/*
 * Copyright (c) 2016, Alliance for Open Media. All rights reserved
 *
 * 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.
 */
#include <assert.h>
#include <smmintrin.h> /* SSE4.1 */

#include "./av1_rtcd.h"
#include "./aom_config.h"
#include "av1/common/av1_inv_txfm1d_cfg.h"
#include "av1/common/x86/highbd_txfm_utility_sse4.h"

static INLINE void load_buffer_4x4(const int32_t *coeff, __m128i *in) {
  in[0] = _mm_load_si128((const __m128i *)(coeff + 0));
  in[1] = _mm_load_si128((const __m128i *)(coeff + 4));
  in[2] = _mm_load_si128((const __m128i *)(coeff + 8));
  in[3] = _mm_load_si128((const __m128i *)(coeff + 12));
}

static void idct4x4_sse4_1(__m128i *in, int bit) {
  const int32_t *cospi = cospi_arr(bit);
  const __m128i cospi32 = _mm_set1_epi32(cospi[32]);
  const __m128i cospi48 = _mm_set1_epi32(cospi[48]);
  const __m128i cospi16 = _mm_set1_epi32(cospi[16]);
  const __m128i cospim16 = _mm_set1_epi32(-cospi[16]);
  const __m128i rnding = _mm_set1_epi32(1 << (bit - 1));
  __m128i u0, u1, u2, u3;
  __m128i v0, v1, v2, v3, x, y;

  v0 = _mm_unpacklo_epi32(in[0], in[1]);
  v1 = _mm_unpackhi_epi32(in[0], in[1]);
  v2 = _mm_unpacklo_epi32(in[2], in[3]);
  v3 = _mm_unpackhi_epi32(in[2], in[3]);

  u0 = _mm_unpacklo_epi64(v0, v2);
  u1 = _mm_unpackhi_epi64(v0, v2);
  u2 = _mm_unpacklo_epi64(v1, v3);
  u3 = _mm_unpackhi_epi64(v1, v3);

  x = _mm_mullo_epi32(u0, cospi32);
  y = _mm_mullo_epi32(u2, cospi32);
  v0 = _mm_add_epi32(x, y);
  v0 = _mm_add_epi32(v0, rnding);
  v0 = _mm_srai_epi32(v0, bit);

  v1 = _mm_sub_epi32(x, y);
  v1 = _mm_add_epi32(v1, rnding);
  v1 = _mm_srai_epi32(v1, bit);

  x = _mm_mullo_epi32(u1, cospi48);
  y = _mm_mullo_epi32(u3, cospim16);
  v2 = _mm_add_epi32(x, y);
  v2 = _mm_add_epi32(v2, rnding);
  v2 = _mm_srai_epi32(v2, bit);

  x = _mm_mullo_epi32(u1, cospi16);
  y = _mm_mullo_epi32(u3, cospi48);
  v3 = _mm_add_epi32(x, y);
  v3 = _mm_add_epi32(v3, rnding);
  v3 = _mm_srai_epi32(v3, bit);

  in[0] = _mm_add_epi32(v0, v3);
  in[1] = _mm_add_epi32(v1, v2);
  in[2] = _mm_sub_epi32(v1, v2);
  in[3] = _mm_sub_epi32(v0, v3);
}

static void iadst4x4_sse4_1(__m128i *in, int bit) {
  const int32_t *sinpi = sinpi_arr(bit);
  const __m128i rnding = _mm_set1_epi32(1 << (bit - 1));
  const __m128i sinpi1 = _mm_set1_epi32((int)sinpi[1]);
  const __m128i sinpi2 = _mm_set1_epi32((int)sinpi[2]);
  const __m128i sinpi3 = _mm_set1_epi32((int)sinpi[3]);
  const __m128i sinpi4 = _mm_set1_epi32((int)sinpi[4]);
  __m128i t;
  __m128i s0, s1, s2, s3, s4, s5, s6, s7;
  __m128i x0, x1, x2, x3;
  __m128i u0, u1, u2, u3;
  __m128i v0, v1, v2, v3;

  v0 = _mm_unpacklo_epi32(in[0], in[1]);
  v1 = _mm_unpackhi_epi32(in[0], in[1]);
  v2 = _mm_unpacklo_epi32(in[2], in[3]);
  v3 = _mm_unpackhi_epi32(in[2], in[3]);

  x0 = _mm_unpacklo_epi64(v0, v2);
  x1 = _mm_unpackhi_epi64(v0, v2);
  x2 = _mm_unpacklo_epi64(v1, v3);
  x3 = _mm_unpackhi_epi64(v1, v3);

  s0 = _mm_mullo_epi32(x0, sinpi1);
  s1 = _mm_mullo_epi32(x0, sinpi2);
  s2 = _mm_mullo_epi32(x1, sinpi3);
  s3 = _mm_mullo_epi32(x2, sinpi4);
  s4 = _mm_mullo_epi32(x2, sinpi1);
  s5 = _mm_mullo_epi32(x3, sinpi2);
  s6 = _mm_mullo_epi32(x3, sinpi4);
  t = _mm_sub_epi32(x0, x2);
  s7 = _mm_add_epi32(t, x3);

  t = _mm_add_epi32(s0, s3);
  s0 = _mm_add_epi32(t, s5);
  t = _mm_sub_epi32(s1, s4);
  s1 = _mm_sub_epi32(t, s6);
  s3 = s2;
  s2 = _mm_mullo_epi32(s7, sinpi3);

  u0 = _mm_add_epi32(s0, s3);
  u1 = _mm_add_epi32(s1, s3);
  u2 = s2;
  t = _mm_add_epi32(s0, s1);
  u3 = _mm_sub_epi32(t, s3);

  u0 = _mm_add_epi32(u0, rnding);
  u0 = _mm_srai_epi32(u0, bit);

  u1 = _mm_add_epi32(u1, rnding);
  u1 = _mm_srai_epi32(u1, bit);

  u2 = _mm_add_epi32(u2, rnding);
  u2 = _mm_srai_epi32(u2, bit);

  u3 = _mm_add_epi32(u3, rnding);
  u3 = _mm_srai_epi32(u3, bit);

  in[0] = u0;
  in[1] = u1;
  in[2] = u2;
  in[3] = u3;
}

static INLINE void round_shift_4x4(__m128i *in, int shift) {
  __m128i rnding = _mm_set1_epi32(1 << (shift - 1));

  in[0] = _mm_add_epi32(in[0], rnding);
  in[1] = _mm_add_epi32(in[1], rnding);
  in[2] = _mm_add_epi32(in[2], rnding);
  in[3] = _mm_add_epi32(in[3], rnding);

  in[0] = _mm_srai_epi32(in[0], shift);
  in[1] = _mm_srai_epi32(in[1], shift);
  in[2] = _mm_srai_epi32(in[2], shift);
  in[3] = _mm_srai_epi32(in[3], shift);
}

static INLINE __m128i highbd_clamp_epi16(__m128i u, int bd) {
  const __m128i zero = _mm_setzero_si128();
  const __m128i one = _mm_set1_epi16(1);
  const __m128i max = _mm_sub_epi16(_mm_slli_epi16(one, bd), one);
  __m128i clamped, mask;

  mask = _mm_cmpgt_epi16(u, max);
  clamped = _mm_andnot_si128(mask, u);
  mask = _mm_and_si128(mask, max);
  clamped = _mm_or_si128(mask, clamped);
  mask = _mm_cmpgt_epi16(clamped, zero);
  clamped = _mm_and_si128(clamped, mask);

  return clamped;
}

static void write_buffer_4x4(__m128i *in, uint16_t *output, int stride,
                             int fliplr, int flipud, int shift, int bd) {
  const __m128i zero = _mm_setzero_si128();
  __m128i u0, u1, u2, u3;
  __m128i v0, v1, v2, v3;

  round_shift_4x4(in, shift);

  v0 = _mm_loadl_epi64((__m128i const *)(output + 0 * stride));
  v1 = _mm_loadl_epi64((__m128i const *)(output + 1 * stride));
  v2 = _mm_loadl_epi64((__m128i const *)(output + 2 * stride));
  v3 = _mm_loadl_epi64((__m128i const *)(output + 3 * stride));

  v0 = _mm_unpacklo_epi16(v0, zero);
  v1 = _mm_unpacklo_epi16(v1, zero);
  v2 = _mm_unpacklo_epi16(v2, zero);
  v3 = _mm_unpacklo_epi16(v3, zero);

  if (fliplr) {
    in[0] = _mm_shuffle_epi32(in[0], 0x1B);
    in[1] = _mm_shuffle_epi32(in[1], 0x1B);
    in[2] = _mm_shuffle_epi32(in[2], 0x1B);
    in[3] = _mm_shuffle_epi32(in[3], 0x1B);
  }

  if (flipud) {
    u0 = _mm_add_epi32(in[3], v0);
    u1 = _mm_add_epi32(in[2], v1);
    u2 = _mm_add_epi32(in[1], v2);
    u3 = _mm_add_epi32(in[0], v3);
  } else {
    u0 = _mm_add_epi32(in[0], v0);
    u1 = _mm_add_epi32(in[1], v1);
    u2 = _mm_add_epi32(in[2], v2);
    u3 = _mm_add_epi32(in[3], v3);
  }

  v0 = _mm_packus_epi32(u0, u1);
  v2 = _mm_packus_epi32(u2, u3);

  u0 = highbd_clamp_epi16(v0, bd);
  u2 = highbd_clamp_epi16(v2, bd);

  v0 = _mm_unpacklo_epi64(u0, u0);
  v1 = _mm_unpackhi_epi64(u0, u0);
  v2 = _mm_unpacklo_epi64(u2, u2);
  v3 = _mm_unpackhi_epi64(u2, u2);

  _mm_storel_epi64((__m128i *)(output + 0 * stride), v0);
  _mm_storel_epi64((__m128i *)(output + 1 * stride), v1);
  _mm_storel_epi64((__m128i *)(output + 2 * stride), v2);
  _mm_storel_epi64((__m128i *)(output + 3 * stride), v3);
}

void av1_inv_txfm2d_add_4x4_sse4_1(const int32_t *coeff, uint16_t *output,
                                   int stride, TX_TYPE tx_type, int bd) {
  __m128i in[4];
  const int8_t *shift = inv_txfm_shift_ls[TX_4X4];
  const int txw_idx = get_txw_idx(TX_4X4);
  const int txh_idx = get_txh_idx(TX_4X4);

  switch (tx_type) {
    case DCT_DCT:
      load_buffer_4x4(coeff, in);
      idct4x4_sse4_1(in, inv_cos_bit_row[txw_idx][txh_idx]);
      idct4x4_sse4_1(in, inv_cos_bit_col[txw_idx][txh_idx]);
      write_buffer_4x4(in, output, stride, 0, 0, -shift[1], bd);
      break;
    case ADST_DCT:
      load_buffer_4x4(coeff, in);
      idct4x4_sse4_1(in, inv_cos_bit_row[txw_idx][txh_idx]);
      iadst4x4_sse4_1(in, inv_cos_bit_col[txw_idx][txh_idx]);
      write_buffer_4x4(in, output, stride, 0, 0, -shift[1], bd);
      break;
    case DCT_ADST:
      load_buffer_4x4(coeff, in);
      iadst4x4_sse4_1(in, inv_cos_bit_row[txw_idx][txh_idx]);
      idct4x4_sse4_1(in, inv_cos_bit_col[txw_idx][txh_idx]);
      write_buffer_4x4(in, output, stride, 0, 0, -shift[1], bd);
      break;
    case ADST_ADST:
      load_buffer_4x4(coeff, in);
      iadst4x4_sse4_1(in, inv_cos_bit_row[txw_idx][txh_idx]);
      iadst4x4_sse4_1(in, inv_cos_bit_col[txw_idx][txh_idx]);
      write_buffer_4x4(in, output, stride, 0, 0, -shift[1], bd);
      break;
    case FLIPADST_DCT:
      load_buffer_4x4(coeff, in);
      idct4x4_sse4_1(in, inv_cos_bit_row[txw_idx][txh_idx]);
      iadst4x4_sse4_1(in, inv_cos_bit_col[txw_idx][txh_idx]);
      write_buffer_4x4(in, output, stride, 0, 1, -shift[1], bd);
      break;
    case DCT_FLIPADST:
      load_buffer_4x4(coeff, in);
      iadst4x4_sse4_1(in, inv_cos_bit_row[txw_idx][txh_idx]);
      idct4x4_sse4_1(in, inv_cos_bit_col[txw_idx][txh_idx]);
      write_buffer_4x4(in, output, stride, 1, 0, -shift[1], bd);
      break;
    case FLIPADST_FLIPADST:
      load_buffer_4x4(coeff, in);
      iadst4x4_sse4_1(in, inv_cos_bit_row[txw_idx][txh_idx]);
      iadst4x4_sse4_1(in, inv_cos_bit_col[txw_idx][txh_idx]);
      write_buffer_4x4(in, output, stride, 1, 1, -shift[1], bd);
      break;
    case ADST_FLIPADST:
      load_buffer_4x4(coeff, in);
      iadst4x4_sse4_1(in, inv_cos_bit_row[txw_idx][txh_idx]);
      iadst4x4_sse4_1(in, inv_cos_bit_col[txw_idx][txh_idx]);
      write_buffer_4x4(in, output, stride, 1, 0, -shift[1], bd);
      break;
    case FLIPADST_ADST:
      load_buffer_4x4(coeff, in);
      iadst4x4_sse4_1(in, inv_cos_bit_row[txw_idx][txh_idx]);
      iadst4x4_sse4_1(in, inv_cos_bit_col[txw_idx][txh_idx]);
      write_buffer_4x4(in, output, stride, 0, 1, -shift[1], bd);
      break;
    default: assert(0);
  }
}

// 8x8
static void load_buffer_8x8(const int32_t *coeff, __m128i *in) {
  in[0] = _mm_load_si128((const __m128i *)(coeff + 0));
  in[1] = _mm_load_si128((const __m128i *)(coeff + 4));
  in[2] = _mm_load_si128((const __m128i *)(coeff + 8));
  in[3] = _mm_load_si128((const __m128i *)(coeff + 12));
  in[4] = _mm_load_si128((const __m128i *)(coeff + 16));
  in[5] = _mm_load_si128((const __m128i *)(coeff + 20));
  in[6] = _mm_load_si128((const __m128i *)(coeff + 24));
  in[7] = _mm_load_si128((const __m128i *)(coeff + 28));
  in[8] = _mm_load_si128((const __m128i *)(coeff + 32));
  in[9] = _mm_load_si128((const __m128i *)(coeff + 36));
  in[10] = _mm_load_si128((const __m128i *)(coeff + 40));
  in[11] = _mm_load_si128((const __m128i *)(coeff + 44));
  in[12] = _mm_load_si128((const __m128i *)(coeff + 48));
  in[13] = _mm_load_si128((const __m128i *)(coeff + 52));
  in[14] = _mm_load_si128((const __m128i *)(coeff + 56));
  in[15] = _mm_load_si128((const __m128i *)(coeff + 60));
}

static void idct8x8_sse4_1(__m128i *in, __m128i *out, int bit) {
  const int32_t *cospi = cospi_arr(bit);
  const __m128i cospi56 = _mm_set1_epi32(cospi[56]);
  const __m128i cospim8 = _mm_set1_epi32(-cospi[8]);
  const __m128i cospi24 = _mm_set1_epi32(cospi[24]);
  const __m128i cospim40 = _mm_set1_epi32(-cospi[40]);
  const __m128i cospi40 = _mm_set1_epi32(cospi[40]);
  const __m128i cospi8 = _mm_set1_epi32(cospi[8]);
  const __m128i cospi32 = _mm_set1_epi32(cospi[32]);
  const __m128i cospi48 = _mm_set1_epi32(cospi[48]);
  const __m128i cospim16 = _mm_set1_epi32(-cospi[16]);
  const __m128i cospi16 = _mm_set1_epi32(cospi[16]);
  const __m128i rnding = _mm_set1_epi32(1 << (bit - 1));
  __m128i u0, u1, u2, u3, u4, u5, u6, u7;
  __m128i v0, v1, v2, v3, v4, v5, v6, v7;
  __m128i x, y;
  int col;

