Fix performance issue with nanstd and nanvar

[zhujun98]

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Description

[JohanMabille]

I think the failures are due to missing overloads of isnan in xsimd. These functions were not called before your optimization.

I have on going work on xsimd to push these functions, I'll try to push them quickly so that we can merge this PR.

[zhujun98]

I think the failures are due to missing overloads of isnan in xsimd. These functions were not called before your optimization.

I have on going work on xsimd to push these functions, I'll try to push them quickly so that we can merge this PR.

Thanks a lot @JohanMabille ! Actually, the unittest without SIMD failed too. I will investigate it in the meanwhile.

[zhujun98]

I am completely lost and I summarize my findings here:

Test code:

xt::xarray<double> aN = {{ nanv, nanv, 123, 3 }, { 1, 2, nanv, 3 }, { 1, 1, nanv, 3 }};

  xt::xarray<double> ret2 = xt::nanvar(aN, {1});
  std::cout << "Lazy: " << ret2 << std::endl;

  xt::xarray<double> ret = xt::nanvar(aN, {1}, xt::evaluation_strategy::immediate);
  std::cout << "Immediate: " << ret << std::endl;

• First case:

auto sc_shifted = eval(cast<result_type>(sc) - std::move(mrv));
return nanmean<result_type>(square(sc_shifted), std::forward<X>(axes), es);

Result with gcc8:

Lazy: { 2400.      ,     0.666667,     0.888889}
Immediate: { 3600.      ,     0.666667,     0.888889}

Result with Clang7: segfault

	je     0x4198a0                   ; <xt::xreducer_stepper<xt::xreducer_functors<xt::detail::nan_plus, xt::const_value<double>, xt::detail::nan_plus>, xt::xshared_expression<xt::xfunction<xt::detail::lambda_adapt<xt::square_fct>, xt::xarray_container<xt::uvector<double, std::allocator<double> >, (xt::layout_type)1, xt::svector<unsigned long, 4ul, std::allocator<unsigned long>, true>, xt::xtensor_expression_tag> const&> >, std::array<unsigned long, 1ul>, xt::reducer_options<double, std::tuple<xt::evaluation_strategy::lazy_type> > >::aggregate_impl(unsigned long, std::integral_constant<bool, false>) const+784>
	shl    $0x3,%rcx
	neg    %rax
	mov    %rdi,%rsi
	nopw   0x0(%rax,%rax,1)
	vmovsd (%rsi),%xmm0

• Second case:

return nanmean<result_type>(square(cast<result_type>(sc) - std::move(mrv)), std::forward<X>(axes), es);

Result with gcc8:

Lazy: { 3600.      ,     0.666667,     0.888889}
Immediate: { 7365.388889,     4.666667,    12.      }

Result with clang7:

Lazy: { 3600.      ,     0.666667,     0.888889}
Immediate: { 7365.388889,    12.      ,   363.      }

@JohanMabille @tdegeus Can you give some hint? Thank you!