Import aom library

This is the reference implementation for the Alliance for Open Media's av1 video code.

The commit used was 4d668d7feb1f8abd809d1bca0418570a7f142a36.

1 files changed, 809 insertions, 0 deletions

diff --git a/third_party/aom/aom_dsp/fwd_txfm.c b/third_party/aom/aom_dsp/fwd_txfm.c
new file mode 100644
index 000000000..12ee02ba1
--- /dev/null
+++ b/third_party/aom/aom_dsp/fwd_txfm.c
@@ -0,0 +1,809 @@
+/*
+ * 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 "aom_dsp/fwd_txfm.h"
+#include <assert.h>
+#include "./aom_dsp_rtcd.h"
+
+void aom_fdct4x4_c(const int16_t *input, tran_low_t *output, int stride) {
+  // The 2D transform is done with two passes which are actually pretty
+  // similar. In the first one, we transform the columns and transpose
+  // the results. In the second one, we transform the rows. To achieve that,
+  // as the first pass results are transposed, we transpose the columns (that
+  // is the transposed rows) and transpose the results (so that it goes back
+  // in normal/row positions).
+  int pass;
+  // We need an intermediate buffer between passes.
+  tran_low_t intermediate[4 * 4];
+  const tran_low_t *in_low = NULL;
+  tran_low_t *out = intermediate;
+  // Do the two transform/transpose passes
+  for (pass = 0; pass < 2; ++pass) {
+    tran_high_t in_high[4];    // canbe16
+    tran_high_t step[4];       // canbe16
+    tran_high_t temp1, temp2;  // needs32
+    int i;
+    for (i = 0; i < 4; ++i) {
+      // Load inputs.
+      if (pass == 0) {
+        in_high[0] = input[0 * stride] * 16;
+        in_high[1] = input[1 * stride] * 16;
+        in_high[2] = input[2 * stride] * 16;
+        in_high[3] = input[3 * stride] * 16;
+        if (i == 0 && in_high[0]) {
+          ++in_high[0];
+        }
+      } else {
+        assert(in_low != NULL);
+        in_high[0] = in_low[0 * 4];
+        in_high[1] = in_low[1 * 4];
+        in_high[2] = in_low[2 * 4];
+        in_high[3] = in_low[3 * 4];
+        ++in_low;
+      }
+      // Transform.
+      step[0] = in_high[0] + in_high[3];
+      step[1] = in_high[1] + in_high[2];
+      step[2] = in_high[1] - in_high[2];
+      step[3] = in_high[0] - in_high[3];
+      temp1 = (step[0] + step[1]) * cospi_16_64;
+      temp2 = (step[0] - step[1]) * cospi_16_64;
+      out[0] = (tran_low_t)fdct_round_shift(temp1);
+      out[2] = (tran_low_t)fdct_round_shift(temp2);
+      temp1 = step[2] * cospi_24_64 + step[3] * cospi_8_64;
+      temp2 = -step[2] * cospi_8_64 + step[3] * cospi_24_64;
+      out[1] = (tran_low_t)fdct_round_shift(temp1);
+      out[3] = (tran_low_t)fdct_round_shift(temp2);
+      // Do next column (which is a transposed row in second/horizontal pass)
+      ++input;
+      out += 4;
+    }
+    // Setup in/out for next pass.
+    in_low = intermediate;
+    out = output;
+  }
+
+  {
+    int i, j;
+    for (i = 0; i < 4; ++i) {
+      for (j = 0; j < 4; ++j) output[j + i * 4] = (output[j + i * 4] + 1) >> 2;
+    }
+  }
+}
+
+void aom_fdct4x4_1_c(const int16_t *input, tran_low_t *output, int stride) {
+  int r, c;
+  tran_low_t sum = 0;
+  for (r = 0; r < 4; ++r)
+    for (c = 0; c < 4; ++c) sum += input[r * stride + c];
+
+  output[0] = sum << 1;
+}
+
+void aom_fdct8x8_c(const int16_t *input, tran_low_t *final_output, int stride) {
+  int i, j;
+  tran_low_t intermediate[64];
+  int pass;
+  tran_low_t *output = intermediate;
+  const tran_low_t *in = NULL;
+
+  // Transform columns
+  for (pass = 0; pass < 2; ++pass) {
+    tran_high_t s0, s1, s2, s3, s4, s5, s6, s7;  // canbe16
+    tran_high_t t0, t1, t2, t3;                  // needs32
+    tran_high_t x0, x1, x2, x3;                  // canbe16
+
+    for (i = 0; i < 8; i++) {
+      // stage 1
+      if (pass == 0) {
+        s0 = (input[0 * stride] + input[7 * stride]) * 4;
+        s1 = (input[1 * stride] + input[6 * stride]) * 4;
+        s2 = (input[2 * stride] + input[5 * stride]) * 4;
+        s3 = (input[3 * stride] + input[4 * stride]) * 4;
+        s4 = (input[3 * stride] - input[4 * stride]) * 4;
+        s5 = (input[2 * stride] - input[5 * stride]) * 4;
+        s6 = (input[1 * stride] - input[6 * stride]) * 4;
+        s7 = (input[0 * stride] - input[7 * stride]) * 4;
