft_zconvolve_accumulate(PFFFT_Setup *setup, const float *dft_a, const float *dft_b, float *dft_ab, float scaling);
/*
Perform a multiplication of the frequency components of dft_a and
dft_b and put result in dft_ab. The arrays should have
been obtained with pffft_transform(.., PFFFT_FORWARD) and should
*not* have been reordered with pffft_zreorder (otherwise just
perform the operation yourself as the dft coefs are stored as
interleaved complex numbers).
the operation performed is: dft_ab = (dft_a * fdt_b)*scaling
The dft_a, dft_b and dft_ab pointers may alias.
*/
void pffft_zconvolve_no_accu(PFFFT_Setup *setup, const float *dft_a, const float *dft_b, float *dft_ab, float scaling);
/* return 4 or 1 wether support SSE/NEON/Altivec instructions was enabled when building pffft.c */
int pffft_simd_size();
/* return string identifier of used architecture (SSE/NEON/Altivec/..) */
const char * pffft_simd_arch();
/* following functions are identical to the pffftd_ functions */
/* simple helper to get minimum possible fft size */
int pffft_min_fft_size(pffft_transform_t transform);
/* simple helper to determine next power of 2
- without inexact/rounding floating point operations
*/
int pffft_next_power_of_two(int N);
/* simple helper to determine if power of 2 - returns bool */
int pffft_is_power_of_two(int N);
/* simple helper to determine size N is valid
- factorizable to pffft_min_fft_size() with factors 2, 3, 5
returns bool
*/
int pffft_is_valid_size(int N, pffft_transform_t cplx);
/* determine nearest valid transform size (by brute-force testing)
- factorizable to pffft_min_fft_size() with factors 2, 3, 5.
higher: bool-flag to find nearest higher value; else lower.
*/
int pffft_nearest_transform_size(int N, pffft_transform_t cplx, int higher);
/*
the float buffers must have the correct alignment (16-byte boundary
on intel and powerpc). This function may be used to obtain such
correctly aligned buffers.
*/
void *pffft_aligned_malloc(size_t nb_bytes);
void pffft_aligned_free(void *);
#ifdef __cplusplus
}
#endif
#endif /* PFFFT_H */

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/* Copyright (c) 2013 Julien Pommier ( pommier@modartt.com )
Based on original fortran 77 code from FFTPACKv4 from NETLIB,
authored by Dr Paul Swarztrauber of NCAR, in 1985.
As confirmed by the NCAR fftpack software curators, the following
FFTPACKv5 license applies to FFTPACKv4 sources. My changes are
released under the same terms.
FFTPACK license:
http://www.cisl.ucar.edu/css/software/fftpack5/ftpk.html
Copyright (c) 2004 the University Corporation for Atmospheric
Research ("UCAR"). All rights reserved. Developed by NCAR's
Computational and Information Systems Laboratory, UCAR,
www.cisl.ucar.edu.
Redistribution and use of the Software in source and binary forms,
with or without modification, is permitted provided that the
following conditions are met:
- Neither the names of NCAR's Computational and Information Systems
Laboratory, the University Corporation for Atmospheric Research,
nor the names of its sponsors or contributors may be used to
endorse or promote products derived from this Software without
specific prior written permission.
- Redistributions of source code must retain the above copyright
notices, this list of conditions, and the disclaimer below.
- Redistributions in binary form must reproduce the above copyright
notice, this list of conditions, and the disclaimer below in the
documentation and/or other materials provided with the
distribution.
THIS SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING, BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
NONINFRINGEMENT. IN NO EVENT SHALL THE CONTRIBUTORS OR COPYRIGHT
HOLDERS BE LIABLE FOR ANY CLAIM, INDIRECT, INCIDENTAL, SPECIAL,
EXEMPLARY, OR CONSEQUENTIAL DAMAGES OR OTHER LIABILITY, WHETHER IN AN
ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS WITH THE
SOFTWARE.
*/
/*
NOTE: This file is adapted from Julien Pommier's original PFFFT,
which works on 32 bit floating point precision using SSE instructions,
to work with 64 bit floating point precision using AVX instructions.
Author: Dario Mambro @ https://github.com/unevens/pffft
*/
/*
PFFFT : a Pretty Fast FFT.
This is basically an adaptation of the single precision fftpack
(v4) as found on netlib taking advantage of SIMD instruction found
on cpus such as intel x86 (SSE1), powerpc (Altivec), and arm (NEON).
For architectures where no SIMD instruction is available, the code
falls back to a scalar version.
Restrictions:
- 1D transforms only, with 64-bit double precision.
- supports only transforms for inputs of length N of the form
N=(2^a)*(3^b)*(5^c), a >= 5, b >=0, c >= 0 (32, 48, 64, 96, 128,
144, 160, etc are all acceptable lengths). Performance is best for
128<=N<=8192.
- all (double*) pointers in the functions below are expected to
have an "simd-compatible" alignment, that is 32 bytes on x86 and
powerpc CPUs.
You can allocate such buffers with the functions
pffft_aligned_malloc / pffft_aligned_free (or with stuff like
posix_memalign..)
*/
#ifndef PFFFT_DOUBLE_H
#define PFFFT_DOUBLE_H
#include <stddef.h> /* for size_t */
#ifdef __cplusplus
extern "C" {
#endif
/* opaque struct holding internal stuff (precomputed twiddle factors)
this struct can be shared by many threads as it contains only
read-only data.
*/
typedef struct PFFFTD_Setup PFFFTD_Setup;
#ifndef PFFFT_COMMON_ENUMS
#define PFFFT_COMMON_ENUMS
/* direction of the transform */
typedef enum { PFFFT_FORWARD, PFFFT_BACKWARD } pffft_direction_t;
/* type of transform */
typedef enum { PFFFT_REAL, PFFFT_COMPLEX } pffft_transform_t;
#endif
/*
prepare for performing transforms of size N -- the returned
PFFFTD_Setup structure is read-only so it can safely be shared by
multiple concurrent threads.
*/
PFFFTD_Setup *pffftd_new_setup(int N, pffft_transform_t transform);
void pffftd_destroy_setup(PFFFTD_Setup *);
/*
Perform a Fourier transform , The z-domain data is stored in the
most efficient order for transforming it back, or using it for
convolution. If you need to have its content sorted in the
"usual" way, that is as an array of interleaved complex numbers,
either use pffft_transform_ordered , or call pffft_zreorder after
the forward fft, and before the backward fft.
Transforms are not scaled: PFFFT_BACKWARD(PFFFT_FORWARD(x)) = N*x.
Typically you will want to scale the backward transform by 1/N.
The 'work' pointer should point to an area of N (2*N for complex
fft) doubles, properly aligned. If 'work' is NULL, then stack will
be used instead (this is probably the best strategy for small
FFTs, say for N < 16384). Threads usually have a small stack, that
there's no sufficient amount of memory, usually leading to a crash!
Use the heap with pffft_aligned_malloc() in this case.
input and output may alias.
*/
void pffftd_transform(PFFFTD_Setup *setup, const double *input, double *output, double *work, pffft_direction_t direction);
/*
Similar to pffft_transform, but makes sure that the output is
ordered as expected (interleaved complex numbers). This is
similar to calling pffft_transform and then pffft_zreorder.
input and output may alias.
*/
void pffftd_transform_ordered(PFFFTD_Setup *setup, const double *input, double *output, double *work, pffft_direction_t direction);
/*
call pffft_zreorder(.., PFFFT_FORWARD) after pffft_transform(...,
PFFFT_FORWARD) if you want to have the frequency components in
the correct "canonical" order, as interleaved complex numbers.
(for real transforms, both 0-frequency and half frequency
components, which are real, are assembled in the first entry as
F(0)+i*F(n/2+1). Note that the original fftpack did place
F(n/2+1) at the end of the arrays).
input and output should not alias.
*/
void pffftd_zreorder(PFFFTD_Setup *setup, const double *input, double *output, pffft_direction_t direction);
/*
Perform a multiplication of the frequency components of dft_a and
dft_b and accumulate them into dft_ab. The arrays should have
been obtained with pffft_transform(.., PFFFT_FORWARD) and should
*not* have been reordered with pffft_zreorder (otherwise just
perform the operation yourself as the dft coefs are stored as
interleaved complex numbers).
the operation performed is: dft_ab += (dft_a * fdt_b)*scaling
The dft_a, dft_b and dft_ab pointers may alias.
*/
void pffftd_zconvolve_accumulate(PFFFTD_Setup *setup, const double *dft_a, const double *dft_b, double *dft_ab, double scaling);
/*
Perform a multiplication of the frequency components of dft_a and
dft_b and put result in dft_ab. The arrays should have
been obtained with pffft_transform(.., PFFFT_FORWARD) and should
*not* have been reordered with pffft_zreorder (otherwise just
perform the operation yourself as the dft coefs are stored as
interleaved complex numbers).
the operation performed is: dft_ab = (dft_a * fdt_b)*scaling
The dft_a, dft_b and dft_ab pointers may alias.
*/
void pffftd_zconvolve_no_accu(PFFFTD_Setup *setup, const double *dft_a, const double *dft_b, double*dft_ab, double scaling);
/* return 4 or 1 wether support AVX instructions was enabled when building pffft-double.c */
int pffftd_simd_size();
/* return string identifier of used architecture (AVX/..) */
const char * pffftd_simd_arch();
/* simple helper to get minimum possible fft size */
int pffftd_min_fft_size(pffft_transform_t transform);
/* simple helper to determine size N is valid
- factorizable to pffft_min_fft_size() with factors 2, 3, 5
*/
int pffftd_is_valid_size(int N, pffft_transform_t cplx);
/* determine nearest valid transform size (by brute-force testing)
- factorizable to pffft_min_fft_size() with factors 2, 3, 5.
higher: bool-flag to find nearest higher value; else lower.
*/
int pffftd_nearest_transform_size(int N, pffft_transform_t cplx, int higher);
/* following functions are identical to the pffft_ functions - both declared */
/* simple helper to determine next power of 2
- without inexact/rounding floating point operations
*/
int pffftd_next_power_of_two(int N);
int pffft_next_power_of_two(int N);
/* simple helper to determine if power of 2 - returns bool */
int pffftd_is_power_of_two(int N);
int pffft_is_power_of_two(int N);
/*
the double buffers must have the correct alignment (32-byte boundary
on intel and powerpc). This function may be used to obtain such
correctly aligned buffers.
*/
void *pffftd_aligned_malloc(size_t nb_bytes);
void *pffft_aligned_malloc(size_t nb_bytes);
void pffftd_aligned_free(void *);
void pffft_aligned_free(void *);
#ifdef __cplusplus
}
#endif
#endif /* PFFFT_DOUBLE_H */

