constexpr_tests.cpp

/* SPDX-License-Identifier: BSD-3-Clause */
/* Copyright © 2023–2026 GSI Helmholtzzentrum fuer Schwerionenforschung GmbH
 *                       Matthias Kretz <m.kretz@gsi.de>
 */

#include "include/simd"
#include <complex>
#include <stdfloat>

namespace simd = std::simd;

using std::complex;

// test that instantiation of the complete class is well-formed
template class simd::basic_vec<int, typename simd::vec<int, 1>::abi_type>;
template class simd::basic_vec<int, typename simd::vec<int, 5>::abi_type>;
template class simd::basic_vec<int, typename simd::vec<int, 8>::abi_type>;
template class simd::basic_vec<int, typename simd::vec<int, 13>::abi_type>;
template class simd::basic_vec<float, typename simd::vec<float, 8>::abi_type>;
template class simd::basic_vec<float, typename simd::vec<float, 13>::abi_type>;
template class simd::basic_vec<complex<double>, typename simd::vec<complex<double>, 3>::abi_type>;

// LWG4420 ///////////////////////////////////////

#ifdef __STDCPP_FLOAT16_T__
namespace LWG4420
{
  using std::convertible_to;
  using std::constructible_from;
  using std::float16_t;
  using std::array;

  static_assert( convertible_to<simd::vec<float16_t, 4>, simd::vec<float, 4>>);
  static_assert(!convertible_to<simd::vec<float, 4>, simd::vec<float16_t, 4>>);

  static_assert( convertible_to<float16_t, simd::vec<float, 4>>);
  static_assert(!convertible_to<float, simd::vec<float16_t, 4>>);

  static_assert(constructible_from<simd::vec<float16_t, 4>, simd::vec<float, 4>>);

  static_assert(convertible_to<array<float16_t, 4>, simd::vec<float, 4>>);
  static_assert(convertible_to<array<float, 4>, simd::vec<float16_t, 4>>); // Mandates flag_convert

  static_assert([] {
    array<float, 4> f4 = {};
    array<float16_t, 4> h4 = {};

    simd::vec<float, 4> vh2f = h4;
    simd::vec<float, 4> vh2f_b = float16_t();

    simd::vec<float16_t, 4> vf2h = {f4, simd::flag_convert};
#if VIR_CONSTEVAL_BROADCAST
    simd::vec<float16_t, 4> vf2h_b{float()};
#endif

    vh2f = vf2h;
    vf2h = static_cast<decltype(vf2h)>(vh2f);

#if VIR_CONSTEVAL_BROADCAST
    return all_of(vh2f == vh2f_b) && all_of(vf2h == vf2h_b);
#else
    return all_of(vh2f == vh2f_b);
#endif
  }());
}
#endif

constexpr auto default_mask_abi_variant =
#ifdef __AVX512F__
  simd::_AbiVariant::_BitMask;
#else
  simd::_AbiVariant();
#endif

namespace test01
{
  using std::same_as;

  using Abi1 = simd::_Abi_t<1, 1, default_mask_abi_variant>;
  static_assert(same_as<simd::vec<int, 1>::abi_type, Abi1>);
  static_assert(same_as<simd::vec<float, 1>::abi_type, Abi1>);

#if defined __SSE__ && !defined __AVX__
  static_assert(same_as<simd::vec<float>::abi_type, simd::_Abi_t<4, 1>>);
  static_assert(same_as<simd::vec<float, 3>::abi_type, simd::_Abi_t<3, 1>>);
  static_assert(same_as<simd::vec<float, 7>::abi_type, simd::_Abi_t<7, 2>>);

  static_assert(simd::vec<float>::size > 1);
  static_assert(alignof(simd::vec<float>) > alignof(float));
  static_assert(alignof(simd::vec<float, 4>) > alignof(float));
  static_assert(alignof(simd::vec<float, 3>) > alignof(float));
  static_assert(sizeof(simd::vec<float, 7>) == 2 * sizeof(simd::vec<float>));
  static_assert(alignof(simd::vec<float, 7>) == alignof(simd::vec<float>));
#endif
}

namespace test02
{
  using namespace std;
  using namespace std::simd;

  static_assert(!destructible<simd::basic_mask<7>>);

  template <int N>
    using expected_abi = _Abi_t<N, 1, default_mask_abi_variant, _AbiVariant::_CxIleav>;

  static_assert(same_as<simd::vec<complex<float>, 1>::abi_type, expected_abi<1>>);
  static_assert(same_as<simd::vec<complex<double>, 1>::abi_type, expected_abi<1>>);

