[Bug]: 8x communication compared to reported in Cheetah about spu HOT 5 CLOSED

#include "libspu/device/io.h"
#include "libspu/kernel/hlo/basic_binary.h"
#include "libspu/mpc/utils/simulate.h"


template <typename T>
spu::Value infeed(spu::SPUContext* hctx, const xt::xarray<T>& ds) {
  spu::device::ColocatedIo cio(hctx);
  if (hctx->lctx()->Rank() == 0) {
    cio.hostSetVar(fmt::format("x-{}", hctx->lctx()->Rank()), ds);
  }
  cio.sync();
  auto x = cio.deviceGetVar("x-0");
  return x;
}

TEST_P(ObjectivesTest, TestLess) {
  using namespace spu;
  using namespace spu::kernel;
  using namespace spu::mpc;
  //
  // preparing input here ...
  //

  spu::mpc::utils::simulate(2, [&](std::shared_ptr<yacl::link::Context> lctx) {
    spu::RuntimeConfig rt_config;
    rt_config.set_protocol(ProtocolKind::CHEETAH);
    rt_config.mutable_cheetah_2pc_config()->set_ot_kind(
        CheetahOtKind::YACL_Ferret);
    rt_config.set_field(FM32);
    rt_config.set_fxp_fraction_bits(12);

    auto _ctx = std::make_unique<spu::SPUContext>(rt_config, lctx);
    auto ctx = _ctx.get();
    spu::mpc::Factory::RegisterProtocol(ctx, lctx);

    auto x = infeed<double>(ctx, _x);
    auto y = infeed<double>(ctx, _x);
    int64_t numel = x.numel();

    auto b0 = ctx->lctx()->GetStats()->sent_bytes +
              ctx->lctx()->GetStats()->recv_bytes;
    auto comp = hlo::Less(ctx, x, y);

    auto b1 = ctx->lctx()->GetStats()->sent_bytes +
              ctx->lctx()->GetStats()->recv_bytes;

    SPDLOG_INFO("bytes communicated: {}", (b1 - b0) * 1. / numel);

    b0 = ctx->lctx()->GetStats()->sent_bytes +
         ctx->lctx()->GetStats()->recv_bytes;
    comp = hlo::Less(ctx, x, y);
    b1 = ctx->lctx()->GetStats()->sent_bytes +
         ctx->lctx()->GetStats()->recv_bytes;

    SPDLOG_INFO("bytes communicated: {}", (b1 - b0) * 1. / numel);
  });
}

// bazel run -c opt experimental/squirrel:squirrel_demo_main -- --rank=0 --lr=0.2 --field=1
// bazel run -c opt experimental/squirrel:squirrel_demo_main -- --rank=1 --lr=0.3 --field=1

std::unique_ptr<spu::SPUContext> MakeSPUContext() {
  auto lctx = MakeLink(Parties.getValue(), Rank.getValue());

  spu::RuntimeConfig config;
  config.set_protocol(spu::ProtocolKind::CHEETAH);
  config.mutable_cheetah_2pc_config()->set_enable_mul_lsb_error(true);
  // replace `EMP_Ferret` or `YACL_Softspoken` 
  config.mutable_cheetah_2pc_config()->set_ot_kind(
      spu::CheetahOtKind::YACL_Ferret);

  config.set_field(static_cast<spu::FieldType>(Field.getValue()));
  config.set_fxp_fraction_bits(18);
  config.set_fxp_div_goldschmidt_iters(1);
  config.set_enable_hal_profile(EngineTrace.getValue());
  auto hctx = std::make_unique<spu::SPUContext>(config, lctx);
  spu::mpc::Factory::RegisterProtocol(hctx.get(), lctx);
  return hctx;
}

int main(int argc, char** argv) {
  SPDLOG_INFO("in process");
  llvm::cl::ParseCommandLineOptions(argc, argv);
  // YACL_Ferret 
  auto sctx = MakeSPUContext();
  std::vector<size_t> shape = {100};
  xt::xarray<double> input(shape);
  std::fill_n(input.data(), input.size(), LearningRate.getValue());

  auto x = InfeedLabel(sctx.get(), input, sctx->lctx()->Rank() == 0);
  auto y = InfeedLabel(sctx.get(), input, sctx->lctx()->Rank() == 1);

  size_t b0 = sctx->lctx()->GetStats()->sent_bytes +
              sctx->lctx()->GetStats()->recv_bytes;
  auto comp = spu::kernel::hlo::Less(sctx.get(), x, y);
  size_t b1 = sctx->lctx()->GetStats()->sent_bytes +
              sctx->lctx()->GetStats()->recv_bytes;

  printf("size %zd\n", input.size());

  SPDLOG_INFO("bytes communicated: {}", (b1 - b0) * 1. / x.numel());

  b0 = sctx->lctx()->GetStats()->sent_bytes +
       sctx->lctx()->GetStats()->recv_bytes;
  comp = spu::kernel::hlo::Less(sctx.get(), x, y);
  b1 = sctx->lctx()->GetStats()->sent_bytes +
       sctx->lctx()->GetStats()->recv_bytes;

  SPDLOG_INFO("bytes communicated: {}", (b1 - b0) * 1. / x.numel());

  b0 = sctx->lctx()->GetStats()->sent_bytes +
       sctx->lctx()->GetStats()->recv_bytes;
  comp = spu::kernel::hlo::Less(sctx.get(), x, y);
  b1 = sctx->lctx()->GetStats()->sent_bytes +
       sctx->lctx()->GetStats()->recv_bytes;

  SPDLOG_INFO("bytes communicated: {}", (b1 - b0) * 1. / x.numel());

  auto comp_revealed = spu::kernel::hal::dump_public_as<float>(
      sctx.get(),
      spu::kernel::hlo::Cast(sctx.get(), comp, spu::VIS_PUBLIC, comp.dtype()));

  SPDLOG_INFO("comp_revealed: {}", comp_revealed[0]);
  return 0;
}