vp9_idct.c

/*
 *  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 <math.h>

#include "./vp9_rtcd.h"
#include "vp9/common/vp9_systemdependent.h"
#include "vp9/common/vp9_blockd.h"
#include "vp9/common/vp9_idct.h"

#if CONFIG_EMULATE_HARDWARE
// When CONFIG_EMULATE_HARDWARE is 1 the transform performs a
// non-normative method to handle overflows. A stream that causes
// overflows  in the inverse transform is considered invalid in VP9,
// and a hardware implementer is free to choose any reasonable
// method to handle overflows. However to aid in hardware
// verification they can use a specific implementation of the
// WRAPLOW() macro below that is identical to their intended
// hardware implementation (and also use configure options to trigger
// the C-implementation of the transform).
//
// The particular WRAPLOW implementation below performs strict
// overflow wrapping to match common hardware implementations.
// bd of 8 uses trans_low with 16bits, need to remove 16bits
// bd of 10 uses trans_low with 18bits, need to remove 14bits
// bd of 12 uses trans_low with 20bits, need to remove 12bits
// bd of x uses trans_low with 8+x bits, need to remove 24-x bits
#define WRAPLOW(x, bd) ((((int32_t)(x)) << (24 - bd)) >> (24 - bd))
#else
#define WRAPLOW(x, bd) (x)
#endif  // CONFIG_EMULATE_HARDWARE

#if CONFIG_VP9_HIGHBITDEPTH
static INLINE uint16_t highbd_clip_pixel_add(uint16_t dest, tran_high_t trans,
                                             int bd) {
  trans = WRAPLOW(trans, bd);
  return clip_pixel_highbd(WRAPLOW(dest + trans, bd), bd);
}
#endif  // CONFIG_VP9_HIGHBITDEPTH

static INLINE uint8_t clip_pixel_add(uint8_t dest, tran_high_t trans) {
  trans = WRAPLOW(trans, 8);
  return clip_pixel(WRAPLOW(dest + trans, 8));
}

void vp9_iwht4x4_16_add_c(const tran_low_t *input, uint8_t *dest, int stride) {
/* 4-point reversible, orthonormal inverse Walsh-Hadamard in 3.5 adds,
   0.5 shifts per pixel. */
  int i;
  tran_low_t output[16];
  tran_high_t a1, b1, c1, d1, e1;
  const tran_low_t *ip = input;
  tran_low_t *op = output;

  for (i = 0; i < 4; i++) {
    a1 = ip[0] >> UNIT_QUANT_SHIFT;
    c1 = ip[1] >> UNIT_QUANT_SHIFT;
    d1 = ip[2] >> UNIT_QUANT_SHIFT;
    b1 = ip[3] >> UNIT_QUANT_SHIFT;
    a1 += c1;
    d1 -= b1;
    e1 = (a1 - d1) >> 1;
    b1 = e1 - b1;
    c1 = e1 - c1;
    a1 -= b1;
    d1 += c1;
    op[0] = WRAPLOW(a1, 8);
    op[1] = WRAPLOW(b1, 8);
    op[2] = WRAPLOW(c1, 8);
    op[3] = WRAPLOW(d1, 8);
    ip += 4;
    op += 4;
  }

  ip = output;
  for (i = 0; i < 4; i++) {
    a1 = ip[4 * 0];
    c1 = ip[4 * 1];
    d1 = ip[4 * 2];
    b1 = ip[4 * 3];
    a1 += c1;
    d1 -= b1;
    e1 = (a1 - d1) >> 1;
    b1 = e1 - b1;
    c1 = e1 - c1;
    a1 -= b1;
    d1 += c1;
    dest[stride * 0] = clip_pixel_add(dest[stride * 0], a1);
    dest[stride * 1] = clip_pixel_add(dest[stride * 1], b1);
    dest[stride * 2] = clip_pixel_add(dest[stride * 2], c1);
    dest[stride * 3] = clip_pixel_add(dest[stride * 3], d1);

    ip++;
    dest++;
  }
}

void vp9_iwht4x4_1_add_c(const tran_low_t *in, uint8_t *dest, int dest_stride) {
  int i;
  tran_high_t a1, e1;
  tran_low_t tmp[4];
  const tran_low_t *ip = in;
  tran_low_t *op = tmp;

  a1 = ip[0] >> UNIT_QUANT_SHIFT;
  e1 = a1 >> 1;
  a1 -= e1;
  op[0] = WRAPLOW(a1, 8);
  op[1] = op[2] = op[3] = WRAPLOW(e1, 8);

  ip = tmp;
  for (i = 0; i < 4; i++) {
    e1 = ip[0] >> 1;
    a1 = ip[0] - e1;
    dest[dest_stride * 0] = clip_pixel_add(dest[dest_stride * 0], a1);
    dest[dest_stride * 1] = clip_pixel_add(dest[dest_stride * 1], e1);
    dest[dest_stride * 2] = clip_pixel_add(dest[dest_stride * 2], e1);
    dest[dest_stride * 3] = clip_pixel_add(dest[dest_stride * 3], e1);
    ip++;
    dest++;
  }
}

