aom_dsp/x86/fwd_txfm_impl_sse2.h

/*
 * Copyright (c) 2021, Alliance for Open Media. All rights reserved
 *
 * This source code is subject to the terms of the BSD 3-Clause Clear License
 * and the Alliance for Open Media Patent License 1.0. If the BSD 3-Clause Clear
 * License was not distributed with this source code in the LICENSE file, you
 * can obtain it at aomedia.org/license/software-license/bsd-3-c-c/.  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
 * aomedia.org/license/patent-license/.
 */

#include <emmintrin.h>  // SSE2

#include "config/aom_dsp_rtcd.h"

#include "aom_dsp/txfm_common.h"
#include "aom_dsp/x86/fwd_txfm_sse2.h"
#include "aom_dsp/x86/txfm_common_sse2.h"
#include "aom_ports/mem.h"

// TODO(jingning) The high bit-depth functions need rework for performance.
// After we properly fix the high bit-depth function implementations, this
// file's dependency should be substantially simplified.
#if DCT_HIGH_BIT_DEPTH
#define ADD_EPI16 _mm_adds_epi16
#define SUB_EPI16 _mm_subs_epi16

#else
#define ADD_EPI16 _mm_add_epi16
#define SUB_EPI16 _mm_sub_epi16
#endif

static void FDCT4x4_2D_HELPER(const int16_t *input, int stride, __m128i *in0,
                              __m128i *in1) {
  // Constants
  // These are the coefficients used for the multiplies.
  // In the comments, pN means cos(N pi /64) and mN is -cos(N pi /64),
  // where cospi_N_64 = cos(N pi /64)
  const __m128i k__cospi_A =
      octa_set_epi16(cospi_16_64, cospi_16_64, cospi_16_64, cospi_16_64,
                     cospi_16_64, -cospi_16_64, cospi_16_64, -cospi_16_64);
  const __m128i k__cospi_B =
      octa_set_epi16(cospi_16_64, -cospi_16_64, cospi_16_64, -cospi_16_64,
                     cospi_16_64, cospi_16_64, cospi_16_64, cospi_16_64);
  const __m128i k__cospi_C =
      octa_set_epi16(cospi_8_64, cospi_24_64, cospi_8_64, cospi_24_64,
                     cospi_24_64, -cospi_8_64, cospi_24_64, -cospi_8_64);
  const __m128i k__cospi_D =
      octa_set_epi16(cospi_24_64, -cospi_8_64, cospi_24_64, -cospi_8_64,
                     cospi_8_64, cospi_24_64, cospi_8_64, cospi_24_64);
  const __m128i k__cospi_E =
      octa_set_epi16(cospi_16_64, cospi_16_64, cospi_16_64, cospi_16_64,
                     cospi_16_64, cospi_16_64, cospi_16_64, cospi_16_64);
  const __m128i k__cospi_F =
      octa_set_epi16(cospi_16_64, -cospi_16_64, cospi_16_64, -cospi_16_64,
                     cospi_16_64, -cospi_16_64, cospi_16_64, -cospi_16_64);
  const __m128i k__cospi_G =
      octa_set_epi16(cospi_8_64, cospi_24_64, cospi_8_64, cospi_24_64,
                     -cospi_8_64, -cospi_24_64, -cospi_8_64, -cospi_24_64);
  const __m128i k__cospi_H =
      octa_set_epi16(cospi_24_64, -cospi_8_64, cospi_24_64, -cospi_8_64,
                     -cospi_24_64, cospi_8_64, -cospi_24_64, cospi_8_64);

  const __m128i k__DCT_CONST_ROUNDING = _mm_set1_epi32(DCT_CONST_ROUNDING);
  // This second rounding constant saves doing some extra adds at the end
  const __m128i k__DCT_CONST_ROUNDING2 =
      _mm_set1_epi32(DCT_CONST_ROUNDING + (DCT_CONST_ROUNDING << 1));
  const int DCT_CONST_BITS2 = DCT_CONST_BITS + 2;
  const __m128i k__nonzero_bias_a = _mm_setr_epi16(0, 1, 1, 1, 1, 1, 1, 1);
  const __m128i k__nonzero_bias_b = _mm_setr_epi16(1, 0, 0, 0, 0, 0, 0, 0);

