dct.c 39.3 KB
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/*
 *  Copyright (c) 2010 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 <assert.h>
#include <math.h>

#include "./vp10_rtcd.h"
#include "./vpx_config.h"
#include "./vpx_dsp_rtcd.h"

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#include "av1/common/blockd.h"
#include "av1/common/idct.h"
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#include "aom_dsp/fwd_txfm.h"
#include "aom_ports/mem.h"
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static INLINE void range_check(const tran_low_t *input, const int size,
                               const int bit) {
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#if 0  // CONFIG_COEFFICIENT_RANGE_CHECKING
// TODO(angiebird): the range_check is not used because the bit range
// in fdct# is not correct. Since we are going to merge in a new version
// of fdct# from nextgenv2, we won't fix the incorrect bit range now.
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  int i;
  for (i = 0; i < size; ++i) {
    assert(abs(input[i]) < (1 << bit));
  }
#else
  (void)input;
  (void)size;
  (void)bit;
#endif
}

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static void fdct4(const tran_low_t *input, tran_low_t *output) {
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  tran_high_t temp;
  tran_low_t step[4];

  // stage 0
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  range_check(input, 4, 14);
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  // stage 1
  output[0] = input[0] + input[3];
  output[1] = input[1] + input[2];
  output[2] = input[1] - input[2];
  output[3] = input[0] - input[3];

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  range_check(output, 4, 15);
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  // stage 2
  temp = output[0] * cospi_16_64 + output[1] * cospi_16_64;
  step[0] = (tran_low_t)fdct_round_shift(temp);
  temp = output[1] * -cospi_16_64 + output[0] * cospi_16_64;
  step[1] = (tran_low_t)fdct_round_shift(temp);
  temp = output[2] * cospi_24_64 + output[3] * cospi_8_64;
  step[2] = (tran_low_t)fdct_round_shift(temp);
  temp = output[3] * cospi_24_64 + output[2] * -cospi_8_64;
  step[3] = (tran_low_t)fdct_round_shift(temp);

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  range_check(step, 4, 16);
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  // stage 3
  output[0] = step[0];
  output[1] = step[2];
  output[2] = step[1];
  output[3] = step[3];

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  range_check(output, 4, 16);
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}

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static void fdct8(const tran_low_t *input, tran_low_t *output) {
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  tran_high_t temp;
  tran_low_t step[8];

  // stage 0
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  range_check(input, 8, 13);
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  // stage 1
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  output[0] = input[0] + input[7];
  output[1] = input[1] + input[6];
  output[2] = input[2] + input[5];
  output[3] = input[3] + input[4];
  output[4] = input[3] - input[4];
  output[5] = input[2] - input[5];
  output[6] = input[1] - input[6];
  output[7] = input[0] - input[7];

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  range_check(output, 8, 14);
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  // stage 2
  step[0] = output[0] + output[3];
  step[1] = output[1] + output[2];
  step[2] = output[1] - output[2];
  step[3] = output[0] - output[3];
  step[4] = output[4];
  temp = output[5] * -cospi_16_64 + output[6] * cospi_16_64;
  step[5] = (tran_low_t)fdct_round_shift(temp);
  temp = output[6] * cospi_16_64 + output[5] * cospi_16_64;
  step[6] = (tran_low_t)fdct_round_shift(temp);
  step[7] = output[7];

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  range_check(step, 8, 15);
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  // stage 3
  temp = step[0] * cospi_16_64 + step[1] * cospi_16_64;
  output[0] = (tran_low_t)fdct_round_shift(temp);
  temp = step[1] * -cospi_16_64 + step[0] * cospi_16_64;
  output[1] = (tran_low_t)fdct_round_shift(temp);
  temp = step[2] * cospi_24_64 + step[3] * cospi_8_64;
  output[2] = (tran_low_t)fdct_round_shift(temp);
  temp = step[3] * cospi_24_64 + step[2] * -cospi_8_64;
  output[3] = (tran_low_t)fdct_round_shift(temp);
  output[4] = step[4] + step[5];
  output[5] = step[4] - step[5];
  output[6] = step[7] - step[6];
  output[7] = step[7] + step[6];

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  range_check(output, 8, 16);
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  // stage 4
  step[0] = output[0];
  step[1] = output[1];
  step[2] = output[2];
  step[3] = output[3];
  temp = output[4] * cospi_28_64 + output[7] * cospi_4_64;
  step[4] = (tran_low_t)fdct_round_shift(temp);
  temp = output[5] * cospi_12_64 + output[6] * cospi_20_64;
  step[5] = (tran_low_t)fdct_round_shift(temp);
  temp = output[6] * cospi_12_64 + output[5] * -cospi_20_64;
  step[6] = (tran_low_t)fdct_round_shift(temp);
  temp = output[7] * cospi_28_64 + output[4] * -cospi_4_64;
  step[7] = (tran_low_t)fdct_round_shift(temp);

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  range_check(step, 8, 16);
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  // stage 5
  output[0] = step[0];
  output[1] = step[4];
  output[2] = step[2];
  output[3] = step[6];
  output[4] = step[1];
  output[5] = step[5];
  output[6] = step[3];
  output[7] = step[7];

