mirror of
https://github.com/microsoft/DirectXMath
synced 2024-09-19 14:49:54 +00:00
881 lines
39 KiB
C++
881 lines
39 KiB
C++
//--------------------------------------------------------------------------------------
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// File: XDSP.h
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//
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// DirectXMath based Digital Signal Processing (DSP) functions for audio,
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// primarily Fast Fourier Transform (FFT)
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//
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// All buffer parameters must be 16-byte aligned
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//
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// All FFT functions support only single-precision floating-point audio
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//
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// Copyright (c) Microsoft Corporation.
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// Licensed under the MIT License.
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//
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// http://go.microsoft.com/fwlink/?LinkID=615557
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//--------------------------------------------------------------------------------------
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#pragma once
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#include <cassert>
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#include <DirectXMath.h>
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#include <cstdint>
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#include <cstring>
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#ifdef _MSC_VER
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#pragma warning(push)
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#pragma warning(disable: 6001 6262)
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#endif
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#ifdef __clang__
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#pragma clang diagnostic push
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#pragma clang diagnostic ignored "-Wunknown-warning-option"
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#pragma clang diagnostic ignored "-Wunsafe-buffer-usage"
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#endif
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namespace XDSP
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{
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using XMVECTOR = DirectX::XMVECTOR;
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using FXMVECTOR = DirectX::FXMVECTOR;
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using GXMVECTOR = DirectX::GXMVECTOR;
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using CXMVECTOR = DirectX::CXMVECTOR;
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using XMFLOAT4A = DirectX::XMFLOAT4A;
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inline bool ISPOWEROF2(size_t n) { return (((n)&((n)-1)) == 0 && (n) != 0); }
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// Parallel multiplication of four complex numbers, assuming real and imaginary values are stored in separate vectors.
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inline void XM_CALLCONV vmulComplex(
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_Out_ XMVECTOR& rResult, _Out_ XMVECTOR& iResult,
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_In_ FXMVECTOR r1, _In_ FXMVECTOR i1, _In_ FXMVECTOR r2, _In_ GXMVECTOR i2) noexcept
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{
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using namespace DirectX;
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// (r1, i1) * (r2, i2) = (r1r2 - i1i2, r1i2 + r2i1)
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const XMVECTOR vr1r2 = XMVectorMultiply(r1, r2);
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const XMVECTOR vr1i2 = XMVectorMultiply(r1, i2);
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rResult = XMVectorNegativeMultiplySubtract(i1, i2, vr1r2); // real: (r1*r2 - i1*i2)
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iResult = XMVectorMultiplyAdd(r2, i1, vr1i2); // imaginary: (r1*i2 + r2*i1)
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}
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inline void XM_CALLCONV vmulComplex(
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_Inout_ XMVECTOR& r1, _Inout_ XMVECTOR& i1, _In_ FXMVECTOR r2, _In_ FXMVECTOR i2) noexcept
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{
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using namespace DirectX;
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// (r1, i1) * (r2, i2) = (r1r2 - i1i2, r1i2 + r2i1)
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const XMVECTOR vr1r2 = XMVectorMultiply(r1, r2);
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const XMVECTOR vr1i2 = XMVectorMultiply(r1, i2);
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r1 = XMVectorNegativeMultiplySubtract(i1, i2, vr1r2); // real: (r1*r2 - i1*i2)
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i1 = XMVectorMultiplyAdd(r2, i1, vr1i2); // imaginary: (r1*i2 + r2*i1)
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}
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//----------------------------------------------------------------------------------
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// Radix-4 decimation-in-time FFT butterfly.
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// This version assumes that all four elements of the butterfly are
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// adjacent in a single vector.
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//
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// Compute the product of the complex input vector and the
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// 4-element DFT matrix:
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// | 1 1 1 1 | | (r1X,i1X) |
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// | 1 -j -1 j | | (r1Y,i1Y) |
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// | 1 -1 1 -1 | | (r1Z,i1Z) |
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// | 1 j -1 -j | | (r1W,i1W) |
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//
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// This matrix can be decomposed into two simpler ones to reduce the
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// number of additions needed. The decomposed matrices look like this:
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// | 1 0 1 0 | | 1 0 1 0 |
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// | 0 1 0 -j | | 1 0 -1 0 |
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// | 1 0 -1 0 | | 0 1 0 1 |
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// | 0 1 0 j | | 0 1 0 -1 |
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//
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// Combine as follows:
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// | 1 0 1 0 | | (r1X,i1X) | | (r1X + r1Z, i1X + i1Z) |
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// Temp = | 1 0 -1 0 | * | (r1Y,i1Y) | = | (r1X - r1Z, i1X - i1Z) |
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// | 0 1 0 1 | | (r1Z,i1Z) | | (r1Y + r1W, i1Y + i1W) |
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// | 0 1 0 -1 | | (r1W,i1W) | | (r1Y - r1W, i1Y - i1W) |
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//
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// | 1 0 1 0 | | (rTempX,iTempX) | | (rTempX + rTempZ, iTempX + iTempZ) |
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// Result = | 0 1 0 -j | * | (rTempY,iTempY) | = | (rTempY + iTempW, iTempY - rTempW) |
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// | 1 0 -1 0 | | (rTempZ,iTempZ) | | (rTempX - rTempZ, iTempX - iTempZ) |
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// | 0 1 0 j | | (rTempW,iTempW) | | (rTempY - iTempW, iTempY + rTempW) |
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//----------------------------------------------------------------------------------
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inline void ButterflyDIT4_1 (_Inout_ XMVECTOR& r1, _Inout_ XMVECTOR& i1) noexcept
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{
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using namespace DirectX;
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// sign constants for radix-4 butterflies
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static const XMVECTORF32 vDFT4SignBits1 = { { { 1.0f, -1.0f, 1.0f, -1.0f } } };
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static const XMVECTORF32 vDFT4SignBits2 = { { { 1.0f, 1.0f, -1.0f, -1.0f } } };
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static const XMVECTORF32 vDFT4SignBits3 = { { { 1.0f, -1.0f, -1.0f, 1.0f } } };
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// calculating Temp
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// [r1X| r1X|r1Y| r1Y] + [r1Z|-r1Z|r1W|-r1W]
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// [i1X| i1X|i1Y| i1Y] + [i1Z|-i1Z|i1W|-i1W]
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const XMVECTOR r1L = XMVectorSwizzle<0, 0, 1, 1>(r1);
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const XMVECTOR r1H = XMVectorSwizzle<2, 2, 3, 3>(r1);
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const XMVECTOR i1L = XMVectorSwizzle<0, 0, 1, 1>(i1);
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const XMVECTOR i1H = XMVectorSwizzle<2, 2, 3, 3>(i1);
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const XMVECTOR rTemp = XMVectorMultiplyAdd(r1H, vDFT4SignBits1, r1L);
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const XMVECTOR iTemp = XMVectorMultiplyAdd(i1H, vDFT4SignBits1, i1L);
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// calculating Result
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const XMVECTOR rZrWiZiW = XMVectorPermute<2, 3, 6, 7>(rTemp, iTemp); // [rTempZ|rTempW|iTempZ|iTempW]
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const XMVECTOR rZiWrZiW = XMVectorSwizzle<0, 3, 0, 3>(rZrWiZiW); // [rTempZ|iTempW|rTempZ|iTempW]
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const XMVECTOR iZrWiZrW = XMVectorSwizzle<2, 1, 2, 1>(rZrWiZiW); // [rTempZ|iTempW|rTempZ|iTempW]
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// [rTempX| rTempY| rTempX| rTempY] + [rTempZ| iTempW|-rTempZ|-iTempW]
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// [iTempX| iTempY| iTempX| iTempY] + // [iTempZ|-rTempW|-iTempZ| rTempW]
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const XMVECTOR rTempL = XMVectorSwizzle<0, 1, 0, 1>(rTemp);
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const XMVECTOR iTempL = XMVectorSwizzle<0, 1, 0, 1>(iTemp);
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r1 = XMVectorMultiplyAdd(rZiWrZiW, vDFT4SignBits2, rTempL);
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i1 = XMVectorMultiplyAdd(iZrWiZrW, vDFT4SignBits3, iTempL);
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}
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//----------------------------------------------------------------------------------
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// Radix-4 decimation-in-time FFT butterfly.
