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!