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/* Copyright (c) 2013 Julien Pommier ( pommier@modartt.com )
Copyright (c) 2020 Hayati Ayguen ( h_ayguen@web.de )
Based on original fortran 77 code from FFTPACKv4 from NETLIB
(http://www.netlib.org/fftpack), authored by Dr Paul Swarztrauber
of NCAR, in 1985.
As confirmed by the NCAR fftpack software curators, the following
FFTPACKv5 license applies to FFTPACKv4 sources. My changes are
released under the same terms.
FFTPACK license:
http://www.cisl.ucar.edu/css/software/fftpack5/ftpk.html
Copyright (c) 2004 the University Corporation for Atmospheric
Research ("UCAR"). All rights reserved. Developed by NCAR's
Computational and Information Systems Laboratory, UCAR,
www.cisl.ucar.edu.
Redistribution and use of the Software in source and binary forms,
with or without modification, is permitted provided that the
following conditions are met:
- Neither the names of NCAR's Computational and Information Systems
Laboratory, the University Corporation for Atmospheric Research,
nor the names of its sponsors or contributors may be used to
endorse or promote products derived from this Software without
specific prior written permission.
- Redistributions of source code must retain the above copyright
notices, this list of conditions, and the disclaimer below.
- Redistributions in binary form must reproduce the above copyright
notice, this list of conditions, and the disclaimer below in the
documentation and/or other materials provided with the
distribution.
THIS SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING, BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
NONINFRINGEMENT. IN NO EVENT SHALL THE CONTRIBUTORS OR COPYRIGHT
HOLDERS BE LIABLE FOR ANY CLAIM, INDIRECT, INCIDENTAL, SPECIAL,
EXEMPLARY, OR CONSEQUENTIAL DAMAGES OR OTHER LIABILITY, WHETHER IN AN
ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS WITH THE
SOFTWARE.
PFFFT : a Pretty Fast FFT.
This file is largerly based on the original FFTPACK implementation, modified in
order to take advantage of SIMD instructions of modern CPUs.
*/
/*
ChangeLog:
- 2011/10/02, version 1: This is the very first release of this file.
*/
#include "pffft.h"
/* detect compiler flavour */
#if defined(_MSC_VER)
# define COMPILER_MSVC
#elif defined(__GNUC__)
# define COMPILER_GCC
#endif
#include <stdlib.h>
#include <stdint.h>
#include <stdio.h>
#include <math.h>
#include <assert.h>
#if defined(COMPILER_GCC)
# define ALWAYS_INLINE(return_type) inline return_type __attribute__ ((always_inline))
# define NEVER_INLINE(return_type) return_type __attribute__ ((noinline))
# define RESTRICT __restrict
# define VLA_ARRAY_ON_STACK(type__, varname__, size__) type__ varname__[size__];
#elif defined(COMPILER_MSVC)
# define ALWAYS_INLINE(return_type) __forceinline return_type
# define NEVER_INLINE(return_type) __declspec(noinline) return_type
# define RESTRICT __restrict
# define VLA_ARRAY_ON_STACK(type__, varname__, size__) type__ *varname__ = (type__*)_alloca(size__ * sizeof(type__))
#endif
#ifdef COMPILER_MSVC
#pragma warning( disable : 4244 4305 4204 4456 )
#endif
/*
vector support macros: the rest of the code is independant of
SSE/Altivec/NEON -- adding support for other platforms with 4-element
vectors should be limited to these macros
*/
#include "simd/pf_float.h"
/* have code comparable with this definition */
#define SETUP_STRUCT PFFFT_Setup
#define FUNC_NEW_SETUP pffft_new_setup
#define FUNC_DESTROY pffft_destroy_setup
#define FUNC_TRANSFORM_UNORDRD pffft_transform
#define FUNC_TRANSFORM_ORDERED pffft_transform_ordered
#define FUNC_ZREORDER pffft_zreorder
#define FUNC_ZCONVOLVE_ACCUMULATE pffft_zconvolve_accumulate
#define FUNC_ZCONVOLVE_NO_ACCU pffft_zconvolve_no_accu
#define FUNC_ALIGNED_MALLOC pffft_aligned_malloc
#define FUNC_ALIGNED_FREE pffft_aligned_free
#define FUNC_SIMD_SIZE pffft_simd_size
#define FUNC_MIN_FFT_SIZE pffft_min_fft_size
#define FUNC_IS_VALID_SIZE pffft_is_valid_size
#define FUNC_NEAREST_SIZE pffft_nearest_transform_size
#define FUNC_SIMD_ARCH pffft_simd_arch
#define FUNC_VALIDATE_SIMD_A validate_pffft_simd
#define FUNC_VALIDATE_SIMD_EX validate_pffft_simd_ex
#define FUNC_CPLX_FINALIZE pffft_cplx_finalize
#define FUNC_CPLX_PREPROCESS pffft_cplx_preprocess
#define FUNC_REAL_PREPROCESS_4X4 pffft_real_preprocess_4x4
#define FUNC_REAL_PREPROCESS pffft_real_preprocess
#define FUNC_REAL_FINALIZE_4X4 pffft_real_finalize_4x4
#define FUNC_REAL_FINALIZE pffft_real_finalize
#define FUNC_TRANSFORM_INTERNAL pffft_transform_internal
#define FUNC_COS cosf
#define FUNC_SIN sinf
#include "pffft_priv_impl.h"

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#include "pffft.h"
#include <stdlib.h>
/* SSE and co like 16-bytes aligned pointers
* with a 64-byte alignment, we are even aligned on L2 cache lines... */
#define MALLOC_V4SF_ALIGNMENT 64
static void * Valigned_malloc(size_t nb_bytes) {
void *p, *p0 = malloc(nb_bytes + MALLOC_V4SF_ALIGNMENT);
if (!p0) return (void *) 0;
p = (void *) (((size_t) p0 + MALLOC_V4SF_ALIGNMENT) & (~((size_t) (MALLOC_V4SF_ALIGNMENT-1))));
*((void **) p - 1) = p0;
return p;
}
static void Valigned_free(void *p) {
if (p) free(*((void **) p - 1));
}
static int next_power_of_two(int N) {
/* https://graphics.stanford.edu/~seander/bithacks.html#RoundUpPowerOf2 */
/* compute the next highest power of 2 of 32-bit v */
unsigned v = N;
v--;
v |= v >> 1;
v |= v >> 2;
v |= v >> 4;
v |= v >> 8;
v |= v >> 16;
v++;
return v;
}
static int is_power_of_two(int N) {
/* https://graphics.stanford.edu/~seander/bithacks.html#DetermineIfPowerOf2 */
int f = N && !(N & (N - 1));
return f;
}
void *pffft_aligned_malloc(size_t nb_bytes) { return Valigned_malloc(nb_bytes); }
void pffft_aligned_free(void *p) { Valigned_free(p); }
int pffft_next_power_of_two(int N) { return next_power_of_two(N); }
int pffft_is_power_of_two(int N) { return is_power_of_two(N); }
void *pffftd_aligned_malloc(size_t nb_bytes) { return Valigned_malloc(nb_bytes); }
void pffftd_aligned_free(void *p) { Valigned_free(p); }
int pffftd_next_power_of_two(int N) { return next_power_of_two(N); }
int pffftd_is_power_of_two(int N) { return is_power_of_two(N); }

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/* Copyright (c) 2013 Julien Pommier ( pommier@modartt.com )
Copyright (c) 2020 Hayati Ayguen ( h_ayguen@web.de )
Copyright (c) 2020 Dario Mambro ( dario.mambro@gmail.com )
Based on original fortran 77 code from FFTPACKv4 from NETLIB
(http://www.netlib.org/fftpack), authored by Dr Paul Swarztrauber
of NCAR, in 1985.
As confirmed by the NCAR fftpack software curators, the following
FFTPACKv5 license applies to FFTPACKv4 sources. My changes are
released under the same terms.
FFTPACK license:
http://www.cisl.ucar.edu/css/software/fftpack5/ftpk.html
Copyright (c) 2004 the University Corporation for Atmospheric
Research ("UCAR"). All rights reserved. Developed by NCAR's
Computational and Information Systems Laboratory, UCAR,
www.cisl.ucar.edu.
Redistribution and use of the Software in source and binary forms,
with or without modification, is permitted provided that the
following conditions are met:
- Neither the names of NCAR's Computational and Information Systems
Laboratory, the University Corporation for Atmospheric Research,
nor the names of its sponsors or contributors may be used to
endorse or promote products derived from this Software without
specific prior written permission.
- Redistributions of source code must retain the above copyright
notices, this list of conditions, and the disclaimer below.
- Redistributions in binary form must reproduce the above copyright
notice, this list of conditions, and the disclaimer below in the
documentation and/or other materials provided with the
distribution.
THIS SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING, BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
NONINFRINGEMENT. IN NO EVENT SHALL THE CONTRIBUTORS OR COPYRIGHT
HOLDERS BE LIABLE FOR ANY CLAIM, INDIRECT, INCIDENTAL, SPECIAL,
EXEMPLARY, OR CONSEQUENTIAL DAMAGES OR OTHER LIABILITY, WHETHER IN AN
ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS WITH THE
SOFTWARE.
PFFFT : a Pretty Fast FFT.
This file is largerly based on the original FFTPACK implementation, modified in
order to take advantage of SIMD instructions of modern CPUs.
*/
/*
NOTE: This file is adapted from Julien Pommier's original PFFFT,
which works on 32 bit floating point precision using SSE instructions,
to work with 64 bit floating point precision using AVX instructions.
Author: Dario Mambro @ https://github.com/unevens/pffft
*/
#include "pffft_double.h"
/* detect compiler flavour */
#if defined(_MSC_VER)
# define COMPILER_MSVC
#elif defined(__GNUC__)
# define COMPILER_GCC
#endif
#ifdef COMPILER_MSVC
# define _USE_MATH_DEFINES
# include <malloc.h>
#elif defined(__MINGW32__) || defined(__MINGW64__)
# include <malloc.h>
#else
# include <alloca.h>
#endif
#include <stdlib.h>
#include <stdint.h>
#include <stdio.h>
#include <math.h>
#include <assert.h>
#if defined(COMPILER_GCC)
# define ALWAYS_INLINE(return_type) inline return_type __attribute__ ((always_inline))
# define NEVER_INLINE(return_type) return_type __attribute__ ((noinline))
# define RESTRICT __restrict
# define VLA_ARRAY_ON_STACK(type__, varname__, size__) type__ varname__[size__];
#elif defined(COMPILER_MSVC)
# define ALWAYS_INLINE(return_type) __forceinline return_type
# define NEVER_INLINE(return_type) __declspec(noinline) return_type
# define RESTRICT __restrict
# define VLA_ARRAY_ON_STACK(type__, varname__, size__) type__ *varname__ = (type__*)_alloca(size__ * sizeof(type__))
#endif
#ifdef COMPILER_MSVC
#pragma warning( disable : 4244 4305 4204 4456 )
#endif
/*
vector support macros: the rest of the code is independant of
AVX -- adding support for other platforms with 4-element
vectors should be limited to these macros
*/
#include "simd/pf_double.h"
/* have code comparable with this definition */
#define float double
#define SETUP_STRUCT PFFFTD_Setup
#define FUNC_NEW_SETUP pffftd_new_setup
#define FUNC_DESTROY pffftd_destroy_setup
#define FUNC_TRANSFORM_UNORDRD pffftd_transform
#define FUNC_TRANSFORM_ORDERED pffftd_transform_ordered
#define FUNC_ZREORDER pffftd_zreorder
#define FUNC_ZCONVOLVE_ACCUMULATE pffftd_zconvolve_accumulate
#define FUNC_ZCONVOLVE_NO_ACCU pffftd_zconvolve_no_accu
#define FUNC_ALIGNED_MALLOC pffftd_aligned_malloc
#define FUNC_ALIGNED_FREE pffftd_aligned_free
#define FUNC_SIMD_SIZE pffftd_simd_size
#define FUNC_MIN_FFT_SIZE pffftd_min_fft_size
#define FUNC_IS_VALID_SIZE pffftd_is_valid_size
#define FUNC_NEAREST_SIZE pffftd_nearest_transform_size
#define FUNC_SIMD_ARCH pffftd_simd_arch
#define FUNC_VALIDATE_SIMD_A validate_pffftd_simd
#define FUNC_VALIDATE_SIMD_EX validate_pffftd_simd_ex
#define FUNC_CPLX_FINALIZE pffftd_cplx_finalize
#define FUNC_CPLX_PREPROCESS pffftd_cplx_preprocess
#define FUNC_REAL_PREPROCESS_4X4 pffftd_real_preprocess_4x4
#define FUNC_REAL_PREPROCESS pffftd_real_preprocess
#define FUNC_REAL_FINALIZE_4X4 pffftd_real_finalize_4x4
#define FUNC_REAL_FINALIZE pffftd_real_finalize
#define FUNC_TRANSFORM_INTERNAL pffftd_transform_internal
#define FUNC_COS cos
#define FUNC_SIN sin
#include "pffft_priv_impl.h"