  // Note:
  //  Even column: 0, 2, ..., 14
  //  Odd column: 1, 3, ..., 15
  //  one even column plus one odd column constructs one row (8 coeffs)
  //  total we have 8 rows (8x8).
  for (col = 0; col < 2; ++col) {
    // stage 0
    // stage 1
    // stage 2
    u0 = in[0 * 2 + col];
    u1 = in[4 * 2 + col];
    u2 = in[2 * 2 + col];
    u3 = in[6 * 2 + col];

    x = _mm_mullo_epi32(in[1 * 2 + col], cospi56);
    y = _mm_mullo_epi32(in[7 * 2 + col], cospim8);
    u4 = _mm_add_epi32(x, y);
    u4 = _mm_add_epi32(u4, rnding);
    u4 = _mm_srai_epi32(u4, bit);

    x = _mm_mullo_epi32(in[1 * 2 + col], cospi8);
    y = _mm_mullo_epi32(in[7 * 2 + col], cospi56);
    u7 = _mm_add_epi32(x, y);
    u7 = _mm_add_epi32(u7, rnding);
    u7 = _mm_srai_epi32(u7, bit);

    x = _mm_mullo_epi32(in[5 * 2 + col], cospi24);
    y = _mm_mullo_epi32(in[3 * 2 + col], cospim40);
    u5 = _mm_add_epi32(x, y);
    u5 = _mm_add_epi32(u5, rnding);
    u5 = _mm_srai_epi32(u5, bit);

    x = _mm_mullo_epi32(in[5 * 2 + col], cospi40);
    y = _mm_mullo_epi32(in[3 * 2 + col], cospi24);
    u6 = _mm_add_epi32(x, y);
    u6 = _mm_add_epi32(u6, rnding);
    u6 = _mm_srai_epi32(u6, bit);

    // stage 3
    x = _mm_mullo_epi32(u0, cospi32);
    y = _mm_mullo_epi32(u1, cospi32);
    v0 = _mm_add_epi32(x, y);
    v0 = _mm_add_epi32(v0, rnding);
    v0 = _mm_srai_epi32(v0, bit);

    v1 = _mm_sub_epi32(x, y);
    v1 = _mm_add_epi32(v1, rnding);
    v1 = _mm_srai_epi32(v1, bit);

    x = _mm_mullo_epi32(u2, cospi48);
    y = _mm_mullo_epi32(u3, cospim16);
    v2 = _mm_add_epi32(x, y);
    v2 = _mm_add_epi32(v2, rnding);
    v2 = _mm_srai_epi32(v2, bit);

    x = _mm_mullo_epi32(u2, cospi16);
    y = _mm_mullo_epi32(u3, cospi48);
    v3 = _mm_add_epi32(x, y);
    v3 = _mm_add_epi32(v3, rnding);
    v3 = _mm_srai_epi32(v3, bit);

    v4 = _mm_add_epi32(u4, u5);
    v5 = _mm_sub_epi32(u4, u5);
    v6 = _mm_sub_epi32(u7, u6);
    v7 = _mm_add_epi32(u6, u7);

    // stage 4
    u0 = _mm_add_epi32(v0, v3);
    u1 = _mm_add_epi32(v1, v2);
    u2 = _mm_sub_epi32(v1, v2);
    u3 = _mm_sub_epi32(v0, v3);
    u4 = v4;
    u7 = v7;

    x = _mm_mullo_epi32(v5, cospi32);
    y = _mm_mullo_epi32(v6, cospi32);
    u6 = _mm_add_epi32(y, x);
    u6 = _mm_add_epi32(u6, rnding);
    u6 = _mm_srai_epi32(u6, bit);

    u5 = _mm_sub_epi32(y, x);
    u5 = _mm_add_epi32(u5, rnding);
    u5 = _mm_srai_epi32(u5, bit);

    // stage 5
    out[0 * 2 + col] = _mm_add_epi32(u0, u7);
    out[1 * 2 + col] = _mm_add_epi32(u1, u6);
    out[2 * 2 + col] = _mm_add_epi32(u2, u5);
    out[3 * 2 + col] = _mm_add_epi32(u3, u4);
    out[4 * 2 + col] = _mm_sub_epi32(u3, u4);
    out[5 * 2 + col] = _mm_sub_epi32(u2, u5);
    out[6 * 2 + col] = _mm_sub_epi32(u1, u6);
    out[7 * 2 + col] = _mm_sub_epi32(u0, u7);
  }
}

static void iadst8x8_sse4_1(__m128i *in, __m128i *out, int bit) {
  const int32_t *cospi = cospi_arr(bit);
  const __m128i cospi4 = _mm_set1_epi32(cospi[4]);
  const __m128i cospi60 = _mm_set1_epi32(cospi[60]);
  const __m128i cospi20 = _mm_set1_epi32(cospi[20]);
  const __m128i cospi44 = _mm_set1_epi32(cospi[44]);
  const __m128i cospi36 = _mm_set1_epi32(cospi[36]);
  const __m128i cospi28 = _mm_set1_epi32(cospi[28]);
  const __m128i cospi52 = _mm_set1_epi32(cospi[52]);
  const __m128i cospi12 = _mm_set1_epi32(cospi[12]);
  const __m128i cospi16 = _mm_set1_epi32(cospi[16]);
  const __m128i cospi48 = _mm_set1_epi32(cospi[48]);
  const __m128i cospim48 = _mm_set1_epi32(-cospi[48]);
  const __m128i cospi32 = _mm_set1_epi32(cospi[32]);
  const __m128i rnding = _mm_set1_epi32(1 << (bit - 1));
  const __m128i kZero = _mm_setzero_si128();
  __m128i u[8], v[8], x;

  // Even 8 points: 0, 2, ..., 14
  // stage 0
  // stage 1
  // stage 2
  // (1)
  u[0] = _mm_mullo_epi32(in[14], cospi4);
  x = _mm_mullo_epi32(in[0], cospi60);
  u[0] = _mm_add_epi32(u[0], x);
  u[0] = _mm_add_epi32(u[0], rnding);
  u[0] = _mm_srai_epi32(u[0], bit);

  u[1] = _mm_mullo_epi32(in[14], cospi60);
  x = _mm_mullo_epi32(in[0], cospi4);
  u[1] = _mm_sub_epi32(u[1], x);
  u[1] = _mm_add_epi32(u[1], rnding);
  u[1] = _mm_srai_epi32(u[1], bit);

  // (2)
  u[2] = _mm_mullo_epi32(in[10], cospi20);
  x = _mm_mullo_epi32(in[4], cospi44);
  u[2] = _mm_add_epi32(u[2], x);
  u[2] = _mm_add_epi32(u[2], rnding);
  u[2] = _mm_srai_epi32(u[2], bit);

  u[3] = _mm_mullo_epi32(in[10], cospi44);
  x = _mm_mullo_epi32(in[4], cospi20);
  u[3] = _mm_sub_epi32(u[3], x);
  u[3] = _mm_add_epi32(u[3], rnding);
  u[3] = _mm_srai_epi32(u[3], bit);

  // (3)
  u[4] = _mm_mullo_epi32(in[6], cospi36);
  x = _mm_mullo_epi32(in[8], cospi28);
  u[4] = _mm_add_epi32(u[4], x);
  u[4] = _mm_add_epi32(u[4], rnding);
  u[4] = _mm_srai_epi32(u[4], bit);

  u[5] = _mm_mullo_epi32(in[6], cospi28);
  x = _mm_mullo_epi32(in[8], cospi36);
  u[5] = _mm_sub_epi32(u[5], x);
  u[5] = _mm_add_epi32(u[5], rnding);
  u[5] = _mm_srai_epi32(u[5], bit);

  // (4)
  u[6] = _mm_mullo_epi32(in[2], cospi52);
  x = _mm_mullo_epi32(in[12], cospi12);
  u[6] = _mm_add_epi32(u[6], x);
  u[6] = _mm_add_epi32(u[6], rnding);
  u[6] = _mm_srai_epi32(u[6], bit);

  u[7] = _mm_mullo_epi32(in[2], cospi12);
  x = _mm_mullo_epi32(in[12], cospi52);
  u[7] = _mm_sub_epi32(u[7], x);
  u[7] = _mm_add_epi32(u[7], rnding);
  u[7] = _mm_srai_epi32(u[7], bit);

  // stage 3
  v[0] = _mm_add_epi32(u[0], u[4]);
  v[4] = _mm_sub_epi32(u[0], u[4]);
  v[1] = _mm_add_epi32(u[1], u[5]);
  v[5] = _mm_sub_epi32(u[1], u[5]);
  v[2] = _mm_add_epi32(u[2], u[6]);
  v[6] = _mm_sub_epi32(u[2], u[6]);
  v[3] = _mm_add_epi32(u[3], u[7]);
  v[7] = _mm_sub_epi32(u[3], u[7]);

  // stage 4
  u[0] = v[0];
  u[1] = v[1];
  u[2] = v[2];
  u[3] = v[3];

  u[4] = _mm_mullo_epi32(v[4], cospi16);
  x = _mm_mullo_epi32(v[5], cospi48);
  u[4] = _mm_add_epi32(u[4], x);
  u[4] = _mm_add_epi32(u[4], rnding);
  u[4] = _mm_srai_epi32(u[4], bit);

  u[5] = _mm_mullo_epi32(v[4], cospi48);
  x = _mm_mullo_epi32(v[5], cospi16);
  u[5] = _mm_sub_epi32(u[5], x);
  u[5] = _mm_add_epi32(u[5], rnding);
  u[5] = _mm_srai_epi32(u[5], bit);

  u[6] = _mm_mullo_epi32(v[6], cospim48);
  x = _mm_mullo_epi32(v[7], cospi16);
  u[6] = _mm_add_epi32(u[6], x);
  u[6] = _mm_add_epi32(u[6], rnding);
  u[6] = _mm_srai_epi32(u[6], bit);

  u[7] = _mm_mullo_epi32(v[6], cospi16);
  x = _mm_mullo_epi32(v[7], cospim48);
  u[7] = _mm_sub_epi32(u[7], x);
  u[7] = _mm_add_epi32(u[7], rnding);
  u[7] = _mm_srai_epi32(u[7], bit);

  // stage 5
  v[0] = _mm_add_epi32(u[0], u[2]);
  v[2] = _mm_sub_epi32(u[0], u[2]);
  v[1] = _mm_add_epi32(u[1], u[3]);
  v[3] = _mm_sub_epi32(u[1], u[3]);
  v[4] = _mm_add_epi32(u[4], u[6]);
  v[6] = _mm_sub_epi32(u[4], u[6]);
  v[5] = _mm_add_epi32(u[5], u[7]);
  v[7] = _mm_sub_epi32(u[5], u[7]);

  // stage 6
  u[0] = v[0];
  u[1] = v[1];
  u[4] = v[4];
  u[5] = v[5];

  v[0] = _mm_mullo_epi32(v[2], cospi32);
  x = _mm_mullo_epi32(v[3], cospi32);
  u[2] = _mm_add_epi32(v[0], x);
  u[2] = _mm_add_epi32(u[2], rnding);
  u[2] = _mm_srai_epi32(u[2], bit);

  u[3] = _mm_sub_epi32(v[0], x);
  u[3] = _mm_add_epi32(u[3], rnding);
  u[3] = _mm_srai_epi32(u[3], bit);

  v[0] = _mm_mullo_epi32(v[6], cospi32);
  x = _mm_mullo_epi32(v[7], cospi32);
  u[6] = _mm_add_epi32(v[0], x);
  u[6] = _mm_add_epi32(u[6], rnding);
  u[6] = _mm_srai_epi32(u[6], bit);

  u[7] = _mm_sub_epi32(v[0], x);
  u[7] = _mm_add_epi32(u[7], rnding);
  u[7] = _mm_srai_epi32(u[7], bit);

  // stage 7
  out[0] = u[0];
  out[2] = _mm_sub_epi32(kZero, u[4]);
  out[4] = u[6];
  out[6] = _mm_sub_epi32(kZero, u[2]);
  out[8] = u[3];
  out[10] = _mm_sub_epi32(kZero, u[7]);
  out[12] = u[5];
  out[14] = _mm_sub_epi32(kZero, u[1]);

  // Odd 8 points: 1, 3, ..., 15
  // stage 0
  // stage 1
  // stage 2
  // (1)
  u[0] = _mm_mullo_epi32(in[15], cospi4);
  x = _mm_mullo_epi32(in[1], cospi60);
  u[0] = _mm_add_epi32(u[0], x);
  u[0] = _mm_add_epi32(u[0], rnding);
  u[0] = _mm_srai_epi32(u[0], bit);

  u[1] = _mm_mullo_epi32(in[15], cospi60);
  x = _mm_mullo_epi32(in[1], cospi4);
  u[1] = _mm_sub_epi32(u[1], x);
  u[1] = _mm_add_epi32(u[1], rnding);
  u[1] = _mm_srai_epi32(u[1], bit);

  // (2)
  u[2] = _mm_mullo_epi32(in[11], cospi20);
  x = _mm_mullo_epi32(in[5], cospi44);
  u[2] = _mm_add_epi32(u[2], x);
  u[2] = _mm_add_epi32(u[2], rnding);
  u[2] = _mm_srai_epi32(u[2], bit);

  u[3] = _mm_mullo_epi32(in[11], cospi44);
  x = _mm_mullo_epi32(in[5], cospi20);
  u[3] = _mm_sub_epi32(u[3], x);
  u[3] = _mm_add_epi32(u[3], rnding);
  u[3] = _mm_srai_epi32(u[3], bit);

  // (3)
  u[4] = _mm_mullo_epi32(in[7], cospi36);
  x = _mm_mullo_epi32(in[9], cospi28);
  u[4] = _mm_add_epi32(u[4], x);
  u[4] = _mm_add_epi32(u[4], rnding);
  u[4] = _mm_srai_epi32(u[4], bit);

  u[5] = _mm_mullo_epi32(in[7], cospi28);
  x = _mm_mullo_epi32(in[9], cospi36);
  u[5] = _mm_sub_epi32(u[5], x);
  u[5] = _mm_add_epi32(u[5], rnding);
  u[5] = _mm_srai_epi32(u[5], bit);

