av1/common/av1_fwd_txfm1d.c

/*
 *  Copyright (c) 2015 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 <stdlib.h>
#include "av1/common/av1_fwd_txfm1d.h"
#if CONFIG_COEFFICIENT_RANGE_CHECKING
#define range_check(stage, input, buf, size, bit)                         \
  {                                                                       \
    int i, j;                                                             \
    for (i = 0; i < size; ++i) {                                          \
      int buf_bit = get_max_bit(abs(buf[i])) + 1;                         \
      if (buf_bit > bit) {                                                \
        printf("======== %s %d overflow ========\n", __FILE__, __LINE__); \
        printf("stage: %d node: %d\n", stage, i);                         \
        printf("bit: %d buf_bit: %d buf[i]: %d\n", bit, buf_bit, buf[i]); \
        printf("input:\n");                                               \
        for (j = 0; j < size; j++) {                                      \
          printf("%d,", input[j]);                                        \
        }                                                                 \
        printf("\n");                                                     \
        assert(0);                                                        \
      }                                                                   \
    }                                                                     \
  }
#else
#define range_check(stage, input, buf, size, bit) \
  {                                               \
    (void)stage;                                  \
    (void)input;                                  \
    (void)buf;                                    \
    (void)size;                                   \
    (void)bit;                                    \
  }
#endif

void av1_fdct4_new(const int32_t *input, int32_t *output, const int8_t *cos_bit,
                   const int8_t *stage_range) {
  const int32_t size = 4;
  const int32_t *cospi;

  int32_t stage = 0;
  int32_t *bf0, *bf1;
  int32_t step[4];

  // stage 0;
  range_check(stage, input, input, size, stage_range[stage]);

  // stage 1;
  stage++;
  bf1 = output;
  bf1[0] = input[0] + input[3];
  bf1[1] = input[1] + input[2];
  bf1[2] = -input[2] + input[1];
  bf1[3] = -input[3] + input[0];
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 2
  stage++;
  cospi = cospi_arr[cos_bit[stage] - cos_bit_min];
  bf0 = output;
  bf1 = step;
  bf1[0] = half_btf(cospi[32], bf0[0], cospi[32], bf0[1], cos_bit[stage]);
  bf1[1] = half_btf(-cospi[32], bf0[1], cospi[32], bf0[0], cos_bit[stage]);
  bf1[2] = half_btf(cospi[48], bf0[2], cospi[16], bf0[3], cos_bit[stage]);
  bf1[3] = half_btf(cospi[48], bf0[3], -cospi[16], bf0[2], cos_bit[stage]);
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 3
  stage++;
  bf0 = step;
  bf1 = output;
  bf1[0] = bf0[0];
  bf1[1] = bf0[2];
  bf1[2] = bf0[1];
  bf1[3] = bf0[3];
  range_check(stage, input, bf1, size, stage_range[stage]);
}

void av1_fdct8_new(const int32_t *input, int32_t *output, const int8_t *cos_bit,
                   const int8_t *stage_range) {
  const int32_t size = 8;
  const int32_t *cospi;

  int32_t stage = 0;
  int32_t *bf0, *bf1;
  int32_t step[8];

  // stage 0;
  range_check(stage, input, input, size, stage_range[stage]);

  // stage 1;
  stage++;
  bf1 = output;
  bf1[0] = input[0] + input[7];
  bf1[1] = input[1] + input[6];
  bf1[2] = input[2] + input[5];
  bf1[3] = input[3] + input[4];
  bf1[4] = -input[4] + input[3];
  bf1[5] = -input[5] + input[2];
  bf1[6] = -input[6] + input[1];
  bf1[7] = -input[7] + input[0];
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 2
  stage++;
  cospi = cospi_arr[cos_bit[stage] - cos_bit_min];
  bf0 = output;
  bf1 = step;
  bf1[0] = bf0[0] + bf0[3];
  bf1[1] = bf0[1] + bf0[2];
  bf1[2] = -bf0[2] + bf0[1];
  bf1[3] = -bf0[3] + bf0[0];
  bf1[4] = bf0[4];
  bf1[5] = half_btf(-cospi[32], bf0[5], cospi[32], bf0[6], cos_bit[stage]);
  bf1[6] = half_btf(cospi[32], bf0[6], cospi[32], bf0[5], cos_bit[stage]);
  bf1[7] = bf0[7];
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 3
  stage++;
  cospi = cospi_arr[cos_bit[stage] - cos_bit_min];
  bf0 = step;
  bf1 = output;
  bf1[0] = half_btf(cospi[32], bf0[0], cospi[32], bf0[1], cos_bit[stage]);
  bf1[1] = half_btf(-cospi[32], bf0[1], cospi[32], bf0[0], cos_bit[stage]);
  bf1[2] = half_btf(cospi[48], bf0[2], cospi[16], bf0[3], cos_bit[stage]);
  bf1[3] = half_btf(cospi[48], bf0[3], -cospi[16], bf0[2], cos_bit[stage]);
  bf1[4] = bf0[4] + bf0[5];
  bf1[5] = -bf0[5] + bf0[4];
  bf1[6] = -bf0[6] + bf0[7];
  bf1[7] = bf0[7] + bf0[6];
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 4
  stage++;
  cospi = cospi_arr[cos_bit[stage] - cos_bit_min];
  bf0 = output;
  bf1 = step;
  bf1[0] = bf0[0];
  bf1[1] = bf0[1];
  bf1[2] = bf0[2];
  bf1[3] = bf0[3];
  bf1[4] = half_btf(cospi[56], bf0[4], cospi[8], bf0[7], cos_bit[stage]);
  bf1[5] = half_btf(cospi[24], bf0[5], cospi[40], bf0[6], cos_bit[stage]);
  bf1[6] = half_btf(cospi[24], bf0[6], -cospi[40], bf0[5], cos_bit[stage]);
  bf1[7] = half_btf(cospi[56], bf0[7], -cospi[8], bf0[4], cos_bit[stage]);
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 5
  stage++;
  bf0 = step;
  bf1 = output;
  bf1[0] = bf0[0];
  bf1[1] = bf0[4];
  bf1[2] = bf0[2];
  bf1[3] = bf0[6];
  bf1[4] = bf0[1];
  bf1[5] = bf0[5];
  bf1[6] = bf0[3];
  bf1[7] = bf0[7];
  range_check(stage, input, bf1, size, stage_range[stage]);
}

void av1_fdct16_new(const int32_t *input, int32_t *output,
                    const int8_t *cos_bit, const int8_t *stage_range) {
  const int32_t size = 16;
  const int32_t *cospi;

  int32_t stage = 0;
  int32_t *bf0, *bf1;
  int32_t step[16];

  // stage 0;
  range_check(stage, input, input, size, stage_range[stage]);

