fwd_dct32x32_impl_avx2.h 160 KB
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/*
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 * Copyright (c) 2016, Alliance for Open Media. All rights reserved
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 *
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 * This source code is subject to the terms of the BSD 2 Clause License and
 * the Alliance for Open Media Patent License 1.0. If the BSD 2 Clause License
 * was not distributed with this source code in the LICENSE file, you can
 * obtain it at www.aomedia.org/license/software. If the Alliance for Open
 * Media Patent License 1.0 was not distributed with this source code in the
 * PATENTS file, you can obtain it at www.aomedia.org/license/patent.
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 */

#include <immintrin.h>  // AVX2
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#include "aom_dsp/txfm_common.h"
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#define pair256_set_epi16(a, b)                                            \
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  _mm256_set_epi16((int16_t)(b), (int16_t)(a), (int16_t)(b), (int16_t)(a), \
                   (int16_t)(b), (int16_t)(a), (int16_t)(b), (int16_t)(a), \
                   (int16_t)(b), (int16_t)(a), (int16_t)(b), (int16_t)(a), \
                   (int16_t)(b), (int16_t)(a), (int16_t)(b), (int16_t)(a))
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#define pair256_set_epi32(a, b)                                                \
  _mm256_set_epi32((int)(b), (int)(a), (int)(b), (int)(a), (int)(b), (int)(a), \
                   (int)(b), (int)(a))
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#if FDCT32x32_HIGH_PRECISION
static INLINE __m256i k_madd_epi32_avx2(__m256i a, __m256i b) {
  __m256i buf0, buf1;
  buf0 = _mm256_mul_epu32(a, b);
  a = _mm256_srli_epi64(a, 32);
  b = _mm256_srli_epi64(b, 32);
  buf1 = _mm256_mul_epu32(a, b);
  return _mm256_add_epi64(buf0, buf1);
}

static INLINE __m256i k_packs_epi64_avx2(__m256i a, __m256i b) {
  __m256i buf0 = _mm256_shuffle_epi32(a, _MM_SHUFFLE(0, 0, 2, 0));
  __m256i buf1 = _mm256_shuffle_epi32(b, _MM_SHUFFLE(0, 0, 2, 0));
  return _mm256_unpacklo_epi64(buf0, buf1);
}
#endif

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void FDCT32x32_2D_AVX2(const int16_t *input, int16_t *output_org, int stride) {
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  // Calculate pre-multiplied strides
  const int str1 = stride;
  const int str2 = 2 * stride;
  const int str3 = 2 * stride + str1;
  // We need an intermediate buffer between passes.
  DECLARE_ALIGNED(32, int16_t, intermediate[32 * 32]);
  // Constants
  //    When we use them, in one case, they are all the same. In all others
  //    it's a pair of them that we need to repeat four times. This is done
  //    by constructing the 32 bit constant corresponding to that pair.
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  const __m256i k__cospi_p16_p16 = _mm256_set1_epi16((int16_t)cospi_16_64);
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  const __m256i k__cospi_p16_m16 =
      pair256_set_epi16(+cospi_16_64, -cospi_16_64);
  const __m256i k__cospi_m08_p24 = pair256_set_epi16(-cospi_8_64, cospi_24_64);
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  const __m256i k__cospi_m24_m08 = pair256_set_epi16(-cospi_24_64, -cospi_8_64);
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  const __m256i k__cospi_p24_p08 = pair256_set_epi16(+cospi_24_64, cospi_8_64);
  const __m256i k__cospi_p12_p20 = pair256_set_epi16(+cospi_12_64, cospi_20_64);
  const __m256i k__cospi_m20_p12 = pair256_set_epi16(-cospi_20_64, cospi_12_64);
  const __m256i k__cospi_m04_p28 = pair256_set_epi16(-cospi_4_64, cospi_28_64);
  const __m256i k__cospi_p28_p04 = pair256_set_epi16(+cospi_28_64, cospi_4_64);
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  const __m256i k__cospi_m28_m04 = pair256_set_epi16(-cospi_28_64, -cospi_4_64);
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  const __m256i k__cospi_m12_m20 =
      pair256_set_epi16(-cospi_12_64, -cospi_20_64);
  const __m256i k__cospi_p30_p02 = pair256_set_epi16(+cospi_30_64, cospi_2_64);
  const __m256i k__cospi_p14_p18 = pair256_set_epi16(+cospi_14_64, cospi_18_64);
  const __m256i k__cospi_p22_p10 = pair256_set_epi16(+cospi_22_64, cospi_10_64);
  const __m256i k__cospi_p06_p26 = pair256_set_epi16(+cospi_6_64, cospi_26_64);
  const __m256i k__cospi_m26_p06 = pair256_set_epi16(-cospi_26_64, cospi_6_64);
  const __m256i k__cospi_m10_p22 = pair256_set_epi16(-cospi_10_64, cospi_22_64);
  const __m256i k__cospi_m18_p14 = pair256_set_epi16(-cospi_18_64, cospi_14_64);
  const __m256i k__cospi_m02_p30 = pair256_set_epi16(-cospi_2_64, cospi_30_64);
  const __m256i k__cospi_p31_p01 = pair256_set_epi16(+cospi_31_64, cospi_1_64);
  const __m256i k__cospi_p15_p17 = pair256_set_epi16(+cospi_15_64, cospi_17_64);
  const __m256i k__cospi_p23_p09 = pair256_set_epi16(+cospi_23_64, cospi_9_64);
  const __m256i k__cospi_p07_p25 = pair256_set_epi16(+cospi_7_64, cospi_25_64);
  const __m256i k__cospi_m25_p07 = pair256_set_epi16(-cospi_25_64, cospi_7_64);
  const __m256i k__cospi_m09_p23 = pair256_set_epi16(-cospi_9_64, cospi_23_64);
  const __m256i k__cospi_m17_p15 = pair256_set_epi16(-cospi_17_64, cospi_15_64);
  const __m256i k__cospi_m01_p31 = pair256_set_epi16(-cospi_1_64, cospi_31_64);
  const __m256i k__cospi_p27_p05 = pair256_set_epi16(+cospi_27_64, cospi_5_64);
  const __m256i k__cospi_p11_p21 = pair256_set_epi16(+cospi_11_64, cospi_21_64);
  const __m256i k__cospi_p19_p13 = pair256_set_epi16(+cospi_19_64, cospi_13_64);
  const __m256i k__cospi_p03_p29 = pair256_set_epi16(+cospi_3_64, cospi_29_64);
  const __m256i k__cospi_m29_p03 = pair256_set_epi16(-cospi_29_64, cospi_3_64);
  const __m256i k__cospi_m13_p19 = pair256_set_epi16(-cospi_13_64, cospi_19_64);
  const __m256i k__cospi_m21_p11 = pair256_set_epi16(-cospi_21_64, cospi_11_64);
  const __m256i k__cospi_m05_p27 = pair256_set_epi16(-cospi_5_64, cospi_27_64);
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  const __m256i k__DCT_CONST_ROUNDING = _mm256_set1_epi32(DCT_CONST_ROUNDING);
  const __m256i kZero = _mm256_set1_epi16(0);
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  const __m256i kOne = _mm256_set1_epi16(1);
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  // Do the two transform/transpose passes
  int pass;
  for (pass = 0; pass < 2; ++pass) {
    // We process sixteen columns (transposed rows in second pass) at a time.
    int column_start;
    for (column_start = 0; column_start < 32; column_start += 16) {
      __m256i step1[32];
      __m256i step2[32];
      __m256i step3[32];
      __m256i out[32];
      // Stage 1
      // Note: even though all the loads below are aligned, using the aligned
      //       intrinsic make the code slightly slower.
      if (0 == pass) {
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        const int16_t *in = &input[column_start];
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        // step1[i] =  (in[ 0 * stride] + in[(32 -  1) * stride]) << 2;
        // Note: the next four blocks could be in a loop. That would help the
        //       instruction cache but is actually slower.
