DST，蝶形运算

转自：http://blog.youkuaiyun.com/tianzhaixing2013/article/details/8723204

/** MxN forward transform (2D)
*  \param block input data (residual)
*  \param coeff output data (transform coefficients)
*  \param iWidth input data (width of transform)
*  \param iHeight input data (height of transform)
*/

//对帧内预测模式的4x4块进行DST变换，其余的根据块大小分别做蝶形快速变换（4x4，8x8，16x16，32x32）
void xTrMxN(Int bitDepth, Short *block,Short *coeff, Int iWidth, Int iHeight, UInt uiMode)
{
  Int shift_1st = g_aucConvertToBit[iWidth]  + 1 + bitDepth-8; // log2(iWidth) - 1 + g_bitDepth - 8
  Int shift_2nd = g_aucConvertToBit[iHeight]  + 8;             // log2(iHeight) + 6

  Short tmp[ 64 * 64 ];

  if( iWidth == 4 && iHeight == 4)
  {
    if (uiMode != REG_DCT)
    {//离散正弦变换DST
      fastForwardDst(block,tmp,shift_1st); // Forward DST BY FAST ALGORITHM, block input, tmp output
      fastForwardDst(tmp,coeff,shift_2nd); // Forward DST BY FAST ALGORITHM, tmp input, coeff output
    }
    else
    {//4*4蝶形运算
      partialButterfly4(block, tmp, shift_1st, iHeight);
      partialButterfly4(tmp, coeff, shift_2nd, iWidth);
    }

  }
  else if( iWidth == 8 && iHeight == 8)
  { //8*8蝶形运算
    partialButterfly8( block, tmp, shift_1st, iHeight );
    partialButterfly8( tmp, coeff, shift_2nd, iWidth );
  }
  else if( iWidth == 16 && iHeight == 16)
  { //16*16蝶形运算
    partialButterfly16( block, tmp, shift_1st, iHeight );
    partialButterfly16( tmp, coeff, shift_2nd, iWidth );
  }
  else if( iWidth == 32 && iHeight == 32)
  { //32*32蝶形运算
    partialButterfly32( block, tmp, shift_1st, iHeight );
    partialButterfly32( tmp, coeff, shift_2nd, iWidth );
  }
}
/** MxN inverse transform (2D)反变换针对2D的情况
*  \param coeff input data (transform coefficients)
*  \param block output data (residual)
*  \param iWidth input data (width of transform)
*  \param iHeight input data (height of transform)
*/
void xITrMxN(Int bitDepth, Short *coeff,Short *block, Int iWidth, Int iHeight, UInt uiMode)
{
  Int shift_1st = SHIFT_INV_1ST;
  Int shift_2nd = SHIFT_INV_2ND - (bitDepth-8);

  Short tmp[ 64*64];
  if( iWidth == 4 && iHeight == 4)
  {
    if (uiMode != REG_DCT)
    {
      fastInverseDst(coeff,tmp,shift_1st); // Inverse DST by FAST Algorithm, coeff input, tmp output
      fastInverseDst(tmp,block,shift_2nd); // Inverse DST by FAST Algorithm, tmp input, coeff output
    }
    else
    {
      partialButterflyInverse4(coeff,tmp,shift_1st,iWidth);
      partialButterflyInverse4(tmp,block,shift_2nd,iHeight);
    }
  }
  else if( iWidth == 8 && iHeight == 8)
  {
    partialButterflyInverse8(coeff,tmp,shift_1st,iWidth);
    partialButterflyInverse8(tmp,block,shift_2nd,iHeight);
  }
  else if( iWidth == 16 && iHeight == 16)
  {
    partialButterflyInverse16(coeff,tmp,shift_1st,iWidth);
    partialButterflyInverse16(tmp,block,shift_2nd,iHeight);
  }
  else if( iWidth == 32 && iHeight == 32)
  {
    partialButterflyInverse32(coeff,tmp,shift_1st,iWidth);
    partialButterflyInverse32(tmp,block,shift_2nd,iHeight);
  }
}