av1/common/x86/av1_inv_txfm_ssse3.c

/*
 * Copyright (c) 2018, 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 "config/aom_config.h"
#include "config/av1_rtcd.h"

#include "av1/common/av1_inv_txfm1d_cfg.h"
#include "av1/common/x86/av1_inv_txfm_ssse3.h"
#include "av1/common/x86/av1_txfm_sse2.h"

// TODO(venkatsanampudi@ittiam.com): move this to header file

// Sqrt2, Sqrt2^2, Sqrt2^3, Sqrt2^4, Sqrt2^5
static int32_t NewSqrt2list[TX_SIZES] = { 5793, 2 * 4096, 2 * 5793, 4 * 4096,
                                          4 * 5793 };

// TODO(binpengsmail@gmail.com): replace some for loop with do {} while

static void idct4_sse2(const __m128i *input, __m128i *output) {
  const int8_t cos_bit = INV_COS_BIT;
  const int32_t *cospi = cospi_arr(INV_COS_BIT);
  const __m128i __rounding = _mm_set1_epi32(1 << (INV_COS_BIT - 1));

  const __m128i cospi_p32_p32 = pair_set_epi16(cospi[32], cospi[32]);
  const __m128i cospi_p32_m32 = pair_set_epi16(cospi[32], -cospi[32]);
  const __m128i cospi_p48_m16 = pair_set_epi16(cospi[48], -cospi[16]);
  const __m128i cospi_p16_p48 = pair_set_epi16(cospi[16], cospi[48]);

  // stage 1
  __m128i x[4];
  x[0] = input[0];
  x[1] = input[2];
  x[2] = input[1];
  x[3] = input[3];

  // stage 2
  btf_16_sse2(cospi_p32_p32, cospi_p32_m32, x[0], x[1], x[0], x[1]);
  btf_16_sse2(cospi_p48_m16, cospi_p16_p48, x[2], x[3], x[2], x[3]);

  // stage 3
  btf_16_adds_subs_out_sse2(output[0], output[3], x[0], x[3]);
  btf_16_adds_subs_out_sse2(output[1], output[2], x[1], x[2]);
}

static void idct4_w4_sse2(const __m128i *input, __m128i *output) {
  const int8_t cos_bit = INV_COS_BIT;
  const int32_t *cospi = cospi_arr(INV_COS_BIT);
  const __m128i __rounding = _mm_set1_epi32(1 << (INV_COS_BIT - 1));

  const __m128i cospi_p32_p32 = pair_set_epi16(cospi[32], cospi[32]);
  const __m128i cospi_p32_m32 = pair_set_epi16(cospi[32], -cospi[32]);
  const __m128i cospi_p48_m16 = pair_set_epi16(cospi[48], -cospi[16]);
  const __m128i cospi_p16_p48 = pair_set_epi16(cospi[16], cospi[48]);

  // stage 1
  __m128i x[4];
  x[0] = input[0];
  x[1] = input[2];
  x[2] = input[1];
  x[3] = input[3];

  // stage 2
  btf_16_4p_sse2(cospi_p32_p32, cospi_p32_m32, x[0], x[1], x[0], x[1]);
  btf_16_4p_sse2(cospi_p48_m16, cospi_p16_p48, x[2], x[3], x[2], x[3]);

  // stage 3
  btf_16_adds_subs_out_sse2(output[0], output[3], x[0], x[3]);
  btf_16_adds_subs_out_sse2(output[1], output[2], x[1], x[2]);
}

static void idct8_low1_ssse3(const __m128i *input, __m128i *output) {
  const int32_t *cospi = cospi_arr(INV_COS_BIT);

  // stage 1
  __m128i x[2];
  x[0] = input[0];

  // stage 2
  // stage 3
  btf_16_ssse3(cospi[32], cospi[32], x[0], x[0], x[1]);

  // stage 4
  // stage 5
  output[0] = x[0];
  output[7] = x[0];
  output[1] = x[1];
  output[6] = x[1];
  output[2] = x[1];
  output[5] = x[1];
  output[3] = x[0];
  output[4] = x[0];
}

static void idct8_sse2(const __m128i *input, __m128i *output) {
  const int8_t cos_bit = INV_COS_BIT;
  const int32_t *cospi = cospi_arr(INV_COS_BIT);
  const __m128i __rounding = _mm_set1_epi32(1 << (INV_COS_BIT - 1));

  const __m128i cospi_p56_m08 = pair_set_epi16(cospi[56], -cospi[8]);
  const __m128i cospi_p08_p56 = pair_set_epi16(cospi[8], cospi[56]);
  const __m128i cospi_p24_m40 = pair_set_epi16(cospi[24], -cospi[40]);
  const __m128i cospi_p40_p24 = pair_set_epi16(cospi[40], cospi[24]);
  const __m128i cospi_p32_p32 = pair_set_epi16(cospi[32], cospi[32]);
  const __m128i cospi_p32_m32 = pair_set_epi16(cospi[32], -cospi[32]);
  const __m128i cospi_p48_m16 = pair_set_epi16(cospi[48], -cospi[16]);
  const __m128i cospi_p16_p48 = pair_set_epi16(cospi[16], cospi[48]);
  const __m128i cospi_m32_p32 = pair_set_epi16(-cospi[32], cospi[32]);

  // stage 1
  __m128i x[8];
  x[0] = input[0];
  x[1] = input[4];
  x[2] = input[2];
  x[3] = input[6];
  x[4] = input[1];
  x[5] = input[5];
  x[6] = input[3];
  x[7] = input[7];

  // stage 2
  btf_16_sse2(cospi_p56_m08, cospi_p08_p56, x[4], x[7], x[4], x[7]);
  btf_16_sse2(cospi_p24_m40, cospi_p40_p24, x[5], x[6], x[5], x[6]);

  // stage 3
  btf_16_sse2(cospi_p32_p32, cospi_p32_m32, x[0], x[1], x[0], x[1]);
  btf_16_sse2(cospi_p48_m16, cospi_p16_p48, x[2], x[3], x[2], x[3]);
  btf_16_adds_subs_sse2(x[4], x[5]);
  btf_16_subs_adds_sse2(x[7], x[6]);

  // stage 4
  btf_16_adds_subs_sse2(x[0], x[3]);
  btf_16_adds_subs_sse2(x[1], x[2]);
  btf_16_sse2(cospi_m32_p32, cospi_p32_p32, x[5], x[6], x[5], x[6]);

  // stage 5
  btf_16_adds_subs_out_sse2(output[0], output[7], x[0], x[7]);
  btf_16_adds_subs_out_sse2(output[1], output[6], x[1], x[6]);
  btf_16_adds_subs_out_sse2(output[2], output[5], x[2], x[5]);
  btf_16_adds_subs_out_sse2(output[3], output[4], x[3], x[4]);
}

static void idct8_w4_sse2(const __m128i *input, __m128i *output) {
  const int8_t cos_bit = INV_COS_BIT;
  const int32_t *cospi = cospi_arr(INV_COS_BIT);
  const __m128i __rounding = _mm_set1_epi32(1 << (INV_COS_BIT - 1));

  const __m128i cospi_p56_m08 = pair_set_epi16(cospi[56], -cospi[8]);
  const __m128i cospi_p08_p56 = pair_set_epi16(cospi[8], cospi[56]);
  const __m128i cospi_p24_m40 = pair_set_epi16(cospi[24], -cospi[40]);
  const __m128i cospi_p40_p24 = pair_set_epi16(cospi[40], cospi[24]);
  const __m128i cospi_p32_p32 = pair_set_epi16(cospi[32], cospi[32]);
  const __m128i cospi_p32_m32 = pair_set_epi16(cospi[32], -cospi[32]);
  const __m128i cospi_p48_m16 = pair_set_epi16(cospi[48], -cospi[16]);
  const __m128i cospi_p16_p48 = pair_set_epi16(cospi[16], cospi[48]);
  const __m128i cospi_m32_p32 = pair_set_epi16(-cospi[32], cospi[32]);

  // stage 1
  __m128i x[8];
  x[0] = input[0];
  x[1] = input[4];
  x[2] = input[2];
  x[3] = input[6];
  x[4] = input[1];
  x[5] = input[5];
  x[6] = input[3];
  x[7] = input[7];

  // stage 2
  btf_16_4p_sse2(cospi_p56_m08, cospi_p08_p56, x[4], x[7], x[4], x[7]);
  btf_16_4p_sse2(cospi_p24_m40, cospi_p40_p24, x[5], x[6], x[5], x[6]);

  // stage 3
  btf_16_4p_sse2(cospi_p32_p32, cospi_p32_m32, x[0], x[1], x[0], x[1]);
  btf_16_4p_sse2(cospi_p48_m16, cospi_p16_p48, x[2], x[3], x[2], x[3]);
  btf_16_adds_subs_sse2(x[4], x[5]);
  btf_16_subs_adds_sse2(x[7], x[6]);

  // stage 4
  btf_16_adds_subs_sse2(x[0], x[3]);
  btf_16_adds_subs_sse2(x[1], x[2]);
  btf_16_4p_sse2(cospi_m32_p32, cospi_p32_p32, x[5], x[6], x[5], x[6]);

  // stage 5
  btf_16_adds_subs_out_sse2(output[0], output[7], x[0], x[7]);
  btf_16_adds_subs_out_sse2(output[1], output[6], x[1], x[6]);
  btf_16_adds_subs_out_sse2(output[2], output[5], x[2], x[5]);
  btf_16_adds_subs_out_sse2(output[3], output[4], x[3], x[4]);
}

static INLINE void idct16_stage5_sse2(__m128i *x, const int32_t *cospi,
                                      const __m128i __rounding,
                                      int8_t cos_bit) {
  const __m128i cospi_m32_p32 = pair_set_epi16(-cospi[32], cospi[32]);
  const __m128i cospi_p32_p32 = pair_set_epi16(cospi[32], cospi[32]);
  btf_16_adds_subs_sse2(x[0], x[3]);
  btf_16_adds_subs_sse2(x[1], x[2]);
  btf_16_sse2(cospi_m32_p32, cospi_p32_p32, x[5], x[6], x[5], x[6]);
  btf_16_adds_subs_sse2(x[8], x[11]);
  btf_16_adds_subs_sse2(x[9], x[10]);
  btf_16_subs_adds_sse2(x[15], x[12]);
  btf_16_subs_adds_sse2(x[14], x[13]);
}

static INLINE void idct16_stage6_sse2(__m128i *x, const int32_t *cospi,
                                      const __m128i __rounding,
                                      int8_t cos_bit) {
  const __m128i cospi_m32_p32 = pair_set_epi16(-cospi[32], cospi[32]);
  const __m128i cospi_p32_p32 = pair_set_epi16(cospi[32], cospi[32]);
  btf_16_adds_subs_sse2(x[0], x[7]);
  btf_16_adds_subs_sse2(x[1], x[6]);
  btf_16_adds_subs_sse2(x[2], x[5]);
  btf_16_adds_subs_sse2(x[3], x[4]);
  btf_16_sse2(cospi_m32_p32, cospi_p32_p32, x[10], x[13], x[10], x[13]);
  btf_16_sse2(cospi_m32_p32, cospi_p32_p32, x[11], x[12], x[11], x[12]);
}

static INLINE void idct16_stage7_sse2(__m128i *output, __m128i *x) {
  btf_16_adds_subs_out_sse2(output[0], output[15], x[0], x[15]);
  btf_16_adds_subs_out_sse2(output[1], output[14], x[1], x[14]);
  btf_16_adds_subs_out_sse2(output[2], output[13], x[2], x[13]);
  btf_16_adds_subs_out_sse2(output[3], output[12], x[3], x[12]);
  btf_16_adds_subs_out_sse2(output[4], output[11], x[4], x[11]);
  btf_16_adds_subs_out_sse2(output[5], output[10], x[5], x[10]);
  btf_16_adds_subs_out_sse2(output[6], output[9], x[6], x[9]);
  btf_16_adds_subs_out_sse2(output[7], output[8], x[7], x[8]);
}

static void idct16_low1_ssse3(const __m128i *input, __m128i *output) {
  const int32_t *cospi = cospi_arr(INV_COS_BIT);

  // stage 1
  __m128i x[2];
  x[0] = input[0];

  // stage 2
  // stage 3
  // stage 4
  btf_16_ssse3(cospi[32], cospi[32], x[0], x[0], x[1]);

  // stage 5
  // stage 6
  // stage 7
  output[0] = x[0];
  output[15] = x[0];
  output[1] = x[1];
  output[14] = x[1];
  output[2] = x[1];
  output[13] = x[1];
  output[3] = x[0];
  output[12] = x[0];
  output[4] = x[0];
  output[11] = x[0];
  output[5] = x[1];
  output[10] = x[1];
  output[6] = x[1];
  output[9] = x[1];
  output[7] = x[0];
  output[8] = x[0];
}

static void idct16_low8_ssse3(const __m128i *input, __m128i *output) {
  const int8_t cos_bit = INV_COS_BIT;
  const int32_t *cospi = cospi_arr(INV_COS_BIT);
  const __m128i __rounding = _mm_set1_epi32(1 << (INV_COS_BIT - 1));
  const __m128i cospi_m16_p48 = pair_set_epi16(-cospi[16], cospi[48]);
  const __m128i cospi_p48_p16 = pair_set_epi16(cospi[48], cospi[16]);
  const __m128i cospi_m48_m16 = pair_set_epi16(-cospi[48], -cospi[16]);

  // stage 1
  __m128i x[16];
  x[0] = input[0];
  x[2] = input[4];
  x[4] = input[2];
  x[6] = input[6];
  x[8] = input[1];
  x[10] = input[5];
  x[12] = input[3];
  x[14] = input[7];

  // stage 2
  btf_16_ssse3(cospi[60], cospi[4], x[8], x[8], x[15]);
  btf_16_ssse3(-cospi[36], cospi[28], x[14], x[9], x[14]);
  btf_16_ssse3(cospi[44], cospi[20], x[10], x[10], x[13]);
  btf_16_ssse3(-cospi[52], cospi[12], x[12], x[11], x[12]);

  // stage 3
  btf_16_ssse3(cospi[56], cospi[8], x[4], x[4], x[7]);
  btf_16_ssse3(-cospi[40], cospi[24], x[6], x[5], x[6]);
  btf_16_adds_subs_sse2(x[8], x[9]);
  btf_16_subs_adds_sse2(x[11], x[10]);
  btf_16_adds_subs_sse2(x[12], x[13]);
  btf_16_subs_adds_sse2(x[15], x[14]);