  // (4)
  u[6] = _mm_mullo_epi32(in[3], cospi52);
  x = _mm_mullo_epi32(in[13], cospi12);
  u[6] = _mm_add_epi32(u[6], x);
  u[6] = _mm_add_epi32(u[6], rnding);
  u[6] = _mm_srai_epi32(u[6], bit);

  u[7] = _mm_mullo_epi32(in[3], cospi12);
  x = _mm_mullo_epi32(in[13], cospi52);
  u[7] = _mm_sub_epi32(u[7], x);
  u[7] = _mm_add_epi32(u[7], rnding);
  u[7] = _mm_srai_epi32(u[7], bit);

  // stage 3
  v[0] = _mm_add_epi32(u[0], u[4]);
  v[4] = _mm_sub_epi32(u[0], u[4]);
  v[1] = _mm_add_epi32(u[1], u[5]);
  v[5] = _mm_sub_epi32(u[1], u[5]);
  v[2] = _mm_add_epi32(u[2], u[6]);
  v[6] = _mm_sub_epi32(u[2], u[6]);
  v[3] = _mm_add_epi32(u[3], u[7]);
  v[7] = _mm_sub_epi32(u[3], u[7]);

  // stage 4
  u[0] = v[0];
  u[1] = v[1];
  u[2] = v[2];
  u[3] = v[3];

  u[4] = _mm_mullo_epi32(v[4], cospi16);
  x = _mm_mullo_epi32(v[5], cospi48);
  u[4] = _mm_add_epi32(u[4], x);
  u[4] = _mm_add_epi32(u[4], rnding);
  u[4] = _mm_srai_epi32(u[4], bit);

  u[5] = _mm_mullo_epi32(v[4], cospi48);
  x = _mm_mullo_epi32(v[5], cospi16);
  u[5] = _mm_sub_epi32(u[5], x);
  u[5] = _mm_add_epi32(u[5], rnding);
  u[5] = _mm_srai_epi32(u[5], bit);

  u[6] = _mm_mullo_epi32(v[6], cospim48);
  x = _mm_mullo_epi32(v[7], cospi16);
  u[6] = _mm_add_epi32(u[6], x);
  u[6] = _mm_add_epi32(u[6], rnding);
  u[6] = _mm_srai_epi32(u[6], bit);

  u[7] = _mm_mullo_epi32(v[6], cospi16);
  x = _mm_mullo_epi32(v[7], cospim48);
  u[7] = _mm_sub_epi32(u[7], x);
  u[7] = _mm_add_epi32(u[7], rnding);
  u[7] = _mm_srai_epi32(u[7], bit);

  // stage 5
  v[0] = _mm_add_epi32(u[0], u[2]);
  v[2] = _mm_sub_epi32(u[0], u[2]);
  v[1] = _mm_add_epi32(u[1], u[3]);
  v[3] = _mm_sub_epi32(u[1], u[3]);
  v[4] = _mm_add_epi32(u[4], u[6]);
  v[6] = _mm_sub_epi32(u[4], u[6]);
  v[5] = _mm_add_epi32(u[5], u[7]);
  v[7] = _mm_sub_epi32(u[5], u[7]);

  // stage 6
  u[0] = v[0];
  u[1] = v[1];
  u[4] = v[4];
  u[5] = v[5];

  v[0] = _mm_mullo_epi32(v[2], cospi32);
  x = _mm_mullo_epi32(v[3], cospi32);
  u[2] = _mm_add_epi32(v[0], x);
  u[2] = _mm_add_epi32(u[2], rnding);
  u[2] = _mm_srai_epi32(u[2], bit);

  u[3] = _mm_sub_epi32(v[0], x);
  u[3] = _mm_add_epi32(u[3], rnding);
  u[3] = _mm_srai_epi32(u[3], bit);

  v[0] = _mm_mullo_epi32(v[6], cospi32);
  x = _mm_mullo_epi32(v[7], cospi32);
  u[6] = _mm_add_epi32(v[0], x);
  u[6] = _mm_add_epi32(u[6], rnding);
  u[6] = _mm_srai_epi32(u[6], bit);

  u[7] = _mm_sub_epi32(v[0], x);
  u[7] = _mm_add_epi32(u[7], rnding);
  u[7] = _mm_srai_epi32(u[7], bit);

  // stage 7
  out[1] = u[0];
  out[3] = _mm_sub_epi32(kZero, u[4]);
  out[5] = u[6];
  out[7] = _mm_sub_epi32(kZero, u[2]);
  out[9] = u[3];
  out[11] = _mm_sub_epi32(kZero, u[7]);
  out[13] = u[5];
  out[15] = _mm_sub_epi32(kZero, u[1]);
}

static void round_shift_8x8(__m128i *in, int shift) {
  round_shift_4x4(&in[0], shift);
  round_shift_4x4(&in[4], shift);
  round_shift_4x4(&in[8], shift);
  round_shift_4x4(&in[12], shift);
}

static __m128i get_recon_8x8(const __m128i pred, __m128i res_lo, __m128i res_hi,
                             int fliplr, int bd) {
  __m128i x0, x1;
  const __m128i zero = _mm_setzero_si128();

  x0 = _mm_unpacklo_epi16(pred, zero);
  x1 = _mm_unpackhi_epi16(pred, zero);

  if (fliplr) {
    res_lo = _mm_shuffle_epi32(res_lo, 0x1B);
    res_hi = _mm_shuffle_epi32(res_hi, 0x1B);
    x0 = _mm_add_epi32(res_hi, x0);
    x1 = _mm_add_epi32(res_lo, x1);

  } else {
    x0 = _mm_add_epi32(res_lo, x0);
    x1 = _mm_add_epi32(res_hi, x1);
  }

  x0 = _mm_packus_epi32(x0, x1);
  return highbd_clamp_epi16(x0, bd);
}

static void write_buffer_8x8(__m128i *in, uint16_t *output, int stride,
                             int fliplr, int flipud, int shift, int bd) {
  __m128i u0, u1, u2, u3, u4, u5, u6, u7;
  __m128i v0, v1, v2, v3, v4, v5, v6, v7;

  round_shift_8x8(in, shift);

  v0 = _mm_load_si128((__m128i const *)(output + 0 * stride));
  v1 = _mm_load_si128((__m128i const *)(output + 1 * stride));
  v2 = _mm_load_si128((__m128i const *)(output + 2 * stride));
  v3 = _mm_load_si128((__m128i const *)(output + 3 * stride));
  v4 = _mm_load_si128((__m128i const *)(output + 4 * stride));
  v5 = _mm_load_si128((__m128i const *)(output + 5 * stride));
  v6 = _mm_load_si128((__m128i const *)(output + 6 * stride));
  v7 = _mm_load_si128((__m128i const *)(output + 7 * stride));

  if (flipud) {
    u0 = get_recon_8x8(v0, in[14], in[15], fliplr, bd);
    u1 = get_recon_8x8(v1, in[12], in[13], fliplr, bd);
    u2 = get_recon_8x8(v2, in[10], in[11], fliplr, bd);
    u3 = get_recon_8x8(v3, in[8], in[9], fliplr, bd);
    u4 = get_recon_8x8(v4, in[6], in[7], fliplr, bd);
    u5 = get_recon_8x8(v5, in[4], in[5], fliplr, bd);
    u6 = get_recon_8x8(v6, in[2], in[3], fliplr, bd);
    u7 = get_recon_8x8(v7, in[0], in[1], fliplr, bd);
  } else {
    u0 = get_recon_8x8(v0, in[0], in[1], fliplr, bd);
    u1 = get_recon_8x8(v1, in[2], in[3], fliplr, bd);
    u2 = get_recon_8x8(v2, in[4], in[5], fliplr, bd);
    u3 = get_recon_8x8(v3, in[6], in[7], fliplr, bd);
    u4 = get_recon_8x8(v4, in[8], in[9], fliplr, bd);
    u5 = get_recon_8x8(v5, in[10], in[11], fliplr, bd);
    u6 = get_recon_8x8(v6, in[12], in[13], fliplr, bd);
    u7 = get_recon_8x8(v7, in[14], in[15], fliplr, bd);
  }

  _mm_store_si128((__m128i *)(output + 0 * stride), u0);
  _mm_store_si128((__m128i *)(output + 1 * stride), u1);
  _mm_store_si128((__m128i *)(output + 2 * stride), u2);
  _mm_store_si128((__m128i *)(output + 3 * stride), u3);
  _mm_store_si128((__m128i *)(output + 4 * stride), u4);
  _mm_store_si128((__m128i *)(output + 5 * stride), u5);
  _mm_store_si128((__m128i *)(output + 6 * stride), u6);
  _mm_store_si128((__m128i *)(output + 7 * stride), u7);
}

void av1_inv_txfm2d_add_8x8_sse4_1(const int32_t *coeff, uint16_t *output,
                                   int stride, TX_TYPE tx_type, int bd) {
  __m128i in[16], out[16];
  const int8_t *shift = inv_txfm_shift_ls[TX_8X8];
  const int txw_idx = get_txw_idx(TX_8X8);
  const int txh_idx = get_txh_idx(TX_8X8);

  switch (tx_type) {
    case DCT_DCT:
      load_buffer_8x8(coeff, in);
      transpose_8x8(in, out);
      idct8x8_sse4_1(out, in, inv_cos_bit_row[txw_idx][txh_idx]);
      transpose_8x8(in, out);
      round_shift_8x8(out, -shift[0]);
      idct8x8_sse4_1(out, in, inv_cos_bit_col[txw_idx][txh_idx]);
      write_buffer_8x8(in, output, stride, 0, 0, -shift[1], bd);
      break;
    case DCT_ADST:
      load_buffer_8x8(coeff, in);
      transpose_8x8(in, out);
      iadst8x8_sse4_1(out, in, inv_cos_bit_row[txw_idx][txh_idx]);
      transpose_8x8(in, out);
      round_shift_8x8(out, -shift[0]);
      idct8x8_sse4_1(out, in, inv_cos_bit_col[txw_idx][txh_idx]);
      write_buffer_8x8(in, output, stride, 0, 0, -shift[1], bd);
      break;
    case ADST_DCT:
      load_buffer_8x8(coeff, in);
      transpose_8x8(in, out);
      idct8x8_sse4_1(out, in, inv_cos_bit_row[txw_idx][txh_idx]);
      transpose_8x8(in, out);
      round_shift_8x8(out, -shift[0]);
      iadst8x8_sse4_1(out, in, inv_cos_bit_col[txw_idx][txh_idx]);
      write_buffer_8x8(in, output, stride, 0, 0, -shift[1], bd);
      break;
    case ADST_ADST:
      load_buffer_8x8(coeff, in);
      transpose_8x8(in, out);
      iadst8x8_sse4_1(out, in, inv_cos_bit_row[txw_idx][txh_idx]);
      transpose_8x8(in, out);
      round_shift_8x8(out, -shift[0]);
      iadst8x8_sse4_1(out, in, inv_cos_bit_col[txw_idx][txh_idx]);
      write_buffer_8x8(in, output, stride, 0, 0, -shift[1], bd);
      break;
    case FLIPADST_DCT:
      load_buffer_8x8(coeff, in);
      transpose_8x8(in, out);
      idct8x8_sse4_1(out, in, inv_cos_bit_row[txw_idx][txh_idx]);
      transpose_8x8(in, out);
      round_shift_8x8(out, -shift[0]);
      iadst8x8_sse4_1(out, in, inv_cos_bit_col[txw_idx][txh_idx]);
      write_buffer_8x8(in, output, stride, 0, 1, -shift[1], bd);
      break;
    case DCT_FLIPADST:
      load_buffer_8x8(coeff, in);
      transpose_8x8(in, out);
      iadst8x8_sse4_1(out, in, inv_cos_bit_row[txw_idx][txh_idx]);
      transpose_8x8(in, out);
      round_shift_8x8(out, -shift[0]);
      idct8x8_sse4_1(out, in, inv_cos_bit_col[txw_idx][txh_idx]);
      write_buffer_8x8(in, output, stride, 1, 0, -shift[1], bd);
      break;
    case ADST_FLIPADST:
      load_buffer_8x8(coeff, in);
      transpose_8x8(in, out);
      iadst8x8_sse4_1(out, in, inv_cos_bit_row[txw_idx][txh_idx]);
      transpose_8x8(in, out);
      round_shift_8x8(out, -shift[0]);
      iadst8x8_sse4_1(out, in, inv_cos_bit_col[txw_idx][txh_idx]);
      write_buffer_8x8(in, output, stride, 1, 0, -shift[1], bd);
      break;
    case FLIPADST_FLIPADST:
      load_buffer_8x8(coeff, in);
      transpose_8x8(in, out);
      iadst8x8_sse4_1(out, in, inv_cos_bit_row[txw_idx][txh_idx]);
      transpose_8x8(in, out);
      round_shift_8x8(out, -shift[0]);
      iadst8x8_sse4_1(out, in, inv_cos_bit_col[txw_idx][txh_idx]);
      write_buffer_8x8(in, output, stride, 1, 1, -shift[1], bd);
      break;
    case FLIPADST_ADST:
      load_buffer_8x8(coeff, in);
      transpose_8x8(in, out);
      iadst8x8_sse4_1(out, in, inv_cos_bit_row[txw_idx][txh_idx]);
      transpose_8x8(in, out);
      round_shift_8x8(out, -shift[0]);
      iadst8x8_sse4_1(out, in, inv_cos_bit_col[txw_idx][txh_idx]);
      write_buffer_8x8(in, output, stride, 0, 1, -shift[1], bd);
      break;
    default: assert(0);
  }
}

// 16x16
static void load_buffer_16x16(const int32_t *coeff, __m128i *in) {
  int i;
  for (i = 0; i < 64; ++i) {
    in[i] = _mm_load_si128((const __m128i *)(coeff + (i << 2)));
  }
}

static void assign_8x8_input_from_16x16(const __m128i *in, __m128i *in8x8,
                                        int col) {
  int i;
  for (i = 0; i < 16; i += 2) {
    in8x8[i] = in[col];
    in8x8[i + 1] = in[col + 1];
    col += 4;
  }
}

static void swap_addr(uint16_t **output1, uint16_t **output2) {
  uint16_t *tmp;
  tmp = *output1;
  *output1 = *output2;
  *output2 = tmp;
}

static void write_buffer_16x16(__m128i *in, uint16_t *output, int stride,
                               int fliplr, int flipud, int shift, int bd) {
  __m128i in8x8[16];
  uint16_t *leftUp = &output[0];
  uint16_t *rightUp = &output[8];
  uint16_t *leftDown = &output[8 * stride];
  uint16_t *rightDown = &output[8 * stride + 8];

  if (fliplr) {
    swap_addr(&leftUp, &rightUp);
    swap_addr(&leftDown, &rightDown);
  }

  if (flipud) {
    swap_addr(&leftUp, &leftDown);
    swap_addr(&rightUp, &rightDown);
  }

  // Left-up quarter
  assign_8x8_input_from_16x16(in, in8x8, 0);
  write_buffer_8x8(in8x8, leftUp, stride, fliplr, flipud, shift, bd);

  // Right-up quarter
  assign_8x8_input_from_16x16(in, in8x8, 2);
  write_buffer_8x8(in8x8, rightUp, stride, fliplr, flipud, shift, bd);