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// This version assumes that elements of the butterfly are
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// in different vectors, so that each vector in the input
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// contains elements from four different butterflies.
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// The four separate butterflies are processed in parallel.
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//
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// The calculations here are the same as the ones in the single-vector
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// radix-4 DFT, but instead of being done on a single vector (X,Y,Z,W)
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// they are done in parallel on sixteen independent complex values.
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// There is no interdependence between the vector elements:
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// | 1 0 1 0 | | (rIn0,iIn0) | | (rIn0 + rIn2, iIn0 + iIn2) |
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// | 1 0 -1 0 | * | (rIn1,iIn1) | = Temp = | (rIn0 - rIn2, iIn0 - iIn2) |
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// | 0 1 0 1 | | (rIn2,iIn2) | | (rIn1 + rIn3, iIn1 + iIn3) |
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// | 0 1 0 -1 | | (rIn3,iIn3) | | (rIn1 - rIn3, iIn1 - iIn3) |
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//
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// | 1 0 1 0 | | (rTemp0,iTemp0) | | (rTemp0 + rTemp2, iTemp0 + iTemp2) |
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// Result = | 0 1 0 -j | * | (rTemp1,iTemp1) | = | (rTemp1 + iTemp3, iTemp1 - rTemp3) |
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// | 1 0 -1 0 | | (rTemp2,iTemp2) | | (rTemp0 - rTemp2, iTemp0 - iTemp2) |
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// | 0 1 0 j | | (rTemp3,iTemp3) | | (rTemp1 - iTemp3, iTemp1 + rTemp3) |
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//----------------------------------------------------------------------------------
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inline void ButterflyDIT4_4(
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_Inout_ XMVECTOR& r0,
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_Inout_ XMVECTOR& r1,
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_Inout_ XMVECTOR& r2,
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_Inout_ XMVECTOR& r3,
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_Inout_ XMVECTOR& i0,
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_Inout_ XMVECTOR& i1,
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_Inout_ XMVECTOR& i2,
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_Inout_ XMVECTOR& i3,
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_In_reads_(uStride * 4) const XMVECTOR* __restrict pUnityTableReal,
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_In_reads_(uStride * 4) const XMVECTOR* __restrict pUnityTableImaginary,
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_In_ size_t uStride,
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_In_ const bool fLast) noexcept
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{
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using namespace DirectX;
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assert(pUnityTableReal);
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assert(pUnityTableImaginary);
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assert(reinterpret_cast<uintptr_t>(pUnityTableReal) % 16 == 0);
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assert(reinterpret_cast<uintptr_t>(pUnityTableImaginary) % 16 == 0);
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assert(ISPOWEROF2(uStride));
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// calculating Temp
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const XMVECTOR rTemp0 = XMVectorAdd(r0, r2);
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const XMVECTOR iTemp0 = XMVectorAdd(i0, i2);
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const XMVECTOR rTemp2 = XMVectorAdd(r1, r3);
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const XMVECTOR iTemp2 = XMVectorAdd(i1, i3);
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const XMVECTOR rTemp1 = XMVectorSubtract(r0, r2);
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const XMVECTOR iTemp1 = XMVectorSubtract(i0, i2);
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const XMVECTOR rTemp3 = XMVectorSubtract(r1, r3);
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const XMVECTOR iTemp3 = XMVectorSubtract(i1, i3);
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XMVECTOR rTemp4 = XMVectorAdd(rTemp0, rTemp2);
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XMVECTOR iTemp4 = XMVectorAdd(iTemp0, iTemp2);
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XMVECTOR rTemp5 = XMVectorAdd(rTemp1, iTemp3);
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XMVECTOR iTemp5 = XMVectorSubtract(iTemp1, rTemp3);
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XMVECTOR rTemp6 = XMVectorSubtract(rTemp0, rTemp2);
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XMVECTOR iTemp6 = XMVectorSubtract(iTemp0, iTemp2);
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XMVECTOR rTemp7 = XMVectorSubtract(rTemp1, iTemp3);
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XMVECTOR iTemp7 = XMVectorAdd(iTemp1, rTemp3);
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// calculating Result
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// vmulComplex(rTemp0, iTemp0, rTemp0, iTemp0, pUnityTableReal[0], pUnityTableImaginary[0]); // first one is always trivial
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vmulComplex(rTemp5, iTemp5, pUnityTableReal[uStride], pUnityTableImaginary[uStride]);
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vmulComplex(rTemp6, iTemp6, pUnityTableReal[uStride * 2], pUnityTableImaginary[uStride * 2]);
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vmulComplex(rTemp7, iTemp7, pUnityTableReal[uStride * 3], pUnityTableImaginary[uStride * 3]);
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if (fLast)
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{
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ButterflyDIT4_1(rTemp4, iTemp4);
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ButterflyDIT4_1(rTemp5, iTemp5);
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ButterflyDIT4_1(rTemp6, iTemp6);
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ButterflyDIT4_1(rTemp7, iTemp7);
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}
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r0 = rTemp4; i0 = iTemp4;
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r1 = rTemp5; i1 = iTemp5;
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r2 = rTemp6; i2 = iTemp6;
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r3 = rTemp7; i3 = iTemp7;
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}
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//==================================================================================
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// F-U-N-C-T-I-O-N-S
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//==================================================================================
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//----------------------------------------------------------------------------------
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// DESCRIPTION:
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// 4-sample FFT.