  // Load inputs.
  *in0 = _mm_loadl_epi64((const __m128i *)(input + 0 * stride));
  *in1 = _mm_loadl_epi64((const __m128i *)(input + 1 * stride));
  *in1 = _mm_unpacklo_epi64(
      *in1, _mm_loadl_epi64((const __m128i *)(input + 2 * stride)));
  *in0 = _mm_unpacklo_epi64(
      *in0, _mm_loadl_epi64((const __m128i *)(input + 3 * stride)));
  // in0 = [i0 i1 i2 i3 iC iD iE iF]
  // in1 = [i4 i5 i6 i7 i8 i9 iA iB]
  // multiply by 16 to give some extra precision
  *in0 = _mm_slli_epi16(*in0, 4);
  *in1 = _mm_slli_epi16(*in1, 4);
  // if (i == 0 && input[0]) input[0] += 1;
  // add 1 to the upper left pixel if it is non-zero, which helps reduce
  // the round-trip error
  {
    // The mask will only contain whether the first value is zero, all
    // other comparison will fail as something shifted by 4 (above << 4)
    // can never be equal to one. To increment in the non-zero case, we
    // add the mask and one for the first element:
    //   - if zero, mask = -1, v = v - 1 + 1 = v
    //   - if non-zero, mask = 0, v = v + 0 + 1 = v + 1
    __m128i mask = _mm_cmpeq_epi16(*in0, k__nonzero_bias_a);
    *in0 = _mm_add_epi16(*in0, mask);
    *in0 = _mm_add_epi16(*in0, k__nonzero_bias_b);
  }
  // There are 4 total stages, alternating between an add/subtract stage
  // followed by an multiply-and-add stage.
  {
    // Stage 1: Add/subtract

    // in0 = [i0 i1 i2 i3 iC iD iE iF]
    // in1 = [i4 i5 i6 i7 i8 i9 iA iB]
    const __m128i r0 = _mm_unpacklo_epi16(*in0, *in1);
    const __m128i r1 = _mm_unpackhi_epi16(*in0, *in1);
    // r0 = [i0 i4 i1 i5 i2 i6 i3 i7]
    // r1 = [iC i8 iD i9 iE iA iF iB]
    const __m128i r2 = _mm_shuffle_epi32(r0, 0xB4);
    const __m128i r3 = _mm_shuffle_epi32(r1, 0xB4);
    // r2 = [i0 i4 i1 i5 i3 i7 i2 i6]
    // r3 = [iC i8 iD i9 iF iB iE iA]

    const __m128i t0 = _mm_add_epi16(r2, r3);
    const __m128i t1 = _mm_sub_epi16(r2, r3);
    // t0 = [a0 a4 a1 a5 a3 a7 a2 a6]
    // t1 = [aC a8 aD a9 aF aB aE aA]

    // Stage 2: multiply by constants (which gets us into 32 bits).
    // The constants needed here are:
    // k__cospi_A = [p16 p16 p16 p16 p16 m16 p16 m16]
    // k__cospi_B = [p16 m16 p16 m16 p16 p16 p16 p16]
    // k__cospi_C = [p08 p24 p08 p24 p24 m08 p24 m08]
    // k__cospi_D = [p24 m08 p24 m08 p08 p24 p08 p24]
    const __m128i u0 = _mm_madd_epi16(t0, k__cospi_A);
    const __m128i u2 = _mm_madd_epi16(t0, k__cospi_B);
    const __m128i u1 = _mm_madd_epi16(t1, k__cospi_C);
    const __m128i u3 = _mm_madd_epi16(t1, k__cospi_D);
    // Then add and right-shift to get back to 16-bit range
    const __m128i v0 = _mm_add_epi32(u0, k__DCT_CONST_ROUNDING);
    const __m128i v1 = _mm_add_epi32(u1, k__DCT_CONST_ROUNDING);
    const __m128i v2 = _mm_add_epi32(u2, k__DCT_CONST_ROUNDING);
    const __m128i v3 = _mm_add_epi32(u3, k__DCT_CONST_ROUNDING);
    const __m128i w0 = _mm_srai_epi32(v0, DCT_CONST_BITS);
    const __m128i w1 = _mm_srai_epi32(v1, DCT_CONST_BITS);
    const __m128i w2 = _mm_srai_epi32(v2, DCT_CONST_BITS);
    const __m128i w3 = _mm_srai_epi32(v3, DCT_CONST_BITS);
    // w0 = [b0 b1 b7 b6]
    // w1 = [b8 b9 bF bE]
    // w2 = [b4 b5 b3 b2]
    // w3 = [bC bD bB bA]
    const __m128i x0 = _mm_packs_epi32(w0, w1);
    const __m128i x1 = _mm_packs_epi32(w2, w3);