#if defined __AVX512F__
  static_assert(same_as<simd::vec<complex<float>, 2>::abi_type,
			_Abi_t<2, 1, _AbiVariant::_CxIleav, _AbiVariant::_BitMask>>);
  static_assert(same_as<simd::vec<complex<double>, 2>::abi_type,
			_Abi_t<2, 1, _AbiVariant::_CxIleav, _AbiVariant::_BitMask>>);
  static_assert(same_as<simd::vec<complex<float>, 4>::abi_type,
			_Abi_t<4, 1, _AbiVariant::_CxIleav, _AbiVariant::_BitMask>>);
  static_assert(same_as<simd::vec<complex<double>, 4>::abi_type,
			_Abi_t<4, 1, _AbiVariant::_CxIleav, _AbiVariant::_BitMask>>);
#elif defined __AVX__
  static_assert(same_as<simd::vec<complex<float>, 2>::abi_type,
			_Abi_t<2, 1, _AbiVariant::_CxIleav>>);
  static_assert(same_as<simd::vec<complex<double>, 2>::abi_type,
			_Abi_t<2, 1, _AbiVariant::_CxIleav>>);
  static_assert(same_as<simd::vec<complex<float>, 4>::abi_type,
			_Abi_t<4, 1, _AbiVariant::_CxIleav>>);
  static_assert(same_as<simd::vec<complex<double>, 4>::abi_type,
			_Abi_t<4, 2, _AbiVariant::_CxIleav>>);
#elif defined __SSE__
  static_assert(same_as<simd::vec<complex<float>, 2>::abi_type,
			_Abi_t<2, 1, _AbiVariant::_CxIleav>>);
  static_assert(same_as<simd::vec<complex<double>, 2>::abi_type,
			_Abi_t<2, 2, _AbiVariant::_CxIleav>>);
  static_assert(same_as<simd::vec<complex<float>, 4>::abi_type,
			_Abi_t<4, 2, _AbiVariant::_CxIleav>>);
  static_assert(same_as<simd::vec<complex<double>, 4>::abi_type,
			_Abi_t<4, 4, _AbiVariant::_CxIleav>>);
#endif

  static_assert(same_as<simd::vec<int>::mask_type, simd::mask<int>>);
  static_assert(same_as<simd::vec<float>::mask_type, simd::mask<float>>);
  static_assert(same_as<simd::vec<float, 1>::mask_type, simd::mask<float, 1>>);

  static_assert(destructible<simd::vec<complex<float>>>);
  static_assert(same_as<simd::vec<complex<float>>::mask_type, simd::mask<complex<float>>>);
  static_assert(same_as<simd::vec<complex<float>, 1>::mask_type, simd::mask<complex<float>, 1>>);

  // ensure 'true ? int : vec<float>' doesn't work
  template <typename T>
    concept has_type_member = requires { typename T::type; };
#if VIR_CONSTEVAL_BROADCAST
  static_assert(has_type_member<common_type<int, simd::vec<float>>>);
#else
  static_assert(!has_type_member<common_type<int, simd::vec<float>>>);
#endif

#ifdef __clang__
#pragma clang diagnostic ignored "-Wunused-const-variable"
#endif
  constexpr simd::vec<complex<double>>::mask_type k = {};
}

#if defined __AVX__ && !defined __AVX2__
static_assert(alignof(simd::mask<int, 8>) == 16);
static_assert(alignof(simd::mask<float, 8>) == 32);
static_assert(alignof(simd::mask<int, 16>) == 16);
static_assert(alignof(simd::mask<float, 16>) == 32);
static_assert(alignof(simd::mask<long long, 4>) == 16);
static_assert(alignof(simd::mask<double, 4>) == 32);
static_assert(alignof(simd::mask<long long, 8>) == 16);
static_assert(alignof(simd::mask<double, 8>) == 32);
static_assert(std::same_as<decltype(+simd::mask<float, 8>()), simd::vec<int, 8>>);
#endif

#if defined __SSE__ && !defined __F16C__ && defined __STDCPP_FLOAT16_T__
static_assert(simd::vec<std::float16_t>::size() == 1);
static_assert(simd::mask<std::float16_t>::size() == 1);
static_assert(simd::vec<std::complex<std::float16_t>>::size() == 1);
static_assert(simd::mask<std::complex<std::float16_t>>::size() == 1);
static_assert(alignof(simd::vec<std::float16_t, 8>) == alignof(std::float16_t));
static_assert(alignof(simd::rebind_t<std::float16_t, simd::vec<float>>) == alignof(std::float16_t));
static_assert(simd::rebind_t<std::float16_t, simd::mask<float>>::abi_type::_S_nreg
		== simd::vec<float>::size());
#endif

template <auto X>
  using Ic = std::integral_constant<std::remove_const_t<decltype(X)>, X>;

static_assert( std::convertible_to<Ic<1>, simd::vec<float>>);
static_assert(!std::convertible_to<Ic<1.1>, simd::vec<float>>);
static_assert(!std::convertible_to<simd::vec<int, 4>, simd::vec<float, 4>>);
static_assert(!std::convertible_to<simd::vec<float, 4>, simd::vec<int, 4>>);
#if VIR_CONSTEVAL_BROADCAST
static_assert( std::convertible_to<int, simd::vec<float>>);
#else
static_assert(!std::convertible_to<int, simd::vec<float>>);
#endif
static_assert( std::convertible_to<simd::vec<int, 4>, simd::vec<double, 4>>);