        {
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          const int16_t *ina = in + 0 * str1;
          const int16_t *inb = in + 31 * str1;
          __m256i *step1a = &step1[0];
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          __m256i *step1b = &step1[31];
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          const __m256i ina0 = _mm256_loadu_si256((const __m256i *)(ina));
          const __m256i ina1 =
              _mm256_loadu_si256((const __m256i *)(ina + str1));
          const __m256i ina2 =
              _mm256_loadu_si256((const __m256i *)(ina + str2));
          const __m256i ina3 =
              _mm256_loadu_si256((const __m256i *)(ina + str3));
          const __m256i inb3 =
              _mm256_loadu_si256((const __m256i *)(inb - str3));
          const __m256i inb2 =
              _mm256_loadu_si256((const __m256i *)(inb - str2));
          const __m256i inb1 =
              _mm256_loadu_si256((const __m256i *)(inb - str1));
          const __m256i inb0 = _mm256_loadu_si256((const __m256i *)(inb));
          step1a[0] = _mm256_add_epi16(ina0, inb0);
          step1a[1] = _mm256_add_epi16(ina1, inb1);
          step1a[2] = _mm256_add_epi16(ina2, inb2);
          step1a[3] = _mm256_add_epi16(ina3, inb3);
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          step1b[-3] = _mm256_sub_epi16(ina3, inb3);
          step1b[-2] = _mm256_sub_epi16(ina2, inb2);
          step1b[-1] = _mm256_sub_epi16(ina1, inb1);
          step1b[-0] = _mm256_sub_epi16(ina0, inb0);
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          step1a[0] = _mm256_slli_epi16(step1a[0], 2);
          step1a[1] = _mm256_slli_epi16(step1a[1], 2);
          step1a[2] = _mm256_slli_epi16(step1a[2], 2);
          step1a[3] = _mm256_slli_epi16(step1a[3], 2);
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          step1b[-3] = _mm256_slli_epi16(step1b[-3], 2);
          step1b[-2] = _mm256_slli_epi16(step1b[-2], 2);
          step1b[-1] = _mm256_slli_epi16(step1b[-1], 2);
          step1b[-0] = _mm256_slli_epi16(step1b[-0], 2);
        }
        {
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          const int16_t *ina = in + 4 * str1;
          const int16_t *inb = in + 27 * str1;
          __m256i *step1a = &step1[4];
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          __m256i *step1b = &step1[27];
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          const __m256i ina0 = _mm256_loadu_si256((const __m256i *)(ina));
          const __m256i ina1 =
              _mm256_loadu_si256((const __m256i *)(ina + str1));
          const __m256i ina2 =
              _mm256_loadu_si256((const __m256i *)(ina + str2));
          const __m256i ina3 =
              _mm256_loadu_si256((const __m256i *)(ina + str3));
          const __m256i inb3 =
              _mm256_loadu_si256((const __m256i *)(inb - str3));
          const __m256i inb2 =
              _mm256_loadu_si256((const __m256i *)(inb - str2));
          const __m256i inb1 =
              _mm256_loadu_si256((const __m256i *)(inb - str1));
          const __m256i inb0 = _mm256_loadu_si256((const __m256i *)(inb));
          step1a[0] = _mm256_add_epi16(ina0, inb0);
          step1a[1] = _mm256_add_epi16(ina1, inb1);
          step1a[2] = _mm256_add_epi16(ina2, inb2);
          step1a[3] = _mm256_add_epi16(ina3, inb3);
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          step1b[-3] = _mm256_sub_epi16(ina3, inb3);
          step1b[-2] = _mm256_sub_epi16(ina2, inb2);
          step1b[-1] = _mm256_sub_epi16(ina1, inb1);
          step1b[-0] = _mm256_sub_epi16(ina0, inb0);
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          step1a[0] = _mm256_slli_epi16(step1a[0], 2);
          step1a[1] = _mm256_slli_epi16(step1a[1], 2);
          step1a[2] = _mm256_slli_epi16(step1a[2], 2);
          step1a[3] = _mm256_slli_epi16(step1a[3], 2);
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          step1b[-3] = _mm256_slli_epi16(step1b[-3], 2);
          step1b[-2] = _mm256_slli_epi16(step1b[-2], 2);
          step1b[-1] = _mm256_slli_epi16(step1b[-1], 2);
          step1b[-0] = _mm256_slli_epi16(step1b[-0], 2);
        }
        {
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          const int16_t *ina = in + 8 * str1;
          const int16_t *inb = in + 23 * str1;
          __m256i *step1a = &step1[8];
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          __m256i *step1b = &step1[23];
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          const __m256i ina0 = _mm256_loadu_si256((const __m256i *)(ina));
          const __m256i ina1 =
              _mm256_loadu_si256((const __m256i *)(ina + str1));
          const __m256i ina2 =
              _mm256_loadu_si256((const __m256i *)(ina + str2));
          const __m256i ina3 =
              _mm256_loadu_si256((const __m256i *)(ina + str3));
          const __m256i inb3 =
              _mm256_loadu_si256((const __m256i *)(inb - str3));
          const __m256i inb2 =
              _mm256_loadu_si256((const __m256i *)(inb - str2));
          const __m256i inb1 =
              _mm256_loadu_si256((const __m256i *)(inb - str1));
          const __m256i inb0 = _mm256_loadu_si256((const __m256i *)(inb));
          step1a[0] = _mm256_add_epi16(ina0, inb0);
          step1a[1] = _mm256_add_epi16(ina1, inb1);
          step1a[2] = _mm256_add_epi16(ina2, inb2);
          step1a[3] = _mm256_add_epi16(ina3, inb3);
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          step1b[-3] = _mm256_sub_epi16(ina3, inb3);
          step1b[-2] = _mm256_sub_epi16(ina2, inb2);
          step1b[-1] = _mm256_sub_epi16(ina1, inb1);
          step1b[-0] = _mm256_sub_epi16(ina0, inb0);
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          step1a[0] = _mm256_slli_epi16(step1a[0], 2);
          step1a[1] = _mm256_slli_epi16(step1a[1], 2);
          step1a[2] = _mm256_slli_epi16(step1a[2], 2);
          step1a[3] = _mm256_slli_epi16(step1a[3], 2);
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          step1b[-3] = _mm256_slli_epi16(step1b[-3], 2);
          step1b[-2] = _mm256_slli_epi16(step1b[-2], 2);
          step1b[-1] = _mm256_slli_epi16(step1b[-1], 2);
          step1b[-0] = _mm256_slli_epi16(step1b[-0], 2);
        }
        {
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          const int16_t *ina = in + 12 * str1;
          const int16_t *inb = in + 19 * str1;
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          __m256i *step1a = &step1[12];
          __m256i *step1b = &step1[19];
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          const __m256i ina0 = _mm256_loadu_si256((const __m256i *)(ina));
          const __m256i ina1 =
              _mm256_loadu_si256((const __m256i *)(ina + str1));
          const __m256i ina2 =
              _mm256_loadu_si256((const __m256i *)(ina + str2));
          const __m256i ina3 =
              _mm256_loadu_si256((const __m256i *)(ina + str3));
          const __m256i inb3 =
              _mm256_loadu_si256((const __m256i *)(inb - str3));
          const __m256i inb2 =
              _mm256_loadu_si256((const __m256i *)(inb - str2));
          const __m256i inb1 =
              _mm256_loadu_si256((const __m256i *)(inb - str1));
          const __m256i inb0 = _mm256_loadu_si256((const __m256i *)(inb));
          step1a[0] = _mm256_add_epi16(ina0, inb0);
          step1a[1] = _mm256_add_epi16(ina1, inb1);
          step1a[2] = _mm256_add_epi16(ina2, inb2);
          step1a[3] = _mm256_add_epi16(ina3, inb3);
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          step1b[-3] = _mm256_sub_epi16(ina3, inb3);
          step1b[-2] = _mm256_sub_epi16(ina2, inb2);
          step1b[-1] = _mm256_sub_epi16(ina1, inb1);
          step1b[-0] = _mm256_sub_epi16(ina0, inb0);
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          step1a[0] = _mm256_slli_epi16(step1a[0], 2);
          step1a[1] = _mm256_slli_epi16(step1a[1], 2);
          step1a[2] = _mm256_slli_epi16(step1a[2], 2);
          step1a[3] = _mm256_slli_epi16(step1a[3], 2);
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          step1b[-3] = _mm256_slli_epi16(step1b[-3], 2);
          step1b[-2] = _mm256_slli_epi16(step1b[-2], 2);
          step1b[-1] = _mm256_slli_epi16(step1b[-1], 2);
          step1b[-0] = _mm256_slli_epi16(step1b[-0], 2);
        }
      } else {
        int16_t *in = &intermediate[column_start];
        // step1[i] =  in[ 0 * 32] + in[(32 -  1) * 32];
        // Note: using the same approach as above to have common offset is
        //       counter-productive as all offsets can be calculated at compile
        //       time.
        // Note: the next four blocks could be in a loop. That would help the
        //       instruction cache but is actually slower.