  // stage 4
  btf_16_ssse3(cospi[32], cospi[32], x[0], x[0], x[1]);
  btf_16_ssse3(cospi[48], cospi[16], x[2], x[2], x[3]);
  btf_16_adds_subs_sse2(x[4], x[5]);
  btf_16_subs_adds_sse2(x[7], x[6]);
  btf_16_sse2(cospi_m16_p48, cospi_p48_p16, x[9], x[14], x[9], x[14]);
  btf_16_sse2(cospi_m48_m16, cospi_m16_p48, x[10], x[13], x[10], x[13]);

  idct16_stage5_sse2(x, cospi, __rounding, cos_bit);
  idct16_stage6_sse2(x, cospi, __rounding, cos_bit);
  idct16_stage7_sse2(output, x);
}

static void idct16_sse2(const __m128i *input, __m128i *output) {
  const int8_t cos_bit = INV_COS_BIT;
  const int32_t *cospi = cospi_arr(INV_COS_BIT);
  const __m128i __rounding = _mm_set1_epi32(1 << (INV_COS_BIT - 1));

  const __m128i cospi_p60_m04 = pair_set_epi16(cospi[60], -cospi[4]);
  const __m128i cospi_p04_p60 = pair_set_epi16(cospi[4], cospi[60]);
  const __m128i cospi_p28_m36 = pair_set_epi16(cospi[28], -cospi[36]);
  const __m128i cospi_p36_p28 = pair_set_epi16(cospi[36], cospi[28]);
  const __m128i cospi_p44_m20 = pair_set_epi16(cospi[44], -cospi[20]);
  const __m128i cospi_p20_p44 = pair_set_epi16(cospi[20], cospi[44]);
  const __m128i cospi_p12_m52 = pair_set_epi16(cospi[12], -cospi[52]);
  const __m128i cospi_p52_p12 = pair_set_epi16(cospi[52], cospi[12]);
  const __m128i cospi_p56_m08 = pair_set_epi16(cospi[56], -cospi[8]);
  const __m128i cospi_p08_p56 = pair_set_epi16(cospi[8], cospi[56]);
  const __m128i cospi_p24_m40 = pair_set_epi16(cospi[24], -cospi[40]);
  const __m128i cospi_p40_p24 = pair_set_epi16(cospi[40], cospi[24]);
  const __m128i cospi_p32_p32 = pair_set_epi16(cospi[32], cospi[32]);
  const __m128i cospi_p32_m32 = pair_set_epi16(cospi[32], -cospi[32]);
  const __m128i cospi_p48_m16 = pair_set_epi16(cospi[48], -cospi[16]);
  const __m128i cospi_p16_p48 = pair_set_epi16(cospi[16], cospi[48]);
  const __m128i cospi_m16_p48 = pair_set_epi16(-cospi[16], cospi[48]);
  const __m128i cospi_p48_p16 = pair_set_epi16(cospi[48], cospi[16]);
  const __m128i cospi_m48_m16 = pair_set_epi16(-cospi[48], -cospi[16]);

  // stage 1
  __m128i x[16];
  x[0] = input[0];
  x[1] = input[8];
  x[2] = input[4];
  x[3] = input[12];
  x[4] = input[2];
  x[5] = input[10];
  x[6] = input[6];
  x[7] = input[14];
  x[8] = input[1];
  x[9] = input[9];
  x[10] = input[5];
  x[11] = input[13];
  x[12] = input[3];
  x[13] = input[11];
  x[14] = input[7];
  x[15] = input[15];

  // stage 2
  btf_16_sse2(cospi_p60_m04, cospi_p04_p60, x[8], x[15], x[8], x[15]);
  btf_16_sse2(cospi_p28_m36, cospi_p36_p28, x[9], x[14], x[9], x[14]);
  btf_16_sse2(cospi_p44_m20, cospi_p20_p44, x[10], x[13], x[10], x[13]);
  btf_16_sse2(cospi_p12_m52, cospi_p52_p12, x[11], x[12], x[11], x[12]);

  // stage 3
  btf_16_sse2(cospi_p56_m08, cospi_p08_p56, x[4], x[7], x[4], x[7]);
  btf_16_sse2(cospi_p24_m40, cospi_p40_p24, x[5], x[6], x[5], x[6]);
  btf_16_adds_subs_sse2(x[8], x[9]);
  btf_16_subs_adds_sse2(x[11], x[10]);
  btf_16_adds_subs_sse2(x[12], x[13]);
  btf_16_subs_adds_sse2(x[15], x[14]);

  // stage 4
  btf_16_sse2(cospi_p32_p32, cospi_p32_m32, x[0], x[1], x[0], x[1]);
  btf_16_sse2(cospi_p48_m16, cospi_p16_p48, x[2], x[3], x[2], x[3]);
  btf_16_adds_subs_sse2(x[4], x[5]);
  btf_16_subs_adds_sse2(x[7], x[6]);
  btf_16_sse2(cospi_m16_p48, cospi_p48_p16, x[9], x[14], x[9], x[14]);
  btf_16_sse2(cospi_m48_m16, cospi_m16_p48, x[10], x[13], x[10], x[13]);

  // stage 5~7
  idct16_stage5_sse2(x, cospi, __rounding, cos_bit);
  idct16_stage6_sse2(x, cospi, __rounding, cos_bit);
  idct16_stage7_sse2(output, x);
}

static void idct16_w4_sse2(const __m128i *input, __m128i *output) {
  const int8_t cos_bit = INV_COS_BIT;
  const int32_t *cospi = cospi_arr(INV_COS_BIT);
  const __m128i __rounding = _mm_set1_epi32(1 << (INV_COS_BIT - 1));

  const __m128i cospi_p60_m04 = pair_set_epi16(cospi[60], -cospi[4]);
  const __m128i cospi_p04_p60 = pair_set_epi16(cospi[4], cospi[60]);
  const __m128i cospi_p28_m36 = pair_set_epi16(cospi[28], -cospi[36]);
  const __m128i cospi_p36_p28 = pair_set_epi16(cospi[36], cospi[28]);
  const __m128i cospi_p44_m20 = pair_set_epi16(cospi[44], -cospi[20]);
  const __m128i cospi_p20_p44 = pair_set_epi16(cospi[20], cospi[44]);
  const __m128i cospi_p12_m52 = pair_set_epi16(cospi[12], -cospi[52]);
  const __m128i cospi_p52_p12 = pair_set_epi16(cospi[52], cospi[12]);
  const __m128i cospi_p56_m08 = pair_set_epi16(cospi[56], -cospi[8]);
  const __m128i cospi_p08_p56 = pair_set_epi16(cospi[8], cospi[56]);
  const __m128i cospi_p24_m40 = pair_set_epi16(cospi[24], -cospi[40]);
  const __m128i cospi_p40_p24 = pair_set_epi16(cospi[40], cospi[24]);
  const __m128i cospi_p32_p32 = pair_set_epi16(cospi[32], cospi[32]);
  const __m128i cospi_p32_m32 = pair_set_epi16(cospi[32], -cospi[32]);
  const __m128i cospi_p48_m16 = pair_set_epi16(cospi[48], -cospi[16]);
  const __m128i cospi_p16_p48 = pair_set_epi16(cospi[16], cospi[48]);
  const __m128i cospi_m16_p48 = pair_set_epi16(-cospi[16], cospi[48]);
  const __m128i cospi_p48_p16 = pair_set_epi16(cospi[48], cospi[16]);
  const __m128i cospi_m48_m16 = pair_set_epi16(-cospi[48], -cospi[16]);
  const __m128i cospi_m32_p32 = pair_set_epi16(-cospi[32], cospi[32]);

  // stage 1
  __m128i x[16];
  x[0] = input[0];
  x[1] = input[8];
  x[2] = input[4];
  x[3] = input[12];
  x[4] = input[2];
  x[5] = input[10];
  x[6] = input[6];
  x[7] = input[14];
  x[8] = input[1];
  x[9] = input[9];
  x[10] = input[5];
  x[11] = input[13];
  x[12] = input[3];
  x[13] = input[11];
  x[14] = input[7];
  x[15] = input[15];

  // stage 2
  btf_16_4p_sse2(cospi_p60_m04, cospi_p04_p60, x[8], x[15], x[8], x[15]);
  btf_16_4p_sse2(cospi_p28_m36, cospi_p36_p28, x[9], x[14], x[9], x[14]);
  btf_16_4p_sse2(cospi_p44_m20, cospi_p20_p44, x[10], x[13], x[10], x[13]);
  btf_16_4p_sse2(cospi_p12_m52, cospi_p52_p12, x[11], x[12], x[11], x[12]);

  // stage 3
  btf_16_4p_sse2(cospi_p56_m08, cospi_p08_p56, x[4], x[7], x[4], x[7]);
  btf_16_4p_sse2(cospi_p24_m40, cospi_p40_p24, x[5], x[6], x[5], x[6]);
  btf_16_adds_subs_sse2(x[8], x[9]);
  btf_16_subs_adds_sse2(x[11], x[10]);
  btf_16_adds_subs_sse2(x[12], x[13]);
  btf_16_subs_adds_sse2(x[15], x[14]);

  // stage 4
  btf_16_4p_sse2(cospi_p32_p32, cospi_p32_m32, x[0], x[1], x[0], x[1]);
  btf_16_4p_sse2(cospi_p48_m16, cospi_p16_p48, x[2], x[3], x[2], x[3]);
  btf_16_adds_subs_sse2(x[4], x[5]);
  btf_16_subs_adds_sse2(x[7], x[6]);
  btf_16_4p_sse2(cospi_m16_p48, cospi_p48_p16, x[9], x[14], x[9], x[14]);
  btf_16_4p_sse2(cospi_m48_m16, cospi_m16_p48, x[10], x[13], x[10], x[13]);

  // stage 5
  btf_16_adds_subs_sse2(x[0], x[3]);
  btf_16_adds_subs_sse2(x[1], x[2]);
  btf_16_4p_sse2(cospi_m32_p32, cospi_p32_p32, x[5], x[6], x[5], x[6]);
  btf_16_adds_subs_sse2(x[8], x[11]);
  btf_16_adds_subs_sse2(x[9], x[10]);
  btf_16_subs_adds_sse2(x[15], x[12]);
  btf_16_subs_adds_sse2(x[14], x[13]);

  // stage 6
  btf_16_adds_subs_sse2(x[0], x[7]);
  btf_16_adds_subs_sse2(x[1], x[6]);
  btf_16_adds_subs_sse2(x[2], x[5]);
  btf_16_adds_subs_sse2(x[3], x[4]);
  btf_16_4p_sse2(cospi_m32_p32, cospi_p32_p32, x[10], x[13], x[10], x[13]);
  btf_16_4p_sse2(cospi_m32_p32, cospi_p32_p32, x[11], x[12], x[11], x[12]);

  // stage 7
  idct16_stage7_sse2(output, x);
}

static INLINE void idct32_high16_stage3_sse2(__m128i *x) {
  btf_16_adds_subs_sse2(x[16], x[17]);
  btf_16_subs_adds_sse2(x[19], x[18]);
  btf_16_adds_subs_sse2(x[20], x[21]);
  btf_16_subs_adds_sse2(x[23], x[22]);
  btf_16_adds_subs_sse2(x[24], x[25]);
  btf_16_subs_adds_sse2(x[27], x[26]);
  btf_16_adds_subs_sse2(x[28], x[29]);
  btf_16_subs_adds_sse2(x[31], x[30]);
}

static INLINE void idct32_high16_stage4_sse2(__m128i *x, const int32_t *cospi,
                                             const __m128i __rounding,
                                             int8_t cos_bit) {
  const __m128i cospi_m08_p56 = pair_set_epi16(-cospi[8], cospi[56]);
  const __m128i cospi_p56_p08 = pair_set_epi16(cospi[56], cospi[8]);
  const __m128i cospi_m56_m08 = pair_set_epi16(-cospi[56], -cospi[8]);
  const __m128i cospi_m40_p24 = pair_set_epi16(-cospi[40], cospi[24]);
  const __m128i cospi_p24_p40 = pair_set_epi16(cospi[24], cospi[40]);
  const __m128i cospi_m24_m40 = pair_set_epi16(-cospi[24], -cospi[40]);
  btf_16_sse2(cospi_m08_p56, cospi_p56_p08, x[17], x[30], x[17], x[30]);
  btf_16_sse2(cospi_m56_m08, cospi_m08_p56, x[18], x[29], x[18], x[29]);
  btf_16_sse2(cospi_m40_p24, cospi_p24_p40, x[21], x[26], x[21], x[26]);
  btf_16_sse2(cospi_m24_m40, cospi_m40_p24, x[22], x[25], x[22], x[25]);
}

static INLINE void idct32_high24_stage5_sse2(__m128i *x, const int32_t *cospi,
                                             const __m128i __rounding,
                                             int8_t cos_bit) {
  const __m128i cospi_m16_p48 = pair_set_epi16(-cospi[16], cospi[48]);
  const __m128i cospi_p48_p16 = pair_set_epi16(cospi[48], cospi[16]);
  const __m128i cospi_m48_m16 = pair_set_epi16(-cospi[48], -cospi[16]);
  btf_16_sse2(cospi_m16_p48, cospi_p48_p16, x[9], x[14], x[9], x[14]);
  btf_16_sse2(cospi_m48_m16, cospi_m16_p48, x[10], x[13], x[10], x[13]);
  btf_16_adds_subs_sse2(x[16], x[19]);
  btf_16_adds_subs_sse2(x[17], x[18]);
  btf_16_subs_adds_sse2(x[23], x[20]);
  btf_16_subs_adds_sse2(x[22], x[21]);
  btf_16_adds_subs_sse2(x[24], x[27]);
  btf_16_adds_subs_sse2(x[25], x[26]);
  btf_16_subs_adds_sse2(x[31], x[28]);
  btf_16_subs_adds_sse2(x[30], x[29]);
}

static INLINE void idct32_high28_stage6_sse2(__m128i *x, const int32_t *cospi,
                                             const __m128i __rounding,
                                             int8_t cos_bit) {
  const __m128i cospi_m32_p32 = pair_set_epi16(-cospi[32], cospi[32]);
  const __m128i cospi_p32_p32 = pair_set_epi16(cospi[32], cospi[32]);
  const __m128i cospi_m16_p48 = pair_set_epi16(-cospi[16], cospi[48]);
  const __m128i cospi_p48_p16 = pair_set_epi16(cospi[48], cospi[16]);
  const __m128i cospi_m48_m16 = pair_set_epi16(-cospi[48], -cospi[16]);
  btf_16_sse2(cospi_m32_p32, cospi_p32_p32, x[5], x[6], x[5], x[6]);
  btf_16_adds_subs_sse2(x[8], x[11]);
  btf_16_adds_subs_sse2(x[9], x[10]);
  btf_16_subs_adds_sse2(x[15], x[12]);
  btf_16_subs_adds_sse2(x[14], x[13]);
  btf_16_sse2(cospi_m16_p48, cospi_p48_p16, x[18], x[29], x[18], x[29]);
  btf_16_sse2(cospi_m16_p48, cospi_p48_p16, x[19], x[28], x[19], x[28]);
  btf_16_sse2(cospi_m48_m16, cospi_m16_p48, x[20], x[27], x[20], x[27]);
  btf_16_sse2(cospi_m48_m16, cospi_m16_p48, x[21], x[26], x[21], x[26]);
}