template <typename V>
  concept has_static_size = requires {
    { V::size } -> std::convertible_to<int>;
    { V::size() } -> std::signed_integral;
    { auto(V::size.value) } -> std::signed_integral;
  };

template <typename V, typename T = typename V::value_type>
  concept usable_vec_or_mask
    = std::destructible<V>
	&& std::is_nothrow_move_constructible_v<V>
	&& std::is_nothrow_move_assignable_v<V>
	&& std::is_nothrow_default_constructible_v<V>
	&& std::is_trivially_copyable_v<V>
	&& std::is_standard_layout_v<V>
	&& std::ranges::random_access_range<V&>
	&& !std::ranges::output_range<V&, T>
	&& std::constructible_from<V, T> // broadcast
#if SIMD_CONCEPTS
	&& simd::regular<V>
	&& simd::equality_comparable<V>
#endif
	&& has_static_size<V>
	&& simd::__simd_vec_or_mask_type<V>
      ;

template <typename V, typename T = typename V::value_type>
  concept usable_vec
    = usable_vec_or_mask<V, T>
	&& !std::convertible_to<V, std::array<T, V::size()>>
	&& std::convertible_to<std::array<T, V::size()>, V>
	&& std::constructible_from<V, simd::rebind_t<int, V>>
	&& std::constructible_from<V, simd::rebind_t<float, V>>
	&& !std::constructible_from<V, simd::resize_t<V::size() + 1, V>>
	&& !std::constructible_from<V, simd::resize_t<V::size() + 1, typename V::mask_type>>
	&& !std::constructible_from<typename V::mask_type, V>
#if SIMD_CONCEPTS
      // Not for masks because std::integral<bool> is true but datapar::integral looks for a
      // basic_vec specialization.
	&& simd::integral<V> == std::integral<T>
      // Not for masks because no implicit conversion from bool -> mask
	&& simd::equality_comparable_with<V, T>
	&& simd::equality_comparable_with<T, V>
#endif
      ;

template <typename M, typename T = typename M::value_type>
  concept usable_mask
    = std::is_same_v<T, bool>
	&& usable_vec_or_mask<M, T>
	&& std::convertible_to<std::bitset<M::size()>, M>
	&& std::constructible_from<M, unsigned long long>
	&& std::constructible_from<M, unsigned char>
	&& std::constructible_from<M, simd::rebind_t<int, M>>
	&& std::constructible_from<M, simd::rebind_t<float, M>>
	&& !std::constructible_from<M, simd::resize_t<M::size() + 1, M>>
	&& !std::convertible_to<unsigned long long, M>
	&& !std::convertible_to<unsigned char, M>
	&& !std::convertible_to<bool, M>
	&& !std::constructible_from<M, std::bitset<M::size() + 1>>
	&& !std::constructible_from<M, std::bitset<M::size() - 1>>
	&& !std::constructible_from<M, int>
	&& !std::constructible_from<M, float>
      ;

template <typename T>
  struct test_usable_simd
  {
    static_assert(!usable_vec<simd::vec<T, 0>>);
    static_assert(!has_static_size<simd::vec<T, 0>>);
    static_assert(usable_vec<simd::vec<T, 1>>);
    static_assert(usable_vec<simd::vec<T, 2>>);
    static_assert(usable_vec<simd::vec<T, 3>>);
    static_assert(usable_vec<simd::vec<T, 4>>);
    static_assert(usable_vec<simd::vec<T, 7>>);
    static_assert(usable_vec<simd::vec<T, 8>>);
    static_assert(usable_vec<simd::vec<T, 16>>);
    static_assert(usable_vec<simd::vec<T, 32>>);
    static_assert(usable_vec<simd::vec<T, 63>>);
    static_assert(usable_vec<simd::vec<T, 64>>);

    static_assert(!usable_mask<simd::mask<T, 0>>);
    static_assert(!has_static_size<simd::mask<T, 0>>);
    static_assert(usable_mask<simd::mask<T, 1>>);
    static_assert(usable_mask<simd::mask<T, 2>>);
    static_assert(usable_mask<simd::mask<T, 3>>);
    static_assert(usable_mask<simd::mask<T, 4>>);
    static_assert(usable_mask<simd::mask<T, 7>>);
    static_assert(usable_mask<simd::mask<T, 8>>);
    static_assert(usable_mask<simd::mask<T, 16>>);
    static_assert(usable_mask<simd::mask<T, 32>>);
    static_assert(usable_mask<simd::mask<T, 63>>);
    static_assert(usable_mask<simd::mask<T, 64>>);
  };

