add range_check for fdct in vp10

Unify the style of fdct4() fdct8() fdct16()
Add fdct32()
Add range_check() at each stage
Add unit test at ../../test/vp10_dct_test.cc

Change-Id: I13f76d9046c3ea473c82024b09a5bc8662e2c28e

1 files changed, 691 insertions, 203 deletions

diff --git a/vp10/encoder/dct.c b/vp10/encoder/dct.c
index 288d5d092..80ace06cd 100644
--- a/vp10/encoder/dct.c
+++ b/vp10/encoder/dct.c
@@ -20,216 +20,704 @@
 #include "vpx_dsp/fwd_txfm.h"
 #include "vpx_ports/mem.h"
 
+static INLINE void range_check(const tran_low_t *input, const int size,
+                               const int bit) {
+#if CONFIG_COEFFICIENT_RANGE_CHECKING
+  int i;
+  for (i = 0; i < size; ++i) {
+    assert(abs(input[i]) < (1 << bit));
+  }
+#else
+  (void)input;
+  (void)size;
+  (void)bit;
+#endif
+}
+
 static void fdct4(const tran_low_t *input, tran_low_t *output) {
-  tran_high_t step[4];
-  tran_high_t temp1, temp2;
-
-  step[0] = input[0] + input[3];
-  step[1] = input[1] + input[2];
-  step[2] = input[1] - input[2];
-  step[3] = input[0] - input[3];
-
-  temp1 = (step[0] + step[1]) * cospi_16_64;
-  temp2 = (step[0] - step[1]) * cospi_16_64;
-  output[0] = (tran_low_t)fdct_round_shift(temp1);
-  output[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;
-  output[1] = (tran_low_t)fdct_round_shift(temp1);
-  output[3] = (tran_low_t)fdct_round_shift(temp2);
+  tran_high_t temp;
+  tran_low_t step[4];
+
+  // stage 0
+  range_check(input, 4, 11);
+
+  // stage 1
+  output[0] = input[0] + input[3];
+  output[1] = input[1] + input[2];
+  output[2] = input[1] - input[2];
+  output[3] = input[0] - input[3];
+
+  range_check(output, 4, 12);
+
+  // stage 2
+  temp = output[0] * cospi_16_64 + output[1] * cospi_16_64;
+  step[0] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[1] * -cospi_16_64 + output[0] * cospi_16_64;
+  step[1] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[2] * cospi_24_64 + output[3] * cospi_8_64;
+  step[2] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[3] * cospi_24_64 + output[2] * -cospi_8_64;
+  step[3] = (tran_low_t)fdct_round_shift(temp);
+
+  range_check(step, 4, 13);
+
+  // stage 3
+  output[0] = step[0];
+  output[1] = step[2];
+  output[2] = step[1];
+  output[3] = step[3];
+
+  range_check(output, 4, 13);
 }
 
 static void fdct8(const tran_low_t *input, tran_low_t *output) {
-  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
+  tran_high_t temp;
+  tran_low_t step[8];
+
+  // stage 0
+  range_check(input, 8, 12);
 
   // stage 1
-  s0 = input[0] + input[7];
-  s1 = input[1] + input[6];
-  s2 = input[2] + input[5];
-  s3 = input[3] + input[4];
-  s4 = input[3] - input[4];
-  s5 = input[2] - input[5];
-  s6 = input[1] - input[6];
-  s7 = input[0] - input[7];
-
-  // fdct4(step, step);
-  x0 = s0 + s3;
-  x1 = s1 + s2;
-  x2 = s1 - s2;
-  x3 = s0 - s3;
-  t0 = (x0 + x1) * cospi_16_64;
-  t1 = (x0 - x1) * cospi_16_64;
-  t2 =  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 = (tran_low_t)fdct_round_shift(t0);
-  t3 = (tran_low_t)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[0] = input[0] + input[7];
+  output[1] = input[1] + input[6];
+  output[2] = input[2] + input[5];
+  output[3] = input[3] + input[4];
+  output[4] = input[3] - input[4];
+  output[5] = input[2] - input[5];
+  output[6] = input[1] - input[6];
+  output[7] = input[0] - input[7];
+
+  range_check(output, 8, 13);
+
+  // stage 2
+  step[0] = output[0] + output[3];
+  step[1] = output[1] + output[2];
+  step[2] = output[1] - output[2];
+  step[3] = output[0] - output[3];
+  step[4] = output[4];
+  temp = output[5] * -cospi_16_64 + output[6] * cospi_16_64;
