// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
// SPDX-FileCopyrightText: The Eigen Authors
// SPDX-License-Identifier: MPL-2.0

#include <sstream>

#include "main.h"
#include "product_test_helpers.h"

#define VERIFY_HALF_BITS_EQUAL(h, bits) \
  VERIFY_IS_EQUAL((numext::bit_cast<numext::uint16_t>(h)), (static_cast<numext::uint16_t>(bits)))

// Make sure it's possible to forward declare Eigen::half
namespace Eigen {
struct half;
}

using Eigen::half;

void test_conversion() {
  using Eigen::half_impl::__half_raw;

  // Round-trip bit-cast with uint16.
  VERIFY_IS_EQUAL(numext::bit_cast<half>(numext::bit_cast<numext::uint16_t>(half(1.0f))), half(1.0f));
  VERIFY_IS_EQUAL(numext::bit_cast<half>(numext::bit_cast<numext::uint16_t>(half(0.5f))), half(0.5f));
  VERIFY_IS_EQUAL(numext::bit_cast<half>(numext::bit_cast<numext::uint16_t>(half(-0.33333f))), half(-0.33333f));
  VERIFY_IS_EQUAL(numext::bit_cast<half>(numext::bit_cast<numext::uint16_t>(half(0.0f))), half(0.0f));

  // Conversion from float.
  VERIFY_HALF_BITS_EQUAL(half(1.0f), 0x3c00);
  VERIFY_HALF_BITS_EQUAL(half(0.5f), 0x3800);
  VERIFY_HALF_BITS_EQUAL(half(0.33333f), 0x3555);
  VERIFY_HALF_BITS_EQUAL(half(0.0f), 0x0000);
  VERIFY_HALF_BITS_EQUAL(half(-0.0f), 0x8000);
  VERIFY_HALF_BITS_EQUAL(half(65504.0f), 0x7bff);
  VERIFY_HALF_BITS_EQUAL(half(65536.0f), 0x7c00);  // Becomes infinity.

  // Denormals.
  VERIFY_HALF_BITS_EQUAL(half(-5.96046e-08f), 0x8001);
  VERIFY_HALF_BITS_EQUAL(half(5.96046e-08f), 0x0001);
  VERIFY_HALF_BITS_EQUAL(half(1.19209e-07f), 0x0002);

  // Verify round-to-nearest-even behavior.
  float val1 = float(half(__half_raw(0x3c00)));
  float val2 = float(half(__half_raw(0x3c01)));
  float val3 = float(half(__half_raw(0x3c02)));
  VERIFY_HALF_BITS_EQUAL(half(0.5f * (val1 + val2)), 0x3c00);
  VERIFY_HALF_BITS_EQUAL(half(0.5f * (val2 + val3)), 0x3c02);

  // Conversion from int.
  VERIFY_HALF_BITS_EQUAL(half(-1), 0xbc00);
  VERIFY_HALF_BITS_EQUAL(half(0), 0x0000);
  VERIFY_HALF_BITS_EQUAL(half(1), 0x3c00);
  VERIFY_HALF_BITS_EQUAL(half(2), 0x4000);
  VERIFY_HALF_BITS_EQUAL(half(3), 0x4200);

  // Conversion from bool.
  VERIFY_HALF_BITS_EQUAL(half(false), 0x0000);
  VERIFY_HALF_BITS_EQUAL(half(true), 0x3c00);

  // Conversion to float.
  VERIFY_IS_EQUAL(float(half(__half_raw(0x0000))), 0.0f);
  VERIFY_IS_EQUAL(float(half(__half_raw(0x3c00))), 1.0f);

  // Denormals.
  VERIFY_IS_APPROX(float(half(__half_raw(0x8001))), -5.96046e-08f);
  VERIFY_IS_APPROX(float(half(__half_raw(0x0001))), 5.96046e-08f);
  VERIFY_IS_APPROX(float(half(__half_raw(0x0002))), 1.19209e-07f);