static void idct4(const tran_low_t *input, tran_low_t *output) {
  tran_low_t step[4];
  tran_high_t temp1, temp2;
  // stage 1
  temp1 = (input[0] + input[2]) * cospi_16_64;
  temp2 = (input[0] - input[2]) * cospi_16_64;
  step[0] = WRAPLOW(dct_const_round_shift(temp1), 8);
  step[1] = WRAPLOW(dct_const_round_shift(temp2), 8);
  temp1 = input[1] * cospi_24_64 - input[3] * cospi_8_64;
  temp2 = input[1] * cospi_8_64 + input[3] * cospi_24_64;
  step[2] = WRAPLOW(dct_const_round_shift(temp1), 8);
  step[3] = WRAPLOW(dct_const_round_shift(temp2), 8);

  // stage 2
  output[0] = WRAPLOW(step[0] + step[3], 8);
  output[1] = WRAPLOW(step[1] + step[2], 8);
  output[2] = WRAPLOW(step[1] - step[2], 8);
  output[3] = WRAPLOW(step[0] - step[3], 8);
}

void vp9_idct4x4_16_add_c(const tran_low_t *input, uint8_t *dest, int stride) {
  tran_low_t out[4 * 4];
  tran_low_t *outptr = out;
  int i, j;
  tran_low_t temp_in[4], temp_out[4];

  // Rows
  for (i = 0; i < 4; ++i) {
    idct4(input, outptr);
    input += 4;
    outptr += 4;
  }

  // Columns
  for (i = 0; i < 4; ++i) {
    for (j = 0; j < 4; ++j)
      temp_in[j] = out[j * 4 + i];
    idct4(temp_in, temp_out);
    for (j = 0; j < 4; ++j) {
      dest[j * stride + i] = clip_pixel_add(dest[j * stride + i],
                                            ROUND_POWER_OF_TWO(temp_out[j], 4));
    }
  }
}

void vp9_idct4x4_1_add_c(const tran_low_t *input, uint8_t *dest,
                         int dest_stride) {
  int i;
  tran_high_t a1;
  tran_low_t out = WRAPLOW(dct_const_round_shift(input[0] * cospi_16_64), 8);
  out = WRAPLOW(dct_const_round_shift(out * cospi_16_64), 8);
  a1 = ROUND_POWER_OF_TWO(out, 4);

  for (i = 0; i < 4; i++) {
    dest[0] = clip_pixel_add(dest[0], a1);
    dest[1] = clip_pixel_add(dest[1], a1);
    dest[2] = clip_pixel_add(dest[2], a1);
    dest[3] = clip_pixel_add(dest[3], a1);
    dest += dest_stride;
  }
}

static void idct8(const tran_low_t *input, tran_low_t *output) {
  tran_low_t step1[8], step2[8];
  tran_high_t temp1, temp2;
  // stage 1
  step1[0] = input[0];
  step1[2] = input[4];
  step1[1] = input[2];
  step1[3] = input[6];
  temp1 = input[1] * cospi_28_64 - input[7] * cospi_4_64;
  temp2 = input[1] * cospi_4_64 + input[7] * cospi_28_64;
  step1[4] = WRAPLOW(dct_const_round_shift(temp1), 8);
  step1[7] = WRAPLOW(dct_const_round_shift(temp2), 8);
  temp1 = input[5] * cospi_12_64 - input[3] * cospi_20_64;
  temp2 = input[5] * cospi_20_64 + input[3] * cospi_12_64;
  step1[5] = WRAPLOW(dct_const_round_shift(temp1), 8);
  step1[6] = WRAPLOW(dct_const_round_shift(temp2), 8);

  // stage 2 & stage 3 - even half
  idct4(step1, step1);

  // stage 2 - odd half
  step2[4] = WRAPLOW(step1[4] + step1[5], 8);
  step2[5] = WRAPLOW(step1[4] - step1[5], 8);
  step2[6] = WRAPLOW(-step1[6] + step1[7], 8);
  step2[7] = WRAPLOW(step1[6] + step1[7], 8);

  // stage 3 -odd half
  step1[4] = step2[4];
  temp1 = (step2[6] - step2[5]) * cospi_16_64;
  temp2 = (step2[5] + step2[6]) * cospi_16_64;
  step1[5] = WRAPLOW(dct_const_round_shift(temp1), 8);
  step1[6] = WRAPLOW(dct_const_round_shift(temp2), 8);
  step1[7] = step2[7];

  // stage 4
  output[0] = WRAPLOW(step1[0] + step1[7], 8);
  output[1] = WRAPLOW(step1[1] + step1[6], 8);
  output[2] = WRAPLOW(step1[2] + step1[5], 8);
  output[3] = WRAPLOW(step1[3] + step1[4], 8);
  output[4] = WRAPLOW(step1[3] - step1[4], 8);
  output[5] = WRAPLOW(step1[2] - step1[5], 8);
  output[6] = WRAPLOW(step1[1] - step1[6], 8);
  output[7] = WRAPLOW(step1[0] - step1[7], 8);
}

void vp9_idct8x8_64_add_c(const tran_low_t *input, uint8_t *dest, int stride) {
  tran_low_t out[8 * 8];
  tran_low_t *outptr = out;
  int i, j;
  tran_low_t temp_in[8], temp_out[8];