+  step[5] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[6] * cospi_16_64 + output[5] * cospi_16_64;
+  step[6] = (tran_low_t)fdct_round_shift(temp);
+  step[7] = output[7];
+
+  range_check(step, 8, 14);
+
+  // stage 3
+  temp = step[0] * cospi_16_64 + step[1] * cospi_16_64;
+  output[0] = (tran_low_t)fdct_round_shift(temp);
+  temp = step[1] * -cospi_16_64 + step[0] * cospi_16_64;
+  output[1] = (tran_low_t)fdct_round_shift(temp);
+  temp = step[2] * cospi_24_64 + step[3] * cospi_8_64;
+  output[2] = (tran_low_t)fdct_round_shift(temp);
+  temp = step[3] * cospi_24_64 + step[2] * -cospi_8_64;
+  output[3] = (tran_low_t)fdct_round_shift(temp);
+  output[4] = step[4] + step[5];
+  output[5] = step[4] - step[5];
+  output[6] = step[7] - step[6];
+  output[7] = step[7] + step[6];
+
+  range_check(output, 8, 14);
+
+  // stage 4
+  step[0] = output[0];
+  step[1] = output[1];
+  step[2] = output[2];
+  step[3] = output[3];
+  temp = output[4] * cospi_28_64 + output[7] * cospi_4_64;
+  step[4] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[5] * cospi_12_64 + output[6] * cospi_20_64;
+  step[5] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[6] * cospi_12_64 + output[5] * -cospi_20_64;
+  step[6] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[7] * cospi_28_64 + output[4] * -cospi_4_64;
+  step[7] = (tran_low_t)fdct_round_shift(temp);
+
+  range_check(step, 8, 14);
+
+  // stage 5
+  output[0] = step[0];
+  output[1] = step[4];
+  output[2] = step[2];
+  output[3] = step[6];
+  output[4] = step[1];
+  output[5] = step[5];
+  output[6] = step[3];
+  output[7] = step[7];
+
+  range_check(output, 8, 14);
 }
 
-static void fdct16(const tran_low_t in[16], tran_low_t out[16]) {
-  tran_high_t step1[8];      // canbe16
-  tran_high_t step2[8];      // canbe16
-  tran_high_t step3[8];      // canbe16
-  tran_high_t input[8];      // canbe16
-  tran_high_t temp1, temp2;  // needs32
-
-  // step 1
-  input[0] = in[0] + in[15];
-  input[1] = in[1] + in[14];
-  input[2] = in[2] + in[13];
-  input[3] = in[3] + in[12];
-  input[4] = in[4] + in[11];
-  input[5] = in[5] + in[10];
-  input[6] = in[6] + in[ 9];
-  input[7] = in[7] + in[ 8];
-
-  step1[0] = in[7] - in[ 8];
-  step1[1] = in[6] - in[ 9];
-  step1[2] = in[5] - in[10];
-  step1[3] = in[4] - in[11];
-  step1[4] = in[3] - in[12];
-  step1[5] = in[2] - in[13];
-  step1[6] = in[1] - in[14];
-  step1[7] = in[0] - in[15];
-
-  // fdct8(step, step);
-  {
-    tran_high_t s0, s1, s2, s3, s4, s5, s6, s7;  // canbe16
-    tran_high_t t0, t1, t2, t3;                  // needs32
-    tran_high_t x0, x1, x2, x3;                  // canbe16
+static void fdct16(const tran_low_t *input, tran_low_t *output) {
+  tran_high_t temp;
+  tran_low_t step[16];
 
-    // stage 1
-    s0 = input[0] + input[7];
-    s1 = input[1] + input[6];
-    s2 = input[2] + input[5];
-    s3 = input[3] + input[4];
-    s4 = input[3] - input[4];
-    s5 = input[2] - input[5];
-    s6 = input[1] - input[6];
-    s7 = input[0] - input[7];
-
-    // fdct4(step, step);
-    x0 = s0 + s3;
-    x1 = s1 + s2;
-    x2 = s1 - s2;
-    x3 = s0 - s3;
-    t0 = (x0 + x1) * cospi_16_64;
-    t1 = (x0 - x1) * cospi_16_64;
-    t2 = x3 * cospi_8_64  + x2 * cospi_24_64;
-    t3 = x3 * cospi_24_64 - x2 * cospi_8_64;
-    out[0] = (tran_low_t)fdct_round_shift(t0);
-    out[4] = (tran_low_t)fdct_round_shift(t2);
-    out[8] = (tran_low_t)fdct_round_shift(t1);
-    out[12] = (tran_low_t)fdct_round_shift(t3);
-
-    // Stage 2
-    t0 = (s6 - s5) * cospi_16_64;
-    t1 = (s6 + s5) * cospi_16_64;
-    t2 = fdct_round_shift(t0);
-    t3 = fdct_round_shift(t1);
-
-    // Stage 3
-    x0 = s4 + t2;