  // Left-down quarter
  assign_8x8_input_from_16x16(in, in8x8, 32);
  write_buffer_8x8(in8x8, leftDown, stride, fliplr, flipud, shift, bd);

  // Right-down quarter
  assign_8x8_input_from_16x16(in, in8x8, 34);
  write_buffer_8x8(in8x8, rightDown, stride, fliplr, flipud, shift, bd);
}

static void idct16x16_sse4_1(__m128i *in, __m128i *out, int bit) {
  const int32_t *cospi = cospi_arr(bit);
  const __m128i cospi60 = _mm_set1_epi32(cospi[60]);
  const __m128i cospim4 = _mm_set1_epi32(-cospi[4]);
  const __m128i cospi28 = _mm_set1_epi32(cospi[28]);
  const __m128i cospim36 = _mm_set1_epi32(-cospi[36]);
  const __m128i cospi44 = _mm_set1_epi32(cospi[44]);
  const __m128i cospi20 = _mm_set1_epi32(cospi[20]);
  const __m128i cospim20 = _mm_set1_epi32(-cospi[20]);
  const __m128i cospi12 = _mm_set1_epi32(cospi[12]);
  const __m128i cospim52 = _mm_set1_epi32(-cospi[52]);
  const __m128i cospi52 = _mm_set1_epi32(cospi[52]);
  const __m128i cospi36 = _mm_set1_epi32(cospi[36]);
  const __m128i cospi4 = _mm_set1_epi32(cospi[4]);
  const __m128i cospi56 = _mm_set1_epi32(cospi[56]);
  const __m128i cospim8 = _mm_set1_epi32(-cospi[8]);
  const __m128i cospi24 = _mm_set1_epi32(cospi[24]);
  const __m128i cospim40 = _mm_set1_epi32(-cospi[40]);
  const __m128i cospi40 = _mm_set1_epi32(cospi[40]);
  const __m128i cospi8 = _mm_set1_epi32(cospi[8]);
  const __m128i cospi32 = _mm_set1_epi32(cospi[32]);
  const __m128i cospi48 = _mm_set1_epi32(cospi[48]);
  const __m128i cospi16 = _mm_set1_epi32(cospi[16]);
  const __m128i cospim16 = _mm_set1_epi32(-cospi[16]);
  const __m128i cospim48 = _mm_set1_epi32(-cospi[48]);
  const __m128i rnding = _mm_set1_epi32(1 << (bit - 1));
  __m128i u[16], v[16], x, y;
  int col;

  for (col = 0; col < 4; ++col) {
    // stage 0
    // stage 1
    u[0] = in[0 * 4 + col];
    u[1] = in[8 * 4 + col];
    u[2] = in[4 * 4 + col];
    u[3] = in[12 * 4 + col];
    u[4] = in[2 * 4 + col];
    u[5] = in[10 * 4 + col];
    u[6] = in[6 * 4 + col];
    u[7] = in[14 * 4 + col];
    u[8] = in[1 * 4 + col];
    u[9] = in[9 * 4 + col];
    u[10] = in[5 * 4 + col];
    u[11] = in[13 * 4 + col];
    u[12] = in[3 * 4 + col];
    u[13] = in[11 * 4 + col];
    u[14] = in[7 * 4 + col];
    u[15] = in[15 * 4 + col];

    // stage 2
    v[0] = u[0];
    v[1] = u[1];
    v[2] = u[2];
    v[3] = u[3];
    v[4] = u[4];
    v[5] = u[5];
    v[6] = u[6];
    v[7] = u[7];

    v[8] = half_btf_sse4_1(&cospi60, &u[8], &cospim4, &u[15], &rnding, bit);
    v[9] = half_btf_sse4_1(&cospi28, &u[9], &cospim36, &u[14], &rnding, bit);
    v[10] = half_btf_sse4_1(&cospi44, &u[10], &cospim20, &u[13], &rnding, bit);
    v[11] = half_btf_sse4_1(&cospi12, &u[11], &cospim52, &u[12], &rnding, bit);
    v[12] = half_btf_sse4_1(&cospi52, &u[11], &cospi12, &u[12], &rnding, bit);
    v[13] = half_btf_sse4_1(&cospi20, &u[10], &cospi44, &u[13], &rnding, bit);
    v[14] = half_btf_sse4_1(&cospi36, &u[9], &cospi28, &u[14], &rnding, bit);
    v[15] = half_btf_sse4_1(&cospi4, &u[8], &cospi60, &u[15], &rnding, bit);

    // stage 3
    u[0] = v[0];
    u[1] = v[1];
    u[2] = v[2];
    u[3] = v[3];
    u[4] = half_btf_sse4_1(&cospi56, &v[4], &cospim8, &v[7], &rnding, bit);
    u[5] = half_btf_sse4_1(&cospi24, &v[5], &cospim40, &v[6], &rnding, bit);
    u[6] = half_btf_sse4_1(&cospi40, &v[5], &cospi24, &v[6], &rnding, bit);
    u[7] = half_btf_sse4_1(&cospi8, &v[4], &cospi56, &v[7], &rnding, bit);
    u[8] = _mm_add_epi32(v[8], v[9]);
    u[9] = _mm_sub_epi32(v[8], v[9]);
    u[10] = _mm_sub_epi32(v[11], v[10]);
    u[11] = _mm_add_epi32(v[10], v[11]);
    u[12] = _mm_add_epi32(v[12], v[13]);
    u[13] = _mm_sub_epi32(v[12], v[13]);
    u[14] = _mm_sub_epi32(v[15], v[14]);
    u[15] = _mm_add_epi32(v[14], v[15]);

    // stage 4
    x = _mm_mullo_epi32(u[0], cospi32);
    y = _mm_mullo_epi32(u[1], cospi32);
    v[0] = _mm_add_epi32(x, y);
    v[0] = _mm_add_epi32(v[0], rnding);
    v[0] = _mm_srai_epi32(v[0], bit);

    v[1] = _mm_sub_epi32(x, y);
    v[1] = _mm_add_epi32(v[1], rnding);
    v[1] = _mm_srai_epi32(v[1], bit);

    v[2] = half_btf_sse4_1(&cospi48, &u[2], &cospim16, &u[3], &rnding, bit);
    v[3] = half_btf_sse4_1(&cospi16, &u[2], &cospi48, &u[3], &rnding, bit);
    v[4] = _mm_add_epi32(u[4], u[5]);
    v[5] = _mm_sub_epi32(u[4], u[5]);
    v[6] = _mm_sub_epi32(u[7], u[6]);
    v[7] = _mm_add_epi32(u[6], u[7]);
    v[8] = u[8];
    v[9] = half_btf_sse4_1(&cospim16, &u[9], &cospi48, &u[14], &rnding, bit);
    v[10] = half_btf_sse4_1(&cospim48, &u[10], &cospim16, &u[13], &rnding, bit);
    v[11] = u[11];
    v[12] = u[12];
    v[13] = half_btf_sse4_1(&cospim16, &u[10], &cospi48, &u[13], &rnding, bit);
    v[14] = half_btf_sse4_1(&cospi48, &u[9], &cospi16, &u[14], &rnding, bit);
    v[15] = u[15];

    // stage 5
    u[0] = _mm_add_epi32(v[0], v[3]);
    u[1] = _mm_add_epi32(v[1], v[2]);
    u[2] = _mm_sub_epi32(v[1], v[2]);
    u[3] = _mm_sub_epi32(v[0], v[3]);
    u[4] = v[4];

    x = _mm_mullo_epi32(v[5], cospi32);
    y = _mm_mullo_epi32(v[6], cospi32);
    u[5] = _mm_sub_epi32(y, x);
    u[5] = _mm_add_epi32(u[5], rnding);
    u[5] = _mm_srai_epi32(u[5], bit);

    u[6] = _mm_add_epi32(y, x);
    u[6] = _mm_add_epi32(u[6], rnding);
    u[6] = _mm_srai_epi32(u[6], bit);

    u[7] = v[7];
    u[8] = _mm_add_epi32(v[8], v[11]);
    u[9] = _mm_add_epi32(v[9], v[10]);
    u[10] = _mm_sub_epi32(v[9], v[10]);
    u[11] = _mm_sub_epi32(v[8], v[11]);
    u[12] = _mm_sub_epi32(v[15], v[12]);
    u[13] = _mm_sub_epi32(v[14], v[13]);
    u[14] = _mm_add_epi32(v[13], v[14]);
    u[15] = _mm_add_epi32(v[12], v[15]);

    // stage 6
    v[0] = _mm_add_epi32(u[0], u[7]);
    v[1] = _mm_add_epi32(u[1], u[6]);
    v[2] = _mm_add_epi32(u[2], u[5]);
    v[3] = _mm_add_epi32(u[3], u[4]);
    v[4] = _mm_sub_epi32(u[3], u[4]);
    v[5] = _mm_sub_epi32(u[2], u[5]);
    v[6] = _mm_sub_epi32(u[1], u[6]);
    v[7] = _mm_sub_epi32(u[0], u[7]);
    v[8] = u[8];
    v[9] = u[9];

    x = _mm_mullo_epi32(u[10], cospi32);
    y = _mm_mullo_epi32(u[13], cospi32);
    v[10] = _mm_sub_epi32(y, x);
    v[10] = _mm_add_epi32(v[10], rnding);
    v[10] = _mm_srai_epi32(v[10], bit);

    v[13] = _mm_add_epi32(x, y);
    v[13] = _mm_add_epi32(v[13], rnding);
    v[13] = _mm_srai_epi32(v[13], bit);

    x = _mm_mullo_epi32(u[11], cospi32);
    y = _mm_mullo_epi32(u[12], cospi32);
    v[11] = _mm_sub_epi32(y, x);
    v[11] = _mm_add_epi32(v[11], rnding);
    v[11] = _mm_srai_epi32(v[11], bit);

    v[12] = _mm_add_epi32(x, y);
    v[12] = _mm_add_epi32(v[12], rnding);
    v[12] = _mm_srai_epi32(v[12], bit);

    v[14] = u[14];
    v[15] = u[15];

    // stage 7
    out[0 * 4 + col] = _mm_add_epi32(v[0], v[15]);
    out[1 * 4 + col] = _mm_add_epi32(v[1], v[14]);
    out[2 * 4 + col] = _mm_add_epi32(v[2], v[13]);
    out[3 * 4 + col] = _mm_add_epi32(v[3], v[12]);
    out[4 * 4 + col] = _mm_add_epi32(v[4], v[11]);
    out[5 * 4 + col] = _mm_add_epi32(v[5], v[10]);
    out[6 * 4 + col] = _mm_add_epi32(v[6], v[9]);
    out[7 * 4 + col] = _mm_add_epi32(v[7], v[8]);
    out[8 * 4 + col] = _mm_sub_epi32(v[7], v[8]);
    out[9 * 4 + col] = _mm_sub_epi32(v[6], v[9]);
    out[10 * 4 + col] = _mm_sub_epi32(v[5], v[10]);
    out[11 * 4 + col] = _mm_sub_epi32(v[4], v[11]);
    out[12 * 4 + col] = _mm_sub_epi32(v[3], v[12]);
    out[13 * 4 + col] = _mm_sub_epi32(v[2], v[13]);
    out[14 * 4 + col] = _mm_sub_epi32(v[1], v[14]);
    out[15 * 4 + col] = _mm_sub_epi32(v[0], v[15]);
  }
}

static void iadst16x16_sse4_1(__m128i *in, __m128i *out, int bit) {
  const int32_t *cospi = cospi_arr(bit);
  const __m128i cospi2 = _mm_set1_epi32(cospi[2]);
  const __m128i cospi62 = _mm_set1_epi32(cospi[62]);
  const __m128i cospi10 = _mm_set1_epi32(cospi[10]);
  const __m128i cospi54 = _mm_set1_epi32(cospi[54]);
  const __m128i cospi18 = _mm_set1_epi32(cospi[18]);
  const __m128i cospi46 = _mm_set1_epi32(cospi[46]);
  const __m128i cospi26 = _mm_set1_epi32(cospi[26]);
  const __m128i cospi38 = _mm_set1_epi32(cospi[38]);
  const __m128i cospi34 = _mm_set1_epi32(cospi[34]);
  const __m128i cospi30 = _mm_set1_epi32(cospi[30]);
  const __m128i cospi42 = _mm_set1_epi32(cospi[42]);
  const __m128i cospi22 = _mm_set1_epi32(cospi[22]);
  const __m128i cospi50 = _mm_set1_epi32(cospi[50]);
  const __m128i cospi14 = _mm_set1_epi32(cospi[14]);
  const __m128i cospi58 = _mm_set1_epi32(cospi[58]);
  const __m128i cospi6 = _mm_set1_epi32(cospi[6]);
  const __m128i cospi8 = _mm_set1_epi32(cospi[8]);
  const __m128i cospi56 = _mm_set1_epi32(cospi[56]);
  const __m128i cospi40 = _mm_set1_epi32(cospi[40]);
  const __m128i cospi24 = _mm_set1_epi32(cospi[24]);
  const __m128i cospim56 = _mm_set1_epi32(-cospi[56]);
  const __m128i cospim24 = _mm_set1_epi32(-cospi[24]);
  const __m128i cospi48 = _mm_set1_epi32(cospi[48]);
  const __m128i cospi16 = _mm_set1_epi32(cospi[16]);
  const __m128i cospim48 = _mm_set1_epi32(-cospi[48]);
  const __m128i cospi32 = _mm_set1_epi32(cospi[32]);
  const __m128i rnding = _mm_set1_epi32(1 << (bit - 1));
  __m128i u[16], v[16], x, y;
  const int col_num = 4;
  int col;