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  range_check(output, 8, 16);
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}

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static void fdct16(const tran_low_t in[16], tran_low_t out[16]) {
  tran_high_t step1[8];
  tran_high_t step2[8];
  tran_high_t step3[8];
  tran_high_t input[8];
  tran_high_t temp1, temp2;

  // step 1
  input[0] = in[0] + in[15];
  input[1] = in[1] + in[14];
  input[2] = in[2] + in[13];
  input[3] = in[3] + in[12];
  input[4] = in[4] + in[11];
  input[5] = in[5] + in[10];
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  input[6] = in[6] + in[9];
  input[7] = in[7] + in[8];
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  step1[0] = in[7] - in[8];
  step1[1] = in[6] - in[9];
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  step1[2] = in[5] - in[10];
  step1[3] = in[4] - in[11];
  step1[4] = in[3] - in[12];
  step1[5] = in[2] - in[13];
  step1[6] = in[1] - in[14];
  step1[7] = in[0] - in[15];

  // fdct8(step, step);
  {
    tran_high_t s0, s1, s2, s3, s4, s5, s6, s7;
    tran_high_t t0, t1, t2, t3;
    tran_high_t x0, x1, x2, x3;

    // stage 1
    s0 = input[0] + input[7];
    s1 = input[1] + input[6];
    s2 = input[2] + input[5];
    s3 = input[3] + input[4];
    s4 = input[3] - input[4];
    s5 = input[2] - input[5];
    s6 = input[1] - input[6];
    s7 = input[0] - input[7];

    // fdct4(step, step);
    x0 = s0 + s3;
    x1 = s1 + s2;
    x2 = s1 - s2;
    x3 = s0 - s3;
    t0 = (x0 + x1) * cospi_16_64;
    t1 = (x0 - x1) * cospi_16_64;
    t2 = x3 * cospi_8_64 + x2 * cospi_24_64;
    t3 = x3 * cospi_24_64 - x2 * cospi_8_64;
    out[0] = (tran_low_t)fdct_round_shift(t0);
    out[4] = (tran_low_t)fdct_round_shift(t2);
    out[8] = (tran_low_t)fdct_round_shift(t1);
    out[12] = (tran_low_t)fdct_round_shift(t3);

    // Stage 2
    t0 = (s6 - s5) * cospi_16_64;
    t1 = (s6 + s5) * cospi_16_64;
    t2 = fdct_round_shift(t0);
    t3 = fdct_round_shift(t1);

    // Stage 3
    x0 = s4 + t2;
    x1 = s4 - t2;
    x2 = s7 - t3;
    x3 = s7 + t3;

    // Stage 4
    t0 = x0 * cospi_28_64 + x3 * cospi_4_64;
    t1 = x1 * cospi_12_64 + x2 * cospi_20_64;
    t2 = x2 * cospi_12_64 + x1 * -cospi_20_64;
    t3 = x3 * cospi_28_64 + x0 * -cospi_4_64;
    out[2] = (tran_low_t)fdct_round_shift(t0);
    out[6] = (tran_low_t)fdct_round_shift(t2);
    out[10] = (tran_low_t)fdct_round_shift(t1);
    out[14] = (tran_low_t)fdct_round_shift(t3);
  }
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  // step 2
  temp1 = (step1[5] - step1[2]) * cospi_16_64;
  temp2 = (step1[4] - step1[3]) * cospi_16_64;
  step2[2] = fdct_round_shift(temp1);
  step2[3] = fdct_round_shift(temp2);
  temp1 = (step1[4] + step1[3]) * cospi_16_64;
  temp2 = (step1[5] + step1[2]) * cospi_16_64;
  step2[4] = fdct_round_shift(temp1);
  step2[5] = fdct_round_shift(temp2);

  // step 3
  step3[0] = step1[0] + step2[3];
  step3[1] = step1[1] + step2[2];
  step3[2] = step1[1] - step2[2];
  step3[3] = step1[0] - step2[3];
  step3[4] = step1[7] - step2[4];
  step3[5] = step1[6] - step2[5];
  step3[6] = step1[6] + step2[5];
  step3[7] = step1[7] + step2[4];

  // step 4
  temp1 = step3[1] * -cospi_8_64 + step3[6] * cospi_24_64;
  temp2 = step3[2] * cospi_24_64 + step3[5] * cospi_8_64;
  step2[1] = fdct_round_shift(temp1);
  step2[2] = fdct_round_shift(temp2);
  temp1 = step3[2] * cospi_8_64 - step3[5] * cospi_24_64;
  temp2 = step3[1] * cospi_24_64 + step3[6] * cospi_8_64;
  step2[5] = fdct_round_shift(temp1);
  step2[6] = fdct_round_shift(temp2);

  // step 5
  step1[0] = step3[0] + step2[1];
  step1[1] = step3[0] - step2[1];
  step1[2] = step3[3] + step2[2];
  step1[3] = step3[3] - step2[2];
  step1[4] = step3[4] - step2[5];
  step1[5] = step3[4] + step2[5];
  step1[6] = step3[7] - step2[6];
  step1[7] = step3[7] + step2[6];