        {
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          __m256i in00 = _mm256_loadu_si256((const __m256i *)(in + 0 * 32));
          __m256i in01 = _mm256_loadu_si256((const __m256i *)(in + 1 * 32));
          __m256i in02 = _mm256_loadu_si256((const __m256i *)(in + 2 * 32));
          __m256i in03 = _mm256_loadu_si256((const __m256i *)(in + 3 * 32));
          __m256i in28 = _mm256_loadu_si256((const __m256i *)(in + 28 * 32));
          __m256i in29 = _mm256_loadu_si256((const __m256i *)(in + 29 * 32));
          __m256i in30 = _mm256_loadu_si256((const __m256i *)(in + 30 * 32));
          __m256i in31 = _mm256_loadu_si256((const __m256i *)(in + 31 * 32));
          step1[0] = _mm256_add_epi16(in00, in31);
          step1[1] = _mm256_add_epi16(in01, in30);
          step1[2] = _mm256_add_epi16(in02, in29);
          step1[3] = _mm256_add_epi16(in03, in28);
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          step1[28] = _mm256_sub_epi16(in03, in28);
          step1[29] = _mm256_sub_epi16(in02, in29);
          step1[30] = _mm256_sub_epi16(in01, in30);
          step1[31] = _mm256_sub_epi16(in00, in31);
        }
        {
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          __m256i in04 = _mm256_loadu_si256((const __m256i *)(in + 4 * 32));
          __m256i in05 = _mm256_loadu_si256((const __m256i *)(in + 5 * 32));
          __m256i in06 = _mm256_loadu_si256((const __m256i *)(in + 6 * 32));
          __m256i in07 = _mm256_loadu_si256((const __m256i *)(in + 7 * 32));
          __m256i in24 = _mm256_loadu_si256((const __m256i *)(in + 24 * 32));
          __m256i in25 = _mm256_loadu_si256((const __m256i *)(in + 25 * 32));
          __m256i in26 = _mm256_loadu_si256((const __m256i *)(in + 26 * 32));
          __m256i in27 = _mm256_loadu_si256((const __m256i *)(in + 27 * 32));
          step1[4] = _mm256_add_epi16(in04, in27);
          step1[5] = _mm256_add_epi16(in05, in26);
          step1[6] = _mm256_add_epi16(in06, in25);
          step1[7] = _mm256_add_epi16(in07, in24);
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          step1[24] = _mm256_sub_epi16(in07, in24);
          step1[25] = _mm256_sub_epi16(in06, in25);
          step1[26] = _mm256_sub_epi16(in05, in26);
          step1[27] = _mm256_sub_epi16(in04, in27);
        }
        {
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          __m256i in08 = _mm256_loadu_si256((const __m256i *)(in + 8 * 32));
          __m256i in09 = _mm256_loadu_si256((const __m256i *)(in + 9 * 32));
          __m256i in10 = _mm256_loadu_si256((const __m256i *)(in + 10 * 32));
          __m256i in11 = _mm256_loadu_si256((const __m256i *)(in + 11 * 32));
          __m256i in20 = _mm256_loadu_si256((const __m256i *)(in + 20 * 32));
          __m256i in21 = _mm256_loadu_si256((const __m256i *)(in + 21 * 32));
          __m256i in22 = _mm256_loadu_si256((const __m256i *)(in + 22 * 32));
          __m256i in23 = _mm256_loadu_si256((const __m256i *)(in + 23 * 32));
          step1[8] = _mm256_add_epi16(in08, in23);
          step1[9] = _mm256_add_epi16(in09, in22);
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          step1[10] = _mm256_add_epi16(in10, in21);
          step1[11] = _mm256_add_epi16(in11, in20);
          step1[20] = _mm256_sub_epi16(in11, in20);
          step1[21] = _mm256_sub_epi16(in10, in21);
          step1[22] = _mm256_sub_epi16(in09, in22);
          step1[23] = _mm256_sub_epi16(in08, in23);
        }
        {
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          __m256i in12 = _mm256_loadu_si256((const __m256i *)(in + 12 * 32));
          __m256i in13 = _mm256_loadu_si256((const __m256i *)(in + 13 * 32));
          __m256i in14 = _mm256_loadu_si256((const __m256i *)(in + 14 * 32));
          __m256i in15 = _mm256_loadu_si256((const __m256i *)(in + 15 * 32));
          __m256i in16 = _mm256_loadu_si256((const __m256i *)(in + 16 * 32));
          __m256i in17 = _mm256_loadu_si256((const __m256i *)(in + 17 * 32));
          __m256i in18 = _mm256_loadu_si256((const __m256i *)(in + 18 * 32));
          __m256i in19 = _mm256_loadu_si256((const __m256i *)(in + 19 * 32));
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          step1[12] = _mm256_add_epi16(in12, in19);
          step1[13] = _mm256_add_epi16(in13, in18);
          step1[14] = _mm256_add_epi16(in14, in17);
          step1[15] = _mm256_add_epi16(in15, in16);
          step1[16] = _mm256_sub_epi16(in15, in16);
          step1[17] = _mm256_sub_epi16(in14, in17);
          step1[18] = _mm256_sub_epi16(in13, in18);
          step1[19] = _mm256_sub_epi16(in12, in19);
        }
      }
      // Stage 2
      {
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        step2[0] = _mm256_add_epi16(step1[0], step1[15]);
        step2[1] = _mm256_add_epi16(step1[1], step1[14]);
        step2[2] = _mm256_add_epi16(step1[2], step1[13]);
        step2[3] = _mm256_add_epi16(step1[3], step1[12]);
        step2[4] = _mm256_add_epi16(step1[4], step1[11]);
        step2[5] = _mm256_add_epi16(step1[5], step1[10]);
        step2[6] = _mm256_add_epi16(step1[6], step1[9]);
        step2[7] = _mm256_add_epi16(step1[7], step1[8]);
        step2[8] = _mm256_sub_epi16(step1[7], step1[8]);
        step2[9] = _mm256_sub_epi16(step1[6], step1[9]);
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        step2[10] = _mm256_sub_epi16(step1[5], step1[10]);
        step2[11] = _mm256_sub_epi16(step1[4], step1[11]);
        step2[12] = _mm256_sub_epi16(step1[3], step1[12]);
        step2[13] = _mm256_sub_epi16(step1[2], step1[13]);
        step2[14] = _mm256_sub_epi16(step1[1], step1[14]);
        step2[15] = _mm256_sub_epi16(step1[0], step1[15]);
      }
      {
        const __m256i s2_20_0 = _mm256_unpacklo_epi16(step1[27], step1[20]);
        const __m256i s2_20_1 = _mm256_unpackhi_epi16(step1[27], step1[20]);
        const __m256i s2_21_0 = _mm256_unpacklo_epi16(step1[26], step1[21]);
        const __m256i s2_21_1 = _mm256_unpackhi_epi16(step1[26], step1[21]);
        const __m256i s2_22_0 = _mm256_unpacklo_epi16(step1[25], step1[22]);
        const __m256i s2_22_1 = _mm256_unpackhi_epi16(step1[25], step1[22]);
        const __m256i s2_23_0 = _mm256_unpacklo_epi16(step1[24], step1[23]);
        const __m256i s2_23_1 = _mm256_unpackhi_epi16(step1[24], step1[23]);
        const __m256i s2_20_2 = _mm256_madd_epi16(s2_20_0, k__cospi_p16_m16);
        const __m256i s2_20_3 = _mm256_madd_epi16(s2_20_1, k__cospi_p16_m16);
        const __m256i s2_21_2 = _mm256_madd_epi16(s2_21_0, k__cospi_p16_m16);
        const __m256i s2_21_3 = _mm256_madd_epi16(s2_21_1, k__cospi_p16_m16);
        const __m256i s2_22_2 = _mm256_madd_epi16(s2_22_0, k__cospi_p16_m16);
        const __m256i s2_22_3 = _mm256_madd_epi16(s2_22_1, k__cospi_p16_m16);
        const __m256i s2_23_2 = _mm256_madd_epi16(s2_23_0, k__cospi_p16_m16);
        const __m256i s2_23_3 = _mm256_madd_epi16(s2_23_1, k__cospi_p16_m16);
        const __m256i s2_24_2 = _mm256_madd_epi16(s2_23_0, k__cospi_p16_p16);
        const __m256i s2_24_3 = _mm256_madd_epi16(s2_23_1, k__cospi_p16_p16);
        const __m256i s2_25_2 = _mm256_madd_epi16(s2_22_0, k__cospi_p16_p16);