  // stage 1;
  stage++;
  bf1 = output;
  bf1[0] = input[0] + input[15];
  bf1[1] = input[1] + input[14];
  bf1[2] = input[2] + input[13];
  bf1[3] = input[3] + input[12];
  bf1[4] = input[4] + input[11];
  bf1[5] = input[5] + input[10];
  bf1[6] = input[6] + input[9];
  bf1[7] = input[7] + input[8];
  bf1[8] = -input[8] + input[7];
  bf1[9] = -input[9] + input[6];
  bf1[10] = -input[10] + input[5];
  bf1[11] = -input[11] + input[4];
  bf1[12] = -input[12] + input[3];
  bf1[13] = -input[13] + input[2];
  bf1[14] = -input[14] + input[1];
  bf1[15] = -input[15] + input[0];
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 2
  stage++;
  cospi = cospi_arr[cos_bit[stage] - cos_bit_min];
  bf0 = output;
  bf1 = step;
  bf1[0] = bf0[0] + bf0[7];
  bf1[1] = bf0[1] + bf0[6];
  bf1[2] = bf0[2] + bf0[5];
  bf1[3] = bf0[3] + bf0[4];
  bf1[4] = -bf0[4] + bf0[3];
  bf1[5] = -bf0[5] + bf0[2];
  bf1[6] = -bf0[6] + bf0[1];
  bf1[7] = -bf0[7] + bf0[0];
  bf1[8] = bf0[8];
  bf1[9] = bf0[9];
  bf1[10] = half_btf(-cospi[32], bf0[10], cospi[32], bf0[13], cos_bit[stage]);
  bf1[11] = half_btf(-cospi[32], bf0[11], cospi[32], bf0[12], cos_bit[stage]);
  bf1[12] = half_btf(cospi[32], bf0[12], cospi[32], bf0[11], cos_bit[stage]);
  bf1[13] = half_btf(cospi[32], bf0[13], cospi[32], bf0[10], cos_bit[stage]);
  bf1[14] = bf0[14];
  bf1[15] = bf0[15];
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 3
  stage++;
  cospi = cospi_arr[cos_bit[stage] - cos_bit_min];
  bf0 = step;
  bf1 = output;
  bf1[0] = bf0[0] + bf0[3];
  bf1[1] = bf0[1] + bf0[2];
  bf1[2] = -bf0[2] + bf0[1];
  bf1[3] = -bf0[3] + bf0[0];
  bf1[4] = bf0[4];
  bf1[5] = half_btf(-cospi[32], bf0[5], cospi[32], bf0[6], cos_bit[stage]);
  bf1[6] = half_btf(cospi[32], bf0[6], cospi[32], bf0[5], cos_bit[stage]);
  bf1[7] = bf0[7];
  bf1[8] = bf0[8] + bf0[11];
  bf1[9] = bf0[9] + bf0[10];
  bf1[10] = -bf0[10] + bf0[9];
  bf1[11] = -bf0[11] + bf0[8];
  bf1[12] = -bf0[12] + bf0[15];
  bf1[13] = -bf0[13] + bf0[14];
  bf1[14] = bf0[14] + bf0[13];
  bf1[15] = bf0[15] + bf0[12];
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 4
  stage++;
  cospi = cospi_arr[cos_bit[stage] - cos_bit_min];
  bf0 = output;
  bf1 = step;
  bf1[0] = half_btf(cospi[32], bf0[0], cospi[32], bf0[1], cos_bit[stage]);
  bf1[1] = half_btf(-cospi[32], bf0[1], cospi[32], bf0[0], cos_bit[stage]);
  bf1[2] = half_btf(cospi[48], bf0[2], cospi[16], bf0[3], cos_bit[stage]);
  bf1[3] = half_btf(cospi[48], bf0[3], -cospi[16], bf0[2], cos_bit[stage]);
  bf1[4] = bf0[4] + bf0[5];
  bf1[5] = -bf0[5] + bf0[4];
  bf1[6] = -bf0[6] + bf0[7];
  bf1[7] = bf0[7] + bf0[6];
  bf1[8] = bf0[8];
  bf1[9] = half_btf(-cospi[16], bf0[9], cospi[48], bf0[14], cos_bit[stage]);
  bf1[10] = half_btf(-cospi[48], bf0[10], -cospi[16], bf0[13], cos_bit[stage]);
  bf1[11] = bf0[11];
  bf1[12] = bf0[12];
  bf1[13] = half_btf(cospi[48], bf0[13], -cospi[16], bf0[10], cos_bit[stage]);
  bf1[14] = half_btf(cospi[16], bf0[14], cospi[48], bf0[9], cos_bit[stage]);
  bf1[15] = bf0[15];
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 5
  stage++;
  cospi = cospi_arr[cos_bit[stage] - cos_bit_min];
  bf0 = step;
  bf1 = output;
  bf1[0] = bf0[0];
  bf1[1] = bf0[1];
  bf1[2] = bf0[2];
  bf1[3] = bf0[3];
  bf1[4] = half_btf(cospi[56], bf0[4], cospi[8], bf0[7], cos_bit[stage]);
  bf1[5] = half_btf(cospi[24], bf0[5], cospi[40], bf0[6], cos_bit[stage]);
  bf1[6] = half_btf(cospi[24], bf0[6], -cospi[40], bf0[5], cos_bit[stage]);
  bf1[7] = half_btf(cospi[56], bf0[7], -cospi[8], bf0[4], cos_bit[stage]);
  bf1[8] = bf0[8] + bf0[9];
  bf1[9] = -bf0[9] + bf0[8];
  bf1[10] = -bf0[10] + bf0[11];
  bf1[11] = bf0[11] + bf0[10];
  bf1[12] = bf0[12] + bf0[13];
  bf1[13] = -bf0[13] + bf0[12];
  bf1[14] = -bf0[14] + bf0[15];
  bf1[15] = bf0[15] + bf0[14];
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 6
  stage++;
  cospi = cospi_arr[cos_bit[stage] - cos_bit_min];
  bf0 = output;
  bf1 = step;
  bf1[0] = bf0[0];
  bf1[1] = bf0[1];
  bf1[2] = bf0[2];
  bf1[3] = bf0[3];
  bf1[4] = bf0[4];
  bf1[5] = bf0[5];
  bf1[6] = bf0[6];
  bf1[7] = bf0[7];
  bf1[8] = half_btf(cospi[60], bf0[8], cospi[4], bf0[15], cos_bit[stage]);
  bf1[9] = half_btf(cospi[28], bf0[9], cospi[36], bf0[14], cos_bit[stage]);
  bf1[10] = half_btf(cospi[44], bf0[10], cospi[20], bf0[13], cos_bit[stage]);
  bf1[11] = half_btf(cospi[12], bf0[11], cospi[52], bf0[12], cos_bit[stage]);
  bf1[12] = half_btf(cospi[12], bf0[12], -cospi[52], bf0[11], cos_bit[stage]);
  bf1[13] = half_btf(cospi[44], bf0[13], -cospi[20], bf0[10], cos_bit[stage]);
  bf1[14] = half_btf(cospi[28], bf0[14], -cospi[36], bf0[9], cos_bit[stage]);
  bf1[15] = half_btf(cospi[60], bf0[15], -cospi[4], bf0[8], cos_bit[stage]);
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 7
  stage++;
  bf0 = step;
  bf1 = output;
  bf1[0] = bf0[0];
  bf1[1] = bf0[8];
  bf1[2] = bf0[4];
  bf1[3] = bf0[12];
  bf1[4] = bf0[2];
  bf1[5] = bf0[10];
  bf1[6] = bf0[6];
  bf1[7] = bf0[14];
  bf1[8] = bf0[1];
  bf1[9] = bf0[9];
  bf1[10] = bf0[5];
  bf1[11] = bf0[13];
  bf1[12] = bf0[3];
  bf1[13] = bf0[11];
  bf1[14] = bf0[7];
  bf1[15] = bf0[15];
  range_check(stage, input, bf1, size, stage_range[stage]);
}

void av1_fdct32_new(const int32_t *input, int32_t *output,
                    const int8_t *cos_bit, const int8_t *stage_range) {
  const int32_t size = 32;
  const int32_t *cospi;

  int32_t stage = 0;
  int32_t *bf0, *bf1;
  int32_t step[32];

  // stage 0;
  range_check(stage, input, input, size, stage_range[stage]);