+        ++input;
+      } else {
+        s0 = in[0 * 8] + in[7 * 8];
+        s1 = in[1 * 8] + in[6 * 8];
+        s2 = in[2 * 8] + in[5 * 8];
+        s3 = in[3 * 8] + in[4 * 8];
+        s4 = in[3 * 8] - in[4 * 8];
+        s5 = in[2 * 8] - in[5 * 8];
+        s6 = in[1 * 8] - in[6 * 8];
+        s7 = in[0 * 8] - in[7 * 8];
+        ++in;
+      }
+
+      // fdct4(step, step);
+      x0 = s0 + s3;
+      x1 = s1 + s2;
+      x2 = s1 - s2;
+      x3 = s0 - s3;
+      t0 = (x0 + x1) * cospi_16_64;
+      t1 = (x0 - x1) * cospi_16_64;
+      t2 = x2 * cospi_24_64 + x3 * cospi_8_64;
+      t3 = -x2 * cospi_8_64 + x3 * cospi_24_64;
+      output[0] = (tran_low_t)fdct_round_shift(t0);
+      output[2] = (tran_low_t)fdct_round_shift(t2);
+      output[4] = (tran_low_t)fdct_round_shift(t1);
+      output[6] = (tran_low_t)fdct_round_shift(t3);
+
+      // Stage 2
+      t0 = (s6 - s5) * cospi_16_64;
+      t1 = (s6 + s5) * cospi_16_64;
+      t2 = fdct_round_shift(t0);
+      t3 = fdct_round_shift(t1);
+
+      // Stage 3
+      x0 = s4 + t2;
+      x1 = s4 - t2;
+      x2 = s7 - t3;
+      x3 = s7 + t3;
+
+      // Stage 4
+      t0 = x0 * cospi_28_64 + x3 * cospi_4_64;
+      t1 = x1 * cospi_12_64 + x2 * cospi_20_64;
+      t2 = x2 * cospi_12_64 + x1 * -cospi_20_64;
+      t3 = x3 * cospi_28_64 + x0 * -cospi_4_64;
+      output[1] = (tran_low_t)fdct_round_shift(t0);
+      output[3] = (tran_low_t)fdct_round_shift(t2);
+      output[5] = (tran_low_t)fdct_round_shift(t1);
+      output[7] = (tran_low_t)fdct_round_shift(t3);
+      output += 8;
+    }
+    in = intermediate;
+    output = final_output;
+  }
+
+  // Rows
+  for (i = 0; i < 8; ++i) {
+    for (j = 0; j < 8; ++j) final_output[j + i * 8] /= 2;
+  }
+}
+
+void aom_fdct8x8_1_c(const int16_t *input, tran_low_t *output, int stride) {
+  int r, c;
+  tran_low_t sum = 0;
+  for (r = 0; r < 8; ++r)
+    for (c = 0; c < 8; ++c) sum += input[r * stride + c];
+
+  output[0] = sum;
+}
+
+void aom_fdct16x16_c(const int16_t *input, tran_low_t *output, int stride) {
+  // The 2D transform is done with two passes which are actually pretty
+  // similar. In the first one, we transform the columns and transpose
+  // the results. In the second one, we transform the rows. To achieve that,
+  // as the first pass results are transposed, we transpose the columns (that
+  // is the transposed rows) and transpose the results (so that it goes back
+  // in normal/row positions).
+  int pass;
+  // We need an intermediate buffer between passes.
+  tran_low_t intermediate[256];
+  const tran_low_t *in_low = NULL;
+  tran_low_t *out = intermediate;
+  // Do the two transform/transpose passes
+  for (pass = 0; pass < 2; ++pass) {
+    tran_high_t step1[8];      // canbe16
+    tran_high_t step2[8];      // canbe16
+    tran_high_t step3[8];      // canbe16
+    tran_high_t in_high[8];    // canbe16
+    tran_high_t temp1, temp2;  // needs32
+    int i;
+    for (i = 0; i < 16; i++) {
+      if (0 == pass) {
+        // Calculate input for the first 8 results.
+        in_high[0] = (input[0 * stride] + input[15 * stride]) * 4;
+        in_high[1] = (input[1 * stride] + input[14 * stride]) * 4;
+        in_high[2] = (input[2 * stride] + input[13 * stride]) * 4;
+        in_high[3] = (input[3 * stride] + input[12 * stride]) * 4;
+        in_high[4] = (input[4 * stride] + input[11 * stride]) * 4;
+        in_high[5] = (input[5 * stride] + input[10 * stride]) * 4;
+        in_high[6] = (input[6 * stride] + input[9 * stride]) * 4;
+        in_high[7] = (input[7 * stride] + input[8 * stride]) * 4;
+        // Calculate input for the next 8 results.
+        step1[0] = (input[7 * stride] - input[8 * stride]) * 4;
+        step1[1] = (input[6 * stride] - input[9 * stride]) * 4;
+        step1[2] = (input[5 * stride] - input[10 * stride]) * 4;
+        step1[3] = (input[4 * stride] - input[11 * stride]) * 4;
+        step1[4] = (input[3 * stride] - input[12 * stride]) * 4;
+        step1[5] = (input[2 * stride] - input[13 * stride]) * 4;
+        step1[6] = (input[1 * stride] - input[14 * stride]) * 4;
+        step1[7] = (input[0 * stride] - input[15 * stride]) * 4;
+      } else {
+        // Calculate input for the first 8 results.
