crossxtex/DirectXTex/BC.cpp

//-------------------------------------------------------------------------------------
// BC.cpp
//  
// Block-compression (BC) functionality for BC1, BC2, BC3 (orginal DXTn formats)
//
// Copyright (c) Microsoft Corporation. All rights reserved.
// Licensed under the MIT License.
//
// http://go.microsoft.com/fwlink/?LinkId=248926
//-------------------------------------------------------------------------------------

#include "DirectXTexP.h"

// Experiemental encoding variants, not enabled by default
//#define COLOR_WEIGHTS
//#define COLOR_AVG_0WEIGHTS

#include "BC.h"

using namespace DirectX;
using namespace DirectX::PackedVector;

namespace
{
    //-------------------------------------------------------------------------------------
    // Constants
    //-------------------------------------------------------------------------------------

    // Perceptual weightings for the importance of each channel.
    const HDRColorA g_Luminance(0.2125f / 0.7154f, 1.0f, 0.0721f / 0.7154f, 1.0f);
    const HDRColorA g_LuminanceInv(0.7154f / 0.2125f, 1.0f, 0.7154f / 0.0721f, 1.0f);

    //-------------------------------------------------------------------------------------
    // Decode/Encode RGB 5/6/5 colors
    //-------------------------------------------------------------------------------------
    inline void Decode565(_Out_ HDRColorA *pColor, _In_ const uint16_t w565)
    {
        pColor->r = static_cast<float>((w565 >> 11) & 31) * (1.0f / 31.0f);
        pColor->g = static_cast<float>((w565 >> 5) & 63) * (1.0f / 63.0f);
        pColor->b = static_cast<float>((w565 >> 0) & 31) * (1.0f / 31.0f);
        pColor->a = 1.0f;
    }

    inline uint16_t Encode565(_In_ const HDRColorA *pColor)
    {
        HDRColorA Color;

        Color.r = (pColor->r < 0.0f) ? 0.0f : (pColor->r > 1.0f) ? 1.0f : pColor->r;
        Color.g = (pColor->g < 0.0f) ? 0.0f : (pColor->g > 1.0f) ? 1.0f : pColor->g;
        Color.b = (pColor->b < 0.0f) ? 0.0f : (pColor->b > 1.0f) ? 1.0f : pColor->b;
        Color.a = pColor->a;

        uint16_t w;

        w = static_cast<uint16_t>(
            (static_cast<int32_t>(Color.r * 31.0f + 0.5f) << 11)
            | (static_cast<int32_t>(Color.g * 63.0f + 0.5f) << 5)
            | (static_cast<int32_t>(Color.b * 31.0f + 0.5f) << 0));

        return w;
    }


    //-------------------------------------------------------------------------------------
    void OptimizeRGB(
        _Out_ HDRColorA *pX,
        _Out_ HDRColorA *pY,
        _In_reads_(NUM_PIXELS_PER_BLOCK) const HDRColorA *pPoints,
        uint32_t cSteps,
        DWORD flags)
    {
        static const float fEpsilon = (0.25f / 64.0f) * (0.25f / 64.0f);
        static const float pC3[] = { 2.0f / 2.0f, 1.0f / 2.0f, 0.0f / 2.0f };
        static const float pD3[] = { 0.0f / 2.0f, 1.0f / 2.0f, 2.0f / 2.0f };
        static const float pC4[] = { 3.0f / 3.0f, 2.0f / 3.0f, 1.0f / 3.0f, 0.0f / 3.0f };
        static const float pD4[] = { 0.0f / 3.0f, 1.0f / 3.0f, 2.0f / 3.0f, 3.0f / 3.0f };

        const float *pC = (3 == cSteps) ? pC3 : pC4;
        const float *pD = (3 == cSteps) ? pD3 : pD4;

        // Find Min and Max points, as starting point
        HDRColorA X = (flags & BC_FLAGS_UNIFORM) ? HDRColorA(1.f, 1.f, 1.f, 1.f) : g_Luminance;
        HDRColorA Y = HDRColorA(0.0f, 0.0f, 0.0f, 1.0f);

        for (size_t iPoint = 0; iPoint < NUM_PIXELS_PER_BLOCK; iPoint++)
        {
#ifdef COLOR_WEIGHTS
            if (pPoints[iPoint].a > 0.0f)
#endif // COLOR_WEIGHTS
            {
                if (pPoints[iPoint].r < X.r)
                    X.r = pPoints[iPoint].r;

                if (pPoints[iPoint].g < X.g)
                    X.g = pPoints[iPoint].g;

                if (pPoints[iPoint].b < X.b)
                    X.b = pPoints[iPoint].b;

                if (pPoints[iPoint].r > Y.r)
                    Y.r = pPoints[iPoint].r;

                if (pPoints[iPoint].g > Y.g)
                    Y.g = pPoints[iPoint].g;

                if (pPoints[iPoint].b > Y.b)
                    Y.b = pPoints[iPoint].b;
            }
        }

        // Diagonal axis
        HDRColorA AB(Y.r - X.r, Y.g - X.g, Y.b - X.b, 0.0f);

        float fAB = AB.r * AB.r + AB.g * AB.g + AB.b * AB.b;