static INLINE void idct32_stage7_sse2(__m128i *x, const int32_t *cospi,
                                      const __m128i __rounding,
                                      int8_t cos_bit) {
  const __m128i cospi_m32_p32 = pair_set_epi16(-cospi[32], cospi[32]);
  const __m128i cospi_p32_p32 = pair_set_epi16(cospi[32], cospi[32]);
  btf_16_adds_subs_sse2(x[0], x[7]);
  btf_16_adds_subs_sse2(x[1], x[6]);
  btf_16_adds_subs_sse2(x[2], x[5]);
  btf_16_adds_subs_sse2(x[3], x[4]);
  btf_16_sse2(cospi_m32_p32, cospi_p32_p32, x[10], x[13], x[10], x[13]);
  btf_16_sse2(cospi_m32_p32, cospi_p32_p32, x[11], x[12], x[11], x[12]);
  btf_16_adds_subs_sse2(x[16], x[23]);
  btf_16_adds_subs_sse2(x[17], x[22]);
  btf_16_adds_subs_sse2(x[18], x[21]);
  btf_16_adds_subs_sse2(x[19], x[20]);
  btf_16_subs_adds_sse2(x[31], x[24]);
  btf_16_subs_adds_sse2(x[30], x[25]);
  btf_16_subs_adds_sse2(x[29], x[26]);
  btf_16_subs_adds_sse2(x[28], x[27]);
}

static INLINE void idct32_stage8_sse2(__m128i *x, const int32_t *cospi,
                                      const __m128i __rounding,
                                      int8_t cos_bit) {
  const __m128i cospi_m32_p32 = pair_set_epi16(-cospi[32], cospi[32]);
  const __m128i cospi_p32_p32 = pair_set_epi16(cospi[32], cospi[32]);
  btf_16_adds_subs_sse2(x[0], x[15]);
  btf_16_adds_subs_sse2(x[1], x[14]);
  btf_16_adds_subs_sse2(x[2], x[13]);
  btf_16_adds_subs_sse2(x[3], x[12]);
  btf_16_adds_subs_sse2(x[4], x[11]);
  btf_16_adds_subs_sse2(x[5], x[10]);
  btf_16_adds_subs_sse2(x[6], x[9]);
  btf_16_adds_subs_sse2(x[7], x[8]);
  btf_16_sse2(cospi_m32_p32, cospi_p32_p32, x[20], x[27], x[20], x[27]);
  btf_16_sse2(cospi_m32_p32, cospi_p32_p32, x[21], x[26], x[21], x[26]);
  btf_16_sse2(cospi_m32_p32, cospi_p32_p32, x[22], x[25], x[22], x[25]);
  btf_16_sse2(cospi_m32_p32, cospi_p32_p32, x[23], x[24], x[23], x[24]);
}

static INLINE void idct32_stage9_sse2(__m128i *output, __m128i *x) {
  btf_16_adds_subs_out_sse2(output[0], output[31], x[0], x[31]);
  btf_16_adds_subs_out_sse2(output[1], output[30], x[1], x[30]);
  btf_16_adds_subs_out_sse2(output[2], output[29], x[2], x[29]);
  btf_16_adds_subs_out_sse2(output[3], output[28], x[3], x[28]);
  btf_16_adds_subs_out_sse2(output[4], output[27], x[4], x[27]);
  btf_16_adds_subs_out_sse2(output[5], output[26], x[5], x[26]);
  btf_16_adds_subs_out_sse2(output[6], output[25], x[6], x[25]);
  btf_16_adds_subs_out_sse2(output[7], output[24], x[7], x[24]);
  btf_16_adds_subs_out_sse2(output[8], output[23], x[8], x[23]);
  btf_16_adds_subs_out_sse2(output[9], output[22], x[9], x[22]);
  btf_16_adds_subs_out_sse2(output[10], output[21], x[10], x[21]);
  btf_16_adds_subs_out_sse2(output[11], output[20], x[11], x[20]);
  btf_16_adds_subs_out_sse2(output[12], output[19], x[12], x[19]);
  btf_16_adds_subs_out_sse2(output[13], output[18], x[13], x[18]);
  btf_16_adds_subs_out_sse2(output[14], output[17], x[14], x[17]);
  btf_16_adds_subs_out_sse2(output[15], output[16], x[15], x[16]);
}

static void idct32_low1_ssse3(const __m128i *input, __m128i *output) {
  const int32_t *cospi = cospi_arr(INV_COS_BIT);

  // stage 1
  __m128i x[2];
  x[0] = input[0];

  // stage 2
  // stage 3
  // stage 4
  // stage 5
  btf_16_ssse3(cospi[32], cospi[32], x[0], x[0], x[1]);

  // stage 6
  // stage 7
  // stage 8
  // stage 9
  output[0] = x[0];
  output[31] = x[0];
  output[1] = x[1];
  output[30] = x[1];
  output[2] = x[1];
  output[29] = x[1];
  output[3] = x[0];
  output[28] = x[0];
  output[4] = x[0];
  output[27] = x[0];
  output[5] = x[1];
  output[26] = x[1];
  output[6] = x[1];
  output[25] = x[1];
  output[7] = x[0];
  output[24] = x[0];
  output[8] = x[0];
  output[23] = x[0];
  output[9] = x[1];
  output[22] = x[1];
  output[10] = x[1];
  output[21] = x[1];
  output[11] = x[0];
  output[20] = x[0];
  output[12] = x[0];
  output[19] = x[0];
  output[13] = x[1];
  output[18] = x[1];
  output[14] = x[1];
  output[17] = x[1];
  output[15] = x[0];
  output[16] = x[0];
}

static void idct32_low8_ssse3(const __m128i *input, __m128i *output) {
  const int8_t cos_bit = INV_COS_BIT;
  const int32_t *cospi = cospi_arr(INV_COS_BIT);
  const __m128i __rounding = _mm_set1_epi32(1 << (INV_COS_BIT - 1));

  // stage 1
  __m128i x[32];
  x[0] = input[0];
  x[4] = input[4];
  x[8] = input[2];
  x[12] = input[6];
  x[16] = input[1];
  x[20] = input[5];
  x[24] = input[3];
  x[28] = input[7];

  // stage 2
  btf_16_ssse3(cospi[62], cospi[2], x[16], x[16], x[31]);
  btf_16_ssse3(-cospi[50], cospi[14], x[28], x[19], x[28]);
  btf_16_ssse3(cospi[54], cospi[10], x[20], x[20], x[27]);
  btf_16_ssse3(-cospi[58], cospi[6], x[24], x[23], x[24]);

  // stage 3
  btf_16_ssse3(cospi[60], cospi[4], x[8], x[8], x[15]);
  btf_16_ssse3(-cospi[52], cospi[12], x[12], x[11], x[12]);
  x[17] = x[16];
  x[18] = x[19];
  x[21] = x[20];
  x[22] = x[23];
  x[25] = x[24];
  x[26] = x[27];
  x[29] = x[28];
  x[30] = x[31];

  // stage 4
  btf_16_ssse3(cospi[56], cospi[8], x[4], x[4], x[7]);
  x[9] = x[8];
  x[10] = x[11];
  x[13] = x[12];
  x[14] = x[15];
  idct32_high16_stage4_sse2(x, cospi, __rounding, cos_bit);

  // stage 5
  btf_16_ssse3(cospi[32], cospi[32], x[0], x[0], x[1]);
  x[5] = x[4];
  x[6] = x[7];
  idct32_high24_stage5_sse2(x, cospi, __rounding, cos_bit);
  // stage 6
  x[3] = x[0];
  x[2] = x[1];
  idct32_high28_stage6_sse2(x, cospi, __rounding, cos_bit);

  idct32_stage7_sse2(x, cospi, __rounding, cos_bit);
  idct32_stage8_sse2(x, cospi, __rounding, cos_bit);
  idct32_stage9_sse2(output, x);
}

static void idct32_low16_ssse3(const __m128i *input, __m128i *output) {
  const int8_t cos_bit = INV_COS_BIT;
  const int32_t *cospi = cospi_arr(INV_COS_BIT);
  const __m128i __rounding = _mm_set1_epi32(1 << (INV_COS_BIT - 1));

  // stage 1
  __m128i x[32];
  x[0] = input[0];
  x[2] = input[8];
  x[4] = input[4];
  x[6] = input[12];
  x[8] = input[2];
  x[10] = input[10];
  x[12] = input[6];
  x[14] = input[14];
  x[16] = input[1];
  x[18] = input[9];
  x[20] = input[5];
  x[22] = input[13];
  x[24] = input[3];
  x[26] = input[11];
  x[28] = input[7];
  x[30] = input[15];

  // stage 2
  btf_16_ssse3(cospi[62], cospi[2], x[16], x[16], x[31]);
  btf_16_ssse3(-cospi[34], cospi[30], x[30], x[17], x[30]);
  btf_16_ssse3(cospi[46], cospi[18], x[18], x[18], x[29]);
  btf_16_ssse3(-cospi[50], cospi[14], x[28], x[19], x[28]);
  btf_16_ssse3(cospi[54], cospi[10], x[20], x[20], x[27]);
  btf_16_ssse3(-cospi[42], cospi[22], x[26], x[21], x[26]);
  btf_16_ssse3(cospi[38], cospi[26], x[22], x[22], x[25]);
  btf_16_ssse3(-cospi[58], cospi[6], x[24], x[23], x[24]);

  // stage 3
  btf_16_ssse3(cospi[60], cospi[4], x[8], x[8], x[15]);
  btf_16_ssse3(-cospi[36], cospi[28], x[14], x[9], x[14]);
  btf_16_ssse3(cospi[44], cospi[20], x[10], x[10], x[13]);
  btf_16_ssse3(-cospi[52], cospi[12], x[12], x[11], x[12]);
  idct32_high16_stage3_sse2(x);

  // stage 4
  btf_16_ssse3(cospi[56], cospi[8], x[4], x[4], x[7]);
  btf_16_ssse3(-cospi[40], cospi[24], x[6], x[5], x[6]);
  btf_16_adds_subs_sse2(x[8], x[9]);
  btf_16_subs_adds_sse2(x[11], x[10]);
  btf_16_adds_subs_sse2(x[12], x[13]);
  btf_16_subs_adds_sse2(x[15], x[14]);
  idct32_high16_stage4_sse2(x, cospi, __rounding, cos_bit);

  // stage 5
  btf_16_ssse3(cospi[32], cospi[32], x[0], x[0], x[1]);
  btf_16_ssse3(cospi[48], cospi[16], x[2], x[2], x[3]);
  btf_16_adds_subs_sse2(x[4], x[5]);
  btf_16_subs_adds_sse2(x[7], x[6]);
  idct32_high24_stage5_sse2(x, cospi, __rounding, cos_bit);

  btf_16_adds_subs_sse2(x[0], x[3]);
  btf_16_adds_subs_sse2(x[1], x[2]);
  idct32_high28_stage6_sse2(x, cospi, __rounding, cos_bit);

  idct32_stage7_sse2(x, cospi, __rounding, cos_bit);
  idct32_stage8_sse2(x, cospi, __rounding, cos_bit);
  idct32_stage9_sse2(output, x);
}

static void idct32_sse2(const __m128i *input, __m128i *output) {
  const int8_t cos_bit = INV_COS_BIT;
  const int32_t *cospi = cospi_arr(INV_COS_BIT);
  const __m128i __rounding = _mm_set1_epi32(1 << (INV_COS_BIT - 1));

  const __m128i cospi_p62_m02 = pair_set_epi16(cospi[62], -cospi[2]);
  const __m128i cospi_p02_p62 = pair_set_epi16(cospi[2], cospi[62]);
  const __m128i cospi_p30_m34 = pair_set_epi16(cospi[30], -cospi[34]);
  const __m128i cospi_p34_p30 = pair_set_epi16(cospi[34], cospi[30]);
  const __m128i cospi_p46_m18 = pair_set_epi16(cospi[46], -cospi[18]);
  const __m128i cospi_p18_p46 = pair_set_epi16(cospi[18], cospi[46]);
  const __m128i cospi_p14_m50 = pair_set_epi16(cospi[14], -cospi[50]);
  const __m128i cospi_p50_p14 = pair_set_epi16(cospi[50], cospi[14]);
  const __m128i cospi_p54_m10 = pair_set_epi16(cospi[54], -cospi[10]);
  const __m128i cospi_p10_p54 = pair_set_epi16(cospi[10], cospi[54]);
  const __m128i cospi_p22_m42 = pair_set_epi16(cospi[22], -cospi[42]);
  const __m128i cospi_p42_p22 = pair_set_epi16(cospi[42], cospi[22]);
  const __m128i cospi_p38_m26 = pair_set_epi16(cospi[38], -cospi[26]);
  const __m128i cospi_p26_p38 = pair_set_epi16(cospi[26], cospi[38]);
  const __m128i cospi_p06_m58 = pair_set_epi16(cospi[6], -cospi[58]);
  const __m128i cospi_p58_p06 = pair_set_epi16(cospi[58], cospi[6]);
  const __m128i cospi_p60_m04 = pair_set_epi16(cospi[60], -cospi[4]);
  const __m128i cospi_p04_p60 = pair_set_epi16(cospi[4], cospi[60]);
  const __m128i cospi_p28_m36 = pair_set_epi16(cospi[28], -cospi[36]);
  const __m128i cospi_p36_p28 = pair_set_epi16(cospi[36], cospi[28]);
  const __m128i cospi_p44_m20 = pair_set_epi16(cospi[44], -cospi[20]);
  const __m128i cospi_p20_p44 = pair_set_epi16(cospi[20], cospi[44]);
  const __m128i cospi_p12_m52 = pair_set_epi16(cospi[12], -cospi[52]);
  const __m128i cospi_p52_p12 = pair_set_epi16(cospi[52], cospi[12]);
  const __m128i cospi_p56_m08 = pair_set_epi16(cospi[56], -cospi[8]);
  const __m128i cospi_p08_p56 = pair_set_epi16(cospi[8], cospi[56]);
  const __m128i cospi_p24_m40 = pair_set_epi16(cospi[24], -cospi[40]);
  const __m128i cospi_p40_p24 = pair_set_epi16(cospi[40], cospi[24]);
  const __m128i cospi_p32_p32 = pair_set_epi16(cospi[32], cospi[32]);
  const __m128i cospi_p32_m32 = pair_set_epi16(cospi[32], -cospi[32]);
  const __m128i cospi_p48_m16 = pair_set_epi16(cospi[48], -cospi[16]);
  const __m128i cospi_p16_p48 = pair_set_epi16(cospi[16], cospi[48]);

