x265的DCT

news/2024/9/16 19:12:02/

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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