        // Single color block.. no need to root-find
        if (fAB < FLT_MIN)
        {
            pX->r = X.r; pX->g = X.g; pX->b = X.b; pX->a = 1.0f;
            pY->r = Y.r; pY->g = Y.g; pY->b = Y.b; pY->a = 1.0f;
            return;
        }

        // Try all four axis directions, to determine which diagonal best fits data
        float fABInv = 1.0f / fAB;

        HDRColorA Dir(AB.r * fABInv, AB.g * fABInv, AB.b * fABInv, 0.0f);

        HDRColorA Mid(
            (X.r + Y.r) * 0.5f,
            (X.g + Y.g) * 0.5f,
            (X.b + Y.b) * 0.5f,
            0.0f);

        float fDir[4] = {};

        for (size_t iPoint = 0; iPoint < NUM_PIXELS_PER_BLOCK; iPoint++)
        {
            HDRColorA Pt;
            Pt.r = (pPoints[iPoint].r - Mid.r) * Dir.r;
            Pt.g = (pPoints[iPoint].g - Mid.g) * Dir.g;
            Pt.b = (pPoints[iPoint].b - Mid.b) * Dir.b;
            Pt.a = 0.0f;

            float f;

#ifdef COLOR_WEIGHTS
            f = Pt.r + Pt.g + Pt.b;
            fDir[0] += pPoints[iPoint].a * f * f;

            f = Pt.r + Pt.g - Pt.b;
            fDir[1] += pPoints[iPoint].a * f * f;

            f = Pt.r - Pt.g + Pt.b;
            fDir[2] += pPoints[iPoint].a * f * f;

            f = Pt.r - Pt.g - Pt.b;
            fDir[3] += pPoints[iPoint].a * f * f;
#else
            f = Pt.r + Pt.g + Pt.b;
            fDir[0] += f * f;

            f = Pt.r + Pt.g - Pt.b;
            fDir[1] += f * f;

            f = Pt.r - Pt.g + Pt.b;
            fDir[2] += f * f;

            f = Pt.r - Pt.g - Pt.b;
            fDir[3] += f * f;
#endif // COLOR_WEIGHTS
        }

        float fDirMax = fDir[0];
        size_t  iDirMax = 0;

        for (size_t iDir = 1; iDir < 4; iDir++)
        {
            if (fDir[iDir] > fDirMax)
            {
                fDirMax = fDir[iDir];
                iDirMax = iDir;
            }
        }

        if (iDirMax & 2)
        {
            float f = X.g; X.g = Y.g; Y.g = f;
        }

        if (iDirMax & 1)
        {
            float f = X.b; X.b = Y.b; Y.b = f;
        }


        // Two color block.. no need to root-find
        if (fAB < 1.0f / 4096.0f)
        {
            pX->r = X.r; pX->g = X.g; pX->b = X.b; pX->a = 1.0f;
            pY->r = Y.r; pY->g = Y.g; pY->b = Y.b; pY->a = 1.0f;
            return;
        }

        // Use Newton's Method to find local minima of sum-of-squares error.
        auto fSteps = static_cast<float>(cSteps - 1);

        for (size_t iIteration = 0; iIteration < 8; iIteration++)
        {
            // Calculate new steps
            HDRColorA pSteps[4];

            for (size_t iStep = 0; iStep < cSteps; iStep++)
            {
                pSteps[iStep].r = X.r * pC[iStep] + Y.r * pD[iStep];
                pSteps[iStep].g = X.g * pC[iStep] + Y.g * pD[iStep];
                pSteps[iStep].b = X.b * pC[iStep] + Y.b * pD[iStep];
                pSteps[iStep].a = 1.0f;
            }


            // Calculate color direction
            Dir.r = Y.r - X.r;
            Dir.g = Y.g - X.g;
            Dir.b = Y.b - X.b;

            float fLen = (Dir.r * Dir.r + Dir.g * Dir.g + Dir.b * Dir.b);

            if (fLen < (1.0f / 4096.0f))
                break;

            float fScale = fSteps / fLen;

            Dir.r *= fScale;
            Dir.g *= fScale;
            Dir.b *= fScale;


            // Evaluate function, and derivatives
            float d2X = 0.f;
            float d2Y = 0.f;
            HDRColorA dX = {};
            HDRColorA dY = {};

            for (size_t iPoint = 0; iPoint < NUM_PIXELS_PER_BLOCK; iPoint++)
            {
                float fDot = (pPoints[iPoint].r - X.r) * Dir.r +
                    (pPoints[iPoint].g - X.g) * Dir.g +
                    (pPoints[iPoint].b - X.b) * Dir.b;


                uint32_t iStep;
                if (fDot <= 0.0f)
                    iStep = 0;
                else if (fDot >= fSteps)
                    iStep = cSteps - 1;
                else
                    iStep = uint32_t(fDot + 0.5f);


                HDRColorA Diff;
                Diff.r = pSteps[iStep].r - pPoints[iPoint].r;
                Diff.g = pSteps[iStep].g - pPoints[iPoint].g;
                Diff.b = pSteps[iStep].b - pPoints[iPoint].b;
                Diff.a = 0.0f;