  // stage 1
  __m128i x[32];
  x[0] = input[0];
  x[1] = input[16];
  x[2] = input[8];
  x[3] = input[24];
  x[4] = input[4];
  x[5] = input[20];
  x[6] = input[12];
  x[7] = input[28];
  x[8] = input[2];
  x[9] = input[18];
  x[10] = input[10];
  x[11] = input[26];
  x[12] = input[6];
  x[13] = input[22];
  x[14] = input[14];
  x[15] = input[30];
  x[16] = input[1];
  x[17] = input[17];
  x[18] = input[9];
  x[19] = input[25];
  x[20] = input[5];
  x[21] = input[21];
  x[22] = input[13];
  x[23] = input[29];
  x[24] = input[3];
  x[25] = input[19];
  x[26] = input[11];
  x[27] = input[27];
  x[28] = input[7];
  x[29] = input[23];
  x[30] = input[15];
  x[31] = input[31];

  // stage 2
  btf_16_sse2(cospi_p62_m02, cospi_p02_p62, x[16], x[31], x[16], x[31]);
  btf_16_sse2(cospi_p30_m34, cospi_p34_p30, x[17], x[30], x[17], x[30]);
  btf_16_sse2(cospi_p46_m18, cospi_p18_p46, x[18], x[29], x[18], x[29]);
  btf_16_sse2(cospi_p14_m50, cospi_p50_p14, x[19], x[28], x[19], x[28]);
  btf_16_sse2(cospi_p54_m10, cospi_p10_p54, x[20], x[27], x[20], x[27]);
  btf_16_sse2(cospi_p22_m42, cospi_p42_p22, x[21], x[26], x[21], x[26]);
  btf_16_sse2(cospi_p38_m26, cospi_p26_p38, x[22], x[25], x[22], x[25]);
  btf_16_sse2(cospi_p06_m58, cospi_p58_p06, x[23], x[24], x[23], x[24]);

  // stage 3
  btf_16_sse2(cospi_p60_m04, cospi_p04_p60, x[8], x[15], x[8], x[15]);
  btf_16_sse2(cospi_p28_m36, cospi_p36_p28, x[9], x[14], x[9], x[14]);
  btf_16_sse2(cospi_p44_m20, cospi_p20_p44, x[10], x[13], x[10], x[13]);
  btf_16_sse2(cospi_p12_m52, cospi_p52_p12, x[11], x[12], x[11], x[12]);
  idct32_high16_stage3_sse2(x);

  // stage 4
  btf_16_sse2(cospi_p56_m08, cospi_p08_p56, x[4], x[7], x[4], x[7]);
  btf_16_sse2(cospi_p24_m40, cospi_p40_p24, x[5], x[6], x[5], x[6]);
  btf_16_adds_subs_sse2(x[8], x[9]);
  btf_16_subs_adds_sse2(x[11], x[10]);
  btf_16_adds_subs_sse2(x[12], x[13]);
  btf_16_subs_adds_sse2(x[15], x[14]);
  idct32_high16_stage4_sse2(x, cospi, __rounding, cos_bit);

  // stage 5
  btf_16_sse2(cospi_p32_p32, cospi_p32_m32, x[0], x[1], x[0], x[1]);
  btf_16_sse2(cospi_p48_m16, cospi_p16_p48, x[2], x[3], x[2], x[3]);
  btf_16_adds_subs_sse2(x[4], x[5]);
  btf_16_adds_subs_sse2(x[7], x[6]);
  idct32_high24_stage5_sse2(x, cospi, __rounding, cos_bit);

  // stage 6
  btf_16_adds_subs_sse2(x[0], x[3]);
  btf_16_adds_subs_sse2(x[1], x[2]);
  idct32_high28_stage6_sse2(x, cospi, __rounding, cos_bit);

  // stage 7~8
  idct32_stage7_sse2(x, cospi, __rounding, cos_bit);
  idct32_stage8_sse2(x, cospi, __rounding, cos_bit);
  idct32_stage9_sse2(output, x);
}

static INLINE void idct64_stage4_high32_sse2(__m128i *x, const int32_t *cospi,
                                             const __m128i __rounding,
                                             int8_t cos_bit) {
  const __m128i cospi_m04_p60 = pair_set_epi16(-cospi[4], cospi[60]);
  const __m128i cospi_p60_p04 = pair_set_epi16(cospi[60], cospi[4]);
  const __m128i cospi_m60_m04 = pair_set_epi16(-cospi[60], -cospi[4]);
  const __m128i cospi_m36_p28 = pair_set_epi16(-cospi[36], cospi[28]);
  const __m128i cospi_p28_p36 = pair_set_epi16(cospi[28], cospi[36]);
  const __m128i cospi_m28_m36 = pair_set_epi16(-cospi[28], -cospi[36]);
  const __m128i cospi_m20_p44 = pair_set_epi16(-cospi[20], cospi[44]);
  const __m128i cospi_p44_p20 = pair_set_epi16(cospi[44], cospi[20]);
  const __m128i cospi_m44_m20 = pair_set_epi16(-cospi[44], -cospi[20]);
  const __m128i cospi_m52_p12 = pair_set_epi16(-cospi[52], cospi[12]);
  const __m128i cospi_p12_p52 = pair_set_epi16(cospi[12], cospi[52]);
  const __m128i cospi_m12_m52 = pair_set_epi16(-cospi[12], -cospi[52]);
  btf_16_sse2(cospi_m04_p60, cospi_p60_p04, x[33], x[62], x[33], x[62]);
  btf_16_sse2(cospi_m60_m04, cospi_m04_p60, x[34], x[61], x[34], x[61]);
  btf_16_sse2(cospi_m36_p28, cospi_p28_p36, x[37], x[58], x[37], x[58]);
  btf_16_sse2(cospi_m28_m36, cospi_m36_p28, x[38], x[57], x[38], x[57]);
  btf_16_sse2(cospi_m20_p44, cospi_p44_p20, x[41], x[54], x[41], x[54]);
  btf_16_sse2(cospi_m44_m20, cospi_m20_p44, x[42], x[53], x[42], x[53]);
  btf_16_sse2(cospi_m52_p12, cospi_p12_p52, x[45], x[50], x[45], x[50]);
  btf_16_sse2(cospi_m12_m52, cospi_m52_p12, x[46], x[49], x[46], x[49]);
}

static INLINE void idct64_stage5_high48_sse2(__m128i *x, const int32_t *cospi,
                                             const __m128i __rounding,
                                             int8_t cos_bit) {
  const __m128i cospi_m08_p56 = pair_set_epi16(-cospi[8], cospi[56]);
  const __m128i cospi_p56_p08 = pair_set_epi16(cospi[56], cospi[8]);
  const __m128i cospi_m56_m08 = pair_set_epi16(-cospi[56], -cospi[8]);
  const __m128i cospi_m40_p24 = pair_set_epi16(-cospi[40], cospi[24]);
  const __m128i cospi_p24_p40 = pair_set_epi16(cospi[24], cospi[40]);
  const __m128i cospi_m24_m40 = pair_set_epi16(-cospi[24], -cospi[40]);
  btf_16_sse2(cospi_m08_p56, cospi_p56_p08, x[17], x[30], x[17], x[30]);
  btf_16_sse2(cospi_m56_m08, cospi_m08_p56, x[18], x[29], x[18], x[29]);
  btf_16_sse2(cospi_m40_p24, cospi_p24_p40, x[21], x[26], x[21], x[26]);
  btf_16_sse2(cospi_m24_m40, cospi_m40_p24, x[22], x[25], x[22], x[25]);
  btf_16_adds_subs_sse2(x[32], x[35]);
  btf_16_adds_subs_sse2(x[33], x[34]);
  btf_16_subs_adds_sse2(x[39], x[36]);
  btf_16_subs_adds_sse2(x[38], x[37]);
  btf_16_adds_subs_sse2(x[40], x[43]);
  btf_16_adds_subs_sse2(x[41], x[42]);
  btf_16_subs_adds_sse2(x[47], x[44]);
  btf_16_subs_adds_sse2(x[46], x[45]);
  btf_16_adds_subs_sse2(x[48], x[51]);
  btf_16_adds_subs_sse2(x[49], x[50]);
  btf_16_subs_adds_sse2(x[55], x[52]);
  btf_16_subs_adds_sse2(x[54], x[53]);
  btf_16_adds_subs_sse2(x[56], x[59]);
  btf_16_adds_subs_sse2(x[57], x[58]);
  btf_16_subs_adds_sse2(x[63], x[60]);
  btf_16_subs_adds_sse2(x[62], x[61]);
}

static INLINE void idct64_stage6_high32_sse2(__m128i *x, const int32_t *cospi,
                                             const __m128i __rounding,
                                             int8_t cos_bit) {
  const __m128i cospi_m08_p56 = pair_set_epi16(-cospi[8], cospi[56]);
  const __m128i cospi_p56_p08 = pair_set_epi16(cospi[56], cospi[8]);
  const __m128i cospi_m56_m08 = pair_set_epi16(-cospi[56], -cospi[8]);
  const __m128i cospi_m40_p24 = pair_set_epi16(-cospi[40], cospi[24]);
  const __m128i cospi_p24_p40 = pair_set_epi16(cospi[24], cospi[40]);
  const __m128i cospi_m24_m40 = pair_set_epi16(-cospi[24], -cospi[40]);
  btf_16_sse2(cospi_m08_p56, cospi_p56_p08, x[34], x[61], x[34], x[61]);
  btf_16_sse2(cospi_m08_p56, cospi_p56_p08, x[35], x[60], x[35], x[60]);
  btf_16_sse2(cospi_m56_m08, cospi_m08_p56, x[36], x[59], x[36], x[59]);
  btf_16_sse2(cospi_m56_m08, cospi_m08_p56, x[37], x[58], x[37], x[58]);
  btf_16_sse2(cospi_m40_p24, cospi_p24_p40, x[42], x[53], x[42], x[53]);
  btf_16_sse2(cospi_m40_p24, cospi_p24_p40, x[43], x[52], x[43], x[52]);
  btf_16_sse2(cospi_m24_m40, cospi_m40_p24, x[44], x[51], x[44], x[51]);
  btf_16_sse2(cospi_m24_m40, cospi_m40_p24, x[45], x[50], x[45], x[50]);
}

static INLINE void idct64_stage6_high48_sse2(__m128i *x, const int32_t *cospi,
                                             const __m128i __rounding,
                                             int8_t cos_bit) {
  btf_16_adds_subs_sse2(x[16], x[19]);
  btf_16_adds_subs_sse2(x[17], x[18]);
  btf_16_subs_adds_sse2(x[23], x[20]);
  btf_16_subs_adds_sse2(x[22], x[21]);
  btf_16_adds_subs_sse2(x[24], x[27]);
  btf_16_adds_subs_sse2(x[25], x[26]);
  btf_16_subs_adds_sse2(x[31], x[28]);
  btf_16_subs_adds_sse2(x[30], x[29]);
  idct64_stage6_high32_sse2(x, cospi, __rounding, cos_bit);
}

static INLINE void idct64_stage7_high48_sse2(__m128i *x, const int32_t *cospi,
                                             const __m128i __rounding,
                                             int8_t cos_bit) {
  const __m128i cospi_m16_p48 = pair_set_epi16(-cospi[16], cospi[48]);
  const __m128i cospi_p48_p16 = pair_set_epi16(cospi[48], cospi[16]);
  const __m128i cospi_m48_m16 = pair_set_epi16(-cospi[48], -cospi[16]);
  btf_16_sse2(cospi_m16_p48, cospi_p48_p16, x[18], x[29], x[18], x[29]);
  btf_16_sse2(cospi_m16_p48, cospi_p48_p16, x[19], x[28], x[19], x[28]);
  btf_16_sse2(cospi_m48_m16, cospi_m16_p48, x[20], x[27], x[20], x[27]);
  btf_16_sse2(cospi_m48_m16, cospi_m16_p48, x[21], x[26], x[21], x[26]);
  btf_16_adds_subs_sse2(x[32], x[39]);
  btf_16_adds_subs_sse2(x[33], x[38]);
  btf_16_adds_subs_sse2(x[34], x[37]);
  btf_16_adds_subs_sse2(x[35], x[36]);
  btf_16_subs_adds_sse2(x[47], x[40]);
  btf_16_subs_adds_sse2(x[46], x[41]);
  btf_16_subs_adds_sse2(x[45], x[42]);
  btf_16_subs_adds_sse2(x[44], x[43]);
  btf_16_adds_subs_sse2(x[48], x[55]);
  btf_16_adds_subs_sse2(x[49], x[54]);
  btf_16_adds_subs_sse2(x[50], x[53]);
  btf_16_adds_subs_sse2(x[51], x[52]);
  btf_16_subs_adds_sse2(x[63], x[56]);
  btf_16_subs_adds_sse2(x[62], x[57]);
  btf_16_subs_adds_sse2(x[61], x[58]);
  btf_16_subs_adds_sse2(x[60], x[59]);
}

static INLINE void idct64_stage8_high48_sse2(__m128i *x, const int32_t *cospi,
                                             const __m128i __rounding,
                                             int8_t cos_bit) {
  const __m128i cospi_m16_p48 = pair_set_epi16(-cospi[16], cospi[48]);
  const __m128i cospi_p48_p16 = pair_set_epi16(cospi[48], cospi[16]);
  const __m128i cospi_m48_m16 = pair_set_epi16(-cospi[48], -cospi[16]);
  btf_16_adds_subs_sse2(x[16], x[23]);
  btf_16_adds_subs_sse2(x[17], x[22]);
  btf_16_adds_subs_sse2(x[18], x[21]);
  btf_16_adds_subs_sse2(x[19], x[20]);
  btf_16_subs_adds_sse2(x[31], x[24]);
  btf_16_subs_adds_sse2(x[30], x[25]);
  btf_16_subs_adds_sse2(x[29], x[26]);
  btf_16_subs_adds_sse2(x[28], x[27]);
  btf_16_sse2(cospi_m16_p48, cospi_p48_p16, x[36], x[59], x[36], x[59]);
  btf_16_sse2(cospi_m16_p48, cospi_p48_p16, x[37], x[58], x[37], x[58]);
  btf_16_sse2(cospi_m16_p48, cospi_p48_p16, x[38], x[57], x[38], x[57]);
  btf_16_sse2(cospi_m16_p48, cospi_p48_p16, x[39], x[56], x[39], x[56]);
  btf_16_sse2(cospi_m48_m16, cospi_m16_p48, x[40], x[55], x[40], x[55]);
  btf_16_sse2(cospi_m48_m16, cospi_m16_p48, x[41], x[54], x[41], x[54]);
  btf_16_sse2(cospi_m48_m16, cospi_m16_p48, x[42], x[53], x[42], x[53]);
  btf_16_sse2(cospi_m48_m16, cospi_m16_p48, x[43], x[52], x[43], x[52]);
}

