814 lines
35 KiB
C++
814 lines
35 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. All rights reserved.
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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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#pragma warning(push)
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#pragma warning(disable: 6001 6262)
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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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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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XMVECTOR vr1r2 = XMVectorMultiply(r1, r2);
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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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XMVECTOR vr1r2 = XMVectorMultiply(r1, r2);
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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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XMVECTOR r1L = XMVectorSwizzle<0,0,1,1>( r1 );
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XMVECTOR r1H = XMVectorSwizzle<2,2,3,3>( r1 );
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XMVECTOR i1L = XMVectorSwizzle<0,0,1,1>( i1 );
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XMVECTOR i1H = XMVectorSwizzle<2,2,3,3>( i1 );
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XMVECTOR rTemp = XMVectorMultiplyAdd( r1H, vDFT4SignBits1, r1L );
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XMVECTOR iTemp = XMVectorMultiplyAdd( i1H, vDFT4SignBits1, i1L );
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// calculating Result
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XMVECTOR rZrWiZiW = XMVectorPermute<2,3,6,7>(rTemp,iTemp); // [rTempZ|rTempW|iTempZ|iTempW]
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XMVECTOR rZiWrZiW = XMVectorSwizzle<0,3,0,3>(rZrWiZiW); // [rTempZ|iTempW|rTempZ|iTempW]
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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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XMVECTOR rTempL = XMVectorSwizzle<0,1,0,1>(rTemp);
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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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XMVECTOR rTemp0 = XMVectorAdd(r0, r2);
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XMVECTOR iTemp0 = XMVectorAdd(i0, i2);
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XMVECTOR rTemp2 = XMVectorAdd(r1, r3);
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XMVECTOR iTemp2 = XMVectorAdd(i1, i3);
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XMVECTOR rTemp1 = XMVectorSubtract(r0, r2);
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XMVECTOR iTemp1 = XMVectorSubtract(i0, i2);
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XMVECTOR rTemp3 = XMVectorSubtract(r1, r3);
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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,
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_Inout_updates_((uLength*uCount)/4) XMVECTOR* __restrict pImaginary,
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_In_reads_(uLength*uCount) const XMVECTOR* __restrict pUnityTable,
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_In_ const size_t uLength,
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_In_ 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(pUnityTable);
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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
|
|
{
|
|
assert(pUnityTable);
|
|
assert(uLength > 16);
|
|
_Analysis_assume_(uLength > 16);
|
|
assert(ISPOWEROF2(uLength));
|
|
|
|
float* __restrict pfUnityTable = reinterpret_cast<float* __restrict>(pUnityTable);
|
|
|
|
// initialize unity table for recursive FFT lengths: uLength, uLength/4, uLength/16... > 16
|
|
do
|
|
{
|
|
float flStep = 6.283185307f / float(uLength); // 2PI / FFT length
|
|
uLength >>= 2;
|
|
|
|
// 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
|
|
for (size_t i=0; i<4; ++i)
|
|
{
|
|
for (size_t j=0; j<uLength; ++j)
|
|
{
|
|
size_t uIndex = (i*uLength) + j;
|
|
pfUnityTable[uIndex] = cosf(float(i)*float(j)*flStep); // real component
|
|
#pragma warning(suppress: 6386)
|
|
pfUnityTable[uIndex + uLength*4] = -sinf(float(i)*float(j)*flStep); // imaginary component
|
|
}
|
|
}
|
|
pfUnityTable += uLength*8;
|
|
}
|
|
while (uLength > 16);
|
|
}
|
|
|
|
//----------------------------------------------------------------------------------
|
|
// DESCRIPTION:
|
|
// The FFT functions generate output in bit reversed order.
|
|
// Use this function to re-arrange them into order of increasing frequency.
|
|
//
|
|
// REMARKS:
|
|
//
|
|
// 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 float* __restrict pfInput = reinterpret_cast<const float*>(pInput);
|
|
const size_t uLength = size_t(1) << uLog2Length;
|
|
|
|
if ((uLog2Length & 0x1) == 0)
|
|
{
|
|
// even powers of two
|
|
for (size_t uIndex=0; uIndex < uLength; ++uIndex)
|
|
{
|
|
size_t n = uIndex;
|
|
n = ( (n & 0xcccccccc) >> 2 ) | ( (n & 0x33333333) << 2 );
|
|
n = ( (n & 0xf0f0f0f0) >> 4 ) | ( (n & 0x0f0f0f0f) << 4 );
|
|
n = ( (n & 0xff00ff00) >> 8 ) | ( (n & 0x00ff00ff) << 8 );
|
|
n = ( (n & 0xffff0000) >> 16 ) | ( (n & 0x0000ffff) << 16 );
|
|
n >>= (32 - uLog2Length);
|
|
pfOutput[n] = pfInput[uIndex];
|
|
}
|
|
}
|
|
else
|
|
{
|
|
// odd powers of two
|
|
for (size_t uIndex=0; uIndex < uLength; ++uIndex)
|
|
{
|
|
size_t n = (uIndex>>3);
|
|
n = ( (n & 0xcccccccc) >> 2 ) | ( (n & 0x33333333) << 2 );
|
|
n = ( (n & 0xf0f0f0f0) >> 4 ) | ( (n & 0x0f0f0f0f) << 4 );
|
|
n = ( (n & 0xff00ff00) >> 8 ) | ( (n & 0x00ff00ff) << 8 );
|
|
n = ( (n & 0xffff0000) >> 16 ) | ( (n & 0x0000ffff) << 16 );
|
|
n >>= (32 - (uLog2Length-3));
|
|
n |= ((uIndex & 0x7) << (uLog2Length - 3));
|
|
pfOutput[n] = pfInput[uIndex];
|
|
}
|
|
}
|
|
}
|
|
|
|
//----------------------------------------------------------------------------------
|
|
// 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
|
|
//----------------------------------------------------------------------------------
|
|
#pragma warning(suppress: 6101)
|
|
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));
|
|
|
|
float flOneOverLength = 1.0f / float(uLength);
|
|
|
|
// result = sqrtf((real/uLength)^2 + (imaginary/uLength)^2) * 2
|
|
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);
|
|
|
|
XMVECTOR vRealTemp[768];
|
|
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);
|
|
|
|
XMVECTOR vRealTemp[768] = {};
|
|
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
|
|
|
|
#pragma warning(pop)
|