idct.c

/*
 * Copyright (c) 2016, Alliance for Open Media. All rights reserved
 *
 * This source code is subject to the terms of the BSD 2 Clause License and
 * the Alliance for Open Media Patent License 1.0. If the BSD 2 Clause License
 * was not distributed with this source code in the LICENSE file, you can
 * obtain it at www.aomedia.org/license/software. If the Alliance for Open
 * Media Patent License 1.0 was not distributed with this source code in the
 * PATENTS file, you can obtain it at www.aomedia.org/license/patent.
 */

#include <math.h>

#include "./aom_dsp_rtcd.h"
#include "./av1_rtcd.h"
#include "aom_dsp/inv_txfm.h"
#include "aom_ports/mem.h"
#include "av1/common/av1_inv_txfm1d_cfg.h"
#include "av1/common/blockd.h"
#include "av1/common/enums.h"
#include "av1/common/idct.h"
#if CONFIG_DAALA_TX4 || CONFIG_DAALA_TX8 || CONFIG_DAALA_TX16 || \
    CONFIG_DAALA_TX32 || CONFIG_DAALA_TX64
#include "av1/common/daala_tx.h"
#endif

int av1_get_tx_scale(const TX_SIZE tx_size) {
  const int pels = tx_size_2d[tx_size];
  return (pels > 256) + (pels > 1024) + (pels > 4096);
}

// NOTE: The implementation of all inverses need to be aware of the fact
// that input and output could be the same buffer.

static void iidtx4_c(const tran_low_t *input, tran_low_t *output) {
  int i;
  for (i = 0; i < 4; ++i) {
    output[i] = (tran_low_t)dct_const_round_shift(input[i] * Sqrt2);
  }
}

static void iidtx8_c(const tran_low_t *input, tran_low_t *output) {
  int i;
  for (i = 0; i < 8; ++i) {
    output[i] = input[i] * 2;
  }
}

static void iidtx16_c(const tran_low_t *input, tran_low_t *output) {
  int i;
  for (i = 0; i < 16; ++i) {
    output[i] = (tran_low_t)dct_const_round_shift(input[i] * 2 * Sqrt2);
  }
}

static void iidtx32_c(const tran_low_t *input, tran_low_t *output) {
  int i;
  for (i = 0; i < 32; ++i) {
    output[i] = input[i] * 4;
  }
}

#if CONFIG_TX64X64 && !CONFIG_DAALA_TX64
static void iidtx64_c(const tran_low_t *input, tran_low_t *output) {
  int i;
  for (i = 0; i < 64; ++i) {
    output[i] = (tran_low_t)dct_const_round_shift(input[i] * 4 * Sqrt2);
  }
}
#endif  // CONFIG_TX64X64

// For use in lieu of ADST
static void ihalfright32_c(const tran_low_t *input, tran_low_t *output) {
  int i;
  tran_low_t inputhalf[16];
  // Multiply input by sqrt(2)
  for (i = 0; i < 16; ++i) {
    inputhalf[i] = (tran_low_t)dct_const_round_shift(input[i] * Sqrt2);
  }
  for (i = 0; i < 16; ++i) {
    output[i] = input[16 + i] * 4;
  }
  aom_idct16_c(inputhalf, output + 16);
  // Note overall scaling factor is 4 times orthogonal
}

#if CONFIG_TX64X64 && !CONFIG_DAALA_TX64
static void idct64_col_c(const tran_low_t *input, tran_low_t *output) {
  int32_t in[64], out[64];
  int i;
  for (i = 0; i < 64; ++i) in[i] = (int32_t)input[i];
  av1_idct64_new(in, out, inv_cos_bit_col_dct_64, inv_stage_range_col_dct_64);
  for (i = 0; i < 64; ++i) output[i] = (tran_low_t)out[i];
}

static void idct64_row_c(const tran_low_t *input, tran_low_t *output) {
  int32_t in[64], out[64];
  int i;
  for (i = 0; i < 64; ++i) in[i] = (int32_t)input[i];
  av1_idct64_new(in, out, inv_cos_bit_row_dct_64, inv_stage_range_row_dct_64);
  for (i = 0; i < 64; ++i) output[i] = (tran_low_t)out[i];
}

// For use in lieu of ADST
static void ihalfright64_c(const tran_low_t *input, tran_low_t *output) {
  int i;
  tran_low_t inputhalf[32];
  // Multiply input by sqrt(2)
  for (i = 0; i < 32; ++i) {
    inputhalf[i] = (tran_low_t)dct_const_round_shift(input[i] * Sqrt2);
  }
  for (i = 0; i < 32; ++i) {
    output[i] = (tran_low_t)dct_const_round_shift(input[32 + i] * 4 * Sqrt2);
  }
  aom_idct32_c(inputhalf, output + 32);
  // Note overall scaling factor is 4 * sqrt(2)  times orthogonal
}
#endif  // CONFIG_TX64X64

// Inverse identity transform and add.
static void inv_idtx_add_c(const tran_low_t *input, uint8_t *dest, int stride,
                           int bsx, int bsy, TX_TYPE tx_type) {
  int r, c;
  const int pels = bsx * bsy;
  const int shift = 3 - ((pels > 256) + (pels > 1024));
  if (tx_type == IDTX) {
    for (r = 0; r < bsy; ++r) {
      for (c = 0; c < bsx; ++c)
        dest[c] = clip_pixel_add(dest[c], input[c] >> shift);
      dest += stride;
      input += bsx;
    }
  }
}

