#include "vpx_ports/mem.h"
void vp9_fdct4x4_sse2(const int16_t *input, int16_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;
+ // This 2D transform implements 4 vertical 1D transforms followed
+ // by 4 horizontal 1D transforms. The multiplies and adds are as given
+ // by Chen, Smith and Fralick ('77). The commands for moving the data
+ // around have been minimized by hand.
+ // For the purposes of the comments, the 16 inputs are referred to at i0
+ // through iF (in raster order), intermediate variables are a0, b0, c0
+ // through f, and correspond to the in-place computations mapped to input
+ // locations. The outputs, o0 through oF are labeled according to the
+ // output locations.
+
// Constants
- // When we use them, in one case, they are all the same. In all others
- // it's a pair of them that we need to repeat four times. This is done
- // by constructing the 32 bit constant corresponding to that pair.
- 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_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);
+ // These are the coefficients used for the multiplies.
+ // In the comments, pN means cos(N pi /64) and mN is -cos(N pi /64),
+ // where cospi_N_64 = cos(N pi /64)
+ const __m128i k__cospi_A = _mm_setr_epi16(cospi_16_64, cospi_16_64,
+ cospi_16_64, cospi_16_64,
+ cospi_16_64, -cospi_16_64,
+ cospi_16_64, -cospi_16_64);
+ const __m128i k__cospi_B = _mm_setr_epi16(cospi_16_64, -cospi_16_64,
+ cospi_16_64, -cospi_16_64,
+ cospi_16_64, cospi_16_64,
+ cospi_16_64, cospi_16_64);
+ const __m128i k__cospi_C = _mm_setr_epi16(cospi_8_64, cospi_24_64,
+ cospi_8_64, cospi_24_64,
+ cospi_24_64, -cospi_8_64,
+ cospi_24_64, -cospi_8_64);
+ const __m128i k__cospi_D = _mm_setr_epi16(cospi_24_64, -cospi_8_64,
+ cospi_24_64, -cospi_8_64,
+ cospi_8_64, cospi_24_64,
+ cospi_8_64, cospi_24_64);
+ const __m128i k__cospi_E = _mm_setr_epi16(cospi_16_64, cospi_16_64,
+ cospi_16_64, cospi_16_64,
+ cospi_16_64, cospi_16_64,
+ cospi_16_64, cospi_16_64);
+ const __m128i k__cospi_F = _mm_setr_epi16(cospi_16_64, -cospi_16_64,
+ cospi_16_64, -cospi_16_64,
+ cospi_16_64, -cospi_16_64,
+ cospi_16_64, -cospi_16_64);
+ const __m128i k__cospi_G = _mm_setr_epi16(cospi_8_64, cospi_24_64,
+ cospi_8_64, cospi_24_64,
+ -cospi_8_64, -cospi_24_64,
+ -cospi_8_64, -cospi_24_64);
+ const __m128i k__cospi_H = _mm_setr_epi16(cospi_24_64, -cospi_8_64,
+ cospi_24_64, -cospi_8_64,
+ -cospi_24_64, cospi_8_64,
+ -cospi_24_64, cospi_8_64);
+
const __m128i k__DCT_CONST_ROUNDING = _mm_set1_epi32(DCT_CONST_ROUNDING);
+ // This second rounding constant saves doing some extra adds at the end
+ const __m128i k__DCT_CONST_ROUNDING2 = _mm_set1_epi32(DCT_CONST_ROUNDING
+ +(DCT_CONST_ROUNDING << 1));
+ const int DCT_CONST_BITS2 = DCT_CONST_BITS+2;
const __m128i k__nonzero_bias_a = _mm_setr_epi16(0, 1, 1, 1, 1, 1, 1, 1);
const __m128i k__nonzero_bias_b = _mm_setr_epi16(1, 0, 0, 0, 0, 0, 0, 0);
- const __m128i kOne = _mm_set1_epi16(1);
__m128i in0, in1;
+
// Load inputs.