template <template <typename> class Tpl>
  struct instantiate_all_vectorizable
  {
    Tpl<float> a;
    Tpl<double> b;
    Tpl<char> c;
    Tpl<char8_t> c8;
    Tpl<char16_t> d;
    Tpl<char32_t> e;
    Tpl<wchar_t> f;
    Tpl<signed char> g;
    Tpl<unsigned char> h;
    Tpl<short> i;
    Tpl<unsigned short> j;
    Tpl<int> k;
    Tpl<unsigned int> l;
    Tpl<long> m;
    Tpl<unsigned long> n;
    Tpl<long long> o;
    Tpl<unsigned long long> p;
#ifdef __STDCPP_FLOAT16_T__
    Tpl<std::float16_t> q;
    Tpl<std::complex<std::float16_t>> qc;
#endif
#ifdef __STDCPP_FLOAT32_T__
    Tpl<std::float32_t> r;
    Tpl<std::complex<std::float32_t>> rc;
#endif
#ifdef __STDCPP_FLOAT64_T__
    Tpl<std::float64_t> s;
    Tpl<std::complex<std::float64_t>> sc;
#endif
    Tpl<std::complex<float>> u;
    Tpl<std::complex<double>> v;
  };

template struct instantiate_all_vectorizable<test_usable_simd>;

// vec broadcast ctor ///////////////
namespace test_broadcast
{
  using std::constructible_from;
  using std::complex;
  using simd::vec;

  static_assert(constructible_from<simd::vec<complex<float>>, complex<float>>);
  static_assert(constructible_from<simd::vec<complex<double>>, complex<float>>);

  constexpr simd::vec<complex<double>, 2> cd2 = 1.f; // broadcast real from float
  static_assert(all_of(cd2.real() == 1));
  static_assert(all_of(cd2.imag() == 0));
  static_assert(all_of(cd2 == complex{1.f, 0.f}));
}

// vec generator ctor ///////////////

namespace test_generator
{
  struct udt_convertible_to_float
  { operator float() const; };

  static_assert( std::constructible_from<simd::vec<float>, float (&)(int)>);
  static_assert(!std::convertible_to<float (&)(int), simd::vec<float>>);
  static_assert(!std::constructible_from<simd::vec<float>, int (&)(int)>);
  static_assert(!std::constructible_from<simd::vec<float>, double (&)(int)>);
  static_assert( std::constructible_from<simd::vec<float>, short (&)(int)>);
  static_assert(!std::constructible_from<simd::vec<float>, long double (&)(int)>);
  static_assert( std::constructible_from<simd::vec<float>, udt_convertible_to_float (&)(int)>);
  static_assert( std::constructible_from<simd::vec<std::complex<double>>,
					 std::complex<double> (&)(int)>);
  static_assert( std::constructible_from<simd::vec<std::complex<double>>,
					 std::complex<float> (&)(int)>);
}

// mask generator ctor ///////////////

static_assert(
  all_of(simd::mask<float, 4>([](int) { return true; }) == simd::mask<float, 4>(true)));
static_assert(
  all_of(simd::mask<float, 4>([](int) { return false; }) == simd::mask<float, 4>(false)));
static_assert(
  all_of(simd::mask<float, 4>([](int i) { return i < 2; })
	   == simd::mask<float, 4>([](int i) {
		return std::array{true, true, false, false}[i];
	      })));

static_assert(all_of((simd::vec<int, 4>([](int i) { return i << 10; }) >> 10)
		== simd::__iota<simd::vec<int, 4>>));

// vec iterators /////////////////////

#if SIMD_IS_A_RANGE
static_assert([] { simd::vec<float> x = {}; return x.begin() == x.begin(); }());
static_assert([] { simd::vec<float> x = {}; return x.begin() == x.cbegin(); }());
static_assert([] { simd::vec<float> x = {}; return x.cbegin() == x.begin(); }());
static_assert([] { simd::vec<float> x = {}; return x.cbegin() == x.cbegin(); }());
static_assert([] { simd::vec<float> x = {}; return x.begin() + x.size() == x.end(); }());
static_assert([] { simd::vec<float> x = {}; return x.end() == x.begin() + x.size(); }());
static_assert([] { simd::vec<float> x = {}; return x.begin() < x.end(); }());
static_assert([] { simd::vec<float> x = {}; return x.begin() <= x.end(); }());
static_assert(![] { simd::vec<float> x = {}; return x.begin() > x.end(); }());
static_assert(![] { simd::vec<float> x = {}; return x.begin() >= x.end(); }());
static_assert(![] { simd::vec<float> x = {}; return x.end() < x.begin(); }());
static_assert(![] { simd::vec<float> x = {}; return x.end() <= x.begin(); }());
static_assert([] { simd::vec<float> x = {}; return x.end() > x.begin(); }());
static_assert([] { simd::vec<float> x = {}; return x.end() >= x.begin(); }());
static_assert([] { simd::vec<float> x = {}; return x.end() - x.begin(); }() == simd::vec<float>::size());
static_assert([] { simd::vec<float> x = {}; return x.begin() - x.end(); }() == -simd::vec<float>::size());
static_assert([] { simd::vec<float> x = {}; return x.begin() - x.begin(); }() == 0);
static_assert([] { simd::vec<float> x = {}; return x.begin() + 1 - x.begin(); }() == 1);
static_assert([] { simd::vec<float> x = {}; return x.begin() + 1 - x.cbegin(); }() == 1);
#endif