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//
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// PARAMETERS:
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// pReal - [inout] real components, must have at least uCount elements
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// pImaginary - [inout] imaginary components, must have at least uCount elements
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// uCount - [in] number of FFT iterations
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//----------------------------------------------------------------------------------
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inline void FFT4(
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_Inout_updates_(uCount) XMVECTOR* __restrict pReal,
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_Inout_updates_(uCount) XMVECTOR* __restrict pImaginary,
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const size_t uCount = 1) noexcept
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{
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assert(pReal);
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assert(pImaginary);
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assert(reinterpret_cast<uintptr_t>(pReal) % 16 == 0);
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assert(reinterpret_cast<uintptr_t>(pImaginary) % 16 == 0);
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assert(ISPOWEROF2(uCount));
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for (size_t uIndex = 0; uIndex < uCount; ++uIndex)
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{
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ButterflyDIT4_1(pReal[uIndex], pImaginary[uIndex]);
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}
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}
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//----------------------------------------------------------------------------------
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// DESCRIPTION:
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// 8-sample FFT.
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//
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// PARAMETERS:
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// pReal - [inout] real components, must have at least uCount*2 elements
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// pImaginary - [inout] imaginary components, must have at least uCount*2 elements
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// uCount - [in] number of FFT iterations
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//----------------------------------------------------------------------------------
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inline void FFT8(
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_Inout_updates_(uCount * 2) XMVECTOR* __restrict pReal,
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_Inout_updates_(uCount * 2) XMVECTOR* __restrict pImaginary,
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_In_ const size_t uCount = 1) noexcept
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{
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using namespace DirectX;
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assert(pReal);
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assert(pImaginary);
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assert(reinterpret_cast<uintptr_t>(pReal) % 16 == 0);
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assert(reinterpret_cast<uintptr_t>(pImaginary) % 16 == 0);
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assert(ISPOWEROF2(uCount));
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static const XMVECTORF32 wr1 = { { { 1.0f, 0.70710677f, 0.0f, -0.70710677f } } };
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static const XMVECTORF32 wi1 = { { { 0.0f, -0.70710677f, -1.0f, -0.70710677f } } };
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static const XMVECTORF32 wr2 = { { { -1.0f, -0.70710677f, 0.0f, 0.70710677f } } };
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static const XMVECTORF32 wi2 = { { { 0.0f, 0.70710677f, 1.0f, 0.70710677f } } };
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for (size_t uIndex = 0; uIndex < uCount; ++uIndex)
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{
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XMVECTOR* __restrict pR = pReal + uIndex * 2;
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XMVECTOR* __restrict pI = pImaginary + uIndex * 2;
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XMVECTOR oddsR = XMVectorPermute<1, 3, 5, 7>(pR[0], pR[1]);
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XMVECTOR evensR = XMVectorPermute<0, 2, 4, 6>(pR[0], pR[1]);
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XMVECTOR oddsI = XMVectorPermute<1, 3, 5, 7>(pI[0], pI[1]);
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XMVECTOR evensI = XMVectorPermute<0, 2, 4, 6>(pI[0], pI[1]);
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ButterflyDIT4_1(oddsR, oddsI);
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ButterflyDIT4_1(evensR, evensI);
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XMVECTOR r, i;
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vmulComplex(r, i, oddsR, oddsI, wr1, wi1);
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pR[0] = XMVectorAdd(evensR, r);
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pI[0] = XMVectorAdd(evensI, i);
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vmulComplex(r, i, oddsR, oddsI, wr2, wi2);
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pR[1] = XMVectorAdd(evensR, r);
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pI[1] = XMVectorAdd(evensI, i);
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}
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}
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//----------------------------------------------------------------------------------
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// DESCRIPTION:
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// 16-sample FFT.
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//
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// PARAMETERS:
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// pReal - [inout] real components, must have at least uCount*4 elements
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// pImaginary - [inout] imaginary components, must have at least uCount*4 elements
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// uCount - [in] number of FFT iterations
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//----------------------------------------------------------------------------------
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inline void FFT16(
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_Inout_updates_(uCount * 4) XMVECTOR* __restrict pReal,
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_Inout_updates_(uCount * 4) XMVECTOR* __restrict pImaginary,
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_In_ const size_t uCount = 1) noexcept
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{
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using namespace DirectX;
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assert(pReal);
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assert(pImaginary);
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assert(reinterpret_cast<uintptr_t>(pReal) % 16 == 0);
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assert(reinterpret_cast<uintptr_t>(pImaginary) % 16 == 0);
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assert(ISPOWEROF2(uCount));
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static const XMVECTORF32 aUnityTableReal[4] = {
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{ { { 1.0f, 1.0f, 1.0f, 1.0f } } },
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{ { { 1.0f, 0.92387950f, 0.70710677f, 0.38268343f } } },
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{ { { 1.0f, 0.70710677f, -4.3711388e-008f, -0.70710677f } } },
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{ { { 1.0f, 0.38268343f, -0.70710677f, -0.92387950f } } }
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};
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static const XMVECTORF32 aUnityTableImaginary[4] =
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{
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{ { { -0.0f, -0.0f, -0.0f, -0.0f } } },
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{ { { -0.0f, -0.38268343f, -0.70710677f, -0.92387950f } } },
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{ { { -0.0f, -0.70710677f, -1.0f, -0.70710677f } } },
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{ { { -0.0f, -0.92387950f, -0.70710677f, 0.38268343f } } }
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};
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for (size_t uIndex = 0; uIndex < uCount; ++uIndex)
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{
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ButterflyDIT4_4(pReal[uIndex * 4],
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pReal[uIndex * 4 + 1],
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pReal[uIndex * 4 + 2],
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pReal[uIndex * 4 + 3],
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pImaginary[uIndex * 4],
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pImaginary[uIndex * 4 + 1],
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pImaginary[uIndex * 4 + 2],
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pImaginary[uIndex * 4 + 3],
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reinterpret_cast<const XMVECTOR*>(aUnityTableReal),
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reinterpret_cast<const XMVECTOR*>(aUnityTableImaginary),
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1, true);
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}
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}
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//----------------------------------------------------------------------------------
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// DESCRIPTION:
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// 2^N-sample FFT.