  // First transform rows
  for (i = 0; i < 8; ++i) {
    idct8(input, outptr);
    input += 8;
    outptr += 8;
  }

  // Then transform columns
  for (i = 0; i < 8; ++i) {
    for (j = 0; j < 8; ++j)
      temp_in[j] = out[j * 8 + i];
    idct8(temp_in, temp_out);
    for (j = 0; j < 8; ++j) {
      dest[j * stride + i] = clip_pixel_add(dest[j * stride + i],
                                            ROUND_POWER_OF_TWO(temp_out[j], 5));
    }
  }
}

void vp9_idct8x8_1_add_c(const tran_low_t *input, uint8_t *dest, int stride) {
  int i, j;
  tran_high_t a1;
  tran_low_t out = WRAPLOW(dct_const_round_shift(input[0] * cospi_16_64), 8);
  out = WRAPLOW(dct_const_round_shift(out * cospi_16_64), 8);
  a1 = ROUND_POWER_OF_TWO(out, 5);
  for (j = 0; j < 8; ++j) {
    for (i = 0; i < 8; ++i)
      dest[i] = clip_pixel_add(dest[i], a1);
    dest += stride;
  }
}

static void iadst4(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[0];
  tran_high_t x1 = input[1];
  tran_high_t x2 = input[2];
  tran_high_t 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_2_9 * x0;
  s2 = sinpi_3_9 * x1;
  s3 = sinpi_4_9 * x2;
  s4 = sinpi_1_9 * x2;
  s5 = sinpi_2_9 * x3;
  s6 = sinpi_4_9 * x3;
  s7 = x0 - x2 + x3;

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

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

  // 1-D transform scaling factor is sqrt(2).
  // The overall dynamic range is 14b (input) + 14b (multiplication scaling)
  // + 1b (addition) = 29b.
  // Hence the output bit depth is 15b.
  output[0] = WRAPLOW(dct_const_round_shift(s0), 8);
  output[1] = WRAPLOW(dct_const_round_shift(s1), 8);
  output[2] = WRAPLOW(dct_const_round_shift(s2), 8);
  output[3] = WRAPLOW(dct_const_round_shift(s3), 8);
}

void vp9_iht4x4_16_add_c(const tran_low_t *input, uint8_t *dest, int stride,
                         int tx_type) {
  const transform_2d IHT_4[] = {
    { idct4, idct4  },  // DCT_DCT  = 0
    { iadst4, idct4  },   // ADST_DCT = 1
    { idct4, iadst4 },    // DCT_ADST = 2
    { iadst4, iadst4 }      // ADST_ADST = 3
  };

  int i, j;
  tran_low_t out[4 * 4];
  tran_low_t *outptr = out;
  tran_low_t temp_in[4], temp_out[4];

  // inverse transform row vectors
  for (i = 0; i < 4; ++i) {
    IHT_4[tx_type].rows(input, outptr);
    input  += 4;
    outptr += 4;
  }

  // inverse transform column vectors
  for (i = 0; i < 4; ++i) {
    for (j = 0; j < 4; ++j)
      temp_in[j] = out[j * 4 + i];
    IHT_4[tx_type].cols(temp_in, temp_out);
    for (j = 0; j < 4; ++j) {
      dest[j * stride + i] = clip_pixel_add(dest[j * stride + i],
                                            ROUND_POWER_OF_TWO(temp_out[j], 4));
    }
  }
}

static void iadst8(const tran_low_t *input, tran_low_t *output) {
  int 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];

  if (!(x0 | x1 | x2 | x3 | x4 | x5 | x6 | x7)) {
    output[0] = output[1] = output[2] = output[3] = output[4]
              = output[5] = output[6] = output[7] = 0;
    return;
  }

  // stage 1
  s0 = cospi_2_64  * x0 + cospi_30_64 * x1;
  s1 = cospi_30_64 * x0 - cospi_2_64  * x1;
  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;
  s6 = cospi_26_64 * x6 + cospi_6_64  * x7;
  s7 = cospi_6_64  * x6 - cospi_26_64 * x7;

  x0 = WRAPLOW(dct_const_round_shift(s0 + s4), 8);
  x1 = WRAPLOW(dct_const_round_shift(s1 + s5), 8);
  x2 = WRAPLOW(dct_const_round_shift(s2 + s6), 8);
  x3 = WRAPLOW(dct_const_round_shift(s3 + s7), 8);
  x4 = WRAPLOW(dct_const_round_shift(s0 - s4), 8);
  x5 = WRAPLOW(dct_const_round_shift(s1 - s5), 8);
  x6 = WRAPLOW(dct_const_round_shift(s2 - s6), 8);
  x7 = WRAPLOW(dct_const_round_shift(s3 - s7), 8);