  // step 6
  temp1 = step1[0] * cospi_30_64 + step1[7] * cospi_2_64;
  temp2 = step1[1] * cospi_14_64 + step1[6] * cospi_18_64;
  out[1] = (tran_low_t)fdct_round_shift(temp1);
  out[9] = (tran_low_t)fdct_round_shift(temp2);

  temp1 = step1[2] * cospi_22_64 + step1[5] * cospi_10_64;
  temp2 = step1[3] * cospi_6_64 + step1[4] * cospi_26_64;
  out[5] = (tran_low_t)fdct_round_shift(temp1);
  out[13] = (tran_low_t)fdct_round_shift(temp2);

  temp1 = step1[3] * -cospi_26_64 + step1[4] * cospi_6_64;
  temp2 = step1[2] * -cospi_10_64 + step1[5] * cospi_22_64;
  out[3] = (tran_low_t)fdct_round_shift(temp1);
  out[11] = (tran_low_t)fdct_round_shift(temp2);

  temp1 = step1[1] * -cospi_18_64 + step1[6] * cospi_14_64;
  temp2 = step1[0] * -cospi_2_64 + step1[7] * cospi_30_64;
  out[7] = (tran_low_t)fdct_round_shift(temp1);
  out[15] = (tran_low_t)fdct_round_shift(temp2);
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}

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/* TODO(angiebird): Unify this with vp10_fwd_txfm.c: vp10_fdct32
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static void fdct32(const tran_low_t *input, tran_low_t *output) {
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  tran_high_t temp;
  tran_low_t step[32];

  // stage 0
  range_check(input, 32, 14);

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

  range_check(output, 32, 15);
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  // stage 2
  step[0] = output[0] + output[15];
  step[1] = output[1] + output[14];
  step[2] = output[2] + output[13];
  step[3] = output[3] + output[12];
  step[4] = output[4] + output[11];
  step[5] = output[5] + output[10];
  step[6] = output[6] + output[9];
  step[7] = output[7] + output[8];
  step[8] = output[7] - output[8];
  step[9] = output[6] - output[9];
  step[10] = output[5] - output[10];
  step[11] = output[4] - output[11];
  step[12] = output[3] - output[12];
  step[13] = output[2] - output[13];
  step[14] = output[1] - output[14];
  step[15] = output[0] - output[15];
  step[16] = output[16];
  step[17] = output[17];
  step[18] = output[18];
  step[19] = output[19];
  temp = output[20] * -cospi_16_64 + output[27] * cospi_16_64;
  step[20] = (tran_low_t)fdct_round_shift(temp);
  temp = output[21] * -cospi_16_64 + output[26] * cospi_16_64;
  step[21] = (tran_low_t)fdct_round_shift(temp);
  temp = output[22] * -cospi_16_64 + output[25] * cospi_16_64;
  step[22] = (tran_low_t)fdct_round_shift(temp);
  temp = output[23] * -cospi_16_64 + output[24] * cospi_16_64;
  step[23] = (tran_low_t)fdct_round_shift(temp);
  temp = output[24] * cospi_16_64 + output[23] * cospi_16_64;
  step[24] = (tran_low_t)fdct_round_shift(temp);
  temp = output[25] * cospi_16_64 + output[22] * cospi_16_64;
  step[25] = (tran_low_t)fdct_round_shift(temp);
  temp = output[26] * cospi_16_64 + output[21] * cospi_16_64;
  step[26] = (tran_low_t)fdct_round_shift(temp);
  temp = output[27] * cospi_16_64 + output[20] * cospi_16_64;
  step[27] = (tran_low_t)fdct_round_shift(temp);
  step[28] = output[28];
  step[29] = output[29];
  step[30] = output[30];
  step[31] = output[31];

  range_check(step, 32, 16);

  // stage 3
  output[0] = step[0] + step[7];
  output[1] = step[1] + step[6];
  output[2] = step[2] + step[5];
  output[3] = step[3] + step[4];
  output[4] = step[3] - step[4];
  output[5] = step[2] - step[5];
  output[6] = step[1] - step[6];
  output[7] = step[0] - step[7];
  output[8] = step[8];
  output[9] = step[9];
  temp = step[10] * -cospi_16_64 + step[13] * cospi_16_64;
  output[10] = (tran_low_t)fdct_round_shift(temp);
  temp = step[11] * -cospi_16_64 + step[12] * cospi_16_64;
  output[11] = (tran_low_t)fdct_round_shift(temp);
  temp = step[12] * cospi_16_64 + step[11] * cospi_16_64;
  output[12] = (tran_low_t)fdct_round_shift(temp);
  temp = step[13] * cospi_16_64 + step[10] * cospi_16_64;
  output[13] = (tran_low_t)fdct_round_shift(temp);
  output[14] = step[14];
  output[15] = step[15];
  output[16] = step[16] + step[23];
  output[17] = step[17] + step[22];
  output[18] = step[18] + step[21];
  output[19] = step[19] + step[20];
  output[20] = step[19] - step[20];
  output[21] = step[18] - step[21];
  output[22] = step[17] - step[22];
  output[23] = step[16] - step[23];
  output[24] = step[31] - step[24];
  output[25] = step[30] - step[25];
  output[26] = step[29] - step[26];
  output[27] = step[28] - step[27];
  output[28] = step[28] + step[27];
  output[29] = step[29] + step[26];
  output[30] = step[30] + step[25];
  output[31] = step[31] + step[24];

  range_check(output, 32, 17);