#define FLIPUD_PTR(dest, stride, size)       \
  do {                                       \
    (dest) = (dest) + ((size)-1) * (stride); \
    (stride) = -(stride);                    \
  } while (0)

static void maybe_flip_strides(uint8_t **dst, int *dstride, tran_low_t **src,
                               int *sstride, TX_TYPE tx_type, int sizey,
                               int sizex) {
  // Note that the transpose of src will be added to dst. In order to LR
  // flip the addends (in dst coordinates), we UD flip the src. To UD flip
  // the addends, we UD flip the dst.
  switch (tx_type) {
    case DCT_DCT:
    case ADST_DCT:
    case DCT_ADST:
    case ADST_ADST:
    case IDTX:
    case V_DCT:
    case H_DCT:
    case V_ADST:
    case H_ADST: break;
    case FLIPADST_DCT:
    case FLIPADST_ADST:
    case V_FLIPADST:
      // flip UD
      FLIPUD_PTR(*dst, *dstride, sizey);
      break;
    case DCT_FLIPADST:
    case ADST_FLIPADST:
    case H_FLIPADST:
      // flip LR
      FLIPUD_PTR(*src, *sstride, sizex);
      break;
    case FLIPADST_FLIPADST:
      // flip UD
      FLIPUD_PTR(*dst, *dstride, sizey);
      // flip LR
      FLIPUD_PTR(*src, *sstride, sizex);
      break;
    default: assert(0); break;
  }
}

#if CONFIG_HIGHBITDEPTH
#if CONFIG_TX64X64
static void highbd_inv_idtx_add_c(const tran_low_t *input, uint8_t *dest8,
                                  int stride, int bsx, int bsy, TX_TYPE tx_type,
                                  int bd) {
  int r, c;
  const int pels = bsx * bsy;
  const int shift = 3 - ((pels > 256) + (pels > 1024));
  uint16_t *dest = CONVERT_TO_SHORTPTR(dest8);

  if (tx_type == IDTX) {
    for (r = 0; r < bsy; ++r) {
      for (c = 0; c < bsx; ++c)
        dest[c] = highbd_clip_pixel_add(dest[c], input[c] >> shift, bd);
      dest += stride;
      input += bsx;
    }
  }
}
#endif  // CONFIG_TX64X64
#endif  // CONFIG_HIGHBITDEPTH

#if CONFIG_LGT
void ilgt4(const tran_low_t *input, tran_low_t *output,
           const tran_high_t *lgtmtx) {
  if (!lgtmtx) assert(0);

  // evaluate s[j] = sum of all lgtmtx[j]*input[i] over i=1,...,4
  tran_high_t s[4] = { 0 };
  for (int i = 0; i < 4; ++i)
    for (int j = 0; j < 4; ++j) s[j] += lgtmtx[i * 4 + j] * input[i];

  for (int i = 0; i < 4; ++i) output[i] = WRAPLOW(dct_const_round_shift(s[i]));
}

void ilgt8(const tran_low_t *input, tran_low_t *output,
           const tran_high_t *lgtmtx) {
  if (!lgtmtx) assert(0);

  // evaluate s[j] = sum of all lgtmtx[j]*input[i] over i=1,...,8
  tran_high_t s[8] = { 0 };
  for (int i = 0; i < 8; ++i)
    for (int j = 0; j < 8; ++j) s[j] += lgtmtx[i * 8 + j] * input[i];

  for (int i = 0; i < 8; ++i) output[i] = WRAPLOW(dct_const_round_shift(s[i]));
}
#endif  // CONFIG_LGT

#if CONFIG_LGT
// get_lgt4 and get_lgt8 return 1 and pick a lgt matrix if LGT is chosen to
// apply. Otherwise they return 0
int get_lgt4(const TxfmParam *txfm_param, int is_col,
             const tran_high_t **lgtmtx) {
  assert(av1_ext_tx_used[txfm_param->tx_set_type][txfm_param->tx_type]);
  if (is_col && (vtx_tab[txfm_param->tx_type] == ADST_1D ||
                 vtx_tab[txfm_param->tx_type] == FLIPADST_1D)) {
    lgtmtx[0] = txfm_param->is_inter ? &lgt4_170[0][0] : &lgt4_140[0][0];
    return 1;
  } else if (!is_col && (htx_tab[txfm_param->tx_type] == ADST_1D ||
                         htx_tab[txfm_param->tx_type] == FLIPADST_1D)) {
    lgtmtx[0] = txfm_param->is_inter ? &lgt4_170[0][0] : &lgt4_140[0][0];
    return 1;
  }
  lgtmtx[0] = NULL;
  return 0;
}

int get_lgt8(const TxfmParam *txfm_param, int is_col,
             const tran_high_t **lgtmtx) {
  assert(av1_ext_tx_used[txfm_param->tx_set_type][txfm_param->tx_type]);
  if (is_col && (vtx_tab[txfm_param->tx_type] == ADST_1D ||
                 vtx_tab[txfm_param->tx_type] == FLIPADST_1D)) {
    lgtmtx[0] = txfm_param->is_inter ? &lgt8_170[0][0] : &lgt8_150[0][0];
    return 1;
  } else if (!is_col && (htx_tab[txfm_param->tx_type] == ADST_1D ||
                         htx_tab[txfm_param->tx_type] == FLIPADST_1D)) {
    lgtmtx[0] = txfm_param->is_inter ? &lgt8_170[0][0] : &lgt8_150[0][0];
    return 1;
  }
  lgtmtx[0] = NULL;
  return 0;
}
#endif  // CONFIG_LGT

