x265的DCT

news2024/11/28 14:15:19

文章目录

  • DCT相关背景知识
      • DCT变换系数矩阵
          • 32x32变换矩阵系数
          • 其他尺寸变换矩阵系数
      • 变换计算过程
          • 流程图
  • 代码实现
      • 数据
          • 残差变换系数
          • 对应残差
      • 我的简单实现
          • 实现细节
          • 实现代码
      • x265对应代码实现
      • openHEVC代码实现

DCT相关背景知识

DCT变换系数矩阵

标准提供了32x32的系数矩阵，4x4、8x8、16x16的矩阵都可以从中提取出来

32x32变换矩阵系数

左半边
右半边

其他尺寸变换矩阵系数

其他尺寸矩阵变换系数
从上面来看，4x4的变换矩阵，系数为：
[ 64 64 64 64 83 36 − 36 − 83 64 − 64 − 64 64 36 − 83 83 − 36 ] \begin{bmatrix} 64 & 64 & 64 & 64 \\ 83 & 36 & -36 & -83 \\ 64 & -64 & -64 & 64 \\ 36 & -83 & 83 & -36 \end{bmatrix} ​64836436​6436−64−83​64−36−6483​64−8364−36​ ​
其他尺寸的变换系数矩阵也可以从图中对应找到