  // stage 2
  s0 = x0;
  s1 = x1;
  s2 = x2;
  s3 = x3;
  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;

  x0 = WRAPLOW(s0 + s2, 8);
  x1 = WRAPLOW(s1 + s3, 8);
  x2 = WRAPLOW(s0 - s2, 8);
  x3 = WRAPLOW(s1 - s3, 8);
  x4 = WRAPLOW(dct_const_round_shift(s4 + s6), 8);
  x5 = WRAPLOW(dct_const_round_shift(s5 + s7), 8);
  x6 = WRAPLOW(dct_const_round_shift(s4 - s6), 8);
  x7 = WRAPLOW(dct_const_round_shift(s5 - s7), 8);

  // 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 = WRAPLOW(dct_const_round_shift(s2), 8);
  x3 = WRAPLOW(dct_const_round_shift(s3), 8);
  x6 = WRAPLOW(dct_const_round_shift(s6), 8);
  x7 = WRAPLOW(dct_const_round_shift(s7), 8);

  output[0] = WRAPLOW(x0, 8);
  output[1] = WRAPLOW(-x4, 8);
  output[2] = WRAPLOW(x6, 8);
  output[3] = WRAPLOW(-x2, 8);
  output[4] = WRAPLOW(x3, 8);
  output[5] = WRAPLOW(-x7, 8);
  output[6] = WRAPLOW(x5, 8);
  output[7] = WRAPLOW(-x1, 8);
}

static const transform_2d IHT_8[] = {
  { idct8,  idct8  },  // DCT_DCT  = 0
  { iadst8, idct8  },  // ADST_DCT = 1
  { idct8,  iadst8 },  // DCT_ADST = 2
  { iadst8, iadst8 }   // ADST_ADST = 3
};

void vp9_iht8x8_64_add_c(const tran_low_t *input, uint8_t *dest, int stride,
                         int tx_type) {
  int i, j;
  tran_low_t out[8 * 8];
  tran_low_t *outptr = out;
  tran_low_t temp_in[8], temp_out[8];
  const transform_2d ht = IHT_8[tx_type];

  // inverse transform row vectors
  for (i = 0; i < 8; ++i) {
    ht.rows(input, outptr);
    input += 8;
    outptr += 8;
  }

  // inverse transform column vectors
  for (i = 0; i < 8; ++i) {
    for (j = 0; j < 8; ++j)
      temp_in[j] = out[j * 8 + i];
    ht.cols(temp_in, temp_out);
    for (j = 0; j < 8; ++j) {
      dest[j * stride + i] = clip_pixel_add(dest[j * stride + i],
                                            ROUND_POWER_OF_TWO(temp_out[j], 5));
    }
  }
}

void vp9_idct8x8_12_add_c(const tran_low_t *input, uint8_t *dest, int stride) {
  tran_low_t out[8 * 8] = { 0 };
  tran_low_t *outptr = out;
  int i, j;
  tran_low_t temp_in[8], temp_out[8];

  // First transform rows
  // only first 4 row has non-zero coefs
  for (i = 0; i < 4; ++i) {
    idct8(input, outptr);
    input += 8;
    outptr += 8;
  }

  // Then transform columns
  for (i = 0; i < 8; ++i) {
    for (j = 0; j < 8; ++j)
      temp_in[j] = out[j * 8 + i];
    idct8(temp_in, temp_out);
    for (j = 0; j < 8; ++j) {
      dest[j * stride + i] = clip_pixel_add(dest[j * stride + i],
                                            ROUND_POWER_OF_TWO(temp_out[j], 5));
    }
  }
}

static void idct16(const tran_low_t *input, tran_low_t *output) {
  tran_low_t step1[16], step2[16];
  tran_high_t temp1, temp2;

  // stage 1
  step1[0] = input[0/2];
  step1[1] = input[16/2];
  step1[2] = input[8/2];
  step1[3] = input[24/2];
  step1[4] = input[4/2];
  step1[5] = input[20/2];
  step1[6] = input[12/2];
  step1[7] = input[28/2];
  step1[8] = input[2/2];
  step1[9] = input[18/2];
  step1[10] = input[10/2];
  step1[11] = input[26/2];
  step1[12] = input[6/2];
  step1[13] = input[22/2];
  step1[14] = input[14/2];
  step1[15] = input[30/2];

  // stage 2
  step2[0] = step1[0];
  step2[1] = step1[1];
  step2[2] = step1[2];
  step2[3] = step1[3];
  step2[4] = step1[4];
  step2[5] = step1[5];
  step2[6] = step1[6];
  step2[7] = step1[7];

  temp1 = step1[8] * cospi_30_64 - step1[15] * cospi_2_64;
  temp2 = step1[8] * cospi_2_64 + step1[15] * cospi_30_64;
  step2[8] = WRAPLOW(dct_const_round_shift(temp1), 8);
  step2[15] = WRAPLOW(dct_const_round_shift(temp2), 8);

  temp1 = step1[9] * cospi_14_64 - step1[14] * cospi_18_64;
  temp2 = step1[9] * cospi_18_64 + step1[14] * cospi_14_64;
  step2[9] = WRAPLOW(dct_const_round_shift(temp1), 8);
  step2[14] = WRAPLOW(dct_const_round_shift(temp2), 8);

  temp1 = step1[10] * cospi_22_64 - step1[13] * cospi_10_64;
  temp2 = step1[10] * cospi_10_64 + step1[13] * cospi_22_64;
  step2[10] = WRAPLOW(dct_const_round_shift(temp1), 8);
  step2[13] = WRAPLOW(dct_const_round_shift(temp2), 8);

  temp1 = step1[11] * cospi_6_64 - step1[12] * cospi_26_64;
  temp2 = step1[11] * cospi_26_64 + step1[12] * cospi_6_64;
  step2[11] = WRAPLOW(dct_const_round_shift(temp1), 8);
  step2[12] = WRAPLOW(dct_const_round_shift(temp2), 8);

