xref: /external/libvpx/libvpx/vp9/encoder/x86/vp9_dct_sse2.c

/*
 *  Copyright (c) 2012 The WebM project authors. All Rights Reserved.
 *
 *  Use of this source code is governed by a BSD-style license
 *  that can be found in the LICENSE file in the root of the source
 *  tree. An additional intellectual property rights grant can be found
 *  in the file PATENTS.  All contributing project authors may
 *  be found in the AUTHORS file in the root of the source tree.
 */

#include <emmintrin.h>  // SSE2
#include "vp9/common/vp9_idct.h"  // for cospi constants
#include "vpx_ports/mem.h"

void vp9_fdct4x4_sse2(const int16_t *input, int16_t *output, int stride) {
  // This 2D transform implements 4 vertical 1D transforms followed
  // by 4 horizontal 1D transforms.  The multiplies and adds are as given
  // by Chen, Smith and Fralick ('77).  The commands for moving the data
  // around have been minimized by hand.
  // For the purposes of the comments, the 16 inputs are referred to at i0
  // through iF (in raster order), intermediate variables are a0, b0, c0
  // through f, and correspond to the in-place computations mapped to input
  // locations.  The outputs, o0 through oF are labeled according to the
  // output locations.

  // Constants
  // These are the coefficients used for the multiplies.
  // In the comments, pN means cos(N pi /64) and mN is -cos(N pi /64),
  // where cospi_N_64 = cos(N pi /64)
  const __m128i k__cospi_A = _mm_setr_epi16(cospi_16_64, cospi_16_64,
                                            cospi_16_64, cospi_16_64,
                                            cospi_16_64, -cospi_16_64,
                                            cospi_16_64, -cospi_16_64);
  const __m128i k__cospi_B = _mm_setr_epi16(cospi_16_64, -cospi_16_64,
                                            cospi_16_64, -cospi_16_64,
                                            cospi_16_64, cospi_16_64,
                                            cospi_16_64, cospi_16_64);
  const __m128i k__cospi_C = _mm_setr_epi16(cospi_8_64, cospi_24_64,
                                            cospi_8_64, cospi_24_64,
                                            cospi_24_64, -cospi_8_64,
                                            cospi_24_64, -cospi_8_64);
  const __m128i k__cospi_D = _mm_setr_epi16(cospi_24_64, -cospi_8_64,
                                            cospi_24_64, -cospi_8_64,
                                            cospi_8_64, cospi_24_64,
                                            cospi_8_64, cospi_24_64);
  const __m128i k__cospi_E = _mm_setr_epi16(cospi_16_64, cospi_16_64,
                                            cospi_16_64, cospi_16_64,
                                            cospi_16_64, cospi_16_64,
                                            cospi_16_64, cospi_16_64);
  const __m128i k__cospi_F = _mm_setr_epi16(cospi_16_64, -cospi_16_64,
                                            cospi_16_64, -cospi_16_64,
                                            cospi_16_64, -cospi_16_64,
                                            cospi_16_64, -cospi_16_64);
  const __m128i k__cospi_G = _mm_setr_epi16(cospi_8_64, cospi_24_64,
                                            cospi_8_64, cospi_24_64,
                                            -cospi_8_64, -cospi_24_64,
                                            -cospi_8_64, -cospi_24_64);
  const __m128i k__cospi_H = _mm_setr_epi16(cospi_24_64, -cospi_8_64,
                                            cospi_24_64, -cospi_8_64,
                                            -cospi_24_64, cospi_8_64,
                                            -cospi_24_64, cospi_8_64);

  const __m128i k__DCT_CONST_ROUNDING = _mm_set1_epi32(DCT_CONST_ROUNDING);
  // This second rounding constant saves doing some extra adds at the end
  const __m128i k__DCT_CONST_ROUNDING2 = _mm_set1_epi32(DCT_CONST_ROUNDING
                                               +(DCT_CONST_ROUNDING << 1));
  const int DCT_CONST_BITS2 =  DCT_CONST_BITS+2;
  const __m128i k__nonzero_bias_a = _mm_setr_epi16(0, 1, 1, 1, 1, 1, 1, 1);
  const __m128i k__nonzero_bias_b = _mm_setr_epi16(1, 0, 0, 0, 0, 0, 0, 0);
  __m128i in0, in1;

  // Load inputs.
  {
    in0  = _mm_loadl_epi64((const __m128i *)(input +  0 * stride));
    in1  = _mm_loadl_epi64((const __m128i *)(input +  1 * stride));
    in1  = _mm_unpacklo_epi64(in1, _mm_loadl_epi64((const __m128i *)
           (input +  2 * stride)));
    in0  = _mm_unpacklo_epi64(in0, _mm_loadl_epi64((const __m128i *)
           (input +  3 * stride)));
    // in0 = [i0 i1 i2 i3 iC iD iE iF]
    // in1 = [i4 i5 i6 i7 i8 i9 iA iB]


    // multiply by 16 to give some extra precision
    in0 = _mm_slli_epi16(in0, 4);
    in1 = _mm_slli_epi16(in1, 4);
    // if (i == 0 && input[0]) input[0] += 1;
    // add 1 to the upper left pixel if it is non-zero, which helps reduce
    // the round-trip error
    {
      // The mask will only contain whether the first value is zero, all
      // other comparison will fail as something shifted by 4 (above << 4)
      // can never be equal to one. To increment in the non-zero case, we
      // add the mask and one for the first element:
      //   - if zero, mask = -1, v = v - 1 + 1 = v
      //   - if non-zero, mask = 0, v = v + 0 + 1 = v + 1
      __m128i mask = _mm_cmpeq_epi16(in0, k__nonzero_bias_a);
      in0 = _mm_add_epi16(in0, mask);
      in0 = _mm_add_epi16(in0, k__nonzero_bias_b);
    }
  }
  // There are 4 total stages, alternating between an add/subtract stage
  // followed by an multiply-and-add stage.
  {
    // Stage 1: Add/subtract

