（1）xIntraRecBlk调用invTransformNxN处理TU块
if (pcCU->getCbf(uiAbsPartIdx, compID, rTu.GetTransformDepthRel()) != 0){m_pcTrQuant->invTransformNxN( rTu, compID, piResi, uiStride, pcCoeff, cQP DEBUG_STRING_PASS_INTO(psDebug) );}
（2）invTransformNxN 用于执行逆量化逆变换操作，将编码时的变换系数（Transform Coefficients）转换回原始的残差值（Residuals）
Void TComTrQuant::invTransformNxN( TComTU &rTu,const ComponentID compID,Pel *pcResidual,const UInt uiStride,TCoeff * pcCoeff,const QpParam &cQPDEBUG_STRING_FN_DECLAREP(psDebug)) {TComDataCU* pcCU=rTu.getCU();const UInt uiAbsPartIdx = rTu.GetAbsPartIdxTU();const TComRectangle &rect = rTu.getRect(compID);const UInt uiWidth = rect.width;const UInt uiHeight = rect.height;
// 对于非正方形的 TU，需要进一步递归分割处理if (uiWidth != uiHeight) //for intra, the TU will have been split above this level, so this condition won't be true, hence this only affects inter {TComTURecurse subTURecurse(rTu, false, TComTU::VERTICAL_SPLIT, true, compID);do{const UInt lineOffset = subTURecurse.GetSectionNumber() * subTURecurse.getRect(compID).height;Pel *subTUResidual = pcResidual + (lineOffset * uiStride);TCoeff *subTUCoefficients = pcCoeff + (lineOffset * subTURecurse.getRect(compID).width);invTransformNxN(subTURecurse, compID, subTUResidual, uiStride, subTUCoefficients, cQP DEBUG_STRING_PASS_INTO(psDebug)); } while (subTURecurse.nextSection(rTu));return;}#if DEBUG_STRINGif (psDebug){std::stringstream ss(stringstream::out);printBlockToStream(ss, (compID==0)?"###InvTran ip Ch0: " : ((compID==1)?"###InvTran ip Ch1: ":"###InvTran ip Ch2: "), pcCoeff, uiWidth, uiHeight, uiWidth);DEBUG_STRING_APPEND((*psDebug), ss.str())} #endif
// 如果开启了旁路模式，直接将系数复制为残差if(pcCU->getCUTransquantBypass(uiAbsPartIdx)){const Bool rotateResidual = rTu.isNonTransformedResidualRotated(compID);const UInt uiSizeMinus1 = (uiWidth * uiHeight) - 1;for (UInt y = 0, coefficientIndex = 0; y<uiHeight; y++){for (UInt x = 0; x<uiWidth; x++, coefficientIndex++){pcResidual[(y * uiStride) + x] = Pel(pcCoeff[rotateResidual ? (uiSizeMinus1 - coefficientIndex) : coefficientIndex]);}}}else{ #if DEBUG_TRANSFORM_AND_QUANTISEstd::cout << g_debugCounter << ": " << uiWidth << "x" << uiHeight << " channel " << compID << " TU at input to dequantiser\n";printBlock(pcCoeff, uiWidth, uiHeight, uiWidth); #endif
//xDeQuant对变换系数进行反量化，结果存储在m_plTempCoeff中。xDeQuant(rTu, pcCoeff, m_plTempCoeff, compID, cQP);#if DEBUG_TRANSFORM_AND_QUANTISEstd::cout << g_debugCounter << ": " << uiWidth << "x" << uiHeight << " channel " << compID << " TU between dequantiser and inverse-transform\n";printBlock(m_plTempCoeff, uiWidth, uiHeight, uiWidth); #endif#if DEBUG_STRINGif (psDebug){std::stringstream ss(stringstream::out);printBlockToStream(ss, "###InvTran deq: ", m_plTempCoeff, uiWidth, uiHeight, uiWidth);(*psDebug)+=ss.str();} #endif // 是否使用了变换跳过（Transform Skip）模式if(pcCU->getTransformSkip(uiAbsPartIdx, compID)){xITransformSkip( m_plTempCoeff, pcResidual, uiStride, rTu, compID );#if DEBUG_STRINGif (psDebug){std::stringstream ss(stringstream::out);printBlockToStream(ss, "###InvTran resi: ", pcResidual, uiWidth, uiHeight, uiStride);(*psDebug)+=ss.str();(*psDebug)+="(<- was a Transform-skipped block)\n";} #endif}else{ #if O0043_BEST_EFFORT_DECODINGconst Int channelBitDepth = pcCU->getSlice()->getSPS()->getStreamBitDepth(toChannelType(compID)); #elseconst Int channelBitDepth = pcCU->getSlice()->getSPS()->getBitDepth(toChannelType(compID)); #endif
