Enable sse2 implmentation of 8x8 ADST/DCT

This commit makes use of the butterfly structure to enable the sse2
version implementation of 8x8 ADST/DCT hybrid transform coding.

The runtime of hybrid transform module goes down from 1170 cycles
to 245 cycles. Overall speed-up around 1.5%.

Change-Id: Ic808ffd21ece8a9d0410d8c0243d7b6c28ac3b3f

2 files changed, 494 insertions, 1 deletions

diff --git a/vp9/common/vp9_rtcd_defs.sh b/vp9/common/vp9_rtcd_defs.sh
index 575b619a1..10e06493a 100644
--- a/vp9/common/vp9_rtcd_defs.sh
+++ b/vp9/common/vp9_rtcd_defs.sh
@@ -551,7 +551,7 @@ prototype void vp9_short_fht4x4 "int16_t *InputData, int16_t *OutputData, int pi
 specialize vp9_short_fht4x4
 
 prototype void vp9_short_fht8x8 "int16_t *InputData, int16_t *OutputData, int pitch, int tx_type"
-specialize vp9_short_fht8x8
+specialize vp9_short_fht8x8 sse2
 
 prototype void vp9_short_fht16x16 "int16_t *InputData, int16_t *OutputData, int pitch, int tx_type"
 specialize vp9_short_fht16x16
diff --git a/vp9/encoder/x86/vp9_dct_sse2.c b/vp9/encoder/x86/vp9_dct_sse2.c
index aaacebee2..96c0cb67b 100644
--- a/vp9/encoder/x86/vp9_dct_sse2.c
+++ b/vp9/encoder/x86/vp9_dct_sse2.c
@@ -10,6 +10,7 @@
 
 #include <emmintrin.h>  // SSE2
 #include "vp9/common/vp9_idct.h"  // for cospi constants
+#include "vpx_ports/mem.h"
 
 void vp9_short_fdct4x4_sse2(int16_t *input, int16_t *output, int pitch) {
   // The 2D transform is done with two passes which are actually pretty
@@ -373,6 +374,498 @@ void vp9_short_fdct8x8_sse2(int16_t *input, int16_t *output, int pitch) {
   }
 }
 
+// load 8x8 array
+static INLINE void load_buffer_8x8(int16_t *input, __m128i in[8], int stride) {
+  in[0]  = _mm_load_si128((__m128i *)(input + 0 * stride));
+  in[1]  = _mm_load_si128((__m128i *)(input + 1 * stride));
+  in[2]  = _mm_load_si128((__m128i *)(input + 2 * stride));
+  in[3]  = _mm_load_si128((__m128i *)(input + 3 * stride));
+  in[4]  = _mm_load_si128((__m128i *)(input + 4 * stride));
+  in[5]  = _mm_load_si128((__m128i *)(input + 5 * stride));
+  in[6]  = _mm_load_si128((__m128i *)(input + 6 * stride));
+  in[7]  = _mm_load_si128((__m128i *)(input + 7 * stride));
+
+  in[0] = _mm_slli_epi16(in[0], 2);
+  in[1] = _mm_slli_epi16(in[1], 2);
+  in[2] = _mm_slli_epi16(in[2], 2);
+  in[3] = _mm_slli_epi16(in[3], 2);
+  in[4] = _mm_slli_epi16(in[4], 2);
+  in[5] = _mm_slli_epi16(in[5], 2);
+  in[6] = _mm_slli_epi16(in[6], 2);
+  in[7] = _mm_slli_epi16(in[7], 2);
+}
+
+// write 8x8 array
+static INLINE void write_buffer_8x8(int16_t *output, __m128i res[8]) {