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

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

    // Stage 2: multiply by constants (which gets us into 32 bits).
    // The constants needed here are:
    // k__cospi_A = [p16 p16 p16 p16 p16 m16 p16 m16]
    // k__cospi_B = [p16 m16 p16 m16 p16 p16 p16 p16]
    // k__cospi_C = [p08 p24 p08 p24 p24 m08 p24 m08]
    // k__cospi_D = [p24 m08 p24 m08 p08 p24 p08 p24]
    const __m128i u0 = _mm_madd_epi16(t0, k__cospi_A);
    const __m128i u2 = _mm_madd_epi16(t0, k__cospi_B);
    const __m128i u1 = _mm_madd_epi16(t1, k__cospi_C);
    const __m128i u3 = _mm_madd_epi16(t1, k__cospi_D);
    // Then add and right-shift to get back to 16-bit range
    const __m128i v0 = _mm_add_epi32(u0, k__DCT_CONST_ROUNDING);
    const __m128i v1 = _mm_add_epi32(u1, k__DCT_CONST_ROUNDING);
    const __m128i v2 = _mm_add_epi32(u2, k__DCT_CONST_ROUNDING);
    const __m128i v3 = _mm_add_epi32(u3, k__DCT_CONST_ROUNDING);
    const __m128i w0 = _mm_srai_epi32(v0, DCT_CONST_BITS);
    const __m128i w1 = _mm_srai_epi32(v1, DCT_CONST_BITS);
    const __m128i w2 = _mm_srai_epi32(v2, DCT_CONST_BITS);
    const __m128i w3 = _mm_srai_epi32(v3, DCT_CONST_BITS);
    // w0 = [b0 b1 b7 b6]
    // w1 = [b8 b9 bF bE]
    // w2 = [b4 b5 b3 b2]
    // w3 = [bC bD bB bA]
    const __m128i x0 = _mm_packs_epi32(w0, w1);
    const __m128i x1 = _mm_packs_epi32(w2, w3);
    // x0 = [b0 b1 b7 b6 b8 b9 bF bE]
    // x1 = [b4 b5 b3 b2 bC bD bB bA]
    in0 = _mm_shuffle_epi32(x0, 0xD8);
    in1 = _mm_shuffle_epi32(x1, 0x8D);
    // in0 = [b0 b1 b8 b9 b7 b6 bF bE]
    // in1 = [b3 b2 bB bA b4 b5 bC bD]
  }
  {
    // vertical DCTs finished. Now we do the horizontal DCTs.
    // Stage 3: Add/subtract

    const __m128i t0 = _mm_add_epi16(in0, in1);
    const __m128i t1 = _mm_sub_epi16(in0, in1);
    // t0 = [c0 c1 c8 c9  c4  c5  cC  cD]
    // t1 = [c3 c2 cB cA -c7 -c6 -cF -cE]

    // Stage 4: multiply by constants (which gets us into 32 bits).
    // The constants needed here are:
    // k__cospi_E = [p16 p16 p16 p16 p16 p16 p16 p16]
    // k__cospi_F = [p16 m16 p16 m16 p16 m16 p16 m16]
    // k__cospi_G = [p08 p24 p08 p24 m08 m24 m08 m24]
    // k__cospi_H = [p24 m08 p24 m08 m24 p08 m24 p08]
    const __m128i u0 = _mm_madd_epi16(t0, k__cospi_E);
    const __m128i u1 = _mm_madd_epi16(t0, k__cospi_F);
    const __m128i u2 = _mm_madd_epi16(t1, k__cospi_G);
    const __m128i u3 = _mm_madd_epi16(t1, k__cospi_H);
    // Then add and right-shift to get back to 16-bit range
    // but this combines the final right-shift as well to save operations
    // This unusual rounding operations is to maintain bit-accurate
    // compatibility with the c version of this function which has two
    // rounding steps in a row.
    const __m128i v0 = _mm_add_epi32(u0, k__DCT_CONST_ROUNDING2);
    const __m128i v1 = _mm_add_epi32(u1, k__DCT_CONST_ROUNDING2);
    const __m128i v2 = _mm_add_epi32(u2, k__DCT_CONST_ROUNDING2);
    const __m128i v3 = _mm_add_epi32(u3, k__DCT_CONST_ROUNDING2);
    const __m128i w0 = _mm_srai_epi32(v0, DCT_CONST_BITS2);
    const __m128i w1 = _mm_srai_epi32(v1, DCT_CONST_BITS2);
    const __m128i w2 = _mm_srai_epi32(v2, DCT_CONST_BITS2);
    const __m128i w3 = _mm_srai_epi32(v3, DCT_CONST_BITS2);
    // w0 = [o0 o4 o8 oC]
    // w1 = [o2 o6 oA oE]
    // w2 = [o1 o5 o9 oD]
    // w3 = [o3 o7 oB oF]
    // remember the o's are numbered according to the correct output location
    const __m128i x0 = _mm_packs_epi32(w0, w1);
    const __m128i x1 = _mm_packs_epi32(w2, w3);
    // x0 = [o0 o4 o8 oC o2 o6 oA oE]
    // x1 = [o1 o5 o9 oD o3 o7 oB oF]
    const __m128i y0 = _mm_unpacklo_epi16(x0, x1);
    const __m128i y1 = _mm_unpackhi_epi16(x0, x1);
    // y0 = [o0 o1 o4 o5 o8 o9 oC oD]
    // y1 = [o2 o3 o6 o7 oA oB oE oF]
    in0 = _mm_unpacklo_epi32(y0, y1);
    // in0 = [o0 o1 o2 o3 o4 o5 o6 o7]
    in1 = _mm_unpackhi_epi32(y0, y1);
    // in1 = [o8 o9 oA oB oC oD oE oF]
  }
  // Post-condition (v + 1) >> 2 is now incorporated into previous
  // add and right-shift commands.  Only 2 store instructions needed
  // because we are using the fact that 1/3 are stored just after 0/2.
  {
     _mm_storeu_si128((__m128i *)(output + 0 * 4), in0);
     _mm_storeu_si128((__m128i *)(output + 2 * 4), in1);
  }
}


static INLINE void load_buffer_4x4(const int16_t *input, __m128i *in,
                                   int stride) {
  const __m128i k__nonzero_bias_a = _mm_setr_epi16(0, 1, 1, 1, 1, 1, 1, 1);
  const __m128i k__nonzero_bias_b = _mm_setr_epi16(1, 0, 0, 0, 0, 0, 0, 0);
  __m128i mask;