  // stage 1;
  stage++;
  bf1 = output;
  bf1[0] = input[0] + input[31];
  bf1[1] = input[1] + input[30];
  bf1[2] = input[2] + input[29];
  bf1[3] = input[3] + input[28];
  bf1[4] = input[4] + input[27];
  bf1[5] = input[5] + input[26];
  bf1[6] = input[6] + input[25];
  bf1[7] = input[7] + input[24];
  bf1[8] = input[8] + input[23];
  bf1[9] = input[9] + input[22];
  bf1[10] = input[10] + input[21];
  bf1[11] = input[11] + input[20];
  bf1[12] = input[12] + input[19];
  bf1[13] = input[13] + input[18];
  bf1[14] = input[14] + input[17];
  bf1[15] = input[15] + input[16];
  bf1[16] = -input[16] + input[15];
  bf1[17] = -input[17] + input[14];
  bf1[18] = -input[18] + input[13];
  bf1[19] = -input[19] + input[12];
  bf1[20] = -input[20] + input[11];
  bf1[21] = -input[21] + input[10];
  bf1[22] = -input[22] + input[9];
  bf1[23] = -input[23] + input[8];
  bf1[24] = -input[24] + input[7];
  bf1[25] = -input[25] + input[6];
  bf1[26] = -input[26] + input[5];
  bf1[27] = -input[27] + input[4];
  bf1[28] = -input[28] + input[3];
  bf1[29] = -input[29] + input[2];
  bf1[30] = -input[30] + input[1];
  bf1[31] = -input[31] + input[0];
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 2
  stage++;
  cospi = cospi_arr[cos_bit[stage] - cos_bit_min];
  bf0 = output;
  bf1 = step;
  bf1[0] = bf0[0] + bf0[15];
  bf1[1] = bf0[1] + bf0[14];
  bf1[2] = bf0[2] + bf0[13];
  bf1[3] = bf0[3] + bf0[12];
  bf1[4] = bf0[4] + bf0[11];
  bf1[5] = bf0[5] + bf0[10];
  bf1[6] = bf0[6] + bf0[9];
  bf1[7] = bf0[7] + bf0[8];
  bf1[8] = -bf0[8] + bf0[7];
  bf1[9] = -bf0[9] + bf0[6];
  bf1[10] = -bf0[10] + bf0[5];
  bf1[11] = -bf0[11] + bf0[4];
  bf1[12] = -bf0[12] + bf0[3];
  bf1[13] = -bf0[13] + bf0[2];
  bf1[14] = -bf0[14] + bf0[1];
  bf1[15] = -bf0[15] + bf0[0];
  bf1[16] = bf0[16];
  bf1[17] = bf0[17];
  bf1[18] = bf0[18];
  bf1[19] = bf0[19];
  bf1[20] = half_btf(-cospi[32], bf0[20], cospi[32], bf0[27], cos_bit[stage]);
  bf1[21] = half_btf(-cospi[32], bf0[21], cospi[32], bf0[26], cos_bit[stage]);
  bf1[22] = half_btf(-cospi[32], bf0[22], cospi[32], bf0[25], cos_bit[stage]);
  bf1[23] = half_btf(-cospi[32], bf0[23], cospi[32], bf0[24], cos_bit[stage]);
  bf1[24] = half_btf(cospi[32], bf0[24], cospi[32], bf0[23], cos_bit[stage]);
  bf1[25] = half_btf(cospi[32], bf0[25], cospi[32], bf0[22], cos_bit[stage]);
  bf1[26] = half_btf(cospi[32], bf0[26], cospi[32], bf0[21], cos_bit[stage]);
  bf1[27] = half_btf(cospi[32], bf0[27], cospi[32], bf0[20], cos_bit[stage]);
  bf1[28] = bf0[28];
  bf1[29] = bf0[29];
  bf1[30] = bf0[30];
  bf1[31] = bf0[31];
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 3
  stage++;
  cospi = cospi_arr[cos_bit[stage] - cos_bit_min];
  bf0 = step;
  bf1 = output;
  bf1[0] = bf0[0] + bf0[7];
  bf1[1] = bf0[1] + bf0[6];
  bf1[2] = bf0[2] + bf0[5];
  bf1[3] = bf0[3] + bf0[4];
  bf1[4] = -bf0[4] + bf0[3];
  bf1[5] = -bf0[5] + bf0[2];
  bf1[6] = -bf0[6] + bf0[1];
  bf1[7] = -bf0[7] + bf0[0];
  bf1[8] = bf0[8];
  bf1[9] = bf0[9];
  bf1[10] = half_btf(-cospi[32], bf0[10], cospi[32], bf0[13], cos_bit[stage]);
  bf1[11] = half_btf(-cospi[32], bf0[11], cospi[32], bf0[12], cos_bit[stage]);
  bf1[12] = half_btf(cospi[32], bf0[12], cospi[32], bf0[11], cos_bit[stage]);
  bf1[13] = half_btf(cospi[32], bf0[13], cospi[32], bf0[10], cos_bit[stage]);
  bf1[14] = bf0[14];
  bf1[15] = bf0[15];
  bf1[16] = bf0[16] + bf0[23];
  bf1[17] = bf0[17] + bf0[22];
  bf1[18] = bf0[18] + bf0[21];
  bf1[19] = bf0[19] + bf0[20];
  bf1[20] = -bf0[20] + bf0[19];
  bf1[21] = -bf0[21] + bf0[18];
  bf1[22] = -bf0[22] + bf0[17];
  bf1[23] = -bf0[23] + bf0[16];
  bf1[24] = -bf0[24] + bf0[31];
  bf1[25] = -bf0[25] + bf0[30];
  bf1[26] = -bf0[26] + bf0[29];
  bf1[27] = -bf0[27] + bf0[28];
  bf1[28] = bf0[28] + bf0[27];
  bf1[29] = bf0[29] + bf0[26];
  bf1[30] = bf0[30] + bf0[25];
  bf1[31] = bf0[31] + bf0[24];
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 4
  stage++;
  cospi = cospi_arr[cos_bit[stage] - cos_bit_min];
  bf0 = output;
  bf1 = step;
  bf1[0] = bf0[0] + bf0[3];
  bf1[1] = bf0[1] + bf0[2];
  bf1[2] = -bf0[2] + bf0[1];
  bf1[3] = -bf0[3] + bf0[0];
  bf1[4] = bf0[4];
  bf1[5] = half_btf(-cospi[32], bf0[5], cospi[32], bf0[6], cos_bit[stage]);
  bf1[6] = half_btf(cospi[32], bf0[6], cospi[32], bf0[5], cos_bit[stage]);
  bf1[7] = bf0[7];
  bf1[8] = bf0[8] + bf0[11];
  bf1[9] = bf0[9] + bf0[10];
  bf1[10] = -bf0[10] + bf0[9];
  bf1[11] = -bf0[11] + bf0[8];
  bf1[12] = -bf0[12] + bf0[15];
  bf1[13] = -bf0[13] + bf0[14];
  bf1[14] = bf0[14] + bf0[13];
  bf1[15] = bf0[15] + bf0[12];
  bf1[16] = bf0[16];
  bf1[17] = bf0[17];
  bf1[18] = half_btf(-cospi[16], bf0[18], cospi[48], bf0[29], cos_bit[stage]);
  bf1[19] = half_btf(-cospi[16], bf0[19], cospi[48], bf0[28], cos_bit[stage]);
  bf1[20] = half_btf(-cospi[48], bf0[20], -cospi[16], bf0[27], cos_bit[stage]);
  bf1[21] = half_btf(-cospi[48], bf0[21], -cospi[16], bf0[26], cos_bit[stage]);
  bf1[22] = bf0[22];
  bf1[23] = bf0[23];
  bf1[24] = bf0[24];
  bf1[25] = bf0[25];
  bf1[26] = half_btf(cospi[48], bf0[26], -cospi[16], bf0[21], cos_bit[stage]);
  bf1[27] = half_btf(cospi[48], bf0[27], -cospi[16], bf0[20], cos_bit[stage]);
  bf1[28] = half_btf(cospi[16], bf0[28], cospi[48], bf0[19], cos_bit[stage]);
  bf1[29] = half_btf(cospi[16], bf0[29], cospi[48], bf0[18], cos_bit[stage]);
  bf1[30] = bf0[30];
  bf1[31] = bf0[31];
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 5
  stage++;
  cospi = cospi_arr[cos_bit[stage] - cos_bit_min];
  bf0 = step;
  bf1 = output;
  bf1[0] = half_btf(cospi[32], bf0[0], cospi[32], bf0[1], cos_bit[stage]);
  bf1[1] = half_btf(-cospi[32], bf0[1], cospi[32], bf0[0], cos_bit[stage]);
  bf1[2] = half_btf(cospi[48], bf0[2], cospi[16], bf0[3], cos_bit[stage]);
  bf1[3] = half_btf(cospi[48], bf0[3], -cospi[16], bf0[2], cos_bit[stage]);
  bf1[4] = bf0[4] + bf0[5];
  bf1[5] = -bf0[5] + bf0[4];
  bf1[6] = -bf0[6] + bf0[7];
  bf1[7] = bf0[7] + bf0[6];
  bf1[8] = bf0[8];
  bf1[9] = half_btf(-cospi[16], bf0[9], cospi[48], bf0[14], cos_bit[stage]);
  bf1[10] = half_btf(-cospi[48], bf0[10], -cospi[16], bf0[13], cos_bit[stage]);
  bf1[11] = bf0[11];
  bf1[12] = bf0[12];
  bf1[13] = half_btf(cospi[48], bf0[13], -cospi[16], bf0[10], cos_bit[stage]);
  bf1[14] = half_btf(cospi[16], bf0[14], cospi[48], bf0[9], cos_bit[stage]);
  bf1[15] = bf0[15];
  bf1[16] = bf0[16] + bf0[19];
  bf1[17] = bf0[17] + bf0[18];
  bf1[18] = -bf0[18] + bf0[17];
  bf1[19] = -bf0[19] + bf0[16];
  bf1[20] = -bf0[20] + bf0[23];
  bf1[21] = -bf0[21] + bf0[22];
  bf1[22] = bf0[22] + bf0[21];
  bf1[23] = bf0[23] + bf0[20];
  bf1[24] = bf0[24] + bf0[27];
  bf1[25] = bf0[25] + bf0[26];
  bf1[26] = -bf0[26] + bf0[25];
  bf1[27] = -bf0[27] + bf0[24];
  bf1[28] = -bf0[28] + bf0[31];
  bf1[29] = -bf0[29] + bf0[30];
  bf1[30] = bf0[30] + bf0[29];
  bf1[31] = bf0[31] + bf0[28];
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 6
  stage++;
  cospi = cospi_arr[cos_bit[stage] - cos_bit_min];
  bf0 = output;
  bf1 = step;
  bf1[0] = bf0[0];
  bf1[1] = bf0[1];
  bf1[2] = bf0[2];
  bf1[3] = bf0[3];
  bf1[4] = half_btf(cospi[56], bf0[4], cospi[8], bf0[7], cos_bit[stage]);
  bf1[5] = half_btf(cospi[24], bf0[5], cospi[40], bf0[6], cos_bit[stage]);
  bf1[6] = half_btf(cospi[24], bf0[6], -cospi[40], bf0[5], cos_bit[stage]);
  bf1[7] = half_btf(cospi[56], bf0[7], -cospi[8], bf0[4], cos_bit[stage]);
  bf1[8] = bf0[8] + bf0[9];
  bf1[9] = -bf0[9] + bf0[8];
  bf1[10] = -bf0[10] + bf0[11];
  bf1[11] = bf0[11] + bf0[10];
  bf1[12] = bf0[12] + bf0[13];
  bf1[13] = -bf0[13] + bf0[12];
  bf1[14] = -bf0[14] + bf0[15];
  bf1[15] = bf0[15] + bf0[14];
  bf1[16] = bf0[16];
  bf1[17] = half_btf(-cospi[8], bf0[17], cospi[56], bf0[30], cos_bit[stage]);
  bf1[18] = half_btf(-cospi[56], bf0[18], -cospi[8], bf0[29], cos_bit[stage]);
  bf1[19] = bf0[19];
  bf1[20] = bf0[20];
  bf1[21] = half_btf(-cospi[40], bf0[21], cospi[24], bf0[26], cos_bit[stage]);
  bf1[22] = half_btf(-cospi[24], bf0[22], -cospi[40], bf0[25], cos_bit[stage]);
  bf1[23] = bf0[23];
  bf1[24] = bf0[24];
  bf1[25] = half_btf(cospi[24], bf0[25], -cospi[40], bf0[22], cos_bit[stage]);
  bf1[26] = half_btf(cospi[40], bf0[26], cospi[24], bf0[21], cos_bit[stage]);
  bf1[27] = bf0[27];
  bf1[28] = bf0[28];
  bf1[29] = half_btf(cospi[56], bf0[29], -cospi[8], bf0[18], cos_bit[stage]);
  bf1[30] = half_btf(cospi[8], bf0[30], cospi[56], bf0[17], cos_bit[stage]);
  bf1[31] = bf0[31];
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 7
  stage++;
  cospi = cospi_arr[cos_bit[stage] - cos_bit_min];
  bf0 = step;
  bf1 = output;
  bf1[0] = bf0[0];
  bf1[1] = bf0[1];
  bf1[2] = bf0[2];
  bf1[3] = bf0[3];
  bf1[4] = bf0[4];
  bf1[5] = bf0[5];
  bf1[6] = bf0[6];
  bf1[7] = bf0[7];
  bf1[8] = half_btf(cospi[60], bf0[8], cospi[4], bf0[15], cos_bit[stage]);
  bf1[9] = half_btf(cospi[28], bf0[9], cospi[36], bf0[14], cos_bit[stage]);
  bf1[10] = half_btf(cospi[44], bf0[10], cospi[20], bf0[13], cos_bit[stage]);
  bf1[11] = half_btf(cospi[12], bf0[11], cospi[52], bf0[12], cos_bit[stage]);
  bf1[12] = half_btf(cospi[12], bf0[12], -cospi[52], bf0[11], cos_bit[stage]);
  bf1[13] = half_btf(cospi[44], bf0[13], -cospi[20], bf0[10], cos_bit[stage]);
  bf1[14] = half_btf(cospi[28], bf0[14], -cospi[36], bf0[9], cos_bit[stage]);
  bf1[15] = half_btf(cospi[60], bf0[15], -cospi[4], bf0[8], cos_bit[stage]);
  bf1[16] = bf0[16] + bf0[17];
  bf1[17] = -bf0[17] + bf0[16];
  bf1[18] = -bf0[18] + bf0[19];
  bf1[19] = bf0[19] + bf0[18];
  bf1[20] = bf0[20] + bf0[21];
  bf1[21] = -bf0[21] + bf0[20];
  bf1[22] = -bf0[22] + bf0[23];
  bf1[23] = bf0[23] + bf0[22];
  bf1[24] = bf0[24] + bf0[25];
  bf1[25] = -bf0[25] + bf0[24];
  bf1[26] = -bf0[26] + bf0[27];
  bf1[27] = bf0[27] + bf0[26];
  bf1[28] = bf0[28] + bf0[29];
  bf1[29] = -bf0[29] + bf0[28];
  bf1[30] = -bf0[30] + bf0[31];
  bf1[31] = bf0[31] + bf0[30];
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 8
  stage++;
  cospi = cospi_arr[cos_bit[stage] - cos_bit_min];
  bf0 = output;
  bf1 = step;
  bf1[0] = bf0[0];
  bf1[1] = bf0[1];
  bf1[2] = bf0[2];
  bf1[3] = bf0[3];
  bf1[4] = bf0[4];
  bf1[5] = bf0[5];
  bf1[6] = bf0[6];
  bf1[7] = bf0[7];
  bf1[8] = bf0[8];
  bf1[9] = bf0[9];
  bf1[10] = bf0[10];
  bf1[11] = bf0[11];
  bf1[12] = bf0[12];
  bf1[13] = bf0[13];
  bf1[14] = bf0[14];
  bf1[15] = bf0[15];
  bf1[16] = half_btf(cospi[62], bf0[16], cospi[2], bf0[31], cos_bit[stage]);
  bf1[17] = half_btf(cospi[30], bf0[17], cospi[34], bf0[30], cos_bit[stage]);
  bf1[18] = half_btf(cospi[46], bf0[18], cospi[18], bf0[29], cos_bit[stage]);
  bf1[19] = half_btf(cospi[14], bf0[19], cospi[50], bf0[28], cos_bit[stage]);
  bf1[20] = half_btf(cospi[54], bf0[20], cospi[10], bf0[27], cos_bit[stage]);
  bf1[21] = half_btf(cospi[22], bf0[21], cospi[42], bf0[26], cos_bit[stage]);
  bf1[22] = half_btf(cospi[38], bf0[22], cospi[26], bf0[25], cos_bit[stage]);
  bf1[23] = half_btf(cospi[6], bf0[23], cospi[58], bf0[24], cos_bit[stage]);
  bf1[24] = half_btf(cospi[6], bf0[24], -cospi[58], bf0[23], cos_bit[stage]);
  bf1[25] = half_btf(cospi[38], bf0[25], -cospi[26], bf0[22], cos_bit[stage]);
  bf1[26] = half_btf(cospi[22], bf0[26], -cospi[42], bf0[21], cos_bit[stage]);
  bf1[27] = half_btf(cospi[54], bf0[27], -cospi[10], bf0[20], cos_bit[stage]);
  bf1[28] = half_btf(cospi[14], bf0[28], -cospi[50], bf0[19], cos_bit[stage]);
  bf1[29] = half_btf(cospi[46], bf0[29], -cospi[18], bf0[18], cos_bit[stage]);
  bf1[30] = half_btf(cospi[30], bf0[30], -cospi[34], bf0[17], cos_bit[stage]);
  bf1[31] = half_btf(cospi[62], bf0[31], -cospi[2], bf0[16], cos_bit[stage]);
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 9
  stage++;
  bf0 = step;
  bf1 = output;
  bf1[0] = bf0[0];
  bf1[1] = bf0[16];
  bf1[2] = bf0[8];
  bf1[3] = bf0[24];
  bf1[4] = bf0[4];
  bf1[5] = bf0[20];
  bf1[6] = bf0[12];
  bf1[7] = bf0[28];
  bf1[8] = bf0[2];
  bf1[9] = bf0[18];
  bf1[10] = bf0[10];
  bf1[11] = bf0[26];
  bf1[12] = bf0[6];
  bf1[13] = bf0[22];
  bf1[14] = bf0[14];
  bf1[15] = bf0[30];
  bf1[16] = bf0[1];
  bf1[17] = bf0[17];
  bf1[18] = bf0[9];
  bf1[19] = bf0[25];
  bf1[20] = bf0[5];
  bf1[21] = bf0[21];
  bf1[22] = bf0[13];
  bf1[23] = bf0[29];
  bf1[24] = bf0[3];
  bf1[25] = bf0[19];
  bf1[26] = bf0[11];
  bf1[27] = bf0[27];
  bf1[28] = bf0[7];
  bf1[29] = bf0[23];
  bf1[30] = bf0[15];
  bf1[31] = bf0[31];
  range_check(stage, input, bf1, size, stage_range[stage]);
}