  // NaNs and infinities.
  VERIFY(!(numext::isinf)(float(half(65504.0f))));  // Largest finite number.
  VERIFY(!(numext::isnan)(float(half(0.0f))));
  VERIFY((numext::isfinite)(float(half(65504.0f))));
  VERIFY((numext::isfinite)(float(half(0.0f))));
  VERIFY((numext::isinf)(float(half(__half_raw(0xfc00)))));
  VERIFY((numext::isnan)(float(half(__half_raw(0xfc01)))));
  VERIFY((numext::isinf)(float(half(__half_raw(0x7c00)))));
  VERIFY((numext::isnan)(float(half(__half_raw(0x7c01)))));

  VERIFY((numext::isnan)(float(NumTraits<half>::quiet_NaN())));
  VERIFY((numext::isinf)(float(NumTraits<half>::infinity())));
  VERIFY((numext::isinf)(float(-NumTraits<half>::infinity())));

  // Exactly same checks as above, just directly on the half representation.
  VERIFY(!(numext::isinf)(half(__half_raw(0x7bff))));
  VERIFY(!(numext::isnan)(half(__half_raw(0x0000))));
  VERIFY((numext::isinf)(half(__half_raw(0xfc00))));
  VERIFY((numext::isnan)(half(__half_raw(0xfc01))));
  VERIFY((numext::isinf)(half(__half_raw(0x7c00))));
  VERIFY((numext::isnan)(half(__half_raw(0x7c01))));

  VERIFY((numext::isnan)(NumTraits<half>::quiet_NaN()));
  VERIFY((numext::isinf)(NumTraits<half>::infinity()));
  VERIFY((numext::isinf)(-NumTraits<half>::infinity()));

  // Conversion to bool
  VERIFY(!static_cast<bool>(half(0.0)));
  VERIFY(!static_cast<bool>(half(-0.0)));
  VERIFY(static_cast<bool>(half(__half_raw(0x7bff))));
  VERIFY(static_cast<bool>(half(-0.33333)));
  VERIFY(static_cast<bool>(half(1.0)));
  VERIFY(static_cast<bool>(half(-1.0)));
  VERIFY(static_cast<bool>(half(-5.96046e-08f)));

  // A double rounds to half once: just above the midpoint 1 + 2^-11 it rounds up, although its float rounding is
  // the midpoint itself, which ties down. The same holds below the midpoint and for tiny values.
  VERIFY_IS_EQUAL(numext::bit_cast<numext::uint16_t>(half(1.0 + std::ldexp(1.0, -11) + std::ldexp(1.0, -40))), 0x3c01);
  VERIFY_IS_EQUAL(numext::bit_cast<numext::uint16_t>(
                      half(-(1.0 + std::ldexp(1.0, -10) + std::ldexp(1.0, -11) - std::ldexp(1.0, -40)))),
                  0xbc01);
  VERIFY_IS_EQUAL(numext::bit_cast<numext::uint16_t>(half(std::ldexp(1.0, -25) + std::ldexp(1.0, -60))), 0x0001);
  VERIFY_IS_EQUAL(
      numext::bit_cast<numext::uint16_t>(half(std::complex<double>(std::ldexp(1.0, -25) + std::ldexp(1.0, -60)))),
      0x0001);
  // Beyond float's range a double overflows to infinity or underflows to zero, keeping its sign.
  VERIFY_IS_EQUAL(numext::bit_cast<numext::uint16_t>(half(1e39)), 0x7c00);
  VERIFY_IS_EQUAL(numext::bit_cast<numext::uint16_t>(half(-1e39)), 0xfc00);
  VERIFY_IS_EQUAL(numext::bit_cast<numext::uint16_t>(half(1e-300)), 0x0000);
  VERIFY_IS_EQUAL(numext::bit_cast<numext::uint16_t>(half(-1e-300)), 0x8000);
  VERIFY((numext::isnan)(half(std::numeric_limits<double>::quiet_NaN())));
  // Integers convert through float directly: those it rounds overflow half anyway.
  VERIFY_IS_EQUAL(numext::bit_cast<numext::uint16_t>(half(int32_t(65519))), 0x7bff);
  VERIFY_IS_EQUAL(numext::bit_cast<numext::uint16_t>(half(-int64_t(65520))), 0xfc00);
  VERIFY_IS_EQUAL(numext::bit_cast<numext::uint16_t>(half((std::numeric_limits<uint64_t>::max)())), 0x7c00);
}