  in[0] = _mm_loadl_epi64((const __m128i *)(input + 0 * stride));
  in[1] = _mm_loadl_epi64((const __m128i *)(input + 1 * stride));
  in[2] = _mm_loadl_epi64((const __m128i *)(input + 2 * stride));
  in[3] = _mm_loadl_epi64((const __m128i *)(input + 3 * stride));

  in[0] = _mm_slli_epi16(in[0], 4);
  in[1] = _mm_slli_epi16(in[1], 4);
  in[2] = _mm_slli_epi16(in[2], 4);
  in[3] = _mm_slli_epi16(in[3], 4);

  mask = _mm_cmpeq_epi16(in[0], k__nonzero_bias_a);
  in[0] = _mm_add_epi16(in[0], mask);
  in[0] = _mm_add_epi16(in[0], k__nonzero_bias_b);
}

static INLINE void write_buffer_4x4(int16_t *output, __m128i *res) {
  const __m128i kOne = _mm_set1_epi16(1);
  __m128i in01 = _mm_unpacklo_epi64(res[0], res[1]);
  __m128i in23 = _mm_unpacklo_epi64(res[2], res[3]);
  __m128i out01 = _mm_add_epi16(in01, kOne);
  __m128i out23 = _mm_add_epi16(in23, kOne);
  out01 = _mm_srai_epi16(out01, 2);
  out23 = _mm_srai_epi16(out23, 2);
  _mm_store_si128((__m128i *)(output + 0 * 8), out01);
  _mm_store_si128((__m128i *)(output + 1 * 8), out23);
}

static INLINE void transpose_4x4(__m128i *res) {
  // Combine and transpose
  // 00 01 02 03 20 21 22 23
  // 10 11 12 13 30 31 32 33
  const __m128i tr0_0 = _mm_unpacklo_epi16(res[0], res[1]);
  const __m128i tr0_1 = _mm_unpackhi_epi16(res[0], res[1]);

  // 00 10 01 11 02 12 03 13
  // 20 30 21 31 22 32 23 33
  res[0] = _mm_unpacklo_epi32(tr0_0, tr0_1);
  res[2] = _mm_unpackhi_epi32(tr0_0, tr0_1);

  // 00 10 20 30 01 11 21 31
  // 02 12 22 32 03 13 23 33
  // only use the first 4 16-bit integers
  res[1] = _mm_unpackhi_epi64(res[0], res[0]);
  res[3] = _mm_unpackhi_epi64(res[2], res[2]);
}

void fdct4_sse2(__m128i *in) {
  const __m128i k__cospi_p16_p16 = _mm_set1_epi16(cospi_16_64);
  const __m128i k__cospi_p16_m16 = pair_set_epi16(cospi_16_64, -cospi_16_64);
  const __m128i k__cospi_p08_p24 = pair_set_epi16(cospi_8_64, cospi_24_64);
  const __m128i k__cospi_p24_m08 = pair_set_epi16(cospi_24_64, -cospi_8_64);
  const __m128i k__DCT_CONST_ROUNDING = _mm_set1_epi32(DCT_CONST_ROUNDING);

  __m128i u[4], v[4];
  u[0]=_mm_unpacklo_epi16(in[0], in[1]);
  u[1]=_mm_unpacklo_epi16(in[3], in[2]);

  v[0] = _mm_add_epi16(u[0], u[1]);
  v[1] = _mm_sub_epi16(u[0], u[1]);

  u[0] = _mm_madd_epi16(v[0], k__cospi_p16_p16);  // 0
  u[1] = _mm_madd_epi16(v[0], k__cospi_p16_m16);  // 2
  u[2] = _mm_madd_epi16(v[1], k__cospi_p08_p24);  // 1
  u[3] = _mm_madd_epi16(v[1], k__cospi_p24_m08);  // 3

  v[0] = _mm_add_epi32(u[0], k__DCT_CONST_ROUNDING);
  v[1] = _mm_add_epi32(u[1], k__DCT_CONST_ROUNDING);
  v[2] = _mm_add_epi32(u[2], k__DCT_CONST_ROUNDING);
  v[3] = _mm_add_epi32(u[3], k__DCT_CONST_ROUNDING);
  u[0] = _mm_srai_epi32(v[0], DCT_CONST_BITS);
  u[1] = _mm_srai_epi32(v[1], DCT_CONST_BITS);
  u[2] = _mm_srai_epi32(v[2], DCT_CONST_BITS);
  u[3] = _mm_srai_epi32(v[3], DCT_CONST_BITS);

  in[0] = _mm_packs_epi32(u[0], u[1]);
  in[1] = _mm_packs_epi32(u[2], u[3]);
  transpose_4x4(in);
}

void fadst4_sse2(__m128i *in) {
  const __m128i k__sinpi_p01_p02 = pair_set_epi16(sinpi_1_9, sinpi_2_9);
  const __m128i k__sinpi_p04_m01 = pair_set_epi16(sinpi_4_9, -sinpi_1_9);
  const __m128i k__sinpi_p03_p04 = pair_set_epi16(sinpi_3_9, sinpi_4_9);
  const __m128i k__sinpi_m03_p02 = pair_set_epi16(-sinpi_3_9, sinpi_2_9);
  const __m128i k__sinpi_p03_p03 = _mm_set1_epi16(sinpi_3_9);
  const __m128i kZero = _mm_set1_epi16(0);
  const __m128i k__DCT_CONST_ROUNDING = _mm_set1_epi32(DCT_CONST_ROUNDING);
  __m128i u[8], v[8];
  __m128i in7 = _mm_add_epi16(in[0], in[1]);

  u[0] = _mm_unpacklo_epi16(in[0], in[1]);
  u[1] = _mm_unpacklo_epi16(in[2], in[3]);
  u[2] = _mm_unpacklo_epi16(in7, kZero);
  u[3] = _mm_unpacklo_epi16(in[2], kZero);
  u[4] = _mm_unpacklo_epi16(in[3], kZero);