变换计算过程

流程图

流程图
需要注意的是：

  1. 左乘表示列变换，右乘表示行变换
  2. 反变换的过程中，进行了两次Scale

伸缩矩阵，具体定义为：
伸缩矩阵

代码实现

数据

残差变换系数

残差变换系数

对应残差

残差

我的简单实现

实现细节
  1. 实现公式
    R = D T ⋅ C × S I T 1 ⋅ D × S I T 2 R = D^T \cdot C \times S_{IT1} \cdot D \times S_{IT2} R=DT⋅C×SIT1​⋅D×SIT2​
  2. 暂时忽略伸缩
    R = D T ⋅ C ⋅ D R = D^T \cdot C \cdot D R=DT⋅C⋅D
  3. 稍加处理
    R = ( C T ⋅ D ) T ⋅ D R = { (C^T \cdot D) }^T \cdot D R=(CT⋅D)T⋅D
  4. 重点来了，到这里之后。
    就可以把公式可以分成两部分
    T m p = C T ⋅ D R = T m p T ⋅ D Tmp =C^T \cdot D \\ R = { Tmp }^T \cdot D Tmp=CT⋅DR=TmpT⋅D
  5. 加入伸缩
    T m p = C T ⋅ D × S I T 1 R = T m p T ⋅ D × S I T 2 Tmp =C^T \cdot D \times S_{IT1} \\ R = { Tmp }^T \cdot D \times S_{IT2} Tmp=CT⋅D×SIT1​R=TmpT⋅D×SIT2​
  6. 也就是说，我们可以这样定义函数。
    y = f u n ( a , b , s ) = a T ⋅ b × s y = fun(a,b,s) = a^T \cdot b \times s y=fun(a,b,s)=aT⋅b×s
    函数步骤为：先转置，再列变换，然后伸缩
    也就是说，我们只需要实现这个函数，然后调用两次即可
实现代码
// 变换系数
static const signed char transform[32][32] = {
    { 64,  64,  64,  64,  64,  64,  64,  64,  64,  64,  64,  64,  64,  64,  64,  64,
      64,  64,  64,  64,  64,  64,  64,  64,  64,  64,  64,  64,  64,  64,  64,  64 },
    { 90,  90,  88,  85,  82,  78,  73,  67,  61,  54,  46,  38,  31,  22,  13,   4,
      -4, -13, -22, -31, -38, -46, -54, -61, -67, -73, -78, -82, -85, -88, -90, -90 },
    { 90,  87,  80,  70,  57,  43,  25,   9,  -9, -25, -43, -57, -70, -80, -87, -90,
     -90, -87, -80, -70, -57, -43, -25,  -9,   9,  25,  43,  57,  70,  80,  87,  90 },
    { 90,  82,  67,  46,  22,  -4, -31, -54, -73, -85, -90, -88, -78, -61, -38, -13,
      13,  38,  61,  78,  88,  90,  85,  73,  54,  31,   4, -22, -46, -67, -82, -90 },
    { 89,  75,  50,  18, -18, -50, -75, -89, -89, -75, -50, -18,  18,  50,  75,  89,
      89,  75,  50,  18, -18, -50, -75, -89, -89, -75, -50, -18,  18,  50,  75,  89 },
    { 88,  67,  31, -13, -54, -82, -90, -78, -46, -4,   38,  73,  90,  85,  61,  22,
     -22, -61, -85, -90, -73, -38,   4,  46,  78,  90,  82,  54,  13, -31, -67, -88 },
    { 87,  57,   9, -43, -80, -90, -70, -25,  25,  70,  90,  80,  43,  -9, -57, -87,
     -87, -57,  -9,  43,  80,  90,  70,  25, -25, -70, -90, -80, -43,   9,  57,  87 },
    { 85,  46, -13, -67, -90, -73, -22,  38,  82,  88,  54,  -4, -61, -90, -78, -31,
      31,  78,  90,  61,   4, -54, -88, -82, -38,  22,  73,  90,  67,  13, -46, -85 },
    { 83,  36, -36, -83, -83, -36,  36,  83,  83,  36, -36, -83, -83, -36,  36,  83,
      83,  36, -36, -83, -83, -36,  36,  83,  83,  36, -36, -83, -83, -36,  36,  83 },
    { 82,  22, -54, -90, -61,  13,  78,  85,  31, -46, -90, -67,   4,  73,  88,  38,
     -38, -88, -73,  -4,  67,  90,  46, -31, -85, -78, -13,  61,  90,  54, -22, -82 },
    { 80,   9, -70, -87, -25,  57,  90,  43, -43, -90, -57,  25,  87,  70,  -9, -80,
     -80,  -9,  70,  87,  25, -57, -90, -43,  43,  90,  57, -25, -87, -70,   9,  80 },
    { 78,  -4, -82, -73,  13,  85,  67, -22, -88, -61,  31,  90,  54, -38, -90, -46,
      46,  90,  38, -54, -90, -31,  61,  88,  22, -67, -85, -13,  73,  82,   4, -78 },
    { 75, -18, -89, -50,  50,  89,  18, -75, -75,  18,  89,  50, -50, -89, -18,  75,
      75, -18, -89, -50,  50,  89,  18, -75, -75,  18,  89,  50, -50, -89, -18,  75 },
    { 73, -31, -90, -22,  78,  67, -38, -90, -13,  82,  61, -46, -88,  -4,  85,  54,