{
in0 = _mm_loadl_epi64((const __m128i *)(input + 0 * stride));
+ in1 = _mm_loadl_epi64((const __m128i *)(input + 1 * stride));
+ in1 = _mm_unpacklo_epi64(in1, _mm_loadl_epi64((const __m128i *)
+ (input + 2 * stride)));
in0 = _mm_unpacklo_epi64(in0, _mm_loadl_epi64((const __m128i *)
- (input + 1 * stride)));
- in1 = _mm_loadl_epi64((const __m128i *)(input + 2 * stride));
- in1 = _mm_unpacklo_epi64(_mm_loadl_epi64((const __m128i *)
- (input + 3 * stride)), in1);
+ (input + 3 * stride)));
+ // in0 = [i0 i1 i2 i3 iC iD iE iF]
+ // in1 = [i4 i5 i6 i7 i8 i9 iA iB]
+
- // x = x << 4
+ // multiply by 16 to give some extra precision
in0 = _mm_slli_epi16(in0, 4);
in1 = _mm_slli_epi16(in1, 4);
// if (i == 0 && input[0]) input[0] += 1;
+ // add 1 to the upper left pixel if it is non-zero, which helps reduce
+ // the round-trip error
{
// The mask will only contain whether the first value is zero, all
// other comparison will fail as something shifted by 4 (above << 4)
in0 = _mm_add_epi16(in0, k__nonzero_bias_b);
}
}
- // Do the two transform/transpose passes
- for (pass = 0; pass < 2; ++pass) {
- // Transform 1/2: Add/subtract
- const __m128i r0 = _mm_add_epi16(in0, in1);
- const __m128i r1 = _mm_sub_epi16(in0, in1);
- const __m128i r2 = _mm_unpacklo_epi64(r0, r1);
- const __m128i r3 = _mm_unpackhi_epi64(r0, r1);
- // Transform 1/2: Interleave to do the multiply by constants which gets us
- // into 32 bits.
- const __m128i t0 = _mm_unpacklo_epi16(r2, r3);
- const __m128i t2 = _mm_unpackhi_epi16(r2, r3);
- const __m128i u0 = _mm_madd_epi16(t0, k__cospi_p16_p16);
- const __m128i u2 = _mm_madd_epi16(t0, k__cospi_p16_m16);
- const __m128i u4 = _mm_madd_epi16(t2, k__cospi_p08_p24);
- const __m128i u6 = _mm_madd_epi16(t2, k__cospi_p24_m08);
+ // There are 4 total stages, alternating between an add/subtract stage
+ // followed by an multiply-and-add stage.
+ {
+ // Stage 1: Add/subtract
+
+ // in0 = [i0 i1 i2 i3 iC iD iE iF]
+ // in1 = [i4 i5 i6 i7 i8 i9 iA iB]
+ const __m128i r0 = _mm_unpacklo_epi16(in0, in1);
+ const __m128i r1 = _mm_unpackhi_epi16(in0, in1);
+ // r0 = [i0 i4 i1 i5 i2 i6 i3 i7]
+ // r1 = [iC i8 iD i9 iE iA iF iB]
+ const __m128i r2 = _mm_shuffle_epi32(r0, 0xB4);
+ const __m128i r3 = _mm_shuffle_epi32(r1, 0xB4);
+ // r2 = [i0 i4 i1 i5 i3 i7 i2 i6]
+ // r3 = [iC i8 iD i9 iF iB iE iA]
+
+ const __m128i t0 = _mm_add_epi16(r2, r3);
+ const __m128i t1 = _mm_sub_epi16(r2, r3);
+ // t0 = [a0 a4 a1 a5 a3 a7 a2 a6]
+ // t1 = [aC a8 aD a9 aF aB aE aA]
+
+ // Stage 2: multiply by constants (which gets us into 32 bits).