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//
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// REMARKS:
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// For FFTs length 16 and below, call FFT16(), FFT8(), or FFT4().
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//
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// PARAMETERS:
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// pReal - [inout] real components, must have at least (uLength*uCount)/4 elements
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// pImaginary - [inout] imaginary components, must have at least (uLength*uCount)/4 elements
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// pUnityTable - [in] unity table, must have at least uLength*uCount elements, see FFTInitializeUnityTable()
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// uLength - [in] FFT length in samples, must be a power of 2 > 16
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// uCount - [in] number of FFT iterations
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//----------------------------------------------------------------------------------
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inline void FFT (
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_Inout_updates_((uLength * uCount) / 4) XMVECTOR* __restrict pReal,
|
|
_Inout_updates_((uLength * uCount) / 4) XMVECTOR* __restrict pImaginary,
|
|
_In_reads_(uLength * uCount) const XMVECTOR* __restrict pUnityTable,
|
|
_In_ const size_t uLength,
|
|
_In_ const size_t uCount = 1) noexcept
|
|
{
|
|
assert(pReal);
|
|
assert(pImaginary);
|
|
assert(pUnityTable);
|
|
assert(reinterpret_cast<uintptr_t>(pReal) % 16 == 0);
|
|
assert(reinterpret_cast<uintptr_t>(pImaginary) % 16 == 0);
|
|
assert(reinterpret_cast<uintptr_t>(pUnityTable) % 16 == 0);
|
|
assert(uLength > 16);
|
|
_Analysis_assume_(uLength > 16);
|
|
assert(ISPOWEROF2(uLength));
|
|
assert(ISPOWEROF2(uCount));
|
|
|
|
const XMVECTOR* __restrict pUnityTableReal = pUnityTable;
|
|
const XMVECTOR* __restrict pUnityTableImaginary = pUnityTable + (uLength >> 2);
|
|
const size_t uTotal = uCount * uLength;
|
|
const size_t uTotal_vectors = uTotal >> 2;
|
|
const size_t uStage_vectors = uLength >> 2;
|
|
const size_t uStage_vectors_mask = uStage_vectors - 1;
|
|
const size_t uStride = uLength >> 4; // stride between butterfly elements
|
|
const size_t uStrideMask = uStride - 1;
|
|
const size_t uStride2 = uStride * 2;
|
|
const size_t uStride3 = uStride * 3;
|
|
const size_t uStrideInvMask = ~uStrideMask;
|
|
|
|
for (size_t uIndex=0; uIndex < (uTotal_vectors >> 2); ++uIndex)
|
|
{
|
|
const size_t n = ((uIndex & uStrideInvMask) << 2) + (uIndex & uStrideMask);
|
|
ButterflyDIT4_4(pReal[n],
|
|
pReal[n + uStride],
|
|
pReal[n + uStride2],
|
|
pReal[n + uStride3],
|
|
pImaginary[n ],
|
|
pImaginary[n + uStride],
|
|
pImaginary[n + uStride2],
|
|
pImaginary[n + uStride3],
|
|
pUnityTableReal + (n & uStage_vectors_mask),
|
|
pUnityTableImaginary + (n & uStage_vectors_mask),
|
|
uStride, false);
|
|
}
|
|
|
|
if (uLength > 16 * 4)
|
|
{
|
|
FFT(pReal, pImaginary, pUnityTable + (uLength >> 1), uLength >> 2, uCount * 4);
|
|
}
|
|
else if (uLength == 16 * 4)
|
|
{
|
|
FFT16(pReal, pImaginary, uCount * 4);
|
|
}
|
|
else if (uLength == 8 * 4)
|
|
{
|
|
FFT8(pReal, pImaginary, uCount * 4);
|
|
}
|
|
else if (uLength == 4 * 4)
|
|
{
|
|
FFT4(pReal, pImaginary, uCount * 4);
|
|
}
|
|
}
|
|
|
|
//----------------------------------------------------------------------------------
|
|
// DESCRIPTION:
|
|
// Initializes unity roots lookup table used by FFT functions.
|
|
// Once initialized, the table need not be initialized again unless a
|
|
// different FFT length is desired.
|
|
//
|
|
// REMARKS:
|
|
// The unity tables of FFT length 16 and below are hard coded into the
|
|
// respective FFT functions and so need not be initialized.
|
|
//
|
|
// PARAMETERS:
|
|
// pUnityTable - [out] unity table, receives unity roots lookup table, must have at least uLength elements
|
|
// uLength - [in] FFT length in frames, must be a power of 2 > 16
|
|
//----------------------------------------------------------------------------------
|
|
inline void FFTInitializeUnityTable (_Out_writes_(uLength) XMVECTOR* __restrict pUnityTable, _In_ size_t uLength) noexcept
|
|
{
|
|
using namespace DirectX;
|
|
|
|
assert(pUnityTable);
|
|
assert(uLength > 16);
|
|
_Analysis_assume_(uLength > 16);
|
|
assert(ISPOWEROF2(uLength));
|
|
|
|
// initialize unity table for recursive FFT lengths: uLength, uLength/4, uLength/16... > 16
|
|
// pUnityTable[0 to uLength*4-1] contains real components for current FFT length
|
|
// pUnityTable[uLength*4 to uLength*8-1] contains imaginary components for current FFT length
|
|
static const XMVECTORF32 vXM0123 = { { { 0.0f, 1.0f, 2.0f, 3.0f } } };
|
|
uLength >>= 2;
|
|
XMVECTOR vlStep = XMVectorReplicate(XM_PIDIV2 / float(uLength));
|
|
do
|
|
{
|
|
uLength >>= 2;
|
|
XMVECTOR vJP = vXM0123;
|
|
for (size_t j = 0; j < uLength; ++j)
|
|
{
|
|
XMVECTOR vSin, vCos;
|
|
XMVECTOR viJP, vlS;
|
|
|
|
pUnityTable[j] = g_XMOne;
|
|
pUnityTable[j + uLength * 4] = XMVectorZero();
|
|
|
|
vlS = XMVectorMultiply(vJP, vlStep);
|
|
XMVectorSinCos(&vSin, &vCos, vlS);
|
|
pUnityTable[j + uLength] = vCos;
|
|
pUnityTable[j + uLength * 5] = XMVectorMultiply(vSin, g_XMNegativeOne);
|
|
|
|
viJP = XMVectorAdd(vJP, vJP);
|
|
vlS = XMVectorMultiply(viJP, vlStep);
|
|
XMVectorSinCos(&vSin, &vCos, vlS);
|
|
pUnityTable[j + uLength * 2] = vCos;
|
|
pUnityTable[j + uLength * 6] = XMVectorMultiply(vSin, g_XMNegativeOne);
|
|
|
|
viJP = XMVectorAdd(viJP, vJP);
|
|
vlS = XMVectorMultiply(viJP, vlStep);
|
|
XMVectorSinCos(&vSin, &vCos, vlS);
|
|
pUnityTable[j + uLength * 3] = vCos;
|
|
pUnityTable[j + uLength * 7] = XMVectorMultiply(vSin, g_XMNegativeOne);
|
|
|
|
vJP = XMVectorAdd(vJP, g_XMFour);
|
|
}
|
|
vlStep = XMVectorMultiply(vlStep, g_XMFour);
|
|
pUnityTable += uLength * 8;
|
|
} while (uLength > 4);
|
|
}
|
|
|
|
//----------------------------------------------------------------------------------
|
|
// DESCRIPTION:
|
|
// The FFT functions generate output in bit reversed order.
