c++: Is table lookup vectorizable for small lookup-table - c++

Question

I want to vectorize the following snippet of code with SIMD intrinsics is this possible?
unsigned char chain[3][3] = {
3, 2, 1, // y --> x
4, -1, 0, // |
5, 6, 7 // |
}; // v
std::vector<int> x;
std::vector<int> y;
//initialize x, y
std::vector<int> chain_code(x.size());
for(std::size_t i = 0; i < x.size(); ++i
chain_code[i] = chain[x[i]][y[i]];
EDIT:
Support for: SSE - SSE4.2 and AVX
Architectur: Sandy Bridge i5 2500

Answer 1

If you make your x, y, chain_node 8-bit integers (instead of 32-bit ones), then you can process 16 values at once.
Here is the code using SSSE3:
std::vector<uint8_t> x;
std::vector<uint8_t> y;
...
int n = x.size();
std::vector<uint8_t> chain_code(n);
//initialize table register
__m128i table = _mm_setr_epi8(
chain[0][0], chain[0][1], chain[0][2], 99,
chain[1][0], chain[1][1], chain[1][2], 99,
chain[2][0], chain[2][1], chain[2][2], 99,
99, 99, 99, 99
);
int b = (n / 16) * 16;
for (int i = 0; i < b; i += 16) {
//load 16 X/Y bytes
__m128i regX = _mm_loadu_si128((__m128i*)&x[i]);
__m128i regY = _mm_loadu_si128((__m128i*)&y[i]);
//shift all X values left by 2 bits (as 16-bit integers)
__m128i regX4 = _mm_slli_epi16(regX, 2);
//calculate linear indices (x * 4 + y)
__m128i indices = _mm_add_epi8(regX4, regY);
//perform 16 lookups
__m128i res = _mm_shuffle_epi8(table, indices);
//store results
_mm_storeu_si128((__m128i*)&chain_code[i], res);
}
for (int i = b; i < n; i++)
chain_code[i] = chain[x[i]][y[i]];
The fully working version of this code is here. Generated assembly is quite simple (MSVC2013 x64):
movdqu xmm1, XMMWORD PTR [rdi+rax]
movdqu xmm0, XMMWORD PTR [rax]
psllw xmm1, 2
paddb xmm1, xmm0
movdqa xmm0, xmm6
pshufb xmm0, xmm1
movdqu XMMWORD PTR [rsi+rax], xmm0
P.S. I guess you'll have various performance issues with std::vector containers. Perhaps unaligned accesses are no longer expensive, but filling vector with zeros will certainly happen. And it can take more time than the vectorized code.