+        assert(in_low != NULL);
+        in_high[0] = ((in_low[0 * 16] + 1) >> 2) + ((in_low[15 * 16] + 1) >> 2);
+        in_high[1] = ((in_low[1 * 16] + 1) >> 2) + ((in_low[14 * 16] + 1) >> 2);
+        in_high[2] = ((in_low[2 * 16] + 1) >> 2) + ((in_low[13 * 16] + 1) >> 2);
+        in_high[3] = ((in_low[3 * 16] + 1) >> 2) + ((in_low[12 * 16] + 1) >> 2);
+        in_high[4] = ((in_low[4 * 16] + 1) >> 2) + ((in_low[11 * 16] + 1) >> 2);
+        in_high[5] = ((in_low[5 * 16] + 1) >> 2) + ((in_low[10 * 16] + 1) >> 2);
+        in_high[6] = ((in_low[6 * 16] + 1) >> 2) + ((in_low[9 * 16] + 1) >> 2);
+        in_high[7] = ((in_low[7 * 16] + 1) >> 2) + ((in_low[8 * 16] + 1) >> 2);
+        // Calculate input for the next 8 results.
+        step1[0] = ((in_low[7 * 16] + 1) >> 2) - ((in_low[8 * 16] + 1) >> 2);
+        step1[1] = ((in_low[6 * 16] + 1) >> 2) - ((in_low[9 * 16] + 1) >> 2);
+        step1[2] = ((in_low[5 * 16] + 1) >> 2) - ((in_low[10 * 16] + 1) >> 2);
+        step1[3] = ((in_low[4 * 16] + 1) >> 2) - ((in_low[11 * 16] + 1) >> 2);
+        step1[4] = ((in_low[3 * 16] + 1) >> 2) - ((in_low[12 * 16] + 1) >> 2);
+        step1[5] = ((in_low[2 * 16] + 1) >> 2) - ((in_low[13 * 16] + 1) >> 2);
+        step1[6] = ((in_low[1 * 16] + 1) >> 2) - ((in_low[14 * 16] + 1) >> 2);
+        step1[7] = ((in_low[0 * 16] + 1) >> 2) - ((in_low[15 * 16] + 1) >> 2);
+        in_low++;
+      }
+      // Work on the first eight values; fdct8(input, even_results);
+      {
+        tran_high_t s0, s1, s2, s3, s4, s5, s6, s7;  // canbe16
+        tran_high_t t0, t1, t2, t3;                  // needs32
+        tran_high_t x0, x1, x2, x3;                  // canbe16
+
+        // stage 1
+        s0 = in_high[0] + in_high[7];
+        s1 = in_high[1] + in_high[6];
+        s2 = in_high[2] + in_high[5];
+        s3 = in_high[3] + in_high[4];
+        s4 = in_high[3] - in_high[4];
+        s5 = in_high[2] - in_high[5];
+        s6 = in_high[1] - in_high[6];
+        s7 = in_high[0] - in_high[7];
+
+        // fdct4(step, step);
+        x0 = s0 + s3;
+        x1 = s1 + s2;
+        x2 = s1 - s2;
+        x3 = s0 - s3;
+        t0 = (x0 + x1) * cospi_16_64;
+        t1 = (x0 - x1) * cospi_16_64;
+        t2 = x3 * cospi_8_64 + x2 * cospi_24_64;
+        t3 = x3 * cospi_24_64 - x2 * cospi_8_64;
+        out[0] = (tran_low_t)fdct_round_shift(t0);
+        out[4] = (tran_low_t)fdct_round_shift(t2);
+        out[8] = (tran_low_t)fdct_round_shift(t1);
+        out[12] = (tran_low_t)fdct_round_shift(t3);
+
+        // Stage 2
+        t0 = (s6 - s5) * cospi_16_64;
+        t1 = (s6 + s5) * cospi_16_64;
+        t2 = fdct_round_shift(t0);
+        t3 = fdct_round_shift(t1);
+
+        // Stage 3
+        x0 = s4 + t2;
+        x1 = s4 - t2;
+        x2 = s7 - t3;
+        x3 = s7 + t3;
+
+        // Stage 4
+        t0 = x0 * cospi_28_64 + x3 * cospi_4_64;
+        t1 = x1 * cospi_12_64 + x2 * cospi_20_64;
+        t2 = x2 * cospi_12_64 + x1 * -cospi_20_64;
+        t3 = x3 * cospi_28_64 + x0 * -cospi_4_64;
+        out[2] = (tran_low_t)fdct_round_shift(t0);
+        out[6] = (tran_low_t)fdct_round_shift(t2);
+        out[10] = (tran_low_t)fdct_round_shift(t1);
+        out[14] = (tran_low_t)fdct_round_shift(t3);
+      }
+      // Work on the next eight values; step1 -> odd_results