        const __m256i s2_25_3 = _mm256_madd_epi16(s2_22_1, k__cospi_p16_p16);
        const __m256i s2_26_2 = _mm256_madd_epi16(s2_21_0, k__cospi_p16_p16);
        const __m256i s2_26_3 = _mm256_madd_epi16(s2_21_1, k__cospi_p16_p16);
        const __m256i s2_27_2 = _mm256_madd_epi16(s2_20_0, k__cospi_p16_p16);
        const __m256i s2_27_3 = _mm256_madd_epi16(s2_20_1, k__cospi_p16_p16);
        // dct_const_round_shift
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        const __m256i s2_20_4 =
            _mm256_add_epi32(s2_20_2, k__DCT_CONST_ROUNDING);
        const __m256i s2_20_5 =
            _mm256_add_epi32(s2_20_3, k__DCT_CONST_ROUNDING);
        const __m256i s2_21_4 =
            _mm256_add_epi32(s2_21_2, k__DCT_CONST_ROUNDING);
        const __m256i s2_21_5 =
            _mm256_add_epi32(s2_21_3, k__DCT_CONST_ROUNDING);
        const __m256i s2_22_4 =
            _mm256_add_epi32(s2_22_2, k__DCT_CONST_ROUNDING);
        const __m256i s2_22_5 =
            _mm256_add_epi32(s2_22_3, k__DCT_CONST_ROUNDING);
        const __m256i s2_23_4 =
            _mm256_add_epi32(s2_23_2, k__DCT_CONST_ROUNDING);
        const __m256i s2_23_5 =
            _mm256_add_epi32(s2_23_3, k__DCT_CONST_ROUNDING);
        const __m256i s2_24_4 =
            _mm256_add_epi32(s2_24_2, k__DCT_CONST_ROUNDING);
        const __m256i s2_24_5 =
            _mm256_add_epi32(s2_24_3, k__DCT_CONST_ROUNDING);
        const __m256i s2_25_4 =
            _mm256_add_epi32(s2_25_2, k__DCT_CONST_ROUNDING);
        const __m256i s2_25_5 =
            _mm256_add_epi32(s2_25_3, k__DCT_CONST_ROUNDING);
        const __m256i s2_26_4 =
            _mm256_add_epi32(s2_26_2, k__DCT_CONST_ROUNDING);
        const __m256i s2_26_5 =
            _mm256_add_epi32(s2_26_3, k__DCT_CONST_ROUNDING);
        const __m256i s2_27_4 =
            _mm256_add_epi32(s2_27_2, k__DCT_CONST_ROUNDING);
        const __m256i s2_27_5 =
            _mm256_add_epi32(s2_27_3, k__DCT_CONST_ROUNDING);
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        const __m256i s2_20_6 = _mm256_srai_epi32(s2_20_4, DCT_CONST_BITS);
        const __m256i s2_20_7 = _mm256_srai_epi32(s2_20_5, DCT_CONST_BITS);
        const __m256i s2_21_6 = _mm256_srai_epi32(s2_21_4, DCT_CONST_BITS);
        const __m256i s2_21_7 = _mm256_srai_epi32(s2_21_5, DCT_CONST_BITS);
        const __m256i s2_22_6 = _mm256_srai_epi32(s2_22_4, DCT_CONST_BITS);
        const __m256i s2_22_7 = _mm256_srai_epi32(s2_22_5, DCT_CONST_BITS);
        const __m256i s2_23_6 = _mm256_srai_epi32(s2_23_4, DCT_CONST_BITS);
        const __m256i s2_23_7 = _mm256_srai_epi32(s2_23_5, DCT_CONST_BITS);
        const __m256i s2_24_6 = _mm256_srai_epi32(s2_24_4, DCT_CONST_BITS);
        const __m256i s2_24_7 = _mm256_srai_epi32(s2_24_5, DCT_CONST_BITS);
        const __m256i s2_25_6 = _mm256_srai_epi32(s2_25_4, DCT_CONST_BITS);
        const __m256i s2_25_7 = _mm256_srai_epi32(s2_25_5, DCT_CONST_BITS);
        const __m256i s2_26_6 = _mm256_srai_epi32(s2_26_4, DCT_CONST_BITS);
        const __m256i s2_26_7 = _mm256_srai_epi32(s2_26_5, DCT_CONST_BITS);
        const __m256i s2_27_6 = _mm256_srai_epi32(s2_27_4, DCT_CONST_BITS);
        const __m256i s2_27_7 = _mm256_srai_epi32(s2_27_5, DCT_CONST_BITS);
        // Combine
        step2[20] = _mm256_packs_epi32(s2_20_6, s2_20_7);
        step2[21] = _mm256_packs_epi32(s2_21_6, s2_21_7);
        step2[22] = _mm256_packs_epi32(s2_22_6, s2_22_7);
        step2[23] = _mm256_packs_epi32(s2_23_6, s2_23_7);
        step2[24] = _mm256_packs_epi32(s2_24_6, s2_24_7);
        step2[25] = _mm256_packs_epi32(s2_25_6, s2_25_7);
        step2[26] = _mm256_packs_epi32(s2_26_6, s2_26_7);
        step2[27] = _mm256_packs_epi32(s2_27_6, s2_27_7);
      }

#if !FDCT32x32_HIGH_PRECISION
      // dump the magnitude by half, hence the intermediate values are within
      // the range of 16 bits.
      if (1 == pass) {
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        __m256i s3_00_0 = _mm256_cmpgt_epi16(kZero, step2[0]);
        __m256i s3_01_0 = _mm256_cmpgt_epi16(kZero, step2[1]);
        __m256i s3_02_0 = _mm256_cmpgt_epi16(kZero, step2[2]);
        __m256i s3_03_0 = _mm256_cmpgt_epi16(kZero, step2[3]);
        __m256i s3_04_0 = _mm256_cmpgt_epi16(kZero, step2[4]);
        __m256i s3_05_0 = _mm256_cmpgt_epi16(kZero, step2[5]);
        __m256i s3_06_0 = _mm256_cmpgt_epi16(kZero, step2[6]);
        __m256i s3_07_0 = _mm256_cmpgt_epi16(kZero, step2[7]);
        __m256i s2_08_0 = _mm256_cmpgt_epi16(kZero, step2[8]);
        __m256i s2_09_0 = _mm256_cmpgt_epi16(kZero, step2[9]);
        __m256i s3_10_0 = _mm256_cmpgt_epi16(kZero, step2[10]);
        __m256i s3_11_0 = _mm256_cmpgt_epi16(kZero, step2[11]);
        __m256i s3_12_0 = _mm256_cmpgt_epi16(kZero, step2[12]);
        __m256i s3_13_0 = _mm256_cmpgt_epi16(kZero, step2[13]);
        __m256i s2_14_0 = _mm256_cmpgt_epi16(kZero, step2[14]);
        __m256i s2_15_0 = _mm256_cmpgt_epi16(kZero, step2[15]);
        __m256i s3_16_0 = _mm256_cmpgt_epi16(kZero, step1[16]);
        __m256i s3_17_0 = _mm256_cmpgt_epi16(kZero, step1[17]);
        __m256i s3_18_0 = _mm256_cmpgt_epi16(kZero, step1[18]);
        __m256i s3_19_0 = _mm256_cmpgt_epi16(kZero, step1[19]);
        __m256i s3_20_0 = _mm256_cmpgt_epi16(kZero, step2[20]);
        __m256i s3_21_0 = _mm256_cmpgt_epi16(kZero, step2[21]);
        __m256i s3_22_0 = _mm256_cmpgt_epi16(kZero, step2[22]);
        __m256i s3_23_0 = _mm256_cmpgt_epi16(kZero, step2[23]);
        __m256i s3_24_0 = _mm256_cmpgt_epi16(kZero, step2[24]);
        __m256i s3_25_0 = _mm256_cmpgt_epi16(kZero, step2[25]);
        __m256i s3_26_0 = _mm256_cmpgt_epi16(kZero, step2[26]);
        __m256i s3_27_0 = _mm256_cmpgt_epi16(kZero, step2[27]);
        __m256i s3_28_0 = _mm256_cmpgt_epi16(kZero, step1[28]);
        __m256i s3_29_0 = _mm256_cmpgt_epi16(kZero, step1[29]);
        __m256i s3_30_0 = _mm256_cmpgt_epi16(kZero, step1[30]);
        __m256i s3_31_0 = _mm256_cmpgt_epi16(kZero, step1[31]);

        step2[0] = _mm256_sub_epi16(step2[0], s3_00_0);
        step2[1] = _mm256_sub_epi16(step2[1], s3_01_0);
        step2[2] = _mm256_sub_epi16(step2[2], s3_02_0);
        step2[3] = _mm256_sub_epi16(step2[3], s3_03_0);
        step2[4] = _mm256_sub_epi16(step2[4], s3_04_0);
        step2[5] = _mm256_sub_epi16(step2[5], s3_05_0);
        step2[6] = _mm256_sub_epi16(step2[6], s3_06_0);
        step2[7] = _mm256_sub_epi16(step2[7], s3_07_0);
        step2[8] = _mm256_sub_epi16(step2[8], s2_08_0);
        step2[9] = _mm256_sub_epi16(step2[9], s2_09_0);
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        step2[10] = _mm256_sub_epi16(step2[10], s3_10_0);
        step2[11] = _mm256_sub_epi16(step2[11], s3_11_0);
        step2[12] = _mm256_sub_epi16(step2[12], s3_12_0);
        step2[13] = _mm256_sub_epi16(step2[13], s3_13_0);
        step2[14] = _mm256_sub_epi16(step2[14], s2_14_0);
        step2[15] = _mm256_sub_epi16(step2[15], s2_15_0);
        step1[16] = _mm256_sub_epi16(step1[16], s3_16_0);
        step1[17] = _mm256_sub_epi16(step1[17], s3_17_0);
        step1[18] = _mm256_sub_epi16(step1[18], s3_18_0);
        step1[19] = _mm256_sub_epi16(step1[19], s3_19_0);
        step2[20] = _mm256_sub_epi16(step2[20], s3_20_0);