void av1_fadst4_new(const int32_t *input, int32_t *output,
                    const int8_t *cos_bit, const int8_t *stage_range) {
  const int32_t size = 4;
  const int32_t *cospi;

  int32_t stage = 0;
  int32_t *bf0, *bf1;
  int32_t step[4];

  // stage 0;
  range_check(stage, input, input, size, stage_range[stage]);

  // stage 1;
  stage++;
  bf1 = output;
  bf1[0] = input[3];
  bf1[1] = input[0];
  bf1[2] = input[1];
  bf1[3] = input[2];
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 2
  stage++;
  cospi = cospi_arr[cos_bit[stage] - cos_bit_min];
  bf0 = output;
  bf1 = step;
  bf1[0] = half_btf(cospi[8], bf0[0], cospi[56], bf0[1], cos_bit[stage]);
  bf1[1] = half_btf(-cospi[8], bf0[1], cospi[56], bf0[0], cos_bit[stage]);
  bf1[2] = half_btf(cospi[40], bf0[2], cospi[24], bf0[3], cos_bit[stage]);
  bf1[3] = half_btf(-cospi[40], bf0[3], cospi[24], bf0[2], cos_bit[stage]);
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 3
  stage++;
  cospi = cospi_arr[cos_bit[stage] - cos_bit_min];
  bf0 = step;
  bf1 = output;
  bf1[0] = bf0[0] + bf0[2];
  bf1[1] = bf0[1] + bf0[3];
  bf1[2] = -bf0[2] + bf0[0];
  bf1[3] = -bf0[3] + bf0[1];
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 4
  stage++;
  cospi = cospi_arr[cos_bit[stage] - cos_bit_min];
  bf0 = output;
  bf1 = step;
  bf1[0] = bf0[0];
  bf1[1] = bf0[1];
  bf1[2] = half_btf(cospi[32], bf0[2], cospi[32], bf0[3], cos_bit[stage]);
  bf1[3] = half_btf(-cospi[32], bf0[3], cospi[32], bf0[2], cos_bit[stage]);
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 5
  stage++;
  bf0 = step;
  bf1 = output;
  bf1[0] = bf0[0];
  bf1[1] = -bf0[2];
  bf1[2] = bf0[3];
  bf1[3] = -bf0[1];
  range_check(stage, input, bf1, size, stage_range[stage]);
}

void av1_fadst8_new(const int32_t *input, int32_t *output,
                    const int8_t *cos_bit, const int8_t *stage_range) {
  const int32_t size = 8;
  const int32_t *cospi;

  int32_t stage = 0;
  int32_t *bf0, *bf1;
  int32_t step[8];

  // stage 0;
  range_check(stage, input, input, size, stage_range[stage]);