void test_numtraits() {
  std::cout << "epsilon       = " << NumTraits<half>::epsilon() << "  (0x" << std::hex
            << numext::bit_cast<numext::uint16_t>(NumTraits<half>::epsilon()) << ")" << std::endl;
  std::cout << "highest       = " << NumTraits<half>::highest() << "  (0x" << std::hex
            << numext::bit_cast<numext::uint16_t>(NumTraits<half>::highest()) << ")" << std::endl;
  std::cout << "lowest        = " << NumTraits<half>::lowest() << "  (0x" << std::hex
            << numext::bit_cast<numext::uint16_t>(NumTraits<half>::lowest()) << ")" << std::endl;
  std::cout << "min           = " << (std::numeric_limits<half>::min)() << "  (0x" << std::hex
            << numext::bit_cast<numext::uint16_t>(half((std::numeric_limits<half>::min)())) << ")" << std::endl;
  std::cout << "denorm min    = " << (std::numeric_limits<half>::denorm_min)() << "  (0x" << std::hex
            << numext::bit_cast<numext::uint16_t>(half((std::numeric_limits<half>::denorm_min)())) << ")" << std::endl;
  std::cout << "infinity      = " << NumTraits<half>::infinity() << "  (0x" << std::hex
            << numext::bit_cast<numext::uint16_t>(NumTraits<half>::infinity()) << ")" << std::endl;
  std::cout << "quiet nan     = " << NumTraits<half>::quiet_NaN() << "  (0x" << std::hex
            << numext::bit_cast<numext::uint16_t>(NumTraits<half>::quiet_NaN()) << ")" << std::endl;
  std::cout << "signaling nan = " << std::numeric_limits<half>::signaling_NaN() << "  (0x" << std::hex
            << numext::bit_cast<numext::uint16_t>(std::numeric_limits<half>::signaling_NaN()) << ")" << std::endl;

  VERIFY(NumTraits<half>::IsSigned);

  // The fp16 machine epsilon is 2^-10 = 0x1400, and NumTraits must agree with
  // std::numeric_limits (NumTraits used to return 2^-13, making every
  // epsilon-based threshold 8x too tight).
  VERIFY_HALF_BITS_EQUAL(NumTraits<half>::epsilon(), 0x1400);
  VERIFY_HALF_BITS_EQUAL(std::numeric_limits<half>::epsilon(), 0x1400);
  VERIFY_IS_EQUAL(numext::bit_cast<numext::uint16_t>(NumTraits<half>::epsilon()),
                  numext::bit_cast<numext::uint16_t>(std::numeric_limits<half>::epsilon()));

  VERIFY_IS_EQUAL(numext::bit_cast<numext::uint16_t>(std::numeric_limits<half>::infinity()),
                  numext::bit_cast<numext::uint16_t>(half(std::numeric_limits<float>::infinity())));
  // There is no guarantee that casting a 32-bit NaN to 16-bit has a precise
  // bit pattern.  We test that it is in fact a NaN, then test the signaling
  // bit (msb of significand is 1 for quiet, 0 for signaling).
  const numext::uint16_t HALF_QUIET_BIT = 0x0200;
  VERIFY((numext::isnan)(std::numeric_limits<half>::quiet_NaN()) &&
         (numext::isnan)(half(std::numeric_limits<float>::quiet_NaN())) &&
         ((numext::bit_cast<numext::uint16_t>(std::numeric_limits<half>::quiet_NaN()) & HALF_QUIET_BIT) > 0) &&
         ((numext::bit_cast<numext::uint16_t>(half(std::numeric_limits<float>::quiet_NaN())) & HALF_QUIET_BIT) > 0));
  // After a cast to half, a signaling NaN may become non-signaling
  // (e.g. in the case of casting float to native __fp16). Thus, we check that
  // both are NaN, and that only the `numeric_limits` version is signaling.
  VERIFY((numext::isnan)(std::numeric_limits<half>::signaling_NaN()) &&
         (numext::isnan)(half(std::numeric_limits<float>::signaling_NaN())) &&
         ((numext::bit_cast<numext::uint16_t>(std::numeric_limits<half>::signaling_NaN()) & HALF_QUIET_BIT) == 0));