void av1_iht4x4_16_add_c(const tran_low_t *input, uint8_t *dest, int stride,
                         const TxfmParam *txfm_param) {
  const TX_TYPE tx_type = txfm_param->tx_type;
#if CONFIG_MRC_TX
  assert(tx_type != MRC_DCT && "Invalid tx type for tx size");
#endif  // CONFIG_MRC_TX
#if !CONFIG_DAALA_TX4
  if (tx_type == DCT_DCT) {
    aom_idct4x4_16_add(input, dest, stride);
    return;
  }
#endif
  static const transform_2d IHT_4[] = {
#if CONFIG_DAALA_TX4
    { daala_idct4, daala_idct4 },  // DCT_DCT  = 0
    { daala_idst4, daala_idct4 },  // ADST_DCT = 1
    { daala_idct4, daala_idst4 },  // DCT_ADST = 2
    { daala_idst4, daala_idst4 },  // ADST_ADST = 3
    { daala_idst4, daala_idct4 },  // FLIPADST_DCT
    { daala_idct4, daala_idst4 },  // DCT_FLIPADST
    { daala_idst4, daala_idst4 },  // FLIPADST_FLIPADST
    { daala_idst4, daala_idst4 },  // ADST_FLIPADST
    { daala_idst4, daala_idst4 },  // FLIPADST_ADST
    { daala_idtx4, daala_idtx4 },  // IDTX
    { daala_idct4, daala_idtx4 },  // V_DCT
    { daala_idtx4, daala_idct4 },  // H_DCT
    { daala_idst4, daala_idtx4 },  // V_ADST
    { daala_idtx4, daala_idst4 },  // H_ADST
    { daala_idst4, daala_idtx4 },  // V_FLIPADST
    { daala_idtx4, daala_idst4 },  // H_FLIPADST
#else
    { aom_idct4_c, aom_idct4_c },    // DCT_DCT  = 0
    { aom_iadst4_c, aom_idct4_c },   // ADST_DCT = 1
    { aom_idct4_c, aom_iadst4_c },   // DCT_ADST = 2
    { aom_iadst4_c, aom_iadst4_c },  // ADST_ADST = 3
    { aom_iadst4_c, aom_idct4_c },   // FLIPADST_DCT
    { aom_idct4_c, aom_iadst4_c },   // DCT_FLIPADST
    { aom_iadst4_c, aom_iadst4_c },  // FLIPADST_FLIPADST
    { aom_iadst4_c, aom_iadst4_c },  // ADST_FLIPADST
    { aom_iadst4_c, aom_iadst4_c },  // FLIPADST_ADST
    { iidtx4_c, iidtx4_c },          // IDTX
    { aom_idct4_c, iidtx4_c },       // V_DCT
    { iidtx4_c, aom_idct4_c },       // H_DCT
    { aom_iadst4_c, iidtx4_c },      // V_ADST
    { iidtx4_c, aom_iadst4_c },      // H_ADST
    { aom_iadst4_c, iidtx4_c },      // V_FLIPADST
    { iidtx4_c, aom_iadst4_c },      // H_FLIPADST
#endif
  };

  int i, j;
  tran_low_t tmp[4][4];
  tran_low_t out[4][4];
  tran_low_t *outp = &out[0][0];
  int outstride = 4;

#if CONFIG_DCT_ONLY
  assert(tx_type == DCT_DCT);
#endif

#if CONFIG_LGT
  const tran_high_t *lgtmtx_col[1];
  const tran_high_t *lgtmtx_row[1];
  int use_lgt_col = get_lgt4(txfm_param, 1, lgtmtx_col);
  int use_lgt_row = get_lgt4(txfm_param, 0, lgtmtx_row);
#endif

  // inverse transform row vectors
  for (i = 0; i < 4; ++i) {
#if CONFIG_DAALA_TX4
    tran_low_t temp_in[4];
    for (j = 0; j < 4; j++) temp_in[j] = input[j] * 2;
    IHT_4[tx_type].rows(temp_in, out[i]);
#else
#if CONFIG_LGT
    if (use_lgt_row)
      ilgt4(input, out[i], lgtmtx_row[0]);
    else
#endif
      IHT_4[tx_type].rows(input, out[i]);
#endif
    input += 4;
  }

  // transpose
  for (i = 0; i < 4; i++) {
    for (j = 0; j < 4; j++) {
      tmp[j][i] = out[i][j];
    }
  }

  // inverse transform column vectors
  for (i = 0; i < 4; ++i) {
#if CONFIG_LGT
    if (use_lgt_col)
      ilgt4(tmp[i], out[i], lgtmtx_col[0]);
    else
#endif
      IHT_4[tx_type].cols(tmp[i], out[i]);
  }

  maybe_flip_strides(&dest, &stride, &outp, &outstride, tx_type, 4, 4);

  // Sum with the destination
  for (i = 0; i < 4; ++i) {
    for (j = 0; j < 4; ++j) {
      int d = i * stride + j;
      int s = j * outstride + i;
#if CONFIG_DAALA_TX4
      dest[d] = clip_pixel_add(dest[d], ROUND_POWER_OF_TWO(outp[s], 4));
#else
      dest[d] = clip_pixel_add(dest[d], ROUND_POWER_OF_TWO(outp[s], 4));
#endif
    }
  }
}