  // stage 3
  step1[0] = step2[0];
  step1[1] = step2[1];
  step1[2] = step2[2];
  step1[3] = step2[3];

  temp1 = step2[4] * cospi_28_64 - step2[7] * cospi_4_64;
  temp2 = step2[4] * cospi_4_64 + step2[7] * cospi_28_64;
  step1[4] = WRAPLOW(dct_const_round_shift(temp1), 8);
  step1[7] = WRAPLOW(dct_const_round_shift(temp2), 8);
  temp1 = step2[5] * cospi_12_64 - step2[6] * cospi_20_64;
  temp2 = step2[5] * cospi_20_64 + step2[6] * cospi_12_64;
  step1[5] = WRAPLOW(dct_const_round_shift(temp1), 8);
  step1[6] = WRAPLOW(dct_const_round_shift(temp2), 8);

  step1[8] = WRAPLOW(step2[8] + step2[9], 8);
  step1[9] = WRAPLOW(step2[8] - step2[9], 8);
  step1[10] = WRAPLOW(-step2[10] + step2[11], 8);
  step1[11] = WRAPLOW(step2[10] + step2[11], 8);
  step1[12] = WRAPLOW(step2[12] + step2[13], 8);
  step1[13] = WRAPLOW(step2[12] - step2[13], 8);
  step1[14] = WRAPLOW(-step2[14] + step2[15], 8);
  step1[15] = WRAPLOW(step2[14] + step2[15], 8);

  // stage 4
  temp1 = (step1[0] + step1[1]) * cospi_16_64;
  temp2 = (step1[0] - step1[1]) * cospi_16_64;
  step2[0] = WRAPLOW(dct_const_round_shift(temp1), 8);
  step2[1] = WRAPLOW(dct_const_round_shift(temp2), 8);
  temp1 = step1[2] * cospi_24_64 - step1[3] * cospi_8_64;
  temp2 = step1[2] * cospi_8_64 + step1[3] * cospi_24_64;
  step2[2] = WRAPLOW(dct_const_round_shift(temp1), 8);
  step2[3] = WRAPLOW(dct_const_round_shift(temp2), 8);
  step2[4] = WRAPLOW(step1[4] + step1[5], 8);
  step2[5] = WRAPLOW(step1[4] - step1[5], 8);
  step2[6] = WRAPLOW(-step1[6] + step1[7], 8);
  step2[7] = WRAPLOW(step1[6] + step1[7], 8);

  step2[8] = step1[8];
  step2[15] = step1[15];
  temp1 = -step1[9] * cospi_8_64 + step1[14] * cospi_24_64;
  temp2 = step1[9] * cospi_24_64 + step1[14] * cospi_8_64;
  step2[9] = WRAPLOW(dct_const_round_shift(temp1), 8);
  step2[14] = WRAPLOW(dct_const_round_shift(temp2), 8);
  temp1 = -step1[10] * cospi_24_64 - step1[13] * cospi_8_64;
  temp2 = -step1[10] * cospi_8_64 + step1[13] * cospi_24_64;
  step2[10] = WRAPLOW(dct_const_round_shift(temp1), 8);
  step2[13] = WRAPLOW(dct_const_round_shift(temp2), 8);
  step2[11] = step1[11];
  step2[12] = step1[12];

  // stage 5
  step1[0] = WRAPLOW(step2[0] + step2[3], 8);
  step1[1] = WRAPLOW(step2[1] + step2[2], 8);
  step1[2] = WRAPLOW(step2[1] - step2[2], 8);
  step1[3] = WRAPLOW(step2[0] - step2[3], 8);
  step1[4] = step2[4];
  temp1 = (step2[6] - step2[5]) * cospi_16_64;
  temp2 = (step2[5] + step2[6]) * cospi_16_64;
  step1[5] = WRAPLOW(dct_const_round_shift(temp1), 8);
  step1[6] = WRAPLOW(dct_const_round_shift(temp2), 8);
  step1[7] = step2[7];

  step1[8] = WRAPLOW(step2[8] + step2[11], 8);
  step1[9] = WRAPLOW(step2[9] + step2[10], 8);
  step1[10] = WRAPLOW(step2[9] - step2[10], 8);
  step1[11] = WRAPLOW(step2[8] - step2[11], 8);
  step1[12] = WRAPLOW(-step2[12] + step2[15], 8);
  step1[13] = WRAPLOW(-step2[13] + step2[14], 8);
  step1[14] = WRAPLOW(step2[13] + step2[14], 8);
  step1[15] = WRAPLOW(step2[12] + step2[15], 8);