  VERIFY((std::numeric_limits<half>::min)() > half(0.f));
  VERIFY((std::numeric_limits<half>::denorm_min)() > half(0.f));
  VERIFY((std::numeric_limits<half>::min)() / half(2) > half(0.f));
  VERIFY_IS_EQUAL((std::numeric_limits<half>::denorm_min)() / half(2), half(0.f));

  // Test to see that we are able to link against the symbols for digits and
  // digits10.
  volatile const int& digits10 = std::numeric_limits<half>::digits10;
  volatile const int& digits = std::numeric_limits<half>::digits;
  VERIFY((digits10) != (digits));
}

void test_arithmetic() {
  VERIFY_IS_EQUAL(float(half(2) + half(2)), 4);
  VERIFY_IS_EQUAL(float(half(2) + half(-2)), 0);
  VERIFY_IS_APPROX(float(half(0.33333f) + half(0.66667f)), 1.0f);
  VERIFY_IS_EQUAL(float(half(2.0f) * half(-5.5f)), -11.0f);
  VERIFY_IS_APPROX(float(half(1.0f) / half(3.0f)), 0.33333f);
  VERIFY_IS_EQUAL(float(-half(4096.0f)), -4096.0f);
  VERIFY_IS_EQUAL(float(-half(-4096.0f)), 4096.0f);

  // fma rounds once: a * b = 2145/2048 is a midpoint of half, and c = 2^-24 rounds the sum up, not to even. A float
  // fma rounds the sum to that midpoint first.
  const half tiny = half(std::ldexp(1.0f, -24));
  VERIFY_IS_EQUAL(float(numext::fma(half(33.f / 32), half(65.f / 64), tiny)), 1.f + 49.f / 1024);
  VERIFY_IS_EQUAL(float(numext::fma(half(-33.f / 32), half(65.f / 64), -tiny)), -1.f - 49.f / 1024);

  half x(3);
  half y = ++x;
  VERIFY_IS_EQUAL(x, half(4));
  VERIFY_IS_EQUAL(y, half(4));
  y = --x;
  VERIFY_IS_EQUAL(x, half(3));
  VERIFY_IS_EQUAL(y, half(3));
  y = x++;
  VERIFY_IS_EQUAL(x, half(4));
  VERIFY_IS_EQUAL(y, half(3));
  y = x--;
  VERIFY_IS_EQUAL(x, half(3));
  VERIFY_IS_EQUAL(y, half(4));
}

void test_comparison() {
  VERIFY(half(1.0f) > half(0.5f));
  VERIFY(half(0.5f) < half(1.0f));
  VERIFY(!(half(1.0f) < half(0.5f)));
  VERIFY(!(half(0.5f) > half(1.0f)));

  VERIFY(!(half(4.0f) > half(4.0f)));
  VERIFY(!(half(4.0f) < half(4.0f)));

  VERIFY(!(half(0.0f) < half(-0.0f)));
  VERIFY(!(half(-0.0f) < half(0.0f)));
  VERIFY(!(half(0.0f) > half(-0.0f)));
  VERIFY(!(half(-0.0f) > half(0.0f)));
#if EIGEN_HAS_STD_HASH
  // Equal values hash alike.
  VERIFY_IS_EQUAL(std::hash<half>()(half(0.0f)), std::hash<half>()(half(-0.0f)));
#endif