|
|
// Use this function to re-arrange them into order of increasing frequency.
|
|
//
|
|
// REMARKS:
|
|
// Exponential values and bits correspond, so the reversed upper index can be omitted depending on the number of exponents.
|
|
//
|
|
// PARAMETERS:
|
|
// pOutput - [out] output buffer, receives samples in order of increasing frequency, cannot overlap pInput, must have at least (1<<uLog2Length)/4 elements
|
|
// pInput - [in] input buffer, samples in bit reversed order as generated by FFT functions, cannot overlap pOutput, must have at least (1<<uLog2Length)/4 elements
|
|
// uLog2Length - [in] LOG (base 2) of FFT length in samples, must be >= 2
|
|
//----------------------------------------------------------------------------------
|
|
inline void FFTUnswizzle (
|
|
_Out_writes_((1 << uLog2Length) / 4) XMVECTOR* __restrict pOutput,
|
|
_In_reads_((1 << uLog2Length) / 4) const XMVECTOR* __restrict pInput,
|
|
_In_ const size_t uLog2Length) noexcept
|
|
{
|
|
assert(pOutput);
|
|
assert(pInput);
|
|
assert(uLog2Length >= 2);
|
|
_Analysis_assume_(uLog2Length >= 2);
|
|
|
|
float* __restrict pfOutput = reinterpret_cast<float*>(pOutput);
|
|
const size_t uLength = size_t(1) << (uLog2Length - 2);
|
|
|
|
static const unsigned char cSwizzleTable[256] = {
|
|
0x00, 0x40, 0x80, 0xC0, 0x10, 0x50, 0x90, 0xD0, 0x20, 0x60, 0xA0, 0xE0, 0x30, 0x70, 0xB0, 0xF0,
|
|
0x04, 0x44, 0x84, 0xC4, 0x14, 0x54, 0x94, 0xD4, 0x24, 0x64, 0xA4, 0xE4, 0x34, 0x74, 0xB4, 0xF4,
|
|
0x08, 0x48, 0x88, 0xC8, 0x18, 0x58, 0x98, 0xD8, 0x28, 0x68, 0xA8, 0xE8, 0x38, 0x78, 0xB8, 0xF8,
|
|
0x0C, 0x4C, 0x8C, 0xCC, 0x1C, 0x5C, 0x9C, 0xDC, 0x2C, 0x6C, 0xAC, 0xEC, 0x3C, 0x7C, 0xBC, 0xFC,
|
|
0x01, 0x41, 0x81, 0xC1, 0x11, 0x51, 0x91, 0xD1, 0x21, 0x61, 0xA1, 0xE1, 0x31, 0x71, 0xB1, 0xF1,
|
|
0x05, 0x45, 0x85, 0xC5, 0x15, 0x55, 0x95, 0xD5, 0x25, 0x65, 0xA5, 0xE5, 0x35, 0x75, 0xB5, 0xF5,
|
|
0x09, 0x49, 0x89, 0xC9, 0x19, 0x59, 0x99, 0xD9, 0x29, 0x69, 0xA9, 0xE9, 0x39, 0x79, 0xB9, 0xF9,
|
|
0x0D, 0x4D, 0x8D, 0xCD, 0x1D, 0x5D, 0x9D, 0xDD, 0x2D, 0x6D, 0xAD, 0xED, 0x3D, 0x7D, 0xBD, 0xFD,
|
|
0x02, 0x42, 0x82, 0xC2, 0x12, 0x52, 0x92, 0xD2, 0x22, 0x62, 0xA2, 0xE2, 0x32, 0x72, 0xB2, 0xF2,
|
|
0x06, 0x46, 0x86, 0xC6, 0x16, 0x56, 0x96, 0xD6, 0x26, 0x66, 0xA6, 0xE6, 0x36, 0x76, 0xB6, 0xF6,
|
|
0x0A, 0x4A, 0x8A, 0xCA, 0x1A, 0x5A, 0x9A, 0xDA, 0x2A, 0x6A, 0xAA, 0xEA, 0x3A, 0x7A, 0xBA, 0xFA,
|
|
0x0E, 0x4E, 0x8E, 0xCE, 0x1E, 0x5E, 0x9E, 0xDE, 0x2E, 0x6E, 0xAE, 0xEE, 0x3E, 0x7E, 0xBE, 0xFE,
|
|
0x03, 0x43, 0x83, 0xC3, 0x13, 0x53, 0x93, 0xD3, 0x23, 0x63, 0xA3, 0xE3, 0x33, 0x73, 0xB3, 0xF3,
|
|
0x07, 0x47, 0x87, 0xC7, 0x17, 0x57, 0x97, 0xD7, 0x27, 0x67, 0xA7, 0xE7, 0x37, 0x77, 0xB7, 0xF7,
|
|
0x0B, 0x4B, 0x8B, 0xCB, 0x1B, 0x5B, 0x9B, 0xDB, 0x2B, 0x6B, 0xAB, 0xEB, 0x3B, 0x7B, 0xBB, 0xFB,
|
|
0x0F, 0x4F, 0x8F, 0xCF, 0x1F, 0x5F, 0x9F, 0xDF, 0x2F, 0x6F, 0xAF, 0xEF, 0x3F, 0x7F, 0xBF, 0xFF
|
|
};
|
|
if ((uLog2Length & 1) == 0)
|
|
{
|
|
// even powers of two
|
|
const size_t uRev32 = 32 - uLog2Length;
|
|
for (size_t uIndex = 0; uIndex < uLength; ++uIndex)
|
|
{
|
|
XMFLOAT4A f4a;
|
|
XMStoreFloat4A(&f4a, pInput[uIndex]);
|
|
const size_t n = uIndex * 4;
|
|
const size_t uAddr = (static_cast<size_t>(cSwizzleTable[n & 0xff]) << 24) |
|
|
(static_cast<size_t>(cSwizzleTable[(n >> 8) & 0xff]) << 16) |