static INLINE void idct64_stage9_sse2(__m128i *x, const int32_t *cospi,
                                      const __m128i __rounding,
                                      int8_t cos_bit) {
  const __m128i cospi_m32_p32 = pair_set_epi16(-cospi[32], cospi[32]);
  const __m128i cospi_p32_p32 = pair_set_epi16(cospi[32], cospi[32]);
  btf_16_adds_subs_sse2(x[0], x[15]);
  btf_16_adds_subs_sse2(x[1], x[14]);
  btf_16_adds_subs_sse2(x[2], x[13]);
  btf_16_adds_subs_sse2(x[3], x[12]);
  btf_16_adds_subs_sse2(x[4], x[11]);
  btf_16_adds_subs_sse2(x[5], x[10]);
  btf_16_adds_subs_sse2(x[6], x[9]);
  btf_16_adds_subs_sse2(x[7], x[8]);
  btf_16_sse2(cospi_m32_p32, cospi_p32_p32, x[20], x[27], x[20], x[27]);
  btf_16_sse2(cospi_m32_p32, cospi_p32_p32, x[21], x[26], x[21], x[26]);
  btf_16_sse2(cospi_m32_p32, cospi_p32_p32, x[22], x[25], x[22], x[25]);
  btf_16_sse2(cospi_m32_p32, cospi_p32_p32, x[23], x[24], x[23], x[24]);
  btf_16_adds_subs_sse2(x[32], x[47]);
  btf_16_adds_subs_sse2(x[33], x[46]);
  btf_16_adds_subs_sse2(x[34], x[45]);
  btf_16_adds_subs_sse2(x[35], x[44]);
  btf_16_adds_subs_sse2(x[36], x[43]);
  btf_16_adds_subs_sse2(x[37], x[42]);
  btf_16_adds_subs_sse2(x[38], x[41]);
  btf_16_adds_subs_sse2(x[39], x[40]);
  btf_16_subs_adds_sse2(x[63], x[48]);
  btf_16_subs_adds_sse2(x[62], x[49]);
  btf_16_subs_adds_sse2(x[61], x[50]);
  btf_16_subs_adds_sse2(x[60], x[51]);
  btf_16_subs_adds_sse2(x[59], x[52]);
  btf_16_subs_adds_sse2(x[58], x[53]);
  btf_16_subs_adds_sse2(x[57], x[54]);
  btf_16_subs_adds_sse2(x[56], x[55]);
}

static INLINE void idct64_stage10_sse2(__m128i *x, const int32_t *cospi,
                                       const __m128i __rounding,
                                       int8_t cos_bit) {
  const __m128i cospi_m32_p32 = pair_set_epi16(-cospi[32], cospi[32]);
  const __m128i cospi_p32_p32 = pair_set_epi16(cospi[32], cospi[32]);
  btf_16_adds_subs_sse2(x[0], x[31]);
  btf_16_adds_subs_sse2(x[1], x[30]);
  btf_16_adds_subs_sse2(x[2], x[29]);
  btf_16_adds_subs_sse2(x[3], x[28]);
  btf_16_adds_subs_sse2(x[4], x[27]);
  btf_16_adds_subs_sse2(x[5], x[26]);
  btf_16_adds_subs_sse2(x[6], x[25]);
  btf_16_adds_subs_sse2(x[7], x[24]);
  btf_16_adds_subs_sse2(x[8], x[23]);
  btf_16_adds_subs_sse2(x[9], x[22]);
  btf_16_adds_subs_sse2(x[10], x[21]);
  btf_16_adds_subs_sse2(x[11], x[20]);
  btf_16_adds_subs_sse2(x[12], x[19]);
  btf_16_adds_subs_sse2(x[13], x[18]);
  btf_16_adds_subs_sse2(x[14], x[17]);
  btf_16_adds_subs_sse2(x[15], x[16]);
  btf_16_sse2(cospi_m32_p32, cospi_p32_p32, x[40], x[55], x[40], x[55]);
  btf_16_sse2(cospi_m32_p32, cospi_p32_p32, x[41], x[54], x[41], x[54]);
  btf_16_sse2(cospi_m32_p32, cospi_p32_p32, x[42], x[53], x[42], x[53]);
  btf_16_sse2(cospi_m32_p32, cospi_p32_p32, x[43], x[52], x[43], x[52]);
  btf_16_sse2(cospi_m32_p32, cospi_p32_p32, x[44], x[51], x[44], x[51]);
  btf_16_sse2(cospi_m32_p32, cospi_p32_p32, x[45], x[50], x[45], x[50]);
  btf_16_sse2(cospi_m32_p32, cospi_p32_p32, x[46], x[49], x[46], x[49]);
  btf_16_sse2(cospi_m32_p32, cospi_p32_p32, x[47], x[48], x[47], x[48]);
}

static INLINE void idct64_stage11_sse2(__m128i *output, __m128i *x) {
  btf_16_adds_subs_out_sse2(output[0], output[63], x[0], x[63]);
  btf_16_adds_subs_out_sse2(output[1], output[62], x[1], x[62]);
  btf_16_adds_subs_out_sse2(output[2], output[61], x[2], x[61]);
  btf_16_adds_subs_out_sse2(output[3], output[60], x[3], x[60]);
  btf_16_adds_subs_out_sse2(output[4], output[59], x[4], x[59]);
  btf_16_adds_subs_out_sse2(output[5], output[58], x[5], x[58]);
  btf_16_adds_subs_out_sse2(output[6], output[57], x[6], x[57]);
  btf_16_adds_subs_out_sse2(output[7], output[56], x[7], x[56]);
  btf_16_adds_subs_out_sse2(output[8], output[55], x[8], x[55]);
  btf_16_adds_subs_out_sse2(output[9], output[54], x[9], x[54]);
  btf_16_adds_subs_out_sse2(output[10], output[53], x[10], x[53]);
  btf_16_adds_subs_out_sse2(output[11], output[52], x[11], x[52]);
  btf_16_adds_subs_out_sse2(output[12], output[51], x[12], x[51]);
  btf_16_adds_subs_out_sse2(output[13], output[50], x[13], x[50]);
  btf_16_adds_subs_out_sse2(output[14], output[49], x[14], x[49]);
  btf_16_adds_subs_out_sse2(output[15], output[48], x[15], x[48]);
  btf_16_adds_subs_out_sse2(output[16], output[47], x[16], x[47]);
  btf_16_adds_subs_out_sse2(output[17], output[46], x[17], x[46]);
  btf_16_adds_subs_out_sse2(output[18], output[45], x[18], x[45]);
  btf_16_adds_subs_out_sse2(output[19], output[44], x[19], x[44]);
  btf_16_adds_subs_out_sse2(output[20], output[43], x[20], x[43]);
  btf_16_adds_subs_out_sse2(output[21], output[42], x[21], x[42]);
  btf_16_adds_subs_out_sse2(output[22], output[41], x[22], x[41]);
  btf_16_adds_subs_out_sse2(output[23], output[40], x[23], x[40]);
  btf_16_adds_subs_out_sse2(output[24], output[39], x[24], x[39]);
  btf_16_adds_subs_out_sse2(output[25], output[38], x[25], x[38]);
  btf_16_adds_subs_out_sse2(output[26], output[37], x[26], x[37]);
  btf_16_adds_subs_out_sse2(output[27], output[36], x[27], x[36]);
  btf_16_adds_subs_out_sse2(output[28], output[35], x[28], x[35]);
  btf_16_adds_subs_out_sse2(output[29], output[34], x[29], x[34]);
  btf_16_adds_subs_out_sse2(output[30], output[33], x[30], x[33]);
  btf_16_adds_subs_out_sse2(output[31], output[32], x[31], x[32]);
}

static void idct64_low1_ssse3(const __m128i *input, __m128i *output) {
  const int32_t *cospi = cospi_arr(INV_COS_BIT);

  // stage 1
  __m128i x[32];
  x[0] = input[0];

  // stage 2
  // stage 3
  // stage 4
  // stage 5
  // stage 6
  btf_16_ssse3(cospi[32], cospi[32], x[0], x[0], x[1]);

  // stage 7
  // stage 8
  // stage 9
  // stage 10
  // stage 11
  output[0] = x[0];
  output[63] = x[0];
  output[1] = x[1];
  output[62] = x[1];
  output[2] = x[1];
  output[61] = x[1];
  output[3] = x[0];
  output[60] = x[0];
  output[4] = x[0];
  output[59] = x[0];
  output[5] = x[1];
  output[58] = x[1];
  output[6] = x[1];
  output[57] = x[1];
  output[7] = x[0];
  output[56] = x[0];
  output[8] = x[0];
  output[55] = x[0];
  output[9] = x[1];
  output[54] = x[1];
  output[10] = x[1];
  output[53] = x[1];
  output[11] = x[0];
  output[52] = x[0];
  output[12] = x[0];
  output[51] = x[0];
  output[13] = x[1];
  output[50] = x[1];
  output[14] = x[1];
  output[49] = x[1];
  output[15] = x[0];
  output[48] = x[0];
  output[16] = x[0];
  output[47] = x[0];
  output[17] = x[1];
  output[46] = x[1];
  output[18] = x[1];
  output[45] = x[1];
  output[19] = x[0];
  output[44] = x[0];
  output[20] = x[0];
  output[43] = x[0];
  output[21] = x[1];
  output[42] = x[1];
  output[22] = x[1];
  output[41] = x[1];
  output[23] = x[0];
  output[40] = x[0];
  output[24] = x[0];
  output[39] = x[0];
  output[25] = x[1];
  output[38] = x[1];
  output[26] = x[1];
  output[37] = x[1];
  output[27] = x[0];
  output[36] = x[0];
  output[28] = x[0];
  output[35] = x[0];
  output[29] = x[1];
  output[34] = x[1];
  output[30] = x[1];
  output[33] = x[1];
  output[31] = x[0];
  output[32] = x[0];
}

static void idct64_low8_ssse3(const __m128i *input, __m128i *output) {
  const int8_t cos_bit = INV_COS_BIT;
  const int32_t *cospi = cospi_arr(INV_COS_BIT);
  const __m128i __rounding = _mm_set1_epi32(1 << (INV_COS_BIT - 1));
  const __m128i cospi_m04_p60 = pair_set_epi16(-cospi[4], cospi[60]);
  const __m128i cospi_p60_p04 = pair_set_epi16(cospi[60], cospi[4]);
  const __m128i cospi_m36_p28 = pair_set_epi16(-cospi[36], cospi[28]);
  const __m128i cospi_m28_m36 = pair_set_epi16(-cospi[28], -cospi[36]);
  const __m128i cospi_m20_p44 = pair_set_epi16(-cospi[20], cospi[44]);
  const __m128i cospi_p44_p20 = pair_set_epi16(cospi[44], cospi[20]);
  const __m128i cospi_m52_p12 = pair_set_epi16(-cospi[52], cospi[12]);
  const __m128i cospi_m12_m52 = pair_set_epi16(-cospi[12], -cospi[52]);
  const __m128i cospi_m08_p56 = pair_set_epi16(-cospi[8], cospi[56]);
  const __m128i cospi_p56_p08 = pair_set_epi16(cospi[56], cospi[8]);
  const __m128i cospi_m40_p24 = pair_set_epi16(-cospi[40], cospi[24]);
  const __m128i cospi_m24_m40 = pair_set_epi16(-cospi[24], -cospi[40]);
  const __m128i cospi_p32_p32 = pair_set_epi16(cospi[32], cospi[32]);
  const __m128i cospi_m16_p48 = pair_set_epi16(-cospi[16], cospi[48]);
  const __m128i cospi_p48_p16 = pair_set_epi16(cospi[48], cospi[16]);
  const __m128i cospi_m32_p32 = pair_set_epi16(-cospi[32], cospi[32]);

  // stage 1
  __m128i x[64];
  x[0] = input[0];
  x[8] = input[4];
  x[16] = input[2];
  x[24] = input[6];
  x[32] = input[1];
  x[40] = input[5];
  x[48] = input[3];
  x[56] = input[7];

  // stage 2
  btf_16_ssse3(cospi[63], cospi[1], x[32], x[32], x[63]);
  btf_16_ssse3(-cospi[57], cospi[7], x[56], x[39], x[56]);
  btf_16_ssse3(cospi[59], cospi[5], x[40], x[40], x[55]);
  btf_16_ssse3(-cospi[61], cospi[3], x[48], x[47], x[48]);

  // stage 3
  btf_16_ssse3(cospi[62], cospi[2], x[16], x[16], x[31]);
  btf_16_ssse3(-cospi[58], cospi[6], x[24], x[23], x[24]);
  x[33] = x[32];
  x[38] = x[39];
  x[41] = x[40];
  x[46] = x[47];
  x[49] = x[48];
  x[54] = x[55];
  x[57] = x[56];
  x[62] = x[63];

  // stage 4
  btf_16_ssse3(cospi[60], cospi[4], x[8], x[8], x[15]);
  x[17] = x[16];
  x[22] = x[23];
  x[25] = x[24];
  x[30] = x[31];
  btf_16_sse2(cospi_m04_p60, cospi_p60_p04, x[33], x[62], x[33], x[62]);
  btf_16_sse2(cospi_m28_m36, cospi_m36_p28, x[38], x[57], x[38], x[57]);
  btf_16_sse2(cospi_m20_p44, cospi_p44_p20, x[41], x[54], x[41], x[54]);
  btf_16_sse2(cospi_m12_m52, cospi_m52_p12, x[46], x[49], x[46], x[49]);

  // stage 5
  x[9] = x[8];
  x[14] = x[15];
  btf_16_sse2(cospi_m08_p56, cospi_p56_p08, x[17], x[30], x[17], x[30]);
  btf_16_sse2(cospi_m24_m40, cospi_m40_p24, x[22], x[25], x[22], x[25]);
  x[35] = x[32];
  x[34] = x[33];
  x[36] = x[39];
  x[37] = x[38];
  x[43] = x[40];
  x[42] = x[41];
  x[44] = x[47];
  x[45] = x[46];
  x[51] = x[48];
  x[50] = x[49];
  x[52] = x[55];
  x[53] = x[54];
  x[59] = x[56];
  x[58] = x[57];
  x[60] = x[63];
  x[61] = x[62];

  // stage 6
  btf_16_ssse3(cospi[32], cospi[32], x[0], x[0], x[1]);
  btf_16_sse2(cospi_m16_p48, cospi_p48_p16, x[9], x[14], x[9], x[14]);
  x[19] = x[16];
  x[18] = x[17];
  x[20] = x[23];
  x[21] = x[22];
  x[27] = x[24];
  x[26] = x[25];
  x[28] = x[31];
  x[29] = x[30];
  idct64_stage6_high32_sse2(x, cospi, __rounding, cos_bit);

  // stage 7
  x[3] = x[0];
  x[2] = x[1];
  x[11] = x[8];
  x[10] = x[9];
  x[12] = x[15];
  x[13] = x[14];
  idct64_stage7_high48_sse2(x, cospi, __rounding, cos_bit);