+ // The constants needed here are:
+ // k__cospi_A = [p16 p16 p16 p16 p16 m16 p16 m16]
+ // k__cospi_B = [p16 m16 p16 m16 p16 p16 p16 p16]
+ // k__cospi_C = [p08 p24 p08 p24 p24 m08 p24 m08]
+ // k__cospi_D = [p24 m08 p24 m08 p08 p24 p08 p24]
+ const __m128i u0 = _mm_madd_epi16(t0, k__cospi_A);
+ const __m128i u2 = _mm_madd_epi16(t0, k__cospi_B);
+ const __m128i u1 = _mm_madd_epi16(t1, k__cospi_C);
+ const __m128i u3 = _mm_madd_epi16(t1, k__cospi_D);
+ // Then add and right-shift to get back to 16-bit range
const __m128i v0 = _mm_add_epi32(u0, k__DCT_CONST_ROUNDING);
+ const __m128i v1 = _mm_add_epi32(u1, k__DCT_CONST_ROUNDING);
const __m128i v2 = _mm_add_epi32(u2, k__DCT_CONST_ROUNDING);
- const __m128i v4 = _mm_add_epi32(u4, k__DCT_CONST_ROUNDING);
- const __m128i v6 = _mm_add_epi32(u6, k__DCT_CONST_ROUNDING);
+ const __m128i v3 = _mm_add_epi32(u3, k__DCT_CONST_ROUNDING);
const __m128i w0 = _mm_srai_epi32(v0, DCT_CONST_BITS);
+ const __m128i w1 = _mm_srai_epi32(v1, DCT_CONST_BITS);
const __m128i w2 = _mm_srai_epi32(v2, DCT_CONST_BITS);
- const __m128i w4 = _mm_srai_epi32(v4, DCT_CONST_BITS);
- const __m128i w6 = _mm_srai_epi32(v6, DCT_CONST_BITS);
- // Combine and transpose
- const __m128i res0 = _mm_packs_epi32(w0, w2);
- const __m128i res1 = _mm_packs_epi32(w4, w6);
- // 00 01 02 03 20 21 22 23
- // 10 11 12 13 30 31 32 33
- const __m128i tr0_0 = _mm_unpacklo_epi16(res0, res1);
- const __m128i tr0_1 = _mm_unpackhi_epi16(res0, res1);
- // 00 10 01 11 02 12 03 13
- // 20 30 21 31 22 32 23 33
- in0 = _mm_unpacklo_epi32(tr0_0, tr0_1);
- in1 = _mm_unpackhi_epi32(tr0_0, tr0_1);
- in1 = _mm_shuffle_epi32(in1, 0x4E);
- // 00 10 20 30 01 11 21 31 in0 contains 0 followed by 1
- // 02 12 22 32 03 13 23 33 in1 contains 2 followed by 3
+ const __m128i w3 = _mm_srai_epi32(v3, DCT_CONST_BITS);
+ // w0 = [b0 b1 b7 b6]
+ // w1 = [b8 b9 bF bE]
+ // w2 = [b4 b5 b3 b2]
+ // w3 = [bC bD bB bA]
+ const __m128i x0 = _mm_packs_epi32(w0, w1);
+ const __m128i x1 = _mm_packs_epi32(w2, w3);
+ // x0 = [b0 b1 b7 b6 b8 b9 bF bE]
+ // x1 = [b4 b5 b3 b2 bC bD bB bA]
+ in0 = _mm_shuffle_epi32(x0, 0xD8);
+ in1 = _mm_shuffle_epi32(x1, 0x8D);
+ // in0 = [b0 b1 b8 b9 b7 b6 bF bE]
+ // in1 = [b3 b2 bB bA b4 b5 bC bD]
}
- in1 = _mm_shuffle_epi32(in1, 0x4E);
- // Post-condition output and store it (v + 1) >> 2, taking advantage
- // of the fact 1/3 are stored just after 0/2.
{
- __m128i out01 = _mm_add_epi16(in0, kOne);
- __m128i out23 = _mm_add_epi16(in1, kOne);
- out01 = _mm_srai_epi16(out01, 2);
- out23 = _mm_srai_epi16(out23, 2);
- _mm_storeu_si128((__m128i *)(output + 0 * 4), out01);
- _mm_storeu_si128((__m128i *)(output + 2 * 4), out23);
+ // vertical DCTs finished. Now we do the horizontal DCTs.