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/* Copyright (c) 2013 Julien Pommier ( pommier@modartt.com )
Redistribution and use of the Software in source and binary forms,
with or without modification, is permitted provided that the
following conditions are met:
- Neither the names of NCAR's Computational and Information Systems
Laboratory, the University Corporation for Atmospheric Research,
nor the names of its sponsors or contributors may be used to
endorse or promote products derived from this Software without
specific prior written permission.
- Redistributions of source code must retain the above copyright
notices, this list of conditions, and the disclaimer below.
- Redistributions in binary form must reproduce the above copyright
notice, this list of conditions, and the disclaimer below in the
documentation and/or other materials provided with the
distribution.
THIS SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING, BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
NONINFRINGEMENT. IN NO EVENT SHALL THE CONTRIBUTORS OR COPYRIGHT
HOLDERS BE LIABLE FOR ANY CLAIM, INDIRECT, INCIDENTAL, SPECIAL,
EXEMPLARY, OR CONSEQUENTIAL DAMAGES OR OTHER LIABILITY, WHETHER IN AN
ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS WITH THE
SOFTWARE.
*/
#ifndef PF_ALTIVEC_FLT_H
#define PF_ALTIVEC_FLT_H
/*
Altivec support macros
*/
#if !defined(PFFFT_SIMD_DISABLE) && (defined(__ppc__) || defined(__ppc64__))
#pragma message( __FILE__ ": ALTIVEC float macros are defined" )
typedef vector float v4sf;
# define SIMD_SZ 4
typedef union v4sf_union {
v4sf v;
float f[SIMD_SZ];
} v4sf_union;
# define VREQUIRES_ALIGN 1 /* not sure, if really required */
# define VARCH "ALTIVEC"
# define VZERO() ((vector float) vec_splat_u8(0))
# define VMUL(a,b) vec_madd(a,b, VZERO())
# define VADD(a,b) vec_add(a,b)
# define VMADD(a,b,c) vec_madd(a,b,c)
# define VSUB(a,b) vec_sub(a,b)
inline v4sf ld_ps1(const float *p) { v4sf v=vec_lde(0,p); return vec_splat(vec_perm(v, v, vec_lvsl(0, p)), 0); }
# define LD_PS1(p) ld_ps1(&p)
# define INTERLEAVE2(in1, in2, out1, out2) { v4sf tmp__ = vec_mergeh(in1, in2); out2 = vec_mergel(in1, in2); out1 = tmp__; }
# define UNINTERLEAVE2(in1, in2, out1, out2) { \
vector unsigned char vperm1 = (vector unsigned char)(0,1,2,3,8,9,10,11,16,17,18,19,24,25,26,27); \
vector unsigned char vperm2 = (vector unsigned char)(4,5,6,7,12,13,14,15,20,21,22,23,28,29,30,31); \
v4sf tmp__ = vec_perm(in1, in2, vperm1); out2 = vec_perm(in1, in2, vperm2); out1 = tmp__; \
}
# define VTRANSPOSE4(x0,x1,x2,x3) { \
v4sf y0 = vec_mergeh(x0, x2); \
v4sf y1 = vec_mergel(x0, x2); \
v4sf y2 = vec_mergeh(x1, x3); \
v4sf y3 = vec_mergel(x1, x3); \
x0 = vec_mergeh(y0, y2); \
x1 = vec_mergel(y0, y2); \
x2 = vec_mergeh(y1, y3); \
x3 = vec_mergel(y1, y3); \
}
# define VSWAPHL(a,b) vec_perm(a,b, (vector unsigned char)(16,17,18,19,20,21,22,23,8,9,10,11,12,13,14,15))
# define VALIGNED(ptr) ((((uintptr_t)(ptr)) & 0xF) == 0)
#endif
#endif /* PF_SSE1_FLT_H */

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/*
Copyright (c) 2020 Dario Mambro ( dario.mambro@gmail.com )
*/
/* Copyright (c) 2013 Julien Pommier ( pommier@modartt.com )
Redistribution and use of the Software in source and binary forms,
with or without modification, is permitted provided that the
following conditions are met:
- Neither the names of NCAR's Computational and Information Systems
Laboratory, the University Corporation for Atmospheric Research,
nor the names of its sponsors or contributors may be used to
endorse or promote products derived from this Software without
specific prior written permission.
- Redistributions of source code must retain the above copyright
notices, this list of conditions, and the disclaimer below.
- Redistributions in binary form must reproduce the above copyright
notice, this list of conditions, and the disclaimer below in the
documentation and/or other materials provided with the
distribution.
THIS SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING, BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
NONINFRINGEMENT. IN NO EVENT SHALL THE CONTRIBUTORS OR COPYRIGHT
HOLDERS BE LIABLE FOR ANY CLAIM, INDIRECT, INCIDENTAL, SPECIAL,
EXEMPLARY, OR CONSEQUENTIAL DAMAGES OR OTHER LIABILITY, WHETHER IN AN
ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS WITH THE
SOFTWARE.
*/
#ifndef PF_AVX_DBL_H
#define PF_AVX_DBL_H
/*
vector support macros: the rest of the code is independant of
AVX -- adding support for other platforms with 4-element
vectors should be limited to these macros
*/
/*
AVX support macros
*/
#if !defined(SIMD_SZ) && !defined(PFFFT_SIMD_DISABLE) && defined(__AVX__)
#pragma message( __FILE__ ": AVX macros are defined" )
#include <immintrin.h>
typedef __m256d v4sf;
/* 4 doubles by simd vector */
# define SIMD_SZ 4
typedef union v4sf_union {
v4sf v;
double f[SIMD_SZ];
} v4sf_union;
# define VARCH "AVX"
# define VREQUIRES_ALIGN 1
# define VZERO() _mm256_setzero_pd()
# define VMUL(a,b) _mm256_mul_pd(a,b)
# define VADD(a,b) _mm256_add_pd(a,b)
# define VMADD(a,b,c) _mm256_add_pd(_mm256_mul_pd(a,b), c)
# define VSUB(a,b) _mm256_sub_pd(a,b)
# define LD_PS1(p) _mm256_set1_pd(p)
# define VLOAD_UNALIGNED(ptr) _mm256_loadu_pd(ptr)
# define VLOAD_ALIGNED(ptr) _mm256_load_pd(ptr)
/* INTERLEAVE2 (in1, in2, out1, out2) pseudo code:
out1 = [ in1[0], in2[0], in1[1], in2[1] ]
out2 = [ in1[2], in2[2], in1[3], in2[3] ]
*/
# define INTERLEAVE2(in1, in2, out1, out2) { \
__m128d low1__ = _mm256_castpd256_pd128(in1); \
__m128d low2__ = _mm256_castpd256_pd128(in2); \
__m128d high1__ = _mm256_extractf128_pd(in1, 1); \
__m128d high2__ = _mm256_extractf128_pd(in2, 1); \
__m256d tmp__ = _mm256_insertf128_pd( \
_mm256_castpd128_pd256(_mm_shuffle_pd(low1__, low2__, 0)), \
_mm_shuffle_pd(low1__, low2__, 3), \
1); \
out2 = _mm256_insertf128_pd( \
_mm256_castpd128_pd256(_mm_shuffle_pd(high1__, high2__, 0)), \
_mm_shuffle_pd(high1__, high2__, 3), \
1); \
out1 = tmp__; \
}
/*UNINTERLEAVE2(in1, in2, out1, out2) pseudo code:
out1 = [ in1[0], in1[2], in2[0], in2[2] ]
out2 = [ in1[1], in1[3], in2[1], in2[3] ]
*/
# define UNINTERLEAVE2(in1, in2, out1, out2) { \
__m128d low1__ = _mm256_castpd256_pd128(in1); \
__m128d low2__ = _mm256_castpd256_pd128(in2); \
__m128d high1__ = _mm256_extractf128_pd(in1, 1); \
__m128d high2__ = _mm256_extractf128_pd(in2, 1); \
__m256d tmp__ = _mm256_insertf128_pd( \
_mm256_castpd128_pd256(_mm_shuffle_pd(low1__, high1__, 0)), \
_mm_shuffle_pd(low2__, high2__, 0), \
1); \
out2 = _mm256_insertf128_pd( \
_mm256_castpd128_pd256(_mm_shuffle_pd(low1__, high1__, 3)), \
_mm_shuffle_pd(low2__, high2__, 3), \
1); \
out1 = tmp__; \
}
# define VTRANSPOSE4(row0, row1, row2, row3) { \
__m256d tmp3, tmp2, tmp1, tmp0; \
\
tmp0 = _mm256_shuffle_pd((row0),(row1), 0x0); \
tmp2 = _mm256_shuffle_pd((row0),(row1), 0xF); \
tmp1 = _mm256_shuffle_pd((row2),(row3), 0x0); \
tmp3 = _mm256_shuffle_pd((row2),(row3), 0xF); \
\
(row0) = _mm256_permute2f128_pd(tmp0, tmp1, 0x20); \
(row1) = _mm256_permute2f128_pd(tmp2, tmp3, 0x20); \
(row2) = _mm256_permute2f128_pd(tmp0, tmp1, 0x31); \
(row3) = _mm256_permute2f128_pd(tmp2, tmp3, 0x31); \
}
/*VSWAPHL(a, b) pseudo code:
return [ b[0], b[1], a[2], a[3] ]
*/
# define VSWAPHL(a,b) \
_mm256_insertf128_pd(_mm256_castpd128_pd256(_mm256_castpd256_pd128(b)), _mm256_extractf128_pd(a, 1), 1)
/* reverse/flip all floats */
# define VREV_S(a) _mm256_insertf128_pd(_mm256_castpd128_pd256(_mm_permute_pd(_mm256_extractf128_pd(a, 1),1)), _mm_permute_pd(_mm256_castpd256_pd128(a), 1), 1)
/* reverse/flip complex floats */
# define VREV_C(a) _mm256_insertf128_pd(_mm256_castpd128_pd256(_mm256_extractf128_pd(a, 1)), _mm256_castpd256_pd128(a), 1)
# define VALIGNED(ptr) ((((uintptr_t)(ptr)) & 0x1F) == 0)
#endif
#endif /* PF_AVX_DBL_H */