  // stage 8
  x[7] = x[0];
  x[6] = x[1];
  x[5] = x[2];
  x[4] = x[3];
  btf_16_sse2(cospi_m32_p32, cospi_p32_p32, x[10], x[13], x[10], x[13]);
  btf_16_sse2(cospi_m32_p32, cospi_p32_p32, x[11], x[12], x[11], x[12]);
  idct64_stage8_high48_sse2(x, cospi, __rounding, cos_bit);

  idct64_stage9_sse2(x, cospi, __rounding, cos_bit);
  idct64_stage10_sse2(x, cospi, __rounding, cos_bit);
  idct64_stage11_sse2(output, x);
}

static void idct64_low16_ssse3(const __m128i *input, __m128i *output) {
  const int8_t cos_bit = INV_COS_BIT;
  const int32_t *cospi = cospi_arr(INV_COS_BIT);
  const __m128i __rounding = _mm_set1_epi32(1 << (INV_COS_BIT - 1));

  const __m128i cospi_p32_p32 = pair_set_epi16(cospi[32], cospi[32]);
  const __m128i cospi_m16_p48 = pair_set_epi16(-cospi[16], cospi[48]);
  const __m128i cospi_p48_p16 = pair_set_epi16(cospi[48], cospi[16]);
  const __m128i cospi_m48_m16 = pair_set_epi16(-cospi[48], -cospi[16]);
  const __m128i cospi_m32_p32 = pair_set_epi16(-cospi[32], cospi[32]);

  // stage 1
  __m128i x[64];
  x[0] = input[0];
  x[4] = input[8];
  x[8] = input[4];
  x[12] = input[12];
  x[16] = input[2];
  x[20] = input[10];
  x[24] = input[6];
  x[28] = input[14];
  x[32] = input[1];
  x[36] = input[9];
  x[40] = input[5];
  x[44] = input[13];
  x[48] = input[3];
  x[52] = input[11];
  x[56] = input[7];
  x[60] = input[15];

  // stage 2
  btf_16_ssse3(cospi[63], cospi[1], x[32], x[32], x[63]);
  btf_16_ssse3(-cospi[49], cospi[15], x[60], x[35], x[60]);
  btf_16_ssse3(cospi[55], cospi[9], x[36], x[36], x[59]);
  btf_16_ssse3(-cospi[57], cospi[7], x[56], x[39], x[56]);
  btf_16_ssse3(cospi[59], cospi[5], x[40], x[40], x[55]);
  btf_16_ssse3(-cospi[53], cospi[11], x[52], x[43], x[52]);
  btf_16_ssse3(cospi[51], cospi[13], x[44], x[44], x[51]);
  btf_16_ssse3(-cospi[61], cospi[3], x[48], x[47], x[48]);

  // stage 3
  btf_16_ssse3(cospi[62], cospi[2], x[16], x[16], x[31]);
  btf_16_ssse3(-cospi[50], cospi[14], x[28], x[19], x[28]);
  btf_16_ssse3(cospi[54], cospi[10], x[20], x[20], x[27]);
  btf_16_ssse3(-cospi[58], cospi[6], x[24], x[23], x[24]);
  x[33] = x[32];
  x[34] = x[35];
  x[37] = x[36];
  x[38] = x[39];
  x[41] = x[40];
  x[42] = x[43];
  x[45] = x[44];
  x[46] = x[47];
  x[49] = x[48];
  x[50] = x[51];
  x[53] = x[52];
  x[54] = x[55];
  x[57] = x[56];
  x[58] = x[59];
  x[61] = x[60];
  x[62] = x[63];

  // stage 4
  btf_16_ssse3(cospi[60], cospi[4], x[8], x[8], x[15]);
  btf_16_ssse3(-cospi[52], cospi[12], x[12], x[11], x[12]);
  x[17] = x[16];
  x[18] = x[19];
  x[21] = x[20];
  x[22] = x[23];
  x[25] = x[24];
  x[26] = x[27];
  x[29] = x[28];
  x[30] = x[31];
  idct64_stage4_high32_sse2(x, cospi, __rounding, cos_bit);

  // stage 5
  btf_16_ssse3(cospi[56], cospi[8], x[4], x[4], x[7]);
  x[9] = x[8];
  x[10] = x[11];
  x[13] = x[12];
  x[14] = x[15];
  idct64_stage5_high48_sse2(x, cospi, __rounding, cos_bit);

  // stage 6
  btf_16_ssse3(cospi[32], cospi[32], x[0], x[0], x[1]);
  x[5] = x[4];
  x[6] = x[7];
  btf_16_sse2(cospi_m16_p48, cospi_p48_p16, x[9], x[14], x[9], x[14]);
  btf_16_sse2(cospi_m48_m16, cospi_m16_p48, x[10], x[13], x[10], x[13]);
  idct64_stage6_high48_sse2(x, cospi, __rounding, cos_bit);

  // stage 7
  x[3] = x[0];
  x[2] = x[1];
  btf_16_sse2(cospi_m32_p32, cospi_p32_p32, x[5], x[6], x[5], x[6]);
  btf_16_adds_subs_sse2(x[8], x[11]);
  btf_16_adds_subs_sse2(x[9], x[10]);
  btf_16_subs_adds_sse2(x[15], x[12]);
  btf_16_subs_adds_sse2(x[14], x[13]);
  idct64_stage7_high48_sse2(x, cospi, __rounding, cos_bit);

  // stage 8
  btf_16_adds_subs_sse2(x[0], x[7]);
  btf_16_adds_subs_sse2(x[1], x[6]);
  btf_16_adds_subs_sse2(x[2], x[5]);
  btf_16_adds_subs_sse2(x[3], x[4]);
  btf_16_sse2(cospi_m32_p32, cospi_p32_p32, x[10], x[13], x[10], x[13]);
  btf_16_sse2(cospi_m32_p32, cospi_p32_p32, x[11], x[12], x[11], x[12]);
  idct64_stage8_high48_sse2(x, cospi, __rounding, cos_bit);

  idct64_stage9_sse2(x, cospi, __rounding, cos_bit);
  idct64_stage10_sse2(x, cospi, __rounding, cos_bit);
  idct64_stage11_sse2(output, x);
}

static void idct64_low32_ssse3(const __m128i *input, __m128i *output) {
  const int8_t cos_bit = INV_COS_BIT;
  const int32_t *cospi = cospi_arr(INV_COS_BIT);
  const __m128i __rounding = _mm_set1_epi32(1 << (INV_COS_BIT - 1));

  const __m128i cospi_p32_p32 = pair_set_epi16(cospi[32], cospi[32]);
  const __m128i cospi_m16_p48 = pair_set_epi16(-cospi[16], cospi[48]);
  const __m128i cospi_p48_p16 = pair_set_epi16(cospi[48], cospi[16]);
  const __m128i cospi_m48_m16 = pair_set_epi16(-cospi[48], -cospi[16]);
  const __m128i cospi_m32_p32 = pair_set_epi16(-cospi[32], cospi[32]);

  // stage 1
  __m128i x[64];
  x[0] = input[0];
  x[2] = input[16];
  x[4] = input[8];
  x[6] = input[24];
  x[8] = input[4];
  x[10] = input[20];
  x[12] = input[12];
  x[14] = input[28];
  x[16] = input[2];
  x[18] = input[18];
  x[20] = input[10];
  x[22] = input[26];
  x[24] = input[6];
  x[26] = input[22];
  x[28] = input[14];
  x[30] = input[30];
  x[32] = input[1];
  x[34] = input[17];
  x[36] = input[9];
  x[38] = input[25];
  x[40] = input[5];
  x[42] = input[21];
  x[44] = input[13];
  x[46] = input[29];
  x[48] = input[3];
  x[50] = input[19];
  x[52] = input[11];
  x[54] = input[27];
  x[56] = input[7];
  x[58] = input[23];
  x[60] = input[15];
  x[62] = input[31];

  // stage 2
  btf_16_ssse3(cospi[63], cospi[1], x[32], x[32], x[63]);
  btf_16_ssse3(-cospi[33], cospi[31], x[62], x[33], x[62]);
  btf_16_ssse3(cospi[47], cospi[17], x[34], x[34], x[61]);
  btf_16_ssse3(-cospi[49], cospi[15], x[60], x[35], x[60]);
  btf_16_ssse3(cospi[55], cospi[9], x[36], x[36], x[59]);
  btf_16_ssse3(-cospi[41], cospi[23], x[58], x[37], x[58]);
  btf_16_ssse3(cospi[39], cospi[25], x[38], x[38], x[57]);
  btf_16_ssse3(-cospi[57], cospi[7], x[56], x[39], x[56]);
  btf_16_ssse3(cospi[59], cospi[5], x[40], x[40], x[55]);
  btf_16_ssse3(-cospi[37], cospi[27], x[54], x[41], x[54]);
  btf_16_ssse3(cospi[43], cospi[21], x[42], x[42], x[53]);
  btf_16_ssse3(-cospi[53], cospi[11], x[52], x[43], x[52]);
  btf_16_ssse3(cospi[51], cospi[13], x[44], x[44], x[51]);
  btf_16_ssse3(-cospi[45], cospi[19], x[50], x[45], x[50]);
  btf_16_ssse3(cospi[35], cospi[29], x[46], x[46], x[49]);
  btf_16_ssse3(-cospi[61], cospi[3], x[48], x[47], x[48]);

  // stage 3
  btf_16_ssse3(cospi[62], cospi[2], x[16], x[16], x[31]);
  btf_16_ssse3(-cospi[34], cospi[30], x[30], x[17], x[30]);
  btf_16_ssse3(cospi[46], cospi[18], x[18], x[18], x[29]);
  btf_16_ssse3(-cospi[50], cospi[14], x[28], x[19], x[28]);
  btf_16_ssse3(cospi[54], cospi[10], x[20], x[20], x[27]);
  btf_16_ssse3(-cospi[42], cospi[22], x[26], x[21], x[26]);
  btf_16_ssse3(cospi[38], cospi[26], x[22], x[22], x[25]);
  btf_16_ssse3(-cospi[58], cospi[6], x[24], x[23], x[24]);
  btf_16_adds_subs_sse2(x[32], x[33]);
  btf_16_subs_adds_sse2(x[35], x[34]);
  btf_16_adds_subs_sse2(x[36], x[37]);
  btf_16_subs_adds_sse2(x[39], x[38]);
  btf_16_adds_subs_sse2(x[40], x[41]);
  btf_16_subs_adds_sse2(x[43], x[42]);
  btf_16_adds_subs_sse2(x[44], x[45]);
  btf_16_subs_adds_sse2(x[47], x[46]);
  btf_16_adds_subs_sse2(x[48], x[49]);
  btf_16_subs_adds_sse2(x[51], x[50]);
  btf_16_adds_subs_sse2(x[52], x[53]);
  btf_16_subs_adds_sse2(x[55], x[54]);
  btf_16_adds_subs_sse2(x[56], x[57]);
  btf_16_subs_adds_sse2(x[59], x[58]);
  btf_16_adds_subs_sse2(x[60], x[61]);
  btf_16_subs_adds_sse2(x[63], x[62]);

  // stage 4
  btf_16_ssse3(cospi[60], cospi[4], x[8], x[8], x[15]);
  btf_16_ssse3(-cospi[36], cospi[28], x[14], x[9], x[14]);
  btf_16_ssse3(cospi[44], cospi[20], x[10], x[10], x[13]);
  btf_16_ssse3(-cospi[52], cospi[12], x[12], x[11], x[12]);
  btf_16_adds_subs_sse2(x[16], x[17]);
  btf_16_subs_adds_sse2(x[19], x[18]);
  btf_16_adds_subs_sse2(x[20], x[21]);
  btf_16_subs_adds_sse2(x[23], x[22]);
  btf_16_adds_subs_sse2(x[24], x[25]);
  btf_16_subs_adds_sse2(x[27], x[26]);
  btf_16_adds_subs_sse2(x[28], x[29]);
  btf_16_subs_adds_sse2(x[31], x[30]);
  idct64_stage4_high32_sse2(x, cospi, __rounding, cos_bit);

  // stage 5
  btf_16_ssse3(cospi[56], cospi[8], x[4], x[4], x[7]);
  btf_16_ssse3(-cospi[40], cospi[24], x[6], x[5], x[6]);
  btf_16_adds_subs_sse2(x[8], x[9]);
  btf_16_subs_adds_sse2(x[11], x[10]);
  btf_16_adds_subs_sse2(x[12], x[13]);
  btf_16_subs_adds_sse2(x[15], x[14]);
  idct64_stage5_high48_sse2(x, cospi, __rounding, cos_bit);

  // stage 6
  btf_16_ssse3(cospi[32], cospi[32], x[0], x[0], x[1]);
  btf_16_ssse3(cospi[48], cospi[16], x[2], x[2], x[3]);
  btf_16_adds_subs_sse2(x[4], x[5]);
  btf_16_subs_adds_sse2(x[7], x[6]);
  btf_16_sse2(cospi_m16_p48, cospi_p48_p16, x[9], x[14], x[9], x[14]);
  btf_16_sse2(cospi_m48_m16, cospi_m16_p48, x[10], x[13], x[10], x[13]);
  idct64_stage6_high48_sse2(x, cospi, __rounding, cos_bit);

  // stage 7
  btf_16_adds_subs_sse2(x[0], x[3]);
  btf_16_adds_subs_sse2(x[1], x[2]);
  btf_16_sse2(cospi_m32_p32, cospi_p32_p32, x[5], x[6], x[5], x[6]);
  btf_16_adds_subs_sse2(x[8], x[11]);
  btf_16_adds_subs_sse2(x[9], x[10]);
  btf_16_subs_adds_sse2(x[15], x[12]);
  btf_16_subs_adds_sse2(x[14], x[13]);
  idct64_stage7_high48_sse2(x, cospi, __rounding, cos_bit);

  // stage 8
  btf_16_adds_subs_sse2(x[0], x[7]);
  btf_16_adds_subs_sse2(x[1], x[6]);
  btf_16_adds_subs_sse2(x[2], x[5]);
  btf_16_adds_subs_sse2(x[3], x[4]);
  btf_16_sse2(cospi_m32_p32, cospi_p32_p32, x[10], x[13], x[10], x[13]);
  btf_16_sse2(cospi_m32_p32, cospi_p32_p32, x[11], x[12], x[11], x[12]);
  idct64_stage8_high48_sse2(x, cospi, __rounding, cos_bit);