  // stage 4
  step[0] = output[0] + output[3];
  step[1] = output[1] + output[2];
  step[2] = output[1] - output[2];
  step[3] = output[0] - output[3];
  step[4] = output[4];
  temp = output[5] * -cospi_16_64 + output[6] * cospi_16_64;
  step[5] = (tran_low_t)fdct_round_shift(temp);
  temp = output[6] * cospi_16_64 + output[5] * cospi_16_64;
  step[6] = (tran_low_t)fdct_round_shift(temp);
  step[7] = output[7];
  step[8] = output[8] + output[11];
  step[9] = output[9] + output[10];
  step[10] = output[9] - output[10];
  step[11] = output[8] - output[11];
  step[12] = output[15] - output[12];
  step[13] = output[14] - output[13];
  step[14] = output[14] + output[13];
  step[15] = output[15] + output[12];
  step[16] = output[16];
  step[17] = output[17];
  temp = output[18] * -cospi_8_64 + output[29] * cospi_24_64;
  step[18] = (tran_low_t)fdct_round_shift(temp);
  temp = output[19] * -cospi_8_64 + output[28] * cospi_24_64;
  step[19] = (tran_low_t)fdct_round_shift(temp);
  temp = output[20] * -cospi_24_64 + output[27] * -cospi_8_64;
  step[20] = (tran_low_t)fdct_round_shift(temp);
  temp = output[21] * -cospi_24_64 + output[26] * -cospi_8_64;
  step[21] = (tran_low_t)fdct_round_shift(temp);
  step[22] = output[22];
  step[23] = output[23];
  step[24] = output[24];
  step[25] = output[25];
  temp = output[26] * cospi_24_64 + output[21] * -cospi_8_64;
  step[26] = (tran_low_t)fdct_round_shift(temp);
  temp = output[27] * cospi_24_64 + output[20] * -cospi_8_64;
  step[27] = (tran_low_t)fdct_round_shift(temp);
  temp = output[28] * cospi_8_64 + output[19] * cospi_24_64;
  step[28] = (tran_low_t)fdct_round_shift(temp);
  temp = output[29] * cospi_8_64 + output[18] * cospi_24_64;
  step[29] = (tran_low_t)fdct_round_shift(temp);
  step[30] = output[30];
  step[31] = output[31];

  range_check(step, 32, 18);

  // stage 5
  temp = step[0] * cospi_16_64 + step[1] * cospi_16_64;
  output[0] = (tran_low_t)fdct_round_shift(temp);
  temp = step[1] * -cospi_16_64 + step[0] * cospi_16_64;
  output[1] = (tran_low_t)fdct_round_shift(temp);
  temp = step[2] * cospi_24_64 + step[3] * cospi_8_64;
  output[2] = (tran_low_t)fdct_round_shift(temp);
  temp = step[3] * cospi_24_64 + step[2] * -cospi_8_64;
  output[3] = (tran_low_t)fdct_round_shift(temp);
  output[4] = step[4] + step[5];
  output[5] = step[4] - step[5];
  output[6] = step[7] - step[6];
  output[7] = step[7] + step[6];
  output[8] = step[8];
  temp = step[9] * -cospi_8_64 + step[14] * cospi_24_64;
  output[9] = (tran_low_t)fdct_round_shift(temp);
  temp = step[10] * -cospi_24_64 + step[13] * -cospi_8_64;
  output[10] = (tran_low_t)fdct_round_shift(temp);
  output[11] = step[11];
  output[12] = step[12];
  temp = step[13] * cospi_24_64 + step[10] * -cospi_8_64;
  output[13] = (tran_low_t)fdct_round_shift(temp);
  temp = step[14] * cospi_8_64 + step[9] * cospi_24_64;
  output[14] = (tran_low_t)fdct_round_shift(temp);
  output[15] = step[15];
  output[16] = step[16] + step[19];
  output[17] = step[17] + step[18];
  output[18] = step[17] - step[18];
  output[19] = step[16] - step[19];
  output[20] = step[23] - step[20];
  output[21] = step[22] - step[21];
  output[22] = step[22] + step[21];
  output[23] = step[23] + step[20];
  output[24] = step[24] + step[27];
  output[25] = step[25] + step[26];
  output[26] = step[25] - step[26];
  output[27] = step[24] - step[27];
  output[28] = step[31] - step[28];
  output[29] = step[30] - step[29];
  output[30] = step[30] + step[29];
  output[31] = step[31] + step[28];

  range_check(output, 32, 18);