void av1_iht4x8_32_add_c(const tran_low_t *input, uint8_t *dest, int stride,
                         const TxfmParam *txfm_param) {
  const TX_TYPE tx_type = txfm_param->tx_type;
#if CONFIG_MRC_TX
  assert(tx_type != MRC_DCT && "Invalid tx type for tx size");
#endif  // CONFIG_MRC_TX
#if CONFIG_DCT_ONLY
  assert(tx_type == DCT_DCT);
#endif
  static const transform_2d IHT_4x8[] = {
#if CONFIG_DAALA_TX4 && CONFIG_DAALA_TX8
    { daala_idct8, daala_idct4 },  // DCT_DCT  = 0
    { daala_idst8, daala_idct4 },  // ADST_DCT = 1
    { daala_idct8, daala_idst4 },  // DCT_ADST = 2
    { daala_idst8, daala_idst4 },  // ADST_ADST = 3
    { daala_idst8, daala_idct4 },  // FLIPADST_DCT
    { daala_idct8, daala_idst4 },  // DCT_FLIPADST
    { daala_idst8, daala_idst4 },  // FLIPADST_FLIPADST
    { daala_idst8, daala_idst4 },  // ADST_FLIPADST
    { daala_idst8, daala_idst4 },  // FLIPADST_ADST
    { daala_idtx8, daala_idtx4 },  // IDTX
    { daala_idct8, daala_idtx4 },  // V_DCT
    { daala_idtx8, daala_idct4 },  // H_DCT
    { daala_idst8, daala_idtx4 },  // V_ADST
    { daala_idtx8, daala_idst4 },  // H_ADST
    { daala_idst8, daala_idtx4 },  // V_FLIPADST
    { daala_idtx8, daala_idst4 },  // H_FLIPADST
#else
    { aom_idct8_c, aom_idct4_c },    // DCT_DCT
    { aom_iadst8_c, aom_idct4_c },   // ADST_DCT
    { aom_idct8_c, aom_iadst4_c },   // DCT_ADST
    { aom_iadst8_c, aom_iadst4_c },  // ADST_ADST
    { aom_iadst8_c, aom_idct4_c },   // FLIPADST_DCT
    { aom_idct8_c, aom_iadst4_c },   // DCT_FLIPADST
    { aom_iadst8_c, aom_iadst4_c },  // FLIPADST_FLIPADST
    { aom_iadst8_c, aom_iadst4_c },  // ADST_FLIPADST
    { aom_iadst8_c, aom_iadst4_c },  // FLIPADST_ADST
    { iidtx8_c, iidtx4_c },          // IDTX
    { aom_idct8_c, iidtx4_c },       // V_DCT
    { iidtx8_c, aom_idct4_c },       // H_DCT
    { aom_iadst8_c, iidtx4_c },      // V_ADST
    { iidtx8_c, aom_iadst4_c },      // H_ADST
    { aom_iadst8_c, iidtx4_c },      // V_FLIPADST
    { iidtx8_c, aom_iadst4_c },      // H_FLIPADST
#endif
  };

  const int n = 4;
  const int n2 = 8;
  int i, j;
  tran_low_t out[4][8], tmp[4][8], outtmp[4];
  tran_low_t *outp = &out[0][0];
  int outstride = n2;

#if CONFIG_LGT
  const tran_high_t *lgtmtx_col[1];
  const tran_high_t *lgtmtx_row[1];
  int use_lgt_col = get_lgt8(txfm_param, 1, lgtmtx_col);
  int use_lgt_row = get_lgt4(txfm_param, 0, lgtmtx_row);
#endif

  // Multi-way scaling matrix (bits):
  // LGT/AV1 row,col     input+0, rowTX+.5, mid+.5, colTX+1, out-5 == -3
  // LGT row, Daala col  input+0, rowTX+.5, mid+.5, colTX+0, out-4 == -3
  // Daala row, LGT col  input+1, rowTX+0,  mid+0,  colTX+1, out-5 == -3
  // Daala row,col       input+1, rowTX+0,  mid+0,  colTX+0, out-4 == -3

  // inverse transform row vectors and transpose
  for (i = 0; i < n2; ++i) {
#if CONFIG_LGT
    if (use_lgt_row) {
      // Scaling cases 1 and 2 above
      // No input scaling
      // Row transform (LGT; scales up .5 bits)
      ilgt4(input, outtmp, lgtmtx_row[0]);
      // Transpose and mid scaling up by .5 bit
      for (j = 0; j < n; ++j)
        tmp[j][i] = (tran_low_t)dct_const_round_shift(outtmp[j] * Sqrt2);
    } else {
#endif
#if CONFIG_DAALA_TX4 && CONFIG_DAALA_TX8
      // Daala row transform; Scaling cases 3 and 4 above
      tran_low_t temp_in[4];
      // Input scaling up by 1 bit
      for (j = 0; j < n; j++) temp_in[j] = input[j] * 2;
      // Row transform; Daala does not scale
      IHT_4x8[tx_type].rows(temp_in, outtmp);
      // Transpose; no mid scaling
      for (j = 0; j < n; ++j) tmp[j][i] = outtmp[j];
#else
    // AV1 row transform; Scaling case 1 only
    // Row transform (AV1 scales up .5 bits)
    IHT_4x8[tx_type].rows(input, outtmp);
    // Transpose and mid scaling up by .5 bit
    for (j = 0; j < n; ++j)
      tmp[j][i] = (tran_low_t)dct_const_round_shift(outtmp[j] * Sqrt2);
#endif
#if CONFIG_LGT
    }
#endif
    input += n;
  }

  // inverse transform column vectors
  // AV1/LGT column TX scales up by 1 bit, Daala does not scale
  for (i = 0; i < n; ++i) {
#if CONFIG_LGT
    if (use_lgt_col)
      ilgt8(tmp[i], out[i], lgtmtx_col[0]);
    else
#endif
      IHT_4x8[tx_type].cols(tmp[i], out[i]);
  }

  maybe_flip_strides(&dest, &stride, &outp, &outstride, tx_type, n2, n);

  // Sum with the destination
  for (i = 0; i < n2; ++i) {
    for (j = 0; j < n; ++j) {
      int d = i * stride + j;
      int s = j * outstride + i;
#if CONFIG_DAALA_TX4 && CONFIG_DAALA_TX8
#if CONFIG_LGT
      if (use_lgt_col)
        // Output Scaling cases 1, 3
        dest[d] = clip_pixel_add(dest[d], ROUND_POWER_OF_TWO(outp[s], 5));
      else
#endif
        // Output scaling cases 2, 4
        dest[d] = clip_pixel_add(dest[d], ROUND_POWER_OF_TWO(outp[s], 4));
#else
      // Output scaling case 1 only
      dest[d] = clip_pixel_add(dest[d], ROUND_POWER_OF_TWO(outp[s], 5));
#endif
    }
  }
}