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/* Copyright (c) 2013 Julien Pommier ( pommier@modartt.com )
Redistribution and use of the Software in source and binary forms,
with or without modification, is permitted provided that the
following conditions are met:
- Neither the names of NCAR's Computational and Information Systems
Laboratory, the University Corporation for Atmospheric Research,
nor the names of its sponsors or contributors may be used to
endorse or promote products derived from this Software without
specific prior written permission.
- Redistributions of source code must retain the above copyright
notices, this list of conditions, and the disclaimer below.
- Redistributions in binary form must reproduce the above copyright
notice, this list of conditions, and the disclaimer below in the
documentation and/or other materials provided with the
distribution.
THIS SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING, BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
NONINFRINGEMENT. IN NO EVENT SHALL THE CONTRIBUTORS OR COPYRIGHT
HOLDERS BE LIABLE FOR ANY CLAIM, INDIRECT, INCIDENTAL, SPECIAL,
EXEMPLARY, OR CONSEQUENTIAL DAMAGES OR OTHER LIABILITY, WHETHER IN AN
ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS WITH THE
SOFTWARE.
*/
#ifndef PF_DBL_H
#define PF_DBL_H
#include <assert.h>
#include <string.h>
#include <stdint.h>
/*
* SIMD reference material:
*
* general SIMD introduction:
* https://www.linuxjournal.com/content/introduction-gcc-compiler-intrinsics-vector-processing
*
* SSE 1:
* https://software.intel.com/sites/landingpage/IntrinsicsGuide/
*
* ARM NEON:
* https://developer.arm.com/architectures/instruction-sets/simd-isas/neon/intrinsics
*
* Altivec:
* https://www.nxp.com/docs/en/reference-manual/ALTIVECPIM.pdf
* https://gcc.gnu.org/onlinedocs/gcc-4.9.2/gcc/PowerPC-AltiVec_002fVSX-Built-in-Functions.html
* better one?
*
*/
typedef double vsfscalar;
#include "pf_avx_double.h"
#include "pf_sse2_double.h"
#include "pf_neon_double.h"
#ifndef SIMD_SZ
# if !defined(PFFFT_SIMD_DISABLE)
# pragma message( "building double with simd disabled !" )
# define PFFFT_SIMD_DISABLE /* fallback to scalar code */
# endif
#endif
#include "pf_scalar_double.h"
/* shortcuts for complex multiplcations */
#define VCPLXMUL(ar,ai,br,bi) { v4sf tmp; tmp=VMUL(ar,bi); ar=VMUL(ar,br); ar=VSUB(ar,VMUL(ai,bi)); ai=VMUL(ai,br); ai=VADD(ai,tmp); }
#define VCPLXMULCONJ(ar,ai,br,bi) { v4sf tmp; tmp=VMUL(ar,bi); ar=VMUL(ar,br); ar=VADD(ar,VMUL(ai,bi)); ai=VMUL(ai,br); ai=VSUB(ai,tmp); }
#ifndef SVMUL
/* multiply a scalar with a vector */
#define SVMUL(f,v) VMUL(LD_PS1(f),v)
#endif
#endif /* PF_DBL_H */

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/* Copyright (c) 2013 Julien Pommier ( pommier@modartt.com )
Redistribution and use of the Software in source and binary forms,
with or without modification, is permitted provided that the
following conditions are met:
- Neither the names of NCAR's Computational and Information Systems
Laboratory, the University Corporation for Atmospheric Research,
nor the names of its sponsors or contributors may be used to
endorse or promote products derived from this Software without
specific prior written permission.
- Redistributions of source code must retain the above copyright
notices, this list of conditions, and the disclaimer below.
- Redistributions in binary form must reproduce the above copyright
notice, this list of conditions, and the disclaimer below in the
documentation and/or other materials provided with the
distribution.
THIS SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING, BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
NONINFRINGEMENT. IN NO EVENT SHALL THE CONTRIBUTORS OR COPYRIGHT
HOLDERS BE LIABLE FOR ANY CLAIM, INDIRECT, INCIDENTAL, SPECIAL,
EXEMPLARY, OR CONSEQUENTIAL DAMAGES OR OTHER LIABILITY, WHETHER IN AN
ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS WITH THE
SOFTWARE.
*/
#ifndef PF_FLT_H
#define PF_FLT_H
#include <assert.h>
#include <string.h>
#include <stdint.h>
/*
* SIMD reference material:
*
* general SIMD introduction:
* https://www.linuxjournal.com/content/introduction-gcc-compiler-intrinsics-vector-processing
*
* SSE 1:
* https://software.intel.com/sites/landingpage/IntrinsicsGuide/
*
* ARM NEON:
* https://developer.arm.com/architectures/instruction-sets/simd-isas/neon/intrinsics
*
* Altivec:
* https://www.nxp.com/docs/en/reference-manual/ALTIVECPIM.pdf
* https://gcc.gnu.org/onlinedocs/gcc-4.9.2/gcc/PowerPC-AltiVec_002fVSX-Built-in-Functions.html
* better one?
*
*/
typedef float vsfscalar;
#include "pf_sse1_float.h"
#include "pf_neon_float.h"
#include "pf_altivec_float.h"
#ifndef SIMD_SZ
# if !defined(PFFFT_SIMD_DISABLE)
# pragma message( "building float with simd disabled !" )
# define PFFFT_SIMD_DISABLE /* fallback to scalar code */
# endif
#endif
#include "pf_scalar_float.h"
/* shortcuts for complex multiplcations */
#define VCPLXMUL(ar,ai,br,bi) { v4sf tmp; tmp=VMUL(ar,bi); ar=VMUL(ar,br); ar=VSUB(ar,VMUL(ai,bi)); ai=VMUL(ai,br); ai=VADD(ai,tmp); }
#define VCPLXMULCONJ(ar,ai,br,bi) { v4sf tmp; tmp=VMUL(ar,bi); ar=VMUL(ar,br); ar=VADD(ar,VMUL(ai,bi)); ai=VMUL(ai,br); ai=VSUB(ai,tmp); }
#ifndef SVMUL
/* multiply a scalar with a vector */
#define SVMUL(f,v) VMUL(LD_PS1(f),v)
#endif
#endif /* PF_FLT_H */