+  res[0] = _mm_srai_epi16(res[0], 1);
+  res[1] = _mm_srai_epi16(res[1], 1);
+  res[2] = _mm_srai_epi16(res[2], 1);
+  res[3] = _mm_srai_epi16(res[3], 1);
+  res[4] = _mm_srai_epi16(res[4], 1);
+  res[5] = _mm_srai_epi16(res[5], 1);
+  res[6] = _mm_srai_epi16(res[6], 1);
+  res[7] = _mm_srai_epi16(res[7], 1);
+
+  _mm_store_si128((__m128i *)(output + 0 * 8), res[0]);
+  _mm_store_si128((__m128i *)(output + 1 * 8), res[1]);
+  _mm_store_si128((__m128i *)(output + 2 * 8), res[2]);
+  _mm_store_si128((__m128i *)(output + 3 * 8), res[3]);
+  _mm_store_si128((__m128i *)(output + 4 * 8), res[4]);
+  _mm_store_si128((__m128i *)(output + 5 * 8), res[5]);
+  _mm_store_si128((__m128i *)(output + 6 * 8), res[6]);
+  _mm_store_si128((__m128i *)(output + 7 * 8), res[7]);
+}
+
+// perform in-place transpose
+static INLINE void array_transpose_8x8(__m128i res[8]) {
+  const __m128i tr0_0 = _mm_unpacklo_epi16(res[0], res[1]);
+  const __m128i tr0_1 = _mm_unpacklo_epi16(res[2], res[3]);
+  const __m128i tr0_2 = _mm_unpackhi_epi16(res[0], res[1]);
+  const __m128i tr0_3 = _mm_unpackhi_epi16(res[2], res[3]);
+  const __m128i tr0_4 = _mm_unpacklo_epi16(res[4], res[5]);
+  const __m128i tr0_5 = _mm_unpacklo_epi16(res[6], res[7]);
+  const __m128i tr0_6 = _mm_unpackhi_epi16(res[4], res[5]);
+  const __m128i tr0_7 = _mm_unpackhi_epi16(res[6], res[7]);
+  // 00 10 01 11 02 12 03 13
+  // 20 30 21 31 22 32 23 33
+  // 04 14 05 15 06 16 07 17
+  // 24 34 25 35 26 36 27 37
+  // 40 50 41 51 42 52 43 53
+  // 60 70 61 71 62 72 63 73
+  // 44 54 45 55 46 56 47 57
+  // 64 74 65 75 66 76 67 77
+  const __m128i tr1_0 = _mm_unpacklo_epi32(tr0_0, tr0_1);
+  const __m128i tr1_1 = _mm_unpacklo_epi32(tr0_4, tr0_5);
+  const __m128i tr1_2 = _mm_unpackhi_epi32(tr0_0, tr0_1);
+  const __m128i tr1_3 = _mm_unpackhi_epi32(tr0_4, tr0_5);
+  const __m128i tr1_4 = _mm_unpacklo_epi32(tr0_2, tr0_3);
+  const __m128i tr1_5 = _mm_unpacklo_epi32(tr0_6, tr0_7);
+  const __m128i tr1_6 = _mm_unpackhi_epi32(tr0_2, tr0_3);
+  const __m128i tr1_7 = _mm_unpackhi_epi32(tr0_6, tr0_7);
+  // 00 10 20 30 01 11 21 31
+  // 40 50 60 70 41 51 61 71
+  // 02 12 22 32 03 13 23 33
+  // 42 52 62 72 43 53 63 73
+  // 04 14 24 34 05 15 25 35
+  // 44 54 64 74 45 55 65 75
+  // 06 16 26 36 07 17 27 37
+  // 46 56 66 76 47 57 67 77
+  res[0] = _mm_unpacklo_epi64(tr1_0, tr1_1);
+  res[1] = _mm_unpackhi_epi64(tr1_0, tr1_1);
+  res[2] = _mm_unpacklo_epi64(tr1_2, tr1_3);
+  res[3] = _mm_unpackhi_epi64(tr1_2, tr1_3);
+  res[4] = _mm_unpacklo_epi64(tr1_4, tr1_5);
+  res[5] = _mm_unpackhi_epi64(tr1_4, tr1_5);