     -54, -85,   4,  88,  46, -61, -82,  13,  90,  38, -67, -78,  22,  90,  31, -73 },
    { 70, -43, -87,   9,  90,  25, -80, -57,  57,  80, -25, -90,  -9,  87,  43, -70,
     -70,  43,  87,  -9, -90, -25,  80,  57, -57, -80,  25,  90,   9, -87, -43,  70 },
    { 67, -54, -78,  38,  85, -22, -90,   4,  90,  13, -88, -31,  82,  46, -73, -61,
      61,  73, -46, -82,  31,  88, -13, -90,  -4,  90,  22, -85, -38,  78,  54, -67 },
    { 64, -64, -64,  64,  64, -64, -64,  64,  64, -64, -64,  64,  64, -64, -64,  64,
      64, -64, -64,  64,  64, -64, -64,  64,  64, -64, -64,  64,  64, -64, -64,  64 },
    { 61, -73, -46,  82,  31, -88, -13,  90,  -4, -90,  22,  85, -38, -78,  54,  67,
     -67, -54,  78,  38, -85, -22,  90,   4, -90,  13,  88, -31, -82,  46,  73, -61 },
    { 57, -80, -25,  90,  -9, -87,  43,  70, -70, -43,  87,   9, -90,  25,  80, -57,
     -57,  80,  25, -90,   9,  87, -43, -70,  70,  43, -87,  -9,  90, -25, -80,  57 },
    { 54, -85,  -4,  88, -46, -61,  82,  13, -90,  38,  67, -78, -22,  90, -31, -73,
      73,  31, -90,  22,  78, -67, -38,  90, -13, -82,  61,  46, -88,   4,  85, -54 },
    { 50, -89,  18,  75, -75, -18,  89, -50, -50,  89, -18, -75,  75,  18, -89,  50,
      50, -89,  18,  75, -75, -18,  89, -50, -50,  89, -18, -75,  75,  18, -89,  50 },
    { 46, -90,  38,  54, -90,  31,  61, -88,  22,  67, -85,  13,  73, -82,   4,  78,
     -78,  -4,  82, -73, -13,  85, -67, -22,  88, -61, -31,  90, -54, -38,  90, -46 },
    { 43, -90,  57,  25, -87,  70,   9, -80,  80,  -9, -70,  87, -25, -57,  90, -43,
     -43,  90, -57, -25,  87, -70,  -9,  80, -80,   9,  70, -87,  25,  57, -90,  43 },
    { 38, -88,  73,  -4, -67,  90, -46, -31,  85, -78,  13,  61, -90,  54,  22, -82,
      82, -22, -54,  90, -61, -13,  78, -85,  31,  46, -90,  67,   4, -73,  88, -38 },
    { 36, -83,  83, -36, -36,  83, -83,  36,  36, -83,  83, -36, -36,  83, -83,  36,
      36, -83,  83, -36, -36,  83, -83,  36,  36, -83,  83, -36, -36,  83, -83,  36 },
    { 31, -78,  90, -61,   4,  54, -88,  82, -38, -22,  73, -90,  67, -13, -46,  85,
     -85,  46,  13, -67,  90, -73,  22,  38, -82,  88, -54,  -4,  61, -90,  78, -31 },
    { 25, -70,  90, -80,  43,   9, -57,  87, -87,  57,  -9, -43,  80, -90,  70, -25,
     -25,  70, -90,  80, -43,  -9,  57, -87,  87, -57,   9,  43, -80,  90, -70,  25 },
    { 22, -61,  85, -90,  73, -38,  -4,  46, -78,  90, -82,  54, -13, -31,  67, -88,
      88, -67,  31,  13, -54,  82, -90,  78, -46,   4,  38, -73,  90, -85,  61, -22 },
    { 18, -50,  75, -89,  89, -75,  50, -18, -18,  50, -75,  89, -89,  75, -50,  18,
      18, -50,  75, -89,  89, -75,  50, -18, -18,  50, -75,  89, -89,  75, -50,  18 },
    { 13, -38,  61, -78,  88, -90,  85, -73,  54, -31,   4,  22, -46,  67, -82,  90,
     -90,  82, -67,  46, -22,  -4,  31, -54,  73, -85,  90, -88,  78, -61,  38, -13 },
    {  9, -25,  43, -57,  70, -80,  87, -90,  90, -87,  80, -70,  57, -43,  25, -9,
      -9,  25, -43,  57, -70,  80, -87,  90, -90,  87, -80,  70, -57,  43, -25,   9 },
    {  4, -13,  22, -31,  38, -46,  54, -61,  67, -73,  78, -82,  85, -88,  90, -90,
      90, -90,  88, -85,  82, -78,  73, -67,  61, -54,  46, -38,  31, -22,  13,  -4 },
};