void av1_iht8x4_32_add_c(const tran_low_t *input, uint8_t *dest, int stride,
                         const TxfmParam *txfm_param) {
  const TX_TYPE tx_type = txfm_param->tx_type;
#if CONFIG_MRC_TX
  assert(tx_type != MRC_DCT && "Invalid tx type for tx size");
#endif  // CONFIG_MRC_TX
#if CONFIG_DCT_ONLY
  assert(tx_type == DCT_DCT);
#endif
  static const transform_2d IHT_8x4[] = {
#if CONFIG_DAALA_TX4 && CONFIG_DAALA_TX8
    { daala_idct4, daala_idct8 },  // DCT_DCT  = 0
    { daala_idst4, daala_idct8 },  // ADST_DCT = 1
    { daala_idct4, daala_idst8 },  // DCT_ADST = 2
    { daala_idst4, daala_idst8 },  // ADST_ADST = 3
    { daala_idst4, daala_idct8 },  // FLIPADST_DCT
    { daala_idct4, daala_idst8 },  // DCT_FLIPADST
    { daala_idst4, daala_idst8 },  // FLIPADST_FLIPADST
    { daala_idst4, daala_idst8 },  // ADST_FLIPADST
    { daala_idst4, daala_idst8 },  // FLIPADST_ADST
    { daala_idtx4, daala_idtx8 },  // IDTX
    { daala_idct4, daala_idtx8 },  // V_DCT
    { daala_idtx4, daala_idct8 },  // H_DCT
    { daala_idst4, daala_idtx8 },  // V_ADST
    { daala_idtx4, daala_idst8 },  // H_ADST
    { daala_idst4, daala_idtx8 },  // V_FLIPADST
    { daala_idtx4, daala_idst8 },  // H_FLIPADST
#else
    { aom_idct4_c, aom_idct8_c },    // DCT_DCT
    { aom_iadst4_c, aom_idct8_c },   // ADST_DCT
    { aom_idct4_c, aom_iadst8_c },   // DCT_ADST
    { aom_iadst4_c, aom_iadst8_c },  // ADST_ADST
    { aom_iadst4_c, aom_idct8_c },   // FLIPADST_DCT
    { aom_idct4_c, aom_iadst8_c },   // DCT_FLIPADST
    { aom_iadst4_c, aom_iadst8_c },  // FLIPADST_FLIPADST
    { aom_iadst4_c, aom_iadst8_c },  // ADST_FLIPADST
    { aom_iadst4_c, aom_iadst8_c },  // FLIPADST_ADST
    { iidtx4_c, iidtx8_c },          // IDTX
    { aom_idct4_c, iidtx8_c },       // V_DCT
    { iidtx4_c, aom_idct8_c },       // H_DCT
    { aom_iadst4_c, iidtx8_c },      // V_ADST
    { iidtx4_c, aom_iadst8_c },      // H_ADST
    { aom_iadst4_c, iidtx8_c },      // V_FLIPADST
    { iidtx4_c, aom_iadst8_c },      // H_FLIPADST
#endif
  };

  const int n = 4;
  const int n2 = 8;

  int i, j;
  tran_low_t out[8][4], tmp[8][4], outtmp[8];
  tran_low_t *outp = &out[0][0];
  int outstride = n;

#if CONFIG_LGT
  const tran_high_t *lgtmtx_col[1];
  const tran_high_t *lgtmtx_row[1];
  int use_lgt_col = get_lgt4(txfm_param, 1, lgtmtx_col);
  int use_lgt_row = get_lgt8(txfm_param, 0, lgtmtx_row);
#endif

  // Multi-way scaling matrix (bits):
  // LGT/AV1 row,col     input+0, rowTX+1, mid+.5, colTX+.5, out-5 == -3
  // LGT row, Daala col  input+0, rowTX+1, mid+.5, colTX+.5, out-4 == -3
  // Daala row, LGT col  input+1, rowTX+0, mid+0,  colTX+1,  out-5 == -3
  // Daala row,col       input+1, rowTX+0, mid+0,  colTX+0,  out-4 == -3

  // inverse transform row vectors and transpose
  for (i = 0; i < n; ++i) {
#if CONFIG_LGT
    if (use_lgt_row) {
      // Scaling cases 1 and 2 above
      // No input scaling
      // Row transform (LGT; scales up 1 bit)
      ilgt8(input, outtmp, lgtmtx_row[0]);
      // Transpose and mid scaling up by .5 bit
      for (j = 0; j < n2; ++j)
        tmp[j][i] = (tran_low_t)dct_const_round_shift(outtmp[j] * Sqrt2);
    } else {
#endif
#if CONFIG_DAALA_TX4 && CONFIG_DAALA_TX8
      // Daala row transform; Scaling cases 3 and 4 above
      tran_low_t temp_in[8];
      // Input scaling up by 1 bit
      for (j = 0; j < n2; j++) temp_in[j] = input[j] * 2;
      // Row transform; Daala does not scale
      IHT_8x4[tx_type].rows(temp_in, outtmp);
      // Transpose; no mid scaling
      for (j = 0; j < n2; ++j) tmp[j][i] = outtmp[j];
#else
    // AV1 row transform; Scaling case 1 only
    // Row transform (AV1 scales up 1 bit)
    IHT_8x4[tx_type].rows(input, outtmp);
    // Transpose and mid scaling up by .5 bit
    for (j = 0; j < n2; ++j)
      tmp[j][i] = (tran_low_t)dct_const_round_shift(outtmp[j] * Sqrt2);
#endif
#if CONFIG_LGT
    }
#endif
    input += n2;
  }

  // inverse transform column vectors
  // AV1 and LGT scale up by .5 bits; Daala does not scale
  for (i = 0; i < n2; ++i) {
#if CONFIG_LGT
    if (use_lgt_col)
      ilgt4(tmp[i], out[i], lgtmtx_col[0]);
    else
#endif
      IHT_8x4[tx_type].cols(tmp[i], out[i]);
  }

  maybe_flip_strides(&dest, &stride, &outp, &outstride, tx_type, n, n2);