  // stage 1;
  stage++;
  bf1 = output;
  bf1[0] = input[7];
  bf1[1] = input[0];
  bf1[2] = input[5];
  bf1[3] = input[2];
  bf1[4] = input[3];
  bf1[5] = input[4];
  bf1[6] = input[1];
  bf1[7] = input[6];
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 2
  stage++;
  cospi = cospi_arr[cos_bit[stage] - cos_bit_min];
  bf0 = output;
  bf1 = step;
  bf1[0] = half_btf(cospi[4], bf0[0], cospi[60], bf0[1], cos_bit[stage]);
  bf1[1] = half_btf(-cospi[4], bf0[1], cospi[60], bf0[0], cos_bit[stage]);
  bf1[2] = half_btf(cospi[20], bf0[2], cospi[44], bf0[3], cos_bit[stage]);
  bf1[3] = half_btf(-cospi[20], bf0[3], cospi[44], bf0[2], cos_bit[stage]);
  bf1[4] = half_btf(cospi[36], bf0[4], cospi[28], bf0[5], cos_bit[stage]);
  bf1[5] = half_btf(-cospi[36], bf0[5], cospi[28], bf0[4], cos_bit[stage]);
  bf1[6] = half_btf(cospi[52], bf0[6], cospi[12], bf0[7], cos_bit[stage]);
  bf1[7] = half_btf(-cospi[52], bf0[7], cospi[12], bf0[6], cos_bit[stage]);
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 3
  stage++;
  cospi = cospi_arr[cos_bit[stage] - cos_bit_min];
  bf0 = step;
  bf1 = output;
  bf1[0] = bf0[0] + bf0[4];
  bf1[1] = bf0[1] + bf0[5];
  bf1[2] = bf0[2] + bf0[6];
  bf1[3] = bf0[3] + bf0[7];
  bf1[4] = -bf0[4] + bf0[0];
  bf1[5] = -bf0[5] + bf0[1];
  bf1[6] = -bf0[6] + bf0[2];
  bf1[7] = -bf0[7] + bf0[3];
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 4
  stage++;
  cospi = cospi_arr[cos_bit[stage] - cos_bit_min];
  bf0 = output;
  bf1 = step;
  bf1[0] = bf0[0];
  bf1[1] = bf0[1];
  bf1[2] = bf0[2];
  bf1[3] = bf0[3];
  bf1[4] = half_btf(cospi[16], bf0[4], cospi[48], bf0[5], cos_bit[stage]);
  bf1[5] = half_btf(-cospi[16], bf0[5], cospi[48], bf0[4], cos_bit[stage]);
  bf1[6] = half_btf(-cospi[48], bf0[6], cospi[16], bf0[7], cos_bit[stage]);
  bf1[7] = half_btf(cospi[48], bf0[7], cospi[16], bf0[6], cos_bit[stage]);
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 5
  stage++;
  cospi = cospi_arr[cos_bit[stage] - cos_bit_min];
  bf0 = step;
  bf1 = output;
  bf1[0] = bf0[0] + bf0[2];
  bf1[1] = bf0[1] + bf0[3];
  bf1[2] = -bf0[2] + bf0[0];
  bf1[3] = -bf0[3] + bf0[1];
  bf1[4] = bf0[4] + bf0[6];
  bf1[5] = bf0[5] + bf0[7];
  bf1[6] = -bf0[6] + bf0[4];
  bf1[7] = -bf0[7] + bf0[5];
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 6
  stage++;
  cospi = cospi_arr[cos_bit[stage] - cos_bit_min];
  bf0 = output;
  bf1 = step;
  bf1[0] = bf0[0];
  bf1[1] = bf0[1];
  bf1[2] = half_btf(cospi[32], bf0[2], cospi[32], bf0[3], cos_bit[stage]);
  bf1[3] = half_btf(-cospi[32], bf0[3], cospi[32], bf0[2], cos_bit[stage]);
  bf1[4] = bf0[4];
  bf1[5] = bf0[5];
  bf1[6] = half_btf(cospi[32], bf0[6], cospi[32], bf0[7], cos_bit[stage]);
  bf1[7] = half_btf(-cospi[32], bf0[7], cospi[32], bf0[6], cos_bit[stage]);
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 7
  stage++;
  bf0 = step;
  bf1 = output;
  bf1[0] = bf0[0];
  bf1[1] = -bf0[4];
  bf1[2] = bf0[6];
  bf1[3] = -bf0[2];
  bf1[4] = bf0[3];
  bf1[5] = -bf0[7];
  bf1[6] = bf0[5];
  bf1[7] = -bf0[1];
  range_check(stage, input, bf1, size, stage_range[stage]);
}

void av1_fadst16_new(const int32_t *input, int32_t *output,
                     const int8_t *cos_bit, const int8_t *stage_range) {
  const int32_t size = 16;
  const int32_t *cospi;

  int32_t stage = 0;
  int32_t *bf0, *bf1;
  int32_t step[16];

  // stage 0;
  range_check(stage, input, input, size, stage_range[stage]);

  // stage 1;
  stage++;
  bf1 = output;
  bf1[0] = input[15];
  bf1[1] = input[0];
  bf1[2] = input[13];
  bf1[3] = input[2];
  bf1[4] = input[11];
  bf1[5] = input[4];
  bf1[6] = input[9];
  bf1[7] = input[6];
  bf1[8] = input[7];
  bf1[9] = input[8];
  bf1[10] = input[5];
  bf1[11] = input[10];
  bf1[12] = input[3];
  bf1[13] = input[12];
  bf1[14] = input[1];
  bf1[15] = input[14];
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 2
  stage++;
  cospi = cospi_arr[cos_bit[stage] - cos_bit_min];
  bf0 = output;
  bf1 = step;
  bf1[0] = half_btf(cospi[2], bf0[0], cospi[62], bf0[1], cos_bit[stage]);
  bf1[1] = half_btf(-cospi[2], bf0[1], cospi[62], bf0[0], cos_bit[stage]);
  bf1[2] = half_btf(cospi[10], bf0[2], cospi[54], bf0[3], cos_bit[stage]);
  bf1[3] = half_btf(-cospi[10], bf0[3], cospi[54], bf0[2], cos_bit[stage]);
  bf1[4] = half_btf(cospi[18], bf0[4], cospi[46], bf0[5], cos_bit[stage]);
  bf1[5] = half_btf(-cospi[18], bf0[5], cospi[46], bf0[4], cos_bit[stage]);
  bf1[6] = half_btf(cospi[26], bf0[6], cospi[38], bf0[7], cos_bit[stage]);
  bf1[7] = half_btf(-cospi[26], bf0[7], cospi[38], bf0[6], cos_bit[stage]);
  bf1[8] = half_btf(cospi[34], bf0[8], cospi[30], bf0[9], cos_bit[stage]);
  bf1[9] = half_btf(-cospi[34], bf0[9], cospi[30], bf0[8], cos_bit[stage]);
  bf1[10] = half_btf(cospi[42], bf0[10], cospi[22], bf0[11], cos_bit[stage]);
  bf1[11] = half_btf(-cospi[42], bf0[11], cospi[22], bf0[10], cos_bit[stage]);
  bf1[12] = half_btf(cospi[50], bf0[12], cospi[14], bf0[13], cos_bit[stage]);
  bf1[13] = half_btf(-cospi[50], bf0[13], cospi[14], bf0[12], cos_bit[stage]);
  bf1[14] = half_btf(cospi[58], bf0[14], cospi[6], bf0[15], cos_bit[stage]);
  bf1[15] = half_btf(-cospi[58], bf0[15], cospi[6], bf0[14], cos_bit[stage]);
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 3
  stage++;
  bf0 = step;
  bf1 = output;
  bf1[0] = bf0[0] + bf0[8];
  bf1[1] = bf0[1] + bf0[9];
  bf1[2] = bf0[2] + bf0[10];
  bf1[3] = bf0[3] + bf0[11];
  bf1[4] = bf0[4] + bf0[12];
  bf1[5] = bf0[5] + bf0[13];
  bf1[6] = bf0[6] + bf0[14];
  bf1[7] = bf0[7] + bf0[15];
  bf1[8] = -bf0[8] + bf0[0];
  bf1[9] = -bf0[9] + bf0[1];
  bf1[10] = -bf0[10] + bf0[2];
  bf1[11] = -bf0[11] + bf0[3];
  bf1[12] = -bf0[12] + bf0[4];
  bf1[13] = -bf0[13] + bf0[5];
  bf1[14] = -bf0[14] + bf0[6];
  bf1[15] = -bf0[15] + bf0[7];
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 4
  stage++;
  cospi = cospi_arr[cos_bit[stage] - cos_bit_min];
  bf0 = output;
  bf1 = step;
  bf1[0] = bf0[0];
  bf1[1] = bf0[1];
  bf1[2] = bf0[2];
  bf1[3] = bf0[3];
  bf1[4] = bf0[4];
  bf1[5] = bf0[5];
  bf1[6] = bf0[6];
  bf1[7] = bf0[7];
  bf1[8] = half_btf(cospi[8], bf0[8], cospi[56], bf0[9], cos_bit[stage]);
  bf1[9] = half_btf(-cospi[8], bf0[9], cospi[56], bf0[8], cos_bit[stage]);
  bf1[10] = half_btf(cospi[40], bf0[10], cospi[24], bf0[11], cos_bit[stage]);
  bf1[11] = half_btf(-cospi[40], bf0[11], cospi[24], bf0[10], cos_bit[stage]);
  bf1[12] = half_btf(-cospi[56], bf0[12], cospi[8], bf0[13], cos_bit[stage]);
  bf1[13] = half_btf(cospi[56], bf0[13], cospi[8], bf0[12], cos_bit[stage]);
  bf1[14] = half_btf(-cospi[24], bf0[14], cospi[40], bf0[15], cos_bit[stage]);
  bf1[15] = half_btf(cospi[24], bf0[15], cospi[40], bf0[14], cos_bit[stage]);
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 5
  stage++;
  bf0 = step;
  bf1 = output;
  bf1[0] = bf0[0] + bf0[4];
  bf1[1] = bf0[1] + bf0[5];
  bf1[2] = bf0[2] + bf0[6];
  bf1[3] = bf0[3] + bf0[7];
  bf1[4] = -bf0[4] + bf0[0];
  bf1[5] = -bf0[5] + bf0[1];
  bf1[6] = -bf0[6] + bf0[2];
  bf1[7] = -bf0[7] + bf0[3];
  bf1[8] = bf0[8] + bf0[12];
  bf1[9] = bf0[9] + bf0[13];
  bf1[10] = bf0[10] + bf0[14];
  bf1[11] = bf0[11] + bf0[15];
  bf1[12] = -bf0[12] + bf0[8];
  bf1[13] = -bf0[13] + bf0[9];
  bf1[14] = -bf0[14] + bf0[10];
  bf1[15] = -bf0[15] + bf0[11];
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 6
  stage++;
  cospi = cospi_arr[cos_bit[stage] - cos_bit_min];
  bf0 = output;
  bf1 = step;
  bf1[0] = bf0[0];
  bf1[1] = bf0[1];
  bf1[2] = bf0[2];
  bf1[3] = bf0[3];
  bf1[4] = half_btf(cospi[16], bf0[4], cospi[48], bf0[5], cos_bit[stage]);
  bf1[5] = half_btf(-cospi[16], bf0[5], cospi[48], bf0[4], cos_bit[stage]);
  bf1[6] = half_btf(-cospi[48], bf0[6], cospi[16], bf0[7], cos_bit[stage]);
  bf1[7] = half_btf(cospi[48], bf0[7], cospi[16], bf0[6], cos_bit[stage]);
  bf1[8] = bf0[8];
  bf1[9] = bf0[9];
  bf1[10] = bf0[10];
  bf1[11] = bf0[11];
  bf1[12] = half_btf(cospi[16], bf0[12], cospi[48], bf0[13], cos_bit[stage]);
  bf1[13] = half_btf(-cospi[16], bf0[13], cospi[48], bf0[12], cos_bit[stage]);
  bf1[14] = half_btf(-cospi[48], bf0[14], cospi[16], bf0[15], cos_bit[stage]);
  bf1[15] = half_btf(cospi[48], bf0[15], cospi[16], bf0[14], cos_bit[stage]);
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 7
  stage++;
  bf0 = step;
  bf1 = output;
  bf1[0] = bf0[0] + bf0[2];
  bf1[1] = bf0[1] + bf0[3];
  bf1[2] = -bf0[2] + bf0[0];
  bf1[3] = -bf0[3] + bf0[1];
  bf1[4] = bf0[4] + bf0[6];
  bf1[5] = bf0[5] + bf0[7];
  bf1[6] = -bf0[6] + bf0[4];
  bf1[7] = -bf0[7] + bf0[5];
  bf1[8] = bf0[8] + bf0[10];
  bf1[9] = bf0[9] + bf0[11];
  bf1[10] = -bf0[10] + bf0[8];
  bf1[11] = -bf0[11] + bf0[9];
  bf1[12] = bf0[12] + bf0[14];
  bf1[13] = bf0[13] + bf0[15];
  bf1[14] = -bf0[14] + bf0[12];
  bf1[15] = -bf0[15] + bf0[13];
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 8
  stage++;
  cospi = cospi_arr[cos_bit[stage] - cos_bit_min];
  bf0 = output;
  bf1 = step;
  bf1[0] = bf0[0];
  bf1[1] = bf0[1];
  bf1[2] = half_btf(cospi[32], bf0[2], cospi[32], bf0[3], cos_bit[stage]);
  bf1[3] = half_btf(-cospi[32], bf0[3], cospi[32], bf0[2], cos_bit[stage]);
  bf1[4] = bf0[4];
  bf1[5] = bf0[5];
  bf1[6] = half_btf(cospi[32], bf0[6], cospi[32], bf0[7], cos_bit[stage]);
  bf1[7] = half_btf(-cospi[32], bf0[7], cospi[32], bf0[6], cos_bit[stage]);
  bf1[8] = bf0[8];
  bf1[9] = bf0[9];
  bf1[10] = half_btf(cospi[32], bf0[10], cospi[32], bf0[11], cos_bit[stage]);
  bf1[11] = half_btf(-cospi[32], bf0[11], cospi[32], bf0[10], cos_bit[stage]);
  bf1[12] = bf0[12];
  bf1[13] = bf0[13];
  bf1[14] = half_btf(cospi[32], bf0[14], cospi[32], bf0[15], cos_bit[stage]);
  bf1[15] = half_btf(-cospi[32], bf0[15], cospi[32], bf0[14], cos_bit[stage]);
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 9
  stage++;
  bf0 = step;
  bf1 = output;
  bf1[0] = bf0[0];
  bf1[1] = -bf0[8];
  bf1[2] = bf0[12];
  bf1[3] = -bf0[4];
  bf1[4] = bf0[6];
  bf1[5] = -bf0[14];
  bf1[6] = bf0[10];
  bf1[7] = -bf0[2];
  bf1[8] = bf0[3];
  bf1[9] = -bf0[11];
  bf1[10] = bf0[15];
  bf1[11] = -bf0[7];
  bf1[12] = bf0[5];
  bf1[13] = -bf0[13];
  bf1[14] = bf0[9];
  bf1[15] = -bf0[1];
  range_check(stage, input, bf1, size, stage_range[stage]);
}