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/*
Copyright (c) 2020 Dario Mambro ( dario.mambro@gmail.com )
*/
/* Copyright (c) 2013 Julien Pommier ( pommier@modartt.com )
Redistribution and use of the Software in source and binary forms,
with or without modification, is permitted provided that the
following conditions are met:
- Neither the names of NCAR's Computational and Information Systems
Laboratory, the University Corporation for Atmospheric Research,
nor the names of its sponsors or contributors may be used to
endorse or promote products derived from this Software without
specific prior written permission.
- Redistributions of source code must retain the above copyright
notices, this list of conditions, and the disclaimer below.
- Redistributions in binary form must reproduce the above copyright
notice, this list of conditions, and the disclaimer below in the
documentation and/or other materials provided with the
distribution.
THIS SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING, BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
NONINFRINGEMENT. IN NO EVENT SHALL THE CONTRIBUTORS OR COPYRIGHT
HOLDERS BE LIABLE FOR ANY CLAIM, INDIRECT, INCIDENTAL, SPECIAL,
EXEMPLARY, OR CONSEQUENTIAL DAMAGES OR OTHER LIABILITY, WHETHER IN AN
ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS WITH THE
SOFTWARE.
*/
#ifndef PF_NEON_DBL_H
#define PF_NEON_DBL_H
/*
NEON 64bit support macros
*/
#if !defined(PFFFT_SIMD_DISABLE) && defined(PFFFT_ENABLE_NEON) && (defined(__aarch64__) || defined(__arm64__))
#pragma message (__FILE__ ": NEON (from AVX) macros are defined" )
#include "pf_neon_double_from_avx.h"
typedef __m256d v4sf;
/* 4 doubles by simd vector */
# define SIMD_SZ 4
typedef union v4sf_union {
v4sf v;
double f[SIMD_SZ];
} v4sf_union;
# define VARCH "NEON"
# define VREQUIRES_ALIGN 1
# define VZERO() _mm256_setzero_pd()
# define VMUL(a,b) _mm256_mul_pd(a,b)
# define VADD(a,b) _mm256_add_pd(a,b)
# define VMADD(a,b,c) _mm256_add_pd(_mm256_mul_pd(a,b), c)
# define VSUB(a,b) _mm256_sub_pd(a,b)
# define LD_PS1(p) _mm256_set1_pd(p)
# define VLOAD_UNALIGNED(ptr) _mm256_loadu_pd(ptr)
# define VLOAD_ALIGNED(ptr) _mm256_load_pd(ptr)
FORCE_INLINE __m256d _mm256_insertf128_pd_1(__m256d a, __m128d b)
{
__m256d res;
res.vect_f64[0] = a.vect_f64[0];
res.vect_f64[1] = b;
return res;
}
FORCE_INLINE __m128d _mm_shuffle_pd_00(__m128d a, __m128d b)
{
float64x1_t al = vget_low_f64(a);
float64x1_t bl = vget_low_f64(b);
return vcombine_f64(al, bl);
}
FORCE_INLINE __m128d _mm_shuffle_pd_11(__m128d a, __m128d b)
{
float64x1_t ah = vget_high_f64(a);
float64x1_t bh = vget_high_f64(b);
return vcombine_f64(ah, bh);
}
FORCE_INLINE __m256d _mm256_shuffle_pd_00(__m256d a, __m256d b)
{
__m256d res;
res.vect_f64[0] = _mm_shuffle_pd_00(a.vect_f64[0],b.vect_f64[0]);
res.vect_f64[1] = _mm_shuffle_pd_00(a.vect_f64[1],b.vect_f64[1]);
return res;
}
FORCE_INLINE __m256d _mm256_shuffle_pd_11(__m256d a, __m256d b)
{
__m256d res;
res.vect_f64[0] = _mm_shuffle_pd_11(a.vect_f64[0],b.vect_f64[0]);
res.vect_f64[1] = _mm_shuffle_pd_11(a.vect_f64[1],b.vect_f64[1]);
return res;
}
FORCE_INLINE __m256d _mm256_permute2f128_pd_0x20(__m256d a, __m256d b) {
__m256d res;
res.vect_f64[0] = a.vect_f64[0];
res.vect_f64[1] = b.vect_f64[0];
return res;
}
FORCE_INLINE __m256d _mm256_permute2f128_pd_0x31(__m256d a, __m256d b)
{
__m256d res;
res.vect_f64[0] = a.vect_f64[1];
res.vect_f64[1] = b.vect_f64[1];
return res;
}
FORCE_INLINE __m256d _mm256_reverse(__m256d x)
{
__m256d res;
float64x2_t low = x.vect_f64[0];
float64x2_t high = x.vect_f64[1];
float64x1_t a = vget_low_f64(low);
float64x1_t b = vget_high_f64(low);
float64x1_t c = vget_low_f64(high);
float64x1_t d = vget_high_f64(high);
res.vect_f64[0] = vcombine_f64(d, c);
res.vect_f64[1] = vcombine_f64(b, a);
return res;
}
/* INTERLEAVE2 (in1, in2, out1, out2) pseudo code:
out1 = [ in1[0], in2[0], in1[1], in2[1] ]
out2 = [ in1[2], in2[2], in1[3], in2[3] ]
*/
# define INTERLEAVE2(in1, in2, out1, out2) { \
__m128d low1__ = _mm256_castpd256_pd128(in1); \
__m128d low2__ = _mm256_castpd256_pd128(in2); \
__m128d high1__ = _mm256_extractf128_pd(in1, 1); \
__m128d high2__ = _mm256_extractf128_pd(in2, 1); \
__m256d tmp__ = _mm256_insertf128_pd_1( \
_mm256_castpd128_pd256(_mm_shuffle_pd_00(low1__, low2__)), \
_mm_shuffle_pd_11(low1__, low2__)); \
out2 = _mm256_insertf128_pd_1( \
_mm256_castpd128_pd256(_mm_shuffle_pd_00(high1__, high2__)), \
_mm_shuffle_pd_11(high1__, high2__)); \
out1 = tmp__; \
}
/*UNINTERLEAVE2(in1, in2, out1, out2) pseudo code:
out1 = [ in1[0], in1[2], in2[0], in2[2] ]
out2 = [ in1[1], in1[3], in2[1], in2[3] ]
*/
# define UNINTERLEAVE2(in1, in2, out1, out2) { \
__m128d low1__ = _mm256_castpd256_pd128(in1); \
__m128d low2__ = _mm256_castpd256_pd128(in2); \
__m128d high1__ = _mm256_extractf128_pd(in1, 1); \
__m128d high2__ = _mm256_extractf128_pd(in2, 1); \
__m256d tmp__ = _mm256_insertf128_pd_1( \
_mm256_castpd128_pd256(_mm_shuffle_pd_00(low1__, high1__)), \
_mm_shuffle_pd_00(low2__, high2__)); \
out2 = _mm256_insertf128_pd_1( \
_mm256_castpd128_pd256(_mm_shuffle_pd_11(low1__, high1__)), \
_mm_shuffle_pd_11(low2__, high2__)); \
out1 = tmp__; \
}
# define VTRANSPOSE4(row0, row1, row2, row3) { \
__m256d tmp3, tmp2, tmp1, tmp0; \
\
tmp0 = _mm256_shuffle_pd_00((row0),(row1)); \
tmp2 = _mm256_shuffle_pd_11((row0),(row1)); \
tmp1 = _mm256_shuffle_pd_00((row2),(row3)); \
tmp3 = _mm256_shuffle_pd_11((row2),(row3)); \
\
(row0) = _mm256_permute2f128_pd_0x20(tmp0, tmp1); \
(row1) = _mm256_permute2f128_pd_0x20(tmp2, tmp3); \
(row2) = _mm256_permute2f128_pd_0x31(tmp0, tmp1); \
(row3) = _mm256_permute2f128_pd_0x31(tmp2, tmp3); \
}
/*VSWAPHL(a, b) pseudo code:
return [ b[0], b[1], a[2], a[3] ]
*/
# define VSWAPHL(a,b) \
_mm256_insertf128_pd_1(_mm256_castpd128_pd256(_mm256_castpd256_pd128(b)), _mm256_extractf128_pd(a, 1))
/* reverse/flip all floats */
# define VREV_S(a) _mm256_reverse(a)
/* reverse/flip complex floats */
# define VREV_C(a) _mm256_insertf128_pd_1(_mm256_castpd128_pd256(_mm256_extractf128_pd(a, 1)), _mm256_castpd256_pd128(a))
# define VALIGNED(ptr) ((((uintptr_t)(ptr)) & 0x1F) == 0)
#endif
#endif /* PF_AVX_DBL_H */

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/*
* Copyright (C) 2020. Huawei Technologies Co., Ltd. All rights reserved.
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
* http://www.apache.org/licenses/LICENSE-2.0
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
//see https://github.com/kunpengcompute/AvxToNeon
#ifndef PF_NEON_DBL_FROM_AVX_H
#define PF_NEON_DBL_FROM_AVX_H
#include <arm_neon.h>
#if defined(__GNUC__) || defined(__clang__)
#pragma push_macro("FORCE_INLINE")
#define FORCE_INLINE static inline __attribute__((always_inline))
#else
#error "Macro name collisions may happens with unknown compiler"
#ifdef FORCE_INLINE
#undef FORCE_INLINE
#endif
#define FORCE_INLINE static inline
#endif
typedef struct {
float32x4_t vect_f32[2];
} __m256;
typedef struct {
float64x2_t vect_f64[2];
} __m256d;
typedef float64x2_t __m128d;
FORCE_INLINE __m256d _mm256_setzero_pd(void)
{
__m256d ret;
ret.vect_f64[0] = ret.vect_f64[1] = vdupq_n_f64(0.0);
return ret;
}
FORCE_INLINE __m256d _mm256_mul_pd(__m256d a, __m256d b)
{
__m256d res_m256d;
res_m256d.vect_f64[0] = vmulq_f64(a.vect_f64[0], b.vect_f64[0]);
res_m256d.vect_f64[1] = vmulq_f64(a.vect_f64[1], b.vect_f64[1]);
return res_m256d;
}
FORCE_INLINE __m256d _mm256_add_pd(__m256d a, __m256d b)
{
__m256d res_m256d;
res_m256d.vect_f64[0] = vaddq_f64(a.vect_f64[0], b.vect_f64[0]);
res_m256d.vect_f64[1] = vaddq_f64(a.vect_f64[1], b.vect_f64[1]);
return res_m256d;
}
FORCE_INLINE __m256d _mm256_sub_pd(__m256d a, __m256d b)
{
__m256d res_m256d;
res_m256d.vect_f64[0] = vsubq_f64(a.vect_f64[0], b.vect_f64[0]);
res_m256d.vect_f64[1] = vsubq_f64(a.vect_f64[1], b.vect_f64[1]);
return res_m256d;
}
FORCE_INLINE __m256d _mm256_set1_pd(double a)
{
__m256d ret;
ret.vect_f64[0] = ret.vect_f64[1] = vdupq_n_f64(a);
return ret;
}
FORCE_INLINE __m256d _mm256_load_pd (double const * mem_addr)
{
__m256d res;
res.vect_f64[0] = vld1q_f64((const double *)mem_addr);
res.vect_f64[1] = vld1q_f64((const double *)mem_addr + 2);
return res;
}
FORCE_INLINE __m256d _mm256_loadu_pd (double const * mem_addr)
{
__m256d res;
res.vect_f64[0] = vld1q_f64((const double *)mem_addr);
res.vect_f64[1] = vld1q_f64((const double *)mem_addr + 2);
return res;
}
FORCE_INLINE __m128d _mm256_castpd256_pd128(__m256d a)
{
return a.vect_f64[0];
}
FORCE_INLINE __m128d _mm256_extractf128_pd (__m256d a, const int imm8)
{
assert(imm8 >= 0 && imm8 <= 1);
return a.vect_f64[imm8];
}
FORCE_INLINE __m256d _mm256_castpd128_pd256(__m128d a)
{
__m256d res;
res.vect_f64[0] = a;
return res;
}
#endif /* PF_AVX_DBL_H */