  // Calculate the column 0, 1, 2, 3
  for (col = 0; col < col_num; ++col) {
    // stage 0
    // stage 1
    // stage 2
    v[0] = _mm_mullo_epi32(in[15 * col_num + col], cospi2);
    x = _mm_mullo_epi32(in[0 * col_num + col], cospi62);
    v[0] = _mm_add_epi32(v[0], x);
    v[0] = _mm_add_epi32(v[0], rnding);
    v[0] = _mm_srai_epi32(v[0], bit);

    v[1] = _mm_mullo_epi32(in[15 * col_num + col], cospi62);
    x = _mm_mullo_epi32(in[0 * col_num + col], cospi2);
    v[1] = _mm_sub_epi32(v[1], x);
    v[1] = _mm_add_epi32(v[1], rnding);
    v[1] = _mm_srai_epi32(v[1], bit);

    v[2] = _mm_mullo_epi32(in[13 * col_num + col], cospi10);
    x = _mm_mullo_epi32(in[2 * col_num + col], cospi54);
    v[2] = _mm_add_epi32(v[2], x);
    v[2] = _mm_add_epi32(v[2], rnding);
    v[2] = _mm_srai_epi32(v[2], bit);

    v[3] = _mm_mullo_epi32(in[13 * col_num + col], cospi54);
    x = _mm_mullo_epi32(in[2 * col_num + col], cospi10);
    v[3] = _mm_sub_epi32(v[3], x);
    v[3] = _mm_add_epi32(v[3], rnding);
    v[3] = _mm_srai_epi32(v[3], bit);

    v[4] = _mm_mullo_epi32(in[11 * col_num + col], cospi18);
    x = _mm_mullo_epi32(in[4 * col_num + col], cospi46);
    v[4] = _mm_add_epi32(v[4], x);
    v[4] = _mm_add_epi32(v[4], rnding);
    v[4] = _mm_srai_epi32(v[4], bit);

    v[5] = _mm_mullo_epi32(in[11 * col_num + col], cospi46);
    x = _mm_mullo_epi32(in[4 * col_num + col], cospi18);
    v[5] = _mm_sub_epi32(v[5], x);
    v[5] = _mm_add_epi32(v[5], rnding);
    v[5] = _mm_srai_epi32(v[5], bit);

    v[6] = _mm_mullo_epi32(in[9 * col_num + col], cospi26);
    x = _mm_mullo_epi32(in[6 * col_num + col], cospi38);
    v[6] = _mm_add_epi32(v[6], x);
    v[6] = _mm_add_epi32(v[6], rnding);
    v[6] = _mm_srai_epi32(v[6], bit);

    v[7] = _mm_mullo_epi32(in[9 * col_num + col], cospi38);
    x = _mm_mullo_epi32(in[6 * col_num + col], cospi26);
    v[7] = _mm_sub_epi32(v[7], x);
    v[7] = _mm_add_epi32(v[7], rnding);
    v[7] = _mm_srai_epi32(v[7], bit);

    v[8] = _mm_mullo_epi32(in[7 * col_num + col], cospi34);
    x = _mm_mullo_epi32(in[8 * col_num + col], cospi30);
    v[8] = _mm_add_epi32(v[8], x);
    v[8] = _mm_add_epi32(v[8], rnding);
    v[8] = _mm_srai_epi32(v[8], bit);

    v[9] = _mm_mullo_epi32(in[7 * col_num + col], cospi30);
    x = _mm_mullo_epi32(in[8 * col_num + col], cospi34);
    v[9] = _mm_sub_epi32(v[9], x);
    v[9] = _mm_add_epi32(v[9], rnding);
    v[9] = _mm_srai_epi32(v[9], bit);

    v[10] = _mm_mullo_epi32(in[5 * col_num + col], cospi42);
    x = _mm_mullo_epi32(in[10 * col_num + col], cospi22);
    v[10] = _mm_add_epi32(v[10], x);
    v[10] = _mm_add_epi32(v[10], rnding);
    v[10] = _mm_srai_epi32(v[10], bit);

    v[11] = _mm_mullo_epi32(in[5 * col_num + col], cospi22);
    x = _mm_mullo_epi32(in[10 * col_num + col], cospi42);
    v[11] = _mm_sub_epi32(v[11], x);
    v[11] = _mm_add_epi32(v[11], rnding);
    v[11] = _mm_srai_epi32(v[11], bit);

    v[12] = _mm_mullo_epi32(in[3 * col_num + col], cospi50);
    x = _mm_mullo_epi32(in[12 * col_num + col], cospi14);
    v[12] = _mm_add_epi32(v[12], x);
    v[12] = _mm_add_epi32(v[12], rnding);
    v[12] = _mm_srai_epi32(v[12], bit);

    v[13] = _mm_mullo_epi32(in[3 * col_num + col], cospi14);
    x = _mm_mullo_epi32(in[12 * col_num + col], cospi50);
    v[13] = _mm_sub_epi32(v[13], x);
    v[13] = _mm_add_epi32(v[13], rnding);
    v[13] = _mm_srai_epi32(v[13], bit);

    v[14] = _mm_mullo_epi32(in[1 * col_num + col], cospi58);
    x = _mm_mullo_epi32(in[14 * col_num + col], cospi6);
    v[14] = _mm_add_epi32(v[14], x);
    v[14] = _mm_add_epi32(v[14], rnding);
    v[14] = _mm_srai_epi32(v[14], bit);

    v[15] = _mm_mullo_epi32(in[1 * col_num + col], cospi6);
    x = _mm_mullo_epi32(in[14 * col_num + col], cospi58);
    v[15] = _mm_sub_epi32(v[15], x);
    v[15] = _mm_add_epi32(v[15], rnding);
    v[15] = _mm_srai_epi32(v[15], bit);

    // stage 3
    u[0] = _mm_add_epi32(v[0], v[8]);
    u[8] = _mm_sub_epi32(v[0], v[8]);
    u[1] = _mm_add_epi32(v[1], v[9]);
    u[9] = _mm_sub_epi32(v[1], v[9]);
    u[2] = _mm_add_epi32(v[2], v[10]);
    u[10] = _mm_sub_epi32(v[2], v[10]);
    u[3] = _mm_add_epi32(v[3], v[11]);
    u[11] = _mm_sub_epi32(v[3], v[11]);
    u[4] = _mm_add_epi32(v[4], v[12]);
    u[12] = _mm_sub_epi32(v[4], v[12]);
    u[5] = _mm_add_epi32(v[5], v[13]);
    u[13] = _mm_sub_epi32(v[5], v[13]);
    u[6] = _mm_add_epi32(v[6], v[14]);
    u[14] = _mm_sub_epi32(v[6], v[14]);
    u[7] = _mm_add_epi32(v[7], v[15]);
    u[15] = _mm_sub_epi32(v[7], v[15]);

    // stage 4
    v[0] = u[0];
    v[1] = u[1];
    v[2] = u[2];
    v[3] = u[3];
    v[4] = u[4];
    v[5] = u[5];
    v[6] = u[6];
    v[7] = u[7];

    v[8] = _mm_mullo_epi32(u[8], cospi8);
    x = _mm_mullo_epi32(u[9], cospi56);
    v[8] = _mm_add_epi32(v[8], x);
    v[8] = _mm_add_epi32(v[8], rnding);
    v[8] = _mm_srai_epi32(v[8], bit);

    v[9] = _mm_mullo_epi32(u[8], cospi56);
    x = _mm_mullo_epi32(u[9], cospi8);
    v[9] = _mm_sub_epi32(v[9], x);
    v[9] = _mm_add_epi32(v[9], rnding);
    v[9] = _mm_srai_epi32(v[9], bit);

    v[10] = _mm_mullo_epi32(u[10], cospi40);
    x = _mm_mullo_epi32(u[11], cospi24);
    v[10] = _mm_add_epi32(v[10], x);
    v[10] = _mm_add_epi32(v[10], rnding);
    v[10] = _mm_srai_epi32(v[10], bit);

    v[11] = _mm_mullo_epi32(u[10], cospi24);
    x = _mm_mullo_epi32(u[11], cospi40);
    v[11] = _mm_sub_epi32(v[11], x);
    v[11] = _mm_add_epi32(v[11], rnding);
    v[11] = _mm_srai_epi32(v[11], bit);

    v[12] = _mm_mullo_epi32(u[12], cospim56);
    x = _mm_mullo_epi32(u[13], cospi8);
    v[12] = _mm_add_epi32(v[12], x);
    v[12] = _mm_add_epi32(v[12], rnding);
    v[12] = _mm_srai_epi32(v[12], bit);

    v[13] = _mm_mullo_epi32(u[12], cospi8);
    x = _mm_mullo_epi32(u[13], cospim56);
    v[13] = _mm_sub_epi32(v[13], x);
    v[13] = _mm_add_epi32(v[13], rnding);
    v[13] = _mm_srai_epi32(v[13], bit);

    v[14] = _mm_mullo_epi32(u[14], cospim24);
    x = _mm_mullo_epi32(u[15], cospi40);
    v[14] = _mm_add_epi32(v[14], x);
    v[14] = _mm_add_epi32(v[14], rnding);
    v[14] = _mm_srai_epi32(v[14], bit);

    v[15] = _mm_mullo_epi32(u[14], cospi40);
    x = _mm_mullo_epi32(u[15], cospim24);
    v[15] = _mm_sub_epi32(v[15], x);
    v[15] = _mm_add_epi32(v[15], rnding);
    v[15] = _mm_srai_epi32(v[15], bit);

    // stage 5
    u[0] = _mm_add_epi32(v[0], v[4]);
    u[4] = _mm_sub_epi32(v[0], v[4]);
    u[1] = _mm_add_epi32(v[1], v[5]);
    u[5] = _mm_sub_epi32(v[1], v[5]);
    u[2] = _mm_add_epi32(v[2], v[6]);
    u[6] = _mm_sub_epi32(v[2], v[6]);
    u[3] = _mm_add_epi32(v[3], v[7]);
    u[7] = _mm_sub_epi32(v[3], v[7]);
    u[8] = _mm_add_epi32(v[8], v[12]);
    u[12] = _mm_sub_epi32(v[8], v[12]);
    u[9] = _mm_add_epi32(v[9], v[13]);
    u[13] = _mm_sub_epi32(v[9], v[13]);
    u[10] = _mm_add_epi32(v[10], v[14]);
    u[14] = _mm_sub_epi32(v[10], v[14]);
    u[11] = _mm_add_epi32(v[11], v[15]);
    u[15] = _mm_sub_epi32(v[11], v[15]);

    // stage 6
    v[0] = u[0];
    v[1] = u[1];
    v[2] = u[2];
    v[3] = u[3];

    v[4] = _mm_mullo_epi32(u[4], cospi16);
    x = _mm_mullo_epi32(u[5], cospi48);
    v[4] = _mm_add_epi32(v[4], x);
    v[4] = _mm_add_epi32(v[4], rnding);
    v[4] = _mm_srai_epi32(v[4], bit);

    v[5] = _mm_mullo_epi32(u[4], cospi48);
    x = _mm_mullo_epi32(u[5], cospi16);
    v[5] = _mm_sub_epi32(v[5], x);
    v[5] = _mm_add_epi32(v[5], rnding);
    v[5] = _mm_srai_epi32(v[5], bit);

    v[6] = _mm_mullo_epi32(u[6], cospim48);
    x = _mm_mullo_epi32(u[7], cospi16);
    v[6] = _mm_add_epi32(v[6], x);
    v[6] = _mm_add_epi32(v[6], rnding);
    v[6] = _mm_srai_epi32(v[6], bit);

    v[7] = _mm_mullo_epi32(u[6], cospi16);
    x = _mm_mullo_epi32(u[7], cospim48);
    v[7] = _mm_sub_epi32(v[7], x);
    v[7] = _mm_add_epi32(v[7], rnding);
    v[7] = _mm_srai_epi32(v[7], bit);

    v[8] = u[8];
    v[9] = u[9];
    v[10] = u[10];
    v[11] = u[11];

    v[12] = _mm_mullo_epi32(u[12], cospi16);
    x = _mm_mullo_epi32(u[13], cospi48);
    v[12] = _mm_add_epi32(v[12], x);
    v[12] = _mm_add_epi32(v[12], rnding);
    v[12] = _mm_srai_epi32(v[12], bit);

    v[13] = _mm_mullo_epi32(u[12], cospi48);
    x = _mm_mullo_epi32(u[13], cospi16);
    v[13] = _mm_sub_epi32(v[13], x);
    v[13] = _mm_add_epi32(v[13], rnding);
    v[13] = _mm_srai_epi32(v[13], bit);

    v[14] = _mm_mullo_epi32(u[14], cospim48);
    x = _mm_mullo_epi32(u[15], cospi16);
    v[14] = _mm_add_epi32(v[14], x);
    v[14] = _mm_add_epi32(v[14], rnding);
    v[14] = _mm_srai_epi32(v[14], bit);

    v[15] = _mm_mullo_epi32(u[14], cospi16);
    x = _mm_mullo_epi32(u[15], cospim48);
    v[15] = _mm_sub_epi32(v[15], x);
    v[15] = _mm_add_epi32(v[15], rnding);
    v[15] = _mm_srai_epi32(v[15], bit);

    // stage 7
    u[0] = _mm_add_epi32(v[0], v[2]);
    u[2] = _mm_sub_epi32(v[0], v[2]);
    u[1] = _mm_add_epi32(v[1], v[3]);
    u[3] = _mm_sub_epi32(v[1], v[3]);
    u[4] = _mm_add_epi32(v[4], v[6]);
    u[6] = _mm_sub_epi32(v[4], v[6]);
    u[5] = _mm_add_epi32(v[5], v[7]);
    u[7] = _mm_sub_epi32(v[5], v[7]);
    u[8] = _mm_add_epi32(v[8], v[10]);
    u[10] = _mm_sub_epi32(v[8], v[10]);
    u[9] = _mm_add_epi32(v[9], v[11]);
    u[11] = _mm_sub_epi32(v[9], v[11]);
    u[12] = _mm_add_epi32(v[12], v[14]);
    u[14] = _mm_sub_epi32(v[12], v[14]);
    u[13] = _mm_add_epi32(v[13], v[15]);
    u[15] = _mm_sub_epi32(v[13], v[15]);

    // stage 8
    v[0] = u[0];
    v[1] = u[1];

    y = _mm_mullo_epi32(u[2], cospi32);
    x = _mm_mullo_epi32(u[3], cospi32);
    v[2] = _mm_add_epi32(y, x);
    v[2] = _mm_add_epi32(v[2], rnding);
    v[2] = _mm_srai_epi32(v[2], bit);

    v[3] = _mm_sub_epi32(y, x);
    v[3] = _mm_add_epi32(v[3], rnding);
    v[3] = _mm_srai_epi32(v[3], bit);

    v[4] = u[4];
    v[5] = u[5];

    y = _mm_mullo_epi32(u[6], cospi32);
    x = _mm_mullo_epi32(u[7], cospi32);
    v[6] = _mm_add_epi32(y, x);
    v[6] = _mm_add_epi32(v[6], rnding);
    v[6] = _mm_srai_epi32(v[6], bit);

    v[7] = _mm_sub_epi32(y, x);
    v[7] = _mm_add_epi32(v[7], rnding);
    v[7] = _mm_srai_epi32(v[7], bit);

    v[8] = u[8];
    v[9] = u[9];

    y = _mm_mullo_epi32(u[10], cospi32);
    x = _mm_mullo_epi32(u[11], cospi32);
    v[10] = _mm_add_epi32(y, x);
    v[10] = _mm_add_epi32(v[10], rnding);
    v[10] = _mm_srai_epi32(v[10], bit);

    v[11] = _mm_sub_epi32(y, x);
    v[11] = _mm_add_epi32(v[11], rnding);
    v[11] = _mm_srai_epi32(v[11], bit);

    v[12] = u[12];
    v[13] = u[13];

    y = _mm_mullo_epi32(u[14], cospi32);
    x = _mm_mullo_epi32(u[15], cospi32);
    v[14] = _mm_add_epi32(y, x);
    v[14] = _mm_add_epi32(v[14], rnding);
    v[14] = _mm_srai_epi32(v[14], bit);

    v[15] = _mm_sub_epi32(y, x);
    v[15] = _mm_add_epi32(v[15], rnding);
    v[15] = _mm_srai_epi32(v[15], bit);