    // x0 = [b0 b1 b7 b6 b8 b9 bF bE]
    // x1 = [b4 b5 b3 b2 bC bD bB bA]
    *in0 = _mm_shuffle_epi32(x0, 0xD8);
    *in1 = _mm_shuffle_epi32(x1, 0x8D);
    // in0 = [b0 b1 b8 b9 b7 b6 bF bE]
    // in1 = [b3 b2 bB bA b4 b5 bC bD]
  }
  {
    // vertical DCTs finished. Now we do the horizontal DCTs.
    // Stage 3: Add/subtract

    const __m128i t0 = ADD_EPI16(*in0, *in1);
    const __m128i t1 = SUB_EPI16(*in0, *in1);

    // Stage 4: multiply by constants (which gets us into 32 bits).
    {
      // The constants needed here are:
      // k__cospi_E = [p16 p16 p16 p16 p16 p16 p16 p16]
      // k__cospi_F = [p16 m16 p16 m16 p16 m16 p16 m16]
      // k__cospi_G = [p08 p24 p08 p24 m08 m24 m08 m24]
      // k__cospi_H = [p24 m08 p24 m08 m24 p08 m24 p08]
      const __m128i u0 = _mm_madd_epi16(t0, k__cospi_E);
      const __m128i u1 = _mm_madd_epi16(t0, k__cospi_F);
      const __m128i u2 = _mm_madd_epi16(t1, k__cospi_G);
      const __m128i u3 = _mm_madd_epi16(t1, k__cospi_H);
      // Then add and right-shift to get back to 16-bit range
      // but this combines the final right-shift as well to save operations
      // This unusual rounding operations is to maintain bit-accurate
      // compatibility with the c version of this function which has two
      // rounding steps in a row.
      const __m128i v0 = _mm_add_epi32(u0, k__DCT_CONST_ROUNDING2);
      const __m128i v1 = _mm_add_epi32(u1, k__DCT_CONST_ROUNDING2);
      const __m128i v2 = _mm_add_epi32(u2, k__DCT_CONST_ROUNDING2);
      const __m128i v3 = _mm_add_epi32(u3, k__DCT_CONST_ROUNDING2);
      const __m128i w0 = _mm_srai_epi32(v0, DCT_CONST_BITS2);
      const __m128i w1 = _mm_srai_epi32(v1, DCT_CONST_BITS2);
      const __m128i w2 = _mm_srai_epi32(v2, DCT_CONST_BITS2);
      const __m128i w3 = _mm_srai_epi32(v3, DCT_CONST_BITS2);
      // w0 = [o0 o4 o8 oC]
      // w1 = [o2 o6 oA oE]
      // w2 = [o1 o5 o9 oD]
      // w3 = [o3 o7 oB oF]
      // remember the o's are numbered according to the correct output location
      const __m128i x0 = _mm_packs_epi32(w0, w1);
      const __m128i x1 = _mm_packs_epi32(w2, w3);
      {
        // x0 = [o0 o4 o8 oC o2 o6 oA oE]
        // x1 = [o1 o5 o9 oD o3 o7 oB oF]
        const __m128i y0 = _mm_unpacklo_epi16(x0, x1);
        const __m128i y1 = _mm_unpackhi_epi16(x0, x1);
        // y0 = [o0 o1 o4 o5 o8 o9 oC oD]
        // y1 = [o2 o3 o6 o7 oA oB oE oF]
        *in0 = _mm_unpacklo_epi32(y0, y1);
        // in0 = [o0 o1 o2 o3 o4 o5 o6 o7]
        *in1 = _mm_unpackhi_epi32(y0, y1);
        // in1 = [o8 o9 oA oB oC oD oE oF]
      }
    }
  }
}