void av1_fadst32_new(const int32_t *input, int32_t *output,
                     const int8_t *cos_bit, const int8_t *stage_range) {
  const int32_t size = 32;
  const int32_t *cospi;

  int32_t stage = 0;
  int32_t *bf0, *bf1;
  int32_t step[32];

  // stage 0;
  range_check(stage, input, input, size, stage_range[stage]);

  // stage 1;
  stage++;
  bf1 = output;
  bf1[0] = input[31];
  bf1[1] = input[0];
  bf1[2] = input[29];
  bf1[3] = input[2];
  bf1[4] = input[27];
  bf1[5] = input[4];
  bf1[6] = input[25];
  bf1[7] = input[6];
  bf1[8] = input[23];
  bf1[9] = input[8];
  bf1[10] = input[21];
  bf1[11] = input[10];
  bf1[12] = input[19];
  bf1[13] = input[12];
  bf1[14] = input[17];
  bf1[15] = input[14];
  bf1[16] = input[15];
  bf1[17] = input[16];
  bf1[18] = input[13];
  bf1[19] = input[18];
  bf1[20] = input[11];
  bf1[21] = input[20];
  bf1[22] = input[9];
  bf1[23] = input[22];
  bf1[24] = input[7];
  bf1[25] = input[24];
  bf1[26] = input[5];
  bf1[27] = input[26];
  bf1[28] = input[3];
  bf1[29] = input[28];
  bf1[30] = input[1];
  bf1[31] = input[30];
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 2
  stage++;
  cospi = cospi_arr[cos_bit[stage] - cos_bit_min];
  bf0 = output;
  bf1 = step;
  bf1[0] = half_btf(cospi[1], bf0[0], cospi[63], bf0[1], cos_bit[stage]);
  bf1[1] = half_btf(-cospi[1], bf0[1], cospi[63], bf0[0], cos_bit[stage]);
  bf1[2] = half_btf(cospi[5], bf0[2], cospi[59], bf0[3], cos_bit[stage]);
  bf1[3] = half_btf(-cospi[5], bf0[3], cospi[59], bf0[2], cos_bit[stage]);
  bf1[4] = half_btf(cospi[9], bf0[4], cospi[55], bf0[5], cos_bit[stage]);
  bf1[5] = half_btf(-cospi[9], bf0[5], cospi[55], bf0[4], cos_bit[stage]);
  bf1[6] = half_btf(cospi[13], bf0[6], cospi[51], bf0[7], cos_bit[stage]);
  bf1[7] = half_btf(-cospi[13], bf0[7], cospi[51], bf0[6], cos_bit[stage]);
  bf1[8] = half_btf(cospi[17], bf0[8], cospi[47], bf0[9], cos_bit[stage]);
  bf1[9] = half_btf(-cospi[17], bf0[9], cospi[47], bf0[8], cos_bit[stage]);
  bf1[10] = half_btf(cospi[21], bf0[10], cospi[43], bf0[11], cos_bit[stage]);
  bf1[11] = half_btf(-cospi[21], bf0[11], cospi[43], bf0[10], cos_bit[stage]);
  bf1[12] = half_btf(cospi[25], bf0[12], cospi[39], bf0[13], cos_bit[stage]);
  bf1[13] = half_btf(-cospi[25], bf0[13], cospi[39], bf0[12], cos_bit[stage]);
  bf1[14] = half_btf(cospi[29], bf0[14], cospi[35], bf0[15], cos_bit[stage]);
  bf1[15] = half_btf(-cospi[29], bf0[15], cospi[35], bf0[14], cos_bit[stage]);
  bf1[16] = half_btf(cospi[33], bf0[16], cospi[31], bf0[17], cos_bit[stage]);
  bf1[17] = half_btf(-cospi[33], bf0[17], cospi[31], bf0[16], cos_bit[stage]);
  bf1[18] = half_btf(cospi[37], bf0[18], cospi[27], bf0[19], cos_bit[stage]);
  bf1[19] = half_btf(-cospi[37], bf0[19], cospi[27], bf0[18], cos_bit[stage]);
  bf1[20] = half_btf(cospi[41], bf0[20], cospi[23], bf0[21], cos_bit[stage]);
  bf1[21] = half_btf(-cospi[41], bf0[21], cospi[23], bf0[20], cos_bit[stage]);
  bf1[22] = half_btf(cospi[45], bf0[22], cospi[19], bf0[23], cos_bit[stage]);
  bf1[23] = half_btf(-cospi[45], bf0[23], cospi[19], bf0[22], cos_bit[stage]);
  bf1[24] = half_btf(cospi[49], bf0[24], cospi[15], bf0[25], cos_bit[stage]);
  bf1[25] = half_btf(-cospi[49], bf0[25], cospi[15], bf0[24], cos_bit[stage]);
  bf1[26] = half_btf(cospi[53], bf0[26], cospi[11], bf0[27], cos_bit[stage]);
  bf1[27] = half_btf(-cospi[53], bf0[27], cospi[11], bf0[26], cos_bit[stage]);
  bf1[28] = half_btf(cospi[57], bf0[28], cospi[7], bf0[29], cos_bit[stage]);
  bf1[29] = half_btf(-cospi[57], bf0[29], cospi[7], bf0[28], cos_bit[stage]);
  bf1[30] = half_btf(cospi[61], bf0[30], cospi[3], bf0[31], cos_bit[stage]);
  bf1[31] = half_btf(-cospi[61], bf0[31], cospi[3], bf0[30], cos_bit[stage]);
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 3
  stage++;
  bf0 = step;
  bf1 = output;
  bf1[0] = bf0[0] + bf0[16];
  bf1[1] = bf0[1] + bf0[17];
  bf1[2] = bf0[2] + bf0[18];
  bf1[3] = bf0[3] + bf0[19];
  bf1[4] = bf0[4] + bf0[20];
  bf1[5] = bf0[5] + bf0[21];
  bf1[6] = bf0[6] + bf0[22];
  bf1[7] = bf0[7] + bf0[23];
  bf1[8] = bf0[8] + bf0[24];
  bf1[9] = bf0[9] + bf0[25];
  bf1[10] = bf0[10] + bf0[26];
  bf1[11] = bf0[11] + bf0[27];
  bf1[12] = bf0[12] + bf0[28];
  bf1[13] = bf0[13] + bf0[29];
  bf1[14] = bf0[14] + bf0[30];
  bf1[15] = bf0[15] + bf0[31];
  bf1[16] = -bf0[16] + bf0[0];
  bf1[17] = -bf0[17] + bf0[1];
  bf1[18] = -bf0[18] + bf0[2];
  bf1[19] = -bf0[19] + bf0[3];
  bf1[20] = -bf0[20] + bf0[4];
  bf1[21] = -bf0[21] + bf0[5];
  bf1[22] = -bf0[22] + bf0[6];
  bf1[23] = -bf0[23] + bf0[7];
  bf1[24] = -bf0[24] + bf0[8];
  bf1[25] = -bf0[25] + bf0[9];
  bf1[26] = -bf0[26] + bf0[10];
  bf1[27] = -bf0[27] + bf0[11];
  bf1[28] = -bf0[28] + bf0[12];
  bf1[29] = -bf0[29] + bf0[13];
  bf1[30] = -bf0[30] + bf0[14];
  bf1[31] = -bf0[31] + bf0[15];
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 4
  stage++;
  cospi = cospi_arr[cos_bit[stage] - cos_bit_min];
  bf0 = output;
  bf1 = step;
  bf1[0] = bf0[0];
  bf1[1] = bf0[1];
  bf1[2] = bf0[2];
  bf1[3] = bf0[3];
  bf1[4] = bf0[4];
  bf1[5] = bf0[5];
  bf1[6] = bf0[6];
  bf1[7] = bf0[7];
  bf1[8] = bf0[8];
  bf1[9] = bf0[9];
  bf1[10] = bf0[10];
  bf1[11] = bf0[11];
  bf1[12] = bf0[12];
  bf1[13] = bf0[13];
  bf1[14] = bf0[14];
  bf1[15] = bf0[15];
  bf1[16] = half_btf(cospi[4], bf0[16], cospi[60], bf0[17], cos_bit[stage]);
  bf1[17] = half_btf(-cospi[4], bf0[17], cospi[60], bf0[16], cos_bit[stage]);
  bf1[18] = half_btf(cospi[20], bf0[18], cospi[44], bf0[19], cos_bit[stage]);
  bf1[19] = half_btf(-cospi[20], bf0[19], cospi[44], bf0[18], cos_bit[stage]);
  bf1[20] = half_btf(cospi[36], bf0[20], cospi[28], bf0[21], cos_bit[stage]);
  bf1[21] = half_btf(-cospi[36], bf0[21], cospi[28], bf0[20], cos_bit[stage]);
  bf1[22] = half_btf(cospi[52], bf0[22], cospi[12], bf0[23], cos_bit[stage]);
  bf1[23] = half_btf(-cospi[52], bf0[23], cospi[12], bf0[22], cos_bit[stage]);
  bf1[24] = half_btf(-cospi[60], bf0[24], cospi[4], bf0[25], cos_bit[stage]);
  bf1[25] = half_btf(cospi[60], bf0[25], cospi[4], bf0[24], cos_bit[stage]);
  bf1[26] = half_btf(-cospi[44], bf0[26], cospi[20], bf0[27], cos_bit[stage]);
  bf1[27] = half_btf(cospi[44], bf0[27], cospi[20], bf0[26], cos_bit[stage]);
  bf1[28] = half_btf(-cospi[28], bf0[28], cospi[36], bf0[29], cos_bit[stage]);
  bf1[29] = half_btf(cospi[28], bf0[29], cospi[36], bf0[28], cos_bit[stage]);
  bf1[30] = half_btf(-cospi[12], bf0[30], cospi[52], bf0[31], cos_bit[stage]);
  bf1[31] = half_btf(cospi[12], bf0[31], cospi[52], bf0[30], cos_bit[stage]);
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 5
  stage++;
  bf0 = step;
  bf1 = output;
  bf1[0] = bf0[0] + bf0[8];
  bf1[1] = bf0[1] + bf0[9];
  bf1[2] = bf0[2] + bf0[10];
  bf1[3] = bf0[3] + bf0[11];
  bf1[4] = bf0[4] + bf0[12];
  bf1[5] = bf0[5] + bf0[13];
  bf1[6] = bf0[6] + bf0[14];
  bf1[7] = bf0[7] + bf0[15];
  bf1[8] = -bf0[8] + bf0[0];
  bf1[9] = -bf0[9] + bf0[1];
  bf1[10] = -bf0[10] + bf0[2];
  bf1[11] = -bf0[11] + bf0[3];
  bf1[12] = -bf0[12] + bf0[4];
  bf1[13] = -bf0[13] + bf0[5];
  bf1[14] = -bf0[14] + bf0[6];
  bf1[15] = -bf0[15] + bf0[7];
  bf1[16] = bf0[16] + bf0[24];
  bf1[17] = bf0[17] + bf0[25];
  bf1[18] = bf0[18] + bf0[26];
  bf1[19] = bf0[19] + bf0[27];
  bf1[20] = bf0[20] + bf0[28];
  bf1[21] = bf0[21] + bf0[29];
  bf1[22] = bf0[22] + bf0[30];
  bf1[23] = bf0[23] + bf0[31];
  bf1[24] = -bf0[24] + bf0[16];
  bf1[25] = -bf0[25] + bf0[17];
  bf1[26] = -bf0[26] + bf0[18];
  bf1[27] = -bf0[27] + bf0[19];
  bf1[28] = -bf0[28] + bf0[20];