  // stage 9~11
  idct64_stage9_sse2(x, cospi, __rounding, cos_bit);
  idct64_stage10_sse2(x, cospi, __rounding, cos_bit);
  idct64_stage11_sse2(output, x);
}

static void iadst4_sse2(const __m128i *input, __m128i *output) {
  const int32_t *sinpi = sinpi_arr(INV_COS_BIT);
  const __m128i sinpi_p01_p04 = pair_set_epi16(sinpi[1], sinpi[4]);
  const __m128i sinpi_p02_m01 = pair_set_epi16(sinpi[2], -sinpi[1]);
  const __m128i sinpi_p03_p02 = pair_set_epi16(sinpi[3], sinpi[2]);
  const __m128i sinpi_p03_m04 = pair_set_epi16(sinpi[3], -sinpi[4]);
  const __m128i sinpi_p03_m03 = pair_set_epi16(sinpi[3], -sinpi[3]);
  const __m128i sinpi_0_p03 = pair_set_epi16(0, sinpi[3]);
  const __m128i sinpi_p04_p02 = pair_set_epi16(sinpi[4], sinpi[2]);
  const __m128i sinpi_m03_m01 = pair_set_epi16(-sinpi[3], -sinpi[1]);
  __m128i x0[4];
  x0[0] = input[0];
  x0[1] = input[1];
  x0[2] = input[2];
  x0[3] = input[3];

  __m128i u[4];
  u[0] = _mm_unpacklo_epi16(x0[0], x0[2]);
  u[1] = _mm_unpackhi_epi16(x0[0], x0[2]);
  u[2] = _mm_unpacklo_epi16(x0[1], x0[3]);
  u[3] = _mm_unpackhi_epi16(x0[1], x0[3]);

  __m128i x1[16];
  x1[0] = _mm_madd_epi16(u[0], sinpi_p01_p04);  // x0*sin1 + x2*sin4
  x1[1] = _mm_madd_epi16(u[1], sinpi_p01_p04);
  x1[2] = _mm_madd_epi16(u[0], sinpi_p02_m01);  // x0*sin2 - x2*sin1
  x1[3] = _mm_madd_epi16(u[1], sinpi_p02_m01);
  x1[4] = _mm_madd_epi16(u[2], sinpi_p03_p02);  // x1*sin3 + x3*sin2
  x1[5] = _mm_madd_epi16(u[3], sinpi_p03_p02);
  x1[6] = _mm_madd_epi16(u[2], sinpi_p03_m04);  // x1*sin3 - x3*sin4
  x1[7] = _mm_madd_epi16(u[3], sinpi_p03_m04);
  x1[8] = _mm_madd_epi16(u[0], sinpi_p03_m03);  // x0*sin3 - x2*sin3
  x1[9] = _mm_madd_epi16(u[1], sinpi_p03_m03);
  x1[10] = _mm_madd_epi16(u[2], sinpi_0_p03);  // x2*sin3
  x1[11] = _mm_madd_epi16(u[3], sinpi_0_p03);
  x1[12] = _mm_madd_epi16(u[0], sinpi_p04_p02);  // x0*sin4 + x2*sin2
  x1[13] = _mm_madd_epi16(u[1], sinpi_p04_p02);
  x1[14] = _mm_madd_epi16(u[2], sinpi_m03_m01);  // -x1*sin3 - x3*sin1
  x1[15] = _mm_madd_epi16(u[3], sinpi_m03_m01);

  __m128i x2[8];
  x2[0] = _mm_add_epi32(x1[0], x1[4]);  // x0*sin1 +x2*sin4 +x1*sin3 +x3*sin2
  x2[1] = _mm_add_epi32(x1[1], x1[5]);
  x2[2] = _mm_add_epi32(x1[2], x1[6]);  // x0*sin2 -x2*sin1 +x1*sin3 -x3*sin4
  x2[3] = _mm_add_epi32(x1[3], x1[7]);
  x2[4] = _mm_add_epi32(x1[8], x1[10]);  // x0*sin3 -x2*sin3 +x3*sin3
  x2[5] = _mm_add_epi32(x1[9], x1[11]);
  x2[6] = _mm_add_epi32(x1[12], x1[14]);  // x0*sin1 +x2*sin4 +x0*sin2 -x2*sin1
  x2[7] = _mm_add_epi32(x1[13], x1[15]);

  const __m128i rounding = _mm_set1_epi32(1 << (INV_COS_BIT - 1));
  for (int i = 0; i < 4; ++i) {
    __m128i out0 = _mm_add_epi32(x2[2 * i], rounding);
    __m128i out1 = _mm_add_epi32(x2[2 * i + 1], rounding);
    out0 = _mm_srai_epi32(out0, INV_COS_BIT);
    out1 = _mm_srai_epi32(out1, INV_COS_BIT);
    output[i] = _mm_packs_epi32(out0, out1);
  }
}

static void iadst4_w4_sse2(const __m128i *input, __m128i *output) {
  const int32_t *sinpi = sinpi_arr(INV_COS_BIT);
  const __m128i sinpi_p01_p04 = pair_set_epi16(sinpi[1], sinpi[4]);
  const __m128i sinpi_p02_m01 = pair_set_epi16(sinpi[2], -sinpi[1]);
  const __m128i sinpi_p03_p02 = pair_set_epi16(sinpi[3], sinpi[2]);
  const __m128i sinpi_p03_m04 = pair_set_epi16(sinpi[3], -sinpi[4]);
  const __m128i sinpi_p03_m03 = pair_set_epi16(sinpi[3], -sinpi[3]);
  const __m128i sinpi_0_p03 = pair_set_epi16(0, sinpi[3]);
  const __m128i sinpi_p04_p02 = pair_set_epi16(sinpi[4], sinpi[2]);
  const __m128i sinpi_m03_m01 = pair_set_epi16(-sinpi[3], -sinpi[1]);
  __m128i x0[4];
  x0[0] = input[0];
  x0[1] = input[1];
  x0[2] = input[2];
  x0[3] = input[3];

  __m128i u[2];
  u[0] = _mm_unpacklo_epi16(x0[0], x0[2]);
  u[1] = _mm_unpacklo_epi16(x0[1], x0[3]);

  __m128i x1[8];
  x1[0] = _mm_madd_epi16(u[0], sinpi_p01_p04);  // x0*sin1 + x2*sin4
  x1[1] = _mm_madd_epi16(u[0], sinpi_p02_m01);  // x0*sin2 - x2*sin1
  x1[2] = _mm_madd_epi16(u[1], sinpi_p03_p02);  // x1*sin3 + x3*sin2
  x1[3] = _mm_madd_epi16(u[1], sinpi_p03_m04);  // x1*sin3 - x3*sin4
  x1[4] = _mm_madd_epi16(u[0], sinpi_p03_m03);  // x0*sin3 - x2*sin3
  x1[5] = _mm_madd_epi16(u[1], sinpi_0_p03);    // x2*sin3
  x1[6] = _mm_madd_epi16(u[0], sinpi_p04_p02);  // x0*sin4 + x2*sin2
  x1[7] = _mm_madd_epi16(u[1], sinpi_m03_m01);  // -x1*sin3 - x3*sin1

  __m128i x2[4];
  x2[0] = _mm_add_epi32(x1[0], x1[2]);  // x0*sin1 + x2*sin4 + x1*sin3 + x3*sin2
  x2[1] = _mm_add_epi32(x1[1], x1[3]);  // x0*sin2 - x2*sin1 + x1*sin3 - x3*sin4
  x2[2] = _mm_add_epi32(x1[4], x1[5]);  // x0*sin3 - x2*sin3 + x3*sin3
  x2[3] = _mm_add_epi32(x1[6], x1[7]);  // x0*sin4 + x2*sin2 - x1*sin3 - x3*sin1

  const __m128i rounding = _mm_set1_epi32(1 << (INV_COS_BIT - 1));
  for (int i = 0; i < 4; ++i) {
    __m128i out0 = _mm_add_epi32(x2[i], rounding);
    out0 = _mm_srai_epi32(out0, INV_COS_BIT);
    output[i] = _mm_packs_epi32(out0, out0);
  }
}

static void iadst8_low1_ssse3(const __m128i *input, __m128i *output) {
  const int8_t cos_bit = INV_COS_BIT;
  const int32_t *cospi = cospi_arr(INV_COS_BIT);
  const __m128i __zero = _mm_setzero_si128();
  const __m128i __rounding = _mm_set1_epi32(1 << (INV_COS_BIT - 1));

  const __m128i cospi_p16_p48 = pair_set_epi16(cospi[16], cospi[48]);
  const __m128i cospi_p48_m16 = pair_set_epi16(cospi[48], -cospi[16]);
  const __m128i cospi_p32_p32 = pair_set_epi16(cospi[32], cospi[32]);
  const __m128i cospi_p32_m32 = pair_set_epi16(cospi[32], -cospi[32]);

  // stage 1
  __m128i x[8];
  x[1] = input[0];

  // stage 2
  btf_16_ssse3(cospi[60], -cospi[4], x[1], x[0], x[1]);

  // stage 3
  x[4] = x[0];
  x[5] = x[1];

  // stage 4
  btf_16_sse2(cospi_p16_p48, cospi_p48_m16, x[4], x[5], x[4], x[5]);

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

  // stage 6
  btf_16_sse2(cospi_p32_p32, cospi_p32_m32, x[2], x[3], x[2], x[3]);
  btf_16_sse2(cospi_p32_p32, cospi_p32_m32, x[6], x[7], x[6], x[7]);

  // stage 7
  output[0] = x[0];
  output[1] = _mm_subs_epi16(__zero, x[4]);
  output[2] = x[6];
  output[3] = _mm_subs_epi16(__zero, x[2]);
  output[4] = x[3];
  output[5] = _mm_subs_epi16(__zero, x[7]);
  output[6] = x[5];
  output[7] = _mm_subs_epi16(__zero, x[1]);
}

static void iadst8_sse2(const __m128i *input, __m128i *output) {
  const int8_t cos_bit = INV_COS_BIT;
  const int32_t *cospi = cospi_arr(INV_COS_BIT);
  const __m128i __zero = _mm_setzero_si128();
  const __m128i __rounding = _mm_set1_epi32(1 << (INV_COS_BIT - 1));

  const __m128i cospi_p04_p60 = pair_set_epi16(cospi[4], cospi[60]);
  const __m128i cospi_p60_m04 = pair_set_epi16(cospi[60], -cospi[4]);
  const __m128i cospi_p20_p44 = pair_set_epi16(cospi[20], cospi[44]);
  const __m128i cospi_p44_m20 = pair_set_epi16(cospi[44], -cospi[20]);
  const __m128i cospi_p36_p28 = pair_set_epi16(cospi[36], cospi[28]);
  const __m128i cospi_p28_m36 = pair_set_epi16(cospi[28], -cospi[36]);
  const __m128i cospi_p52_p12 = pair_set_epi16(cospi[52], cospi[12]);
  const __m128i cospi_p12_m52 = pair_set_epi16(cospi[12], -cospi[52]);
  const __m128i cospi_p16_p48 = pair_set_epi16(cospi[16], cospi[48]);
  const __m128i cospi_p48_m16 = pair_set_epi16(cospi[48], -cospi[16]);
  const __m128i cospi_m48_p16 = pair_set_epi16(-cospi[48], cospi[16]);
  const __m128i cospi_p32_p32 = pair_set_epi16(cospi[32], cospi[32]);
  const __m128i cospi_p32_m32 = pair_set_epi16(cospi[32], -cospi[32]);

  // stage 1
  __m128i x[8];
  x[0] = input[7];
  x[1] = input[0];
  x[2] = input[5];
  x[3] = input[2];
  x[4] = input[3];
  x[5] = input[4];
  x[6] = input[1];
  x[7] = input[6];

  // stage 2
  btf_16_sse2(cospi_p04_p60, cospi_p60_m04, x[0], x[1], x[0], x[1]);
  btf_16_sse2(cospi_p20_p44, cospi_p44_m20, x[2], x[3], x[2], x[3]);
  btf_16_sse2(cospi_p36_p28, cospi_p28_m36, x[4], x[5], x[4], x[5]);
  btf_16_sse2(cospi_p52_p12, cospi_p12_m52, x[6], x[7], x[6], x[7]);

  // stage 3
  btf_16_adds_subs_sse2(x[0], x[4]);
  btf_16_adds_subs_sse2(x[1], x[5]);
  btf_16_adds_subs_sse2(x[2], x[6]);
  btf_16_adds_subs_sse2(x[3], x[7]);

  // stage 4
  btf_16_sse2(cospi_p16_p48, cospi_p48_m16, x[4], x[5], x[4], x[5]);
  btf_16_sse2(cospi_m48_p16, cospi_p16_p48, x[6], x[7], x[6], x[7]);

  // stage 5
  btf_16_adds_subs_sse2(x[0], x[2]);
  btf_16_adds_subs_sse2(x[1], x[3]);
  btf_16_adds_subs_sse2(x[4], x[6]);
  btf_16_adds_subs_sse2(x[5], x[7]);

  // stage 6
  btf_16_sse2(cospi_p32_p32, cospi_p32_m32, x[2], x[3], x[2], x[3]);
  btf_16_sse2(cospi_p32_p32, cospi_p32_m32, x[6], x[7], x[6], x[7]);

  // stage 7
  output[0] = x[0];
  output[1] = _mm_subs_epi16(__zero, x[4]);
  output[2] = x[6];
  output[3] = _mm_subs_epi16(__zero, x[2]);
  output[4] = x[3];
  output[5] = _mm_subs_epi16(__zero, x[7]);
  output[6] = x[5];
  output[7] = _mm_subs_epi16(__zero, x[1]);
}

static void iadst8_w4_sse2(const __m128i *input, __m128i *output) {
  const int8_t cos_bit = INV_COS_BIT;
  const int32_t *cospi = cospi_arr(INV_COS_BIT);
  const __m128i __zero = _mm_setzero_si128();
  const __m128i __rounding = _mm_set1_epi32(1 << (INV_COS_BIT - 1));

  const __m128i cospi_p04_p60 = pair_set_epi16(cospi[4], cospi[60]);
  const __m128i cospi_p60_m04 = pair_set_epi16(cospi[60], -cospi[4]);
  const __m128i cospi_p20_p44 = pair_set_epi16(cospi[20], cospi[44]);
  const __m128i cospi_p44_m20 = pair_set_epi16(cospi[44], -cospi[20]);
  const __m128i cospi_p36_p28 = pair_set_epi16(cospi[36], cospi[28]);
  const __m128i cospi_p28_m36 = pair_set_epi16(cospi[28], -cospi[36]);
  const __m128i cospi_p52_p12 = pair_set_epi16(cospi[52], cospi[12]);
  const __m128i cospi_p12_m52 = pair_set_epi16(cospi[12], -cospi[52]);
  const __m128i cospi_p16_p48 = pair_set_epi16(cospi[16], cospi[48]);
  const __m128i cospi_p48_m16 = pair_set_epi16(cospi[48], -cospi[16]);
  const __m128i cospi_m48_p16 = pair_set_epi16(-cospi[48], cospi[16]);
  const __m128i cospi_p32_p32 = pair_set_epi16(cospi[32], cospi[32]);
  const __m128i cospi_p32_m32 = pair_set_epi16(cospi[32], -cospi[32]);