void FDCT4x4_2D(const int16_t *input, tran_low_t *output, int stride) {
  // This 2D transform implements 4 vertical 1D transforms followed
  // by 4 horizontal 1D transforms.  The multiplies and adds are as given
  // by Chen, Smith and Fralick ('77).  The commands for moving the data
  // around have been minimized by hand.
  // For the purposes of the comments, the 16 inputs are referred to at i0
  // through iF (in raster order), intermediate variables are a0, b0, c0
  // through f, and correspond to the in-place computations mapped to input
  // locations.  The outputs, o0 through oF are labeled according to the
  // output locations.
  __m128i in0, in1;
  FDCT4x4_2D_HELPER(input, stride, &in0, &in1);

  // Post-condition (v + 1) >> 2 is now incorporated into previous
  // add and right-shift commands.  Only 2 store instructions needed
  // because we are using the fact that 1/3 are stored just after 0/2.
  storeu_output(&in0, output + 0 * 4);
  storeu_output(&in1, output + 2 * 4);
}

void FDCT4x4_2D_LP(const int16_t *input, int16_t *output, int stride) {
  __m128i in0, in1;
  FDCT4x4_2D_HELPER(input, stride, &in0, &in1);
  _mm_storeu_si128((__m128i *)(output + 0 * 4), in0);
  _mm_storeu_si128((__m128i *)(output + 2 * 4), in1);
}

void FDCT8x8_2D(const int16_t *input, tran_low_t *output, int stride) {
  int pass;
  // 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.
  const __m128i k__cospi_p16_p16 = _mm_set1_epi16((int16_t)cospi_16_64);
  const __m128i k__cospi_p16_m16 = pair_set_epi16(cospi_16_64, -cospi_16_64);
  const __m128i k__cospi_p24_p08 = pair_set_epi16(cospi_24_64, cospi_8_64);
  const __m128i k__cospi_m08_p24 = pair_set_epi16(-cospi_8_64, cospi_24_64);
  const __m128i k__cospi_p28_p04 = pair_set_epi16(cospi_28_64, cospi_4_64);
  const __m128i k__cospi_m04_p28 = pair_set_epi16(-cospi_4_64, cospi_28_64);
  const __m128i k__cospi_p12_p20 = pair_set_epi16(cospi_12_64, cospi_20_64);
  const __m128i k__cospi_m20_p12 = pair_set_epi16(-cospi_20_64, cospi_12_64);
  const __m128i k__DCT_CONST_ROUNDING = _mm_set1_epi32(DCT_CONST_ROUNDING);
#if DCT_HIGH_BIT_DEPTH
  int overflow;
#endif
  // Load input
  __m128i in0 = _mm_load_si128((const __m128i *)(input + 0 * stride));
  __m128i in1 = _mm_load_si128((const __m128i *)(input + 1 * stride));
  __m128i in2 = _mm_load_si128((const __m128i *)(input + 2 * stride));
  __m128i in3 = _mm_load_si128((const __m128i *)(input + 3 * stride));
  __m128i in4 = _mm_load_si128((const __m128i *)(input + 4 * stride));
  __m128i in5 = _mm_load_si128((const __m128i *)(input + 5 * stride));
  __m128i in6 = _mm_load_si128((const __m128i *)(input + 6 * stride));
  __m128i in7 = _mm_load_si128((const __m128i *)(input + 7 * stride));
  // Pre-condition input (shift by two)
  in0 = _mm_slli_epi16(in0, 2);
  in1 = _mm_slli_epi16(in1, 2);
  in2 = _mm_slli_epi16(in2, 2);
  in3 = _mm_slli_epi16(in3, 2);
  in4 = _mm_slli_epi16(in4, 2);
  in5 = _mm_slli_epi16(in5, 2);
  in6 = _mm_slli_epi16(in6, 2);
  in7 = _mm_slli_epi16(in7, 2);