+      {
+        // step 2
+        temp1 = (step1[5] - step1[2]) * cospi_16_64;
+        temp2 = (step1[4] - step1[3]) * cospi_16_64;
+        step2[2] = fdct_round_shift(temp1);
+        step2[3] = fdct_round_shift(temp2);
+        temp1 = (step1[4] + step1[3]) * cospi_16_64;
+        temp2 = (step1[5] + step1[2]) * cospi_16_64;
+        step2[4] = fdct_round_shift(temp1);
+        step2[5] = fdct_round_shift(temp2);
+        // step 3
+        step3[0] = step1[0] + step2[3];
+        step3[1] = step1[1] + step2[2];
+        step3[2] = step1[1] - step2[2];
+        step3[3] = step1[0] - step2[3];
+        step3[4] = step1[7] - step2[4];
+        step3[5] = step1[6] - step2[5];
+        step3[6] = step1[6] + step2[5];
+        step3[7] = step1[7] + step2[4];
+        // step 4
+        temp1 = step3[1] * -cospi_8_64 + step3[6] * cospi_24_64;
+        temp2 = step3[2] * cospi_24_64 + step3[5] * cospi_8_64;
+        step2[1] = fdct_round_shift(temp1);
+        step2[2] = fdct_round_shift(temp2);
+        temp1 = step3[2] * cospi_8_64 - step3[5] * cospi_24_64;
+        temp2 = step3[1] * cospi_24_64 + step3[6] * cospi_8_64;
+        step2[5] = fdct_round_shift(temp1);
+        step2[6] = fdct_round_shift(temp2);
+        // step 5
+        step1[0] = step3[0] + step2[1];
+        step1[1] = step3[0] - step2[1];
+        step1[2] = step3[3] + step2[2];
+        step1[3] = step3[3] - step2[2];
+        step1[4] = step3[4] - step2[5];
+        step1[5] = step3[4] + step2[5];
+        step1[6] = step3[7] - step2[6];
+        step1[7] = step3[7] + step2[6];
+        // step 6
+        temp1 = step1[0] * cospi_30_64 + step1[7] * cospi_2_64;
+        temp2 = step1[1] * cospi_14_64 + step1[6] * cospi_18_64;
+        out[1] = (tran_low_t)fdct_round_shift(temp1);
+        out[9] = (tran_low_t)fdct_round_shift(temp2);
+        temp1 = step1[2] * cospi_22_64 + step1[5] * cospi_10_64;
+        temp2 = step1[3] * cospi_6_64 + step1[4] * cospi_26_64;
+        out[5] = (tran_low_t)fdct_round_shift(temp1);
+        out[13] = (tran_low_t)fdct_round_shift(temp2);
+        temp1 = step1[3] * -cospi_26_64 + step1[4] * cospi_6_64;
+        temp2 = step1[2] * -cospi_10_64 + step1[5] * cospi_22_64;
+        out[3] = (tran_low_t)fdct_round_shift(temp1);
+        out[11] = (tran_low_t)fdct_round_shift(temp2);
+        temp1 = step1[1] * -cospi_18_64 + step1[6] * cospi_14_64;
+        temp2 = step1[0] * -cospi_2_64 + step1[7] * cospi_30_64;
+        out[7] = (tran_low_t)fdct_round_shift(temp1);
+        out[15] = (tran_low_t)fdct_round_shift(temp2);
+      }
+      // Do next column (which is a transposed row in second/horizontal pass)
+      input++;
+      out += 16;
+    }
+    // Setup in/out for next pass.
+    in_low = intermediate;
+    out = output;
+  }
+}
+
+void aom_fdct16x16_1_c(const int16_t *input, tran_low_t *output, int stride) {
+  int r, c;
+  int sum = 0;
+  for (r = 0; r < 16; ++r)
+    for (c = 0; c < 16; ++c) sum += input[r * stride + c];
+
+  output[0] = (tran_low_t)(sum >> 1);
+}
+
+static INLINE tran_high_t dct_32_round(tran_high_t input) {
+  tran_high_t rv = ROUND_POWER_OF_TWO(input, DCT_CONST_BITS);
+  // TODO(debargha, peter.derivaz): Find new bounds for this assert,
+  // and make the bounds consts.