  // stage 1
  __m128i x[8];
  x[0] = input[7];
  x[1] = input[0];
  x[2] = input[5];
  x[3] = input[2];
  x[4] = input[3];
  x[5] = input[4];
  x[6] = input[1];
  x[7] = input[6];

  // stage 2
  btf_16_4p_sse2(cospi_p04_p60, cospi_p60_m04, x[0], x[1], x[0], x[1]);
  btf_16_4p_sse2(cospi_p20_p44, cospi_p44_m20, x[2], x[3], x[2], x[3]);
  btf_16_4p_sse2(cospi_p36_p28, cospi_p28_m36, x[4], x[5], x[4], x[5]);
  btf_16_4p_sse2(cospi_p52_p12, cospi_p12_m52, x[6], x[7], x[6], x[7]);

  // stage 3
  btf_16_adds_subs_sse2(x[0], x[4]);
  btf_16_adds_subs_sse2(x[1], x[5]);
  btf_16_adds_subs_sse2(x[2], x[6]);
  btf_16_adds_subs_sse2(x[3], x[7]);

  // stage 4
  btf_16_4p_sse2(cospi_p16_p48, cospi_p48_m16, x[4], x[5], x[4], x[5]);
  btf_16_4p_sse2(cospi_m48_p16, cospi_p16_p48, x[6], x[7], x[6], x[7]);

  // stage 5
  btf_16_adds_subs_sse2(x[0], x[2]);
  btf_16_adds_subs_sse2(x[1], x[3]);
  btf_16_adds_subs_sse2(x[4], x[6]);
  btf_16_adds_subs_sse2(x[5], x[7]);

  // stage 6
  btf_16_4p_sse2(cospi_p32_p32, cospi_p32_m32, x[2], x[3], x[2], x[3]);
  btf_16_4p_sse2(cospi_p32_p32, cospi_p32_m32, x[6], x[7], x[6], x[7]);

  // stage 7
  output[0] = x[0];
  output[1] = _mm_subs_epi16(__zero, x[4]);
  output[2] = x[6];
  output[3] = _mm_subs_epi16(__zero, x[2]);
  output[4] = x[3];
  output[5] = _mm_subs_epi16(__zero, x[7]);
  output[6] = x[5];
  output[7] = _mm_subs_epi16(__zero, x[1]);
}

static INLINE void iadst16_stage3_ssse3(__m128i *x) {
  btf_16_adds_subs_sse2(x[0], x[8]);
  btf_16_adds_subs_sse2(x[1], x[9]);
  btf_16_adds_subs_sse2(x[2], x[10]);
  btf_16_adds_subs_sse2(x[3], x[11]);
  btf_16_adds_subs_sse2(x[4], x[12]);
  btf_16_adds_subs_sse2(x[5], x[13]);
  btf_16_adds_subs_sse2(x[6], x[14]);
  btf_16_adds_subs_sse2(x[7], x[15]);
}

static INLINE void iadst16_stage4_ssse3(__m128i *x, const int32_t *cospi,
                                        const __m128i __rounding,
                                        int8_t cos_bit) {
  const __m128i cospi_p08_p56 = pair_set_epi16(cospi[8], cospi[56]);
  const __m128i cospi_p56_m08 = pair_set_epi16(cospi[56], -cospi[8]);
  const __m128i cospi_p40_p24 = pair_set_epi16(cospi[40], cospi[24]);
  const __m128i cospi_p24_m40 = pair_set_epi16(cospi[24], -cospi[40]);
  const __m128i cospi_m56_p08 = pair_set_epi16(-cospi[56], cospi[8]);
  const __m128i cospi_m24_p40 = pair_set_epi16(-cospi[24], cospi[40]);
  btf_16_sse2(cospi_p08_p56, cospi_p56_m08, x[8], x[9], x[8], x[9]);
  btf_16_sse2(cospi_p40_p24, cospi_p24_m40, x[10], x[11], x[10], x[11]);
  btf_16_sse2(cospi_m56_p08, cospi_p08_p56, x[12], x[13], x[12], x[13]);
  btf_16_sse2(cospi_m24_p40, cospi_p40_p24, x[14], x[15], x[14], x[15]);
}

static INLINE void iadst16_stage5_ssse3(__m128i *x) {
  btf_16_adds_subs_sse2(x[0], x[4]);
  btf_16_adds_subs_sse2(x[1], x[5]);
  btf_16_adds_subs_sse2(x[2], x[6]);
  btf_16_adds_subs_sse2(x[3], x[7]);
  btf_16_adds_subs_sse2(x[8], x[12]);
  btf_16_adds_subs_sse2(x[9], x[13]);
  btf_16_adds_subs_sse2(x[10], x[14]);
  btf_16_adds_subs_sse2(x[11], x[15]);
}

static INLINE void iadst16_stage6_ssse3(__m128i *x, const int32_t *cospi,
                                        const __m128i __rounding,
                                        int8_t cos_bit) {
  const __m128i cospi_p16_p48 = pair_set_epi16(cospi[16], cospi[48]);
  const __m128i cospi_p48_m16 = pair_set_epi16(cospi[48], -cospi[16]);
  const __m128i cospi_m48_p16 = pair_set_epi16(-cospi[48], cospi[16]);
  btf_16_sse2(cospi_p16_p48, cospi_p48_m16, x[4], x[5], x[4], x[5]);
  btf_16_sse2(cospi_m48_p16, cospi_p16_p48, x[6], x[7], x[6], x[7]);
  btf_16_sse2(cospi_p16_p48, cospi_p48_m16, x[12], x[13], x[12], x[13]);
  btf_16_sse2(cospi_m48_p16, cospi_p16_p48, x[14], x[15], x[14], x[15]);
}

static INLINE void iadst16_stage7_ssse3(__m128i *x) {
  btf_16_adds_subs_sse2(x[0], x[2]);
  btf_16_adds_subs_sse2(x[1], x[3]);
  btf_16_adds_subs_sse2(x[4], x[6]);
  btf_16_adds_subs_sse2(x[5], x[7]);
  btf_16_adds_subs_sse2(x[8], x[10]);
  btf_16_adds_subs_sse2(x[9], x[11]);
  btf_16_adds_subs_sse2(x[12], x[14]);
  btf_16_adds_subs_sse2(x[13], x[15]);
}

static INLINE void iadst16_stage8_ssse3(__m128i *x, const int32_t *cospi,
                                        const __m128i __rounding,
                                        int8_t cos_bit) {
  const __m128i cospi_p32_p32 = pair_set_epi16(cospi[32], cospi[32]);
  const __m128i cospi_p32_m32 = pair_set_epi16(cospi[32], -cospi[32]);
  btf_16_sse2(cospi_p32_p32, cospi_p32_m32, x[2], x[3], x[2], x[3]);
  btf_16_sse2(cospi_p32_p32, cospi_p32_m32, x[6], x[7], x[6], x[7]);
  btf_16_sse2(cospi_p32_p32, cospi_p32_m32, x[10], x[11], x[10], x[11]);
  btf_16_sse2(cospi_p32_p32, cospi_p32_m32, x[14], x[15], x[14], x[15]);
}

static INLINE void iadst16_stage9_ssse3(__m128i *output, __m128i *x) {
  const __m128i __zero = _mm_setzero_si128();
  output[0] = x[0];
  output[1] = _mm_subs_epi16(__zero, x[8]);
  output[2] = x[12];
  output[3] = _mm_subs_epi16(__zero, x[4]);
  output[4] = x[6];
  output[5] = _mm_subs_epi16(__zero, x[14]);
  output[6] = x[10];
  output[7] = _mm_subs_epi16(__zero, x[2]);
  output[8] = x[3];
  output[9] = _mm_subs_epi16(__zero, x[11]);
  output[10] = x[15];
  output[11] = _mm_subs_epi16(__zero, x[7]);
  output[12] = x[5];
  output[13] = _mm_subs_epi16(__zero, x[13]);
  output[14] = x[9];
  output[15] = _mm_subs_epi16(__zero, x[1]);
}

static void iadst16_low1_ssse3(const __m128i *input, __m128i *output) {
  const int8_t cos_bit = INV_COS_BIT;
  const int32_t *cospi = cospi_arr(INV_COS_BIT);
  const __m128i __rounding = _mm_set1_epi32(1 << (INV_COS_BIT - 1));

  const __m128i cospi_p08_p56 = pair_set_epi16(cospi[8], cospi[56]);
  const __m128i cospi_p56_m08 = pair_set_epi16(cospi[56], -cospi[8]);
  const __m128i cospi_p16_p48 = pair_set_epi16(cospi[16], cospi[48]);
  const __m128i cospi_p48_m16 = pair_set_epi16(cospi[48], -cospi[16]);

  // stage 1
  __m128i x[16];
  x[1] = input[0];

  // stage 2
  btf_16_ssse3(cospi[62], -cospi[2], x[1], x[0], x[1]);

  // stage 3
  x[8] = x[0];
  x[9] = x[1];

  // stage 4
  btf_16_sse2(cospi_p08_p56, cospi_p56_m08, x[8], x[9], x[8], x[9]);

  // stage 5
  x[4] = x[0];
  x[5] = x[1];
  x[12] = x[8];
  x[13] = x[9];

  // stage 6
  btf_16_sse2(cospi_p16_p48, cospi_p48_m16, x[4], x[5], x[4], x[5]);
  btf_16_sse2(cospi_p16_p48, cospi_p48_m16, x[12], x[13], x[12], x[13]);

  // stage 7
  x[2] = x[0];
  x[3] = x[1];
  x[6] = x[4];
  x[7] = x[5];
  x[10] = x[8];
  x[11] = x[9];
  x[14] = x[12];
  x[15] = x[13];

  iadst16_stage8_ssse3(x, cospi, __rounding, cos_bit);
  iadst16_stage9_ssse3(output, x);
}

static void iadst16_low8_ssse3(const __m128i *input, __m128i *output) {
  const int8_t cos_bit = INV_COS_BIT;
  const int32_t *cospi = cospi_arr(INV_COS_BIT);
  const __m128i __rounding = _mm_set1_epi32(1 << (INV_COS_BIT - 1));

  // stage 1
  __m128i x[16];
  x[1] = input[0];
  x[3] = input[2];
  x[5] = input[4];
  x[7] = input[6];
  x[8] = input[7];
  x[10] = input[5];
  x[12] = input[3];
  x[14] = input[1];

  // stage 2
  btf_16_ssse3(cospi[62], -cospi[2], x[1], x[0], x[1]);
  btf_16_ssse3(cospi[54], -cospi[10], x[3], x[2], x[3]);
  btf_16_ssse3(cospi[46], -cospi[18], x[5], x[4], x[5]);
  btf_16_ssse3(cospi[38], -cospi[26], x[7], x[6], x[7]);
  btf_16_ssse3(cospi[34], cospi[30], x[8], x[8], x[9]);
  btf_16_ssse3(cospi[42], cospi[22], x[10], x[10], x[11]);
  btf_16_ssse3(cospi[50], cospi[14], x[12], x[12], x[13]);
  btf_16_ssse3(cospi[58], cospi[6], x[14], x[14], x[15]);

  // stage 3
  iadst16_stage3_ssse3(x);
  iadst16_stage4_ssse3(x, cospi, __rounding, cos_bit);
  iadst16_stage5_ssse3(x);
  iadst16_stage6_ssse3(x, cospi, __rounding, cos_bit);
  iadst16_stage7_ssse3(x);
  iadst16_stage8_ssse3(x, cospi, __rounding, cos_bit);
  iadst16_stage9_ssse3(output, x);
}
static void iadst16_sse2(const __m128i *input, __m128i *output) {
  const int8_t cos_bit = INV_COS_BIT;
  const int32_t *cospi = cospi_arr(INV_COS_BIT);
  const __m128i __rounding = _mm_set1_epi32(1 << (INV_COS_BIT - 1));
  const __m128i cospi_p02_p62 = pair_set_epi16(cospi[2], cospi[62]);
  const __m128i cospi_p62_m02 = pair_set_epi16(cospi[62], -cospi[2]);
  const __m128i cospi_p10_p54 = pair_set_epi16(cospi[10], cospi[54]);
  const __m128i cospi_p54_m10 = pair_set_epi16(cospi[54], -cospi[10]);
  const __m128i cospi_p18_p46 = pair_set_epi16(cospi[18], cospi[46]);
  const __m128i cospi_p46_m18 = pair_set_epi16(cospi[46], -cospi[18]);
  const __m128i cospi_p26_p38 = pair_set_epi16(cospi[26], cospi[38]);
  const __m128i cospi_p38_m26 = pair_set_epi16(cospi[38], -cospi[26]);
  const __m128i cospi_p34_p30 = pair_set_epi16(cospi[34], cospi[30]);
  const __m128i cospi_p30_m34 = pair_set_epi16(cospi[30], -cospi[34]);
  const __m128i cospi_p42_p22 = pair_set_epi16(cospi[42], cospi[22]);
  const __m128i cospi_p22_m42 = pair_set_epi16(cospi[22], -cospi[42]);
  const __m128i cospi_p50_p14 = pair_set_epi16(cospi[50], cospi[14]);
  const __m128i cospi_p14_m50 = pair_set_epi16(cospi[14], -cospi[50]);
  const __m128i cospi_p58_p06 = pair_set_epi16(cospi[58], cospi[6]);
  const __m128i cospi_p06_m58 = pair_set_epi16(cospi[6], -cospi[58]);

  // stage 1
  __m128i x[16];
  x[0] = input[15];
  x[1] = input[0];
  x[2] = input[13];
  x[3] = input[2];
  x[4] = input[11];
  x[5] = input[4];
  x[6] = input[9];
  x[7] = input[6];
  x[8] = input[7];
  x[9] = input[8];
  x[10] = input[5];
  x[11] = input[10];
  x[12] = input[3];
  x[13] = input[12];
  x[14] = input[1];
  x[15] = input[14];

  // stage 2
  btf_16_sse2(cospi_p02_p62, cospi_p62_m02, x[0], x[1], x[0], x[1]);
  btf_16_sse2(cospi_p10_p54, cospi_p54_m10, x[2], x[3], x[2], x[3]);
  btf_16_sse2(cospi_p18_p46, cospi_p46_m18, x[4], x[5], x[4], x[5]);
  btf_16_sse2(cospi_p26_p38, cospi_p38_m26, x[6], x[7], x[6], x[7]);
  btf_16_sse2(cospi_p34_p30, cospi_p30_m34, x[8], x[9], x[8], x[9]);
  btf_16_sse2(cospi_p42_p22, cospi_p22_m42, x[10], x[11], x[10], x[11]);
  btf_16_sse2(cospi_p50_p14, cospi_p14_m50, x[12], x[13], x[12], x[13]);
  btf_16_sse2(cospi_p58_p06, cospi_p06_m58, x[14], x[15], x[14], x[15]);