#ifdef COLOR_WEIGHTS
                float fC = pC[iStep] * pPoints[iPoint].a * (1.0f / 8.0f);
                float fD = pD[iStep] * pPoints[iPoint].a * (1.0f / 8.0f);
#else
                float fC = pC[iStep] * (1.0f / 8.0f);
                float fD = pD[iStep] * (1.0f / 8.0f);
#endif // COLOR_WEIGHTS

                d2X += fC * pC[iStep];
                dX.r += fC * Diff.r;
                dX.g += fC * Diff.g;
                dX.b += fC * Diff.b;

                d2Y += fD * pD[iStep];
                dY.r += fD * Diff.r;
                dY.g += fD * Diff.g;
                dY.b += fD * Diff.b;
            }

            // Move endpoints
            if (d2X > 0.0f)
            {
                float f = -1.0f / d2X;

                X.r += dX.r * f;
                X.g += dX.g * f;
                X.b += dX.b * f;
            }

            if (d2Y > 0.0f)
            {
                float f = -1.0f / d2Y;

                Y.r += dY.r * f;
                Y.g += dY.g * f;
                Y.b += dY.b * f;
            }

            if ((dX.r * dX.r < fEpsilon) && (dX.g * dX.g < fEpsilon) && (dX.b * dX.b < fEpsilon) &&
                (dY.r * dY.r < fEpsilon) && (dY.g * dY.g < fEpsilon) && (dY.b * dY.b < fEpsilon))
            {
                break;
            }
        }

        pX->r = X.r; pX->g = X.g; pX->b = X.b; pX->a = 1.0f;
        pY->r = Y.r; pY->g = Y.g; pY->b = Y.b; pY->a = 1.0f;
    }


    //-------------------------------------------------------------------------------------
    inline void DecodeBC1(
        _Out_writes_(NUM_PIXELS_PER_BLOCK) XMVECTOR *pColor,
        _In_ const D3DX_BC1 *pBC,
        bool isbc1)
    {
        assert(pColor && pBC);
        static_assert(sizeof(D3DX_BC1) == 8, "D3DX_BC1 should be 8 bytes");

        static XMVECTORF32 s_Scale = { { { 1.f / 31.f, 1.f / 63.f, 1.f / 31.f, 1.f } } };

        XMVECTOR clr0 = XMLoadU565(reinterpret_cast<const XMU565*>(&pBC->rgb[0]));
        XMVECTOR clr1 = XMLoadU565(reinterpret_cast<const XMU565*>(&pBC->rgb[1]));

        clr0 = XMVectorMultiply(clr0, s_Scale);
        clr1 = XMVectorMultiply(clr1, s_Scale);

        clr0 = XMVectorSwizzle<2, 1, 0, 3>(clr0);
        clr1 = XMVectorSwizzle<2, 1, 0, 3>(clr1);

        clr0 = XMVectorSelect(g_XMIdentityR3, clr0, g_XMSelect1110);
        clr1 = XMVectorSelect(g_XMIdentityR3, clr1, g_XMSelect1110);

        XMVECTOR clr2, clr3;
        if (isbc1 && (pBC->rgb[0] <= pBC->rgb[1]))
        {
            clr2 = XMVectorLerp(clr0, clr1, 0.5f);
            clr3 = XMVectorZero();  // Alpha of 0
        }
        else
        {
            clr2 = XMVectorLerp(clr0, clr1, 1.f / 3.f);
            clr3 = XMVectorLerp(clr0, clr1, 2.f / 3.f);
        }

        uint32_t dw = pBC->bitmap;

        for (size_t i = 0; i < NUM_PIXELS_PER_BLOCK; ++i, dw >>= 2)
        {
            switch (dw & 3)
            {
            case 0: pColor[i] = clr0; break;
            case 1: pColor[i] = clr1; break;
            case 2: pColor[i] = clr2; break;

            case 3:
            default: pColor[i] = clr3; break;
            }
        }
    }


    //-------------------------------------------------------------------------------------
    void EncodeBC1(
        _Out_ D3DX_BC1 *pBC,
        _In_reads_(NUM_PIXELS_PER_BLOCK) const HDRColorA *pColor,
        bool bColorKey,
        float threshold,
        DWORD flags)
    {
        assert(pBC && pColor);
        static_assert(sizeof(D3DX_BC1) == 8, "D3DX_BC1 should be 8 bytes");

        // Determine if we need to colorkey this block
        uint32_t uSteps;

        if (bColorKey)
        {
            size_t uColorKey = 0;

            for (size_t i = 0; i < NUM_PIXELS_PER_BLOCK; ++i)
            {
                if (pColor[i].a < threshold)
                    uColorKey++;
            }

            if (NUM_PIXELS_PER_BLOCK == uColorKey)
            {
                pBC->rgb[0] = 0x0000;
                pBC->rgb[1] = 0xffff;
                pBC->bitmap = 0xffffffff;
                return;
            }

            uSteps = (uColorKey > 0) ? 3u : 4u;
        }
        else
        {
            uSteps = 4u;
        }

        // Quantize block to R56B5, using Floyd Stienberg error diffusion.  This 
        // increases the chance that colors will map directly to the quantized 
        // axis endpoints.
        HDRColorA Color[NUM_PIXELS_PER_BLOCK];
        HDRColorA Error[NUM_PIXELS_PER_BLOCK];

        if (flags & BC_FLAGS_DITHER_RGB)
            memset(Error, 0x00, NUM_PIXELS_PER_BLOCK * sizeof(HDRColorA));

        size_t i;
        for (i = 0; i < NUM_PIXELS_PER_BLOCK; ++i)
        {
            HDRColorA Clr;
            Clr.r = pColor[i].r;
            Clr.g = pColor[i].g;
            Clr.b = pColor[i].b;
            Clr.a = 1.0f;

            if (flags & BC_FLAGS_DITHER_RGB)
            {
                Clr.r += Error[i].r;
                Clr.g += Error[i].g;
                Clr.b += Error[i].b;
            }