  v[0] = _mm_madd_epi16(u[0], k__sinpi_p01_p02);  // s0 + s2
  v[1] = _mm_madd_epi16(u[1], k__sinpi_p03_p04);  // s4 + s5
  v[2] = _mm_madd_epi16(u[2], k__sinpi_p03_p03);  // x1
  v[3] = _mm_madd_epi16(u[0], k__sinpi_p04_m01);  // s1 - s3
  v[4] = _mm_madd_epi16(u[1], k__sinpi_m03_p02);  // -s4 + s6
  v[5] = _mm_madd_epi16(u[3], k__sinpi_p03_p03);  // s4
  v[6] = _mm_madd_epi16(u[4], k__sinpi_p03_p03);

  u[0] = _mm_add_epi32(v[0], v[1]);
  u[1] = _mm_sub_epi32(v[2], v[6]);
  u[2] = _mm_add_epi32(v[3], v[4]);
  u[3] = _mm_sub_epi32(u[2], u[0]);
  u[4] = _mm_slli_epi32(v[5], 2);
  u[5] = _mm_sub_epi32(u[4], v[5]);
  u[6] = _mm_add_epi32(u[3], u[5]);

  v[0] = _mm_add_epi32(u[0], k__DCT_CONST_ROUNDING);
  v[1] = _mm_add_epi32(u[1], k__DCT_CONST_ROUNDING);
  v[2] = _mm_add_epi32(u[2], k__DCT_CONST_ROUNDING);
  v[3] = _mm_add_epi32(u[6], k__DCT_CONST_ROUNDING);

  u[0] = _mm_srai_epi32(v[0], DCT_CONST_BITS);
  u[1] = _mm_srai_epi32(v[1], DCT_CONST_BITS);
  u[2] = _mm_srai_epi32(v[2], DCT_CONST_BITS);
  u[3] = _mm_srai_epi32(v[3], DCT_CONST_BITS);

  in[0] = _mm_packs_epi32(u[0], u[2]);
  in[1] = _mm_packs_epi32(u[1], u[3]);
  transpose_4x4(in);
}

void vp9_fht4x4_sse2(const int16_t *input, int16_t *output,
                     int stride, int tx_type) {
  __m128i in[4];

  switch (tx_type) {
    case DCT_DCT:
      vp9_fdct4x4_sse2(input, output, stride);
      break;
    case ADST_DCT:
      load_buffer_4x4(input, in, stride);
      fadst4_sse2(in);
      fdct4_sse2(in);
      write_buffer_4x4(output, in);
      break;
    case DCT_ADST:
      load_buffer_4x4(input, in, stride);
      fdct4_sse2(in);
      fadst4_sse2(in);
      write_buffer_4x4(output, in);
      break;
    case ADST_ADST:
      load_buffer_4x4(input, in, stride);
      fadst4_sse2(in);
      fadst4_sse2(in);
      write_buffer_4x4(output, in);
      break;
   default:
     assert(0);
     break;
  }
}

void vp9_fdct8x8_sse2(const int16_t *input, int16_t *output, int stride) {
  int pass;
  // Constants
  //    When we use them, in one case, they are all the same. In all others
  //    it's a pair of them that we need to repeat four times. This is done
  //    by constructing the 32 bit constant corresponding to that pair.
  const __m128i k__cospi_p16_p16 = _mm_set1_epi16(cospi_16_64);
  const __m128i k__cospi_p16_m16 = pair_set_epi16(cospi_16_64, -cospi_16_64);
  const __m128i k__cospi_p24_p08 = pair_set_epi16(cospi_24_64, cospi_8_64);
  const __m128i k__cospi_m08_p24 = pair_set_epi16(-cospi_8_64, cospi_24_64);
  const __m128i k__cospi_p28_p04 = pair_set_epi16(cospi_28_64, cospi_4_64);
  const __m128i k__cospi_m04_p28 = pair_set_epi16(-cospi_4_64, cospi_28_64);
  const __m128i k__cospi_p12_p20 = pair_set_epi16(cospi_12_64, cospi_20_64);
  const __m128i k__cospi_m20_p12 = pair_set_epi16(-cospi_20_64, cospi_12_64);
  const __m128i k__DCT_CONST_ROUNDING = _mm_set1_epi32(DCT_CONST_ROUNDING);
  // Load input
  __m128i in0  = _mm_load_si128((const __m128i *)(input + 0 * stride));
  __m128i in1  = _mm_load_si128((const __m128i *)(input + 1 * stride));
  __m128i in2  = _mm_load_si128((const __m128i *)(input + 2 * stride));
  __m128i in3  = _mm_load_si128((const __m128i *)(input + 3 * stride));
  __m128i in4  = _mm_load_si128((const __m128i *)(input + 4 * stride));
  __m128i in5  = _mm_load_si128((const __m128i *)(input + 5 * stride));
  __m128i in6  = _mm_load_si128((const __m128i *)(input + 6 * stride));
  __m128i in7  = _mm_load_si128((const __m128i *)(input + 7 * stride));
  // Pre-condition input (shift by two)
  in0 = _mm_slli_epi16(in0, 2);
  in1 = _mm_slli_epi16(in1, 2);
  in2 = _mm_slli_epi16(in2, 2);
  in3 = _mm_slli_epi16(in3, 2);
  in4 = _mm_slli_epi16(in4, 2);
  in5 = _mm_slli_epi16(in5, 2);
  in6 = _mm_slli_epi16(in6, 2);
  in7 = _mm_slli_epi16(in7, 2);