  // We do two passes, first the columns, then the rows. The results of the
  // first pass are transposed so that the same column code can be reused. The
  // results of the second pass are also transposed so that the rows (processed
  // as columns) are put back in row positions.
  for (pass = 0; pass < 2; pass++) {
    // To store results of each pass before the transpose.
    __m128i res0, res1, res2, res3, res4, res5, res6, res7;
    // Add/subtract
    const __m128i q0 = ADD_EPI16(in0, in7);
    const __m128i q1 = ADD_EPI16(in1, in6);
    const __m128i q2 = ADD_EPI16(in2, in5);
    const __m128i q3 = ADD_EPI16(in3, in4);
    const __m128i q4 = SUB_EPI16(in3, in4);
    const __m128i q5 = SUB_EPI16(in2, in5);
    const __m128i q6 = SUB_EPI16(in1, in6);
    const __m128i q7 = SUB_EPI16(in0, in7);
#if DCT_HIGH_BIT_DEPTH
    if (pass == 1) {
      overflow =
          check_epi16_overflow_x8(&q0, &q1, &q2, &q3, &q4, &q5, &q6, &q7);
      if (overflow) {
        aom_highbd_fdct8x8_c(input, output, stride);
        return;
      }
    }
#endif  // DCT_HIGH_BIT_DEPTH
    // Work on first four results
    {
      // Add/subtract
      const __m128i r0 = ADD_EPI16(q0, q3);
      const __m128i r1 = ADD_EPI16(q1, q2);
      const __m128i r2 = SUB_EPI16(q1, q2);
      const __m128i r3 = SUB_EPI16(q0, q3);
#if DCT_HIGH_BIT_DEPTH
      overflow = check_epi16_overflow_x4(&r0, &r1, &r2, &r3);
      if (overflow) {
        aom_highbd_fdct8x8_c(input, output, stride);
        return;
      }
#endif  // DCT_HIGH_BIT_DEPTH
      // Interleave to do the multiply by constants which gets us into 32bits
      {
        const __m128i t0 = _mm_unpacklo_epi16(r0, r1);
        const __m128i t1 = _mm_unpackhi_epi16(r0, r1);
        const __m128i t2 = _mm_unpacklo_epi16(r2, r3);
        const __m128i t3 = _mm_unpackhi_epi16(r2, r3);
        const __m128i u0 = _mm_madd_epi16(t0, k__cospi_p16_p16);
        const __m128i u1 = _mm_madd_epi16(t1, k__cospi_p16_p16);
        const __m128i u2 = _mm_madd_epi16(t0, k__cospi_p16_m16);
        const __m128i u3 = _mm_madd_epi16(t1, k__cospi_p16_m16);
        const __m128i u4 = _mm_madd_epi16(t2, k__cospi_p24_p08);
        const __m128i u5 = _mm_madd_epi16(t3, k__cospi_p24_p08);
        const __m128i u6 = _mm_madd_epi16(t2, k__cospi_m08_p24);
        const __m128i u7 = _mm_madd_epi16(t3, k__cospi_m08_p24);
        // dct_const_round_shift
        const __m128i v0 = _mm_add_epi32(u0, k__DCT_CONST_ROUNDING);
        const __m128i v1 = _mm_add_epi32(u1, k__DCT_CONST_ROUNDING);
        const __m128i v2 = _mm_add_epi32(u2, k__DCT_CONST_ROUNDING);
        const __m128i v3 = _mm_add_epi32(u3, k__DCT_CONST_ROUNDING);
        const __m128i v4 = _mm_add_epi32(u4, k__DCT_CONST_ROUNDING);
        const __m128i v5 = _mm_add_epi32(u5, k__DCT_CONST_ROUNDING);
        const __m128i v6 = _mm_add_epi32(u6, k__DCT_CONST_ROUNDING);
        const __m128i v7 = _mm_add_epi32(u7, k__DCT_CONST_ROUNDING);
        const __m128i w0 = _mm_srai_epi32(v0, DCT_CONST_BITS);