    // stage 9
    out[0 * col_num + col] = v[0];
    out[1 * col_num + col] = _mm_sub_epi32(_mm_set1_epi32(0), v[8]);
    out[2 * col_num + col] = v[12];
    out[3 * col_num + col] = _mm_sub_epi32(_mm_set1_epi32(0), v[4]);
    out[4 * col_num + col] = v[6];
    out[5 * col_num + col] = _mm_sub_epi32(_mm_set1_epi32(0), v[14]);
    out[6 * col_num + col] = v[10];
    out[7 * col_num + col] = _mm_sub_epi32(_mm_set1_epi32(0), v[2]);
    out[8 * col_num + col] = v[3];
    out[9 * col_num + col] = _mm_sub_epi32(_mm_set1_epi32(0), v[11]);
    out[10 * col_num + col] = v[15];
    out[11 * col_num + col] = _mm_sub_epi32(_mm_set1_epi32(0), v[7]);
    out[12 * col_num + col] = v[5];
    out[13 * col_num + col] = _mm_sub_epi32(_mm_set1_epi32(0), v[13]);
    out[14 * col_num + col] = v[9];
    out[15 * col_num + col] = _mm_sub_epi32(_mm_set1_epi32(0), v[1]);
  }
}

static void round_shift_16x16(__m128i *in, int shift) {
  round_shift_8x8(&in[0], shift);
  round_shift_8x8(&in[16], shift);
  round_shift_8x8(&in[32], shift);
  round_shift_8x8(&in[48], shift);
}

void av1_inv_txfm2d_add_16x16_sse4_1(const int32_t *coeff, uint16_t *output,
                                     int stride, TX_TYPE tx_type, int bd) {
  __m128i in[64], out[64];
  const int8_t *shift = inv_txfm_shift_ls[TX_16X16];
  const int txw_idx = get_txw_idx(TX_16X16);
  const int txh_idx = get_txh_idx(TX_16X16);

  switch (tx_type) {
    case DCT_DCT:
      load_buffer_16x16(coeff, in);
      transpose_16x16(in, out);
      idct16x16_sse4_1(out, in, inv_cos_bit_row[txw_idx][txh_idx]);
      round_shift_16x16(in, -shift[0]);
      transpose_16x16(in, out);
      idct16x16_sse4_1(out, in, inv_cos_bit_col[txw_idx][txh_idx]);
      write_buffer_16x16(in, output, stride, 0, 0, -shift[1], bd);
      break;
    case DCT_ADST:
      load_buffer_16x16(coeff, in);
      transpose_16x16(in, out);
      iadst16x16_sse4_1(out, in, inv_cos_bit_row[txw_idx][txh_idx]);
      round_shift_16x16(in, -shift[0]);
      transpose_16x16(in, out);
      idct16x16_sse4_1(out, in, inv_cos_bit_col[txw_idx][txh_idx]);
      write_buffer_16x16(in, output, stride, 0, 0, -shift[1], bd);
      break;
    case ADST_DCT:
      load_buffer_16x16(coeff, in);
      transpose_16x16(in, out);
      idct16x16_sse4_1(out, in, inv_cos_bit_row[txw_idx][txh_idx]);
      round_shift_16x16(in, -shift[0]);
      transpose_16x16(in, out);
      iadst16x16_sse4_1(out, in, inv_cos_bit_col[txw_idx][txh_idx]);
      write_buffer_16x16(in, output, stride, 0, 0, -shift[1], bd);
      break;
    case ADST_ADST:
      load_buffer_16x16(coeff, in);
      transpose_16x16(in, out);
      iadst16x16_sse4_1(out, in, inv_cos_bit_row[txw_idx][txh_idx]);
      round_shift_16x16(in, -shift[0]);
      transpose_16x16(in, out);
      iadst16x16_sse4_1(out, in, inv_cos_bit_col[txw_idx][txh_idx]);
      write_buffer_16x16(in, output, stride, 0, 0, -shift[1], bd);
      break;
    case FLIPADST_DCT:
      load_buffer_16x16(coeff, in);
      transpose_16x16(in, out);
      idct16x16_sse4_1(out, in, inv_cos_bit_row[txw_idx][txh_idx]);
      round_shift_16x16(in, -shift[0]);
      transpose_16x16(in, out);
      iadst16x16_sse4_1(out, in, inv_cos_bit_col[txw_idx][txh_idx]);
      write_buffer_16x16(in, output, stride, 0, 1, -shift[1], bd);
      break;
    case DCT_FLIPADST:
      load_buffer_16x16(coeff, in);
      transpose_16x16(in, out);
      iadst16x16_sse4_1(out, in, inv_cos_bit_row[txw_idx][txh_idx]);
      round_shift_16x16(in, -shift[0]);
      transpose_16x16(in, out);
      idct16x16_sse4_1(out, in, inv_cos_bit_col[txw_idx][txh_idx]);
      write_buffer_16x16(in, output, stride, 1, 0, -shift[1], bd);
      break;
    case ADST_FLIPADST:
      load_buffer_16x16(coeff, in);
      transpose_16x16(in, out);
      iadst16x16_sse4_1(out, in, inv_cos_bit_row[txw_idx][txh_idx]);
      round_shift_16x16(in, -shift[0]);
      transpose_16x16(in, out);
      iadst16x16_sse4_1(out, in, inv_cos_bit_col[txw_idx][txh_idx]);
      write_buffer_16x16(in, output, stride, 1, 0, -shift[1], bd);
      break;
    case FLIPADST_FLIPADST:
      load_buffer_16x16(coeff, in);
      transpose_16x16(in, out);
      iadst16x16_sse4_1(out, in, inv_cos_bit_row[txw_idx][txh_idx]);
      round_shift_16x16(in, -shift[0]);
      transpose_16x16(in, out);
      iadst16x16_sse4_1(out, in, inv_cos_bit_col[txw_idx][txh_idx]);
      write_buffer_16x16(in, output, stride, 1, 1, -shift[1], bd);
      break;
    case FLIPADST_ADST:
      load_buffer_16x16(coeff, in);
      transpose_16x16(in, out);
      iadst16x16_sse4_1(out, in, inv_cos_bit_row[txw_idx][txh_idx]);
      round_shift_16x16(in, -shift[0]);
      transpose_16x16(in, out);
      iadst16x16_sse4_1(out, in, inv_cos_bit_col[txw_idx][txh_idx]);
      write_buffer_16x16(in, output, stride, 0, 1, -shift[1], bd);
      break;
    default: assert(0);
  }
}

static void load_buffer_64x64_lower_32x32(const int32_t *coeff, __m128i *in) {
  int i, j;

  __m128i zero = _mm_setzero_si128();

  for (i = 0; i < 32; ++i) {
    for (j = 0; j < 8; ++j) {
      in[16 * i + j] =
          _mm_loadu_si128((const __m128i *)(coeff + 32 * i + 4 * j));
      in[16 * i + j + 8] = zero;
    }
  }

  for (i = 0; i < 512; ++i) in[512 + i] = zero;
}

static void transpose_64x64(__m128i *in, __m128i *out, int do_cols) {
  int i, j;
  for (i = 0; i < (do_cols ? 16 : 8); ++i) {
    for (j = 0; j < 8; ++j) {
      TRANSPOSE_4X4(in[(4 * i + 0) * 16 + j], in[(4 * i + 1) * 16 + j],
                    in[(4 * i + 2) * 16 + j], in[(4 * i + 3) * 16 + j],
                    out[(4 * j + 0) * 16 + i], out[(4 * j + 1) * 16 + i],
                    out[(4 * j + 2) * 16 + i], out[(4 * j + 3) * 16 + i]);
    }
  }
}

static void round_shift_32x32(__m128i *in, int shift) {
  round_shift_16x16(&in[0], shift);
  round_shift_16x16(&in[64], shift);
  round_shift_16x16(&in[128], shift);
  round_shift_16x16(&in[192], shift);
}

static void round_shift_64x64(__m128i *in, int shift) {
  round_shift_32x32(&in[0], shift);
  round_shift_32x32(&in[256], shift);
}

static void assign_16x16_input_from_32x32(const __m128i *in, __m128i *in16x16,
                                          int col) {
  int i;
  for (i = 0; i < 16 * 16 / 4; i += 4) {
    in16x16[i] = in[col];
    in16x16[i + 1] = in[col + 1];
    in16x16[i + 2] = in[col + 2];
    in16x16[i + 3] = in[col + 3];
    col += 8;
  }
}

static void write_buffer_32x32(__m128i *in, uint16_t *output, int stride,
                               int fliplr, int flipud, int shift, int bd) {
  __m128i in16x16[16 * 16 / 4];
  uint16_t *leftUp = &output[0];
  uint16_t *rightUp = &output[16];
  uint16_t *leftDown = &output[16 * stride];
  uint16_t *rightDown = &output[16 * stride + 16];

  if (fliplr) {
    swap_addr(&leftUp, &rightUp);
    swap_addr(&leftDown, &rightDown);
  }

  if (flipud) {
    swap_addr(&leftUp, &leftDown);
    swap_addr(&rightUp, &rightDown);
  }

  // Left-up quarter
  assign_16x16_input_from_32x32(in, in16x16, 0);
  write_buffer_16x16(in16x16, leftUp, stride, fliplr, flipud, shift, bd);

  // Right-up quarter
  assign_16x16_input_from_32x32(in, in16x16, 32 / 2 / 4);
  write_buffer_16x16(in16x16, rightUp, stride, fliplr, flipud, shift, bd);

  // Left-down quarter
  assign_16x16_input_from_32x32(in, in16x16, 32 * 32 / 2 / 4);
  write_buffer_16x16(in16x16, leftDown, stride, fliplr, flipud, shift, bd);

  // Right-down quarter
  assign_16x16_input_from_32x32(in, in16x16, 32 * 32 / 2 / 4 + 32 / 2 / 4);
  write_buffer_16x16(in16x16, rightDown, stride, fliplr, flipud, shift, bd);
}

static void assign_32x32_input_from_64x64(const __m128i *in, __m128i *in32x32,
                                          int col) {
  int i;
  for (i = 0; i < 32 * 32 / 4; i += 8) {
    in32x32[i] = in[col];
    in32x32[i + 1] = in[col + 1];
    in32x32[i + 2] = in[col + 2];
    in32x32[i + 3] = in[col + 3];
    in32x32[i + 4] = in[col + 4];
    in32x32[i + 5] = in[col + 5];
    in32x32[i + 6] = in[col + 6];
    in32x32[i + 7] = in[col + 7];
    col += 16;
  }
}

static void write_buffer_64x64(__m128i *in, uint16_t *output, int stride,
                               int fliplr, int flipud, int shift, int bd) {
  __m128i in32x32[32 * 32 / 4];
  uint16_t *leftUp = &output[0];
  uint16_t *rightUp = &output[32];
  uint16_t *leftDown = &output[32 * stride];
  uint16_t *rightDown = &output[32 * stride + 32];

  if (fliplr) {
    swap_addr(&leftUp, &rightUp);
    swap_addr(&leftDown, &rightDown);
  }

  if (flipud) {
    swap_addr(&leftUp, &leftDown);
    swap_addr(&rightUp, &rightDown);
  }

  // Left-up quarter
  assign_32x32_input_from_64x64(in, in32x32, 0);
  write_buffer_32x32(in32x32, leftUp, stride, fliplr, flipud, shift, bd);

  // Right-up quarter
  assign_32x32_input_from_64x64(in, in32x32, 64 / 2 / 4);
  write_buffer_32x32(in32x32, rightUp, stride, fliplr, flipud, shift, bd);

  // Left-down quarter
  assign_32x32_input_from_64x64(in, in32x32, 64 * 64 / 2 / 4);
  write_buffer_32x32(in32x32, leftDown, stride, fliplr, flipud, shift, bd);

  // Right-down quarter
  assign_32x32_input_from_64x64(in, in32x32, 64 * 64 / 2 / 4 + 64 / 2 / 4);
  write_buffer_32x32(in32x32, rightDown, stride, fliplr, flipud, shift, bd);
}

static void idct64x64_sse4_1(__m128i *in, __m128i *out, int bit, int do_cols) {
  int i, j;
  const int32_t *cospi = cospi_arr(bit);
  const __m128i rnding = _mm_set1_epi32(1 << (bit - 1));
  int col;

  const __m128i cospi1 = _mm_set1_epi32(cospi[1]);
  const __m128i cospi2 = _mm_set1_epi32(cospi[2]);
  const __m128i cospi3 = _mm_set1_epi32(cospi[3]);
  const __m128i cospi4 = _mm_set1_epi32(cospi[4]);
  const __m128i cospi5 = _mm_set1_epi32(cospi[5]);
  const __m128i cospi6 = _mm_set1_epi32(cospi[6]);
  const __m128i cospi7 = _mm_set1_epi32(cospi[7]);
  const __m128i cospi8 = _mm_set1_epi32(cospi[8]);
  const __m128i cospi9 = _mm_set1_epi32(cospi[9]);
  const __m128i cospi10 = _mm_set1_epi32(cospi[10]);
  const __m128i cospi11 = _mm_set1_epi32(cospi[11]);
  const __m128i cospi12 = _mm_set1_epi32(cospi[12]);
  const __m128i cospi13 = _mm_set1_epi32(cospi[13]);
  const __m128i cospi14 = _mm_set1_epi32(cospi[14]);
  const __m128i cospi15 = _mm_set1_epi32(cospi[15]);
  const __m128i cospi16 = _mm_set1_epi32(cospi[16]);
  const __m128i cospi17 = _mm_set1_epi32(cospi[17]);
  const __m128i cospi18 = _mm_set1_epi32(cospi[18]);
  const __m128i cospi19 = _mm_set1_epi32(cospi[19]);
  const __m128i cospi20 = _mm_set1_epi32(cospi[20]);
  const __m128i cospi21 = _mm_set1_epi32(cospi[21]);
  const __m128i cospi22 = _mm_set1_epi32(cospi[22]);
  const __m128i cospi23 = _mm_set1_epi32(cospi[23]);
  const __m128i cospi24 = _mm_set1_epi32(cospi[24]);
  const __m128i cospi25 = _mm_set1_epi32(cospi[25]);
  const __m128i cospi26 = _mm_set1_epi32(cospi[26]);
  const __m128i cospi27 = _mm_set1_epi32(cospi[27]);
  const __m128i cospi28 = _mm_set1_epi32(cospi[28]);
  const __m128i cospi29 = _mm_set1_epi32(cospi[29]);
  const __m128i cospi30 = _mm_set1_epi32(cospi[30]);
  const __m128i cospi31 = _mm_set1_epi32(cospi[31]);
  const __m128i cospi32 = _mm_set1_epi32(cospi[32]);
  const __m128i cospi35 = _mm_set1_epi32(cospi[35]);
  const __m128i cospi36 = _mm_set1_epi32(cospi[36]);
  const __m128i cospi38 = _mm_set1_epi32(cospi[38]);
  const __m128i cospi39 = _mm_set1_epi32(cospi[39]);
  const __m128i cospi40 = _mm_set1_epi32(cospi[40]);
  const __m128i cospi43 = _mm_set1_epi32(cospi[43]);
  const __m128i cospi44 = _mm_set1_epi32(cospi[44]);
  const __m128i cospi46 = _mm_set1_epi32(cospi[46]);
  const __m128i cospi47 = _mm_set1_epi32(cospi[47]);
  const __m128i cospi48 = _mm_set1_epi32(cospi[48]);
  const __m128i cospi51 = _mm_set1_epi32(cospi[51]);
  const __m128i cospi52 = _mm_set1_epi32(cospi[52]);
  const __m128i cospi54 = _mm_set1_epi32(cospi[54]);
  const __m128i cospi55 = _mm_set1_epi32(cospi[55]);
  const __m128i cospi56 = _mm_set1_epi32(cospi[56]);
  const __m128i cospi59 = _mm_set1_epi32(cospi[59]);
  const __m128i cospi60 = _mm_set1_epi32(cospi[60]);
  const __m128i cospi62 = _mm_set1_epi32(cospi[62]);
  const __m128i cospi63 = _mm_set1_epi32(cospi[63]);