+  res[6] = _mm_unpacklo_epi64(tr1_6, tr1_7);
+  res[7] = _mm_unpackhi_epi64(tr1_6, tr1_7);
+  // 00 10 20 30 40 50 60 70
+  // 01 11 21 31 41 51 61 71
+  // 02 12 22 32 42 52 62 72
+  // 03 13 23 33 43 53 63 73
+  // 04 14 24 34 44 54 64 74
+  // 05 15 25 35 45 55 65 75
+  // 06 16 26 36 46 56 66 76
+  // 07 17 27 37 47 57 67 77
+}
+
+void fdct8_1d_sse2(__m128i in[8]) {
+  // constants
+  const __m128i k__cospi_p16_p16 = _mm_set1_epi16(cospi_16_64);
+  const __m128i k__cospi_p16_m16 = pair_set_epi16(cospi_16_64, -cospi_16_64);
+  const __m128i k__cospi_p24_p08 = pair_set_epi16(cospi_24_64, cospi_8_64);
+  const __m128i k__cospi_m08_p24 = pair_set_epi16(-cospi_8_64, cospi_24_64);
+  const __m128i k__cospi_p28_p04 = pair_set_epi16(cospi_28_64, cospi_4_64);
+  const __m128i k__cospi_m04_p28 = pair_set_epi16(-cospi_4_64, cospi_28_64);
+  const __m128i k__cospi_p12_p20 = pair_set_epi16(cospi_12_64, cospi_20_64);
+  const __m128i k__cospi_m20_p12 = pair_set_epi16(-cospi_20_64, cospi_12_64);
+  const __m128i k__DCT_CONST_ROUNDING = _mm_set1_epi32(DCT_CONST_ROUNDING);
+  __m128i u0, u1, u2, u3, u4, u5, u6, u7;
+  __m128i v0, v1, v2, v3, v4, v5, v6, v7;
+  __m128i s0, s1, s2, s3, s4, s5, s6, s7;
+
+  // stage 1
+  s0 = _mm_add_epi16(in[0], in[7]);
+  s1 = _mm_add_epi16(in[1], in[6]);
+  s2 = _mm_add_epi16(in[2], in[5]);
+  s3 = _mm_add_epi16(in[3], in[4]);
+  s4 = _mm_sub_epi16(in[3], in[4]);
+  s5 = _mm_sub_epi16(in[2], in[5]);
+  s6 = _mm_sub_epi16(in[1], in[6]);
+  s7 = _mm_sub_epi16(in[0], in[7]);
+
+  u0 = _mm_add_epi16(s0, s3);
+  u1 = _mm_add_epi16(s1, s2);
+  u2 = _mm_sub_epi16(s1, s2);
+  u3 = _mm_sub_epi16(s0, s3);
+  // interleave and perform butterfly multiplication/addition
+  v0 = _mm_unpacklo_epi16(u0, u1);
+  v1 = _mm_unpackhi_epi16(u0, u1);
+  v2 = _mm_unpacklo_epi16(u2, u3);
+  v3 = _mm_unpackhi_epi16(u2, u3);
+
+  u0 = _mm_madd_epi16(v0, k__cospi_p16_p16);
+  u1 = _mm_madd_epi16(v1, k__cospi_p16_p16);
+  u2 = _mm_madd_epi16(v0, k__cospi_p16_m16);
+  u3 = _mm_madd_epi16(v1, k__cospi_p16_m16);
+  u4 = _mm_madd_epi16(v2, k__cospi_p24_p08);
+  u5 = _mm_madd_epi16(v3, k__cospi_p24_p08);
+  u6 = _mm_madd_epi16(v2, k__cospi_m08_p24);
+  u7 = _mm_madd_epi16(v3, k__cospi_m08_p24);
+
+  // shift and rounding
+  v0 = _mm_add_epi32(u0, k__DCT_CONST_ROUNDING);
+  v1 = _mm_add_epi32(u1, k__DCT_CONST_ROUNDING);
+  v2 = _mm_add_epi32(u2, k__DCT_CONST_ROUNDING);
+  v3 = _mm_add_epi32(u3, k__DCT_CONST_ROUNDING);
+  v4 = _mm_add_epi32(u4, k__DCT_CONST_ROUNDING);
+  v5 = _mm_add_epi32(u5, k__DCT_CONST_ROUNDING);