  // Sum with the destination
  for (i = 0; i < n; ++i) {
    for (j = 0; j < n2; ++j) {
      int d = i * stride + j;
      int s = j * outstride + i;
#if CONFIG_DAALA_TX4 && CONFIG_DAALA_TX8
#if CONFIG_LGT
      if (use_lgt_col)
        // Output scaling cases 1, 3
        dest[d] = clip_pixel_add(dest[d], ROUND_POWER_OF_TWO(outp[s], 5));
      else
#endif
        // Output scaling cases 2, 4
        dest[d] = clip_pixel_add(dest[d], ROUND_POWER_OF_TWO(outp[s], 4));
#else
      // Output scaling case 1
      dest[d] = clip_pixel_add(dest[d], ROUND_POWER_OF_TWO(outp[s], 5));
#endif
    }
  }
}

void av1_iht4x16_64_add_c(const tran_low_t *input, uint8_t *dest, int stride,
                          const TxfmParam *txfm_param) {
  const TX_TYPE tx_type = txfm_param->tx_type;
#if CONFIG_MRC_TX
  assert(tx_type != MRC_DCT && "Invalid tx type for tx size");
#endif  // CONFIG_MRC_TX
#if CONFIG_DCT_ONLY
  assert(tx_type == DCT_DCT);
#endif
  static const transform_2d IHT_4x16[] = {
    { aom_idct16_c, aom_idct4_c },    // DCT_DCT
    { aom_iadst16_c, aom_idct4_c },   // ADST_DCT
    { aom_idct16_c, aom_iadst4_c },   // DCT_ADST
    { aom_iadst16_c, aom_iadst4_c },  // ADST_ADST
    { aom_iadst16_c, aom_idct4_c },   // FLIPADST_DCT
    { aom_idct16_c, aom_iadst4_c },   // DCT_FLIPADST
    { aom_iadst16_c, aom_iadst4_c },  // FLIPADST_FLIPADST
    { aom_iadst16_c, aom_iadst4_c },  // ADST_FLIPADST
    { aom_iadst16_c, aom_iadst4_c },  // FLIPADST_ADST
    { iidtx16_c, iidtx4_c },          // IDTX
    { aom_idct16_c, iidtx4_c },       // V_DCT
    { iidtx16_c, aom_idct4_c },       // H_DCT
    { aom_iadst16_c, iidtx4_c },      // V_ADST
    { iidtx16_c, aom_iadst4_c },      // H_ADST
    { aom_iadst16_c, iidtx4_c },      // V_FLIPADST
    { iidtx16_c, aom_iadst4_c },      // H_FLIPADST
  };

  const int n = 4;
  const int n4 = 16;
  int i, j;
  tran_low_t out[4][16], tmp[4][16], outtmp[4];
  tran_low_t *outp = &out[0][0];
  int outstride = n4;

#if CONFIG_LGT
  const tran_high_t *lgtmtx_row[1];
  int use_lgt_row = get_lgt4(txfm_param, 0, lgtmtx_row);
#endif

  // inverse transform row vectors and transpose
  for (i = 0; i < n4; ++i) {
#if CONFIG_LGT
    if (use_lgt_row)
      ilgt4(input, outtmp, lgtmtx_row[0]);
    else
#endif
      IHT_4x16[tx_type].rows(input, outtmp);
    for (j = 0; j < n; ++j) tmp[j][i] = outtmp[j];
    input += n;
  }

  // inverse transform column vectors
  for (i = 0; i < n; ++i) {
    IHT_4x16[tx_type].cols(tmp[i], out[i]);
  }

  maybe_flip_strides(&dest, &stride, &outp, &outstride, tx_type, n4, n);

  // Sum with the destination
  for (i = 0; i < n4; ++i) {
    for (j = 0; j < n; ++j) {
      int d = i * stride + j;
      int s = j * outstride + i;
      dest[d] = clip_pixel_add(dest[d], ROUND_POWER_OF_TWO(outp[s], 5));
    }
  }
}

void av1_iht16x4_64_add_c(const tran_low_t *input, uint8_t *dest, int stride,
                          const TxfmParam *txfm_param) {
  const TX_TYPE tx_type = txfm_param->tx_type;
#if CONFIG_MRC_TX
  assert(tx_type != MRC_DCT && "Invalid tx type for tx size");
#endif  // CONFIG_MRC_TX
#if CONFIG_DCT_ONLY
  assert(tx_type == DCT_DCT);
#endif
  static const transform_2d IHT_16x4[] = {
    { aom_idct4_c, aom_idct16_c },    // DCT_DCT
    { aom_iadst4_c, aom_idct16_c },   // ADST_DCT
    { aom_idct4_c, aom_iadst16_c },   // DCT_ADST
    { aom_iadst4_c, aom_iadst16_c },  // ADST_ADST
    { aom_iadst4_c, aom_idct16_c },   // FLIPADST_DCT
    { aom_idct4_c, aom_iadst16_c },   // DCT_FLIPADST
    { aom_iadst4_c, aom_iadst16_c },  // FLIPADST_FLIPADST
    { aom_iadst4_c, aom_iadst16_c },  // ADST_FLIPADST
    { aom_iadst4_c, aom_iadst16_c },  // FLIPADST_ADST
    { iidtx4_c, iidtx16_c },          // IDTX
    { aom_idct4_c, iidtx16_c },       // V_DCT
    { iidtx4_c, aom_idct16_c },       // H_DCT
    { aom_iadst4_c, iidtx16_c },      // V_ADST
    { iidtx4_c, aom_iadst16_c },      // H_ADST
    { aom_iadst4_c, iidtx16_c },      // V_FLIPADST
    { iidtx4_c, aom_iadst16_c },      // H_FLIPADST
  };

  const int n = 4;
  const int n4 = 16;

  int i, j;
  tran_low_t out[16][4], tmp[16][4], outtmp[16];
  tran_low_t *outp = &out[0][0];
  int outstride = n;