        step2[21] = _mm256_sub_epi16(step2[21], s3_21_0);
        step2[22] = _mm256_sub_epi16(step2[22], s3_22_0);
        step2[23] = _mm256_sub_epi16(step2[23], s3_23_0);
        step2[24] = _mm256_sub_epi16(step2[24], s3_24_0);
        step2[25] = _mm256_sub_epi16(step2[25], s3_25_0);
        step2[26] = _mm256_sub_epi16(step2[26], s3_26_0);
        step2[27] = _mm256_sub_epi16(step2[27], s3_27_0);
        step1[28] = _mm256_sub_epi16(step1[28], s3_28_0);
        step1[29] = _mm256_sub_epi16(step1[29], s3_29_0);
        step1[30] = _mm256_sub_epi16(step1[30], s3_30_0);
        step1[31] = _mm256_sub_epi16(step1[31], s3_31_0);

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        step2[0] = _mm256_add_epi16(step2[0], kOne);
        step2[1] = _mm256_add_epi16(step2[1], kOne);
        step2[2] = _mm256_add_epi16(step2[2], kOne);
        step2[3] = _mm256_add_epi16(step2[3], kOne);
        step2[4] = _mm256_add_epi16(step2[4], kOne);
        step2[5] = _mm256_add_epi16(step2[5], kOne);
        step2[6] = _mm256_add_epi16(step2[6], kOne);
        step2[7] = _mm256_add_epi16(step2[7], kOne);
        step2[8] = _mm256_add_epi16(step2[8], kOne);
        step2[9] = _mm256_add_epi16(step2[9], kOne);
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        step2[10] = _mm256_add_epi16(step2[10], kOne);
        step2[11] = _mm256_add_epi16(step2[11], kOne);
        step2[12] = _mm256_add_epi16(step2[12], kOne);
        step2[13] = _mm256_add_epi16(step2[13], kOne);
        step2[14] = _mm256_add_epi16(step2[14], kOne);
        step2[15] = _mm256_add_epi16(step2[15], kOne);
        step1[16] = _mm256_add_epi16(step1[16], kOne);
        step1[17] = _mm256_add_epi16(step1[17], kOne);
        step1[18] = _mm256_add_epi16(step1[18], kOne);
        step1[19] = _mm256_add_epi16(step1[19], kOne);
        step2[20] = _mm256_add_epi16(step2[20], kOne);
        step2[21] = _mm256_add_epi16(step2[21], kOne);
        step2[22] = _mm256_add_epi16(step2[22], kOne);
        step2[23] = _mm256_add_epi16(step2[23], kOne);
        step2[24] = _mm256_add_epi16(step2[24], kOne);
        step2[25] = _mm256_add_epi16(step2[25], kOne);
        step2[26] = _mm256_add_epi16(step2[26], kOne);
        step2[27] = _mm256_add_epi16(step2[27], kOne);
        step1[28] = _mm256_add_epi16(step1[28], kOne);
        step1[29] = _mm256_add_epi16(step1[29], kOne);
        step1[30] = _mm256_add_epi16(step1[30], kOne);
        step1[31] = _mm256_add_epi16(step1[31], kOne);

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        step2[0] = _mm256_srai_epi16(step2[0], 2);
        step2[1] = _mm256_srai_epi16(step2[1], 2);
        step2[2] = _mm256_srai_epi16(step2[2], 2);
        step2[3] = _mm256_srai_epi16(step2[3], 2);
        step2[4] = _mm256_srai_epi16(step2[4], 2);
        step2[5] = _mm256_srai_epi16(step2[5], 2);
        step2[6] = _mm256_srai_epi16(step2[6], 2);
        step2[7] = _mm256_srai_epi16(step2[7], 2);
        step2[8] = _mm256_srai_epi16(step2[8], 2);
        step2[9] = _mm256_srai_epi16(step2[9], 2);
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        step2[10] = _mm256_srai_epi16(step2[10], 2);
        step2[11] = _mm256_srai_epi16(step2[11], 2);
        step2[12] = _mm256_srai_epi16(step2[12], 2);
        step2[13] = _mm256_srai_epi16(step2[13], 2);
        step2[14] = _mm256_srai_epi16(step2[14], 2);
        step2[15] = _mm256_srai_epi16(step2[15], 2);
        step1[16] = _mm256_srai_epi16(step1[16], 2);
        step1[17] = _mm256_srai_epi16(step1[17], 2);
        step1[18] = _mm256_srai_epi16(step1[18], 2);
        step1[19] = _mm256_srai_epi16(step1[19], 2);
        step2[20] = _mm256_srai_epi16(step2[20], 2);
        step2[21] = _mm256_srai_epi16(step2[21], 2);
        step2[22] = _mm256_srai_epi16(step2[22], 2);
        step2[23] = _mm256_srai_epi16(step2[23], 2);
        step2[24] = _mm256_srai_epi16(step2[24], 2);
        step2[25] = _mm256_srai_epi16(step2[25], 2);
        step2[26] = _mm256_srai_epi16(step2[26], 2);
        step2[27] = _mm256_srai_epi16(step2[27], 2);
        step1[28] = _mm256_srai_epi16(step1[28], 2);
        step1[29] = _mm256_srai_epi16(step1[29], 2);
        step1[30] = _mm256_srai_epi16(step1[30], 2);
        step1[31] = _mm256_srai_epi16(step1[31], 2);
      }
#endif

#if FDCT32x32_HIGH_PRECISION
      if (pass == 0) {
#endif
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        // Stage 3
        {
          step3[0] = _mm256_add_epi16(step2[(8 - 1)], step2[0]);
          step3[1] = _mm256_add_epi16(step2[(8 - 2)], step2[1]);
          step3[2] = _mm256_add_epi16(step2[(8 - 3)], step2[2]);
          step3[3] = _mm256_add_epi16(step2[(8 - 4)], step2[3]);
          step3[4] = _mm256_sub_epi16(step2[(8 - 5)], step2[4]);
          step3[5] = _mm256_sub_epi16(step2[(8 - 6)], step2[5]);
          step3[6] = _mm256_sub_epi16(step2[(8 - 7)], step2[6]);
          step3[7] = _mm256_sub_epi16(step2[(8 - 8)], step2[7]);
        }
        {
          const __m256i s3_10_0 = _mm256_unpacklo_epi16(step2[13], step2[10]);
          const __m256i s3_10_1 = _mm256_unpackhi_epi16(step2[13], step2[10]);
          const __m256i s3_11_0 = _mm256_unpacklo_epi16(step2[12], step2[11]);
          const __m256i s3_11_1 = _mm256_unpackhi_epi16(step2[12], step2[11]);
          const __m256i s3_10_2 = _mm256_madd_epi16(s3_10_0, k__cospi_p16_m16);
          const __m256i s3_10_3 = _mm256_madd_epi16(s3_10_1, k__cospi_p16_m16);
          const __m256i s3_11_2 = _mm256_madd_epi16(s3_11_0, k__cospi_p16_m16);
          const __m256i s3_11_3 = _mm256_madd_epi16(s3_11_1, k__cospi_p16_m16);
          const __m256i s3_12_2 = _mm256_madd_epi16(s3_11_0, k__cospi_p16_p16);
          const __m256i s3_12_3 = _mm256_madd_epi16(s3_11_1, k__cospi_p16_p16);
          const __m256i s3_13_2 = _mm256_madd_epi16(s3_10_0, k__cospi_p16_p16);
          const __m256i s3_13_3 = _mm256_madd_epi16(s3_10_1, k__cospi_p16_p16);
          // dct_const_round_shift
          const __m256i s3_10_4 =
              _mm256_add_epi32(s3_10_2, k__DCT_CONST_ROUNDING);
          const __m256i s3_10_5 =
              _mm256_add_epi32(s3_10_3, k__DCT_CONST_ROUNDING);
          const __m256i s3_11_4 =
              _mm256_add_epi32(s3_11_2, k__DCT_CONST_ROUNDING);
          const __m256i s3_11_5 =
              _mm256_add_epi32(s3_11_3, k__DCT_CONST_ROUNDING);
          const __m256i s3_12_4 =
              _mm256_add_epi32(s3_12_2, k__DCT_CONST_ROUNDING);
          const __m256i s3_12_5 =
              _mm256_add_epi32(s3_12_3, k__DCT_CONST_ROUNDING);
          const __m256i s3_13_4 =
              _mm256_add_epi32(s3_13_2, k__DCT_CONST_ROUNDING);
          const __m256i s3_13_5 =
              _mm256_add_epi32(s3_13_3, k__DCT_CONST_ROUNDING);
          const __m256i s3_10_6 = _mm256_srai_epi32(s3_10_4, DCT_CONST_BITS);
          const __m256i s3_10_7 = _mm256_srai_epi32(s3_10_5, DCT_CONST_BITS);
          const __m256i s3_11_6 = _mm256_srai_epi32(s3_11_4, DCT_CONST_BITS);
          const __m256i s3_11_7 = _mm256_srai_epi32(s3_11_5, DCT_CONST_BITS);
          const __m256i s3_12_6 = _mm256_srai_epi32(s3_12_4, DCT_CONST_BITS);
          const __m256i s3_12_7 = _mm256_srai_epi32(s3_12_5, DCT_CONST_BITS);
          const __m256i s3_13_6 = _mm256_srai_epi32(s3_13_4, DCT_CONST_BITS);