            Color[i].r = static_cast<float>(static_cast<int32_t>(Clr.r * 31.0f + 0.5f) * (1.0f / 31.0f));
            Color[i].g = static_cast<float>(static_cast<int32_t>(Clr.g * 63.0f + 0.5f) * (1.0f / 63.0f));
            Color[i].b = static_cast<float>(static_cast<int32_t>(Clr.b * 31.0f + 0.5f) * (1.0f / 31.0f));

#ifdef COLOR_WEIGHTS
            Color[i].a = pColor[i].a;
#else
            Color[i].a = 1.0f;
#endif // COLOR_WEIGHTS

            if (flags & BC_FLAGS_DITHER_RGB)
            {
                HDRColorA Diff;
                Diff.r = Color[i].a * (Clr.r - Color[i].r);
                Diff.g = Color[i].a * (Clr.g - Color[i].g);
                Diff.b = Color[i].a * (Clr.b - Color[i].b);
                Diff.a = 0.0f;

                if (3 != (i & 3))
                {
                    assert(i < 15);
                    _Analysis_assume_(i < 15);
                    Error[i + 1].r += Diff.r * (7.0f / 16.0f);
                    Error[i + 1].g += Diff.g * (7.0f / 16.0f);
                    Error[i + 1].b += Diff.b * (7.0f / 16.0f);
                }

                if (i < 12)
                {
                    if (i & 3)
                    {
                        Error[i + 3].r += Diff.r * (3.0f / 16.0f);
                        Error[i + 3].g += Diff.g * (3.0f / 16.0f);
                        Error[i + 3].b += Diff.b * (3.0f / 16.0f);
                    }

                    Error[i + 4].r += Diff.r * (5.0f / 16.0f);
                    Error[i + 4].g += Diff.g * (5.0f / 16.0f);
                    Error[i + 4].b += Diff.b * (5.0f / 16.0f);

                    if (3 != (i & 3))
                    {
                        assert(i < 11);
                        _Analysis_assume_(i < 11);
                        Error[i + 5].r += Diff.r * (1.0f / 16.0f);
                        Error[i + 5].g += Diff.g * (1.0f / 16.0f);
                        Error[i + 5].b += Diff.b * (1.0f / 16.0f);
                    }
                }
            }

            if (!(flags & BC_FLAGS_UNIFORM))
            {
                Color[i].r *= g_Luminance.r;
                Color[i].g *= g_Luminance.g;
                Color[i].b *= g_Luminance.b;
            }
        }

        // Perform 6D root finding function to find two endpoints of color axis.
        // Then quantize and sort the endpoints depending on mode.
        HDRColorA ColorA, ColorB, ColorC, ColorD;

        OptimizeRGB(&ColorA, &ColorB, Color, uSteps, flags);

        if (flags & BC_FLAGS_UNIFORM)
        {
            ColorC = ColorA;
            ColorD = ColorB;
        }
        else
        {
            ColorC.r = ColorA.r * g_LuminanceInv.r;
            ColorC.g = ColorA.g * g_LuminanceInv.g;
            ColorC.b = ColorA.b * g_LuminanceInv.b;
            ColorC.a = ColorA.a;

            ColorD.r = ColorB.r * g_LuminanceInv.r;
            ColorD.g = ColorB.g * g_LuminanceInv.g;
            ColorD.b = ColorB.b * g_LuminanceInv.b;
            ColorD.a = ColorB.a;
        }

        uint16_t wColorA = Encode565(&ColorC);
        uint16_t wColorB = Encode565(&ColorD);

        if ((uSteps == 4) && (wColorA == wColorB))
        {
            pBC->rgb[0] = wColorA;
            pBC->rgb[1] = wColorB;
            pBC->bitmap = 0x00000000;
            return;
        }

        Decode565(&ColorC, wColorA);
        Decode565(&ColorD, wColorB);

        if (flags & BC_FLAGS_UNIFORM)
        {
            ColorA = ColorC;
            ColorB = ColorD;
        }
        else
        {
            ColorA.r = ColorC.r * g_Luminance.r;
            ColorA.g = ColorC.g * g_Luminance.g;
            ColorA.b = ColorC.b * g_Luminance.b;

            ColorB.r = ColorD.r * g_Luminance.r;
            ColorB.g = ColorD.g * g_Luminance.g;
            ColorB.b = ColorD.b * g_Luminance.b;
        }

        // Calculate color steps
        HDRColorA Step[4];

        if ((3 == uSteps) == (wColorA <= wColorB))
        {
            pBC->rgb[0] = wColorA;
            pBC->rgb[1] = wColorB;

            Step[0] = ColorA;
            Step[1] = ColorB;
        }
        else
        {
            pBC->rgb[0] = wColorB;
            pBC->rgb[1] = wColorA;

            Step[0] = ColorB;
            Step[1] = ColorA;
        }

        static const size_t pSteps3[] = { 0, 2, 1 };
        static const size_t pSteps4[] = { 0, 2, 3, 1 };
        const size_t *pSteps;

        if (3 == uSteps)
        {
            pSteps = pSteps3;