// 残差变换系数
short coeffs1[16 * 16] = {
-8730, -180,  -90,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,
    0,    0,  -90,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,
   90,    0,  -90,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,
   90,    0,  -90,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,
   90,    0,  -90,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,
   90,    0,  -90,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,
   90,    0,  -90,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,
   90,    0,  -90,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,
    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,
    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,
    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,
    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,
    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,
    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,
    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,
    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0,    0
};

// 
static void func(short* src, short* dst, int s) {
    short add = (1 << (s - 1));
    for (int r1 = 0; r1 < 16; ++r1) {
        for (int c2 = 0; c2 < 16; ++c2) {
            int tmp = 0;
            for (int t = 0; t < 16; ++t)
                tmp += src[r1 + t * 16] * transform[2 * t][c2];
            dst[r1 * 16 + c2] = ((tmp + add) >> s);
        }
    }
}

static void MyIDCT(short* src, short* dst) {
    func(src, dst, 7);
    func(dst, src, 12);
}

x265对应代码实现

const short g_t16[16][16] =
{
    { 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64 },
    { 90, 87, 80, 70, 57, 43, 25,  9, -9, -25, -43, -57, -70, -80, -87, -90 },
    { 89, 75, 50, 18, -18, -50, -75, -89, -89, -75, -50, -18, 18, 50, 75, 89 },
    { 87, 57,  9, -43, -80, -90, -70, -25, 25, 70, 90, 80, 43, -9, -57, -87 },
    { 83, 36, -36, -83, -83, -36, 36, 83, 83, 36, -36, -83, -83, -36, 36, 83 },
    { 80,  9, -70, -87, -25, 57, 90, 43, -43, -90, -57, 25, 87, 70, -9, -80 },
    { 75, -18, -89, -50, 50, 89, 18, -75, -75, 18, 89, 50, -50, -89, -18, 75 },
    { 70, -43, -87,  9, 90, 25, -80, -57, 57, 80, -25, -90, -9, 87, 43, -70 },
    { 64, -64, -64, 64, 64, -64, -64, 64, 64, -64, -64, 64, 64, -64, -64, 64 },
    { 57, -80, -25, 90, -9, -87, 43, 70, -70, -43, 87,  9, -90, 25, 80, -57 },
    { 50, -89, 18, 75, -75, -18, 89, -50, -50, 89, -18, -75, 75, 18, -89, 50 },
    { 43, -90, 57, 25, -87, 70,  9, -80, 80, -9, -70, 87, -25, -57, 90, -43 },
    { 36, -83, 83, -36, -36, 83, -83, 36, 36, -83, 83, -36, -36, 83, -83, 36 },
    { 25, -70, 90, -80, 43,  9, -57, 87, -87, 57, -9, -43, 80, -90, 70, -25 },
    { 18, -50, 75, -89, 89, -75, 50, -18, -18, 50, -75, 89, -89, 75, -50, 18 },
    {  9, -25, 43, -57, 70, -80, 87, -90, 90, -87, 80, -70, 57, -43, 25, -9 }
};

static void partialButterflyInverse16(const short* src, short* dst, int shift, int line)
{
    int j, k;
    int E[8], O[8];
    int EE[4], EO[4];
    int EEE[2], EEO[2];
    int add = 1 << (shift - 1);

    for (j = 0; j < line; j++)
    {
        /* Utilizing symmetry properties to the maximum to minimize the number of multiplications */
        for (k = 0; k < 8; k++)
        {
            O[k] = g_t16[1][k] * src[line] + g_t16[3][k] * src[3 * line] + g_t16[5][k] * src[5 * line] + g_t16[7][k] * src[7 * line] +
                g_t16[9][k] * src[9 * line] + g_t16[11][k] * src[11 * line] + g_t16[13][k] * src[13 * line] + g_t16[15][k] * src[15 * line];
        }

        for (k = 0; k < 4; k++)
        {
            EO[k] = g_t16[2][k] * src[2 * line] + g_t16[6][k] * src[6 * line] + g_t16[10][k] * src[10 * line] + g_t16[14][k] * src[14 * line];
        }

        EEO[0] = g_t16[4][0] * src[4 * line] + g_t16[12][0] * src[12 * line];
        EEE[0] = g_t16[0][0] * src[0] + g_t16[8][0] * src[8 * line];
        EEO[1] = g_t16[4][1] * src[4 * line] + g_t16[12][1] * src[12 * line];
        EEE[1] = g_t16[0][1] * src[0] + g_t16[8][1] * src[8 * line];

        /* Combining even and odd terms at each hierarchy levels to calculate the final spatial domain vector */
        for (k = 0; k < 2; k++)
        {
            EE[k] = EEE[k] + EEO[k];
            EE[k + 2] = EEE[1 - k] - EEO[1 - k];
        }

        for (k = 0; k < 4; k++)
        {
            E[k] = EE[k] + EO[k];
            E[k + 4] = EE[3 - k] - EO[3 - k];
        }

        for (k = 0; k < 8; k++)
        {
            dst[k] = (short)x265_clip3(-32768, 32767, (E[k] + O[k] + add) >> shift);
            dst[k + 8] = (short)x265_clip3(-32768, 32767, (E[7 - k] - O[7 - k] + add) >> shift);
        }

        src++;
        dst += 16;
    }
}

static void idct16_c(const short* src, short* dst, __int64 dstStride)
{
    const int shift_1st = 7;
    const int shift_2nd = 12 - (X265_DEPTH - 8);