        const __m128i w1 = _mm_srai_epi32(v1, DCT_CONST_BITS);
        const __m128i w2 = _mm_srai_epi32(v2, DCT_CONST_BITS);
        const __m128i w3 = _mm_srai_epi32(v3, DCT_CONST_BITS);
        const __m128i w4 = _mm_srai_epi32(v4, DCT_CONST_BITS);
        const __m128i w5 = _mm_srai_epi32(v5, DCT_CONST_BITS);
        const __m128i w6 = _mm_srai_epi32(v6, DCT_CONST_BITS);
        const __m128i w7 = _mm_srai_epi32(v7, DCT_CONST_BITS);
        // Combine
        res0 = _mm_packs_epi32(w0, w1);
        res4 = _mm_packs_epi32(w2, w3);
        res2 = _mm_packs_epi32(w4, w5);
        res6 = _mm_packs_epi32(w6, w7);
#if DCT_HIGH_BIT_DEPTH
        overflow = check_epi16_overflow_x4(&res0, &res4, &res2, &res6);
        if (overflow) {
          aom_highbd_fdct8x8_c(input, output, stride);
          return;
        }
#endif  // DCT_HIGH_BIT_DEPTH
      }
    }
    // Work on next four results
    {
      // Interleave to do the multiply by constants which gets us into 32bits
      const __m128i d0 = _mm_unpacklo_epi16(q6, q5);
      const __m128i d1 = _mm_unpackhi_epi16(q6, q5);
      const __m128i e0 = _mm_madd_epi16(d0, k__cospi_p16_m16);
      const __m128i e1 = _mm_madd_epi16(d1, k__cospi_p16_m16);
      const __m128i e2 = _mm_madd_epi16(d0, k__cospi_p16_p16);
      const __m128i e3 = _mm_madd_epi16(d1, k__cospi_p16_p16);
      // dct_const_round_shift
      const __m128i f0 = _mm_add_epi32(e0, k__DCT_CONST_ROUNDING);
      const __m128i f1 = _mm_add_epi32(e1, k__DCT_CONST_ROUNDING);
      const __m128i f2 = _mm_add_epi32(e2, k__DCT_CONST_ROUNDING);
      const __m128i f3 = _mm_add_epi32(e3, k__DCT_CONST_ROUNDING);
      const __m128i s0 = _mm_srai_epi32(f0, DCT_CONST_BITS);
      const __m128i s1 = _mm_srai_epi32(f1, DCT_CONST_BITS);
      const __m128i s2 = _mm_srai_epi32(f2, DCT_CONST_BITS);
      const __m128i s3 = _mm_srai_epi32(f3, DCT_CONST_BITS);
      // Combine
      const __m128i r0 = _mm_packs_epi32(s0, s1);
      const __m128i r1 = _mm_packs_epi32(s2, s3);
#if DCT_HIGH_BIT_DEPTH
      overflow = check_epi16_overflow_x2(&r0, &r1);
      if (overflow) {
        aom_highbd_fdct8x8_c(input, output, stride);
        return;
      }
#endif  // DCT_HIGH_BIT_DEPTH
      {
        // Add/subtract
        const __m128i x0 = ADD_EPI16(q4, r0);
        const __m128i x1 = SUB_EPI16(q4, r0);
        const __m128i x2 = SUB_EPI16(q7, r1);
        const __m128i x3 = ADD_EPI16(q7, r1);
#if DCT_HIGH_BIT_DEPTH
        overflow = check_epi16_overflow_x4(&x0, &x1, &x2, &x3);
        if (overflow) {
          aom_highbd_fdct8x8_c(input, output, stride);
          return;
        }
#endif  // DCT_HIGH_BIT_DEPTH
        // Interleave to do the multiply by constants which gets us into 32bits
        {
          const __m128i t0 = _mm_unpacklo_epi16(x0, x3);
          const __m128i t1 = _mm_unpackhi_epi16(x0, x3);
          const __m128i t2 = _mm_unpacklo_epi16(x1, x2);
          const __m128i t3 = _mm_unpackhi_epi16(x1, x2);
          const __m128i u0 = _mm_madd_epi16(t0, k__cospi_p28_p04);