+ // Stage 3: Add/subtract
+
+ const __m128i t0 = _mm_add_epi16(in0, in1);
+ const __m128i t1 = _mm_sub_epi16(in0, in1);
+ // t0 = [c0 c1 c8 c9 c4 c5 cC cD]
+ // t1 = [c3 c2 cB cA -c7 -c6 -cF -cE]
+
+ // Stage 4: multiply by constants (which gets us into 32 bits).
+ // The constants needed here are:
+ // k__cospi_E = [p16 p16 p16 p16 p16 p16 p16 p16]
+ // k__cospi_F = [p16 m16 p16 m16 p16 m16 p16 m16]
+ // k__cospi_G = [p08 p24 p08 p24 m08 m24 m08 m24]
+ // k__cospi_H = [p24 m08 p24 m08 m24 p08 m24 p08]
+ const __m128i u0 = _mm_madd_epi16(t0, k__cospi_E);
+ const __m128i u1 = _mm_madd_epi16(t0, k__cospi_F);
+ const __m128i u2 = _mm_madd_epi16(t1, k__cospi_G);
+ const __m128i u3 = _mm_madd_epi16(t1, k__cospi_H);
+ // Then add and right-shift to get back to 16-bit range
+ // but this combines the final right-shift as well to save operations
+ // This unusual rounding operations is to maintain bit-accurate
+ // compatibility with the c version of this function which has two
+ // rounding steps in a row.
+ const __m128i v0 = _mm_add_epi32(u0, k__DCT_CONST_ROUNDING2);
+ const __m128i v1 = _mm_add_epi32(u1, k__DCT_CONST_ROUNDING2);
+ const __m128i v2 = _mm_add_epi32(u2, k__DCT_CONST_ROUNDING2);
+ const __m128i v3 = _mm_add_epi32(u3, k__DCT_CONST_ROUNDING2);
+ const __m128i w0 = _mm_srai_epi32(v0, DCT_CONST_BITS2);
+ const __m128i w1 = _mm_srai_epi32(v1, DCT_CONST_BITS2);
+ const __m128i w2 = _mm_srai_epi32(v2, DCT_CONST_BITS2);
+ const __m128i w3 = _mm_srai_epi32(v3, DCT_CONST_BITS2);
+ // w0 = [o0 o4 o8 oC]
+ // w1 = [o2 o6 oA oE]
+ // w2 = [o1 o5 o9 oD]
+ // w3 = [o3 o7 oB oF]
+ // remember the o's are numbered according to the correct output location
+ const __m128i x0 = _mm_packs_epi32(w0, w1);
+ const __m128i x1 = _mm_packs_epi32(w2, w3);
+ // x0 = [o0 o4 o8 oC o2 o6 oA oE]
+ // x1 = [o1 o5 o9 oD o3 o7 oB oF]
+ const __m128i y0 = _mm_unpacklo_epi16(x0, x1);
+ const __m128i y1 = _mm_unpackhi_epi16(x0, x1);
+ // y0 = [o0 o1 o4 o5 o8 o9 oC oD]
+ // y1 = [o2 o3 o6 o7 oA oB oE oF]
+ in0 = _mm_unpacklo_epi32(y0, y1);
+ // in0 = [o0 o1 o2 o3 o4 o5 o6 o7]
+ in1 = _mm_unpackhi_epi32(y0, y1);
+ // in1 = [o8 o9 oA oB oC oD oE oF]
+ }
+ // Post-condition (v + 1) >> 2 is now incorporated into previous
+ // add and right-shift commands. Only 2 store instructions needed
+ // because we are using the fact that 1/3 are stored just after 0/2.
+ {
+ _mm_storeu_si128((__m128i *)(output + 0 * 4), in0);
+ _mm_storeu_si128((__m128i *)(output + 2 * 4), in1);
}
}
+
static INLINE void load_buffer_4x4(const int16_t *input, __m128i *in,
int stride) {
const __m128i k__nonzero_bias_a = _mm_setr_epi16(0, 1, 1, 1, 1, 1, 1, 1);
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