  VERIFY(half(0.2f) > half(-1.0f));
  VERIFY(half(-1.0f) < half(0.2f));
  VERIFY(half(-16.0f) < half(-15.0f));

  VERIFY(half(1.0f) == half(1.0f));
  VERIFY(half(1.0f) != half(2.0f));

  // Comparisons with NaNs and infinities.
  VERIFY(!(NumTraits<half>::quiet_NaN() == NumTraits<half>::quiet_NaN()));
  VERIFY(NumTraits<half>::quiet_NaN() != NumTraits<half>::quiet_NaN());

  VERIFY(!(internal::random<half>() == NumTraits<half>::quiet_NaN()));
  VERIFY(!(internal::random<half>() < NumTraits<half>::quiet_NaN()));
  VERIFY(!(internal::random<half>() > NumTraits<half>::quiet_NaN()));
  VERIFY(!(internal::random<half>() <= NumTraits<half>::quiet_NaN()));
  VERIFY(!(internal::random<half>() >= NumTraits<half>::quiet_NaN()));
  VERIFY(internal::random<half>() != NumTraits<half>::quiet_NaN());

  VERIFY(!(NumTraits<half>::quiet_NaN() == internal::random<half>()));
  VERIFY(!(NumTraits<half>::quiet_NaN() < internal::random<half>()));
  VERIFY(!(NumTraits<half>::quiet_NaN() > internal::random<half>()));
  VERIFY(!(NumTraits<half>::quiet_NaN() <= internal::random<half>()));
  VERIFY(!(NumTraits<half>::quiet_NaN() >= internal::random<half>()));
  VERIFY(NumTraits<half>::quiet_NaN() != internal::random<half>());

  VERIFY(internal::random<half>() < NumTraits<half>::infinity());
  VERIFY(internal::random<half>() > -NumTraits<half>::infinity());
}

void test_basic_functions() {
  constexpr float PI = static_cast<float>(EIGEN_PI);

  VERIFY_IS_EQUAL(float(numext::abs(half(3.5f))), 3.5f);
  VERIFY_IS_EQUAL(float(abs(half(3.5f))), 3.5f);
  VERIFY_IS_EQUAL(float(numext::abs(half(-3.5f))), 3.5f);
  VERIFY_IS_EQUAL(float(abs(half(-3.5f))), 3.5f);

  VERIFY_IS_EQUAL(float(numext::floor(half(3.5f))), 3.0f);
  VERIFY_IS_EQUAL(float(floor(half(3.5f))), 3.0f);
  VERIFY_IS_EQUAL(float(numext::floor(half(-3.5f))), -4.0f);
  VERIFY_IS_EQUAL(float(floor(half(-3.5f))), -4.0f);

  VERIFY_IS_EQUAL(float(numext::ceil(half(3.5f))), 4.0f);
  VERIFY_IS_EQUAL(float(ceil(half(3.5f))), 4.0f);
  VERIFY_IS_EQUAL(float(numext::ceil(half(-3.5f))), -3.0f);
  VERIFY_IS_EQUAL(float(ceil(half(-3.5f))), -3.0f);

  VERIFY_IS_APPROX(float(numext::sqrt(half(0.0f))), 0.0f);
  VERIFY_IS_APPROX(float(sqrt(half(0.0f))), 0.0f);
  VERIFY_IS_APPROX(float(numext::sqrt(half(4.0f))), 2.0f);
  VERIFY_IS_APPROX(float(sqrt(half(4.0f))), 2.0f);

  VERIFY_IS_APPROX(float(numext::pow(half(0.0f), half(1.0f))), 0.0f);
  VERIFY_IS_APPROX(float(pow(half(0.0f), half(1.0f))), 0.0f);
  VERIFY_IS_APPROX(float(numext::pow(half(2.0f), half(2.0f))), 4.0f);
  VERIFY_IS_APPROX(float(pow(half(2.0f), half(2.0f))), 4.0f);