-    x1 = s4 - t2;
-    x2 = s7 - t3;
-    x3 = s7 + t3;
-
-    // Stage 4
-    t0 = x0 * cospi_28_64 + x3 *   cospi_4_64;
-    t1 = x1 * cospi_12_64 + x2 *  cospi_20_64;
-    t2 = x2 * cospi_12_64 + x1 * -cospi_20_64;
-    t3 = x3 * cospi_28_64 + x0 *  -cospi_4_64;
-    out[2] = (tran_low_t)fdct_round_shift(t0);
-    out[6] = (tran_low_t)fdct_round_shift(t2);
-    out[10] = (tran_low_t)fdct_round_shift(t1);
-    out[14] = (tran_low_t)fdct_round_shift(t3);
-  }
+  // stage 0
+  range_check(input, 16, 13);
+
+  // stage 1
+  output[0] = input[0] + input[15];
+  output[1] = input[1] + input[14];
+  output[2] = input[2] + input[13];
+  output[3] = input[3] + input[12];
+  output[4] = input[4] + input[11];
+  output[5] = input[5] + input[10];
+  output[6] = input[6] + input[9];
+  output[7] = input[7] + input[8];
+  output[8] = input[7] - input[8];
+  output[9] = input[6] - input[9];
+  output[10] = input[5] - input[10];
+  output[11] = input[4] - input[11];
+  output[12] = input[3] - input[12];
+  output[13] = input[2] - input[13];
+  output[14] = input[1] - input[14];
+  output[15] = input[0] - input[15];
+
+  range_check(output, 16, 14);
+
+  // stage 2
+  step[0] = output[0] + output[7];
+  step[1] = output[1] + output[6];
+  step[2] = output[2] + output[5];
+  step[3] = output[3] + output[4];
+  step[4] = output[3] - output[4];
+  step[5] = output[2] - output[5];
+  step[6] = output[1] - output[6];
+  step[7] = output[0] - output[7];
+  step[8] = output[8];
+  step[9] = output[9];
+  temp = output[10] * -cospi_16_64 + output[13] * cospi_16_64;
+  step[10] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[11] * -cospi_16_64 + output[12] * cospi_16_64;
+  step[11] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[12] * cospi_16_64 + output[11] * cospi_16_64;
+  step[12] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[13] * cospi_16_64 + output[10] * cospi_16_64;
+  step[13] = (tran_low_t)fdct_round_shift(temp);
+  step[14] = output[14];
+  step[15] = output[15];
+
+  range_check(step, 16, 15);
+
+  // stage 3
+  output[0] = step[0] + step[3];
+  output[1] = step[1] + step[2];
+  output[2] = step[1] - step[2];
+  output[3] = step[0] - step[3];
+  output[4] = step[4];
+  temp = step[5] * -cospi_16_64 + step[6] * cospi_16_64;
+  output[5] = (tran_low_t)fdct_round_shift(temp);
+  temp = step[6] * cospi_16_64 + step[5] * cospi_16_64;
+  output[6] = (tran_low_t)fdct_round_shift(temp);
+  output[7] = step[7];
+  output[8] = step[8] + step[11];
+  output[9] = step[9] + step[10];
+  output[10] = step[9] - step[10];
+  output[11] = step[8] - step[11];
+  output[12] = step[15] - step[12];
+  output[13] = step[14] - step[13];
+  output[14] = step[14] + step[13];
+  output[15] = step[15] + step[12];
+
+  range_check(output, 16, 16);
+
+  // stage 4
+  temp = output[0] * cospi_16_64 + output[1] * cospi_16_64;
+  step[0] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[1] * -cospi_16_64 + output[0] * cospi_16_64;
+  step[1] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[2] * cospi_24_64 + output[3] * cospi_8_64;
+  step[2] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[3] * cospi_24_64 + output[2] * -cospi_8_64;
+  step[3] = (tran_low_t)fdct_round_shift(temp);
+  step[4] = output[4] + output[5];
+  step[5] = output[4] - output[5];
+  step[6] = output[7] - output[6];
+  step[7] = output[7] + output[6];
+  step[8] = output[8];
+  temp = output[9] * -cospi_8_64 + output[14] * cospi_24_64;
+  step[9] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[10] * -cospi_24_64 + output[13] * -cospi_8_64;
+  step[10] = (tran_low_t)fdct_round_shift(temp);
+  step[11] = output[11];