// mask to vec ///////////////////////

// Clang says all kinds of expressions are not constant expressions. Why? Come on … explain! 🤷
#ifdef __clang__
#define AVOID_BROKEN_CLANG_FAILURES 1
#endif

#ifndef AVOID_BROKEN_CLANG_FAILURES

static_assert([] constexpr {
  constexpr simd::mask<float, 7> a([](int i) -> bool { return i < 3; });
  constexpr simd::basic_vec b = -a;
  static_assert(b[0] == -(0 < 3));
  static_assert(b[1] == -(1 < 3));
  static_assert(b[2] == -(2 < 3));
  static_assert(b[3] == -(3 < 3));
  return all_of(b == simd::vec<int, 7>([](int i) { return -int(i < 3); }));
}());

static_assert([] constexpr {
  constexpr simd::mask<float, 7> a([](int i) -> bool { return i < 3; });
  constexpr simd::basic_vec b = ~a;
  static_assert(b[0] == ~int(0 < 3));
  static_assert(b[1] == ~int(1 < 3));
  static_assert(b[2] == ~int(2 < 3));
  static_assert(b[3] == ~int(3 < 3));
  return all_of(b == simd::vec<int, 7>([](int i) { return ~int(i < 3); }));
}());

static_assert([] constexpr {
  constexpr simd::mask<float, 4> a([](int i) -> bool { return i < 2; });
  constexpr simd::basic_vec b = a;
  static_assert(b[0] == 1);
  static_assert(b[1] == 1);
  static_assert(b[2] == 0);
  return b[3] == 0;
}());

static_assert([] constexpr {
  // Corner case on AVX w/o AVX2 systems. <float, 5> is an AVX register;
  // <int, 5> is deduced as SSE + scalar.
  constexpr simd::mask<float, 5> a([](int i) -> bool { return i >= 2; });
  constexpr simd::basic_vec b = a;
  static_assert(b[0] == 0);
  static_assert(b[1] == 0);
  static_assert(b[2] == 1);
  static_assert(b[3] == 1);
  static_assert(b[4] == 1);
#if defined __AVX2__ || !defined __AVX__
  static_assert(all_of((b == 1) == a));
#endif
  constexpr simd::mask<float, 8> a8([](int i) -> bool { return i <= 4; });
  constexpr simd::basic_vec b8 = a8;
  static_assert(b8[0] == 1);
  static_assert(b8[1] == 1);
  static_assert(b8[2] == 1);
  static_assert(b8[3] == 1);
  static_assert(b8[4] == 1);
  static_assert(b8[5] == 0);
  static_assert(b8[6] == 0);
  static_assert(b8[7] == 0);
#if SIMD_MASK_IMPLICIT_CONVERSIONS || defined __AVX2__ || !defined __AVX__
  static_assert(all_of((b8 == 1) == a8));
#endif
  constexpr simd::mask<float, 15> a15([](int i) -> bool { return i <= 4; });
  constexpr simd::basic_vec b15 = a15;
  static_assert(b15[0] == 1);
  static_assert(b15[4] == 1);
  static_assert(b15[5] == 0);
  static_assert(b15[8] == 0);
  static_assert(b15[14] == 0);
  static_assert(all_of((b15 == 1) == a15));
  return true;
}());

static_assert([] constexpr {
  constexpr simd::mask<float, 4> a([](int i) -> bool { return i < 2; });
  constexpr simd::basic_vec b = ~a;
  constexpr simd::basic_vec c = a;
  static_assert(c[0] == int(a[0]));
  static_assert(c[1] == int(a[1]));
  static_assert(c[2] == int(a[2]));
  static_assert(c[3] == int(a[3]));
  static_assert(b[0] == ~int(0 < 2));
  static_assert(b[1] == ~int(1 < 2));
  static_assert(b[2] == ~int(2 < 2));
  static_assert(b[3] == ~int(3 < 2));
  return all_of(b == simd::vec<int, 4>([](int i) { return ~int(i < 2); }));
}());
#endif