  // We do two passes, first the columns, then the rows. The results of the
  // first pass are transposed so that the same column code can be reused. The
  // results of the second pass are also transposed so that the rows (processed
  // as columns) are put back in row positions.
  for (pass = 0; pass < 2; pass++) {
    // To store results of each pass before the transpose.
    __m128i res0, res1, res2, res3, res4, res5, res6, res7;
    // Add/subtract
    const __m128i q0 = _mm_add_epi16(in0, in7);
    const __m128i q1 = _mm_add_epi16(in1, in6);
    const __m128i q2 = _mm_add_epi16(in2, in5);
    const __m128i q3 = _mm_add_epi16(in3, in4);
    const __m128i q4 = _mm_sub_epi16(in3, in4);
    const __m128i q5 = _mm_sub_epi16(in2, in5);
    const __m128i q6 = _mm_sub_epi16(in1, in6);
    const __m128i q7 = _mm_sub_epi16(in0, in7);
    // Work on first four results
    {
      // Add/subtract
      const __m128i r0 = _mm_add_epi16(q0, q3);
      const __m128i r1 = _mm_add_epi16(q1, q2);
      const __m128i r2 = _mm_sub_epi16(q1, q2);
      const __m128i r3 = _mm_sub_epi16(q0, q3);
      // Interleave to do the multiply by constants which gets us into 32bits
      const __m128i t0 = _mm_unpacklo_epi16(r0, r1);
      const __m128i t1 = _mm_unpackhi_epi16(r0, r1);
      const __m128i t2 = _mm_unpacklo_epi16(r2, r3);
      const __m128i t3 = _mm_unpackhi_epi16(r2, r3);
      const __m128i u0 = _mm_madd_epi16(t0, k__cospi_p16_p16);
      const __m128i u1 = _mm_madd_epi16(t1, k__cospi_p16_p16);
      const __m128i u2 = _mm_madd_epi16(t0, k__cospi_p16_m16);
      const __m128i u3 = _mm_madd_epi16(t1, k__cospi_p16_m16);
      const __m128i u4 = _mm_madd_epi16(t2, k__cospi_p24_p08);
      const __m128i u5 = _mm_madd_epi16(t3, k__cospi_p24_p08);
      const __m128i u6 = _mm_madd_epi16(t2, k__cospi_m08_p24);
      const __m128i u7 = _mm_madd_epi16(t3, k__cospi_m08_p24);
      // dct_const_round_shift
      const __m128i v0 = _mm_add_epi32(u0, k__DCT_CONST_ROUNDING);
      const __m128i v1 = _mm_add_epi32(u1, k__DCT_CONST_ROUNDING);
      const __m128i v2 = _mm_add_epi32(u2, k__DCT_CONST_ROUNDING);
      const __m128i v3 = _mm_add_epi32(u3, k__DCT_CONST_ROUNDING);
      const __m128i v4 = _mm_add_epi32(u4, k__DCT_CONST_ROUNDING);
      const __m128i v5 = _mm_add_epi32(u5, k__DCT_CONST_ROUNDING);
      const __m128i v6 = _mm_add_epi32(u6, k__DCT_CONST_ROUNDING);
      const __m128i v7 = _mm_add_epi32(u7, k__DCT_CONST_ROUNDING);
      const __m128i w0 = _mm_srai_epi32(v0, DCT_CONST_BITS);
      const __m128i w1 = _mm_srai_epi32(v1, DCT_CONST_BITS);
      const __m128i w2 = _mm_srai_epi32(v2, DCT_CONST_BITS);
      const __m128i w3 = _mm_srai_epi32(v3, DCT_CONST_BITS);
      const __m128i w4 = _mm_srai_epi32(v4, DCT_CONST_BITS);
      const __m128i w5 = _mm_srai_epi32(v5, DCT_CONST_BITS);
      const __m128i w6 = _mm_srai_epi32(v6, DCT_CONST_BITS);
      const __m128i w7 = _mm_srai_epi32(v7, DCT_CONST_BITS);
      // Combine
      res0 = _mm_packs_epi32(w0, w1);
      res4 = _mm_packs_epi32(w2, w3);
      res2 = _mm_packs_epi32(w4, w5);
      res6 = _mm_packs_epi32(w6, w7);
    }
    // Work on next four results
    {
      // Interleave to do the multiply by constants which gets us into 32bits
      const __m128i d0 = _mm_unpacklo_epi16(q6, q5);
      const __m128i d1 = _mm_unpackhi_epi16(q6, q5);
      const __m128i e0 = _mm_madd_epi16(d0, k__cospi_p16_m16);
      const __m128i e1 = _mm_madd_epi16(d1, k__cospi_p16_m16);
      const __m128i e2 = _mm_madd_epi16(d0, k__cospi_p16_p16);
      const __m128i e3 = _mm_madd_epi16(d1, k__cospi_p16_p16);
      // dct_const_round_shift
      const __m128i f0 = _mm_add_epi32(e0, k__DCT_CONST_ROUNDING);
      const __m128i f1 = _mm_add_epi32(e1, k__DCT_CONST_ROUNDING);
      const __m128i f2 = _mm_add_epi32(e2, k__DCT_CONST_ROUNDING);
      const __m128i f3 = _mm_add_epi32(e3, k__DCT_CONST_ROUNDING);
      const __m128i s0 = _mm_srai_epi32(f0, DCT_CONST_BITS);
      const __m128i s1 = _mm_srai_epi32(f1, DCT_CONST_BITS);
      const __m128i s2 = _mm_srai_epi32(f2, DCT_CONST_BITS);
      const __m128i s3 = _mm_srai_epi32(f3, DCT_CONST_BITS);
      // Combine
      const __m128i r0 = _mm_packs_epi32(s0, s1);
      const __m128i r1 = _mm_packs_epi32(s2, s3);
      // Add/subtract
      const __m128i x0 = _mm_add_epi16(q4, r0);
      const __m128i x1 = _mm_sub_epi16(q4, r0);
      const __m128i x2 = _mm_sub_epi16(q7, r1);
      const __m128i x3 = _mm_add_epi16(q7, r1);
      // Interleave to do the multiply by constants which gets us into 32bits
      const __m128i t0 = _mm_unpacklo_epi16(x0, x3);
      const __m128i t1 = _mm_unpackhi_epi16(x0, x3);
      const __m128i t2 = _mm_unpacklo_epi16(x1, x2);
      const __m128i t3 = _mm_unpackhi_epi16(x1, x2);
      const __m128i u0 = _mm_madd_epi16(t0, k__cospi_p28_p04);
      const __m128i u1 = _mm_madd_epi16(t1, k__cospi_p28_p04);
      const __m128i u2 = _mm_madd_epi16(t0, k__cospi_m04_p28);
      const __m128i u3 = _mm_madd_epi16(t1, k__cospi_m04_p28);
      const __m128i u4 = _mm_madd_epi16(t2, k__cospi_p12_p20);
      const __m128i u5 = _mm_madd_epi16(t3, k__cospi_p12_p20);
      const __m128i u6 = _mm_madd_epi16(t2, k__cospi_m20_p12);
      const __m128i u7 = _mm_madd_epi16(t3, k__cospi_m20_p12);
      // dct_const_round_shift
