Option to enable SSE2 optimization about vowpal_wabbit

[zwd-ms]

google benchmark should also show similar results, but it needs to prevent optimizations carefully.

however, in general we could just rely on compiler auto-vectorization to optimize this. Using -O3 -ffast-math -march=native can get much closer to the hand-written intrinsic performance.

#include <benchmark/benchmark.h>

static void BM_inv_sqrt(benchmark::State& state)
{
  volatile float x = 4.f;

  for (auto _ : state)
  {
    benchmark::DoNotOptimize(inv_sqrt(x));
    benchmark::ClobberMemory();
  }
}

static void BM_rsqrt(benchmark::State& state)
{
  volatile float x = 4.f;

  for (auto _ : state)
  {
    benchmark::DoNotOptimize(rsqrt(x));
    benchmark::ClobberMemory();
  }
}

BENCHMARK(BM_inv_sqrt);
BENCHMARK(BM_rsqrt);

BENCHMARK_MAIN();

[zwd-ms]

from GCC doc: https://gcc.gnu.org/onlinedocs/gcc/x86-Options.html#x86-Options

-mrecip

This option enables use of RCPSS and RSQRTSS instructions (and their vectorized variants RCPPS and RSQRTPS) with an additional Newton-Raphson step to increase precision instead of DIVSS and SQRTSS (and their vectorized variants) for single-precision floating-point arguments. These instructions are generated only when -funsafe-math-optimizations is enabled together with -ffinite-math-only and -fno-trapping-math. Note that while the throughput of the sequence is higher than the throughput of the non-reciprocal instruction, the precision of the sequence can be decreased by up to 2 ulp (i.e. the inverse of 1.0 equals 0.99999994).

Note that GCC implements 1.0f/sqrtf(x) in terms of RSQRTSS (or RSQRTPS) already with -ffast-math (or the above option combination), and doesn’t need -mrecip.

Also note that GCC emits the above sequence with additional Newton-Raphson step for vectorized single-float division and vectorized sqrtf(x) already with -ffast-math (or the above option combination), and doesn’t need -mrecip.