|
|
(static_cast<size_t>(cSwizzleTable[(n >> 16) & 0xff]) << 8) |
|
|
(static_cast<size_t>(cSwizzleTable[(n >> 24)]));
|
|
pfOutput[uAddr >> uRev32] = f4a.x;
|
|
pfOutput[(0x40000000 | uAddr) >> uRev32] = f4a.y;
|
|
pfOutput[(0x80000000 | uAddr) >> uRev32] = f4a.z;
|
|
pfOutput[(0xC0000000 | uAddr) >> uRev32] = f4a.w;
|
|
}
|
|
}
|
|
else
|
|
{
|
|
// odd powers of two
|
|
const size_t uRev7 = size_t(1) << (uLog2Length - 3);
|
|
const size_t uRev32 = 32 - (uLog2Length - 3);
|
|
for (size_t uIndex = 0; uIndex < uLength; ++uIndex)
|
|
{
|
|
XMFLOAT4A f4a;
|
|
XMStoreFloat4A(&f4a, pInput[uIndex]);
|
|
const size_t n = (uIndex >> 1);
|
|
size_t uAddr = (((static_cast<size_t>(cSwizzleTable[n & 0xff]) << 24) |
|
|
(static_cast<size_t>(cSwizzleTable[(n >> 8) & 0xff]) << 16) |
|
|
(static_cast<size_t>(cSwizzleTable[(n >> 16) & 0xff]) << 8) |
|
|
(static_cast<size_t>(cSwizzleTable[(n >> 24)]))) >> uRev32) |
|
|
((uIndex & 1) * uRev7 * 4);
|
|
pfOutput[uAddr] = f4a.x;
|
|
uAddr += uRev7;
|
|
pfOutput[uAddr] = f4a.y;
|
|
uAddr += uRev7;
|
|
pfOutput[uAddr] = f4a.z;
|
|
uAddr += uRev7;
|
|
pfOutput[uAddr] = f4a.w;
|
|
}
|
|
}
|
|
}
|
|
|
|
//----------------------------------------------------------------------------------
|
|
// DESCRIPTION:
|
|
// Convert complex components to polar form.
|
|
//
|
|
// PARAMETERS:
|
|
// pOutput - [out] output buffer, receives samples in polar form, must have at least uLength/4 elements
|
|
// pInputReal - [in] input buffer (real components), must have at least uLength/4 elements
|
|
// pInputImaginary - [in] input buffer (imaginary components), must have at least uLength/4 elements
|
|
// uLength - [in] FFT length in samples, must be a power of 2 >= 4
|
|
//----------------------------------------------------------------------------------
|
|
#ifdef _MSC_VER
|
|
#pragma warning(suppress: 6101)
|
|
#endif
|
|
inline void FFTPolar(
|
|
_Out_writes_(uLength / 4) XMVECTOR* __restrict pOutput,
|
|
_In_reads_(uLength / 4) const XMVECTOR* __restrict pInputReal,
|
|
_In_reads_(uLength / 4) const XMVECTOR* __restrict pInputImaginary,
|
|
_In_ const size_t uLength) noexcept
|
|
{
|
|
using namespace DirectX;
|
|
|
|
assert(pOutput);
|
|
assert(pInputReal);
|
|
assert(pInputImaginary);
|
|
assert(uLength >= 4);
|
|
_Analysis_assume_(uLength >= 4);
|
|
assert(ISPOWEROF2(uLength));
|
|
|
|
const float flOneOverLength = 1.0f / float(uLength);
|
|
|
|
// result = sqrtf((real/uLength)^2 + (imaginary/uLength)^2) * 2
|
|
const XMVECTOR vOneOverLength = XMVectorReplicate(flOneOverLength);
|
|
|
|
for (size_t uIndex = 0; uIndex < (uLength >> 2); ++uIndex)
|
|
{
|
|
XMVECTOR vReal = XMVectorMultiply(pInputReal[uIndex], vOneOverLength);
|
|
XMVECTOR vImaginary = XMVectorMultiply(pInputImaginary[uIndex], vOneOverLength);
|
|
XMVECTOR vRR = XMVectorMultiply(vReal, vReal);
|
|
XMVECTOR vII = XMVectorMultiply(vImaginary, vImaginary);
|
|
XMVECTOR vRRplusII = XMVectorAdd(vRR, vII);
|
|
XMVECTOR vTotal = XMVectorSqrt(vRRplusII);
|
|
pOutput[uIndex] = XMVectorAdd(vTotal, vTotal);
|
|
}
|
|
}
|
|
|
|
//----------------------------------------------------------------------------------
|
|
// DESCRIPTION:
|
|
// Deinterleaves audio samples
|
|
//
|
|
// REMARKS:
|
|
// For example, audio of the form [LRLRLR] becomes [LLLRRR].