  VERIFY_IS_EQUAL(float(numext::exp(half(0.0f))), 1.0f);
  VERIFY_IS_EQUAL(float(exp(half(0.0f))), 1.0f);
  VERIFY_IS_APPROX(float(numext::exp(half(PI))), 20.f + PI);
  VERIFY_IS_APPROX(float(exp(half(PI))), 20.f + PI);

  VERIFY_IS_EQUAL(float(numext::expm1(half(0.0f))), 0.0f);
  VERIFY_IS_EQUAL(float(expm1(half(0.0f))), 0.0f);
  VERIFY_IS_APPROX(float(numext::expm1(half(2.0f))), 6.3890561f);
  VERIFY_IS_APPROX(float(expm1(half(2.0f))), 6.3890561f);

  VERIFY_IS_EQUAL(float(numext::log(half(1.0f))), 0.0f);
  VERIFY_IS_EQUAL(float(log(half(1.0f))), 0.0f);
  VERIFY_IS_APPROX(float(numext::log(half(10.0f))), 2.30273f);
  VERIFY_IS_APPROX(float(log(half(10.0f))), 2.30273f);

  VERIFY_IS_EQUAL(float(numext::log1p(half(0.0f))), 0.0f);
  VERIFY_IS_EQUAL(float(log1p(half(0.0f))), 0.0f);
  VERIFY_IS_APPROX(float(numext::log1p(half(10.0f))), 2.3978953f);
  VERIFY_IS_APPROX(float(log1p(half(10.0f))), 2.3978953f);

  VERIFY_IS_APPROX(numext::fmod(half(5.3f), half(2.0f)), half(1.3f));
  VERIFY_IS_APPROX(fmod(half(5.3f), half(2.0f)), half(1.3f));
  VERIFY_IS_APPROX(numext::fmod(half(-18.5f), half(-4.2f)), half(-1.7f));
  VERIFY_IS_APPROX(fmod(half(-18.5f), half(-4.2f)), half(-1.7f));
}

void test_trigonometric_functions() {
  constexpr float PI = static_cast<float>(EIGEN_PI);
  VERIFY_IS_APPROX(numext::cos(half(0.0f)), half(cosf(0.0f)));
  VERIFY_IS_APPROX(cos(half(0.0f)), half(cosf(0.0f)));
  VERIFY_IS_APPROX(numext::cos(half(PI)), half(cosf(PI)));
  // VERIFY_IS_APPROX(numext::cos(half(PI/2)), half(cosf(PI/2)));
  // VERIFY_IS_APPROX(numext::cos(half(3*PI/2)), half(cosf(3*PI/2)));
  VERIFY_IS_APPROX(numext::cos(half(3.5f)), half(cosf(3.5f)));

  VERIFY_IS_APPROX(numext::sin(half(0.0f)), half(sinf(0.0f)));
  VERIFY_IS_APPROX(sin(half(0.0f)), half(sinf(0.0f)));
  //  VERIFY_IS_APPROX(numext::sin(half(PI)), half(sinf(PI)));
  VERIFY_IS_APPROX(numext::sin(half(PI / 2)), half(sinf(PI / 2)));
  VERIFY_IS_APPROX(numext::sin(half(3 * PI / 2)), half(sinf(3 * PI / 2)));
  VERIFY_IS_APPROX(numext::sin(half(3.5f)), half(sinf(3.5f)));

  VERIFY_IS_APPROX(numext::tan(half(0.0f)), half(tanf(0.0f)));
  VERIFY_IS_APPROX(tan(half(0.0f)), half(tanf(0.0f)));
  //  VERIFY_IS_APPROX(numext::tan(half(PI)), half(tanf(PI)));
  //  VERIFY_IS_APPROX(numext::tan(half(PI/2)), half(tanf(PI/2)));
  // VERIFY_IS_APPROX(numext::tan(half(3*PI/2)), half(tanf(3*PI/2)));
  VERIFY_IS_APPROX(numext::tan(half(3.5f)), half(tanf(3.5f)));
}

void test_array() {
  typedef Array<half, 1, Dynamic> ArrayXh;
  Index size = internal::random<Index>(1, 10);
  Index i = internal::random<Index>(0, size - 1);
  ArrayXh a1 = ArrayXh::Random(size), a2 = ArrayXh::Random(size);
  VERIFY_IS_APPROX(a1 + a1, half(2) * a1);
  VERIFY((a1.abs() >= half(0)).all());
  VERIFY_IS_APPROX((a1 * a1).sqrt(), a1.abs());