+  step[12] = output[12];
+  temp = output[13] * cospi_24_64 + output[10] * -cospi_8_64;
+  step[13] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[14] * cospi_8_64 + output[9] * cospi_24_64;
+  step[14] = (tran_low_t)fdct_round_shift(temp);
+  step[15] = output[15];
+
+  range_check(step, 16, 16);
+
+  // stage 5
+  output[0] = step[0];
+  output[1] = step[1];
+  output[2] = step[2];
+  output[3] = step[3];
+  temp = step[4] * cospi_28_64 + step[7] * cospi_4_64;
+  output[4] = (tran_low_t)fdct_round_shift(temp);
+  temp = step[5] * cospi_12_64 + step[6] * cospi_20_64;
+  output[5] = (tran_low_t)fdct_round_shift(temp);
+  temp = step[6] * cospi_12_64 + step[5] * -cospi_20_64;
+  output[6] = (tran_low_t)fdct_round_shift(temp);
+  temp = step[7] * cospi_28_64 + step[4] * -cospi_4_64;
+  output[7] = (tran_low_t)fdct_round_shift(temp);
+  output[8] = step[8] + step[9];
+  output[9] = step[8] - step[9];
+  output[10] = step[11] - step[10];
+  output[11] = step[11] + step[10];
+  output[12] = step[12] + step[13];
+  output[13] = step[12] - step[13];
+  output[14] = step[15] - step[14];
+  output[15] = step[15] + step[14];
+
+  range_check(output, 16, 16);
+
+  // stage 6
+  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];
+  temp = output[8] * cospi_30_64 + output[15] * cospi_2_64;
+  step[8] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[9] * cospi_14_64 + output[14] * cospi_18_64;
+  step[9] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[10] * cospi_22_64 + output[13] * cospi_10_64;
+  step[10] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[11] * cospi_6_64 + output[12] * cospi_26_64;
+  step[11] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[12] * cospi_6_64 + output[11] * -cospi_26_64;
+  step[12] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[13] * cospi_22_64 + output[10] * -cospi_10_64;
+  step[13] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[14] * cospi_14_64 + output[9] * -cospi_18_64;
+  step[14] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[15] * cospi_30_64 + output[8] * -cospi_2_64;
+  step[15] = (tran_low_t)fdct_round_shift(temp);
+
+  range_check(step, 16, 16);
+
+  // stage 7
+  output[0] = step[0];
+  output[1] = step[8];
+  output[2] = step[4];
+  output[3] = step[12];
+  output[4] = step[2];
+  output[5] = step[10];
+  output[6] = step[6];
+  output[7] = step[14];
+  output[8] = step[1];
+  output[9] = step[9];
+  output[10] = step[5];
+  output[11] = step[13];
+  output[12] = step[3];
+  output[13] = step[11];
+  output[14] = step[7];
+  output[15] = step[15];
+
+  range_check(output, 16, 16);
+}
+
+static void fdct32(const tran_low_t *input, tran_low_t *output) {
+  tran_high_t temp;
+  tran_low_t step[32];
+
+  // stage 0
+  range_check(input, 32, 14);
+
+  // stage 1
+  output[0] = input[0] + input[31];
+  output[1] = input[1] + input[30];
+  output[2] = input[2] + input[29];
+  output[3] = input[3] + input[28];
+  output[4] = input[4] + input[27];
+  output[5] = input[5] + input[26];
+  output[6] = input[6] + input[25];
+  output[7] = input[7] + input[24];
+  output[8] = input[8] + input[23];
+  output[9] = input[9] + input[22];
+  output[10] = input[10] + input[21];
+  output[11] = input[11] + input[20];
+  output[12] = input[12] + input[19];
+  output[13] = input[13] + input[18];
+  output[14] = input[14] + input[17];
+  output[15] = input[15] + input[16];
+  output[16] = input[15] - input[16];
+  output[17] = input[14] - input[17];
+  output[18] = input[13] - input[18];
+  output[19] = input[12] - input[19];
+  output[20] = input[11] - input[20];
+  output[21] = input[10] - input[21];
+  output[22] = input[9] - input[22];