      const __m128i v0 = _mm_add_epi32(u0, k__DCT_CONST_ROUNDING);
      const __m128i v1 = _mm_add_epi32(u1, k__DCT_CONST_ROUNDING);
      const __m128i v2 = _mm_add_epi32(u2, k__DCT_CONST_ROUNDING);
      const __m128i v3 = _mm_add_epi32(u3, k__DCT_CONST_ROUNDING);
      const __m128i v4 = _mm_add_epi32(u4, k__DCT_CONST_ROUNDING);
      const __m128i v5 = _mm_add_epi32(u5, k__DCT_CONST_ROUNDING);
      const __m128i v6 = _mm_add_epi32(u6, k__DCT_CONST_ROUNDING);
      const __m128i v7 = _mm_add_epi32(u7, k__DCT_CONST_ROUNDING);
      const __m128i w0 = _mm_srai_epi32(v0, DCT_CONST_BITS);
      const __m128i w1 = _mm_srai_epi32(v1, DCT_CONST_BITS);
      const __m128i w2 = _mm_srai_epi32(v2, DCT_CONST_BITS);
      const __m128i w3 = _mm_srai_epi32(v3, DCT_CONST_BITS);
      const __m128i w4 = _mm_srai_epi32(v4, DCT_CONST_BITS);
      const __m128i w5 = _mm_srai_epi32(v5, DCT_CONST_BITS);
      const __m128i w6 = _mm_srai_epi32(v6, DCT_CONST_BITS);
      const __m128i w7 = _mm_srai_epi32(v7, DCT_CONST_BITS);
      // Combine
      res1 = _mm_packs_epi32(w0, w1);
      res7 = _mm_packs_epi32(w2, w3);
      res5 = _mm_packs_epi32(w4, w5);
      res3 = _mm_packs_epi32(w6, w7);
    }
    // Transpose the 8x8.
    {
      // 00 01 02 03 04 05 06 07
      // 10 11 12 13 14 15 16 17
      // 20 21 22 23 24 25 26 27
      // 30 31 32 33 34 35 36 37
      // 40 41 42 43 44 45 46 47
      // 50 51 52 53 54 55 56 57
      // 60 61 62 63 64 65 66 67
      // 70 71 72 73 74 75 76 77
      const __m128i tr0_0 = _mm_unpacklo_epi16(res0, res1);
      const __m128i tr0_1 = _mm_unpacklo_epi16(res2, res3);
      const __m128i tr0_2 = _mm_unpackhi_epi16(res0, res1);
      const __m128i tr0_3 = _mm_unpackhi_epi16(res2, res3);
      const __m128i tr0_4 = _mm_unpacklo_epi16(res4, res5);
      const __m128i tr0_5 = _mm_unpacklo_epi16(res6, res7);
      const __m128i tr0_6 = _mm_unpackhi_epi16(res4, res5);
      const __m128i tr0_7 = _mm_unpackhi_epi16(res6, res7);
      // 00 10 01 11 02 12 03 13
      // 20 30 21 31 22 32 23 33
      // 04 14 05 15 06 16 07 17
      // 24 34 25 35 26 36 27 37
      // 40 50 41 51 42 52 43 53
      // 60 70 61 71 62 72 63 73
      // 54 54 55 55 56 56 57 57
      // 64 74 65 75 66 76 67 77
      const __m128i tr1_0 = _mm_unpacklo_epi32(tr0_0, tr0_1);
      const __m128i tr1_1 = _mm_unpacklo_epi32(tr0_2, tr0_3);
      const __m128i tr1_2 = _mm_unpackhi_epi32(tr0_0, tr0_1);
      const __m128i tr1_3 = _mm_unpackhi_epi32(tr0_2, tr0_3);
      const __m128i tr1_4 = _mm_unpacklo_epi32(tr0_4, tr0_5);
      const __m128i tr1_5 = _mm_unpacklo_epi32(tr0_6, tr0_7);
      const __m128i tr1_6 = _mm_unpackhi_epi32(tr0_4, tr0_5);
      const __m128i tr1_7 = _mm_unpackhi_epi32(tr0_6, tr0_7);
      // 00 10 20 30 01 11 21 31
      // 40 50 60 70 41 51 61 71
      // 02 12 22 32 03 13 23 33
      // 42 52 62 72 43 53 63 73
      // 04 14 24 34 05 15 21 36
      // 44 54 64 74 45 55 61 76
      // 06 16 26 36 07 17 27 37
      // 46 56 66 76 47 57 67 77
      in0 = _mm_unpacklo_epi64(tr1_0, tr1_4);
      in1 = _mm_unpackhi_epi64(tr1_0, tr1_4);
      in2 = _mm_unpacklo_epi64(tr1_2, tr1_6);
      in3 = _mm_unpackhi_epi64(tr1_2, tr1_6);
      in4 = _mm_unpacklo_epi64(tr1_1, tr1_5);
      in5 = _mm_unpackhi_epi64(tr1_1, tr1_5);
      in6 = _mm_unpacklo_epi64(tr1_3, tr1_7);
      in7 = _mm_unpackhi_epi64(tr1_3, tr1_7);
      // 00 10 20 30 40 50 60 70
      // 01 11 21 31 41 51 61 71
      // 02 12 22 32 42 52 62 72
      // 03 13 23 33 43 53 63 73
      // 04 14 24 34 44 54 64 74
      // 05 15 25 35 45 55 65 75
      // 06 16 26 36 46 56 66 76
      // 07 17 27 37 47 57 67 77
    }
  }
  // Post-condition output and store it
  {
    // Post-condition (division by two)
    //    division of two 16 bits signed numbers using shifts
    //    n / 2 = (n - (n >> 15)) >> 1
    const __m128i sign_in0 = _mm_srai_epi16(in0, 15);
    const __m128i sign_in1 = _mm_srai_epi16(in1, 15);
    const __m128i sign_in2 = _mm_srai_epi16(in2, 15);
    const __m128i sign_in3 = _mm_srai_epi16(in3, 15);
    const __m128i sign_in4 = _mm_srai_epi16(in4, 15);
    const __m128i sign_in5 = _mm_srai_epi16(in5, 15);
    const __m128i sign_in6 = _mm_srai_epi16(in6, 15);
    const __m128i sign_in7 = _mm_srai_epi16(in7, 15);
    in0 = _mm_sub_epi16(in0, sign_in0);
    in1 = _mm_sub_epi16(in1, sign_in1);
    in2 = _mm_sub_epi16(in2, sign_in2);
    in3 = _mm_sub_epi16(in3, sign_in3);
    in4 = _mm_sub_epi16(in4, sign_in4);
    in5 = _mm_sub_epi16(in5, sign_in5);
    in6 = _mm_sub_epi16(in6, sign_in6);
    in7 = _mm_sub_epi16(in7, sign_in7);
    in0 = _mm_srai_epi16(in0, 1);
    in1 = _mm_srai_epi16(in1, 1);
    in2 = _mm_srai_epi16(in2, 1);
    in3 = _mm_srai_epi16(in3, 1);
    in4 = _mm_srai_epi16(in4, 1);
    in5 = _mm_srai_epi16(in5, 1);
    in6 = _mm_srai_epi16(in6, 1);
    in7 = _mm_srai_epi16(in7, 1);
    // store results
    _mm_store_si128((__m128i *)(output + 0 * 8), in0);
    _mm_store_si128((__m128i *)(output + 1 * 8), in1);
    _mm_store_si128((__m128i *)(output + 2 * 8), in2);
    _mm_store_si128((__m128i *)(output + 3 * 8), in3);
    _mm_store_si128((__m128i *)(output + 4 * 8), in4);
    _mm_store_si128((__m128i *)(output + 5 * 8), in5);
    _mm_store_si128((__m128i *)(output + 6 * 8), in6);
    _mm_store_si128((__m128i *)(output + 7 * 8), in7);
  }
}