            HDRColorALerp(&Step[2], &Step[0], &Step[1], 0.5f);
        }
        else
        {
            pSteps = pSteps4;

            HDRColorALerp(&Step[2], &Step[0], &Step[1], 1.0f / 3.0f);
            HDRColorALerp(&Step[3], &Step[0], &Step[1], 2.0f / 3.0f);
        }

        // Calculate color direction
        HDRColorA Dir;
        Dir.r = Step[1].r - Step[0].r;
        Dir.g = Step[1].g - Step[0].g;
        Dir.b = Step[1].b - Step[0].b;
        Dir.a = 0.0f;

        auto fSteps = static_cast<float>(uSteps - 1);
        float fScale = (wColorA != wColorB) ? (fSteps / (Dir.r * Dir.r + Dir.g * Dir.g + Dir.b * Dir.b)) : 0.0f;

        Dir.r *= fScale;
        Dir.g *= fScale;
        Dir.b *= fScale;

        // Encode colors
        uint32_t dw = 0;
        if (flags & BC_FLAGS_DITHER_RGB)
            memset(Error, 0x00, NUM_PIXELS_PER_BLOCK * sizeof(HDRColorA));

        for (i = 0; i < NUM_PIXELS_PER_BLOCK; ++i)
        {
            if ((3 == uSteps) && (pColor[i].a < threshold))
            {
                dw = (3u << 30) | (dw >> 2);
            }
            else
            {
                HDRColorA Clr;
                if (flags & BC_FLAGS_UNIFORM)
                {
                    Clr.r = pColor[i].r;
                    Clr.g = pColor[i].g;
                    Clr.b = pColor[i].b;
                }
                else
                {
                    Clr.r = pColor[i].r * g_Luminance.r;
                    Clr.g = pColor[i].g * g_Luminance.g;
                    Clr.b = pColor[i].b * g_Luminance.b;
                }
                Clr.a = 1.0f;

                if (flags & BC_FLAGS_DITHER_RGB)
                {
                    Clr.r += Error[i].r;
                    Clr.g += Error[i].g;
                    Clr.b += Error[i].b;
                }

                float fDot = (Clr.r - Step[0].r) * Dir.r + (Clr.g - Step[0].g) * Dir.g + (Clr.b - Step[0].b) * Dir.b;

                uint32_t iStep;
                if (fDot <= 0.0f)
                    iStep = 0;
                else if (fDot >= fSteps)
                    iStep = 1;
                else
                    iStep = uint32_t(pSteps[uint32_t(fDot + 0.5f)]);

                dw = (iStep << 30) | (dw >> 2);

                if (flags & BC_FLAGS_DITHER_RGB)
                {
                    HDRColorA Diff;
                    Diff.r = Color[i].a * (Clr.r - Step[iStep].r);
                    Diff.g = Color[i].a * (Clr.g - Step[iStep].g);
                    Diff.b = Color[i].a * (Clr.b - Step[iStep].b);
                    Diff.a = 0.0f;

                    if (3 != (i & 3))
                    {
                        Error[i + 1].r += Diff.r * (7.0f / 16.0f);
                        Error[i + 1].g += Diff.g * (7.0f / 16.0f);
                        Error[i + 1].b += Diff.b * (7.0f / 16.0f);
                    }

                    if (i < 12)
                    {
                        if (i & 3)
                        {
                            Error[i + 3].r += Diff.r * (3.0f / 16.0f);
                            Error[i + 3].g += Diff.g * (3.0f / 16.0f);
                            Error[i + 3].b += Diff.b * (3.0f / 16.0f);
                        }

                        Error[i + 4].r += Diff.r * (5.0f / 16.0f);
                        Error[i + 4].g += Diff.g * (5.0f / 16.0f);
                        Error[i + 4].b += Diff.b * (5.0f / 16.0f);

                        if (3 != (i & 3))
                        {
                            Error[i + 5].r += Diff.r * (1.0f / 16.0f);
                            Error[i + 5].g += Diff.g * (1.0f / 16.0f);
                            Error[i + 5].b += Diff.b * (1.0f / 16.0f);
                        }
                    }
                }
            }
        }

        pBC->bitmap = dw;
    }

    //-------------------------------------------------------------------------------------
#ifdef COLOR_WEIGHTS
    void EncodeSolidBC1(_Out_ D3DX_BC1 *pBC, _In_reads_(NUM_PIXELS_PER_BLOCK) const HDRColorA *pColor)
    {
#ifdef COLOR_AVG_0WEIGHTS
        // Compute avg color
        HDRColorA Color;
        Color.r = pColor[0].r;
        Color.g = pColor[0].g;
        Color.b = pColor[0].b;

        for (size_t i = 1; i < NUM_PIXELS_PER_BLOCK; ++i)
        {
            Color.r += pColor[i].r;
            Color.g += pColor[i].g;
            Color.b += pColor[i].b;
        }

        Color.r *= 1.0f / 16.0f;
        Color.g *= 1.0f / 16.0f;
        Color.b *= 1.0f / 16.0f;

        uint16_t wColor = Encode565(&Color);
#else
        uint16_t wColor = 0x0000;
#endif // COLOR_AVG_0WEIGHTS