+  output[23] = input[8] - input[23];
+  output[24] = input[7] - input[24];
+  output[25] = input[6] - input[25];
+  output[26] = input[5] - input[26];
+  output[27] = input[4] - input[27];
+  output[28] = input[3] - input[28];
+  output[29] = input[2] - input[29];
+  output[30] = input[1] - input[30];
+  output[31] = input[0] - input[31];
+
+  range_check(output, 32, 15);
 
-  // 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);
+  // stage 2
+  step[0] = output[0] + output[15];
+  step[1] = output[1] + output[14];
+  step[2] = output[2] + output[13];
+  step[3] = output[3] + output[12];
+  step[4] = output[4] + output[11];
+  step[5] = output[5] + output[10];
+  step[6] = output[6] + output[9];
+  step[7] = output[7] + output[8];
+  step[8] = output[7] - output[8];
+  step[9] = output[6] - output[9];
+  step[10] = output[5] - output[10];
+  step[11] = output[4] - output[11];
+  step[12] = output[3] - output[12];
+  step[13] = output[2] - output[13];
+  step[14] = output[1] - output[14];
+  step[15] = output[0] - output[15];
+  step[16] = output[16];
+  step[17] = output[17];
+  step[18] = output[18];
+  step[19] = output[19];
+  temp = output[20] * -cospi_16_64 + output[27] * cospi_16_64;
+  step[20] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[21] * -cospi_16_64 + output[26] * cospi_16_64;
+  step[21] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[22] * -cospi_16_64 + output[25] * cospi_16_64;
+  step[22] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[23] * -cospi_16_64 + output[24] * cospi_16_64;
+  step[23] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[24] * cospi_16_64 + output[23] * cospi_16_64;
+  step[24] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[25] * cospi_16_64 + output[22] * cospi_16_64;
+  step[25] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[26] * cospi_16_64 + output[21] * cospi_16_64;
+  step[26] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[27] * cospi_16_64 + output[20] * cospi_16_64;
+  step[27] = (tran_low_t)fdct_round_shift(temp);
+  step[28] = output[28];
+  step[29] = output[29];
+  step[30] = output[30];
+  step[31] = output[31];
+
+  range_check(step, 32, 16);
+
+  // stage 3
+  output[0] = step[0] + step[7];
+  output[1] = step[1] + step[6];
+  output[2] = step[2] + step[5];
+  output[3] = step[3] + step[4];
+  output[4] = step[3] - step[4];
+  output[5] = step[2] - step[5];
+  output[6] = step[1] - step[6];
+  output[7] = step[0] - step[7];
+  output[8] = step[8];
+  output[9] = step[9];
+  temp = step[10] * -cospi_16_64 + step[13] * cospi_16_64;
+  output[10] = (tran_low_t)fdct_round_shift(temp);
+  temp = step[11] * -cospi_16_64 + step[12] * cospi_16_64;
+  output[11] = (tran_low_t)fdct_round_shift(temp);
+  temp = step[12] * cospi_16_64 + step[11] * cospi_16_64;
+  output[12] = (tran_low_t)fdct_round_shift(temp);
+  temp = step[13] * cospi_16_64 + step[10] * cospi_16_64;
+  output[13] = (tran_low_t)fdct_round_shift(temp);
+  output[14] = step[14];
+  output[15] = step[15];
+  output[16] = step[16] + step[23];
+  output[17] = step[17] + step[22];
+  output[18] = step[18] + step[21];
+  output[19] = step[19] + step[20];
+  output[20] = step[19] - step[20];
+  output[21] = step[18] - step[21];
+  output[22] = step[17] - step[22];
+  output[23] = step[16] - step[23];
+  output[24] = step[31] - step[24];
+  output[25] = step[30] - step[25];
+  output[26] = step[29] - step[26];
+  output[27] = step[28] - step[27];
+  output[28] = step[28] + step[27];
+  output[29] = step[29] + step[26];
+  output[30] = step[30] + step[25];
+  output[31] = step[31] + step[24];
+
+  range_check(output, 32, 17);