// load 8x8 array
static INLINE void load_buffer_8x8(const int16_t *input, __m128i *in,
                                   int stride) {
  in[0]  = _mm_load_si128((const __m128i *)(input + 0 * stride));
  in[1]  = _mm_load_si128((const __m128i *)(input + 1 * stride));
  in[2]  = _mm_load_si128((const __m128i *)(input + 2 * stride));
  in[3]  = _mm_load_si128((const __m128i *)(input + 3 * stride));
  in[4]  = _mm_load_si128((const __m128i *)(input + 4 * stride));
  in[5]  = _mm_load_si128((const __m128i *)(input + 5 * stride));
  in[6]  = _mm_load_si128((const __m128i *)(input + 6 * stride));
  in[7]  = _mm_load_si128((const __m128i *)(input + 7 * stride));

  in[0] = _mm_slli_epi16(in[0], 2);
  in[1] = _mm_slli_epi16(in[1], 2);
  in[2] = _mm_slli_epi16(in[2], 2);
  in[3] = _mm_slli_epi16(in[3], 2);
  in[4] = _mm_slli_epi16(in[4], 2);
  in[5] = _mm_slli_epi16(in[5], 2);
  in[6] = _mm_slli_epi16(in[6], 2);
  in[7] = _mm_slli_epi16(in[7], 2);
}

// right shift and rounding
static INLINE void right_shift_8x8(__m128i *res, int const bit) {
  const __m128i kOne = _mm_set1_epi16(1);
  const int bit_m02 = bit - 2;
  __m128i sign0 = _mm_srai_epi16(res[0], 15);
  __m128i sign1 = _mm_srai_epi16(res[1], 15);
  __m128i sign2 = _mm_srai_epi16(res[2], 15);
  __m128i sign3 = _mm_srai_epi16(res[3], 15);
  __m128i sign4 = _mm_srai_epi16(res[4], 15);
  __m128i sign5 = _mm_srai_epi16(res[5], 15);
  __m128i sign6 = _mm_srai_epi16(res[6], 15);
  __m128i sign7 = _mm_srai_epi16(res[7], 15);

  if (bit_m02 >= 0) {
    __m128i k_const_rounding = _mm_slli_epi16(kOne, bit_m02);
    res[0] = _mm_add_epi16(res[0], k_const_rounding);
    res[1] = _mm_add_epi16(res[1], k_const_rounding);
    res[2] = _mm_add_epi16(res[2], k_const_rounding);
    res[3] = _mm_add_epi16(res[3], k_const_rounding);
    res[4] = _mm_add_epi16(res[4], k_const_rounding);
    res[5] = _mm_add_epi16(res[5], k_const_rounding);
    res[6] = _mm_add_epi16(res[6], k_const_rounding);
    res[7] = _mm_add_epi16(res[7], k_const_rounding);
  }

  res[0] = _mm_sub_epi16(res[0], sign0);
  res[1] = _mm_sub_epi16(res[1], sign1);
  res[2] = _mm_sub_epi16(res[2], sign2);
  res[3] = _mm_sub_epi16(res[3], sign3);
  res[4] = _mm_sub_epi16(res[4], sign4);
  res[5] = _mm_sub_epi16(res[5], sign5);
  res[6] = _mm_sub_epi16(res[6], sign6);
  res[7] = _mm_sub_epi16(res[7], sign7);

  res[0] = _mm_srai_epi16(res[0], bit);
  res[1] = _mm_srai_epi16(res[1], bit);
  res[2] = _mm_srai_epi16(res[2], bit);
  res[3] = _mm_srai_epi16(res[3], bit);
  res[4] = _mm_srai_epi16(res[4], bit);
  res[5] = _mm_srai_epi16(res[5], bit);
  res[6] = _mm_srai_epi16(res[6], bit);
  res[7] = _mm_srai_epi16(res[7], bit);
}