#if CONFIG_LGT
  const tran_high_t *lgtmtx_col[1];
  int use_lgt_col = get_lgt4(txfm_param, 1, lgtmtx_col);
#endif

  // inverse transform row vectors and transpose
  for (i = 0; i < n; ++i) {
    IHT_16x4[tx_type].rows(input, outtmp);
    for (j = 0; j < n4; ++j) tmp[j][i] = outtmp[j];
    input += n4;
  }

  // inverse transform column vectors
  for (i = 0; i < n4; ++i) {
#if CONFIG_LGT
    if (use_lgt_col)
      ilgt4(tmp[i], out[i], lgtmtx_col[0]);
    else
#endif
      IHT_16x4[tx_type].cols(tmp[i], out[i]);
  }

  maybe_flip_strides(&dest, &stride, &outp, &outstride, tx_type, n, n4);

  // Sum with the destination
  for (i = 0; i < n; ++i) {
    for (j = 0; j < n4; ++j) {
      int d = i * stride + j;
      int s = j * outstride + i;
      dest[d] = clip_pixel_add(dest[d], ROUND_POWER_OF_TWO(outp[s], 5));
    }
  }
}

void av1_iht8x16_128_add_c(const tran_low_t *input, uint8_t *dest, int stride,
                           const TxfmParam *txfm_param) {
  const TX_TYPE tx_type = txfm_param->tx_type;
#if CONFIG_MRC_TX
  assert(tx_type != MRC_DCT && "Invalid tx type for tx size");
#endif  // CONFIG_MRC_TX
#if CONFIG_DCT_ONLY
  assert(tx_type == DCT_DCT);
#endif
  static const transform_2d IHT_8x16[] = {
#if CONFIG_DAALA_TX8 && CONFIG_DAALA_TX16
    { daala_idct16, daala_idct8 },  // DCT_DCT  = 0
    { daala_idst16, daala_idct8 },  // ADST_DCT = 1
    { daala_idct16, daala_idst8 },  // DCT_ADST = 2
    { daala_idst16, daala_idst8 },  // ADST_ADST = 3
    { daala_idst16, daala_idct8 },  // FLIPADST_DCT
    { daala_idct16, daala_idst8 },  // DCT_FLIPADST
    { daala_idst16, daala_idst8 },  // FLIPADST_FLIPADST
    { daala_idst16, daala_idst8 },  // ADST_FLIPADST
    { daala_idst16, daala_idst8 },  // FLIPADST_ADST
    { daala_idtx16, daala_idtx8 },  // IDTX
    { daala_idct16, daala_idtx8 },  // V_DCT
    { daala_idtx16, daala_idct8 },  // H_DCT
    { daala_idst16, daala_idtx8 },  // V_ADST
    { daala_idtx16, daala_idst8 },  // H_ADST
    { daala_idst16, daala_idtx8 },  // V_FLIPADST
    { daala_idtx16, daala_idst8 },  // H_FLIPADST
#else
    { aom_idct16_c, aom_idct8_c },    // DCT_DCT
    { aom_iadst16_c, aom_idct8_c },   // ADST_DCT
    { aom_idct16_c, aom_iadst8_c },   // DCT_ADST
    { aom_iadst16_c, aom_iadst8_c },  // ADST_ADST
    { aom_iadst16_c, aom_idct8_c },   // FLIPADST_DCT
    { aom_idct16_c, aom_iadst8_c },   // DCT_FLIPADST
    { aom_iadst16_c, aom_iadst8_c },  // FLIPADST_FLIPADST
    { aom_iadst16_c, aom_iadst8_c },  // ADST_FLIPADST
    { aom_iadst16_c, aom_iadst8_c },  // FLIPADST_ADST
    { iidtx16_c, iidtx8_c },          // IDTX
    { aom_idct16_c, iidtx8_c },       // V_DCT
    { iidtx16_c, aom_idct8_c },       // H_DCT
    { aom_iadst16_c, iidtx8_c },      // V_ADST
    { iidtx16_c, aom_iadst8_c },      // H_ADST
    { aom_iadst16_c, iidtx8_c },      // V_FLIPADST
    { iidtx16_c, aom_iadst8_c },      // H_FLIPADST
#endif
  };

  const int n = 8;
  const int n2 = 16;
  int i, j;
  tran_low_t out[8][16], tmp[8][16], outtmp[8];
  tran_low_t *outp = &out[0][0];
  int outstride = n2;

#if CONFIG_LGT
  const tran_high_t *lgtmtx_row[1];
  int use_lgt_row = get_lgt8(txfm_param, 0, lgtmtx_row);
#endif

  // Multi-way scaling matrix (bits):
  // LGT/AV1 row, AV1 col  input+0, rowTX+1, mid+.5, colTX+1.5, out-6 == -3
  // LGT row, Daala col    input+0, rowTX+1, mid+0,  colTX+0,   out-4 == -3
  // Daala row, LGT col    N/A (no 16-point LGT)
  // Daala row,col         input+1, rowTX+0, mid+0,  colTX+0,   out-4 == -3

  // inverse transform row vectors and transpose
  for (i = 0; i < n2; ++i) {
#if CONFIG_LGT
    if (use_lgt_row) {
      // Scaling cases 1 and 2 above
      // No input scaling
      // Row transform (LGT; scales up 1 bit)
      ilgt8(input, outtmp, lgtmtx_row[0]);
      // Transpose and mid scaling
      for (j = 0; j < n; ++j) {
#if CONFIG_DAALA_TX8 && CONFIG_DAALA_TX16
        // Mid scaling case 2
        tmp[j][i] = outtmp[j];
#else
        // Mid scaling case 1
        tmp[j][i] = (tran_low_t)dct_const_round_shift(outtmp[j] * Sqrt2);
#endif
      }
    } else {
#endif
#if CONFIG_DAALA_TX8 && CONFIG_DAALA_TX16
      tran_low_t temp_in[8];
      // Input scaling case 4
      for (j = 0; j < n; j++) temp_in[j] = input[j] * 2;
      // Row transform (Daala does not scale)
      IHT_8x16[tx_type].rows(temp_in, outtmp);
      // Transpose (no mid scaling)
      for (j = 0; j < n; ++j) tmp[j][i] = outtmp[j];
#else
    // Case 1; no input scaling
    // Row transform (AV1 scales up 1 bit)
    IHT_8x16[tx_type].rows(input, outtmp);
    // Transpose and mid scaling up .5 bits
    for (j = 0; j < n; ++j)
      tmp[j][i] = (tran_low_t)dct_const_round_shift(outtmp[j] * Sqrt2);
#endif
#if CONFIG_LGT
    }
#endif
    input += n;
  }