+
+  // stage 4
+  step[0] = output[0] + output[3];
+  step[1] = output[1] + output[2];
+  step[2] = output[1] - output[2];
+  step[3] = output[0] - output[3];
+  step[4] = output[4];
+  temp = output[5] * -cospi_16_64 + output[6] * cospi_16_64;
+  step[5] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[6] * cospi_16_64 + output[5] * cospi_16_64;
+  step[6] = (tran_low_t)fdct_round_shift(temp);
+  step[7] = output[7];
+  step[8] = output[8] + output[11];
+  step[9] = output[9] + output[10];
+  step[10] = output[9] - output[10];
+  step[11] = output[8] - output[11];
+  step[12] = output[15] - output[12];
+  step[13] = output[14] - output[13];
+  step[14] = output[14] + output[13];
+  step[15] = output[15] + output[12];
+  step[16] = output[16];
+  step[17] = output[17];
+  temp = output[18] * -cospi_8_64 + output[29] * cospi_24_64;
+  step[18] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[19] * -cospi_8_64 + output[28] * cospi_24_64;
+  step[19] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[20] * -cospi_24_64 + output[27] * -cospi_8_64;
+  step[20] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[21] * -cospi_24_64 + output[26] * -cospi_8_64;
+  step[21] = (tran_low_t)fdct_round_shift(temp);
+  step[22] = output[22];
+  step[23] = output[23];
+  step[24] = output[24];
+  step[25] = output[25];
+  temp = output[26] * cospi_24_64 + output[21] * -cospi_8_64;
+  step[26] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[27] * cospi_24_64 + output[20] * -cospi_8_64;
+  step[27] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[28] * cospi_8_64 + output[19] * cospi_24_64;
+  step[28] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[29] * cospi_8_64 + output[18] * cospi_24_64;
+  step[29] = (tran_low_t)fdct_round_shift(temp);
+  step[30] = output[30];
+  step[31] = output[31];
+
+  range_check(step, 32, 18);
+
+  // stage 5
+  temp = step[0] * cospi_16_64 + step[1] * cospi_16_64;
+  output[0] = (tran_low_t)fdct_round_shift(temp);
+  temp = step[1] * -cospi_16_64 + step[0] * cospi_16_64;
+  output[1] = (tran_low_t)fdct_round_shift(temp);
+  temp = step[2] * cospi_24_64 + step[3] * cospi_8_64;
+  output[2] = (tran_low_t)fdct_round_shift(temp);
+  temp = step[3] * cospi_24_64 + step[2] * -cospi_8_64;
+  output[3] = (tran_low_t)fdct_round_shift(temp);
+  output[4] = step[4] + step[5];
+  output[5] = step[4] - step[5];
+  output[6] = step[7] - step[6];
+  output[7] = step[7] + step[6];
+  output[8] = step[8];
+  temp = step[9] * -cospi_8_64 + step[14] * cospi_24_64;
+  output[9] = (tran_low_t)fdct_round_shift(temp);
+  temp = step[10] * -cospi_24_64 + step[13] * -cospi_8_64;
+  output[10] = (tran_low_t)fdct_round_shift(temp);
+  output[11] = step[11];
+  output[12] = step[12];
+  temp = step[13] * cospi_24_64 + step[10] * -cospi_8_64;
+  output[13] = (tran_low_t)fdct_round_shift(temp);
+  temp = step[14] * cospi_8_64 + step[9] * cospi_24_64;
+  output[14] = (tran_low_t)fdct_round_shift(temp);
+  output[15] = step[15];
+  output[16] = step[16] + step[19];
+  output[17] = step[17] + step[18];
+  output[18] = step[17] - step[18];
+  output[19] = step[16] - step[19];
+  output[20] = step[23] - step[20];
+  output[21] = step[22] - step[21];
+  output[22] = step[22] + step[21];
+  output[23] = step[23] + step[20];
+  output[24] = step[24] + step[27];
+  output[25] = step[25] + step[26];
+  output[26] = step[25] - step[26];
+  output[27] = step[24] - step[27];
+  output[28] = step[31] - step[28];
+  output[29] = step[30] - step[29];
+  output[30] = step[30] + step[29];
+  output[31] = step[31] + step[28];
+
+  range_check(output, 32, 18);
+
+  // stage 6