+  v6 = _mm_add_epi32(u6, k__DCT_CONST_ROUNDING);
+  v7 = _mm_add_epi32(u7, k__DCT_CONST_ROUNDING);
+
+  u0 = _mm_srai_epi32(v0, DCT_CONST_BITS);
+  u1 = _mm_srai_epi32(v1, DCT_CONST_BITS);
+  u2 = _mm_srai_epi32(v2, DCT_CONST_BITS);
+  u3 = _mm_srai_epi32(v3, DCT_CONST_BITS);
+  u4 = _mm_srai_epi32(v4, DCT_CONST_BITS);
+  u5 = _mm_srai_epi32(v5, DCT_CONST_BITS);
+  u6 = _mm_srai_epi32(v6, DCT_CONST_BITS);
+  u7 = _mm_srai_epi32(v7, DCT_CONST_BITS);
+
+  in[0] = _mm_packs_epi32(u0, u1);
+  in[2] = _mm_packs_epi32(u4, u5);
+  in[4] = _mm_packs_epi32(u2, u3);
+  in[6] = _mm_packs_epi32(u6, u7);
+
+  // stage 2
+  // interleave and perform butterfly multiplication/addition
+  u0 = _mm_unpacklo_epi16(s6, s5);
+  u1 = _mm_unpackhi_epi16(s6, s5);
+  v0 = _mm_madd_epi16(u0, k__cospi_p16_m16);
+  v1 = _mm_madd_epi16(u1, k__cospi_p16_m16);
+  v2 = _mm_madd_epi16(u0, k__cospi_p16_p16);
+  v3 = _mm_madd_epi16(u1, k__cospi_p16_p16);
+
+  // shift and rounding
+  u0 = _mm_add_epi32(v0, k__DCT_CONST_ROUNDING);
+  u1 = _mm_add_epi32(v1, k__DCT_CONST_ROUNDING);
+  u2 = _mm_add_epi32(v2, k__DCT_CONST_ROUNDING);
+  u3 = _mm_add_epi32(v3, k__DCT_CONST_ROUNDING);
+
+  v0 = _mm_srai_epi32(u0, DCT_CONST_BITS);
+  v1 = _mm_srai_epi32(u1, DCT_CONST_BITS);
+  v2 = _mm_srai_epi32(u2, DCT_CONST_BITS);
+  v3 = _mm_srai_epi32(u3, DCT_CONST_BITS);
+
+  u0 = _mm_packs_epi32(v0, v1);
+  u1 = _mm_packs_epi32(v2, v3);
+
+  // stage 3
+  s0 = _mm_add_epi16(s4, u0);
+  s1 = _mm_sub_epi16(s4, u0);
+  s2 = _mm_sub_epi16(s7, u1);
+  s3 = _mm_add_epi16(s7, u1);
+
+  // stage 4
+  u0 = _mm_unpacklo_epi16(s0, s3);
+  u1 = _mm_unpackhi_epi16(s0, s3);
+  u2 = _mm_unpacklo_epi16(s1, s2);
+  u3 = _mm_unpackhi_epi16(s1, s2);
+
+  v0 = _mm_madd_epi16(u0, k__cospi_p28_p04);
+  v1 = _mm_madd_epi16(u1, k__cospi_p28_p04);
+  v2 = _mm_madd_epi16(u2, k__cospi_p12_p20);
+  v3 = _mm_madd_epi16(u3, k__cospi_p12_p20);
+  v4 = _mm_madd_epi16(u2, k__cospi_m20_p12);
+  v5 = _mm_madd_epi16(u3, k__cospi_m20_p12);
+  v6 = _mm_madd_epi16(u0, k__cospi_m04_p28);
+  v7 = _mm_madd_epi16(u1, k__cospi_m04_p28);
+
+  // shift and rounding
+  u0 = _mm_add_epi32(v0, k__DCT_CONST_ROUNDING);
+  u1 = _mm_add_epi32(v1, k__DCT_CONST_ROUNDING);
+  u2 = _mm_add_epi32(v2, k__DCT_CONST_ROUNDING);
+  u3 = _mm_add_epi32(v3, k__DCT_CONST_ROUNDING);
+  u4 = _mm_add_epi32(v4, k__DCT_CONST_ROUNDING);
+  u5 = _mm_add_epi32(v5, k__DCT_CONST_ROUNDING);
+  u6 = _mm_add_epi32(v6, k__DCT_CONST_ROUNDING);
+  u7 = _mm_add_epi32(v7, k__DCT_CONST_ROUNDING);
+
+  v0 = _mm_srai_epi32(u0, DCT_CONST_BITS);
+  v1 = _mm_srai_epi32(u1, DCT_CONST_BITS);