  // stage 6
  step[0] = output[0];
  step[1] = output[1];
  step[2] = output[2];
  step[3] = output[3];
  temp = output[4] * cospi_28_64 + output[7] * cospi_4_64;
  step[4] = (tran_low_t)fdct_round_shift(temp);
  temp = output[5] * cospi_12_64 + output[6] * cospi_20_64;
  step[5] = (tran_low_t)fdct_round_shift(temp);
  temp = output[6] * cospi_12_64 + output[5] * -cospi_20_64;
  step[6] = (tran_low_t)fdct_round_shift(temp);
  temp = output[7] * cospi_28_64 + output[4] * -cospi_4_64;
  step[7] = (tran_low_t)fdct_round_shift(temp);
  step[8] = output[8] + output[9];
  step[9] = output[8] - output[9];
  step[10] = output[11] - output[10];
  step[11] = output[11] + output[10];
  step[12] = output[12] + output[13];
  step[13] = output[12] - output[13];
  step[14] = output[15] - output[14];
  step[15] = output[15] + output[14];
  step[16] = output[16];
  temp = output[17] * -cospi_4_64 + output[30] * cospi_28_64;
  step[17] = (tran_low_t)fdct_round_shift(temp);
  temp = output[18] * -cospi_28_64 + output[29] * -cospi_4_64;
  step[18] = (tran_low_t)fdct_round_shift(temp);
  step[19] = output[19];
  step[20] = output[20];
  temp = output[21] * -cospi_20_64 + output[26] * cospi_12_64;
  step[21] = (tran_low_t)fdct_round_shift(temp);
  temp = output[22] * -cospi_12_64 + output[25] * -cospi_20_64;
  step[22] = (tran_low_t)fdct_round_shift(temp);
  step[23] = output[23];
  step[24] = output[24];
  temp = output[25] * cospi_12_64 + output[22] * -cospi_20_64;
  step[25] = (tran_low_t)fdct_round_shift(temp);
  temp = output[26] * cospi_20_64 + output[21] * cospi_12_64;
  step[26] = (tran_low_t)fdct_round_shift(temp);
  step[27] = output[27];
  step[28] = output[28];
  temp = output[29] * cospi_28_64 + output[18] * -cospi_4_64;
  step[29] = (tran_low_t)fdct_round_shift(temp);
  temp = output[30] * cospi_4_64 + output[17] * cospi_28_64;
  step[30] = (tran_low_t)fdct_round_shift(temp);
  step[31] = output[31];

  range_check(step, 32, 18);

  // stage 7
  output[0] = step[0];
  output[1] = step[1];
  output[2] = step[2];
  output[3] = step[3];
  output[4] = step[4];
  output[5] = step[5];
  output[6] = step[6];
  output[7] = step[7];
  temp = step[8] * cospi_30_64 + step[15] * cospi_2_64;
  output[8] = (tran_low_t)fdct_round_shift(temp);
  temp = step[9] * cospi_14_64 + step[14] * cospi_18_64;
  output[9] = (tran_low_t)fdct_round_shift(temp);
  temp = step[10] * cospi_22_64 + step[13] * cospi_10_64;
  output[10] = (tran_low_t)fdct_round_shift(temp);
  temp = step[11] * cospi_6_64 + step[12] * cospi_26_64;
  output[11] = (tran_low_t)fdct_round_shift(temp);
  temp = step[12] * cospi_6_64 + step[11] * -cospi_26_64;
  output[12] = (tran_low_t)fdct_round_shift(temp);
  temp = step[13] * cospi_22_64 + step[10] * -cospi_10_64;
  output[13] = (tran_low_t)fdct_round_shift(temp);
  temp = step[14] * cospi_14_64 + step[9] * -cospi_18_64;
  output[14] = (tran_low_t)fdct_round_shift(temp);
  temp = step[15] * cospi_30_64 + step[8] * -cospi_2_64;
  output[15] = (tran_low_t)fdct_round_shift(temp);
  output[16] = step[16] + step[17];
  output[17] = step[16] - step[17];
  output[18] = step[19] - step[18];
  output[19] = step[19] + step[18];
  output[20] = step[20] + step[21];
  output[21] = step[20] - step[21];
  output[22] = step[23] - step[22];
  output[23] = step[23] + step[22];
  output[24] = step[24] + step[25];
  output[25] = step[24] - step[25];
  output[26] = step[27] - step[26];
  output[27] = step[27] + step[26];
  output[28] = step[28] + step[29];
  output[29] = step[28] - step[29];
  output[30] = step[31] - step[30];
  output[31] = step[31] + step[30];

  range_check(output, 32, 18);