          const __m256i s3_13_7 = _mm256_srai_epi32(s3_13_5, DCT_CONST_BITS);
          // Combine
          step3[10] = _mm256_packs_epi32(s3_10_6, s3_10_7);
          step3[11] = _mm256_packs_epi32(s3_11_6, s3_11_7);
          step3[12] = _mm256_packs_epi32(s3_12_6, s3_12_7);
          step3[13] = _mm256_packs_epi32(s3_13_6, s3_13_7);
        }
        {
          step3[16] = _mm256_add_epi16(step2[23], step1[16]);
          step3[17] = _mm256_add_epi16(step2[22], step1[17]);
          step3[18] = _mm256_add_epi16(step2[21], step1[18]);
          step3[19] = _mm256_add_epi16(step2[20], step1[19]);
          step3[20] = _mm256_sub_epi16(step1[19], step2[20]);
          step3[21] = _mm256_sub_epi16(step1[18], step2[21]);
          step3[22] = _mm256_sub_epi16(step1[17], step2[22]);
          step3[23] = _mm256_sub_epi16(step1[16], step2[23]);
          step3[24] = _mm256_sub_epi16(step1[31], step2[24]);
          step3[25] = _mm256_sub_epi16(step1[30], step2[25]);
          step3[26] = _mm256_sub_epi16(step1[29], step2[26]);
          step3[27] = _mm256_sub_epi16(step1[28], step2[27]);
          step3[28] = _mm256_add_epi16(step2[27], step1[28]);
          step3[29] = _mm256_add_epi16(step2[26], step1[29]);
          step3[30] = _mm256_add_epi16(step2[25], step1[30]);
          step3[31] = _mm256_add_epi16(step2[24], step1[31]);
        }
655

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        // Stage 4
        {
          step1[0] = _mm256_add_epi16(step3[3], step3[0]);
          step1[1] = _mm256_add_epi16(step3[2], step3[1]);
          step1[2] = _mm256_sub_epi16(step3[1], step3[2]);
          step1[3] = _mm256_sub_epi16(step3[0], step3[3]);
          step1[8] = _mm256_add_epi16(step3[11], step2[8]);
          step1[9] = _mm256_add_epi16(step3[10], step2[9]);
          step1[10] = _mm256_sub_epi16(step2[9], step3[10]);
          step1[11] = _mm256_sub_epi16(step2[8], step3[11]);
          step1[12] = _mm256_sub_epi16(step2[15], step3[12]);
          step1[13] = _mm256_sub_epi16(step2[14], step3[13]);
          step1[14] = _mm256_add_epi16(step3[13], step2[14]);
          step1[15] = _mm256_add_epi16(step3[12], step2[15]);
        }
        {
          const __m256i s1_05_0 = _mm256_unpacklo_epi16(step3[6], step3[5]);
          const __m256i s1_05_1 = _mm256_unpackhi_epi16(step3[6], step3[5]);
          const __m256i s1_05_2 = _mm256_madd_epi16(s1_05_0, k__cospi_p16_m16);
          const __m256i s1_05_3 = _mm256_madd_epi16(s1_05_1, k__cospi_p16_m16);
          const __m256i s1_06_2 = _mm256_madd_epi16(s1_05_0, k__cospi_p16_p16);
          const __m256i s1_06_3 = _mm256_madd_epi16(s1_05_1, k__cospi_p16_p16);
          // dct_const_round_shift
          const __m256i s1_05_4 =
              _mm256_add_epi32(s1_05_2, k__DCT_CONST_ROUNDING);
          const __m256i s1_05_5 =
              _mm256_add_epi32(s1_05_3, k__DCT_CONST_ROUNDING);
          const __m256i s1_06_4 =
              _mm256_add_epi32(s1_06_2, k__DCT_CONST_ROUNDING);
          const __m256i s1_06_5 =
              _mm256_add_epi32(s1_06_3, k__DCT_CONST_ROUNDING);
          const __m256i s1_05_6 = _mm256_srai_epi32(s1_05_4, DCT_CONST_BITS);
          const __m256i s1_05_7 = _mm256_srai_epi32(s1_05_5, DCT_CONST_BITS);
          const __m256i s1_06_6 = _mm256_srai_epi32(s1_06_4, DCT_CONST_BITS);
          const __m256i s1_06_7 = _mm256_srai_epi32(s1_06_5, DCT_CONST_BITS);
          // Combine
          step1[5] = _mm256_packs_epi32(s1_05_6, s1_05_7);
          step1[6] = _mm256_packs_epi32(s1_06_6, s1_06_7);
        }
        {
          const __m256i s1_18_0 = _mm256_unpacklo_epi16(step3[18], step3[29]);
          const __m256i s1_18_1 = _mm256_unpackhi_epi16(step3[18], step3[29]);
          const __m256i s1_19_0 = _mm256_unpacklo_epi16(step3[19], step3[28]);
          const __m256i s1_19_1 = _mm256_unpackhi_epi16(step3[19], step3[28]);
          const __m256i s1_20_0 = _mm256_unpacklo_epi16(step3[20], step3[27]);
          const __m256i s1_20_1 = _mm256_unpackhi_epi16(step3[20], step3[27]);
          const __m256i s1_21_0 = _mm256_unpacklo_epi16(step3[21], step3[26]);
          const __m256i s1_21_1 = _mm256_unpackhi_epi16(step3[21], step3[26]);
          const __m256i s1_18_2 = _mm256_madd_epi16(s1_18_0, k__cospi_m08_p24);
          const __m256i s1_18_3 = _mm256_madd_epi16(s1_18_1, k__cospi_m08_p24);
          const __m256i s1_19_2 = _mm256_madd_epi16(s1_19_0, k__cospi_m08_p24);
          const __m256i s1_19_3 = _mm256_madd_epi16(s1_19_1, k__cospi_m08_p24);
          const __m256i s1_20_2 = _mm256_madd_epi16(s1_20_0, k__cospi_m24_m08);
          const __m256i s1_20_3 = _mm256_madd_epi16(s1_20_1, k__cospi_m24_m08);
          const __m256i s1_21_2 = _mm256_madd_epi16(s1_21_0, k__cospi_m24_m08);
          const __m256i s1_21_3 = _mm256_madd_epi16(s1_21_1, k__cospi_m24_m08);
          const __m256i s1_26_2 = _mm256_madd_epi16(s1_21_0, k__cospi_m08_p24);
          const __m256i s1_26_3 = _mm256_madd_epi16(s1_21_1, k__cospi_m08_p24);
          const __m256i s1_27_2 = _mm256_madd_epi16(s1_20_0, k__cospi_m08_p24);
          const __m256i s1_27_3 = _mm256_madd_epi16(s1_20_1, k__cospi_m08_p24);
          const __m256i s1_28_2 = _mm256_madd_epi16(s1_19_0, k__cospi_p24_p08);
          const __m256i s1_28_3 = _mm256_madd_epi16(s1_19_1, k__cospi_p24_p08);
          const __m256i s1_29_2 = _mm256_madd_epi16(s1_18_0, k__cospi_p24_p08);
          const __m256i s1_29_3 = _mm256_madd_epi16(s1_18_1, k__cospi_p24_p08);
          // dct_const_round_shift
          const __m256i s1_18_4 =
              _mm256_add_epi32(s1_18_2, k__DCT_CONST_ROUNDING);
          const __m256i s1_18_5 =
              _mm256_add_epi32(s1_18_3, k__DCT_CONST_ROUNDING);
          const __m256i s1_19_4 =
              _mm256_add_epi32(s1_19_2, k__DCT_CONST_ROUNDING);
          const __m256i s1_19_5 =
              _mm256_add_epi32(s1_19_3, k__DCT_CONST_ROUNDING);
          const __m256i s1_20_4 =
              _mm256_add_epi32(s1_20_2, k__DCT_CONST_ROUNDING);
          const __m256i s1_20_5 =
              _mm256_add_epi32(s1_20_3, k__DCT_CONST_ROUNDING);
          const __m256i s1_21_4 =
              _mm256_add_epi32(s1_21_2, k__DCT_CONST_ROUNDING);
          const __m256i s1_21_5 =
              _mm256_add_epi32(s1_21_3, k__DCT_CONST_ROUNDING);
          const __m256i s1_26_4 =
              _mm256_add_epi32(s1_26_2, k__DCT_CONST_ROUNDING);
          const __m256i s1_26_5 =
              _mm256_add_epi32(s1_26_3, k__DCT_CONST_ROUNDING);
          const __m256i s1_27_4 =
              _mm256_add_epi32(s1_27_2, k__DCT_CONST_ROUNDING);
          const __m256i s1_27_5 =
              _mm256_add_epi32(s1_27_3, k__DCT_CONST_ROUNDING);
          const __m256i s1_28_4 =
              _mm256_add_epi32(s1_28_2, k__DCT_CONST_ROUNDING);
          const __m256i s1_28_5 =
              _mm256_add_epi32(s1_28_3, k__DCT_CONST_ROUNDING);
          const __m256i s1_29_4 =
              _mm256_add_epi32(s1_29_2, k__DCT_CONST_ROUNDING);
          const __m256i s1_29_5 =
              _mm256_add_epi32(s1_29_3, k__DCT_CONST_ROUNDING);
          const __m256i s1_18_6 = _mm256_srai_epi32(s1_18_4, DCT_CONST_BITS);