+  v2 = _mm_srai_epi32(u2, DCT_CONST_BITS);
+  v3 = _mm_srai_epi32(u3, DCT_CONST_BITS);
+  v4 = _mm_srai_epi32(u4, DCT_CONST_BITS);
+  v5 = _mm_srai_epi32(u5, DCT_CONST_BITS);
+  v6 = _mm_srai_epi32(u6, DCT_CONST_BITS);
+  v7 = _mm_srai_epi32(u7, DCT_CONST_BITS);
+
+  in[1] = _mm_packs_epi32(v0, v1);
+  in[3] = _mm_packs_epi32(v4, v5);
+  in[5] = _mm_packs_epi32(v2, v3);
+  in[7] = _mm_packs_epi32(v6, v7);
+
+  // transpose
+  array_transpose_8x8(in);
+}
+
+void fadst8_1d_sse2(__m128i in[8]) {
+  // Constants
+  const __m128i k__cospi_p02_p30 = pair_set_epi16(cospi_2_64, cospi_30_64);
+  const __m128i k__cospi_p30_m02 = pair_set_epi16(cospi_30_64, -cospi_2_64);
+  const __m128i k__cospi_p10_p22 = pair_set_epi16(cospi_10_64, cospi_22_64);
+  const __m128i k__cospi_p22_m10 = pair_set_epi16(cospi_22_64, -cospi_10_64);
+  const __m128i k__cospi_p18_p14 = pair_set_epi16(cospi_18_64, cospi_14_64);
+  const __m128i k__cospi_p14_m18 = pair_set_epi16(cospi_14_64, -cospi_18_64);
+  const __m128i k__cospi_p26_p06 = pair_set_epi16(cospi_26_64, cospi_6_64);
+  const __m128i k__cospi_p06_m26 = pair_set_epi16(cospi_6_64, -cospi_26_64);
+  const __m128i k__cospi_p08_p24 = pair_set_epi16(cospi_8_64, cospi_24_64);
+  const __m128i k__cospi_p24_m08 = pair_set_epi16(cospi_24_64, -cospi_8_64);
+  const __m128i k__cospi_m24_p08 = pair_set_epi16(-cospi_24_64, cospi_8_64);
+  const __m128i k__cospi_p16_m16 = pair_set_epi16(cospi_16_64, -cospi_16_64);
+  const __m128i k__cospi_p16_p16 = _mm_set1_epi16(cospi_16_64);
+  const __m128i k__const_0 = _mm_set1_epi16(0);
+  const __m128i k__DCT_CONST_ROUNDING = _mm_set1_epi32(DCT_CONST_ROUNDING);
+
+  __m128i u0, u1, u2, u3, u4, u5, u6, u7, u8, u9, u10, u11, u12, u13, u14, u15;
+  __m128i v0, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15;
+  __m128i w0, w1, w2, w3, w4, w5, w6, w7, w8, w9, w10, w11, w12, w13, w14, w15;
+  __m128i s0, s1, s2, s3, s4, s5, s6, s7;
+  __m128i in0, in1, in2, in3, in4, in5, in6, in7;
+
+  // properly aligned for butterfly input
+  in0  = in[7];
+  in1  = in[0];
+  in2  = in[5];
+  in3  = in[2];
+  in4  = in[3];
+  in5  = in[4];
+  in6  = in[1];
+  in7  = in[6];
+
+  // column transformation
+  // stage 1
+  // interleave and multiply/add into 32-bit integer
+  s0 = _mm_unpacklo_epi16(in0, in1);
+  s1 = _mm_unpackhi_epi16(in0, in1);
+  s2 = _mm_unpacklo_epi16(in2, in3);
+  s3 = _mm_unpackhi_epi16(in2, in3);
+  s4 = _mm_unpacklo_epi16(in4, in5);
+  s5 = _mm_unpackhi_epi16(in4, in5);
+  s6 = _mm_unpacklo_epi16(in6, in7);
+  s7 = _mm_unpackhi_epi16(in6, in7);