|
|
//
|
|
// PARAMETERS:
|
|
// pOutput - [out] output buffer, receives samples in deinterleaved form, cannot overlap pInput, must have at least (uChannelCount*uFrameCount)/4 elements
|
|
// pInput - [in] input buffer, cannot overlap pOutput, must have at least (uChannelCount*uFrameCount)/4 elements
|
|
// uChannelCount - [in] number of channels, must be > 1
|
|
// uFrameCount - [in] number of frames of valid data, must be > 0
|
|
//----------------------------------------------------------------------------------
|
|
inline void Deinterleave (
|
|
_Out_writes_((uChannelCount * uFrameCount) / 4) XMVECTOR* __restrict pOutput,
|
|
_In_reads_((uChannelCount * uFrameCount) / 4) const XMVECTOR* __restrict pInput,
|
|
_In_ const size_t uChannelCount,
|
|
_In_ const size_t uFrameCount) noexcept
|
|
{
|
|
assert(pOutput);
|
|
assert(pInput);
|
|
assert(uChannelCount > 1);
|
|
assert(uFrameCount > 0);
|
|
|
|
float* __restrict pfOutput = reinterpret_cast<float* __restrict>(pOutput);
|
|
const float* __restrict pfInput = reinterpret_cast<const float* __restrict>(pInput);
|
|
|
|
for (size_t uChannel = 0; uChannel < uChannelCount; ++uChannel)
|
|
{
|
|
for (size_t uFrame = 0; uFrame < uFrameCount; ++uFrame)
|
|
{
|
|
pfOutput[uChannel * uFrameCount + uFrame] = pfInput[uFrame * uChannelCount + uChannel];
|
|
}
|
|
}
|
|
}
|
|
|
|
//----------------------------------------------------------------------------------
|
|
// DESCRIPTION:
|
|
// Interleaves audio samples
|
|
//
|
|
// REMARKS:
|
|
// For example, audio of the form [LLLRRR] becomes [LRLRLR].
|
|
//
|
|
// PARAMETERS:
|
|
// pOutput - [out] output buffer, receives samples in interleaved form, cannot overlap pInput, must have at least (uChannelCount*uFrameCount)/4 elements
|
|
// pInput - [in] input buffer, cannot overlap pOutput, must have at least (uChannelCount*uFrameCount)/4 elements
|
|
// uChannelCount - [in] number of channels, must be > 1
|
|
// uFrameCount - [in] number of frames of valid data, must be > 0
|
|
//----------------------------------------------------------------------------------
|
|
inline void Interleave(
|
|
_Out_writes_((uChannelCount * uFrameCount) / 4) XMVECTOR* __restrict pOutput,
|
|
_In_reads_((uChannelCount * uFrameCount) / 4) const XMVECTOR* __restrict pInput,
|
|
_In_ const size_t uChannelCount,
|
|
_In_ const size_t uFrameCount) noexcept
|
|
{
|
|
assert(pOutput);
|
|
assert(pInput);
|
|
assert(uChannelCount > 1);
|
|
assert(uFrameCount > 0);
|
|
|
|
float* __restrict pfOutput = reinterpret_cast<float* __restrict>(pOutput);
|
|
const float* __restrict pfInput = reinterpret_cast<const float* __restrict>(pInput);
|
|
|
|
for (size_t uChannel = 0; uChannel < uChannelCount; ++uChannel)
|
|
{
|
|
for (size_t uFrame = 0; uFrame < uFrameCount; ++uFrame)
|
|
{
|
|
pfOutput[uFrame * uChannelCount + uChannel] = pfInput[uChannel * uFrameCount + uFrame];
|
|
}
|
|
}
|
|
}
|
|
|
|
//----------------------------------------------------------------------------------
|
|
// DESCRIPTION:
|
|
// This function applies a 2^N-sample FFT and unswizzles the result such
|
|
// that the samples are in order of increasing frequency.
|
|
// Audio is first deinterleaved if multichannel.
|
|
//
|
|
// PARAMETERS:
|
|
// pReal - [inout] real components, must have at least (1<<uLog2Length*uChannelCount)/4 elements
|
|
// pImaginary - [out] imaginary components, must have at least (1<<uLog2Length*uChannelCount)/4 elements
|
|
// pUnityTable - [in] unity table, must have at least (1<<uLog2Length) elements, see FFTInitializeUnityTable()
|
|
// uChannelCount - [in] number of channels, must be within [1, 6]
|
|
// uLog2Length - [in] LOG (base 2) of FFT length in frames, must within [2, 9]
|
|
//----------------------------------------------------------------------------------
|
|
inline void FFTInterleaved(
|
|
_Inout_updates_(((1 << uLog2Length) * uChannelCount) / 4) XMVECTOR* __restrict pReal,
|
|
_Out_writes_(((1 << uLog2Length) * uChannelCount) / 4) XMVECTOR* __restrict pImaginary,
|
|
_In_reads_(1 << uLog2Length) const XMVECTOR* __restrict pUnityTable,
|
|
_In_ const size_t uChannelCount,
|
|
_In_ const size_t uLog2Length) noexcept
|
|
{
|
|
assert(pReal);
|
|
assert(pImaginary);
|
|
assert(pUnityTable);
|
|
assert(reinterpret_cast<uintptr_t>(pReal) % 16 == 0);
|
|
assert(reinterpret_cast<uintptr_t>(pImaginary) % 16 == 0);
|
|
assert(reinterpret_cast<uintptr_t>(pUnityTable) % 16 == 0);
|
|
assert(uChannelCount > 0 && uChannelCount <= 6);
|
|
assert(uLog2Length >= 2 && uLog2Length <= 9);
|
|
|
|
XM_ALIGNED_DATA(16) XMVECTOR vRealTemp[768];
|
|
XM_ALIGNED_DATA(16) XMVECTOR vImaginaryTemp[768];
|
|
const size_t uLength = size_t(1) << uLog2Length;
|
|
|
|
if (uChannelCount > 1)
|
|
{
|
|
Deinterleave(vRealTemp, pReal, uChannelCount, uLength);
|
|
}
|
|
else
|
|
{
|
|
memcpy_s(vRealTemp, sizeof(vRealTemp), pReal, (uLength >> 2) * sizeof(XMVECTOR));
|
|
}
|
|
|
|
memset(vImaginaryTemp, 0, (uChannelCount * (uLength >> 2)) * sizeof(XMVECTOR));
|
|
|
|
if (uLength > 16)
|
|
{
|
|
for (size_t uChannel = 0; uChannel < uChannelCount; ++uChannel)
|
|
{
|
|
FFT(&vRealTemp[uChannel * (uLength >> 2)], &vImaginaryTemp[uChannel * (uLength >> 2)], pUnityTable, uLength);
|
|
}
|
|
}
|
|
else if (uLength == 16)
|
|
{
|
|
for (size_t uChannel = 0; uChannel < uChannelCount; ++uChannel)
|
|
{
|
|
FFT16(&vRealTemp[uChannel * (uLength >> 2)], &vImaginaryTemp[uChannel * (uLength >> 2)]);
|
|
}
|
|
}
|
|
else if (uLength == 8)
|
|
{
|
|
for (size_t uChannel = 0; uChannel < uChannelCount; ++uChannel)
|
|
{
|
|
FFT8(&vRealTemp[uChannel * (uLength >> 2)], &vImaginaryTemp[uChannel * (uLength >> 2)]);
|
|
}
|
|
}
|
|
else if (uLength == 4)
|
|
{
|
|
for (size_t uChannel = 0; uChannel < uChannelCount; ++uChannel)
|
|
{
|
|
FFT4(&vRealTemp[uChannel * (uLength >> 2)], &vImaginaryTemp[uChannel * (uLength >> 2)]);
|
|
}
|
|
}
|
|
|
|
for (size_t uChannel = 0; uChannel < uChannelCount; ++uChannel)
|
|
{
|
|
FFTUnswizzle(&pReal[uChannel * (uLength >> 2)], &vRealTemp[uChannel * (uLength >> 2)], uLog2Length);
|
|
FFTUnswizzle(&pImaginary[uChannel * (uLength >> 2)], &vImaginaryTemp[uChannel * (uLength >> 2)], uLog2Length);
|
|
}
|
|
}
|
|
|
|
//----------------------------------------------------------------------------------
|
|
// DESCRIPTION:
|
|
// This function applies a 2^N-sample inverse FFT.