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/* Copyright (c) 2013 Julien Pommier ( pommier@modartt.com )
Redistribution and use of the Software in source and binary forms,
with or without modification, is permitted provided that the
following conditions are met:
- Neither the names of NCAR's Computational and Information Systems
Laboratory, the University Corporation for Atmospheric Research,
nor the names of its sponsors or contributors may be used to
endorse or promote products derived from this Software without
specific prior written permission.
- Redistributions of source code must retain the above copyright
notices, this list of conditions, and the disclaimer below.
- Redistributions in binary form must reproduce the above copyright
notice, this list of conditions, and the disclaimer below in the
documentation and/or other materials provided with the
distribution.
THIS SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING, BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
NONINFRINGEMENT. IN NO EVENT SHALL THE CONTRIBUTORS OR COPYRIGHT
HOLDERS BE LIABLE FOR ANY CLAIM, INDIRECT, INCIDENTAL, SPECIAL,
EXEMPLARY, OR CONSEQUENTIAL DAMAGES OR OTHER LIABILITY, WHETHER IN AN
ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS WITH THE
SOFTWARE.
*/
#ifndef PF_NEON_FLT_H
#define PF_NEON_FLT_H
/*
ARM NEON support macros
*/
#if !defined(PFFFT_SIMD_DISABLE) && defined(PFFFT_ENABLE_NEON) && (defined(__arm__) || defined(__aarch64__) || defined(__arm64__))
#pragma message( __FILE__ ": ARM NEON macros are defined" )
# include <arm_neon.h>
typedef float32x4_t v4sf;
# define SIMD_SZ 4
typedef union v4sf_union {
v4sf v;
float f[SIMD_SZ];
} v4sf_union;
# define VARCH "NEON"
# define VREQUIRES_ALIGN 0 /* usually no alignment required */
# define VZERO() vdupq_n_f32(0)
# define VMUL(a,b) vmulq_f32(a,b)
# define VADD(a,b) vaddq_f32(a,b)
# define VMADD(a,b,c) vmlaq_f32(c,a,b)
# define VSUB(a,b) vsubq_f32(a,b)
# define LD_PS1(p) vld1q_dup_f32(&(p))
# define VLOAD_UNALIGNED(ptr) (*((v4sf*)(ptr)))
# define VLOAD_ALIGNED(ptr) (*((v4sf*)(ptr)))
# define INTERLEAVE2(in1, in2, out1, out2) { float32x4x2_t tmp__ = vzipq_f32(in1,in2); out1=tmp__.val[0]; out2=tmp__.val[1]; }
# define UNINTERLEAVE2(in1, in2, out1, out2) { float32x4x2_t tmp__ = vuzpq_f32(in1,in2); out1=tmp__.val[0]; out2=tmp__.val[1]; }
# define VTRANSPOSE4(x0,x1,x2,x3) { \
float32x4x2_t t0_ = vzipq_f32(x0, x2); \
float32x4x2_t t1_ = vzipq_f32(x1, x3); \
float32x4x2_t u0_ = vzipq_f32(t0_.val[0], t1_.val[0]); \
float32x4x2_t u1_ = vzipq_f32(t0_.val[1], t1_.val[1]); \
x0 = u0_.val[0]; x1 = u0_.val[1]; x2 = u1_.val[0]; x3 = u1_.val[1]; \
}
// marginally faster version
//# define VTRANSPOSE4(x0,x1,x2,x3) { asm("vtrn.32 %q0, %q1;\n vtrn.32 %q2,%q3\n vswp %f0,%e2\n vswp %f1,%e3" : "+w"(x0), "+w"(x1), "+w"(x2), "+w"(x3)::); }
# define VSWAPHL(a,b) vcombine_f32(vget_low_f32(b), vget_high_f32(a))
/* reverse/flip all floats */
# define VREV_S(a) vcombine_f32(vrev64_f32(vget_high_f32(a)), vrev64_f32(vget_low_f32(a)))
/* reverse/flip complex floats */
# define VREV_C(a) vextq_f32(a, a, 2)
# define VALIGNED(ptr) ((((uintptr_t)(ptr)) & 0x3) == 0)
#else
/* #pragma message( __FILE__ ": ARM NEON macros are not defined" ) */
#endif
#endif /* PF_NEON_FLT_H */

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/* Copyright (c) 2013 Julien Pommier ( pommier@modartt.com )
Copyright (c) 2020 Hayati Ayguen ( h_ayguen@web.de )
Redistribution and use of the Software in source and binary forms,
with or without modification, is permitted provided that the
following conditions are met:
- Neither the names of NCAR's Computational and Information Systems
Laboratory, the University Corporation for Atmospheric Research,
nor the names of its sponsors or contributors may be used to
endorse or promote products derived from this Software without
specific prior written permission.
- Redistributions of source code must retain the above copyright
notices, this list of conditions, and the disclaimer below.
- Redistributions in binary form must reproduce the above copyright
notice, this list of conditions, and the disclaimer below in the
documentation and/or other materials provided with the
distribution.
THIS SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING, BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
NONINFRINGEMENT. IN NO EVENT SHALL THE CONTRIBUTORS OR COPYRIGHT
HOLDERS BE LIABLE FOR ANY CLAIM, INDIRECT, INCIDENTAL, SPECIAL,
EXEMPLARY, OR CONSEQUENTIAL DAMAGES OR OTHER LIABILITY, WHETHER IN AN
ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS WITH THE
SOFTWARE.
*/
#ifndef PF_SCAL_DBL_H
#define PF_SCAL_DBL_H
/*
fallback mode(s) for situations where SSE/AVX/NEON/Altivec are not available, use scalar mode instead
*/
#if !defined(SIMD_SZ) && defined(PFFFT_SCALVEC_ENABLED)
#pragma message( __FILE__ ": double SCALAR4 macros are defined" )
typedef struct {
vsfscalar a;
vsfscalar b;
vsfscalar c;
vsfscalar d;
} v4sf;
# define SIMD_SZ 4
typedef union v4sf_union {
v4sf v;
vsfscalar f[SIMD_SZ];
} v4sf_union;
# define VARCH "4xScalar"
# define VREQUIRES_ALIGN 0
static ALWAYS_INLINE(v4sf) VZERO() {
v4sf r = { 0.f, 0.f, 0.f, 0.f };
return r;
}
static ALWAYS_INLINE(v4sf) VMUL(v4sf A, v4sf B) {
v4sf r = { A.a * B.a, A.b * B.b, A.c * B.c, A.d * B.d };
return r;
}
static ALWAYS_INLINE(v4sf) VADD(v4sf A, v4sf B) {
v4sf r = { A.a + B.a, A.b + B.b, A.c + B.c, A.d + B.d };
return r;
}
static ALWAYS_INLINE(v4sf) VMADD(v4sf A, v4sf B, v4sf C) {
v4sf r = { A.a * B.a + C.a, A.b * B.b + C.b, A.c * B.c + C.c, A.d * B.d + C.d };
return r;
}
static ALWAYS_INLINE(v4sf) VSUB(v4sf A, v4sf B) {
v4sf r = { A.a - B.a, A.b - B.b, A.c - B.c, A.d - B.d };
return r;
}
static ALWAYS_INLINE(v4sf) LD_PS1(vsfscalar v) {
v4sf r = { v, v, v, v };
return r;
}
# define VLOAD_UNALIGNED(ptr) (*((v4sf*)(ptr)))
# define VLOAD_ALIGNED(ptr) (*((v4sf*)(ptr)))
# define VALIGNED(ptr) ((((uintptr_t)(ptr)) & (sizeof(v4sf)-1) ) == 0)
/* INTERLEAVE2() */
#define INTERLEAVE2( A, B, C, D) \
do { \
v4sf Cr = { A.a, B.a, A.b, B.b }; \
v4sf Dr = { A.c, B.c, A.d, B.d }; \
C = Cr; \
D = Dr; \
} while (0)
/* UNINTERLEAVE2() */
#define UNINTERLEAVE2(A, B, C, D) \
do { \
v4sf Cr = { A.a, A.c, B.a, B.c }; \
v4sf Dr = { A.b, A.d, B.b, B.d }; \
C = Cr; \
D = Dr; \
} while (0)
/* VTRANSPOSE4() */
#define VTRANSPOSE4(A, B, C, D) \
do { \
v4sf Ar = { A.a, B.a, C.a, D.a }; \
v4sf Br = { A.b, B.b, C.b, D.b }; \
v4sf Cr = { A.c, B.c, C.c, D.c }; \
v4sf Dr = { A.d, B.d, C.d, D.d }; \
A = Ar; \
B = Br; \
C = Cr; \
D = Dr; \
} while (0)
/* VSWAPHL() */
static ALWAYS_INLINE(v4sf) VSWAPHL(v4sf A, v4sf B) {
v4sf r = { B.a, B.b, A.c, A.d };
return r;
}
/* reverse/flip all floats */
static ALWAYS_INLINE(v4sf) VREV_S(v4sf A) {
v4sf r = { A.d, A.c, A.b, A.a };
return r;
}
/* reverse/flip complex floats */
static ALWAYS_INLINE(v4sf) VREV_C(v4sf A) {
v4sf r = { A.c, A.d, A.a, A.b };
return r;
}
#else
/* #pragma message( __FILE__ ": double SCALAR4 macros are not defined" ) */
#endif
#if !defined(SIMD_SZ)
#pragma message( __FILE__ ": float SCALAR1 macros are defined" )
typedef vsfscalar v4sf;
# define SIMD_SZ 1
typedef union v4sf_union {
v4sf v;
vsfscalar f[SIMD_SZ];
} v4sf_union;
# define VARCH "Scalar"
# define VREQUIRES_ALIGN 0
# define VZERO() 0.0
# define VMUL(a,b) ((a)*(b))
# define VADD(a,b) ((a)+(b))
# define VMADD(a,b,c) ((a)*(b)+(c))
# define VSUB(a,b) ((a)-(b))
# define LD_PS1(p) (p)
# define VLOAD_UNALIGNED(ptr) (*(ptr))
# define VLOAD_ALIGNED(ptr) (*(ptr))
# define VALIGNED(ptr) ((((uintptr_t)(ptr)) & (sizeof(vsfscalar)-1) ) == 0)
#else
/* #pragma message( __FILE__ ": double SCALAR1 macros are not defined" ) */
#endif
#endif /* PF_SCAL_DBL_H */