// 调用 xIT 执行逆变换
xIT( channelBitDepth, rTu.useDST(compID), m_plTempCoeff, pcResidual, uiStride, uiWidth, uiHeight, pcCU->getSlice()->getSPS()->getMaxLog2TrDynamicRange(toChannelType(compID)) );#if DEBUG_STRINGif (psDebug){std::stringstream ss(stringstream::out);printBlockToStream(ss, "###InvTran resi: ", pcResidual, uiWidth, uiHeight, uiStride);(*psDebug)+=ss.str();(*psDebug)+="(<- was a Transformed block)\n";} #endif}#if DEBUG_TRANSFORM_AND_QUANTISEstd::cout << g_debugCounter << ": " << uiWidth << "x" << uiHeight << " channel " << compID << " TU at output of inverse-transform\n";printBlock(pcResidual, uiWidth, uiHeight, uiStride);g_debugCounter++; #endif}invRdpcmNxN( rTu, compID, pcResidual, uiStride ); }
（3）量化
（4）xIT 用于执行二维逆变换
Void TComTrQuant::xIT( const Int channelBitDepth, Bool useDST, TCoeff* plCoef, Pel* pResidual, UInt uiStride, Int iWidth, Int iHeight, const Int maxLog2TrDynamicRange ) { #if MATRIX_MULTif( iWidth == iHeight ){
// 对于方形矩阵，使用高效的 NxN 逆变换函数（默认关闭）xITr(channelBitDepth, plCoef, pResidual, uiStride, (UInt)iWidth, useDST, maxLog2TrDynamicRange);return;} #endifTCoeff block[ MAX_TU_SIZE * MAX_TU_SIZE ];TCoeff coeff[ MAX_TU_SIZE * MAX_TU_SIZE ];memcpy(coeff, plCoef, (iWidth * iHeight * sizeof(TCoeff))); // 对于非方形块，调用xITrMxN函数，处理 MxN 的逆变换。xITrMxN( channelBitDepth, coeff, block, iWidth, iHeight, useDST, maxLog2TrDynamicRange );for (Int y = 0; y < iHeight; y++){for (Int x = 0; x < iWidth; x++){pResidual[(y * uiStride) + x] = Pel(block[(y * iWidth) + x]);}} }
（5）xITrMxN 实现 MxN 矩阵的二维逆变换。主要根据输入矩阵的宽度 (iWidth) 和高度 (iHeight)，应用逆变换算法（如部分蝶形逆变换、DST）
注意函数中的：
Int shift_1st = TRANSFORM_MATRIX_SHIFT + 1; //1 has been added to shift_1st at the expense of shift_2ndInt shift_2nd = (TRANSFORM_MATRIX_SHIFT + maxLog2TrDynamicRange - 1) - bitDepth;
在 HEVC 中需要进行六次会导致计算结果数量级增大的操作，分别为 2 次 DCT（一次二维 DCT 可以被分为两次一维 DCT）、1 次量化、1 次反量化以及 2 次反 DCT。
在 HEVC 中同样设置了六次对应位置的 Scaling 操作，其 Scaling 系数分别为 ST1,ST2,SQ,SIQ,SIT1,SIT2。
这里的shift_1st，shift_2nd 分别对应 SIT1,SIT2。TRANSFORM_MATRIX_SHIFT默认为6。
- STI=2−(B+M−9)
- ST2=2−(M+6)
- SQ=2−(29−M−B)
- SIT1=2−7
- SIT2=2−(20−B)
- SIQ=2−(M−5+B)
Void xITrMxN(Int bitDepth, TCoeff *coeff, TCoeff *block, Int iWidth, Int iHeight, Bool useDST, const Int maxLog2TrDynamicRange) {const Int TRANSFORM_MATRIX_SHIFT = g_transformMatrixShift[TRANSFORM_INVERSE];Int shift_1st = TRANSFORM_MATRIX_SHIFT + 1; //1 has been added to shift_1st at the expense of shift_2ndInt shift_2nd = (TRANSFORM_MATRIX_SHIFT + maxLog2TrDynamicRange - 1) - bitDepth;const TCoeff clipMinimum = -(1 << maxLog2TrDynamicRange);const TCoeff clipMaximum = (1 << maxLog2TrDynamicRange) - 1;assert(shift_1st >= 0);assert(shift_2nd >= 0);TCoeff tmp[MAX_TU_SIZE * MAX_TU_SIZE];switch (iHeight){case 4:{if ((iWidth == 4) && useDST) // Check for DCT or DST {fastInverseDst( coeff, tmp, shift_1st, clipMinimum, clipMaximum);}else{partialButterflyInverse4 ( coeff, tmp, shift_1st, iWidth, clipMinimum, clipMaximum);}}break;case 8: partialButterflyInverse8 ( coeff, tmp, shift_1st, iWidth, clipMinimum, clipMaximum); break;case 16: