[Accelerate] [vDSP] DFT, FFT, DCT, and Biquad (#24207)

* Swift overlay to vDSP cascaded biquad IIR filter.

* update comment in test

* Swift overlay to vDSP Discrete Cosine Transform

* Swift Overlays to vDSP Fast Fourier Transform and Discrete Fourier Transform

* Tests for DFT and FFT

* Some refactoring and begin documentation.

* Swift overlays to FFT and DFT operations.

* Expand docs.
* Implement `vDSP_destroy_fftsetup` and `vDSP_destroy_fftsetupD`

* Refactor Tests

* Refactor Tests

* Provide transform function that returns the result. Refactoring: parameter names more consistent with other vDSP operations, push `fileprivate` symbols to bottom of file.

* Add apply() function that returns the result.

* Added a version of DFT transform that returns the result.

* update some DFT comments

* Remove FFT overlays from this branch to separate DFT and FFT pull requests.

* [Accelerate] [vDSP] Swift Overlays to FFT Operations

This PR contains Swift overlays to simplify performing 1D and 2D fast Fourier transforms on single- and double-precision data.

This PR includes a subset of the operations (e.g. vDSP_fft_zrop for FFT). My plan is to add the additional operations (e.g. multiple signals, in-place operations, etc.) in a subsequent PR once this is approved.

cc: @moiseev @airspeedswift @stephentyrone

* Composite Branch

Contains FFT, DFT, DCT, and Biquad branches.

Author: stephentyrone

stdlib/public/Darwin/Accelerate/Accelerate.swift

@@ -15,3 +15,13 @@ public enum vDSP {}
 
 /// An enum that acts as a namespace for Swift overlays to vForce based functions.
 public enum vForce {}
+
+extension vDSP {
+    public struct VectorizableFloat {
+        public typealias Scalar = Float
+    }
+    
+    public struct VectorizableDouble {
+        public typealias Scalar = Double
+    }
+}

stdlib/public/Darwin/Accelerate/AccelerateBuffer.swift

@@ -17,16 +17,16 @@
 /// provide the withUnsafeBufferPointer function.
 @available(iOS 9999, macOS 9999, tvOS 9999, watchOS 9999, *)
 public protocol AccelerateBuffer {
-  /// The buffer's element type.
-  associatedtype Element
-  
-  /// The number of elements in the buffer.
-  var count: Int { get }
-  
-  /// Calls a closure with a pointer to the object's contiguous storage.
-  func withUnsafeBufferPointer<R>(
-    _ body: (UnsafeBufferPointer<Element>) throws -> R
-  ) rethrows -> R
+    /// The buffer's element type.
+    associatedtype Element
+    
+    /// The number of elements in the buffer.
+    var count: Int { get }
+    
+    /// Calls a closure with a pointer to the object's contiguous storage.
+    func withUnsafeBufferPointer<R>(
+        _ body: (UnsafeBufferPointer<Element>) throws -> R
+        ) rethrows -> R
 }
 
 /// A mutable object composed of count elements that are stored contiguously
@@ -36,29 +36,29 @@ public protocol AccelerateBuffer {
 /// MutableCollections, but they need not be.
 @available(iOS 9999, macOS 9999, tvOS 9999, watchOS 9999, *)
 public protocol AccelerateMutableBuffer: AccelerateBuffer {
-  /// Calls the given closure with a pointer to the object's mutable
-  /// contiguous storage.
-  mutating func withUnsafeMutableBufferPointer<R>(
-    _ body: (inout UnsafeMutableBufferPointer<Element>) throws -> R
-  ) rethrows -> R
+    /// Calls the given closure with a pointer to the object's mutable
+    /// contiguous storage.
+    mutating func withUnsafeMutableBufferPointer<R>(
+        _ body: (inout UnsafeMutableBufferPointer<Element>) throws -> R
+        ) rethrows -> R
 }
 
 @available(iOS 9999, macOS 9999, tvOS 9999, watchOS 9999, *)
 public extension AccelerateBuffer where Self: Collection {
-  func withUnsafeBufferPointer<R>(
-    _ body: (UnsafeBufferPointer<Element>) throws -> R
-  ) rethrows -> R {
-    return try withContiguousStorageIfAvailable(body)!
-  }
+    func withUnsafeBufferPointer<R>(
+        _ body: (UnsafeBufferPointer<Element>) throws -> R
+        ) rethrows -> R {
+        return try withContiguousStorageIfAvailable(body)!
+    }
 }
 
 @available(iOS 9999, macOS 9999, tvOS 9999, watchOS 9999, *)
 extension AccelerateMutableBuffer where Self: MutableCollection {
-  public mutating func withUnsafeMutableBufferPointer<R>(
-    _ body: (inout UnsafeMutableBufferPointer<Element>) throws -> R
-  ) rethrows -> R {
-    return try withContiguousMutableStorageIfAvailable(body)!
-  }
+    public mutating func withUnsafeMutableBufferPointer<R>(
+        _ body: (inout UnsafeMutableBufferPointer<Element>) throws -> R
+        ) rethrows -> R {
+        return try withContiguousMutableStorageIfAvailable(body)!
+    }
 }
 
 @available(iOS 9999, macOS 9999, tvOS 9999, watchOS 9999, *)

stdlib/public/Darwin/Accelerate/CMakeLists.txt

@@ -4,13 +4,19 @@ include("../../../../cmake/modules/StandaloneOverlay.cmake")
 add_swift_target_library(swiftAccelerate ${SWIFT_SDK_OVERLAY_LIBRARY_BUILD_TYPES} IS_SDK_OVERLAY
   Accelerate.swift
   AccelerateBuffer.swift
+  Quadrature.swift
   vDSP_Arithmetic.swift
+  vDSP_Biquad.swift
   vDSP_ClippingLimitThreshold.swift
   vDSP_ComplexConversion.swift
   vDSP_ComplexOperations.swift
   vDSP_Conversion.swift
   vDSP_Convolution.swift
+  vDSP_DCT.swift
+  vDSP_DFT.swift
   vDSP_DecibelConversion.swift
+  vDSP_FFT.swift
+  vDSP_FFT_DFT_Common.swift
   vDSP_FIR.swift
   vDSP_FillClearGenerate.swift
   vDSP_Geometry.swift
@@ -23,7 +29,6 @@ add_swift_target_library(swiftAccelerate ${SWIFT_SDK_OVERLAY_LIBRARY_BUILD_TYPES
   vDSP_SingleVectorOperations.swift
   vDSP_SlidingWindow.swift
   vForce_Operations.swift
-  Quadrature.swift
 
   "${SWIFT_SOURCE_DIR}/stdlib/linker-support/magic-symbols-for-install-name.c"