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/* Copyright (c) 2013 Julien Pommier ( pommier@modartt.com )
Copyright (c) 2020 Hayati Ayguen ( h_ayguen@web.de )
Redistribution and use of the Software in source and binary forms,
with or without modification, is permitted provided that the
following conditions are met:
- Neither the names of NCAR's Computational and Information Systems
Laboratory, the University Corporation for Atmospheric Research,
nor the names of its sponsors or contributors may be used to
endorse or promote products derived from this Software without
specific prior written permission.
- Redistributions of source code must retain the above copyright
notices, this list of conditions, and the disclaimer below.
- Redistributions in binary form must reproduce the above copyright
notice, this list of conditions, and the disclaimer below in the
documentation and/or other materials provided with the
distribution.
THIS SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING, BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
NONINFRINGEMENT. IN NO EVENT SHALL THE CONTRIBUTORS OR COPYRIGHT
HOLDERS BE LIABLE FOR ANY CLAIM, INDIRECT, INCIDENTAL, SPECIAL,
EXEMPLARY, OR CONSEQUENTIAL DAMAGES OR OTHER LIABILITY, WHETHER IN AN
ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS WITH THE
SOFTWARE.
*/
#ifndef PF_SCAL_FLT_H
#define PF_SCAL_FLT_H
/*
fallback mode(s) for situations where SSE/AVX/NEON/Altivec are not available, use scalar mode instead
*/
#if !defined(SIMD_SZ) && defined(PFFFT_SCALVEC_ENABLED)
#pragma message( __FILE__ ": float SCALAR4 macros are defined" )
typedef struct {
vsfscalar a;
vsfscalar b;
vsfscalar c;
vsfscalar d;
} v4sf;
# define SIMD_SZ 4
typedef union v4sf_union {
v4sf v;
vsfscalar f[SIMD_SZ];
} v4sf_union;
# define VARCH "4xScalar"
# define VREQUIRES_ALIGN 0
static ALWAYS_INLINE(v4sf) VZERO() {
v4sf r = { 0.f, 0.f, 0.f, 0.f };
return r;
}
static ALWAYS_INLINE(v4sf) VMUL(v4sf A, v4sf B) {
v4sf r = { A.a * B.a, A.b * B.b, A.c * B.c, A.d * B.d };
return r;
}
static ALWAYS_INLINE(v4sf) VADD(v4sf A, v4sf B) {
v4sf r = { A.a + B.a, A.b + B.b, A.c + B.c, A.d + B.d };
return r;
}
static ALWAYS_INLINE(v4sf) VMADD(v4sf A, v4sf B, v4sf C) {
v4sf r = { A.a * B.a + C.a, A.b * B.b + C.b, A.c * B.c + C.c, A.d * B.d + C.d };
return r;
}
static ALWAYS_INLINE(v4sf) VSUB(v4sf A, v4sf B) {
v4sf r = { A.a - B.a, A.b - B.b, A.c - B.c, A.d - B.d };
return r;
}
static ALWAYS_INLINE(v4sf) LD_PS1(vsfscalar v) {
v4sf r = { v, v, v, v };
return r;
}
# define VLOAD_UNALIGNED(ptr) (*((v4sf*)(ptr)))
# define VLOAD_ALIGNED(ptr) (*((v4sf*)(ptr)))
# define VALIGNED(ptr) ((((uintptr_t)(ptr)) & (sizeof(v4sf)-1) ) == 0)
/* INTERLEAVE2() */
#define INTERLEAVE2( A, B, C, D) \
do { \
v4sf Cr = { A.a, B.a, A.b, B.b }; \
v4sf Dr = { A.c, B.c, A.d, B.d }; \
C = Cr; \
D = Dr; \
} while (0)
/* UNINTERLEAVE2() */
#define UNINTERLEAVE2(A, B, C, D) \
do { \
v4sf Cr = { A.a, A.c, B.a, B.c }; \
v4sf Dr = { A.b, A.d, B.b, B.d }; \
C = Cr; \
D = Dr; \
} while (0)
/* VTRANSPOSE4() */
#define VTRANSPOSE4(A, B, C, D) \
do { \
v4sf Ar = { A.a, B.a, C.a, D.a }; \
v4sf Br = { A.b, B.b, C.b, D.b }; \
v4sf Cr = { A.c, B.c, C.c, D.c }; \
v4sf Dr = { A.d, B.d, C.d, D.d }; \
A = Ar; \
B = Br; \
C = Cr; \
D = Dr; \
} while (0)
/* VSWAPHL() */
static ALWAYS_INLINE(v4sf) VSWAPHL(v4sf A, v4sf B) {
v4sf r = { B.a, B.b, A.c, A.d };
return r;
}
/* reverse/flip all floats */
static ALWAYS_INLINE(v4sf) VREV_S(v4sf A) {
v4sf r = { A.d, A.c, A.b, A.a };
return r;
}
/* reverse/flip complex floats */
static ALWAYS_INLINE(v4sf) VREV_C(v4sf A) {
v4sf r = { A.c, A.d, A.a, A.b };
return r;
}
#else
/* #pragma message( __FILE__ ": float SCALAR4 macros are not defined" ) */
#endif
#if !defined(SIMD_SZ)
#pragma message( __FILE__ ": float SCALAR1 macros are defined" )
typedef vsfscalar v4sf;
# define SIMD_SZ 1
typedef union v4sf_union {
v4sf v;
vsfscalar f[SIMD_SZ];
} v4sf_union;
# define VARCH "Scalar"
# define VREQUIRES_ALIGN 0
# define VZERO() 0.f
# define VMUL(a,b) ((a)*(b))
# define VADD(a,b) ((a)+(b))
# define VMADD(a,b,c) ((a)*(b)+(c))
# define VSUB(a,b) ((a)-(b))
# define LD_PS1(p) (p)
# define VLOAD_UNALIGNED(ptr) (*(ptr))
# define VLOAD_ALIGNED(ptr) (*(ptr))
# define VALIGNED(ptr) ((((uintptr_t)(ptr)) & (sizeof(vsfscalar)-1) ) == 0)
#else
/* #pragma message( __FILE__ ": float SCALAR1 macros are not defined" ) */
#endif
#endif /* PF_SCAL_FLT_H */

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/* Copyright (c) 2013 Julien Pommier ( pommier@modartt.com )
Redistribution and use of the Software in source and binary forms,
with or without modification, is permitted provided that the
following conditions are met:
- Neither the names of NCAR's Computational and Information Systems
Laboratory, the University Corporation for Atmospheric Research,
nor the names of its sponsors or contributors may be used to
endorse or promote products derived from this Software without
specific prior written permission.
- Redistributions of source code must retain the above copyright
notices, this list of conditions, and the disclaimer below.
- Redistributions in binary form must reproduce the above copyright
notice, this list of conditions, and the disclaimer below in the
documentation and/or other materials provided with the
distribution.
THIS SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING, BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
NONINFRINGEMENT. IN NO EVENT SHALL THE CONTRIBUTORS OR COPYRIGHT
HOLDERS BE LIABLE FOR ANY CLAIM, INDIRECT, INCIDENTAL, SPECIAL,
EXEMPLARY, OR CONSEQUENTIAL DAMAGES OR OTHER LIABILITY, WHETHER IN AN
ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS WITH THE
SOFTWARE.
*/
#ifndef PF_SSE1_FLT_H
#define PF_SSE1_FLT_H
/*
SSE1 support macros
*/
#if !defined(SIMD_SZ) && !defined(PFFFT_SIMD_DISABLE) && (defined(__x86_64__) || defined(_M_X64) || defined(__i386__) || defined(i386) || defined(_M_IX86))
#pragma message( __FILE__ ": SSE1 float macros are defined" )
#include <xmmintrin.h>
typedef __m128 v4sf;
/* 4 floats by simd vector -- this is pretty much hardcoded in the preprocess/finalize functions
* anyway so you will have to work if you want to enable AVX with its 256-bit vectors. */
# define SIMD_SZ 4
typedef union v4sf_union {
v4sf v;
float f[SIMD_SZ];
} v4sf_union;
# define VARCH "SSE1"
# define VREQUIRES_ALIGN 1
# define VZERO() _mm_setzero_ps()
# define VMUL(a,b) _mm_mul_ps(a,b)
# define VADD(a,b) _mm_add_ps(a,b)
# define VMADD(a,b,c) _mm_add_ps(_mm_mul_ps(a,b), c)
# define VSUB(a,b) _mm_sub_ps(a,b)
# define LD_PS1(p) _mm_set1_ps(p)
# define VLOAD_UNALIGNED(ptr) _mm_loadu_ps(ptr)
# define VLOAD_ALIGNED(ptr) _mm_load_ps(ptr)
# define INTERLEAVE2(in1, in2, out1, out2) { v4sf tmp__ = _mm_unpacklo_ps(in1, in2); out2 = _mm_unpackhi_ps(in1, in2); out1 = tmp__; }
# define UNINTERLEAVE2(in1, in2, out1, out2) { v4sf tmp__ = _mm_shuffle_ps(in1, in2, _MM_SHUFFLE(2,0,2,0)); out2 = _mm_shuffle_ps(in1, in2, _MM_SHUFFLE(3,1,3,1)); out1 = tmp__; }
# define VTRANSPOSE4(x0,x1,x2,x3) _MM_TRANSPOSE4_PS(x0,x1,x2,x3)
# define VSWAPHL(a,b) _mm_shuffle_ps(b, a, _MM_SHUFFLE(3,2,1,0))
/* reverse/flip all floats */
# define VREV_S(a) _mm_shuffle_ps(a, a, _MM_SHUFFLE(0,1,2,3))
/* reverse/flip complex floats */
# define VREV_C(a) _mm_shuffle_ps(a, a, _MM_SHUFFLE(1,0,3,2))
# define VALIGNED(ptr) ((((uintptr_t)(ptr)) & 0xF) == 0)
#else
/* #pragma message( __FILE__ ": SSE1 float macros are not defined" ) */
#endif
#endif /* PF_SSE1_FLT_H */