  const __m128i cospim4 = _mm_set1_epi32(-cospi[4]);
  const __m128i cospim8 = _mm_set1_epi32(-cospi[8]);
  const __m128i cospim12 = _mm_set1_epi32(-cospi[12]);
  const __m128i cospim16 = _mm_set1_epi32(-cospi[16]);
  const __m128i cospim20 = _mm_set1_epi32(-cospi[20]);
  const __m128i cospim24 = _mm_set1_epi32(-cospi[24]);
  const __m128i cospim28 = _mm_set1_epi32(-cospi[28]);
  const __m128i cospim32 = _mm_set1_epi32(-cospi[32]);
  const __m128i cospim33 = _mm_set1_epi32(-cospi[33]);
  const __m128i cospim34 = _mm_set1_epi32(-cospi[34]);
  const __m128i cospim36 = _mm_set1_epi32(-cospi[36]);
  const __m128i cospim37 = _mm_set1_epi32(-cospi[37]);
  const __m128i cospim40 = _mm_set1_epi32(-cospi[40]);
  const __m128i cospim41 = _mm_set1_epi32(-cospi[41]);
  const __m128i cospim42 = _mm_set1_epi32(-cospi[42]);
  const __m128i cospim44 = _mm_set1_epi32(-cospi[44]);
  const __m128i cospim45 = _mm_set1_epi32(-cospi[45]);
  const __m128i cospim48 = _mm_set1_epi32(-cospi[48]);
  const __m128i cospim49 = _mm_set1_epi32(-cospi[49]);
  const __m128i cospim50 = _mm_set1_epi32(-cospi[50]);
  const __m128i cospim52 = _mm_set1_epi32(-cospi[52]);
  const __m128i cospim53 = _mm_set1_epi32(-cospi[53]);
  const __m128i cospim56 = _mm_set1_epi32(-cospi[56]);
  const __m128i cospim57 = _mm_set1_epi32(-cospi[57]);
  const __m128i cospim58 = _mm_set1_epi32(-cospi[58]);
  const __m128i cospim60 = _mm_set1_epi32(-cospi[60]);
  const __m128i cospim61 = _mm_set1_epi32(-cospi[61]);

  for (col = 0; col < (do_cols ? 64 / 4 : 32 / 4); ++col) {
    __m128i u[64], v[64];

    // stage 1
    u[32] = in[1 * 16 + col];
    u[34] = in[17 * 16 + col];
    u[36] = in[9 * 16 + col];
    u[38] = in[25 * 16 + col];
    u[40] = in[5 * 16 + col];
    u[42] = in[21 * 16 + col];
    u[44] = in[13 * 16 + col];
    u[46] = in[29 * 16 + col];
    u[48] = in[3 * 16 + col];
    u[50] = in[19 * 16 + col];
    u[52] = in[11 * 16 + col];
    u[54] = in[27 * 16 + col];
    u[56] = in[7 * 16 + col];
    u[58] = in[23 * 16 + col];
    u[60] = in[15 * 16 + col];
    u[62] = in[31 * 16 + col];

    v[16] = in[2 * 16 + col];
    v[18] = in[18 * 16 + col];
    v[20] = in[10 * 16 + col];
    v[22] = in[26 * 16 + col];
    v[24] = in[6 * 16 + col];
    v[26] = in[22 * 16 + col];
    v[28] = in[14 * 16 + col];
    v[30] = in[30 * 16 + col];

    u[8] = in[4 * 16 + col];
    u[10] = in[20 * 16 + col];
    u[12] = in[12 * 16 + col];
    u[14] = in[28 * 16 + col];

    v[4] = in[8 * 16 + col];
    v[6] = in[24 * 16 + col];

    u[0] = in[0 * 16 + col];
    u[2] = in[16 * 16 + col];

    // stage 2
    v[32] = half_btf_0_sse4_1(&cospi63, &u[32], &rnding, bit);
    v[33] = half_btf_0_sse4_1(&cospim33, &u[62], &rnding, bit);
    v[34] = half_btf_0_sse4_1(&cospi47, &u[34], &rnding, bit);
    v[35] = half_btf_0_sse4_1(&cospim49, &u[60], &rnding, bit);
    v[36] = half_btf_0_sse4_1(&cospi55, &u[36], &rnding, bit);
    v[37] = half_btf_0_sse4_1(&cospim41, &u[58], &rnding, bit);
    v[38] = half_btf_0_sse4_1(&cospi39, &u[38], &rnding, bit);
    v[39] = half_btf_0_sse4_1(&cospim57, &u[56], &rnding, bit);
    v[40] = half_btf_0_sse4_1(&cospi59, &u[40], &rnding, bit);
    v[41] = half_btf_0_sse4_1(&cospim37, &u[54], &rnding, bit);
    v[42] = half_btf_0_sse4_1(&cospi43, &u[42], &rnding, bit);
    v[43] = half_btf_0_sse4_1(&cospim53, &u[52], &rnding, bit);
    v[44] = half_btf_0_sse4_1(&cospi51, &u[44], &rnding, bit);
    v[45] = half_btf_0_sse4_1(&cospim45, &u[50], &rnding, bit);
    v[46] = half_btf_0_sse4_1(&cospi35, &u[46], &rnding, bit);
    v[47] = half_btf_0_sse4_1(&cospim61, &u[48], &rnding, bit);
    v[48] = half_btf_0_sse4_1(&cospi3, &u[48], &rnding, bit);
    v[49] = half_btf_0_sse4_1(&cospi29, &u[46], &rnding, bit);
    v[50] = half_btf_0_sse4_1(&cospi19, &u[50], &rnding, bit);
    v[51] = half_btf_0_sse4_1(&cospi13, &u[44], &rnding, bit);
    v[52] = half_btf_0_sse4_1(&cospi11, &u[52], &rnding, bit);
    v[53] = half_btf_0_sse4_1(&cospi21, &u[42], &rnding, bit);
    v[54] = half_btf_0_sse4_1(&cospi27, &u[54], &rnding, bit);
    v[55] = half_btf_0_sse4_1(&cospi5, &u[40], &rnding, bit);
    v[56] = half_btf_0_sse4_1(&cospi7, &u[56], &rnding, bit);
    v[57] = half_btf_0_sse4_1(&cospi25, &u[38], &rnding, bit);
    v[58] = half_btf_0_sse4_1(&cospi23, &u[58], &rnding, bit);
    v[59] = half_btf_0_sse4_1(&cospi9, &u[36], &rnding, bit);
    v[60] = half_btf_0_sse4_1(&cospi15, &u[60], &rnding, bit);
    v[61] = half_btf_0_sse4_1(&cospi17, &u[34], &rnding, bit);
    v[62] = half_btf_0_sse4_1(&cospi31, &u[62], &rnding, bit);
    v[63] = half_btf_0_sse4_1(&cospi1, &u[32], &rnding, bit);

    // stage 3
    u[16] = half_btf_0_sse4_1(&cospi62, &v[16], &rnding, bit);
    u[17] = half_btf_0_sse4_1(&cospim34, &v[30], &rnding, bit);
    u[18] = half_btf_0_sse4_1(&cospi46, &v[18], &rnding, bit);
    u[19] = half_btf_0_sse4_1(&cospim50, &v[28], &rnding, bit);
    u[20] = half_btf_0_sse4_1(&cospi54, &v[20], &rnding, bit);
    u[21] = half_btf_0_sse4_1(&cospim42, &v[26], &rnding, bit);
    u[22] = half_btf_0_sse4_1(&cospi38, &v[22], &rnding, bit);
    u[23] = half_btf_0_sse4_1(&cospim58, &v[24], &rnding, bit);
    u[24] = half_btf_0_sse4_1(&cospi6, &v[24], &rnding, bit);
    u[25] = half_btf_0_sse4_1(&cospi26, &v[22], &rnding, bit);
    u[26] = half_btf_0_sse4_1(&cospi22, &v[26], &rnding, bit);
    u[27] = half_btf_0_sse4_1(&cospi10, &v[20], &rnding, bit);
    u[28] = half_btf_0_sse4_1(&cospi14, &v[28], &rnding, bit);
    u[29] = half_btf_0_sse4_1(&cospi18, &v[18], &rnding, bit);
    u[30] = half_btf_0_sse4_1(&cospi30, &v[30], &rnding, bit);
    u[31] = half_btf_0_sse4_1(&cospi2, &v[16], &rnding, bit);

    for (i = 32; i < 64; i += 4) {
      u[i + 0] = _mm_add_epi32(v[i + 0], v[i + 1]);
      u[i + 1] = _mm_sub_epi32(v[i + 0], v[i + 1]);
      u[i + 2] = _mm_sub_epi32(v[i + 3], v[i + 2]);
      u[i + 3] = _mm_add_epi32(v[i + 3], v[i + 2]);
    }

    // stage 4
    v[8] = half_btf_0_sse4_1(&cospi60, &u[8], &rnding, bit);
    v[9] = half_btf_0_sse4_1(&cospim36, &u[14], &rnding, bit);
    v[10] = half_btf_0_sse4_1(&cospi44, &u[10], &rnding, bit);
    v[11] = half_btf_0_sse4_1(&cospim52, &u[12], &rnding, bit);
    v[12] = half_btf_0_sse4_1(&cospi12, &u[12], &rnding, bit);
    v[13] = half_btf_0_sse4_1(&cospi20, &u[10], &rnding, bit);
    v[14] = half_btf_0_sse4_1(&cospi28, &u[14], &rnding, bit);
    v[15] = half_btf_0_sse4_1(&cospi4, &u[8], &rnding, bit);

    for (i = 16; i < 32; i += 4) {
      v[i + 0] = _mm_add_epi32(u[i + 0], u[i + 1]);
      v[i + 1] = _mm_sub_epi32(u[i + 0], u[i + 1]);
      v[i + 2] = _mm_sub_epi32(u[i + 3], u[i + 2]);
      v[i + 3] = _mm_add_epi32(u[i + 3], u[i + 2]);
    }

    for (i = 32; i < 64; i += 4) {
      v[i + 0] = u[i + 0];
      v[i + 3] = u[i + 3];
    }

    v[33] = half_btf_sse4_1(&cospim4, &u[33], &cospi60, &u[62], &rnding, bit);
    v[34] = half_btf_sse4_1(&cospim60, &u[34], &cospim4, &u[61], &rnding, bit);
    v[37] = half_btf_sse4_1(&cospim36, &u[37], &cospi28, &u[58], &rnding, bit);
    v[38] = half_btf_sse4_1(&cospim28, &u[38], &cospim36, &u[57], &rnding, bit);
    v[41] = half_btf_sse4_1(&cospim20, &u[41], &cospi44, &u[54], &rnding, bit);
    v[42] = half_btf_sse4_1(&cospim44, &u[42], &cospim20, &u[53], &rnding, bit);
    v[45] = half_btf_sse4_1(&cospim52, &u[45], &cospi12, &u[50], &rnding, bit);
    v[46] = half_btf_sse4_1(&cospim12, &u[46], &cospim52, &u[49], &rnding, bit);
    v[49] = half_btf_sse4_1(&cospim52, &u[46], &cospi12, &u[49], &rnding, bit);
    v[50] = half_btf_sse4_1(&cospi12, &u[45], &cospi52, &u[50], &rnding, bit);
    v[53] = half_btf_sse4_1(&cospim20, &u[42], &cospi44, &u[53], &rnding, bit);
    v[54] = half_btf_sse4_1(&cospi44, &u[41], &cospi20, &u[54], &rnding, bit);
    v[57] = half_btf_sse4_1(&cospim36, &u[38], &cospi28, &u[57], &rnding, bit);
    v[58] = half_btf_sse4_1(&cospi28, &u[37], &cospi36, &u[58], &rnding, bit);
    v[61] = half_btf_sse4_1(&cospim4, &u[34], &cospi60, &u[61], &rnding, bit);
    v[62] = half_btf_sse4_1(&cospi60, &u[33], &cospi4, &u[62], &rnding, bit);

    // stage 5
    u[4] = half_btf_0_sse4_1(&cospi56, &v[4], &rnding, bit);
    u[5] = half_btf_0_sse4_1(&cospim40, &v[6], &rnding, bit);
    u[6] = half_btf_0_sse4_1(&cospi24, &v[6], &rnding, bit);
    u[7] = half_btf_0_sse4_1(&cospi8, &v[4], &rnding, bit);

    for (i = 8; i < 16; i += 4) {
      u[i + 0] = _mm_add_epi32(v[i + 0], v[i + 1]);
      u[i + 1] = _mm_sub_epi32(v[i + 0], v[i + 1]);
      u[i + 2] = _mm_sub_epi32(v[i + 3], v[i + 2]);
      u[i + 3] = _mm_add_epi32(v[i + 3], v[i + 2]);
    }

    for (i = 16; i < 32; i += 4) {
      u[i + 0] = v[i + 0];
      u[i + 3] = v[i + 3];
    }

    u[17] = half_btf_sse4_1(&cospim8, &v[17], &cospi56, &v[30], &rnding, bit);
    u[18] = half_btf_sse4_1(&cospim56, &v[18], &cospim8, &v[29], &rnding, bit);
    u[21] = half_btf_sse4_1(&cospim40, &v[21], &cospi24, &v[26], &rnding, bit);
    u[22] = half_btf_sse4_1(&cospim24, &v[22], &cospim40, &v[25], &rnding, bit);
    u[25] = half_btf_sse4_1(&cospim40, &v[22], &cospi24, &v[25], &rnding, bit);
    u[26] = half_btf_sse4_1(&cospi24, &v[21], &cospi40, &v[26], &rnding, bit);
    u[29] = half_btf_sse4_1(&cospim8, &v[18], &cospi56, &v[29], &rnding, bit);
    u[30] = half_btf_sse4_1(&cospi56, &v[17], &cospi8, &v[30], &rnding, bit);

    for (i = 32; i < 64; i += 8) {
      u[i + 0] = _mm_add_epi32(v[i + 0], v[i + 3]);
      u[i + 1] = _mm_add_epi32(v[i + 1], v[i + 2]);
      u[i + 2] = _mm_sub_epi32(v[i + 1], v[i + 2]);
      u[i + 3] = _mm_sub_epi32(v[i + 0], v[i + 3]);

      u[i + 4] = _mm_sub_epi32(v[i + 7], v[i + 4]);
      u[i + 5] = _mm_sub_epi32(v[i + 6], v[i + 5]);
      u[i + 6] = _mm_add_epi32(v[i + 6], v[i + 5]);
      u[i + 7] = _mm_add_epi32(v[i + 7], v[i + 4]);
    }