  // stage 6
  step2[0] = WRAPLOW(step1[0] + step1[7], 8);
  step2[1] = WRAPLOW(step1[1] + step1[6], 8);
  step2[2] = WRAPLOW(step1[2] + step1[5], 8);
  step2[3] = WRAPLOW(step1[3] + step1[4], 8);
  step2[4] = WRAPLOW(step1[3] - step1[4], 8);
  step2[5] = WRAPLOW(step1[2] - step1[5], 8);
  step2[6] = WRAPLOW(step1[1] - step1[6], 8);
  step2[7] = WRAPLOW(step1[0] - step1[7], 8);
  step2[8] = step1[8];
  step2[9] = step1[9];
  temp1 = (-step1[10] + step1[13]) * cospi_16_64;
  temp2 = (step1[10] + step1[13]) * cospi_16_64;
  step2[10] = WRAPLOW(dct_const_round_shift(temp1), 8);
  step2[13] = WRAPLOW(dct_const_round_shift(temp2), 8);
  temp1 = (-step1[11] + step1[12]) * cospi_16_64;
  temp2 = (step1[11] + step1[12]) * cospi_16_64;
  step2[11] = WRAPLOW(dct_const_round_shift(temp1), 8);
  step2[12] = WRAPLOW(dct_const_round_shift(temp2), 8);
  step2[14] = step1[14];
  step2[15] = step1[15];

  // stage 7
  output[0] = WRAPLOW(step2[0] + step2[15], 8);
  output[1] = WRAPLOW(step2[1] + step2[14], 8);
  output[2] = WRAPLOW(step2[2] + step2[13], 8);
  output[3] = WRAPLOW(step2[3] + step2[12], 8);
  output[4] = WRAPLOW(step2[4] + step2[11], 8);
  output[5] = WRAPLOW(step2[5] + step2[10], 8);
  output[6] = WRAPLOW(step2[6] + step2[9], 8);
  output[7] = WRAPLOW(step2[7] + step2[8], 8);
  output[8] = WRAPLOW(step2[7] - step2[8], 8);
  output[9] = WRAPLOW(step2[6] - step2[9], 8);
  output[10] = WRAPLOW(step2[5] - step2[10], 8);
  output[11] = WRAPLOW(step2[4] - step2[11], 8);
  output[12] = WRAPLOW(step2[3] - step2[12], 8);
  output[13] = WRAPLOW(step2[2] - step2[13], 8);
  output[14] = WRAPLOW(step2[1] - step2[14], 8);
  output[15] = WRAPLOW(step2[0] - step2[15], 8);
}

void vp9_idct16x16_256_add_c(const tran_low_t *input, uint8_t *dest,
                             int stride) {
  tran_low_t out[16 * 16];
  tran_low_t *outptr = out;
  int i, j;
  tran_low_t temp_in[16], temp_out[16];

  // First transform rows
  for (i = 0; i < 16; ++i) {
    idct16(input, outptr);
    input += 16;
    outptr += 16;
  }

  // Then transform columns
  for (i = 0; i < 16; ++i) {
    for (j = 0; j < 16; ++j)
      temp_in[j] = out[j * 16 + i];
    idct16(temp_in, temp_out);
    for (j = 0; j < 16; ++j) {
      dest[j * stride + i] = clip_pixel_add(dest[j * stride + i],
                                            ROUND_POWER_OF_TWO(temp_out[j], 6));
    }
  }
}

static void iadst16(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];

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

  // stage 1
  s0 = x0 * cospi_1_64  + x1 * cospi_31_64;
  s1 = x0 * cospi_31_64 - x1 * cospi_1_64;
  s2 = x2 * cospi_5_64  + x3 * cospi_27_64;
  s3 = x2 * cospi_27_64 - x3 * cospi_5_64;
  s4 = x4 * cospi_9_64  + x5 * cospi_23_64;
  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;
  s13 = x12 * cospi_7_64  - x13 * cospi_25_64;
  s14 = x14 * cospi_29_64 + x15 * cospi_3_64;
  s15 = x14 * cospi_3_64  - x15 * cospi_29_64;

  x0 = WRAPLOW(dct_const_round_shift(s0 + s8), 8);
  x1 = WRAPLOW(dct_const_round_shift(s1 + s9), 8);
  x2 = WRAPLOW(dct_const_round_shift(s2 + s10), 8);
  x3 = WRAPLOW(dct_const_round_shift(s3 + s11), 8);
  x4 = WRAPLOW(dct_const_round_shift(s4 + s12), 8);
  x5 = WRAPLOW(dct_const_round_shift(s5 + s13), 8);
  x6 = WRAPLOW(dct_const_round_shift(s6 + s14), 8);
  x7 = WRAPLOW(dct_const_round_shift(s7 + s15), 8);
  x8 = WRAPLOW(dct_const_round_shift(s0 - s8), 8);
  x9 = WRAPLOW(dct_const_round_shift(s1 - s9), 8);
  x10 = WRAPLOW(dct_const_round_shift(s2 - s10), 8);
  x11 = WRAPLOW(dct_const_round_shift(s3 - s11), 8);
  x12 = WRAPLOW(dct_const_round_shift(s4 - s12), 8);
  x13 = WRAPLOW(dct_const_round_shift(s5 - s13), 8);
  x14 = WRAPLOW(dct_const_round_shift(s6 - s14), 8);
  x15 = WRAPLOW(dct_const_round_shift(s7 - s15), 8);