    ALIGN_VAR_32(short, coef[16 * 16]);
    ALIGN_VAR_32(short, block[16 * 16]);

    partialButterflyInverse16(src, coef, shift_1st, 16);
    partialButterflyInverse16(coef, block, shift_2nd, 16);

    for (int i = 0; i < 16; i++)
    {
        memcpy(&dst[i * dstStride], &block[i * 16], 16 * sizeof(short));
    }
}

openHEVC代码实现

static const signed char transform[32][32] = {
    { 64,  64,  64,  64,  64,  64,  64,  64,  64,  64,  64,  64,  64,  64,  64,  64,
      64,  64,  64,  64,  64,  64,  64,  64,  64,  64,  64,  64,  64,  64,  64,  64 },
    { 90,  90,  88,  85,  82,  78,  73,  67,  61,  54,  46,  38,  31,  22,  13,   4,
      -4, -13, -22, -31, -38, -46, -54, -61, -67, -73, -78, -82, -85, -88, -90, -90 },
    { 90,  87,  80,  70,  57,  43,  25,   9,  -9, -25, -43, -57, -70, -80, -87, -90,
     -90, -87, -80, -70, -57, -43, -25,  -9,   9,  25,  43,  57,  70,  80,  87,  90 },
    { 90,  82,  67,  46,  22,  -4, -31, -54, -73, -85, -90, -88, -78, -61, -38, -13,
      13,  38,  61,  78,  88,  90,  85,  73,  54,  31,   4, -22, -46, -67, -82, -90 },
    { 89,  75,  50,  18, -18, -50, -75, -89, -89, -75, -50, -18,  18,  50,  75,  89,
      89,  75,  50,  18, -18, -50, -75, -89, -89, -75, -50, -18,  18,  50,  75,  89 },
    { 88,  67,  31, -13, -54, -82, -90, -78, -46, -4,   38,  73,  90,  85,  61,  22,
     -22, -61, -85, -90, -73, -38,   4,  46,  78,  90,  82,  54,  13, -31, -67, -88 },
    { 87,  57,   9, -43, -80, -90, -70, -25,  25,  70,  90,  80,  43,  -9, -57, -87,
     -87, -57,  -9,  43,  80,  90,  70,  25, -25, -70, -90, -80, -43,   9,  57,  87 },
    { 85,  46, -13, -67, -90, -73, -22,  38,  82,  88,  54,  -4, -61, -90, -78, -31,
      31,  78,  90,  61,   4, -54, -88, -82, -38,  22,  73,  90,  67,  13, -46, -85 },
    { 83,  36, -36, -83, -83, -36,  36,  83,  83,  36, -36, -83, -83, -36,  36,  83,
      83,  36, -36, -83, -83, -36,  36,  83,  83,  36, -36, -83, -83, -36,  36,  83 },
    { 82,  22, -54, -90, -61,  13,  78,  85,  31, -46, -90, -67,   4,  73,  88,  38,
     -38, -88, -73,  -4,  67,  90,  46, -31, -85, -78, -13,  61,  90,  54, -22, -82 },
    { 80,   9, -70, -87, -25,  57,  90,  43, -43, -90, -57,  25,  87,  70,  -9, -80,
     -80,  -9,  70,  87,  25, -57, -90, -43,  43,  90,  57, -25, -87, -70,   9,  80 },
    { 78,  -4, -82, -73,  13,  85,  67, -22, -88, -61,  31,  90,  54, -38, -90, -46,
      46,  90,  38, -54, -90, -31,  61,  88,  22, -67, -85, -13,  73,  82,   4, -78 },
    { 75, -18, -89, -50,  50,  89,  18, -75, -75,  18,  89,  50, -50, -89, -18,  75,
      75, -18, -89, -50,  50,  89,  18, -75, -75,  18,  89,  50, -50, -89, -18,  75 },
    { 73, -31, -90, -22,  78,  67, -38, -90, -13,  82,  61, -46, -88,  -4,  85,  54,
     -54, -85,   4,  88,  46, -61, -82,  13,  90,  38, -67, -78,  22,  90,  31, -73 },
    { 70, -43, -87,   9,  90,  25, -80, -57,  57,  80, -25, -90,  -9,  87,  43, -70,
     -70,  43,  87,  -9, -90, -25,  80,  57, -57, -80,  25,  90,   9, -87, -43,  70 },
    { 67, -54, -78,  38,  85, -22, -90,   4,  90,  13, -88, -31,  82,  46, -73, -61,