          const __m128i u1 = _mm_madd_epi16(t1, k__cospi_p28_p04);
          const __m128i u2 = _mm_madd_epi16(t0, k__cospi_m04_p28);
          const __m128i u3 = _mm_madd_epi16(t1, k__cospi_m04_p28);
          const __m128i u4 = _mm_madd_epi16(t2, k__cospi_p12_p20);
          const __m128i u5 = _mm_madd_epi16(t3, k__cospi_p12_p20);
          const __m128i u6 = _mm_madd_epi16(t2, k__cospi_m20_p12);
          const __m128i u7 = _mm_madd_epi16(t3, k__cospi_m20_p12);
          // dct_const_round_shift
          const __m128i v0 = _mm_add_epi32(u0, k__DCT_CONST_ROUNDING);
          const __m128i v1 = _mm_add_epi32(u1, k__DCT_CONST_ROUNDING);
          const __m128i v2 = _mm_add_epi32(u2, k__DCT_CONST_ROUNDING);
          const __m128i v3 = _mm_add_epi32(u3, k__DCT_CONST_ROUNDING);
          const __m128i v4 = _mm_add_epi32(u4, k__DCT_CONST_ROUNDING);
          const __m128i v5 = _mm_add_epi32(u5, k__DCT_CONST_ROUNDING);
          const __m128i v6 = _mm_add_epi32(u6, k__DCT_CONST_ROUNDING);
          const __m128i v7 = _mm_add_epi32(u7, k__DCT_CONST_ROUNDING);
          const __m128i w0 = _mm_srai_epi32(v0, DCT_CONST_BITS);
          const __m128i w1 = _mm_srai_epi32(v1, DCT_CONST_BITS);
          const __m128i w2 = _mm_srai_epi32(v2, DCT_CONST_BITS);
          const __m128i w3 = _mm_srai_epi32(v3, DCT_CONST_BITS);
          const __m128i w4 = _mm_srai_epi32(v4, DCT_CONST_BITS);
          const __m128i w5 = _mm_srai_epi32(v5, DCT_CONST_BITS);
          const __m128i w6 = _mm_srai_epi32(v6, DCT_CONST_BITS);
          const __m128i w7 = _mm_srai_epi32(v7, DCT_CONST_BITS);
          // Combine
          res1 = _mm_packs_epi32(w0, w1);
          res7 = _mm_packs_epi32(w2, w3);
          res5 = _mm_packs_epi32(w4, w5);
          res3 = _mm_packs_epi32(w6, w7);
#if DCT_HIGH_BIT_DEPTH
          overflow = check_epi16_overflow_x4(&res1, &res7, &res5, &res3);
          if (overflow) {
            aom_highbd_fdct8x8_c(input, output, stride);
            return;
          }
#endif  // DCT_HIGH_BIT_DEPTH
        }
      }
    }
    // Transpose the 8x8.
    {
      // 00 01 02 03 04 05 06 07
      // 10 11 12 13 14 15 16 17
      // 20 21 22 23 24 25 26 27
      // 30 31 32 33 34 35 36 37
      // 40 41 42 43 44 45 46 47
      // 50 51 52 53 54 55 56 57
      // 60 61 62 63 64 65 66 67
      // 70 71 72 73 74 75 76 77
      const __m128i tr0_0 = _mm_unpacklo_epi16(res0, res1);
      const __m128i tr0_1 = _mm_unpacklo_epi16(res2, res3);
      const __m128i tr0_2 = _mm_unpackhi_epi16(res0, res1);
      const __m128i tr0_3 = _mm_unpackhi_epi16(res2, res3);
      const __m128i tr0_4 = _mm_unpacklo_epi16(res4, res5);
      const __m128i tr0_5 = _mm_unpacklo_epi16(res6, res7);
      const __m128i tr0_6 = _mm_unpackhi_epi16(res4, res5);
      const __m128i tr0_7 = _mm_unpackhi_epi16(res6, res7);
      // 00 10 01 11 02 12 03 13
      // 20 30 21 31 22 32 23 33
      // 04 14 05 15 06 16 07 17
      // 24 34 25 35 26 36 27 37
      // 40 50 41 51 42 52 43 53
      // 60 70 61 71 62 72 63 73
      // 54 54 55 55 56 56 57 57