  // stage 8
  step[0] = output[0];
  step[1] = output[1];
  step[2] = output[2];
  step[3] = output[3];
  step[4] = output[4];
  step[5] = output[5];
  step[6] = output[6];
  step[7] = output[7];
  step[8] = output[8];
  step[9] = output[9];
  step[10] = output[10];
  step[11] = output[11];
  step[12] = output[12];
  step[13] = output[13];
  step[14] = output[14];
  step[15] = output[15];
  temp = output[16] * cospi_31_64 + output[31] * cospi_1_64;
  step[16] = (tran_low_t)fdct_round_shift(temp);
  temp = output[17] * cospi_15_64 + output[30] * cospi_17_64;
  step[17] = (tran_low_t)fdct_round_shift(temp);
  temp = output[18] * cospi_23_64 + output[29] * cospi_9_64;
  step[18] = (tran_low_t)fdct_round_shift(temp);
  temp = output[19] * cospi_7_64 + output[28] * cospi_25_64;
  step[19] = (tran_low_t)fdct_round_shift(temp);
  temp = output[20] * cospi_27_64 + output[27] * cospi_5_64;
  step[20] = (tran_low_t)fdct_round_shift(temp);
  temp = output[21] * cospi_11_64 + output[26] * cospi_21_64;
  step[21] = (tran_low_t)fdct_round_shift(temp);
  temp = output[22] * cospi_19_64 + output[25] * cospi_13_64;
  step[22] = (tran_low_t)fdct_round_shift(temp);
  temp = output[23] * cospi_3_64 + output[24] * cospi_29_64;
  step[23] = (tran_low_t)fdct_round_shift(temp);
  temp = output[24] * cospi_3_64 + output[23] * -cospi_29_64;
  step[24] = (tran_low_t)fdct_round_shift(temp);
  temp = output[25] * cospi_19_64 + output[22] * -cospi_13_64;
  step[25] = (tran_low_t)fdct_round_shift(temp);
  temp = output[26] * cospi_11_64 + output[21] * -cospi_21_64;
  step[26] = (tran_low_t)fdct_round_shift(temp);
  temp = output[27] * cospi_27_64 + output[20] * -cospi_5_64;
  step[27] = (tran_low_t)fdct_round_shift(temp);
  temp = output[28] * cospi_7_64 + output[19] * -cospi_25_64;
  step[28] = (tran_low_t)fdct_round_shift(temp);
  temp = output[29] * cospi_23_64 + output[18] * -cospi_9_64;
  step[29] = (tran_low_t)fdct_round_shift(temp);
  temp = output[30] * cospi_15_64 + output[17] * -cospi_17_64;
  step[30] = (tran_low_t)fdct_round_shift(temp);
  temp = output[31] * cospi_31_64 + output[16] * -cospi_1_64;
  step[31] = (tran_low_t)fdct_round_shift(temp);

  range_check(step, 32, 18);

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

  range_check(output, 32, 18);
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}
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*/
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static void fadst4(const tran_low_t *input, tran_low_t *output) {
  tran_high_t x0, x1, x2, x3;
  tran_high_t s0, s1, s2, s3, s4, s5, s6, s7;

  x0 = input[0];
  x1 = input[1];
  x2 = input[2];
  x3 = input[3];

  if (!(x0 | x1 | x2 | x3)) {
    output[0] = output[1] = output[2] = output[3] = 0;
    return;
  }

  s0 = sinpi_1_9 * x0;
  s1 = sinpi_4_9 * x0;
  s2 = sinpi_2_9 * x1;
  s3 = sinpi_1_9 * x1;
  s4 = sinpi_3_9 * x2;
  s5 = sinpi_4_9 * x3;
  s6 = sinpi_2_9 * x3;
  s7 = x0 + x1 - x3;

  x0 = s0 + s2 + s5;
  x1 = sinpi_3_9 * s7;
  x2 = s1 - s3 + s6;
  x3 = s4;

  s0 = x0 + x3;
  s1 = x1;
  s2 = x2 - x3;
  s3 = x2 - x0 + x3;

  // 1-D transform scaling factor is sqrt(2).
  output[0] = (tran_low_t)fdct_round_shift(s0);
  output[1] = (tran_low_t)fdct_round_shift(s1);
  output[2] = (tran_low_t)fdct_round_shift(s2);
  output[3] = (tran_low_t)fdct_round_shift(s3);
}

static void fadst8(const tran_low_t *input, tran_low_t *output) {
  tran_high_t s0, s1, s2, s3, s4, s5, s6, s7;

  tran_high_t x0 = input[7];
  tran_high_t x1 = input[0];
  tran_high_t x2 = input[5];
  tran_high_t x3 = input[2];
  tran_high_t x4 = input[3];
  tran_high_t x5 = input[4];
  tran_high_t x6 = input[1];
  tran_high_t x7 = input[6];

  // stage 1
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  s0 = cospi_2_64 * x0 + cospi_30_64 * x1;
  s1 = cospi_30_64 * x0 - cospi_2_64 * x1;
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  s2 = cospi_10_64 * x2 + cospi_22_64 * x3;
  s3 = cospi_22_64 * x2 - cospi_10_64 * x3;
  s4 = cospi_18_64 * x4 + cospi_14_64 * x5;
  s5 = cospi_14_64 * x4 - cospi_18_64 * x5;
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  s6 = cospi_26_64 * x6 + cospi_6_64 * x7;
  s7 = cospi_6_64 * x6 - cospi_26_64 * x7;
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  x0 = fdct_round_shift(s0 + s4);
  x1 = fdct_round_shift(s1 + s5);
  x2 = fdct_round_shift(s2 + s6);
  x3 = fdct_round_shift(s3 + s7);
  x4 = fdct_round_shift(s0 - s4);
  x5 = fdct_round_shift(s1 - s5);
  x6 = fdct_round_shift(s2 - s6);
  x7 = fdct_round_shift(s3 - s7);