        // Encode solid block
        pBC->rgb[0] = wColor;
        pBC->rgb[1] = wColor;
        pBC->bitmap = 0x00000000;
    }
#endif // COLOR_WEIGHTS
}


//=====================================================================================
// Entry points
//=====================================================================================

//-------------------------------------------------------------------------------------
// BC1 Compression
//-------------------------------------------------------------------------------------
_Use_decl_annotations_
void DirectX::D3DXDecodeBC1(XMVECTOR *pColor, const uint8_t *pBC)
{
    auto pBC1 = reinterpret_cast<const D3DX_BC1 *>(pBC);
    DecodeBC1(pColor, pBC1, true);
}

_Use_decl_annotations_
void DirectX::D3DXEncodeBC1(uint8_t *pBC, const XMVECTOR *pColor, float threshold, DWORD flags)
{
    assert(pBC && pColor);

    HDRColorA Color[NUM_PIXELS_PER_BLOCK];

    if (flags & BC_FLAGS_DITHER_A)
    {
        float fError[NUM_PIXELS_PER_BLOCK] = {};

        for (size_t i = 0; i < NUM_PIXELS_PER_BLOCK; ++i)
        {
            HDRColorA clr;
            XMStoreFloat4(reinterpret_cast<XMFLOAT4*>(&clr), pColor[i]);

            float fAlph = clr.a + fError[i];

            Color[i].r = clr.r;
            Color[i].g = clr.g;
            Color[i].b = clr.b;
            Color[i].a = static_cast<float>(static_cast<int32_t>(clr.a + fError[i] + 0.5f));

            float fDiff = fAlph - Color[i].a;

            if (3 != (i & 3))
            {
                assert(i < 15);
                _Analysis_assume_(i < 15);
                fError[i + 1] += fDiff * (7.0f / 16.0f);
            }

            if (i < 12)
            {
                if (i & 3)
                    fError[i + 3] += fDiff * (3.0f / 16.0f);

                fError[i + 4] += fDiff * (5.0f / 16.0f);

                if (3 != (i & 3))
                {
                    assert(i < 11);
                    _Analysis_assume_(i < 11);
                    fError[i + 5] += fDiff * (1.0f / 16.0f);
                }
            }
        }
    }
    else
    {
        for (size_t i = 0; i < NUM_PIXELS_PER_BLOCK; ++i)
        {
            XMStoreFloat4(reinterpret_cast<XMFLOAT4*>(&Color[i]), pColor[i]);
        }
    }

    auto pBC1 = reinterpret_cast<D3DX_BC1 *>(pBC);
    EncodeBC1(pBC1, Color, true, threshold, flags);
}


//-------------------------------------------------------------------------------------
// BC2 Compression
//-------------------------------------------------------------------------------------
_Use_decl_annotations_
void DirectX::D3DXDecodeBC2(XMVECTOR *pColor, const uint8_t *pBC)
{
    assert(pColor && pBC);
    static_assert(sizeof(D3DX_BC2) == 16, "D3DX_BC2 should be 16 bytes");

    auto pBC2 = reinterpret_cast<const D3DX_BC2 *>(pBC);

    // RGB part
    DecodeBC1(pColor, &pBC2->bc1, false);

    // 4-bit alpha part
    DWORD dw = pBC2->bitmap[0];

    for (size_t i = 0; i < 8; ++i, dw >>= 4)
    {
#pragma prefast(suppress:22103, "writing blocks in two halves confuses tool")
        pColor[i] = XMVectorSetW(pColor[i], static_cast<float>(dw & 0xf) * (1.0f / 15.0f));
    }

    dw = pBC2->bitmap[1];

    for (size_t i = 8; i < NUM_PIXELS_PER_BLOCK; ++i, dw >>= 4)
        pColor[i] = XMVectorSetW(pColor[i], static_cast<float>(dw & 0xf) * (1.0f / 15.0f));
}

_Use_decl_annotations_
void DirectX::D3DXEncodeBC2(uint8_t *pBC, const XMVECTOR *pColor, DWORD flags)
{
    assert(pBC && pColor);
    static_assert(sizeof(D3DX_BC2) == 16, "D3DX_BC2 should be 16 bytes");

    HDRColorA Color[NUM_PIXELS_PER_BLOCK];
    for (size_t i = 0; i < NUM_PIXELS_PER_BLOCK; ++i)
    {
        XMStoreFloat4(reinterpret_cast<XMFLOAT4*>(&Color[i]), pColor[i]);
    }

    auto pBC2 = reinterpret_cast<D3DX_BC2 *>(pBC);

    // 4-bit alpha part.  Dithered using Floyd Stienberg error diffusion.
    pBC2->bitmap[0] = 0;
    pBC2->bitmap[1] = 0;

    float fError[NUM_PIXELS_PER_BLOCK] = {};
    for (size_t i = 0; i < NUM_PIXELS_PER_BLOCK; ++i)
    {
        float fAlph = Color[i].a;
        if (flags & BC_FLAGS_DITHER_A)
            fAlph += fError[i];

        auto u = static_cast<uint32_t>(fAlph * 15.0f + 0.5f);

        pBC2->bitmap[i >> 3] >>= 4;
        pBC2->bitmap[i >> 3] |= (u << 28);

        if (flags & BC_FLAGS_DITHER_A)
        {
            float fDiff = fAlph - float(u) * (1.0f / 15.0f);

            if (3 != (i & 3))
            {
                assert(i < 15);
                _Analysis_assume_(i < 15);
                fError[i + 1] += fDiff * (7.0f / 16.0f);
            }

            if (i < 12)
            {
                if (i & 3)
                    fError[i + 3] += fDiff * (3.0f / 16.0f);

                fError[i + 4] += fDiff * (5.0f / 16.0f);

                if (3 != (i & 3))
                {
                    assert(i < 11);
                    _Analysis_assume_(i < 11);
                    fError[i + 5] += fDiff * (1.0f / 16.0f);
                }
            }
        }
    }