  // inverse transform column vectors
  // AV1 column TX scales up by 1.5 bit, Daala does not scale
  for (i = 0; i < n; ++i) {
    IHT_8x16[tx_type].cols(tmp[i], out[i]);
  }

  maybe_flip_strides(&dest, &stride, &outp, &outstride, tx_type, n2, n);

  // Sum with the destination
  for (i = 0; i < n2; ++i) {
    for (j = 0; j < n; ++j) {
      int d = i * stride + j;
      int s = j * outstride + i;
#if CONFIG_DAALA_TX8 && CONFIG_DAALA_TX16
      // Output scaling cases 2 and 4
      dest[d] = clip_pixel_add(dest[d], ROUND_POWER_OF_TWO(outp[s], 4));
#else
      // Output scaling case 1
      dest[d] = clip_pixel_add(dest[d], ROUND_POWER_OF_TWO(outp[s], 6));
#endif
    }
  }
}

void av1_iht16x8_128_add_c(const tran_low_t *input, uint8_t *dest, int stride,
                           const TxfmParam *txfm_param) {
  const TX_TYPE tx_type = txfm_param->tx_type;
#if CONFIG_MRC_TX
  assert(tx_type != MRC_DCT && "Invalid tx type for tx size");
#endif  // CONFIG_MRC_TX
#if CONFIG_DCT_ONLY
  assert(tx_type == DCT_DCT);
#endif
  static const transform_2d IHT_16x8[] = {
#if CONFIG_DAALA_TX8 && CONFIG_DAALA_TX16
    { daala_idct8, daala_idct16 },  // DCT_DCT  = 0
    { daala_idst8, daala_idct16 },  // ADST_DCT = 1
    { daala_idct8, daala_idst16 },  // DCT_ADST = 2
    { daala_idst8, daala_idst16 },  // ADST_ADST = 3
    { daala_idst8, daala_idct16 },  // FLIPADST_DCT
    { daala_idct8, daala_idst16 },  // DCT_FLIPADST
    { daala_idst8, daala_idst16 },  // FLIPADST_FLIPADST
    { daala_idst8, daala_idst16 },  // ADST_FLIPADST
    { daala_idst8, daala_idst16 },  // FLIPADST_ADST
    { daala_idtx8, daala_idtx16 },  // IDTX
    { daala_idct8, daala_idtx16 },  // V_DCT
    { daala_idtx8, daala_idct16 },  // H_DCT
    { daala_idst8, daala_idtx16 },  // V_ADST
    { daala_idtx8, daala_idst16 },  // H_ADST
    { daala_idst8, daala_idtx16 },  // V_FLIPADST
    { daala_idtx8, daala_idst16 },  // H_FLIPADST
#else
    { aom_idct8_c, aom_idct16_c },    // DCT_DCT
    { aom_iadst8_c, aom_idct16_c },   // ADST_DCT
    { aom_idct8_c, aom_iadst16_c },   // DCT_ADST
    { aom_iadst8_c, aom_iadst16_c },  // ADST_ADST
    { aom_iadst8_c, aom_idct16_c },   // FLIPADST_DCT
    { aom_idct8_c, aom_iadst16_c },   // DCT_FLIPADST
    { aom_iadst8_c, aom_iadst16_c },  // FLIPADST_FLIPADST
    { aom_iadst8_c, aom_iadst16_c },  // ADST_FLIPADST
    { aom_iadst8_c, aom_iadst16_c },  // FLIPADST_ADST
    { iidtx8_c, iidtx16_c },          // IDTX
    { aom_idct8_c, iidtx16_c },       // V_DCT
    { iidtx8_c, aom_idct16_c },       // H_DCT
    { aom_iadst8_c, iidtx16_c },      // V_ADST
    { iidtx8_c, aom_iadst16_c },      // H_ADST
    { aom_iadst8_c, iidtx16_c },      // V_FLIPADST
    { iidtx8_c, aom_iadst16_c },      // H_FLIPADST
#endif
  };

  const int n = 8;
  const int n2 = 16;

  int i, j;
  tran_low_t out[16][8], tmp[16][8], outtmp[16];
  tran_low_t *outp = &out[0][0];
  int outstride = n;

#if CONFIG_LGT
  const tran_high_t *lgtmtx_col[1];
  int use_lgt_col = get_lgt8(txfm_param, 1, lgtmtx_col);
#endif

  // Multi-way scaling matrix (bits):
  // AV1 row, LGT/AV1 col  input+0, rowTX+1.5, mid+.5, colTX+1, out-6 == -3
  // LGT row, Daala col    N/A (no 16-point LGT)
  // Daala row, LGT col    input+1, rowTX+0,   mid+1,  colTX+1, out-6 == -3
  // Daala row, col        input+1, rowTX+0,   mid+0,  colTX+0, out-4 == -3

  // inverse transform row vectors and transpose
  for (i = 0; i < n; ++i) {
#if CONFIG_DAALA_TX8 && CONFIG_DAALA_TX16
    tran_low_t temp_in[16];
    // Input scaling cases 3 and 4
    for (j = 0; j < n2; j++) temp_in[j] = input[j] * 2;
    // Daala row TX, no scaling