      // 64 74 65 75 66 76 67 77
      const __m128i tr1_0 = _mm_unpacklo_epi32(tr0_0, tr0_1);
      const __m128i tr1_1 = _mm_unpacklo_epi32(tr0_2, tr0_3);
      const __m128i tr1_2 = _mm_unpackhi_epi32(tr0_0, tr0_1);
      const __m128i tr1_3 = _mm_unpackhi_epi32(tr0_2, tr0_3);
      const __m128i tr1_4 = _mm_unpacklo_epi32(tr0_4, tr0_5);
      const __m128i tr1_5 = _mm_unpacklo_epi32(tr0_6, tr0_7);
      const __m128i tr1_6 = _mm_unpackhi_epi32(tr0_4, tr0_5);
      const __m128i tr1_7 = _mm_unpackhi_epi32(tr0_6, tr0_7);
      // 00 10 20 30 01 11 21 31
      // 40 50 60 70 41 51 61 71
      // 02 12 22 32 03 13 23 33
      // 42 52 62 72 43 53 63 73
      // 04 14 24 34 05 15 21 36
      // 44 54 64 74 45 55 61 76
      // 06 16 26 36 07 17 27 37
      // 46 56 66 76 47 57 67 77
      in0 = _mm_unpacklo_epi64(tr1_0, tr1_4);
      in1 = _mm_unpackhi_epi64(tr1_0, tr1_4);
      in2 = _mm_unpacklo_epi64(tr1_2, tr1_6);
      in3 = _mm_unpackhi_epi64(tr1_2, tr1_6);
      in4 = _mm_unpacklo_epi64(tr1_1, tr1_5);
      in5 = _mm_unpackhi_epi64(tr1_1, tr1_5);
      in6 = _mm_unpacklo_epi64(tr1_3, tr1_7);
      in7 = _mm_unpackhi_epi64(tr1_3, tr1_7);
      // 00 10 20 30 40 50 60 70
      // 01 11 21 31 41 51 61 71
      // 02 12 22 32 42 52 62 72
      // 03 13 23 33 43 53 63 73
      // 04 14 24 34 44 54 64 74
      // 05 15 25 35 45 55 65 75
      // 06 16 26 36 46 56 66 76
      // 07 17 27 37 47 57 67 77
    }
  }
  // Post-condition output and store it
  {
    // Post-condition (division by two)
    //    division of two 16 bits signed numbers using shifts
    //    n / 2 = (n - (n >> 15)) >> 1
    const __m128i sign_in0 = _mm_srai_epi16(in0, 15);
    const __m128i sign_in1 = _mm_srai_epi16(in1, 15);
    const __m128i sign_in2 = _mm_srai_epi16(in2, 15);
    const __m128i sign_in3 = _mm_srai_epi16(in3, 15);
    const __m128i sign_in4 = _mm_srai_epi16(in4, 15);
    const __m128i sign_in5 = _mm_srai_epi16(in5, 15);
    const __m128i sign_in6 = _mm_srai_epi16(in6, 15);
    const __m128i sign_in7 = _mm_srai_epi16(in7, 15);
    in0 = _mm_sub_epi16(in0, sign_in0);
    in1 = _mm_sub_epi16(in1, sign_in1);
    in2 = _mm_sub_epi16(in2, sign_in2);
    in3 = _mm_sub_epi16(in3, sign_in3);
    in4 = _mm_sub_epi16(in4, sign_in4);
    in5 = _mm_sub_epi16(in5, sign_in5);
    in6 = _mm_sub_epi16(in6, sign_in6);
    in7 = _mm_sub_epi16(in7, sign_in7);
    in0 = _mm_srai_epi16(in0, 1);
    in1 = _mm_srai_epi16(in1, 1);
    in2 = _mm_srai_epi16(in2, 1);
    in3 = _mm_srai_epi16(in3, 1);
    in4 = _mm_srai_epi16(in4, 1);
    in5 = _mm_srai_epi16(in5, 1);
    in6 = _mm_srai_epi16(in6, 1);
    in7 = _mm_srai_epi16(in7, 1);
    // store results
    store_output(&in0, (output + 0 * 8));
    store_output(&in1, (output + 1 * 8));
    store_output(&in2, (output + 2 * 8));
    store_output(&in3, (output + 3 * 8));
    store_output(&in4, (output + 4 * 8));
    store_output(&in5, (output + 5 * 8));
    store_output(&in6, (output + 6 * 8));
    store_output(&in7, (output + 7 * 8));
  }
}

#undef ADD_EPI16
#undef SUB_EPI16