  // stage 2
  s0 = x0;
  s1 = x1;
  s2 = x2;
  s3 = x3;
  s4 = x4;
  s5 = x5;
  s6 = x6;
  s7 = x7;
  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;

  x0 = WRAPLOW(s0 + s4, 8);
  x1 = WRAPLOW(s1 + s5, 8);
  x2 = WRAPLOW(s2 + s6, 8);
  x3 = WRAPLOW(s3 + s7, 8);
  x4 = WRAPLOW(s0 - s4, 8);
  x5 = WRAPLOW(s1 - s5, 8);
  x6 = WRAPLOW(s2 - s6, 8);
  x7 = WRAPLOW(s3 - s7, 8);
  x8 = WRAPLOW(dct_const_round_shift(s8 + s12), 8);
  x9 = WRAPLOW(dct_const_round_shift(s9 + s13), 8);
  x10 = WRAPLOW(dct_const_round_shift(s10 + s14), 8);
  x11 = WRAPLOW(dct_const_round_shift(s11 + s15), 8);
  x12 = WRAPLOW(dct_const_round_shift(s8 - s12), 8);
  x13 = WRAPLOW(dct_const_round_shift(s9 - s13), 8);
  x14 = WRAPLOW(dct_const_round_shift(s10 - s14), 8);
  x15 = WRAPLOW(dct_const_round_shift(s11 - s15), 8);

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

  x0 = WRAPLOW(check_range(s0 + s2), 8);
  x1 = WRAPLOW(check_range(s1 + s3), 8);
  x2 = WRAPLOW(check_range(s0 - s2), 8);
  x3 = WRAPLOW(check_range(s1 - s3), 8);
  x4 = WRAPLOW(dct_const_round_shift(s4 + s6), 8);
  x5 = WRAPLOW(dct_const_round_shift(s5 + s7), 8);
  x6 = WRAPLOW(dct_const_round_shift(s4 - s6), 8);
  x7 = WRAPLOW(dct_const_round_shift(s5 - s7), 8);
  x8 = WRAPLOW(check_range(s8 + s10), 8);
  x9 = WRAPLOW(check_range(s9 + s11), 8);
  x10 = WRAPLOW(check_range(s8 - s10), 8);
  x11 = WRAPLOW(check_range(s9 - s11), 8);
  x12 = WRAPLOW(dct_const_round_shift(s12 + s14), 8);
  x13 = WRAPLOW(dct_const_round_shift(s13 + s15), 8);
  x14 = WRAPLOW(dct_const_round_shift(s12 - s14), 8);
  x15 = WRAPLOW(dct_const_round_shift(s13 - s15), 8);

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

  x2 = WRAPLOW(dct_const_round_shift(s2), 8);
  x3 = WRAPLOW(dct_const_round_shift(s3), 8);
  x6 = WRAPLOW(dct_const_round_shift(s6), 8);
  x7 = WRAPLOW(dct_const_round_shift(s7), 8);
  x10 = WRAPLOW(dct_const_round_shift(s10), 8);
  x11 = WRAPLOW(dct_const_round_shift(s11), 8);
  x14 = WRAPLOW(dct_const_round_shift(s14), 8);
  x15 = WRAPLOW(dct_const_round_shift(s15), 8);

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

static const transform_2d IHT_16[] = {
  { idct16,  idct16  },  // DCT_DCT  = 0
  { iadst16, idct16  },  // ADST_DCT = 1
  { idct16,  iadst16 },  // DCT_ADST = 2
  { iadst16, iadst16 }   // ADST_ADST = 3
};

void vp9_iht16x16_256_add_c(const tran_low_t *input, uint8_t *dest, int stride,
                            int tx_type) {
  int i, j;
  tran_low_t out[16 * 16];
  tran_low_t *outptr = out;
  tran_low_t temp_in[16], temp_out[16];
  const transform_2d ht = IHT_16[tx_type];

  // Rows
  for (i = 0; i < 16; ++i) {
    ht.rows(input, outptr);
    input += 16;
    outptr += 16;
  }

  // Columns
  for (i = 0; i < 16; ++i) {
    for (j = 0; j < 16; ++j)
      temp_in[j] = out[j * 16 + i];
    ht.cols(temp_in, temp_out);
    for (j = 0; j < 16; ++j) {
      dest[j * stride + i] = clip_pixel_add(dest[j * stride + i],
                                            ROUND_POWER_OF_TWO(temp_out[j], 6));
    }
  }
}

void vp9_idct16x16_10_add_c(const tran_low_t *input, uint8_t *dest,
                            int stride) {
  tran_low_t out[16 * 16] = { 0 };
  tran_low_t *outptr = out;
  int i, j;
  tran_low_t temp_in[16], temp_out[16];