      61,  73, -46, -82,  31,  88, -13, -90,  -4,  90,  22, -85, -38,  78,  54, -67 },
    { 64, -64, -64,  64,  64, -64, -64,  64,  64, -64, -64,  64,  64, -64, -64,  64,
      64, -64, -64,  64,  64, -64, -64,  64,  64, -64, -64,  64,  64, -64, -64,  64 },
    { 61, -73, -46,  82,  31, -88, -13,  90,  -4, -90,  22,  85, -38, -78,  54,  67,
     -67, -54,  78,  38, -85, -22,  90,   4, -90,  13,  88, -31, -82,  46,  73, -61 },
    { 57, -80, -25,  90,  -9, -87,  43,  70, -70, -43,  87,   9, -90,  25,  80, -57,
     -57,  80,  25, -90,   9,  87, -43, -70,  70,  43, -87,  -9,  90, -25, -80,  57 },
    { 54, -85,  -4,  88, -46, -61,  82,  13, -90,  38,  67, -78, -22,  90, -31, -73,
      73,  31, -90,  22,  78, -67, -38,  90, -13, -82,  61,  46, -88,   4,  85, -54 },
    { 50, -89,  18,  75, -75, -18,  89, -50, -50,  89, -18, -75,  75,  18, -89,  50,
      50, -89,  18,  75, -75, -18,  89, -50, -50,  89, -18, -75,  75,  18, -89,  50 },
    { 46, -90,  38,  54, -90,  31,  61, -88,  22,  67, -85,  13,  73, -82,   4,  78,
     -78,  -4,  82, -73, -13,  85, -67, -22,  88, -61, -31,  90, -54, -38,  90, -46 },
    { 43, -90,  57,  25, -87,  70,   9, -80,  80,  -9, -70,  87, -25, -57,  90, -43,
     -43,  90, -57, -25,  87, -70,  -9,  80, -80,   9,  70, -87,  25,  57, -90,  43 },
    { 38, -88,  73,  -4, -67,  90, -46, -31,  85, -78,  13,  61, -90,  54,  22, -82,
      82, -22, -54,  90, -61, -13,  78, -85,  31,  46, -90,  67,   4, -73,  88, -38 },
    { 36, -83,  83, -36, -36,  83, -83,  36,  36, -83,  83, -36, -36,  83, -83,  36,
      36, -83,  83, -36, -36,  83, -83,  36,  36, -83,  83, -36, -36,  83, -83,  36 },
    { 31, -78,  90, -61,   4,  54, -88,  82, -38, -22,  73, -90,  67, -13, -46,  85,
     -85,  46,  13, -67,  90, -73,  22,  38, -82,  88, -54,  -4,  61, -90,  78, -31 },
    { 25, -70,  90, -80,  43,   9, -57,  87, -87,  57,  -9, -43,  80, -90,  70, -25,
     -25,  70, -90,  80, -43,  -9,  57, -87,  87, -57,   9,  43, -80,  90, -70,  25 },
    { 22, -61,  85, -90,  73, -38,  -4,  46, -78,  90, -82,  54, -13, -31,  67, -88,
      88, -67,  31,  13, -54,  82, -90,  78, -46,   4,  38, -73,  90, -85,  61, -22 },
    { 18, -50,  75, -89,  89, -75,  50, -18, -18,  50, -75,  89, -89,  75, -50,  18,
      18, -50,  75, -89,  89, -75,  50, -18, -18,  50, -75,  89, -89,  75, -50,  18 },
    { 13, -38,  61, -78,  88, -90,  85, -73,  54, -31,   4,  22, -46,  67, -82,  90,
     -90,  82, -67,  46, -22,  -4,  31, -54,  73, -85,  90, -88,  78, -61,  38, -13 },
    {  9, -25,  43, -57,  70, -80,  87, -90,  90, -87,  80, -70,  57, -43,  25, -9,
      -9,  25, -43,  57, -70,  80, -87,  90, -90,  87, -80,  70, -57,  43, -25,   9 },
    {  4, -13,  22, -31,  38, -46,  54, -61,  67, -73,  78, -82,  85, -88,  90, -90,
      90, -90,  88, -85,  82, -78,  73, -67,  61, -54,  46, -38,  31, -22,  13,  -4 },
};
static __forceinline short av_clip_int16(int a)
{
    if ((a + 0x8000U) & ~0xFFFF) return (a >> 31) ^ 0x7FFF;
    else                      return a;
}