+  step[0] = output[0];
+  step[1] = output[1];
+  step[2] = output[2];
+  step[3] = output[3];
+  temp = output[4] * cospi_28_64 + output[7] * cospi_4_64;
+  step[4] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[5] * cospi_12_64 + output[6] * cospi_20_64;
+  step[5] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[6] * cospi_12_64 + output[5] * -cospi_20_64;
+  step[6] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[7] * cospi_28_64 + output[4] * -cospi_4_64;
+  step[7] = (tran_low_t)fdct_round_shift(temp);
+  step[8] = output[8] + output[9];
+  step[9] = output[8] - output[9];
+  step[10] = output[11] - output[10];
+  step[11] = output[11] + output[10];
+  step[12] = output[12] + output[13];
+  step[13] = output[12] - output[13];
+  step[14] = output[15] - output[14];
+  step[15] = output[15] + output[14];
+  step[16] = output[16];
+  temp = output[17] * -cospi_4_64 + output[30] * cospi_28_64;
+  step[17] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[18] * -cospi_28_64 + output[29] * -cospi_4_64;
+  step[18] = (tran_low_t)fdct_round_shift(temp);
+  step[19] = output[19];
+  step[20] = output[20];
+  temp = output[21] * -cospi_20_64 + output[26] * cospi_12_64;
+  step[21] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[22] * -cospi_12_64 + output[25] * -cospi_20_64;
+  step[22] = (tran_low_t)fdct_round_shift(temp);
+  step[23] = output[23];
+  step[24] = output[24];
+  temp = output[25] * cospi_12_64 + output[22] * -cospi_20_64;
+  step[25] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[26] * cospi_20_64 + output[21] * cospi_12_64;
+  step[26] = (tran_low_t)fdct_round_shift(temp);
+  step[27] = output[27];
+  step[28] = output[28];
+  temp = output[29] * cospi_28_64 + output[18] * -cospi_4_64;
+  step[29] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[30] * cospi_4_64 + output[17] * cospi_28_64;
+  step[30] = (tran_low_t)fdct_round_shift(temp);
+  step[31] = output[31];
+
+  range_check(step, 32, 18);
+
+  // stage 7
+  output[0] = step[0];
+  output[1] = step[1];
+  output[2] = step[2];
+  output[3] = step[3];
+  output[4] = step[4];
+  output[5] = step[5];
+  output[6] = step[6];
+  output[7] = step[7];
+  temp = step[8] * cospi_30_64 + step[15] * cospi_2_64;
+  output[8] = (tran_low_t)fdct_round_shift(temp);
+  temp = step[9] * cospi_14_64 + step[14] * cospi_18_64;
+  output[9] = (tran_low_t)fdct_round_shift(temp);
+  temp = step[10] * cospi_22_64 + step[13] * cospi_10_64;
+  output[10] = (tran_low_t)fdct_round_shift(temp);
+  temp = step[11] * cospi_6_64 + step[12] * cospi_26_64;
+  output[11] = (tran_low_t)fdct_round_shift(temp);
+  temp = step[12] * cospi_6_64 + step[11] * -cospi_26_64;
+  output[12] = (tran_low_t)fdct_round_shift(temp);
+  temp = step[13] * cospi_22_64 + step[10] * -cospi_10_64;
+  output[13] = (tran_low_t)fdct_round_shift(temp);
+  temp = step[14] * cospi_14_64 + step[9] * -cospi_18_64;
+  output[14] = (tran_low_t)fdct_round_shift(temp);
+  temp = step[15] * cospi_30_64 + step[8] * -cospi_2_64;
+  output[15] = (tran_low_t)fdct_round_shift(temp);
+  output[16] = step[16] + step[17];
+  output[17] = step[16] - step[17];
+  output[18] = step[19] - step[18];
+  output[19] = step[19] + step[18];
+  output[20] = step[20] + step[21];
+  output[21] = step[20] - step[21];
+  output[22] = step[23] - step[22];
+  output[23] = step[23] + step[22];
+  output[24] = step[24] + step[25];
+  output[25] = step[24] - step[25];
+  output[26] = step[27] - step[26];
+  output[27] = step[27] + step[26];
+  output[28] = step[28] + step[29];
+  output[29] = step[28] - step[29];
+  output[30] = step[31] - step[30];
+  output[31] = step[31] + step[30];
+