          const __m256i s1_18_7 = _mm256_srai_epi32(s1_18_5, DCT_CONST_BITS);
          const __m256i s1_19_6 = _mm256_srai_epi32(s1_19_4, DCT_CONST_BITS);
          const __m256i s1_19_7 = _mm256_srai_epi32(s1_19_5, DCT_CONST_BITS);
          const __m256i s1_20_6 = _mm256_srai_epi32(s1_20_4, DCT_CONST_BITS);
          const __m256i s1_20_7 = _mm256_srai_epi32(s1_20_5, DCT_CONST_BITS);
          const __m256i s1_21_6 = _mm256_srai_epi32(s1_21_4, DCT_CONST_BITS);
          const __m256i s1_21_7 = _mm256_srai_epi32(s1_21_5, DCT_CONST_BITS);
          const __m256i s1_26_6 = _mm256_srai_epi32(s1_26_4, DCT_CONST_BITS);
          const __m256i s1_26_7 = _mm256_srai_epi32(s1_26_5, DCT_CONST_BITS);
          const __m256i s1_27_6 = _mm256_srai_epi32(s1_27_4, DCT_CONST_BITS);
          const __m256i s1_27_7 = _mm256_srai_epi32(s1_27_5, DCT_CONST_BITS);
          const __m256i s1_28_6 = _mm256_srai_epi32(s1_28_4, DCT_CONST_BITS);
          const __m256i s1_28_7 = _mm256_srai_epi32(s1_28_5, DCT_CONST_BITS);
          const __m256i s1_29_6 = _mm256_srai_epi32(s1_29_4, DCT_CONST_BITS);
          const __m256i s1_29_7 = _mm256_srai_epi32(s1_29_5, DCT_CONST_BITS);
          // Combine
          step1[18] = _mm256_packs_epi32(s1_18_6, s1_18_7);
          step1[19] = _mm256_packs_epi32(s1_19_6, s1_19_7);
          step1[20] = _mm256_packs_epi32(s1_20_6, s1_20_7);
          step1[21] = _mm256_packs_epi32(s1_21_6, s1_21_7);
          step1[26] = _mm256_packs_epi32(s1_26_6, s1_26_7);
          step1[27] = _mm256_packs_epi32(s1_27_6, s1_27_7);
          step1[28] = _mm256_packs_epi32(s1_28_6, s1_28_7);
          step1[29] = _mm256_packs_epi32(s1_29_6, s1_29_7);
        }
        // Stage 5
        {
          step2[4] = _mm256_add_epi16(step1[5], step3[4]);
          step2[5] = _mm256_sub_epi16(step3[4], step1[5]);
          step2[6] = _mm256_sub_epi16(step3[7], step1[6]);
          step2[7] = _mm256_add_epi16(step1[6], step3[7]);
        }
        {
          const __m256i out_00_0 = _mm256_unpacklo_epi16(step1[0], step1[1]);
          const __m256i out_00_1 = _mm256_unpackhi_epi16(step1[0], step1[1]);
          const __m256i out_08_0 = _mm256_unpacklo_epi16(step1[2], step1[3]);
          const __m256i out_08_1 = _mm256_unpackhi_epi16(step1[2], step1[3]);
          const __m256i out_00_2 =
              _mm256_madd_epi16(out_00_0, k__cospi_p16_p16);
          const __m256i out_00_3 =
              _mm256_madd_epi16(out_00_1, k__cospi_p16_p16);
          const __m256i out_16_2 =
              _mm256_madd_epi16(out_00_0, k__cospi_p16_m16);
          const __m256i out_16_3 =
              _mm256_madd_epi16(out_00_1, k__cospi_p16_m16);
          const __m256i out_08_2 =
              _mm256_madd_epi16(out_08_0, k__cospi_p24_p08);
          const __m256i out_08_3 =
              _mm256_madd_epi16(out_08_1, k__cospi_p24_p08);
          const __m256i out_24_2 =
              _mm256_madd_epi16(out_08_0, k__cospi_m08_p24);
          const __m256i out_24_3 =
              _mm256_madd_epi16(out_08_1, k__cospi_m08_p24);
          // dct_const_round_shift
          const __m256i out_00_4 =
              _mm256_add_epi32(out_00_2, k__DCT_CONST_ROUNDING);
          const __m256i out_00_5 =
              _mm256_add_epi32(out_00_3, k__DCT_CONST_ROUNDING);
          const __m256i out_16_4 =
              _mm256_add_epi32(out_16_2, k__DCT_CONST_ROUNDING);
          const __m256i out_16_5 =
              _mm256_add_epi32(out_16_3, k__DCT_CONST_ROUNDING);
          const __m256i out_08_4 =
              _mm256_add_epi32(out_08_2, k__DCT_CONST_ROUNDING);
          const __m256i out_08_5 =
              _mm256_add_epi32(out_08_3, k__DCT_CONST_ROUNDING);
          const __m256i out_24_4 =
              _mm256_add_epi32(out_24_2, k__DCT_CONST_ROUNDING);
          const __m256i out_24_5 =
              _mm256_add_epi32(out_24_3, k__DCT_CONST_ROUNDING);
          const __m256i out_00_6 = _mm256_srai_epi32(out_00_4, DCT_CONST_BITS);
          const __m256i out_00_7 = _mm256_srai_epi32(out_00_5, DCT_CONST_BITS);
          const __m256i out_16_6 = _mm256_srai_epi32(out_16_4, DCT_CONST_BITS);
          const __m256i out_16_7 = _mm256_srai_epi32(out_16_5, DCT_CONST_BITS);
          const __m256i out_08_6 = _mm256_srai_epi32(out_08_4, DCT_CONST_BITS);
          const __m256i out_08_7 = _mm256_srai_epi32(out_08_5, DCT_CONST_BITS);
          const __m256i out_24_6 = _mm256_srai_epi32(out_24_4, DCT_CONST_BITS);
          const __m256i out_24_7 = _mm256_srai_epi32(out_24_5, DCT_CONST_BITS);
          // Combine
          out[0] = _mm256_packs_epi32(out_00_6, out_00_7);
          out[16] = _mm256_packs_epi32(out_16_6, out_16_7);
          out[8] = _mm256_packs_epi32(out_08_6, out_08_7);
          out[24] = _mm256_packs_epi32(out_24_6, out_24_7);
        }
        {
          const __m256i s2_09_0 = _mm256_unpacklo_epi16(step1[9], step1[14]);
          const __m256i s2_09_1 = _mm256_unpackhi_epi16(step1[9], step1[14]);
          const __m256i s2_10_0 = _mm256_unpacklo_epi16(step1[10], step1[13]);
          const __m256i s2_10_1 = _mm256_unpackhi_epi16(step1[10], step1[13]);
          const __m256i s2_09_2 = _mm256_madd_epi16(s2_09_0, k__cospi_m08_p24);
          const __m256i s2_09_3 = _mm256_madd_epi16(s2_09_1, k__cospi_m08_p24);
          const __m256i s2_10_2 = _mm256_madd_epi16(s2_10_0, k__cospi_m24_m08);
          const __m256i s2_10_3 = _mm256_madd_epi16(s2_10_1, k__cospi_m24_m08);
          const __m256i s2_13_2 = _mm256_madd_epi16(s2_10_0, k__cospi_m08_p24);
          const __m256i s2_13_3 = _mm256_madd_epi16(s2_10_1, k__cospi_m08_p24);
          const __m256i s2_14_2 = _mm256_madd_epi16(s2_09_0, k__cospi_p24_p08);
          const __m256i s2_14_3 = _mm256_madd_epi16(s2_09_1, k__cospi_p24_p08);
          // dct_const_round_shift
          const __m256i s2_09_4 =
              _mm256_add_epi32(s2_09_2, k__DCT_CONST_ROUNDING);
          const __m256i s2_09_5 =
              _mm256_add_epi32(s2_09_3, k__DCT_CONST_ROUNDING);
          const __m256i s2_10_4 =
              _mm256_add_epi32(s2_10_2, k__DCT_CONST_ROUNDING);
          const __m256i s2_10_5 =
              _mm256_add_epi32(s2_10_3, k__DCT_CONST_ROUNDING);
          const __m256i s2_13_4 =
              _mm256_add_epi32(s2_13_2, k__DCT_CONST_ROUNDING);
          const __m256i s2_13_5 =
              _mm256_add_epi32(s2_13_3, k__DCT_CONST_ROUNDING);
          const __m256i s2_14_4 =
              _mm256_add_epi32(s2_14_2, k__DCT_CONST_ROUNDING);
          const __m256i s2_14_5 =
              _mm256_add_epi32(s2_14_3, k__DCT_CONST_ROUNDING);
          const __m256i s2_09_6 = _mm256_srai_epi32(s2_09_4, DCT_CONST_BITS);
          const __m256i s2_09_7 = _mm256_srai_epi32(s2_09_5, DCT_CONST_BITS);
          const __m256i s2_10_6 = _mm256_srai_epi32(s2_10_4, DCT_CONST_BITS);
          const __m256i s2_10_7 = _mm256_srai_epi32(s2_10_5, DCT_CONST_BITS);
          const __m256i s2_13_6 = _mm256_srai_epi32(s2_13_4, DCT_CONST_BITS);
          const __m256i s2_13_7 = _mm256_srai_epi32(s2_13_5, DCT_CONST_BITS);
          const __m256i s2_14_6 = _mm256_srai_epi32(s2_14_4, DCT_CONST_BITS);
          const __m256i s2_14_7 = _mm256_srai_epi32(s2_14_5, DCT_CONST_BITS);
          // Combine
          step2[9] = _mm256_packs_epi32(s2_09_6, s2_09_7);