|
|
// Audio is interleaved if multichannel.
|
|
//
|
|
// PARAMETERS:
|
|
// pReal - [inout] real components, must have at least (1<<uLog2Length*uChannelCount)/4 elements
|
|
// pImaginary - [in] imaginary components, must have at least (1<<uLog2Length*uChannelCount)/4 elements
|
|
// pUnityTable - [in] unity table, must have at least (1<<uLog2Length) elements, see FFTInitializeUnityTable()
|
|
// uChannelCount - [in] number of channels, must be > 0
|
|
// uLog2Length - [in] LOG (base 2) of FFT length in frames, must within [2, 9]
|
|
//----------------------------------------------------------------------------------
|
|
inline void IFFTDeinterleaved(
|
|
_Inout_updates_(((1 << uLog2Length) * uChannelCount) / 4) XMVECTOR* __restrict pReal,
|
|
_In_reads_(((1 << uLog2Length) * uChannelCount) / 4) const XMVECTOR* __restrict pImaginary,
|
|
_In_reads_(1 << uLog2Length) const XMVECTOR* __restrict pUnityTable,
|
|
_In_ const size_t uChannelCount,
|
|
_In_ const size_t uLog2Length) noexcept
|
|
{
|
|
using namespace DirectX;
|
|
|
|
assert(pReal);
|
|
assert(pImaginary);
|
|
assert(pUnityTable);
|
|
assert(reinterpret_cast<uintptr_t>(pReal) % 16 == 0);
|
|
assert(reinterpret_cast<uintptr_t>(pImaginary) % 16 == 0);
|
|
assert(reinterpret_cast<uintptr_t>(pUnityTable) % 16 == 0);
|
|
assert(uChannelCount > 0 && uChannelCount <= 6);
|
|
_Analysis_assume_(uChannelCount > 0 && uChannelCount <= 6);
|
|
assert(uLog2Length >= 2 && uLog2Length <= 9);
|
|
_Analysis_assume_(uLog2Length >= 2 && uLog2Length <= 9);
|
|
|
|
XM_ALIGNED_DATA(16) XMVECTOR vRealTemp[768] = {};
|
|
XM_ALIGNED_DATA(16) XMVECTOR vImaginaryTemp[768] = {};
|
|
|
|
const size_t uLength = size_t(1) << uLog2Length;
|
|
|
|
const XMVECTOR vRnp = XMVectorReplicate(1.0f / float(uLength));
|
|
const XMVECTOR vRnm = XMVectorReplicate(-1.0f / float(uLength));
|
|
for (size_t u = 0; u < uChannelCount * (uLength >> 2); u++)
|
|
{
|
|
vRealTemp[u] = XMVectorMultiply(pReal[u], vRnp);
|
|
vImaginaryTemp[u] = XMVectorMultiply(pImaginary[u], vRnm);
|
|
}
|
|
|
|
if (uLength > 16)
|
|
{
|
|
for (size_t uChannel = 0; uChannel < uChannelCount; ++uChannel)
|
|
{
|
|
FFT(&vRealTemp[uChannel * (uLength >> 2)], &vImaginaryTemp[uChannel * (uLength >> 2)], pUnityTable, uLength);
|
|
}
|
|
}
|
|
else if (uLength == 16)
|
|
{
|
|
for (size_t uChannel = 0; uChannel < uChannelCount; ++uChannel)
|
|
{
|
|
FFT16(&vRealTemp[uChannel * (uLength >> 2)], &vImaginaryTemp[uChannel * (uLength >> 2)]);
|
|
}
|
|
}
|
|
else if (uLength == 8)
|
|
{
|
|
for (size_t uChannel = 0; uChannel < uChannelCount; ++uChannel)
|
|
{
|
|
FFT8(&vRealTemp[uChannel * (uLength >> 2)], &vImaginaryTemp[uChannel * (uLength >> 2)]);
|
|
}
|
|
}
|
|
else if (uLength == 4)
|
|
{
|
|
for (size_t uChannel = 0; uChannel < uChannelCount; ++uChannel)
|
|
{
|
|
FFT4(&vRealTemp[uChannel * (uLength >> 2)], &vImaginaryTemp[uChannel * (uLength >> 2)]);
|
|
}
|
|
}
|
|
|
|
for (size_t uChannel = 0; uChannel < uChannelCount; ++uChannel)
|
|
{
|
|
FFTUnswizzle(&vImaginaryTemp[uChannel * (uLength >> 2)], &vRealTemp[uChannel * (uLength >> 2)], uLog2Length);
|
|
}
|
|
|
|
if (uChannelCount > 1)
|
|
{
|
|
Interleave(pReal, vImaginaryTemp, uChannelCount, uLength);
|
|
}
|
|
else
|
|
{
|
|
memcpy_s(pReal, uLength * uChannelCount * sizeof(float), vImaginaryTemp, (uLength >> 2) * sizeof(XMVECTOR));
|
|
}
|
|
}
|
|
|
|
} // namespace XDSP
|
|
|
|
#ifdef __clang__
|
|
#pragma clang diagnostic pop
|
|
#endif
|
|
#ifdef _MSC_VER
|
|
#pragma warning(pop)
|
|
#endif
|