+  // assert(-131072 <= rv && rv <= 131071);
+  return rv;
+}
+
+static INLINE tran_high_t half_round_shift(tran_high_t input) {
+  tran_high_t rv = (input + 1 + (input < 0)) >> 2;
+  return rv;
+}
+
+void aom_fdct32(const tran_high_t *input, tran_high_t *output, int round) {
+  tran_high_t step[32];
+  // Stage 1
+  step[0] = input[0] + input[(32 - 1)];
+  step[1] = input[1] + input[(32 - 2)];
+  step[2] = input[2] + input[(32 - 3)];
+  step[3] = input[3] + input[(32 - 4)];
+  step[4] = input[4] + input[(32 - 5)];
+  step[5] = input[5] + input[(32 - 6)];
+  step[6] = input[6] + input[(32 - 7)];
+  step[7] = input[7] + input[(32 - 8)];
+  step[8] = input[8] + input[(32 - 9)];
+  step[9] = input[9] + input[(32 - 10)];
+  step[10] = input[10] + input[(32 - 11)];
+  step[11] = input[11] + input[(32 - 12)];
+  step[12] = input[12] + input[(32 - 13)];
+  step[13] = input[13] + input[(32 - 14)];
+  step[14] = input[14] + input[(32 - 15)];
+  step[15] = input[15] + input[(32 - 16)];
+  step[16] = -input[16] + input[(32 - 17)];
+  step[17] = -input[17] + input[(32 - 18)];
+  step[18] = -input[18] + input[(32 - 19)];
+  step[19] = -input[19] + input[(32 - 20)];
+  step[20] = -input[20] + input[(32 - 21)];
+  step[21] = -input[21] + input[(32 - 22)];
+  step[22] = -input[22] + input[(32 - 23)];
+  step[23] = -input[23] + input[(32 - 24)];
+  step[24] = -input[24] + input[(32 - 25)];
+  step[25] = -input[25] + input[(32 - 26)];
+  step[26] = -input[26] + input[(32 - 27)];
+  step[27] = -input[27] + input[(32 - 28)];
+  step[28] = -input[28] + input[(32 - 29)];
+  step[29] = -input[29] + input[(32 - 30)];
+  step[30] = -input[30] + input[(32 - 31)];
+  step[31] = -input[31] + input[(32 - 32)];
+
+  // Stage 2
+  output[0] = step[0] + step[16 - 1];
+  output[1] = step[1] + step[16 - 2];
+  output[2] = step[2] + step[16 - 3];
+  output[3] = step[3] + step[16 - 4];
+  output[4] = step[4] + step[16 - 5];
+  output[5] = step[5] + step[16 - 6];
+  output[6] = step[6] + step[16 - 7];
+  output[7] = step[7] + step[16 - 8];
+  output[8] = -step[8] + step[16 - 9];
+  output[9] = -step[9] + step[16 - 10];
+  output[10] = -step[10] + step[16 - 11];
+  output[11] = -step[11] + step[16 - 12];
+  output[12] = -step[12] + step[16 - 13];
+  output[13] = -step[13] + step[16 - 14];
+  output[14] = -step[14] + step[16 - 15];
+  output[15] = -step[15] + step[16 - 16];
+
+  output[16] = step[16];
+  output[17] = step[17];
+  output[18] = step[18];
+  output[19] = step[19];
+
+  output[20] = dct_32_round((-step[20] + step[27]) * cospi_16_64);
+  output[21] = dct_32_round((-step[21] + step[26]) * cospi_16_64);
+  output[22] = dct_32_round((-step[22] + step[25]) * cospi_16_64);
+  output[23] = dct_32_round((-step[23] + step[24]) * cospi_16_64);
+
+  output[24] = dct_32_round((step[24] + step[23]) * cospi_16_64);
+  output[25] = dct_32_round((step[25] + step[22]) * cospi_16_64);
+  output[26] = dct_32_round((step[26] + step[21]) * cospi_16_64);
+  output[27] = dct_32_round((step[27] + step[20]) * cospi_16_64);
+
+  output[28] = step[28];
+  output[29] = step[29];
+  output[30] = step[30];
+  output[31] = step[31];
+
+  // dump the magnitude by 4, hence the intermediate values are within
+  // the range of 16 bits.
+  if (round) {
+    output[0] = half_round_shift(output[0]);
+    output[1] = half_round_shift(output[1]);
+    output[2] = half_round_shift(output[2]);
+    output[3] = half_round_shift(output[3]);
+    output[4] = half_round_shift(output[4]);
+    output[5] = half_round_shift(output[5]);
+    output[6] = half_round_shift(output[6]);
+    output[7] = half_round_shift(output[7]);
+    output[8] = half_round_shift(output[8]);
+    output[9] = half_round_shift(output[9]);
+    output[10] = half_round_shift(output[10]);
+    output[11] = half_round_shift(output[11]);
+    output[12] = half_round_shift(output[12]);
+    output[13] = half_round_shift(output[13]);
+    output[14] = half_round_shift(output[14]);
+    output[15] = half_round_shift(output[15]);
+
+    output[16] = half_round_shift(output[16]);