          step2[10] = _mm256_packs_epi32(s2_10_6, s2_10_7);
          step2[13] = _mm256_packs_epi32(s2_13_6, s2_13_7);
          step2[14] = _mm256_packs_epi32(s2_14_6, s2_14_7);
        }
        {
          step2[16] = _mm256_add_epi16(step1[19], step3[16]);
          step2[17] = _mm256_add_epi16(step1[18], step3[17]);
          step2[18] = _mm256_sub_epi16(step3[17], step1[18]);
          step2[19] = _mm256_sub_epi16(step3[16], step1[19]);
          step2[20] = _mm256_sub_epi16(step3[23], step1[20]);
          step2[21] = _mm256_sub_epi16(step3[22], step1[21]);
          step2[22] = _mm256_add_epi16(step1[21], step3[22]);
          step2[23] = _mm256_add_epi16(step1[20], step3[23]);
          step2[24] = _mm256_add_epi16(step1[27], step3[24]);
          step2[25] = _mm256_add_epi16(step1[26], step3[25]);
          step2[26] = _mm256_sub_epi16(step3[25], step1[26]);
          step2[27] = _mm256_sub_epi16(step3[24], step1[27]);
          step2[28] = _mm256_sub_epi16(step3[31], step1[28]);
          step2[29] = _mm256_sub_epi16(step3[30], step1[29]);
          step2[30] = _mm256_add_epi16(step1[29], step3[30]);
          step2[31] = _mm256_add_epi16(step1[28], step3[31]);
        }
        // Stage 6
        {
          const __m256i out_04_0 = _mm256_unpacklo_epi16(step2[4], step2[7]);
          const __m256i out_04_1 = _mm256_unpackhi_epi16(step2[4], step2[7]);
          const __m256i out_20_0 = _mm256_unpacklo_epi16(step2[5], step2[6]);
          const __m256i out_20_1 = _mm256_unpackhi_epi16(step2[5], step2[6]);
          const __m256i out_12_0 = _mm256_unpacklo_epi16(step2[5], step2[6]);
          const __m256i out_12_1 = _mm256_unpackhi_epi16(step2[5], step2[6]);
          const __m256i out_28_0 = _mm256_unpacklo_epi16(step2[4], step2[7]);
          const __m256i out_28_1 = _mm256_unpackhi_epi16(step2[4], step2[7]);
          const __m256i out_04_2 =
              _mm256_madd_epi16(out_04_0, k__cospi_p28_p04);
          const __m256i out_04_3 =
              _mm256_madd_epi16(out_04_1, k__cospi_p28_p04);
          const __m256i out_20_2 =
              _mm256_madd_epi16(out_20_0, k__cospi_p12_p20);
          const __m256i out_20_3 =
              _mm256_madd_epi16(out_20_1, k__cospi_p12_p20);
          const __m256i out_12_2 =
              _mm256_madd_epi16(out_12_0, k__cospi_m20_p12);
          const __m256i out_12_3 =
              _mm256_madd_epi16(out_12_1, k__cospi_m20_p12);
          const __m256i out_28_2 =
              _mm256_madd_epi16(out_28_0, k__cospi_m04_p28);
          const __m256i out_28_3 =
              _mm256_madd_epi16(out_28_1, k__cospi_m04_p28);
          // dct_const_round_shift
          const __m256i out_04_4 =
              _mm256_add_epi32(out_04_2, k__DCT_CONST_ROUNDING);
          const __m256i out_04_5 =
              _mm256_add_epi32(out_04_3, k__DCT_CONST_ROUNDING);
          const __m256i out_20_4 =
              _mm256_add_epi32(out_20_2, k__DCT_CONST_ROUNDING);
          const __m256i out_20_5 =
              _mm256_add_epi32(out_20_3, k__DCT_CONST_ROUNDING);
          const __m256i out_12_4 =
              _mm256_add_epi32(out_12_2, k__DCT_CONST_ROUNDING);
          const __m256i out_12_5 =
              _mm256_add_epi32(out_12_3, k__DCT_CONST_ROUNDING);
          const __m256i out_28_4 =
              _mm256_add_epi32(out_28_2, k__DCT_CONST_ROUNDING);
          const __m256i out_28_5 =
              _mm256_add_epi32(out_28_3, k__DCT_CONST_ROUNDING);
          const __m256i out_04_6 = _mm256_srai_epi32(out_04_4, DCT_CONST_BITS);
          const __m256i out_04_7 = _mm256_srai_epi32(out_04_5, DCT_CONST_BITS);
          const __m256i out_20_6 = _mm256_srai_epi32(out_20_4, DCT_CONST_BITS);
          const __m256i out_20_7 = _mm256_srai_epi32(out_20_5, DCT_CONST_BITS);
          const __m256i out_12_6 = _mm256_srai_epi32(out_12_4, DCT_CONST_BITS);
          const __m256i out_12_7 = _mm256_srai_epi32(out_12_5, DCT_CONST_BITS);
          const __m256i out_28_6 = _mm256_srai_epi32(out_28_4, DCT_CONST_BITS);
          const __m256i out_28_7 = _mm256_srai_epi32(out_28_5, DCT_CONST_BITS);
          // Combine
          out[4] = _mm256_packs_epi32(out_04_6, out_04_7);
          out[20] = _mm256_packs_epi32(out_20_6, out_20_7);
          out[12] = _mm256_packs_epi32(out_12_6, out_12_7);
          out[28] = _mm256_packs_epi32(out_28_6, out_28_7);
        }
        {
          step3[8] = _mm256_add_epi16(step2[9], step1[8]);
          step3[9] = _mm256_sub_epi16(step1[8], step2[9]);
          step3[10] = _mm256_sub_epi16(step1[11], step2[10]);
          step3[11] = _mm256_add_epi16(step2[10], step1[11]);
          step3[12] = _mm256_add_epi16(step2[13], step1[12]);
          step3[13] = _mm256_sub_epi16(step1[12], step2[13]);
          step3[14] = _mm256_sub_epi16(step1[15], step2[14]);
          step3[15] = _mm256_add_epi16(step2[14], step1[15]);
        }
        {
          const __m256i s3_17_0 = _mm256_unpacklo_epi16(step2[17], step2[30]);
          const __m256i s3_17_1 = _mm256_unpackhi_epi16(step2[17], step2[30]);
          const __m256i s3_18_0 = _mm256_unpacklo_epi16(step2[18], step2[29]);
          const __m256i s3_18_1 = _mm256_unpackhi_epi16(step2[18], step2[29]);
          const __m256i s3_21_0 = _mm256_unpacklo_epi16(step2[21], step2[26]);
          const __m256i s3_21_1 = _mm256_unpackhi_epi16(step2[21], step2[26]);
          const __m256i s3_22_0 = _mm256_unpacklo_epi16(step2[22], step2[25]);
          const __m256i s3_22_1 = _mm256_unpackhi_epi16(step2[22], step2[25]);
          const __m256i s3_17_2 = _mm256_madd_epi16(s3_17_0, k__cospi_m04_p28);
          const __m256i s3_17_3 = _mm256_madd_epi16(s3_17_1, k__cospi_m04_p28);
          const __m256i s3_18_2 = _mm256_madd_epi16(s3_18_0, k__cospi_m28_m04);
          const __m256i s3_18_3 = _mm256_madd_epi16(s3_18_1, k__cospi_m28_m04);
          const __m256i s3_21_2 = _mm256_madd_epi16(s3_21_0, k__cospi_m20_p12);
          const __m256i s3_21_3 = _mm256_madd_epi16(s3_21_1, k__cospi_m20_p12);
          const __m256i s3_22_2 = _mm256_madd_epi16(s3_22_0, k__cospi_m12_m20);
          const __m256i s3_22_3 = _mm256_madd_epi16(s3_22_1, k__cospi_m12_m20);
          const __m256i s3_25_2 = _mm256_madd_epi16(s3_22_0, k__cospi_m20_p12);
          const __m256i s3_25_3 = _mm256_madd_epi16(s3_22_1, k__cospi_m20_p12);
          const __m256i s3_26_2 = _mm256_madd_epi16(s3_21_0, k__cospi_p12_p20);
          const __m256i s3_26_3 = _mm256_madd_epi16(s3_21_1, k__cospi_p12_p20);
          const __m256i s3_29_2 = _mm256_madd_epi16(s3_18_0, k__cospi_m04_p28);
          const __m256i s3_29_3 = _mm256_madd_epi16(s3_18_1, k__cospi_m04_p28);
          const __m256i s3_30_2 = _mm256_madd_epi16(s3_17_0, k__cospi_p28_p04);
          const __m256i s3_30_3 = _mm256_madd_epi16(s3_17_1, k__cospi_p28_p04);
          // dct_const_round_shift
          const __m256i s3_17_4 =
              _mm256_add_epi32(s3_17_2, k__DCT_CONST_ROUNDING);
          const __m256i s3_17_5 =
              _mm256_add_epi32(s3_17_3, k__DCT_CONST_ROUNDING);
          const __m256i s3_18_4 =
              _mm256_add_epi32(s3_18_2, k__DCT_CONST_ROUNDING);
          const __m256i s3_18_5 =
              _mm256_add_epi32(s3_18_3, k__DCT_CONST_ROUNDING);