+  range_check(output, 32, 18);
+
+  // stage 8
+  step[0] = output[0];
+  step[1] = output[1];
+  step[2] = output[2];
+  step[3] = output[3];
+  step[4] = output[4];
+  step[5] = output[5];
+  step[6] = output[6];
+  step[7] = output[7];
+  step[8] = output[8];
+  step[9] = output[9];
+  step[10] = output[10];
+  step[11] = output[11];
+  step[12] = output[12];
+  step[13] = output[13];
+  step[14] = output[14];
+  step[15] = output[15];
+  temp = output[16] * cospi_31_64 + output[31] * cospi_1_64;
+  step[16] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[17] * cospi_15_64 + output[30] * cospi_17_64;
+  step[17] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[18] * cospi_23_64 + output[29] * cospi_9_64;
+  step[18] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[19] * cospi_7_64 + output[28] * cospi_25_64;
+  step[19] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[20] * cospi_27_64 + output[27] * cospi_5_64;
+  step[20] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[21] * cospi_11_64 + output[26] * cospi_21_64;
+  step[21] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[22] * cospi_19_64 + output[25] * cospi_13_64;
+  step[22] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[23] * cospi_3_64 + output[24] * cospi_29_64;
+  step[23] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[24] * cospi_3_64 + output[23] * -cospi_29_64;
+  step[24] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[25] * cospi_19_64 + output[22] * -cospi_13_64;
+  step[25] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[26] * cospi_11_64 + output[21] * -cospi_21_64;
+  step[26] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[27] * cospi_27_64 + output[20] * -cospi_5_64;
+  step[27] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[28] * cospi_7_64 + output[19] * -cospi_25_64;
+  step[28] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[29] * cospi_23_64 + output[18] * -cospi_9_64;
+  step[29] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[30] * cospi_15_64 + output[17] * -cospi_17_64;
+  step[30] = (tran_low_t)fdct_round_shift(temp);
+  temp = output[31] * cospi_31_64 + output[16] * -cospi_1_64;
+  step[31] = (tran_low_t)fdct_round_shift(temp);
+
+  range_check(step, 32, 18);
+
+  // stage 9
+  output[0] = step[0];
+  output[1] = step[16];
+  output[2] = step[8];
+  output[3] = step[24];
+  output[4] = step[4];
+  output[5] = step[20];
+  output[6] = step[12];
+  output[7] = step[28];
+  output[8] = step[2];
+  output[9] = step[18];
+  output[10] = step[10];
+  output[11] = step[26];
+  output[12] = step[6];
+  output[13] = step[22];
+  output[14] = step[14];
+  output[15] = step[30];
+  output[16] = step[1];
+  output[17] = step[17];
+  output[18] = step[9];
+  output[19] = step[25];
+  output[20] = step[5];
+  output[21] = step[21];
+  output[22] = step[13];
+  output[23] = step[29];
+  output[24] = step[3];
+  output[25] = step[19];
+  output[26] = step[11];
+  output[27] = step[27];
+  output[28] = step[7];
+  output[29] = step[23];
+  output[30] = step[15];
+  output[31] = step[31];
+
+  range_check(output, 32, 18);
 }
 
 static void fadst4(const tran_low_t *input, tran_low_t *output) {
@@ -607,19 +1095,19 @@ void vp10_fdct8x8_quant_c(const int16_t *input, int stride,
       output[4 * 8] = (tran_low_t)fdct_round_shift(t1);
       output[6 * 8] = (tran_low_t)fdct_round_shift(t3);
 
-      // Stage 2
+      // 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
+      // stage 3
       x0 = s4 + t2;
       x1 = s4 - t2;
       x2 = s7 - t3;
       x3 = s7 + t3;
 
-      // Stage 4
+      // 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;