+    output[17] = half_round_shift(output[17]);
+    output[18] = half_round_shift(output[18]);
+    output[19] = half_round_shift(output[19]);
+    output[20] = half_round_shift(output[20]);
+    output[21] = half_round_shift(output[21]);
+    output[22] = half_round_shift(output[22]);
+    output[23] = half_round_shift(output[23]);
+    output[24] = half_round_shift(output[24]);
+    output[25] = half_round_shift(output[25]);
+    output[26] = half_round_shift(output[26]);
+    output[27] = half_round_shift(output[27]);
+    output[28] = half_round_shift(output[28]);
+    output[29] = half_round_shift(output[29]);
+    output[30] = half_round_shift(output[30]);
+    output[31] = half_round_shift(output[31]);
+  }
+
+  // Stage 3
+  step[0] = output[0] + output[(8 - 1)];
+  step[1] = output[1] + output[(8 - 2)];
+  step[2] = output[2] + output[(8 - 3)];
+  step[3] = output[3] + output[(8 - 4)];
+  step[4] = -output[4] + output[(8 - 5)];
+  step[5] = -output[5] + output[(8 - 6)];
+  step[6] = -output[6] + output[(8 - 7)];
+  step[7] = -output[7] + output[(8 - 8)];
+  step[8] = output[8];
+  step[9] = output[9];
+  step[10] = dct_32_round((-output[10] + output[13]) * cospi_16_64);
+  step[11] = dct_32_round((-output[11] + output[12]) * cospi_16_64);
+  step[12] = dct_32_round((output[12] + output[11]) * cospi_16_64);
+  step[13] = dct_32_round((output[13] + output[10]) * cospi_16_64);
+  step[14] = output[14];
+  step[15] = output[15];
+
+  step[16] = output[16] + output[23];
+  step[17] = output[17] + output[22];
+  step[18] = output[18] + output[21];
+  step[19] = output[19] + output[20];
+  step[20] = -output[20] + output[19];
+  step[21] = -output[21] + output[18];
+  step[22] = -output[22] + output[17];
+  step[23] = -output[23] + output[16];
+  step[24] = -output[24] + output[31];
+  step[25] = -output[25] + output[30];
+  step[26] = -output[26] + output[29];
+  step[27] = -output[27] + output[28];
+  step[28] = output[28] + output[27];
+  step[29] = output[29] + output[26];
+  step[30] = output[30] + output[25];
+  step[31] = output[31] + output[24];
+
+  // Stage 4
+  output[0] = step[0] + step[3];
+  output[1] = step[1] + step[2];
+  output[2] = -step[2] + step[1];
+  output[3] = -step[3] + step[0];
+  output[4] = step[4];
+  output[5] = dct_32_round((-step[5] + step[6]) * cospi_16_64);
+  output[6] = dct_32_round((step[6] + step[5]) * cospi_16_64);
+  output[7] = step[7];
+  output[8] = step[8] + step[11];
+  output[9] = step[9] + step[10];
+  output[10] = -step[10] + step[9];
+  output[11] = -step[11] + step[8];
+  output[12] = -step[12] + step[15];
+  output[13] = -step[13] + step[14];
+  output[14] = step[14] + step[13];
+  output[15] = step[15] + step[12];
+
+  output[16] = step[16];
+  output[17] = step[17];
+  output[18] = dct_32_round(step[18] * -cospi_8_64 + step[29] * cospi_24_64);
+  output[19] = dct_32_round(step[19] * -cospi_8_64 + step[28] * cospi_24_64);
+  output[20] = dct_32_round(step[20] * -cospi_24_64 + step[27] * -cospi_8_64);
+  output[21] = dct_32_round(step[21] * -cospi_24_64 + step[26] * -cospi_8_64);
+  output[22] = step[22];
+  output[23] = step[23];
+  output[24] = step[24];
+  output[25] = step[25];
+  output[26] = dct_32_round(step[26] * cospi_24_64 + step[21] * -cospi_8_64);
+  output[27] = dct_32_round(step[27] * cospi_24_64 + step[20] * -cospi_8_64);
+  output[28] = dct_32_round(step[28] * cospi_8_64 + step[19] * cospi_24_64);
+  output[29] = dct_32_round(step[29] * cospi_8_64 + step[18] * cospi_24_64);
+  output[30] = step[30];
+  output[31] = step[31];
+
+  // Stage 5
+  step[0] = dct_32_round((output[0] + output[1]) * cospi_16_64);
+  step[1] = dct_32_round((-output[1] + output[0]) * cospi_16_64);
+  step[2] = dct_32_round(output[2] * cospi_24_64 + output[3] * cospi_8_64);
+  step[3] = dct_32_round(output[3] * cospi_24_64 - output[2] * cospi_8_64);
+  step[4] = output[4] + output[5];
+  step[5] = -output[5] + output[4];
+  step[6] = -output[6] + output[7];
+  step[7] = output[7] + output[6];
+  step[8] = output[8];
+  step[9] = dct_32_round(output[9] * -cospi_8_64 + output[14] * cospi_24_64);