+
+  u0 = _mm_madd_epi16(s0, k__cospi_p02_p30);
+  u1 = _mm_madd_epi16(s1, k__cospi_p02_p30);
+  u2 = _mm_madd_epi16(s0, k__cospi_p30_m02);
+  u3 = _mm_madd_epi16(s1, k__cospi_p30_m02);
+  u4 = _mm_madd_epi16(s2, k__cospi_p10_p22);
+  u5 = _mm_madd_epi16(s3, k__cospi_p10_p22);
+  u6 = _mm_madd_epi16(s2, k__cospi_p22_m10);
+  u7 = _mm_madd_epi16(s3, k__cospi_p22_m10);
+  u8 = _mm_madd_epi16(s4, k__cospi_p18_p14);
+  u9 = _mm_madd_epi16(s5, k__cospi_p18_p14);
+  u10 = _mm_madd_epi16(s4, k__cospi_p14_m18);
+  u11 = _mm_madd_epi16(s5, k__cospi_p14_m18);
+  u12 = _mm_madd_epi16(s6, k__cospi_p26_p06);
+  u13 = _mm_madd_epi16(s7, k__cospi_p26_p06);
+  u14 = _mm_madd_epi16(s6, k__cospi_p06_m26);
+  u15 = _mm_madd_epi16(s7, k__cospi_p06_m26);
+
+  // addition
+  w0 = _mm_add_epi32(u0, u8);
+  w1 = _mm_add_epi32(u1, u9);
+  w2 = _mm_add_epi32(u2, u10);
+  w3 = _mm_add_epi32(u3, u11);
+  w4 = _mm_add_epi32(u4, u12);
+  w5 = _mm_add_epi32(u5, u13);
+  w6 = _mm_add_epi32(u6, u14);
+  w7 = _mm_add_epi32(u7, u15);
+  w8 = _mm_sub_epi32(u0, u8);
+  w9 = _mm_sub_epi32(u1, u9);
+  w10 = _mm_sub_epi32(u2, u10);
+  w11 = _mm_sub_epi32(u3, u11);
+  w12 = _mm_sub_epi32(u4, u12);
+  w13 = _mm_sub_epi32(u5, u13);
+  w14 = _mm_sub_epi32(u6, u14);
+  w15 = _mm_sub_epi32(u7, u15);
+
+  // shift and rounding
+  v0 = _mm_add_epi32(w0, k__DCT_CONST_ROUNDING);
+  v1 = _mm_add_epi32(w1, k__DCT_CONST_ROUNDING);
+  v2 = _mm_add_epi32(w2, k__DCT_CONST_ROUNDING);
+  v3 = _mm_add_epi32(w3, k__DCT_CONST_ROUNDING);
+  v4 = _mm_add_epi32(w4, k__DCT_CONST_ROUNDING);
+  v5 = _mm_add_epi32(w5, k__DCT_CONST_ROUNDING);
+  v6 = _mm_add_epi32(w6, k__DCT_CONST_ROUNDING);
+  v7 = _mm_add_epi32(w7, k__DCT_CONST_ROUNDING);
+  v8 = _mm_add_epi32(w8, k__DCT_CONST_ROUNDING);
+  v9 = _mm_add_epi32(w9, k__DCT_CONST_ROUNDING);
+  v10 = _mm_add_epi32(w10, k__DCT_CONST_ROUNDING);
+  v11 = _mm_add_epi32(w11, k__DCT_CONST_ROUNDING);
+  v12 = _mm_add_epi32(w12, k__DCT_CONST_ROUNDING);
+  v13 = _mm_add_epi32(w13, k__DCT_CONST_ROUNDING);
+  v14 = _mm_add_epi32(w14, k__DCT_CONST_ROUNDING);
+  v15 = _mm_add_epi32(w15, k__DCT_CONST_ROUNDING);
+
+  u0 = _mm_srai_epi32(v0, DCT_CONST_BITS);
+  u1 = _mm_srai_epi32(v1, DCT_CONST_BITS);
+  u2 = _mm_srai_epi32(v2, DCT_CONST_BITS);
+  u3 = _mm_srai_epi32(v3, DCT_CONST_BITS);
+  u4 = _mm_srai_epi32(v4, DCT_CONST_BITS);
+  u5 = _mm_srai_epi32(v5, DCT_CONST_BITS);
+  u6 = _mm_srai_epi32(v6, DCT_CONST_BITS);
+  u7 = _mm_srai_epi32(v7, DCT_CONST_BITS);
+  u8 = _mm_srai_epi32(v8, DCT_CONST_BITS);
+  u9 = _mm_srai_epi32(v9, DCT_CONST_BITS);