// mask conversions //////////////////
namespace mask_conversion_tests
{
  using std::complex;
  using simd::mask;

  struct TestResult
  {
    int state;
    unsigned long long a, b;
  };

  template <auto Res>
    consteval void
    check()
    {
      if constexpr (Res.state != 0 && Res.a != Res.b)
	static_assert(Res.a == Res.b);
      else
	static_assert(Res.state == 0);
    }

  template <typename U>
    consteval TestResult
    do_test(const auto& k)
    {
      using M = simd::mask<U, k.size()>;
      if constexpr (std::is_destructible_v<M>)
	{
	  if (!std::ranges::equal(M(k), k))
	    {
	      if constexpr (k.size() <= 64)
		return {1, M(k).to_ullong(), k.to_ullong()};
	      else
		return {1, 0, 0};
	    }
	  else
	    return {0, 0, 0};
	}
      else
	return {0, 0, 0};
    }

  template <typename T, int N, int P = 0>
    consteval void
    do_test()
    {
      if constexpr (std::is_destructible_v<simd::mask<T, N>>)
	{
	  constexpr simd::mask<T, N> k([](int i) {
		      if constexpr (P == 2)
			return std::has_single_bit(unsigned(i));
		      else if constexpr (P == 3)
			return !std::has_single_bit(unsigned(i));
		      else
			return (i & 1) == P;
		    });
	  check<do_test<char>(    k)>();
	  check<do_test<char>(!k)>();
	  check<do_test<short>(    k)>();
	  check<do_test<short>(!k)>();
	  check<do_test<int>(    k)>();
	  check<do_test<int>(!k)>();
	  check<do_test<double>(    k)>();
	  check<do_test<double>(!k)>();
#ifdef __STDCPP_FLOAT16_T__
	  check<do_test<std::float16_t>(    k)>();
	  check<do_test<std::float16_t>(!k)>();
#endif
	  check<do_test<complex<float>>(    k)>();
	  check<do_test<complex<float>>(!k)>();
	  check<do_test<complex<double>>(    k)>();
	  check<do_test<complex<double>>(!k)>();
	  if constexpr (P <= 2)
	    do_test<T, N, P + 1>();
	}
    }

  template <typename T>
    consteval bool
    test()
    {
      using V = simd::mask<T>;
      do_test<T, 1>();
      do_test<T, V::size()>();
      do_test<T, 2 * V::size()>();
      do_test<T, 4 * V::size()>();
      do_test<T, 5 * V::size()>();
      do_test<T, 2 * V::size() + 1>();
      do_test<T, 2 * V::size() - 1>();
      do_test<T, V::size() / 2>();
      do_test<T, V::size() / 3>();
      do_test<T, V::size() / 5>();
      return true;
    }

  static_assert(test<char>());
  static_assert(test<short>());
  static_assert(test<float>());
  static_assert(test<double>());
#ifdef __STDCPP_FLOAT16_T__
  static_assert(test<std::float16_t>());
#endif
  static_assert(test<complex<float>>());
  static_assert(test<complex<double>>());
}

// vec reductions ///////////////////

namespace simd_reduction_tests
{
  static_assert(reduce(simd::vec<int, 7>(1)) == 7);
  static_assert(reduce(simd::vec<int, 7>(2), std::multiplies<>()) == 128);
  static_assert(reduce(simd::vec<int, 8>(2), std::bit_and<>()) == 2);
  static_assert(reduce(simd::vec<int, 8>(2), std::bit_or<>()) == 2);
  static_assert(reduce(simd::vec<int, 8>(2), std::bit_xor<>()) == 0);
  static_assert(reduce(simd::vec<int, 3>(2), std::bit_and<>()) == 2);
  static_assert(reduce(simd::vec<int, 6>(2), std::bit_and<>()) == 2);
  static_assert(reduce(simd::vec<int, 7>(2), std::bit_and<>()) == 2);
  static_assert(reduce(simd::vec<int, 7>(2), std::bit_or<>()) == 2);
  static_assert(reduce(simd::vec<int, 7>(2), std::bit_xor<>()) == 2);
#ifndef AVOID_BROKEN_CLANG_FAILURES
  static_assert(reduce(simd::vec<int, 4>(2), simd::mask<int, 4>(false)) == 0);
  static_assert(reduce(simd::vec<int, 4>(2), simd::mask<int, 4>(false), std::multiplies<>()) == 1);
  static_assert(reduce(simd::vec<int, 4>(2), simd::mask<int, 4>(false), std::bit_and<>()) == ~0);
  static_assert(reduce(simd::vec<int, 4>(2), simd::mask<int, 4>(false), [](auto a, auto b) {
		  return select(a < b, a, b);
		}, __INT_MAX__) == __INT_MAX__);
#endif

  template <typename BinaryOperation>
    concept masked_reduce_works = requires(simd::vec<int, 4> a, simd::vec<int, 4> b) {
      reduce(a, a < b, BinaryOperation());
    };

  static_assert(!masked_reduce_works<std::minus<>>);
}

// mask reductions ///////////////////

static_assert(all_of(simd::vec<float>() == simd::vec<float>()));
static_assert(any_of(simd::vec<float>() == simd::vec<float>()));
static_assert(!none_of(simd::vec<float>() == simd::vec<float>()));
static_assert(reduce_count(simd::vec<float>() == simd::vec<float>()) == simd::vec<float>::size);
static_assert(reduce_min_index(simd::vec<float>() == simd::vec<float>()) == 0);
static_assert(reduce_max_index(simd::vec<float>() == simd::vec<float>()) == simd::vec<float>::size - 1);