  // First transform rows. Since all non-zero dct coefficients are in
  // upper-left 4x4 area, we only need to calculate first 4 rows here.
  for (i = 0; i < 4; ++i) {
    idct16(input, outptr);
    input += 16;
    outptr += 16;
  }

  // Then transform columns
  for (i = 0; i < 16; ++i) {
    for (j = 0; j < 16; ++j)
      temp_in[j] = out[j*16 + i];
    idct16(temp_in, temp_out);
    for (j = 0; j < 16; ++j) {
      dest[j * stride + i] = clip_pixel_add(dest[j * stride + i],
                                            ROUND_POWER_OF_TWO(temp_out[j], 6));
    }
  }
}

void vp9_idct16x16_1_add_c(const tran_low_t *input, uint8_t *dest, int stride) {
  int i, j;
  tran_high_t a1;
  tran_low_t out = WRAPLOW(dct_const_round_shift(input[0] * cospi_16_64), 8);
  out = WRAPLOW(dct_const_round_shift(out * cospi_16_64), 8);
  a1 = ROUND_POWER_OF_TWO(out, 6);
  for (j = 0; j < 16; ++j) {
    for (i = 0; i < 16; ++i)
      dest[i] = clip_pixel_add(dest[i], a1);
    dest += stride;
  }
}

static void idct32(const tran_low_t *input, tran_low_t *output) {
  tran_low_t step1[32], step2[32];
  tran_high_t temp1, temp2;

  // stage 1
  step1[0] = input[0];
  step1[1] = input[16];
  step1[2] = input[8];
  step1[3] = input[24];
  step1[4] = input[4];
  step1[5] = input[20];
  step1[6] = input[12];
  step1[7] = input[28];
  step1[8] = input[2];
  step1[9] = input[18];
  step1[10] = input[10];
  step1[11] = input[26];
  step1[12] = input[6];
  step1[13] = input[22];
  step1[14] = input[14];
  step1[15] = input[30];

  temp1 = input[1] * cospi_31_64 - input[31] * cospi_1_64;
  temp2 = input[1] * cospi_1_64 + input[31] * cospi_31_64;
  step1[16] = WRAPLOW(dct_const_round_shift(temp1), 8);
  step1[31] = WRAPLOW(dct_const_round_shift(temp2), 8);

  temp1 = input[17] * cospi_15_64 - input[15] * cospi_17_64;
  temp2 = input[17] * cospi_17_64 + input[15] * cospi_15_64;
  step1[17] = WRAPLOW(dct_const_round_shift(temp1), 8);
  step1[30] = WRAPLOW(dct_const_round_shift(temp2), 8);

  temp1 = input[9] * cospi_23_64 - input[23] * cospi_9_64;
  temp2 = input[9] * cospi_9_64 + input[23] * cospi_23_64;
  step1[18] = WRAPLOW(dct_const_round_shift(temp1), 8);
  step1[29] = WRAPLOW(dct_const_round_shift(temp2), 8);

  temp1 = input[25] * cospi_7_64 - input[7] * cospi_25_64;
  temp2 = input[25] * cospi_25_64 + input[7] * cospi_7_64;
  step1[19] = WRAPLOW(dct_const_round_shift(temp1), 8);
  step1[28] = WRAPLOW(dct_const_round_shift(temp2), 8);

  temp1 = input[5] * cospi_27_64 - input[27] * cospi_5_64;
  temp2 = input[5] * cospi_5_64 + input[27] * cospi_27_64;
  step1[20] = WRAPLOW(dct_const_round_shift(temp1), 8);
  step1[27] = WRAPLOW(dct_const_round_shift(temp2), 8);

  temp1 = input[21] * cospi_11_64 - input[11] * cospi_21_64;
  temp2 = input[21] * cospi_21_64 + input[11] * cospi_11_64;
  step1[21] = WRAPLOW(dct_const_round_shift(temp1), 8);
  step1[26] = WRAPLOW(dct_const_round_shift(temp2), 8);

  temp1 = input[13] * cospi_19_64 - input[19] * cospi_13_64;
  temp2 = input[13] * cospi_13_64 + input[19] * cospi_19_64;
  step1[22] = WRAPLOW(dct_const_round_shift(temp1), 8);
  step1[25] = WRAPLOW(dct_const_round_shift(temp2), 8);

  temp1 = input[29] * cospi_3_64 - input[3] * cospi_29_64;
  temp2 = input[29] * cospi_29_64 + input[3] * cospi_3_64;
  step1[23] = WRAPLOW(dct_const_round_shift(temp1), 8);
  step1[24] = WRAPLOW(dct_const_round_shift(temp2), 8);

  // stage 2
  step2[0] = step1[0];
  step2[1] = step1[1];
  step2[2] = step1[2];
  step2[3] = step1[3];
  step2[4] = step1[4];
  step2[5] = step1[5];
  step2[6] = step1[6];
  step2[7] = step1[7];

  temp1 = step1[8] * cospi_30_64