  // stage 2
  s0 = x0;
  s1 = x1;
  s2 = x2;
  s3 = x3;
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  s4 = cospi_8_64 * x4 + cospi_24_64 * x5;
  s5 = cospi_24_64 * x4 - cospi_8_64 * x5;
  s6 = -cospi_24_64 * x6 + cospi_8_64 * x7;
  s7 = cospi_8_64 * x6 + cospi_24_64 * x7;
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  x0 = s0 + s2;
  x1 = s1 + s3;
  x2 = s0 - s2;
  x3 = s1 - s3;
  x4 = fdct_round_shift(s4 + s6);
  x5 = fdct_round_shift(s5 + s7);
  x6 = fdct_round_shift(s4 - s6);
  x7 = fdct_round_shift(s5 - s7);

  // stage 3
  s2 = cospi_16_64 * (x2 + x3);
  s3 = cospi_16_64 * (x2 - x3);
  s6 = cospi_16_64 * (x6 + x7);
  s7 = cospi_16_64 * (x6 - x7);

  x2 = fdct_round_shift(s2);
  x3 = fdct_round_shift(s3);
  x6 = fdct_round_shift(s6);
  x7 = fdct_round_shift(s7);

  output[0] = (tran_low_t)x0;
  output[1] = (tran_low_t)-x4;
  output[2] = (tran_low_t)x6;
  output[3] = (tran_low_t)-x2;
  output[4] = (tran_low_t)x3;
  output[5] = (tran_low_t)-x7;
  output[6] = (tran_low_t)x5;
  output[7] = (tran_low_t)-x1;
}

static void fadst16(const tran_low_t *input, tran_low_t *output) {
  tran_high_t s0, s1, s2, s3, s4, s5, s6, s7, s8;
  tran_high_t s9, s10, s11, s12, s13, s14, s15;

  tran_high_t x0 = input[15];
  tran_high_t x1 = input[0];
  tran_high_t x2 = input[13];
  tran_high_t x3 = input[2];
  tran_high_t x4 = input[11];
  tran_high_t x5 = input[4];
  tran_high_t x6 = input[9];
  tran_high_t x7 = input[6];
  tran_high_t x8 = input[7];
  tran_high_t x9 = input[8];
  tran_high_t x10 = input[5];
  tran_high_t x11 = input[10];
  tran_high_t x12 = input[3];
  tran_high_t x13 = input[12];
  tran_high_t x14 = input[1];
  tran_high_t x15 = input[14];

  // stage 1
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  s0 = x0 * cospi_1_64 + x1 * cospi_31_64;
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  s1 = x0 * cospi_31_64 - x1 * cospi_1_64;
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  s2 = x2 * cospi_5_64 + x3 * cospi_27_64;
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  s3 = x2 * cospi_27_64 - x3 * cospi_5_64;
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  s4 = x4 * cospi_9_64 + x5 * cospi_23_64;
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  s5 = x4 * cospi_23_64 - x5 * cospi_9_64;
  s6 = x6 * cospi_13_64 + x7 * cospi_19_64;
  s7 = x6 * cospi_19_64 - x7 * cospi_13_64;
  s8 = x8 * cospi_17_64 + x9 * cospi_15_64;
  s9 = x8 * cospi_15_64 - x9 * cospi_17_64;
  s10 = x10 * cospi_21_64 + x11 * cospi_11_64;
  s11 = x10 * cospi_11_64 - x11 * cospi_21_64;
  s12 = x12 * cospi_25_64 + x13 * cospi_7_64;
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  s13 = x12 * cospi_7_64 - x13 * cospi_25_64;
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  s14 = x14 * cospi_29_64 + x15 * cospi_3_64;
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  s15 = x14 * cospi_3_64 - x15 * cospi_29_64;
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  x0 = fdct_round_shift(s0 + s8);
  x1 = fdct_round_shift(s1 + s9);
  x2 = fdct_round_shift(s2 + s10);
  x3 = fdct_round_shift(s3 + s11);
  x4 = fdct_round_shift(s4 + s12);
  x5 = fdct_round_shift(s5 + s13);
  x6 = fdct_round_shift(s6 + s14);
  x7 = fdct_round_shift(s7 + s15);
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  x8 = fdct_round_shift(s0 - s8);
  x9 = fdct_round_shift(s1 - s9);
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  x10 = fdct_round_shift(s2 - s10);
  x11 = fdct_round_shift(s3 - s11);
  x12 = fdct_round_shift(s4 - s12);
  x13 = fdct_round_shift(s5 - s13);
  x14 = fdct_round_shift(s6 - s14);
  x15 = fdct_round_shift(s7 - s15);

  // stage 2
  s0 = x0;
  s1 = x1;
  s2 = x2;
  s3 = x3;
  s4 = x4;
  s5 = x5;
  s6 = x6;
  s7 = x7;
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  s8 = x8 * cospi_4_64 + x9 * cospi_28_64;
  s9 = x8 * cospi_28_64 - x9 * cospi_4_64;
  s10 = x10 * cospi_20_64 + x11 * cospi_12_64;
  s11 = x10 * cospi_12_64 - x11 * cospi_20_64;
  s12 = -x12 * cospi_28_64 + x13 * cospi_4_64;
  s13 = x12 * cospi_4_64 + x13 * cospi_28_64;
  s14 = -x14 * cospi_12_64 + x15 * cospi_20_64;
  s15 = x14 * cospi_20_64 + x15 * cospi_12_64;
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  x0 = s0 + s4;
  x1 = s1 + s5;
  x2 = s2 + s6;
  x3 = s3 + s7;
  x4 = s0 - s4;
  x5 = s1 - s5;
  x6 = s2 - s6;
  x7 = s3 - s7;
  x8 = fdct_round_shift(s8 + s12);
  x9 = fdct_round_shift(s9 + s13);
  x10 = fdct_round_shift(s10 + s14);
  x11 = fdct_round_shift(s11 + s15);
  x12 = fdct_round_shift(s8 - s12);
  x13 = fdct_round_shift(s9 - s13);
  x14 = fdct_round_shift(s10 - s14);
  x15 = fdct_round_shift(s11 - s15);