    // RGB part
#ifdef COLOR_WEIGHTS
    if (!pBC2->bitmap[0] && !pBC2->bitmap[1])
    {
        EncodeSolidBC1(pBC2->dxt1, Color);
        return;
    }
#endif // COLOR_WEIGHTS

    EncodeBC1(&pBC2->bc1, Color, false, 0.f, flags);
}


//-------------------------------------------------------------------------------------
// BC3 Compression
//-------------------------------------------------------------------------------------
_Use_decl_annotations_
void DirectX::D3DXDecodeBC3(XMVECTOR *pColor, const uint8_t *pBC)
{
    assert(pColor && pBC);
    static_assert(sizeof(D3DX_BC3) == 16, "D3DX_BC3 should be 16 bytes");

    auto pBC3 = reinterpret_cast<const D3DX_BC3 *>(pBC);

    // RGB part
    DecodeBC1(pColor, &pBC3->bc1, false);

    // Adaptive 3-bit alpha part
    float fAlpha[8];

    fAlpha[0] = static_cast<float>(pBC3->alpha[0]) * (1.0f / 255.0f);
    fAlpha[1] = static_cast<float>(pBC3->alpha[1]) * (1.0f / 255.0f);

    if (pBC3->alpha[0] > pBC3->alpha[1])
    {
        for (size_t i = 1; i < 7; ++i)
            fAlpha[i + 1] = (fAlpha[0] * (7 - i) + fAlpha[1] * i) * (1.0f / 7.0f);
    }
    else
    {
        for (size_t i = 1; i < 5; ++i)
            fAlpha[i + 1] = (fAlpha[0] * (5 - i) + fAlpha[1] * i) * (1.0f / 5.0f);

        fAlpha[6] = 0.0f;
        fAlpha[7] = 1.0f;
    }

    DWORD dw = uint32_t(pBC3->bitmap[0]) | uint32_t(pBC3->bitmap[1] << 8) | uint32_t(pBC3->bitmap[2] << 16);

    for (size_t i = 0; i < 8; ++i, dw >>= 3)
        pColor[i] = XMVectorSetW(pColor[i], fAlpha[dw & 0x7]);

    dw = uint32_t(pBC3->bitmap[3]) | uint32_t(pBC3->bitmap[4] << 8) | uint32_t(pBC3->bitmap[5] << 16);

    for (size_t i = 8; i < NUM_PIXELS_PER_BLOCK; ++i, dw >>= 3)
        pColor[i] = XMVectorSetW(pColor[i], fAlpha[dw & 0x7]);
}

_Use_decl_annotations_
void DirectX::D3DXEncodeBC3(uint8_t *pBC, const XMVECTOR *pColor, DWORD flags)
{
    assert(pBC && pColor);
    static_assert(sizeof(D3DX_BC3) == 16, "D3DX_BC3 should be 16 bytes");

    HDRColorA Color[NUM_PIXELS_PER_BLOCK];
    for (size_t i = 0; i < NUM_PIXELS_PER_BLOCK; ++i)
    {
        XMStoreFloat4(reinterpret_cast<XMFLOAT4*>(&Color[i]), pColor[i]);
    }

    auto pBC3 = reinterpret_cast<D3DX_BC3 *>(pBC);

    // Quantize block to A8, using Floyd Stienberg error diffusion.  This 
    // increases the chance that colors will map directly to the quantized 
    // axis endpoints.
    float fAlpha[NUM_PIXELS_PER_BLOCK] = {};
    float fError[NUM_PIXELS_PER_BLOCK] = {};

    float fMinAlpha = Color[0].a;
    float fMaxAlpha = Color[0].a;

    for (size_t i = 0; i < NUM_PIXELS_PER_BLOCK; ++i)
    {
        float fAlph = Color[i].a;
        if (flags & BC_FLAGS_DITHER_A)
            fAlph += fError[i];

        fAlpha[i] = static_cast<int32_t>(fAlph * 255.0f + 0.5f) * (1.0f / 255.0f);

        if (fAlpha[i] < fMinAlpha)
            fMinAlpha = fAlpha[i];
        else if (fAlpha[i] > fMaxAlpha)
            fMaxAlpha = fAlpha[i];

        if (flags & BC_FLAGS_DITHER_A)
        {
            float fDiff = fAlph - fAlpha[i];

            if (3 != (i & 3))
            {
                assert(i < 15);
                _Analysis_assume_(i < 15);
                fError[i + 1] += fDiff * (7.0f / 16.0f);
            }

            if (i < 12)
            {
                if (i & 3)
                    fError[i + 3] += fDiff * (3.0f / 16.0f);

                fError[i + 4] += fDiff * (5.0f / 16.0f);

                if (3 != (i & 3))
                {
                    assert(i < 11);
                    _Analysis_assume_(i < 11);
                    fError[i + 5] += fDiff * (1.0f / 16.0f);
                }
            }
        }
    }