partialButterflyInverse16( coeff, tmp, shift_1st, iWidth, clipMinimum, clipMaximum); break;case 32: partialButterflyInverse32( coeff, tmp, shift_1st, iWidth, clipMinimum, clipMaximum); break;default:assert(0); exit (1); break;}switch (iWidth){// Clipping here is not in the standard, but is used to protect the "Pel" data type into which the inverse-transformed samples will be copiedcase 4:{if ((iHeight == 4) && useDST) // Check for DCT or DST {fastInverseDst( tmp, block, shift_2nd, std::numeric_limits<Pel>::min(), std::numeric_limits<Pel>::max() );}else{partialButterflyInverse4 ( tmp, block, shift_2nd, iHeight, std::numeric_limits<Pel>::min(), std::numeric_limits<Pel>::max());}}break;case 8: partialButterflyInverse8 ( tmp, block, shift_2nd, iHeight, std::numeric_limits<Pel>::min(), std::numeric_limits<Pel>::max()); break;case 16: partialButterflyInverse16( tmp, block, shift_2nd, iHeight, std::numeric_limits<Pel>::min(), std::numeric_limits<Pel>::max()); break;case 32: partialButterflyInverse32( tmp, block, shift_2nd, iHeight, std::numeric_limits<Pel>::min(), std::numeric_limits<Pel>::max()); break;default:assert(0); exit (1); break;} }
再看看对应的变换函数：
其中g_aucConvertToBit[iHeight]函数：from width to log2(width)-2
Void xTrMxN(Int bitDepth, TCoeff *block, TCoeff *coeff, Int iWidth, Int iHeight, Bool useDST, const Int maxLog2TrDynamicRange) {const Int TRANSFORM_MATRIX_SHIFT = g_transformMatrixShift[TRANSFORM_FORWARD];const Int shift_1st = ((g_aucConvertToBit[iWidth] + 2) + bitDepth + TRANSFORM_MATRIX_SHIFT) - maxLog2TrDynamicRange;const Int shift_2nd = (g_aucConvertToBit[iHeight] + 2) + TRANSFORM_MATRIX_SHIFT;assert(shift_1st >= 0);assert(shift_2nd >= 0);TCoeff tmp[ MAX_TU_SIZE * MAX_TU_SIZE ];switch (iWidth){case 4:{if ((iHeight == 4) && useDST) // Check for DCT or DST {fastForwardDst( block, tmp, shift_1st );}else{partialButterfly4 ( block, tmp, shift_1st, iHeight );}}break;case 8: partialButterfly8 ( block, tmp, shift_1st, iHeight ); break;case 16: partialButterfly16( block, tmp, shift_1st, iHeight ); break;case 32: partialButterfly32( block, tmp, shift_1st, iHeight ); break;default:assert(0); exit (1); break;}switch (iHeight){case 4:{if ((iWidth == 4) && useDST) // Check for DCT or DST {fastForwardDst( tmp, coeff, shift_2nd );}else{partialButterfly4 ( tmp, coeff, shift_2nd, iWidth );}}break;case 8: partialButterfly8 ( tmp, coeff, shift_2nd, iWidth ); break;case 16: partialButterfly16( tmp, coeff, shift_2nd, iWidth ); break;case 32: partialButterfly32( tmp, coeff, shift_2nd, iWidth ); break;default:assert(0); exit (1); break;} }
（6）对于4*4使用DST变换的块：
Void fastInverseDst(TCoeff *tmp, TCoeff *block, Int shift, const TCoeff outputMinimum, const TCoeff outputMaximum) // input tmp, output block {Int i;TCoeff c[4];TCoeff rnd_factor = (shift > 0) ? (1<<(shift-1)) : 0;for (i=0; i<4; i++){// Intermediate Variablesc[0] = tmp[ i];c[1] = tmp[4 +i];c[2] = tmp[8 +i];c[3] = tmp[12+i];for (Int column = 0; column < 4; column++){TCoeff &result = block[(i * 4) + column];result = 0;for (Int row = 0; row < 4; row++){result += c[row] * g_as_DST_MAT_4[TRANSFORM_INVERSE][row][column]; // use the defined matrix, rather than hard-wired numbers }result = Clip3( outputMinimum, outputMaximum, rightShift((result + rnd_factor), shift));}} }
SIT1,SIT2