+  u10 = _mm_srai_epi32(v10, DCT_CONST_BITS);
+  u11 = _mm_srai_epi32(v11, DCT_CONST_BITS);
+  u12 = _mm_srai_epi32(v12, DCT_CONST_BITS);
+  u13 = _mm_srai_epi32(v13, DCT_CONST_BITS);
+  u14 = _mm_srai_epi32(v14, DCT_CONST_BITS);
+  u15 = _mm_srai_epi32(v15, DCT_CONST_BITS);
+
+  // back to 16-bit and pack 8 integers into __m128i
+  in[0] = _mm_packs_epi32(u0, u1);
+  in[1] = _mm_packs_epi32(u2, u3);
+  in[2] = _mm_packs_epi32(u4, u5);
+  in[3] = _mm_packs_epi32(u6, u7);
+  in[4] = _mm_packs_epi32(u8, u9);
+  in[5] = _mm_packs_epi32(u10, u11);
+  in[6] = _mm_packs_epi32(u12, u13);
+  in[7] = _mm_packs_epi32(u14, u15);
+
+  // stage 2
+  s0 = _mm_add_epi16(in[0], in[2]);
+  s1 = _mm_add_epi16(in[1], in[3]);
+  s2 = _mm_sub_epi16(in[0], in[2]);
+  s3 = _mm_sub_epi16(in[1], in[3]);
+  u0 = _mm_unpacklo_epi16(in[4], in[5]);
+  u1 = _mm_unpackhi_epi16(in[4], in[5]);
+  u2 = _mm_unpacklo_epi16(in[6], in[7]);
+  u3 = _mm_unpackhi_epi16(in[6], in[7]);
+
+  v0 = _mm_madd_epi16(u0, k__cospi_p08_p24);
+  v1 = _mm_madd_epi16(u1, k__cospi_p08_p24);
+  v2 = _mm_madd_epi16(u0, k__cospi_p24_m08);
+  v3 = _mm_madd_epi16(u1, k__cospi_p24_m08);
+  v4 = _mm_madd_epi16(u2, k__cospi_m24_p08);
+  v5 = _mm_madd_epi16(u3, k__cospi_m24_p08);
+  v6 = _mm_madd_epi16(u2, k__cospi_p08_p24);
+  v7 = _mm_madd_epi16(u3, k__cospi_p08_p24);
+
+  w0 = _mm_add_epi32(v0, v4);
+  w1 = _mm_add_epi32(v1, v5);
+  w2 = _mm_add_epi32(v2, v6);
+  w3 = _mm_add_epi32(v3, v7);
+  w4 = _mm_sub_epi32(v0, v4);
+  w5 = _mm_sub_epi32(v1, v5);
+  w6 = _mm_sub_epi32(v2, v6);
+  w7 = _mm_sub_epi32(v3, v7);
+
+  v0 = _mm_add_epi32(w0, k__DCT_CONST_ROUNDING);
+  v1 = _mm_add_epi32(w1, k__DCT_CONST_ROUNDING);
+  v2 = _mm_add_epi32(w2, k__DCT_CONST_ROUNDING);
+  v3 = _mm_add_epi32(w3, k__DCT_CONST_ROUNDING);
+  v4 = _mm_add_epi32(w4, k__DCT_CONST_ROUNDING);
+  v5 = _mm_add_epi32(w5, k__DCT_CONST_ROUNDING);
+  v6 = _mm_add_epi32(w6, k__DCT_CONST_ROUNDING);
+  v7 = _mm_add_epi32(w7, k__DCT_CONST_ROUNDING);
+
+  u0 = _mm_srai_epi32(v0, DCT_CONST_BITS);
+  u1 = _mm_srai_epi32(v1, DCT_CONST_BITS);
+  u2 = _mm_srai_epi32(v2, DCT_CONST_BITS);
+  u3 = _mm_srai_epi32(v3, DCT_CONST_BITS);
+  u4 = _mm_srai_epi32(v4, DCT_CONST_BITS);
+  u5 = _mm_srai_epi32(v5, DCT_CONST_BITS);
+  u6 = _mm_srai_epi32(v6, DCT_CONST_BITS);
+  u7 = _mm_srai_epi32(v7, DCT_CONST_BITS);
+
+  // back to 16-bit intergers
+  s4 = _mm_packs_epi32(u0, u1);
+  s5 = _mm_packs_epi32(u2, u3);
+  s6 = _mm_packs_epi32(u4, u5);
+  s7 = _mm_packs_epi32(u6, u7);
+
+  // stage 3
+  u0 = _mm_unpacklo_epi16(s2, s3);