  // stage 3
  s0 = x0;
  s1 = x1;
  s2 = x2;
  s3 = x3;
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  s4 = x4 * cospi_8_64 + x5 * cospi_24_64;
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  s5 = x4 * cospi_24_64 - x5 * cospi_8_64;
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  s6 = -x6 * cospi_24_64 + x7 * cospi_8_64;
  s7 = x6 * cospi_8_64 + x7 * cospi_24_64;
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  s8 = x8;
  s9 = x9;
  s10 = x10;
  s11 = x11;
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  s12 = x12 * cospi_8_64 + x13 * cospi_24_64;
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  s13 = x12 * cospi_24_64 - x13 * cospi_8_64;
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  s14 = -x14 * cospi_24_64 + x15 * cospi_8_64;
  s15 = x14 * cospi_8_64 + x15 * cospi_24_64;
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  x0 = s0 + s2;
  x1 = s1 + s3;
  x2 = s0 - s2;
  x3 = s1 - s3;
  x4 = fdct_round_shift(s4 + s6);
  x5 = fdct_round_shift(s5 + s7);
  x6 = fdct_round_shift(s4 - s6);
  x7 = fdct_round_shift(s5 - s7);
  x8 = s8 + s10;
  x9 = s9 + s11;
  x10 = s8 - s10;
  x11 = s9 - s11;
  x12 = fdct_round_shift(s12 + s14);
  x13 = fdct_round_shift(s13 + s15);
  x14 = fdct_round_shift(s12 - s14);
  x15 = fdct_round_shift(s13 - s15);

  // stage 4
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  s2 = (-cospi_16_64) * (x2 + x3);
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  s3 = cospi_16_64 * (x2 - x3);
  s6 = cospi_16_64 * (x6 + x7);
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  s7 = cospi_16_64 * (-x6 + x7);
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  s10 = cospi_16_64 * (x10 + x11);
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  s11 = cospi_16_64 * (-x10 + x11);
  s14 = (-cospi_16_64) * (x14 + x15);
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  s15 = cospi_16_64 * (x14 - x15);

  x2 = fdct_round_shift(s2);
  x3 = fdct_round_shift(s3);
  x6 = fdct_round_shift(s6);
  x7 = fdct_round_shift(s7);
  x10 = fdct_round_shift(s10);
  x11 = fdct_round_shift(s11);
  x14 = fdct_round_shift(s14);
  x15 = fdct_round_shift(s15);

  output[0] = (tran_low_t)x0;
  output[1] = (tran_low_t)-x8;
  output[2] = (tran_low_t)x12;
  output[3] = (tran_low_t)-x4;
  output[4] = (tran_low_t)x6;
  output[5] = (tran_low_t)x14;
  output[6] = (tran_low_t)x10;
  output[7] = (tran_low_t)x2;
  output[8] = (tran_low_t)x3;
  output[9] = (tran_low_t)x11;
  output[10] = (tran_low_t)x15;
  output[11] = (tran_low_t)x7;
  output[12] = (tran_low_t)x5;
  output[13] = (tran_low_t)-x13;
  output[14] = (tran_low_t)x9;
  output[15] = (tran_low_t)-x1;
}

static const transform_2d FHT_4[] = {
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  { fdct4, fdct4 },   // DCT_DCT  = 0
  { fadst4, fdct4 },  // ADST_DCT = 1
  { fdct4, fadst4 },  // DCT_ADST = 2
  { fadst4, fadst4 }  // ADST_ADST = 3
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};

static const transform_2d FHT_8[] = {
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  { fdct8, fdct8 },   // DCT_DCT  = 0
  { fadst8, fdct8 },  // ADST_DCT = 1
  { fdct8, fadst8 },  // DCT_ADST = 2
  { fadst8, fadst8 }  // ADST_ADST = 3
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};

static const transform_2d FHT_16[] = {
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  { fdct16, fdct16 },   // DCT_DCT  = 0
  { fadst16, fdct16 },  // ADST_DCT = 1
  { fdct16, fadst16 },  // DCT_ADST = 2
  { fadst16, fadst16 }  // ADST_ADST = 3
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};

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void vp10_fht4x4_c(const int16_t *input, tran_low_t *output, int stride,
                   int tx_type) {
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  if (tx_type == DCT_DCT) {
    vpx_fdct4x4_c(input, output, stride);
  } else {
    tran_low_t out[4 * 4];
    int i, j;
    tran_low_t temp_in[4], temp_out[4];
    const transform_2d ht = FHT_4[tx_type];

    // Columns
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