+  step[10] = dct_32_round(output[10] * -cospi_24_64 + output[13] * -cospi_8_64);
+  step[11] = output[11];
+  step[12] = output[12];
+  step[13] = dct_32_round(output[13] * cospi_24_64 + output[10] * -cospi_8_64);
+  step[14] = dct_32_round(output[14] * cospi_8_64 + output[9] * cospi_24_64);
+  step[15] = output[15];
+
+  step[16] = output[16] + output[19];
+  step[17] = output[17] + output[18];
+  step[18] = -output[18] + output[17];
+  step[19] = -output[19] + output[16];
+  step[20] = -output[20] + output[23];
+  step[21] = -output[21] + output[22];
+  step[22] = output[22] + output[21];
+  step[23] = output[23] + output[20];
+  step[24] = output[24] + output[27];
+  step[25] = output[25] + output[26];
+  step[26] = -output[26] + output[25];
+  step[27] = -output[27] + output[24];
+  step[28] = -output[28] + output[31];
+  step[29] = -output[29] + output[30];
+  step[30] = output[30] + output[29];
+  step[31] = output[31] + output[28];
+
+  // Stage 6
+  output[0] = step[0];
+  output[1] = step[1];
+  output[2] = step[2];
+  output[3] = step[3];
+  output[4] = dct_32_round(step[4] * cospi_28_64 + step[7] * cospi_4_64);
+  output[5] = dct_32_round(step[5] * cospi_12_64 + step[6] * cospi_20_64);
+  output[6] = dct_32_round(step[6] * cospi_12_64 + step[5] * -cospi_20_64);
+  output[7] = dct_32_round(step[7] * cospi_28_64 + step[4] * -cospi_4_64);
+  output[8] = step[8] + step[9];
+  output[9] = -step[9] + step[8];
+  output[10] = -step[10] + step[11];
+  output[11] = step[11] + step[10];
+  output[12] = step[12] + step[13];
+  output[13] = -step[13] + step[12];
+  output[14] = -step[14] + step[15];
+  output[15] = step[15] + step[14];
+
+  output[16] = step[16];
+  output[17] = dct_32_round(step[17] * -cospi_4_64 + step[30] * cospi_28_64);
+  output[18] = dct_32_round(step[18] * -cospi_28_64 + step[29] * -cospi_4_64);
+  output[19] = step[19];
+  output[20] = step[20];
+  output[21] = dct_32_round(step[21] * -cospi_20_64 + step[26] * cospi_12_64);
+  output[22] = dct_32_round(step[22] * -cospi_12_64 + step[25] * -cospi_20_64);
+  output[23] = step[23];
+  output[24] = step[24];
+  output[25] = dct_32_round(step[25] * cospi_12_64 + step[22] * -cospi_20_64);
+  output[26] = dct_32_round(step[26] * cospi_20_64 + step[21] * cospi_12_64);
+  output[27] = step[27];
+  output[28] = step[28];
+  output[29] = dct_32_round(step[29] * cospi_28_64 + step[18] * -cospi_4_64);
+  output[30] = dct_32_round(step[30] * cospi_4_64 + step[17] * cospi_28_64);
+  output[31] = step[31];
+
+  // Stage 7
+  step[0] = output[0];
+  step[1] = output[1];
+  step[2] = output[2];
+  step[3] = output[3];
+  step[4] = output[4];
+  step[5] = output[5];
+  step[6] = output[6];
+  step[7] = output[7];
+  step[8] = dct_32_round(output[8] * cospi_30_64 + output[15] * cospi_2_64);
+  step[9] = dct_32_round(output[9] * cospi_14_64 + output[14] * cospi_18_64);
+  step[10] = dct_32_round(output[10] * cospi_22_64 + output[13] * cospi_10_64);
+  step[11] = dct_32_round(output[11] * cospi_6_64 + output[12] * cospi_26_64);
+  step[12] = dct_32_round(output[12] * cospi_6_64 + output[11] * -cospi_26_64);
+  step[13] = dct_32_round(output[13] * cospi_22_64 + output[10] * -cospi_10_64);
+  step[14] = dct_32_round(output[14] * cospi_14_64 + output[9] * -cospi_18_64);
+  step[15] = dct_32_round(output[15] * cospi_30_64 + output[8] * -cospi_2_64);
+
+  step[16] = output[16] + output[17];
+  step[17] = -output[17] + output[16];
+  step[18] = -output[18] + output[19];
+  step[19] = output[19] + output[18];
+  step[20] = output[20] + output[21];
+  step[21] = -output[21] + output[20];
+  step[22] = -output[22] + output[23];
+  step[23] = output[23] + output[22];
+  step[24] = output[24] + output[25];
+  step[25] = -output[25] + output[24];
+  step[26] = -output[26] + output[27];
+  step[27] = output[27] + output[26];
+  step[28] = output[28] + output[29];
+  step[29] = -output[29] + output[28];
+  step[30] = -output[30] + output[31];
+  step[31] = output[31] + output[30];
+
+  // Final stage --- outputs indices are bit-reversed.