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/*
Copyright (c) 2020 Dario Mambro ( dario.mambro@gmail.com )
*/
/* Copyright (c) 2013 Julien Pommier ( pommier@modartt.com )
Redistribution and use of the Software in source and binary forms,
with or without modification, is permitted provided that the
following conditions are met:
- Neither the names of NCAR's Computational and Information Systems
Laboratory, the University Corporation for Atmospheric Research,
nor the names of its sponsors or contributors may be used to
endorse or promote products derived from this Software without
specific prior written permission.
- Redistributions of source code must retain the above copyright
notices, this list of conditions, and the disclaimer below.
- Redistributions in binary form must reproduce the above copyright
notice, this list of conditions, and the disclaimer below in the
documentation and/or other materials provided with the
distribution.
THIS SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING, BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
NONINFRINGEMENT. IN NO EVENT SHALL THE CONTRIBUTORS OR COPYRIGHT
HOLDERS BE LIABLE FOR ANY CLAIM, INDIRECT, INCIDENTAL, SPECIAL,
EXEMPLARY, OR CONSEQUENTIAL DAMAGES OR OTHER LIABILITY, WHETHER IN AN
ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS WITH THE
SOFTWARE.
*/
#ifndef PF_SSE2_DBL_H
#define PF_SSE2_DBL_H
//detect sse2 support under MSVC
#if defined ( _M_IX86_FP )
# if _M_IX86_FP == 2
# if !defined(__SSE2__)
# define __SSE2__
# endif
# endif
#endif
/*
SSE2 64bit support macros
*/
#if !defined(SIMD_SZ) && !defined(PFFFT_SIMD_DISABLE) && (defined( __SSE4_2__ ) | defined( __SSE4_1__ ) || defined( __SSE3__ ) || defined( __SSE2__ ) || defined ( __x86_64__ ) || defined( _M_AMD64 ) || defined( _M_X64 ) || defined( __amd64 ))
#pragma message (__FILE__ ": SSE2 double macros are defined" )
#include <emmintrin.h>
typedef struct {
__m128d d128[2];
} m256d;
typedef m256d v4sf;
# define SIMD_SZ 4
typedef union v4sf_union {
v4sf v;
double f[SIMD_SZ];
} v4sf_union;
#if defined(__GNUC__) || defined(__clang__)
#pragma push_macro("FORCE_INLINE")
#define FORCE_INLINE static inline __attribute__((always_inline))
#elif defined (_MSC_VER)
#define FORCE_INLINE static __forceinline
#else
#error "Macro name collisions may happens with unknown compiler"
#ifdef FORCE_INLINE
#undef FORCE_INLINE
#endif
#define FORCE_INLINE static inline
#endif
FORCE_INLINE m256d mm256_setzero_pd(void)
{
m256d ret;
ret.d128[0] = ret.d128[1] = _mm_setzero_pd();
return ret;
}
FORCE_INLINE m256d mm256_mul_pd(m256d a, m256d b)
{
m256d ret;
ret.d128[0] = _mm_mul_pd(a.d128[0], b.d128[0]);
ret.d128[1] = _mm_mul_pd(a.d128[1], b.d128[1]);
return ret;
}
FORCE_INLINE m256d mm256_add_pd(m256d a, m256d b)
{
m256d ret;
ret.d128[0] = _mm_add_pd(a.d128[0], b.d128[0]);
ret.d128[1] = _mm_add_pd(a.d128[1], b.d128[1]);
return ret;
}
FORCE_INLINE m256d mm256_sub_pd(m256d a, m256d b)
{
m256d ret;
ret.d128[0] = _mm_sub_pd(a.d128[0], b.d128[0]);
ret.d128[1] = _mm_sub_pd(a.d128[1], b.d128[1]);
return ret;
}
FORCE_INLINE m256d mm256_set1_pd(double a)
{
m256d ret;
ret.d128[0] = ret.d128[1] = _mm_set1_pd(a);
return ret;
}
FORCE_INLINE m256d mm256_load_pd (double const * mem_addr)
{
m256d res;
res.d128[0] = _mm_load_pd((const double *)mem_addr);
res.d128[1] = _mm_load_pd((const double *)mem_addr + 2);
return res;
}
FORCE_INLINE m256d mm256_loadu_pd (double const * mem_addr)
{
m256d res;
res.d128[0] = _mm_loadu_pd((const double *)mem_addr);
res.d128[1] = _mm_loadu_pd((const double *)mem_addr + 2);
return res;
}
# define VARCH "SSE2"
# define VREQUIRES_ALIGN 1
# define VZERO() mm256_setzero_pd()
# define VMUL(a,b) mm256_mul_pd(a,b)
# define VADD(a,b) mm256_add_pd(a,b)
# define VMADD(a,b,c) mm256_add_pd(mm256_mul_pd(a,b), c)
# define VSUB(a,b) mm256_sub_pd(a,b)
# define LD_PS1(p) mm256_set1_pd(p)
# define VLOAD_UNALIGNED(ptr) mm256_loadu_pd(ptr)
# define VLOAD_ALIGNED(ptr) mm256_load_pd(ptr)
FORCE_INLINE __m128d mm256_castpd256_pd128(m256d a)
{
return a.d128[0];
}
FORCE_INLINE __m128d mm256_extractf128_pd (m256d a, const int imm8)
{
assert(imm8 >= 0 && imm8 <= 1);
return a.d128[imm8];
}
FORCE_INLINE m256d mm256_insertf128_pd_1(m256d a, __m128d b)
{
m256d res;
res.d128[0] = a.d128[0];
res.d128[1] = b;
return res;
}
FORCE_INLINE m256d mm256_castpd128_pd256(__m128d a)
{
m256d res;
res.d128[0] = a;
return res;
}
FORCE_INLINE m256d mm256_shuffle_pd_00(m256d a, m256d b)
{
m256d res;
res.d128[0] = _mm_shuffle_pd(a.d128[0],b.d128[0],0);
res.d128[1] = _mm_shuffle_pd(a.d128[1],b.d128[1],0);
return res;
}
FORCE_INLINE m256d mm256_shuffle_pd_11(m256d a, m256d b)
{
m256d res;
res.d128[0] = _mm_shuffle_pd(a.d128[0],b.d128[0], 3);
res.d128[1] = _mm_shuffle_pd(a.d128[1],b.d128[1], 3);
return res;
}
FORCE_INLINE m256d mm256_permute2f128_pd_0x20(m256d a, m256d b) {
m256d res;
res.d128[0] = a.d128[0];
res.d128[1] = b.d128[0];
return res;
}
FORCE_INLINE m256d mm256_permute2f128_pd_0x31(m256d a, m256d b)
{
m256d res;
res.d128[0] = a.d128[1];
res.d128[1] = b.d128[1];
return res;
}
FORCE_INLINE m256d mm256_reverse(m256d x)
{
m256d res;
res.d128[0] = _mm_shuffle_pd(x.d128[1],x.d128[1],1);
res.d128[1] = _mm_shuffle_pd(x.d128[0],x.d128[0],1);
return res;
}
/* INTERLEAVE2 (in1, in2, out1, out2) pseudo code:
out1 = [ in1[0], in2[0], in1[1], in2[1] ]
out2 = [ in1[2], in2[2], in1[3], in2[3] ]
*/
# define INTERLEAVE2(in1, in2, out1, out2) { \
__m128d low1__ = mm256_castpd256_pd128(in1); \
__m128d low2__ = mm256_castpd256_pd128(in2); \
__m128d high1__ = mm256_extractf128_pd(in1, 1); \
__m128d high2__ = mm256_extractf128_pd(in2, 1); \
m256d tmp__ = mm256_insertf128_pd_1( \
mm256_castpd128_pd256(_mm_shuffle_pd(low1__, low2__, 0)), \
_mm_shuffle_pd(low1__, low2__, 3)); \
out2 = mm256_insertf128_pd_1( \
mm256_castpd128_pd256(_mm_shuffle_pd(high1__, high2__, 0)), \
_mm_shuffle_pd(high1__, high2__, 3)); \
out1 = tmp__; \
}
/*UNINTERLEAVE2(in1, in2, out1, out2) pseudo code:
out1 = [ in1[0], in1[2], in2[0], in2[2] ]
out2 = [ in1[1], in1[3], in2[1], in2[3] ]
*/
# define UNINTERLEAVE2(in1, in2, out1, out2) { \
__m128d low1__ = mm256_castpd256_pd128(in1); \
__m128d low2__ = mm256_castpd256_pd128(in2); \
__m128d high1__ = mm256_extractf128_pd(in1, 1); \
__m128d high2__ = mm256_extractf128_pd(in2, 1); \
m256d tmp__ = mm256_insertf128_pd_1( \
mm256_castpd128_pd256(_mm_shuffle_pd(low1__, high1__, 0)), \
_mm_shuffle_pd(low2__, high2__, 0)); \
out2 = mm256_insertf128_pd_1( \
mm256_castpd128_pd256(_mm_shuffle_pd(low1__, high1__, 3)), \
_mm_shuffle_pd(low2__, high2__, 3)); \
out1 = tmp__; \
}
# define VTRANSPOSE4(row0, row1, row2, row3) { \
m256d tmp3, tmp2, tmp1, tmp0; \
\
tmp0 = mm256_shuffle_pd_00((row0),(row1)); \
tmp2 = mm256_shuffle_pd_11((row0),(row1)); \
tmp1 = mm256_shuffle_pd_00((row2),(row3)); \
tmp3 = mm256_shuffle_pd_11((row2),(row3)); \
\
(row0) = mm256_permute2f128_pd_0x20(tmp0, tmp1); \
(row1) = mm256_permute2f128_pd_0x20(tmp2, tmp3); \
(row2) = mm256_permute2f128_pd_0x31(tmp0, tmp1); \
(row3) = mm256_permute2f128_pd_0x31(tmp2, tmp3); \
}
/*VSWAPHL(a, b) pseudo code:
return [ b[0], b[1], a[2], a[3] ]
*/
# define VSWAPHL(a,b) \
mm256_insertf128_pd_1(mm256_castpd128_pd256(mm256_castpd256_pd128(b)), mm256_extractf128_pd(a, 1))
/* reverse/flip all floats */
# define VREV_S(a) mm256_reverse(a)
/* reverse/flip complex floats */
# define VREV_C(a) mm256_insertf128_pd_1(mm256_castpd128_pd256(mm256_extractf128_pd(a, 1)), mm256_castpd256_pd128(a))
# define VALIGNED(ptr) ((((uintptr_t)(ptr)) & 0x1F) == 0)
#endif
#endif

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import Testing
import ComplexModule
@testable import PFFFT
@Test func fftFloat() async throws {
let fft = try FFT<Complex<Float>>(n: 16)
let signal = fft.makeSignalBuffer()
let spectrum = fft.makeSpectrumBuffer()
signal.mutateEach { (i, v) in
v = Complex(Float(i) + 1.0, Float(i) - 2.0)
}
fft.forward(signal: signal, spectrum: spectrum)
let result = spectrum.map { $0 }
let expected: [Complex<Float>] = [
.init(136.0, 88.0),
.init(-48.218716, 32.218716),
.init(-27.31371, 11.313708),
.init(-19.972847, 3.972846),
.init(-16.0, 0.0),
.init(-13.345428, -2.6545706),
.init(-11.313709, -4.6862917),
.init(-9.591298, -6.408703),
.init(-8.0, -8.0),
.init(-6.408703, -9.591298),
.init(-4.6862917, -11.313708),
.init(-2.6545706, -13.345429),
.init(0.0, -16.0),
.init(3.972845, -19.972847),
.init(11.313707, -27.31371),
.init(32.218716, -48.218716),
]
zip(result, expected).forEach { r, e in
#expect(r.isApproximatelyEqual(to: e))
}
fft.inverse(spectrum: spectrum, signal: signal)
let signalResult = signal.map { $0 }
let signalExpected = (0..<16).map { i in
Complex(Float(i) + 1.0, Float(i) - 2.0) * 16
}
zip(signalResult, signalExpected).forEach { r, e in
#expect(r.isApproximatelyEqual(to: e))
}
}