// chunk ////////////////////////

static_assert([] {
  constexpr auto a = simd::vec<int, 8>([] (int i) { return i; });
  auto a4 = chunk<simd::vec<int, 4>>(a);
  auto a3 = chunk<simd::vec<int, 3>>(a);
  auto a3_ = chunk<3>(a);
  return a4.size() == 2 && std::same_as<decltype(a4), std::array<simd::vec<int, 4>, 2>>
	   && std::tuple_size_v<decltype(a3)> == 3
	   && all_of(std::get<0>(a3) == simd::vec<int, 3>([] (int i) { return i; }))
	   && all_of(std::get<1>(a3) == simd::vec<int, 3>([] (int i) { return i + 3; }))
	   && all_of(std::get<2>(a3) == simd::vec<int, 2>([] (int i) { return i + 6; }))
	   && std::same_as<decltype(a3), decltype(a3_)>
	   && all_of(std::get<0>(a3) == std::get<0>(a3_));
}());

static_assert([] {
  constexpr simd::mask<int, 8> a([] (int i) -> bool { return i & 1; });
  auto a4 = chunk<simd::mask<int, 4>>(a);
  auto a3 = chunk<simd::mask<int, 3>>(a);
  auto a3_ = chunk<3>(a);
  return a4.size() == 2 && std::same_as<decltype(a4), std::array<simd::mask<int, 4>, 2>>
	   && std::tuple_size_v<decltype(a3)> == 3
	   && all_of(std::get<0>(a3) == simd::mask<int, 3>(
					   [] (int i) -> bool { return i & 1; }))
	   && all_of(std::get<1>(a3) == simd::mask<int, 3>(
					   [] (int i) -> bool { return (i + 3) & 1; }))
	   && all_of(std::get<2>(a3) == simd::mask<int, 2>(
					   [] (int i) -> bool { return (i + 6) & 1; }))
	   && std::same_as<decltype(a3), decltype(a3_)>
	   && all_of(std::get<0>(a3) == std::get<0>(a3_));
}());

// cat ///////////////////////////

static_assert(all_of(simd::cat(simd::__iota<simd::vec<int, 3>>, simd::vec<int, 1>(3))
		       == simd::__iota<simd::vec<int, 4>>));

static_assert(all_of(simd::cat(simd::__iota<simd::vec<int, 4>>, simd::__iota<simd::vec<int, 4>> + 4)
		       == simd::__iota<simd::vec<int, 8>>));

static_assert(all_of(simd::cat(simd::__iota<simd::vec<double, 4>>, simd::__iota<simd::vec<double, 2>> + 4)
		       == simd::__iota<simd::vec<double, 6>>));

static_assert(all_of(simd::cat(simd::__iota<simd::vec<double, 4>>, simd::__iota<simd::vec<double, 4>> + 4)
		       == simd::__iota<simd::vec<double, 8>>));

static_assert(all_of(simd::cat(simd::__iota<simd::vec<complex<float>, 1>>,
			       simd::__iota<simd::vec<complex<float>, 1>> + 1.f)
		       == simd::__iota<simd::vec<complex<float>, 2>>));

static_assert(all_of(simd::cat(simd::__iota<simd::vec<complex<float>, 3>>,
			       simd::__iota<simd::vec<complex<float>, 3>> + 3.f)
		       == simd::__iota<simd::vec<complex<float>, 6>>));

static_assert(all_of(simd::cat(simd::__iota<simd::vec<complex<float>, 8>>,
			       simd::__iota<simd::vec<complex<float>, 8>> + 8.f)
		       == simd::__iota<simd::vec<complex<float>, 16>>));

// select ////////////////////////

#ifndef AVOID_BROKEN_CLANG_FAILURES
static_assert(all_of(simd::vec<long long, 8>(std::array{0, 0, 0, 0, 4, 4, 4, 4})
		       == select(simd::__iota<simd::vec<double, 8>> < 4, 0ll, 4ll)));

static_assert(all_of(simd::vec<int, 8>(std::array{0, 0, 0, 0, 4, 4, 4, 4})
		       == select(simd::__iota<simd::vec<float, 8>> < 4.f, 0, 4)));
#endif