#define FFMIN(a,b) ((a) > (b) ? (b) : (a))
#define SET(dst, x)   (dst) = (x)
#define SCALE(dst, x) (dst) = av_clip_int16(((x) + add) >> shift)

#define TR_4(dst, src, dstep, sstep, assign, end)                 \
    do {                                                          \
        const int e0 = 64 * src[0 * sstep] + 64 * src[2 * sstep]; \
        const int e1 = 64 * src[0 * sstep] - 64 * src[2 * sstep]; \
        const int o0 = 83 * src[1 * sstep] + 36 * src[3 * sstep]; \
        const int o1 = 36 * src[1 * sstep] - 83 * src[3 * sstep]; \
                                                                  \
        assign(dst[0 * dstep], e0 + o0);                          \
        assign(dst[1 * dstep], e1 + o1);                          \
        assign(dst[2 * dstep], e1 - o1);                          \
        assign(dst[3 * dstep], e0 - o0);                          \
    } while (0)

#define TR_8(dst, src, dstep, sstep, assign, end)                 \
    do {                                                          \
        int i, j;                                                 \
        int e_8[4];                                               \
        int o_8[4] = { 0 };                                       \
        for (i = 0; i < 4; i++)                                   \
            for (j = 1; j < end; j += 2)                          \
                o_8[i] += transform[4 * j][i] * src[j * sstep];   \
        TR_4(e_8, src, 1, 2 * sstep, SET, 4);                     \
                                                                  \
        for (i = 0; i < 4; i++) {                                 \
            assign(dst[i * dstep], e_8[i] + o_8[i]);              \
            assign(dst[(7 - i) * dstep], e_8[i] - o_8[i]);        \
        }                                                         \
    } while (0)

#define TR_16(dst, src, dstep, sstep, assign, end)                \
    do {                                                          \
        int i, j;                                                 \
        int e_16[8];                                              \
        int o_16[8] = { 0 };                                      \
        for (i = 0; i < 8; i++)                                   \
            for (j = 1; j < end; j += 2)                          \
                o_16[i] += transform[2 * j][i] * src[j * sstep];  \
        TR_8(e_16, src, 1, 2 * sstep, SET, 8);                    \
                                                                  \
        for (i = 0; i < 8; i++) {                                 \
            assign(dst[i * dstep], e_16[i] + o_16[i]);            \
            assign(dst[(15 - i) * dstep], e_16[i] - o_16[i]);     \
        }                                                         \
    } while (0)

static void idct_16x16_8(short* coeffs, int col_limit) {
    int i;
    int      shift = 7;
    int      add = 1 << (shift - 1);
    short* src = coeffs;
    int limit = FFMIN(col_limit, 16);
    int limit2 = FFMIN(col_limit + 4, 16);

    for (i = 0; i < 16; i++) {
        TR_16(src, src, 16, 16, SCALE, limit2);                  
        if (limit2 < 16 && i%4 == 0 && !!i)                        
            limit2 -= 4;                                         
        src++;                                                    
    }      
    shift = 20 - BIT_DEPTH;                                       
    add = 1 << (shift - 1);                                     
    for (i = 0; i < 16; i++) {
        TR_16(coeffs, coeffs, 1, 1, SCALE, limit);             
        coeffs += 16;                                              
    }                                                             
};

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