// write 8x8 array
static INLINE void write_buffer_8x8(int16_t *output, __m128i *res, int stride) {
  _mm_store_si128((__m128i *)(output + 0 * stride), res[0]);
  _mm_store_si128((__m128i *)(output + 1 * stride), res[1]);
  _mm_store_si128((__m128i *)(output + 2 * stride), res[2]);
  _mm_store_si128((__m128i *)(output + 3 * stride), res[3]);
  _mm_store_si128((__m128i *)(output + 4 * stride), res[4]);
  _mm_store_si128((__m128i *)(output + 5 * stride), res[5]);
  _mm_store_si128((__m128i *)(output + 6 * stride), res[6]);
  _mm_store_si128((__m128i *)(output + 7 * stride), res[7]);
}

// perform in-place transpose
static INLINE void array_transpose_8x8(__m128i *in, __m128i *res) {
  const __m128i tr0_0 = _mm_unpacklo_epi16(in[0], in[1]);
  const __m128i tr0_1 = _mm_unpacklo_epi16(in[2], in[3]);
  const __m128i tr0_2 = _mm_unpackhi_epi16(in[0], in[1]);
  const __m128i tr0_3 = _mm_unpackhi_epi16(in[2], in[3]);
  const __m128i tr0_4 = _mm_unpacklo_epi16(in[4], in[5]);
  const __m128i tr0_5 = _mm_unpacklo_epi16(in[6], in[7]);
  const __m128i tr0_6 = _mm_unpackhi_epi16(in[4], in[5]);
  const __m128i tr0_7 = _mm_unpackhi_epi16(in[6], in[7]);
  // 00 10 01 11 02 12 03 13
  // 20 30 21 31 22 32 23 33
  // 04 14 05 15 06 16 07 17
  // 24 34 25 35 26 36 27 37
  // 40 50 41 51 42 52 43 53
  // 60 70 61 71 62 72 63 73
  // 44 54 45 55 46 56 47 57
  // 64 74 65 75 66 76 67 77
  const __m128i tr1_0 = _mm_unpacklo_epi32(tr0_0, tr0_1);
  const __m128i tr1_1 = _mm_unpacklo_epi32(tr0_4, tr0_5);
  const __m128i tr1_2 = _mm_unpackhi_epi32(tr0_0, tr0_1);
  const __m128i tr1_3 = _mm_unpackhi_epi32(tr0_4, tr0_5);
  const __m128i tr1_4 = _mm_unpacklo_epi32(tr0_2, tr0_3);
  const __m128i tr1_5 = _mm_unpacklo_epi32(tr0_6, tr0_7);
  const __m128i tr1_6 = _mm_unpackhi_epi32(tr0_2, tr0_3);
  const __m128i tr1_7 = _mm_unpackhi_epi32(tr0_6, tr0_7);
  // 00 10 20 30 01 11 21 31
  // 40 50 60 70 41 51 61 71
  // 02 12 22 32 03 13 23 33
  // 42 52 62 72 43 53 63 73
  // 04 14 24 34 05 15 25 35
  // 44 54 64 74 45 55 65 75
  // 06 16 26 36 07 17 27 37
  // 46 56 66 76 47 57 67 77
  res[0] = _mm_unpacklo_epi64(tr1_0, tr1_1);
  res[1] = _mm_unpackhi_epi64(tr1_0, tr1_1);
  res[2] = _mm_unpacklo_epi64(tr1_2, tr1_3);
  res[3] = _mm_unpackhi_epi64(tr1_2, tr1_3);
  res[4] = _mm_unpacklo_epi64(tr1_4, tr1_5);
  res[5] = _mm_unpackhi_epi64(tr1_4, tr1_5);
  res[6] = _mm_unpacklo_epi64(tr1_6, tr1_7);
  res[7] = _mm_unpackhi_epi64(tr1_6, tr1_7);
  // 00 10 20 30 40 50 60 70
  // 01 11 21 31 41 51 61 71
  // 02 12 22 32 42 52 62 72
  // 03 13 23 33 43 53 63 73
  // 04 14 24 34 44 54 64 74
  // 05 15 25 35 45 55 65 75
  // 06 16 26 36 46 56 66 76
  // 07 17 27 37 47 57 67 77
}

void fdct8_sse2(__m128i *in) {
  // constants
  const __m128i k__cospi_p16_p16 = _mm_set1_epi16(cospi_16_64);
  const __m128i k__cospi_p16_m16 = pair_set_epi16(cospi_16_64, -cospi_16_64);
  const __m128i k__cospi_p24_p08 = pair_set_epi16(cospi_24_64, cospi_8_64);
  const __m128i k__cospi_m08_p24 = pair_set_epi16(-cospi_8_64, cospi_24_64);
  const __m128i k__cospi_p28_p04 = pair_set_epi16(cospi_28_64, cospi_4_64);
  const __m128i k__cospi_m04_p28 = pair_set_epi16(-cospi_4_64, cospi_28_64);
  const __m128i k__cospi_p12_p20 = pair_set_epi16(cospi_12_64, cospi_20_64);
  const __m128i k__cospi_m20_p12 = pair_set_epi16(-cospi_20_64, cospi_12_64);
  const __m128i k__DCT_CONST_ROUNDING = _mm_set1_epi32(DCT_CONST_ROUNDING);
  __m128i u0, u1, u2, u3, u4, u5, u6, u7;
  __m128i v0, v1, v2, v3, v4, v5, v6, v7;
  __m128i s0, s1, s2, s3, s4, s5, s6, s7;

  // stage 1
  s0 = _mm_add_epi16(in[0], in[7]);
  s1 = _mm_add_epi16(in[1], in[6]);
  s2 = _mm_add_epi16(in[2], in[5]);
  s3 = _mm_add_epi16(in[3], in[4]);
  s4 = _mm_sub_epi16(in[3], in[4]);
  s5 = _mm_sub_epi16(in[2], in[5]);
  s6 = _mm_sub_epi16(in[1], in[6]);
  s7 = _mm_sub_epi16(in[0], in[7]);

  u0 = _mm_add_epi16(s0, s3);
  u1 = _mm_add_epi16(s1, s2);
  u2 = _mm_sub_epi16(s1, s2);
  u3 = _mm_sub_epi16(s0, s3);
  // interleave and perform butterfly multiplication/addition