+  u1 = _mm_unpackhi_epi16(s2, s3);
+  u2 = _mm_unpacklo_epi16(s6, s7);
+  u3 = _mm_unpackhi_epi16(s6, s7);
+
+  v0 = _mm_madd_epi16(u0, k__cospi_p16_p16);
+  v1 = _mm_madd_epi16(u1, k__cospi_p16_p16);
+  v2 = _mm_madd_epi16(u0, k__cospi_p16_m16);
+  v3 = _mm_madd_epi16(u1, k__cospi_p16_m16);
+  v4 = _mm_madd_epi16(u2, k__cospi_p16_p16);
+  v5 = _mm_madd_epi16(u3, k__cospi_p16_p16);
+  v6 = _mm_madd_epi16(u2, k__cospi_p16_m16);
+  v7 = _mm_madd_epi16(u3, k__cospi_p16_m16);
+
+  u0 = _mm_add_epi32(v0, k__DCT_CONST_ROUNDING);
+  u1 = _mm_add_epi32(v1, k__DCT_CONST_ROUNDING);
+  u2 = _mm_add_epi32(v2, k__DCT_CONST_ROUNDING);
+  u3 = _mm_add_epi32(v3, k__DCT_CONST_ROUNDING);
+  u4 = _mm_add_epi32(v4, k__DCT_CONST_ROUNDING);
+  u5 = _mm_add_epi32(v5, k__DCT_CONST_ROUNDING);
+  u6 = _mm_add_epi32(v6, k__DCT_CONST_ROUNDING);
+  u7 = _mm_add_epi32(v7, k__DCT_CONST_ROUNDING);
+
+  v0 = _mm_srai_epi32(u0, DCT_CONST_BITS);
+  v1 = _mm_srai_epi32(u1, DCT_CONST_BITS);
+  v2 = _mm_srai_epi32(u2, DCT_CONST_BITS);
+  v3 = _mm_srai_epi32(u3, DCT_CONST_BITS);
+  v4 = _mm_srai_epi32(u4, DCT_CONST_BITS);
+  v5 = _mm_srai_epi32(u5, DCT_CONST_BITS);
+  v6 = _mm_srai_epi32(u6, DCT_CONST_BITS);
+  v7 = _mm_srai_epi32(u7, DCT_CONST_BITS);
+
+  s2 = _mm_packs_epi32(v0, v1);
+  s3 = _mm_packs_epi32(v2, v3);
+  s6 = _mm_packs_epi32(v4, v5);
+  s7 = _mm_packs_epi32(v6, v7);
+
+  // FIXME(jingning): do subtract using bit inversion?
+  in[0] = s0;
+  in[1] = _mm_sub_epi16(k__const_0, s4);
+  in[2] = s6;
+  in[3] = _mm_sub_epi16(k__const_0, s2);
+  in[4] = s3;
+  in[5] = _mm_sub_epi16(k__const_0, s7);
+  in[6] = s5;
+  in[7] = _mm_sub_epi16(k__const_0, s1);
+
+  // transpose
+  array_transpose_8x8(in);
+}
+
+void vp9_short_fht8x8_sse2(int16_t *input, int16_t *output,
+                           int stride, int tx_type) {
+  __m128i in[8];
+  load_buffer_8x8(input, in, stride);
+  switch (tx_type) {
+    case 0:  // DCT_DCT
+      fdct8_1d_sse2(in);
+      fadst8_1d_sse2(in);
+      break;
+    case 1:  // ADST_DCT
+      fadst8_1d_sse2(in);
+      fdct8_1d_sse2(in);
+      break;
+    case 2:  // DCT_ADST
+      fdct8_1d_sse2(in);
+      fadst8_1d_sse2(in);
+      break;
+    case 3:  // ADST_ADST
+      fadst8_1d_sse2(in);
+      fadst8_1d_sse2(in);
+      break;
+    default:
+      assert(0);
+      break;
+  }
+  write_buffer_8x8(output, in);
+}
+
 void vp9_short_fdct16x16_sse2(int16_t *input, int16_t *output, int pitch) {
   // The 2D transform is done with two passes which are actually pretty
   // similar. In the first one, we transform the columns and transpose