  bf1[29] = -bf0[29] + bf0[21];
  bf1[30] = -bf0[30] + bf0[22];
  bf1[31] = -bf0[31] + bf0[23];
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 6
  stage++;
  cospi = cospi_arr[cos_bit[stage] - cos_bit_min];
  bf0 = output;
  bf1 = step;
  bf1[0] = bf0[0];
  bf1[1] = bf0[1];
  bf1[2] = bf0[2];
  bf1[3] = bf0[3];
  bf1[4] = bf0[4];
  bf1[5] = bf0[5];
  bf1[6] = bf0[6];
  bf1[7] = bf0[7];
  bf1[8] = half_btf(cospi[8], bf0[8], cospi[56], bf0[9], cos_bit[stage]);
  bf1[9] = half_btf(-cospi[8], bf0[9], cospi[56], bf0[8], cos_bit[stage]);
  bf1[10] = half_btf(cospi[40], bf0[10], cospi[24], bf0[11], cos_bit[stage]);
  bf1[11] = half_btf(-cospi[40], bf0[11], cospi[24], bf0[10], cos_bit[stage]);
  bf1[12] = half_btf(-cospi[56], bf0[12], cospi[8], bf0[13], cos_bit[stage]);
  bf1[13] = half_btf(cospi[56], bf0[13], cospi[8], bf0[12], cos_bit[stage]);
  bf1[14] = half_btf(-cospi[24], bf0[14], cospi[40], bf0[15], cos_bit[stage]);
  bf1[15] = half_btf(cospi[24], bf0[15], cospi[40], bf0[14], cos_bit[stage]);
  bf1[16] = bf0[16];
  bf1[17] = bf0[17];
  bf1[18] = bf0[18];
  bf1[19] = bf0[19];
  bf1[20] = bf0[20];
  bf1[21] = bf0[21];
  bf1[22] = bf0[22];
  bf1[23] = bf0[23];
  bf1[24] = half_btf(cospi[8], bf0[24], cospi[56], bf0[25], cos_bit[stage]);
  bf1[25] = half_btf(-cospi[8], bf0[25], cospi[56], bf0[24], cos_bit[stage]);
  bf1[26] = half_btf(cospi[40], bf0[26], cospi[24], bf0[27], cos_bit[stage]);
  bf1[27] = half_btf(-cospi[40], bf0[27], cospi[24], bf0[26], cos_bit[stage]);
  bf1[28] = half_btf(-cospi[56], bf0[28], cospi[8], bf0[29], cos_bit[stage]);
  bf1[29] = half_btf(cospi[56], bf0[29], cospi[8], bf0[28], cos_bit[stage]);
  bf1[30] = half_btf(-cospi[24], bf0[30], cospi[40], bf0[31], cos_bit[stage]);
  bf1[31] = half_btf(cospi[24], bf0[31], cospi[40], bf0[30], cos_bit[stage]);
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 7
  stage++;
  bf0 = step;
  bf1 = output;
  bf1[0] = bf0[0] + bf0[4];
  bf1[1] = bf0[1] + bf0[5];
  bf1[2] = bf0[2] + bf0[6];
  bf1[3] = bf0[3] + bf0[7];
  bf1[4] = -bf0[4] + bf0[0];
  bf1[5] = -bf0[5] + bf0[1];
  bf1[6] = -bf0[6] + bf0[2];
  bf1[7] = -bf0[7] + bf0[3];
  bf1[8] = bf0[8] + bf0[12];
  bf1[9] = bf0[9] + bf0[13];
  bf1[10] = bf0[10] + bf0[14];
  bf1[11] = bf0[11] + bf0[15];
  bf1[12] = -bf0[12] + bf0[8];
  bf1[13] = -bf0[13] + bf0[9];
  bf1[14] = -bf0[14] + bf0[10];
  bf1[15] = -bf0[15] + bf0[11];
  bf1[16] = bf0[16] + bf0[20];
  bf1[17] = bf0[17] + bf0[21];
  bf1[18] = bf0[18] + bf0[22];
  bf1[19] = bf0[19] + bf0[23];
  bf1[20] = -bf0[20] + bf0[16];
  bf1[21] = -bf0[21] + bf0[17];
  bf1[22] = -bf0[22] + bf0[18];
  bf1[23] = -bf0[23] + bf0[19];
  bf1[24] = bf0[24] + bf0[28];
  bf1[25] = bf0[25] + bf0[29];
  bf1[26] = bf0[26] + bf0[30];
  bf1[27] = bf0[27] + bf0[31];
  bf1[28] = -bf0[28] + bf0[24];
  bf1[29] = -bf0[29] + bf0[25];
  bf1[30] = -bf0[30] + bf0[26];
  bf1[31] = -bf0[31] + bf0[27];
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 8
  stage++;
  cospi = cospi_arr[cos_bit[stage] - cos_bit_min];
  bf0 = output;
  bf1 = step;
  bf1[0] = bf0[0];
  bf1[1] = bf0[1];
  bf1[2] = bf0[2];
  bf1[3] = bf0[3];
  bf1[4] = half_btf(cospi[16], bf0[4], cospi[48], bf0[5], cos_bit[stage]);
  bf1[5] = half_btf(-cospi[16], bf0[5], cospi[48], bf0[4], cos_bit[stage]);
  bf1[6] = half_btf(-cospi[48], bf0[6], cospi[16], bf0[7], cos_bit[stage]);
  bf1[7] = half_btf(cospi[48], bf0[7], cospi[16], bf0[6], cos_bit[stage]);
  bf1[8] = bf0[8];
  bf1[9] = bf0[9];
  bf1[10] = bf0[10];
  bf1[11] = bf0[11];
  bf1[12] = half_btf(cospi[16], bf0[12], cospi[48], bf0[13], cos_bit[stage]);
  bf1[13] = half_btf(-cospi[16], bf0[13], cospi[48], bf0[12], cos_bit[stage]);
  bf1[14] = half_btf(-cospi[48], bf0[14], cospi[16], bf0[15], cos_bit[stage]);
  bf1[15] = half_btf(cospi[48], bf0[15], cospi[16], bf0[14], cos_bit[stage]);
  bf1[16] = bf0[16];
  bf1[17] = bf0[17];
  bf1[18] = bf0[18];
  bf1[19] = bf0[19];
  bf1[20] = half_btf(cospi[16], bf0[20], cospi[48], bf0[21], cos_bit[stage]);
  bf1[21] = half_btf(-cospi[16], bf0[21], cospi[48], bf0[20], cos_bit[stage]);
  bf1[22] = half_btf(-cospi[48], bf0[22], cospi[16], bf0[23], cos_bit[stage]);
  bf1[23] = half_btf(cospi[48], bf0[23], cospi[16], bf0[22], cos_bit[stage]);
  bf1[24] = bf0[24];
  bf1[25] = bf0[25];
  bf1[26] = bf0[26];
  bf1[27] = bf0[27];
  bf1[28] = half_btf(cospi[16], bf0[28], cospi[48], bf0[29], cos_bit[stage]);
  bf1[29] = half_btf(-cospi[16], bf0[29], cospi[48], bf0[28], cos_bit[stage]);
  bf1[30] = half_btf(-cospi[48], bf0[30], cospi[16], bf0[31], cos_bit[stage]);
  bf1[31] = half_btf(cospi[48], bf0[31], cospi[16], bf0[30], cos_bit[stage]);
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 9
  stage++;
  bf0 = step;
  bf1 = output;
  bf1[0] = bf0[0] + bf0[2];
  bf1[1] = bf0[1] + bf0[3];
  bf1[2] = -bf0[2] + bf0[0];
  bf1[3] = -bf0[3] + bf0[1];
  bf1[4] = bf0[4] + bf0[6];
  bf1[5] = bf0[5] + bf0[7];
  bf1[6] = -bf0[6] + bf0[4];
  bf1[7] = -bf0[7] + bf0[5];
  bf1[8] = bf0[8] + bf0[10];
  bf1[9] = bf0[9] + bf0[11];
  bf1[10] = -bf0[10] + bf0[8];
  bf1[11] = -bf0[11] + bf0[9];
  bf1[12] = bf0[12] + bf0[14];
  bf1[13] = bf0[13] + bf0[15];
  bf1[14] = -bf0[14] + bf0[12];
  bf1[15] = -bf0[15] + bf0[13];
  bf1[16] = bf0[16] + bf0[18];
  bf1[17] = bf0[17] + bf0[19];
  bf1[18] = -bf0[18] + bf0[16];
  bf1[19] = -bf0[19] + bf0[17];
  bf1[20] = bf0[20] + bf0[22];
  bf1[21] = bf0[21] + bf0[23];
  bf1[22] = -bf0[22] + bf0[20];
  bf1[23] = -bf0[23] + bf0[21];
  bf1[24] = bf0[24] + bf0[26];
  bf1[25] = bf0[25] + bf0[27];
  bf1[26] = -bf0[26] + bf0[24];
  bf1[27] = -bf0[27] + bf0[25];
  bf1[28] = bf0[28] + bf0[30];
  bf1[29] = bf0[29] + bf0[31];
  bf1[30] = -bf0[30] + bf0[28];
  bf1[31] = -bf0[31] + bf0[29];
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 10
  stage++;
  cospi = cospi_arr[cos_bit[stage] - cos_bit_min];
  bf0 = output;
  bf1 = step;
  bf1[0] = bf0[0];
  bf1[1] = bf0[1];
  bf1[2] = half_btf(cospi[32], bf0[2], cospi[32], bf0[3], cos_bit[stage]);
  bf1[3] = half_btf(-cospi[32], bf0[3], cospi[32], bf0[2], cos_bit[stage]);
  bf1[4] = bf0[4];
  bf1[5] = bf0[5];
  bf1[6] = half_btf(cospi[32], bf0[6], cospi[32], bf0[7], cos_bit[stage]);
  bf1[7] = half_btf(-cospi[32], bf0[7], cospi[32], bf0[6], cos_bit[stage]);
  bf1[8] = bf0[8];
  bf1[9] = bf0[9];
  bf1[10] = half_btf(cospi[32], bf0[10], cospi[32], bf0[11], cos_bit[stage]);
  bf1[11] = half_btf(-cospi[32], bf0[11], cospi[32], bf0[10], cos_bit[stage]);
  bf1[12] = bf0[12];
  bf1[13] = bf0[13];
  bf1[14] = half_btf(cospi[32], bf0[14], cospi[32], bf0[15], cos_bit[stage]);
  bf1[15] = half_btf(-cospi[32], bf0[15], cospi[32], bf0[14], cos_bit[stage]);
  bf1[16] = bf0[16];
  bf1[17] = bf0[17];
  bf1[18] = half_btf(cospi[32], bf0[18], cospi[32], bf0[19], cos_bit[stage]);
  bf1[19] = half_btf(-cospi[32], bf0[19], cospi[32], bf0[18], cos_bit[stage]);
  bf1[20] = bf0[20];
  bf1[21] = bf0[21];
  bf1[22] = half_btf(cospi[32], bf0[22], cospi[32], bf0[23], cos_bit[stage]);
  bf1[23] = half_btf(-cospi[32], bf0[23], cospi[32], bf0[22], cos_bit[stage]);
  bf1[24] = bf0[24];
  bf1[25] = bf0[25];
  bf1[26] = half_btf(cospi[32], bf0[26], cospi[32], bf0[27], cos_bit[stage]);
  bf1[27] = half_btf(-cospi[32], bf0[27], cospi[32], bf0[26], cos_bit[stage]);
  bf1[28] = bf0[28];
  bf1[29] = bf0[29];
  bf1[30] = half_btf(cospi[32], bf0[30], cospi[32], bf0[31], cos_bit[stage]);
  bf1[31] = half_btf(-cospi[32], bf0[31], cospi[32], bf0[30], cos_bit[stage]);
  range_check(stage, input, bf1, size, stage_range[stage]);