    // stage 6
    v[0] = half_btf_0_sse4_1(&cospi32, &u[0], &rnding, bit);
    v[1] = half_btf_0_sse4_1(&cospi32, &u[0], &rnding, bit);
    v[2] = half_btf_0_sse4_1(&cospi48, &u[2], &rnding, bit);
    v[3] = half_btf_0_sse4_1(&cospi16, &u[2], &rnding, bit);

    v[4] = _mm_add_epi32(u[4], u[5]);
    v[5] = _mm_sub_epi32(u[4], u[5]);
    v[6] = _mm_sub_epi32(u[7], u[6]);
    v[7] = _mm_add_epi32(u[7], u[6]);

    for (i = 8; i < 16; i += 4) {
      v[i + 0] = u[i + 0];
      v[i + 3] = u[i + 3];
    }

    v[9] = half_btf_sse4_1(&cospim16, &u[9], &cospi48, &u[14], &rnding, bit);
    v[10] = half_btf_sse4_1(&cospim48, &u[10], &cospim16, &u[13], &rnding, bit);
    v[13] = half_btf_sse4_1(&cospim16, &u[10], &cospi48, &u[13], &rnding, bit);
    v[14] = half_btf_sse4_1(&cospi48, &u[9], &cospi16, &u[14], &rnding, bit);

    for (i = 16; i < 32; i += 8) {
      v[i + 0] = _mm_add_epi32(u[i + 0], u[i + 3]);
      v[i + 1] = _mm_add_epi32(u[i + 1], u[i + 2]);
      v[i + 2] = _mm_sub_epi32(u[i + 1], u[i + 2]);
      v[i + 3] = _mm_sub_epi32(u[i + 0], u[i + 3]);

      v[i + 4] = _mm_sub_epi32(u[i + 7], u[i + 4]);
      v[i + 5] = _mm_sub_epi32(u[i + 6], u[i + 5]);
      v[i + 6] = _mm_add_epi32(u[i + 6], u[i + 5]);
      v[i + 7] = _mm_add_epi32(u[i + 7], u[i + 4]);
    }

    for (i = 32; i < 64; i += 8) {
      v[i + 0] = u[i + 0];
      v[i + 1] = u[i + 1];
      v[i + 6] = u[i + 6];
      v[i + 7] = u[i + 7];
    }

    v[34] = half_btf_sse4_1(&cospim8, &u[34], &cospi56, &u[61], &rnding, bit);
    v[35] = half_btf_sse4_1(&cospim8, &u[35], &cospi56, &u[60], &rnding, bit);
    v[36] = half_btf_sse4_1(&cospim56, &u[36], &cospim8, &u[59], &rnding, bit);
    v[37] = half_btf_sse4_1(&cospim56, &u[37], &cospim8, &u[58], &rnding, bit);
    v[42] = half_btf_sse4_1(&cospim40, &u[42], &cospi24, &u[53], &rnding, bit);
    v[43] = half_btf_sse4_1(&cospim40, &u[43], &cospi24, &u[52], &rnding, bit);
    v[44] = half_btf_sse4_1(&cospim24, &u[44], &cospim40, &u[51], &rnding, bit);
    v[45] = half_btf_sse4_1(&cospim24, &u[45], &cospim40, &u[50], &rnding, bit);
    v[50] = half_btf_sse4_1(&cospim40, &u[45], &cospi24, &u[50], &rnding, bit);
    v[51] = half_btf_sse4_1(&cospim40, &u[44], &cospi24, &u[51], &rnding, bit);
    v[52] = half_btf_sse4_1(&cospi24, &u[43], &cospi40, &u[52], &rnding, bit);
    v[53] = half_btf_sse4_1(&cospi24, &u[42], &cospi40, &u[53], &rnding, bit);
    v[58] = half_btf_sse4_1(&cospim8, &u[37], &cospi56, &u[58], &rnding, bit);
    v[59] = half_btf_sse4_1(&cospim8, &u[36], &cospi56, &u[59], &rnding, bit);
    v[60] = half_btf_sse4_1(&cospi56, &u[35], &cospi8, &u[60], &rnding, bit);
    v[61] = half_btf_sse4_1(&cospi56, &u[34], &cospi8, &u[61], &rnding, bit);

    // stage 7
    u[0] = _mm_add_epi32(v[0], v[3]);
    u[1] = _mm_add_epi32(v[1], v[2]);
    u[2] = _mm_sub_epi32(v[1], v[2]);
    u[3] = _mm_sub_epi32(v[0], v[3]);

    u[4] = v[4];
    u[7] = v[7];
    u[5] = half_btf_sse4_1(&cospim32, &v[5], &cospi32, &v[6], &rnding, bit);
    u[6] = half_btf_sse4_1(&cospi32, &v[5], &cospi32, &v[6], &rnding, bit);

    u[8] = _mm_add_epi32(v[8], v[11]);
    u[9] = _mm_add_epi32(v[9], v[10]);
    u[10] = _mm_sub_epi32(v[9], v[10]);
    u[11] = _mm_sub_epi32(v[8], v[11]);
    u[12] = _mm_sub_epi32(v[15], v[12]);
    u[13] = _mm_sub_epi32(v[14], v[13]);
    u[14] = _mm_add_epi32(v[14], v[13]);
    u[15] = _mm_add_epi32(v[15], v[12]);

    for (i = 16; i < 32; i += 8) {
      u[i + 0] = v[i + 0];
      u[i + 1] = v[i + 1];
      u[i + 6] = v[i + 6];
      u[i + 7] = v[i + 7];
    }

    u[18] = half_btf_sse4_1(&cospim16, &v[18], &cospi48, &v[29], &rnding, bit);
    u[19] = half_btf_sse4_1(&cospim16, &v[19], &cospi48, &v[28], &rnding, bit);
    u[20] = half_btf_sse4_1(&cospim48, &v[20], &cospim16, &v[27], &rnding, bit);
    u[21] = half_btf_sse4_1(&cospim48, &v[21], &cospim16, &v[26], &rnding, bit);
    u[26] = half_btf_sse4_1(&cospim16, &v[21], &cospi48, &v[26], &rnding, bit);
    u[27] = half_btf_sse4_1(&cospim16, &v[20], &cospi48, &v[27], &rnding, bit);
    u[28] = half_btf_sse4_1(&cospi48, &v[19], &cospi16, &v[28], &rnding, bit);
    u[29] = half_btf_sse4_1(&cospi48, &v[18], &cospi16, &v[29], &rnding, bit);

    for (i = 32; i < 64; i += 16) {
      for (j = i; j < i + 4; j++) {
        u[j] = _mm_add_epi32(v[j], v[j ^ 7]);
        u[j ^ 7] = _mm_sub_epi32(v[j], v[j ^ 7]);
        u[j ^ 8] = _mm_sub_epi32(v[j ^ 15], v[j ^ 8]);
        u[j ^ 15] = _mm_add_epi32(v[j ^ 15], v[j ^ 8]);
      }
    }

    // stage 8
    for (i = 0; i < 4; ++i) {
      v[i] = _mm_add_epi32(u[i], u[7 - i]);
      v[7 - i] = _mm_sub_epi32(u[i], u[7 - i]);
    }

    v[8] = u[8];
    v[9] = u[9];
    v[14] = u[14];
    v[15] = u[15];

    v[10] = half_btf_sse4_1(&cospim32, &u[10], &cospi32, &u[13], &rnding, bit);
    v[11] = half_btf_sse4_1(&cospim32, &u[11], &cospi32, &u[12], &rnding, bit);
    v[12] = half_btf_sse4_1(&cospi32, &u[11], &cospi32, &u[12], &rnding, bit);
    v[13] = half_btf_sse4_1(&cospi32, &u[10], &cospi32, &u[13], &rnding, bit);

    for (i = 16; i < 20; ++i) {
      v[i] = _mm_add_epi32(u[i], u[i ^ 7]);
      v[i ^ 7] = _mm_sub_epi32(u[i], u[i ^ 7]);
      v[i ^ 8] = _mm_sub_epi32(u[i ^ 15], u[i ^ 8]);
      v[i ^ 15] = _mm_add_epi32(u[i ^ 15], u[i ^ 8]);
    }

    for (i = 32; i < 36; ++i) {
      v[i] = u[i];
      v[i + 12] = u[i + 12];
      v[i + 16] = u[i + 16];
      v[i + 28] = u[i + 28];
    }

    v[36] = half_btf_sse4_1(&cospim16, &u[36], &cospi48, &u[59], &rnding, bit);
    v[37] = half_btf_sse4_1(&cospim16, &u[37], &cospi48, &u[58], &rnding, bit);
    v[38] = half_btf_sse4_1(&cospim16, &u[38], &cospi48, &u[57], &rnding, bit);
    v[39] = half_btf_sse4_1(&cospim16, &u[39], &cospi48, &u[56], &rnding, bit);
    v[40] = half_btf_sse4_1(&cospim48, &u[40], &cospim16, &u[55], &rnding, bit);
    v[41] = half_btf_sse4_1(&cospim48, &u[41], &cospim16, &u[54], &rnding, bit);
    v[42] = half_btf_sse4_1(&cospim48, &u[42], &cospim16, &u[53], &rnding, bit);
    v[43] = half_btf_sse4_1(&cospim48, &u[43], &cospim16, &u[52], &rnding, bit);
    v[52] = half_btf_sse4_1(&cospim16, &u[43], &cospi48, &u[52], &rnding, bit);
    v[53] = half_btf_sse4_1(&cospim16, &u[42], &cospi48, &u[53], &rnding, bit);
    v[54] = half_btf_sse4_1(&cospim16, &u[41], &cospi48, &u[54], &rnding, bit);
    v[55] = half_btf_sse4_1(&cospim16, &u[40], &cospi48, &u[55], &rnding, bit);
    v[56] = half_btf_sse4_1(&cospi48, &u[39], &cospi16, &u[56], &rnding, bit);
    v[57] = half_btf_sse4_1(&cospi48, &u[38], &cospi16, &u[57], &rnding, bit);
    v[58] = half_btf_sse4_1(&cospi48, &u[37], &cospi16, &u[58], &rnding, bit);
    v[59] = half_btf_sse4_1(&cospi48, &u[36], &cospi16, &u[59], &rnding, bit);

    // stage 9
    for (i = 0; i < 8; ++i) {
      u[i] = _mm_add_epi32(v[i], v[15 - i]);
      u[15 - i] = _mm_sub_epi32(v[i], v[15 - i]);
    }

    for (i = 16; i < 20; ++i) {
      u[i] = v[i];
      u[i + 12] = v[i + 12];
    }

    u[20] = half_btf_sse4_1(&cospim32, &v[20], &cospi32, &v[27], &rnding, bit);
    u[21] = half_btf_sse4_1(&cospim32, &v[21], &cospi32, &v[26], &rnding, bit);
    u[22] = half_btf_sse4_1(&cospim32, &v[22], &cospi32, &v[25], &rnding, bit);
    u[23] = half_btf_sse4_1(&cospim32, &v[23], &cospi32, &v[24], &rnding, bit);
    u[24] = half_btf_sse4_1(&cospi32, &v[23], &cospi32, &v[24], &rnding, bit);
    u[25] = half_btf_sse4_1(&cospi32, &v[22], &cospi32, &v[25], &rnding, bit);
    u[26] = half_btf_sse4_1(&cospi32, &v[21], &cospi32, &v[26], &rnding, bit);
    u[27] = half_btf_sse4_1(&cospi32, &v[20], &cospi32, &v[27], &rnding, bit);

    for (i = 32; i < 40; i++) {
      u[i] = _mm_add_epi32(v[i], v[i ^ 15]);
      u[i ^ 15] = _mm_sub_epi32(v[i], v[i ^ 15]);
    }

    for (i = 48; i < 56; i++) {
      u[i] = _mm_sub_epi32(v[i ^ 15], v[i]);
      u[i ^ 15] = _mm_add_epi32(v[i ^ 15], v[i]);
    }

    // stage 10
    for (i = 0; i < 16; i++) {
      v[i] = _mm_add_epi32(u[i], u[31 - i]);
      v[31 - i] = _mm_sub_epi32(u[i], u[31 - i]);
    }

    for (i = 32; i < 40; i++) v[i] = u[i];

    v[40] = half_btf_sse4_1(&cospim32, &u[40], &cospi32, &u[55], &rnding, bit);
    v[41] = half_btf_sse4_1(&cospim32, &u[41], &cospi32, &u[54], &rnding, bit);
    v[42] = half_btf_sse4_1(&cospim32, &u[42], &cospi32, &u[53], &rnding, bit);
    v[43] = half_btf_sse4_1(&cospim32, &u[43], &cospi32, &u[52], &rnding, bit);
    v[44] = half_btf_sse4_1(&cospim32, &u[44], &cospi32, &u[51], &rnding, bit);
    v[45] = half_btf_sse4_1(&cospim32, &u[45], &cospi32, &u[50], &rnding, bit);
    v[46] = half_btf_sse4_1(&cospim32, &u[46], &cospi32, &u[49], &rnding, bit);
    v[47] = half_btf_sse4_1(&cospim32, &u[47], &cospi32, &u[48], &rnding, bit);
    v[48] = half_btf_sse4_1(&cospi32, &u[47], &cospi32, &u[48], &rnding, bit);
    v[49] = half_btf_sse4_1(&cospi32, &u[46], &cospi32, &u[49], &rnding, bit);
    v[50] = half_btf_sse4_1(&cospi32, &u[45], &cospi32, &u[50], &rnding, bit);
    v[51] = half_btf_sse4_1(&cospi32, &u[44], &cospi32, &u[51], &rnding, bit);
    v[52] = half_btf_sse4_1(&cospi32, &u[43], &cospi32, &u[52], &rnding, bit);
    v[53] = half_btf_sse4_1(&cospi32, &u[42], &cospi32, &u[53], &rnding, bit);
    v[54] = half_btf_sse4_1(&cospi32, &u[41], &cospi32, &u[54], &rnding, bit);
    v[55] = half_btf_sse4_1(&cospi32, &u[40], &cospi32, &u[55], &rnding, bit);

    for (i = 56; i < 64; i++) v[i] = u[i];

    // stage 11
    for (i = 0; i < 32; i++) {
      out[16 * (i) + col] = _mm_add_epi32(v[i], v[63 - i]);
      out[16 * (63 - i) + col] = _mm_sub_epi32(v[i], v[63 - i]);
    }
  }
}

void av1_inv_txfm2d_add_64x64_sse4_1(const int32_t *coeff, uint16_t *output,
                                     int stride, TX_TYPE tx_type, int bd) {
  __m128i in[64 * 64 / 4], out[64 * 64 / 4];
  const int8_t *shift = inv_txfm_shift_ls[TX_64X64];
  const int txw_idx = tx_size_wide_log2[TX_64X64] - tx_size_wide_log2[0];
  const int txh_idx = tx_size_high_log2[TX_64X64] - tx_size_high_log2[0];

  switch (tx_type) {
    case DCT_DCT:
      load_buffer_64x64_lower_32x32(coeff, in);
      transpose_64x64(in, out, 0);
      idct64x64_sse4_1(out, in, inv_cos_bit_row[txw_idx][txh_idx], 0);
      // transpose before shift, so shift can apply to 512 contiguous values
      transpose_64x64(in, out, 1);
      round_shift_64x64(out, -shift[0]);
      idct64x64_sse4_1(out, in, inv_cos_bit_col[txw_idx][txh_idx], 1);
      write_buffer_64x64(in, output, stride, 0, 0, -shift[1], bd);
      break;

    default:
      av1_inv_txfm2d_add_64x64_c(coeff, output, stride, tx_type, bd);
      break;
  }
}