#ifdef COLOR_WEIGHTS
    if (0.0f == fMaxAlpha)
    {
        EncodeSolidBC1(&pBC3->dxt1, Color);
        pBC3->alpha[0] = 0x00;
        pBC3->alpha[1] = 0x00;
        memset(pBC3->bitmap, 0x00, 6);
    }
#endif

    // RGB part
    EncodeBC1(&pBC3->bc1, Color, false, 0.f, flags);

    // Alpha part
    if (1.0f == fMinAlpha)
    {
        pBC3->alpha[0] = 0xff;
        pBC3->alpha[1] = 0xff;
        memset(pBC3->bitmap, 0x00, 6);
        return;
    }

    // Optimize and Quantize Min and Max values
    uint32_t uSteps = ((0.0f == fMinAlpha) || (1.0f == fMaxAlpha)) ? 6u : 8u;

    float fAlphaA, fAlphaB;
    OptimizeAlpha<false>(&fAlphaA, &fAlphaB, fAlpha, uSteps);

    auto bAlphaA = static_cast<uint8_t>(static_cast<int32_t>(fAlphaA * 255.0f + 0.5f));
    auto bAlphaB = static_cast<uint8_t>(static_cast<int32_t>(fAlphaB * 255.0f + 0.5f));

    fAlphaA = static_cast<float>(bAlphaA) * (1.0f / 255.0f);
    fAlphaB = static_cast<float>(bAlphaB) * (1.0f / 255.0f);

    // Setup block
    if ((8 == uSteps) && (bAlphaA == bAlphaB))
    {
        pBC3->alpha[0] = bAlphaA;
        pBC3->alpha[1] = bAlphaB;
        memset(pBC3->bitmap, 0x00, 6);
        return;
    }

    static const size_t pSteps6[] = { 0, 2, 3, 4, 5, 1 };
    static const size_t pSteps8[] = { 0, 2, 3, 4, 5, 6, 7, 1 };

    const size_t *pSteps;
    float fStep[8] = {};

    if (6 == uSteps)
    {
        pBC3->alpha[0] = bAlphaA;
        pBC3->alpha[1] = bAlphaB;

        fStep[0] = fAlphaA;
        fStep[1] = fAlphaB;

        for (size_t i = 1; i < 5; ++i)
            fStep[i + 1] = (fStep[0] * (5 - i) + fStep[1] * i) * (1.0f / 5.0f);

        fStep[6] = 0.0f;
        fStep[7] = 1.0f;

        pSteps = pSteps6;
    }
    else
    {
        pBC3->alpha[0] = bAlphaB;
        pBC3->alpha[1] = bAlphaA;

        fStep[0] = fAlphaB;
        fStep[1] = fAlphaA;

        for (size_t i = 1; i < 7; ++i)
            fStep[i + 1] = (fStep[0] * (7 - i) + fStep[1] * i) * (1.0f / 7.0f);

        pSteps = pSteps8;
    }

    // Encode alpha bitmap
    auto fSteps = static_cast<float>(uSteps - 1);
    float fScale = (fStep[0] != fStep[1]) ? (fSteps / (fStep[1] - fStep[0])) : 0.0f;

    if (flags & BC_FLAGS_DITHER_A)
        memset(fError, 0x00, NUM_PIXELS_PER_BLOCK * sizeof(float));

    for (size_t iSet = 0; iSet < 2; iSet++)
    {
        uint32_t dw = 0;

        size_t iMin = iSet * 8;
        size_t iLim = iMin + 8;

        for (size_t i = iMin; i < iLim; ++i)
        {
            float fAlph = Color[i].a;
            if (flags & BC_FLAGS_DITHER_A)
                fAlph += fError[i];
            float fDot = (fAlph - fStep[0]) * fScale;

            uint32_t iStep;
            if (fDot <= 0.0f)
                iStep = ((6 == uSteps) && (fAlph <= fStep[0] * 0.5f)) ? 6u : 0u;
            else if (fDot >= fSteps)
                iStep = ((6 == uSteps) && (fAlph >= (fStep[1] + 1.0f) * 0.5f)) ? 7u : 1u;
            else
                iStep = uint32_t(pSteps[uint32_t(fDot + 0.5f)]);

            dw = (iStep << 21) | (dw >> 3);

            if (flags & BC_FLAGS_DITHER_A)
            {
                float fDiff = (fAlph - fStep[iStep]);

                if (3 != (i & 3))
                    fError[i + 1] += fDiff * (7.0f / 16.0f);

                if (i < 12)
                {
                    if (i & 3)
                        fError[i + 3] += fDiff * (3.0f / 16.0f);

                    fError[i + 4] += fDiff * (5.0f / 16.0f);

                    if (3 != (i & 3))
                        fError[i + 5] += fDiff * (1.0f / 16.0f);
                }
            }
        }

        pBC3->bitmap[0 + iSet * 3] = reinterpret_cast<uint8_t *>(&dw)[0];
        pBC3->bitmap[1 + iSet * 3] = reinterpret_cast<uint8_t *>(&dw)[1];
        pBC3->bitmap[2 + iSet * 3] = reinterpret_cast<uint8_t *>(&dw)[2];
    }
}