+  output[0] = step[0];
+  output[16] = step[1];
+  output[8] = step[2];
+  output[24] = step[3];
+  output[4] = step[4];
+  output[20] = step[5];
+  output[12] = step[6];
+  output[28] = step[7];
+  output[2] = step[8];
+  output[18] = step[9];
+  output[10] = step[10];
+  output[26] = step[11];
+  output[6] = step[12];
+  output[22] = step[13];
+  output[14] = step[14];
+  output[30] = step[15];
+
+  output[1] = dct_32_round(step[16] * cospi_31_64 + step[31] * cospi_1_64);
+  output[17] = dct_32_round(step[17] * cospi_15_64 + step[30] * cospi_17_64);
+  output[9] = dct_32_round(step[18] * cospi_23_64 + step[29] * cospi_9_64);
+  output[25] = dct_32_round(step[19] * cospi_7_64 + step[28] * cospi_25_64);
+  output[5] = dct_32_round(step[20] * cospi_27_64 + step[27] * cospi_5_64);
+  output[21] = dct_32_round(step[21] * cospi_11_64 + step[26] * cospi_21_64);
+  output[13] = dct_32_round(step[22] * cospi_19_64 + step[25] * cospi_13_64);
+  output[29] = dct_32_round(step[23] * cospi_3_64 + step[24] * cospi_29_64);
+  output[3] = dct_32_round(step[24] * cospi_3_64 + step[23] * -cospi_29_64);
+  output[19] = dct_32_round(step[25] * cospi_19_64 + step[22] * -cospi_13_64);
+  output[11] = dct_32_round(step[26] * cospi_11_64 + step[21] * -cospi_21_64);
+  output[27] = dct_32_round(step[27] * cospi_27_64 + step[20] * -cospi_5_64);
+  output[7] = dct_32_round(step[28] * cospi_7_64 + step[19] * -cospi_25_64);
+  output[23] = dct_32_round(step[29] * cospi_23_64 + step[18] * -cospi_9_64);
+  output[15] = dct_32_round(step[30] * cospi_15_64 + step[17] * -cospi_17_64);
+  output[31] = dct_32_round(step[31] * cospi_31_64 + step[16] * -cospi_1_64);
+}
+
+void aom_fdct32x32_c(const int16_t *input, tran_low_t *out, int stride) {
+  int i, j;
+  tran_high_t output[32 * 32];
+
+  // Columns
+  for (i = 0; i < 32; ++i) {
+    tran_high_t temp_in[32], temp_out[32];
+    for (j = 0; j < 32; ++j) temp_in[j] = input[j * stride + i] * 4;
+    aom_fdct32(temp_in, temp_out, 0);
+    for (j = 0; j < 32; ++j)
+      output[j * 32 + i] = (temp_out[j] + 1 + (temp_out[j] > 0)) >> 2;
+  }
+
+  // Rows
+  for (i = 0; i < 32; ++i) {
+    tran_high_t temp_in[32], temp_out[32];
+    for (j = 0; j < 32; ++j) temp_in[j] = output[j + i * 32];
+    aom_fdct32(temp_in, temp_out, 0);
+    for (j = 0; j < 32; ++j)
+      out[j + i * 32] =
+          (tran_low_t)((temp_out[j] + 1 + (temp_out[j] < 0)) >> 2);
+  }
+}
+
+// Note that although we use dct_32_round in dct32 computation flow,
+// this 2d fdct32x32 for rate-distortion optimization loop is operating
+// within 16 bits precision.
+void aom_fdct32x32_rd_c(const int16_t *input, tran_low_t *out, int stride) {
+  int i, j;
+  tran_high_t output[32 * 32];
+
+  // Columns
+  for (i = 0; i < 32; ++i) {
+    tran_high_t temp_in[32], temp_out[32];
+    for (j = 0; j < 32; ++j) temp_in[j] = input[j * stride + i] * 4;
+    aom_fdct32(temp_in, temp_out, 0);
+    for (j = 0; j < 32; ++j)
+      // TODO(cd): see quality impact of only doing
+      //           output[j * 32 + i] = (temp_out[j] + 1) >> 2;
+      //           PS: also change code in aom_dsp/x86/aom_dct_sse2.c
+      output[j * 32 + i] = (temp_out[j] + 1 + (temp_out[j] > 0)) >> 2;
+  }
+
+  // Rows
+  for (i = 0; i < 32; ++i) {
+    tran_high_t temp_in[32], temp_out[32];
+    for (j = 0; j < 32; ++j) temp_in[j] = output[j + i * 32];
+    aom_fdct32(temp_in, temp_out, 1);
+    for (j = 0; j < 32; ++j) out[j + i * 32] = (tran_low_t)temp_out[j];
+  }
+}
+
+void aom_fdct32x32_1_c(const int16_t *input, tran_low_t *output, int stride) {
+  int r, c;
+  int sum = 0;
+  for (r = 0; r < 32; ++r)
+    for (c = 0; c < 32; ++c) sum += input[r * stride + c];
+
+  output[0] = (tran_low_t)(sum >> 3);
+}
+
+#if CONFIG_HIGHBITDEPTH
+void aom_highbd_fdct4x4_c(const int16_t *input, tran_low_t *output,
+                          int stride) {
+  aom_fdct4x4_c(input, output, stride);
+}
+
+void aom_highbd_fdct8x8_c(const int16_t *input, tran_low_t *final_output,
+                          int stride) {
+  aom_fdct8x8_c(input, final_output, stride);
+}
+
+void aom_highbd_fdct8x8_1_c(const int16_t *input, tran_low_t *final_output,
+                            int stride) {
+  aom_fdct8x8_1_c(input, final_output, stride);
+}
+
+void aom_highbd_fdct16x16_c(const int16_t *input, tran_low_t *output,
+                            int stride) {
+  aom_fdct16x16_c(input, output, stride);
+}
+
+void aom_highbd_fdct16x16_1_c(const int16_t *input, tran_low_t *output,
+                              int stride) {
+  aom_fdct16x16_1_c(input, output, stride);
+}
+
+void aom_highbd_fdct32x32_c(const int16_t *input, tran_low_t *out, int stride) {
+  aom_fdct32x32_c(input, out, stride);
+}
+
+void aom_highbd_fdct32x32_rd_c(const int16_t *input, tran_low_t *out,
+                               int stride) {
+  aom_fdct32x32_rd_c(input, out, stride);
+}
+
+void aom_highbd_fdct32x32_1_c(const int16_t *input, tran_low_t *out,
+                              int stride) {
+  aom_fdct32x32_1_c(input, out, stride);
+}
+#endif  // CONFIG_HIGHBITDEPTH