  // stage 11
  stage++;
  bf0 = step;
  bf1 = output;
  bf1[0] = bf0[0];
  bf1[1] = -bf0[16];
  bf1[2] = bf0[24];
  bf1[3] = -bf0[8];
  bf1[4] = bf0[12];
  bf1[5] = -bf0[28];
  bf1[6] = bf0[20];
  bf1[7] = -bf0[4];
  bf1[8] = bf0[6];
  bf1[9] = -bf0[22];
  bf1[10] = bf0[30];
  bf1[11] = -bf0[14];
  bf1[12] = bf0[10];
  bf1[13] = -bf0[26];
  bf1[14] = bf0[18];
  bf1[15] = -bf0[2];
  bf1[16] = bf0[3];
  bf1[17] = -bf0[19];
  bf1[18] = bf0[27];
  bf1[19] = -bf0[11];
  bf1[20] = bf0[15];
  bf1[21] = -bf0[31];
  bf1[22] = bf0[23];
  bf1[23] = -bf0[7];
  bf1[24] = bf0[5];
  bf1[25] = -bf0[21];
  bf1[26] = bf0[29];
  bf1[27] = -bf0[13];
  bf1[28] = bf0[9];
  bf1[29] = -bf0[25];
  bf1[30] = bf0[17];
  bf1[31] = -bf0[1];
  range_check(stage, input, bf1, size, stage_range[stage]);
}