// permute ////////////////////////

namespace permutations
{
  struct _DuplicateEven
  {
    consteval unsigned
    operator()(unsigned __i) const
    { return __i & ~1u; }
  };

  inline constexpr _DuplicateEven duplicate_even {};

  struct _DuplicateOdd
  {
    consteval unsigned
    operator()(unsigned __i) const
    { return __i | 1u; }
  };

  inline constexpr _DuplicateOdd duplicate_odd {};

  template <unsigned _Np>
    struct _SwapNeighbors
    {
      consteval unsigned
      operator()(unsigned __i, unsigned __size) const
      {
	if (__size % (2 * _Np) != 0)
	  abort(); // swap_neighbors<N> permutation requires a multiple of 2N elements
	else if (std::has_single_bit(_Np))
	  return __i ^ _Np;
	else if (__i % (2 * _Np) >= _Np)
	  return __i - _Np;
	else
	  return __i + _Np;
      }
    };

  template <unsigned _Np = 1u>
    inline constexpr _SwapNeighbors<_Np> swap_neighbors {};

  template <int _Position>
    struct _Broadcast
    {
      consteval int
      operator()(int, int __size) const
      { return _Position < 0 ? __size + _Position : _Position; }
    };

  template <int _Position>
    inline constexpr _Broadcast<_Position> broadcast {};

  inline constexpr _Broadcast<0> broadcast_first {};

  inline constexpr _Broadcast<-1> broadcast_last {};

  struct _Reverse
  {
    consteval int
    operator()(int __i, int __size) const
    { return __size - 1 - __i; }
  };

  inline constexpr _Reverse reverse {};

  template <int _Offset>
    struct _Rotate
    {
      consteval int
      operator()(int __i, int __size) const
      {
	__i += _Offset;
	__i %= __size;
	if (__i < 0)
	  __i += __size;
	return __i;
      }
    };

  template <int _Offset>
    inline constexpr _Rotate<_Offset> rotate {};

  template <int _Offset>
    struct _Shift
    {
      consteval int
      operator()(int __i, int __size) const
      {
	const int __j = __i + _Offset;
	if (__j >= __size || -__j > __size)
	  return simd::zero_element;
	else if (__j < 0)
	  return __size + __j;
	else
	  return __j;
      }
    };

  template <int _Offset>
    inline constexpr _Shift<_Offset> shift {};
}

static_assert(
  all_of(simd::permute(simd::__iota<simd::vec<int>>, permutations::duplicate_even)
	   == simd::__iota<simd::vec<int>> / 2 * 2));

static_assert(
  all_of(simd::permute(simd::__iota<simd::vec<int>>, permutations::duplicate_odd)
	   == simd::__iota<simd::vec<int>> / 2 * 2 + 1));

static_assert(
  all_of(simd::permute(simd::__iota<simd::vec<int>>, permutations::swap_neighbors<1>)
	   == simd::vec<int>([](int i) { return i ^ 1; })));

static_assert(
  all_of(simd::permute(simd::__iota<simd::vec<int, 8>>,
		      permutations::swap_neighbors<2>)
	   == simd::vec<int, 8>(std::array{2, 3, 0, 1, 6, 7, 4, 5})));

static_assert(
  all_of(simd::permute(simd::__iota<simd::vec<int, 12>>,
		      permutations::swap_neighbors<3>)
	   == simd::vec<int, 12>(
		std::array{3, 4, 5, 0, 1, 2, 9, 10, 11, 6, 7, 8})));

static_assert(
  all_of(simd::permute(simd::__iota<simd::vec<int>>, permutations::broadcast<1>)
	   == simd::vec<int>(1)));

static_assert(
  all_of(simd::permute(simd::__iota<simd::vec<int>>, permutations::broadcast_first)
	   == simd::vec<int>(0)));

static_assert(
  all_of(simd::permute(simd::__iota<simd::vec<int>>, permutations::broadcast_last)
	   == simd::vec<int>(int(simd::vec<int>::size() - 1))));

static_assert(
  all_of(simd::permute(simd::__iota<simd::vec<int>>, permutations::reverse)
	   == simd::vec<int>([](int i) { return int(simd::vec<int>::size()) - 1 - i; })));

static_assert(
  all_of(simd::permute(simd::__iota<simd::vec<int>>, permutations::rotate<1>)
	   == (simd::__iota<simd::vec<int>> + 1) % int(simd::vec<int>::size())));

static_assert(
  all_of(simd::permute(simd::__iota<simd::vec<int>>, permutations::rotate<2>)
	   == (simd::__iota<simd::vec<int>> + 2) % int(simd::vec<int>::size())));

static_assert(
  all_of(simd::permute(simd::__iota<simd::vec<int, 7>>, permutations::rotate<2>)
	   == simd::vec<int, 7>(std::array {2, 3, 4, 5, 6, 0, 1})));

static_assert(
  all_of(simd::permute(simd::__iota<simd::vec<int, 7>>, permutations::rotate<-2>)
	   == simd::vec<int, 7>(std::array {5, 6, 0, 1, 2, 3, 4})));

// simd::alignment_v /////////////////

template <typename T, int N>
  using vec_n = simd::vec<T, simd::vec<T>::size() * N>;

static_assert(simd::alignment_v<simd::vec<float>> == alignof(simd::vec<float>));
static_assert(simd::alignment_v<vec_n<float, 2>> == alignof(simd::vec<float>));
static_assert(simd::alignment_v<simd::vec<float>, double> == alignof(simd::vec<double>));
static_assert(simd::alignment_v<simd::vec<float>, char> == alignof(simd::vec<char, simd::vec<float>::size()>));