  VERIFY(((a1.min)(a2) <= (a1.max)(a2)).all());
  a1(i) = half(-10.);
  VERIFY_IS_EQUAL(a1.minCoeff(), half(-10.));
  a1(i) = half(10.);
  VERIFY_IS_EQUAL(a1.maxCoeff(), half(10.));

  std::stringstream ss;
  ss << a1;
}

void test_product() {
  using MatrixXh = Matrix<half, Dynamic, Dynamic>;
  Index rows = internal::random<Index>(1, EIGEN_TEST_MAX_SIZE);
  Index cols = internal::random<Index>(1, EIGEN_TEST_MAX_SIZE);
  Index depth = internal::random<Index>(1, EIGEN_TEST_MAX_SIZE);
  MatrixXh Ah = MatrixXh::Random(rows, depth);
  MatrixXh Bh = MatrixXh::Random(depth, cols);
  MatrixXh Ch = MatrixXh::Random(rows, cols);
  MatrixXf Af = Ah.cast<float>();
  MatrixXf Bf = Bh.cast<float>();
  MatrixXf Cf = Ch.cast<float>();
  VERIFY_IS_APPROX(Ch.noalias() += Ah * Bh, (Cf.noalias() += Af * Bf).cast<half>());
}

// The blocked GEMM sums in float and rounds each coefficient once; the sizes keep it off the GEMV and coefficient-based
// paths, which still round in half.
void test_gemm_float_accumulation() {
  using MatrixXh = Matrix<half, Dynamic, Dynamic>;
  Index rows = internal::random<Index>(2, EIGEN_TEST_MAX_SIZE);
  Index cols = internal::random<Index>(2, EIGEN_TEST_MAX_SIZE);
  Index depth = internal::random<Index>(20, EIGEN_TEST_MAX_SIZE);
  MatrixXh A = MatrixXh::Random(rows, depth);
  MatrixXh B = MatrixXh::Random(depth, cols);
  MatrixXh C0 = MatrixXh::Random(rows, cols);
  // References in double, whose rounding error is negligible next to the bound.
  MatrixXd exact = A.cast<double>().eval() * B.cast<double>().eval();
  MatrixXd exact_update = C0.cast<double>() + exact;
  MatrixXh C = C0;
  C.noalias() += A * B;
  VERIFY(verifyProductUpdate<float>(C.cast<double>(), exact_update, half(1), A, B, C0, 1));
  C.noalias() = A * B;
  VERIFY(verifyProduct<float>(C.cast<double>(), exact, A, B, 1));
}

void test_nextafter() {
  VERIFY((numext::isnan)(numext::nextafter(std::numeric_limits<half>::quiet_NaN(), half(1.0f))));
  VERIFY((numext::isnan)(numext::nextafter(half(1.0f), std::numeric_limits<half>::quiet_NaN())));
  VERIFY(numext::nextafter(half(0.0f), half(0.0f)) == half(0.0f));
  VERIFY(numext::nextafter(half(1.0f), half(1.0f)) == half(1.0f));
  VERIFY(numext::nextafter(half(-1.0f), half(-1.0f)) == half(-1.0f));
  VERIFY(numext::nextafter(std::numeric_limits<half>::infinity(), std::numeric_limits<half>::infinity()) ==
         std::numeric_limits<half>::infinity());
  VERIFY(numext::nextafter(std::numeric_limits<half>::infinity(), half(0.0f)) == (std::numeric_limits<half>::max)());
  VERIFY(numext::nextafter(-std::numeric_limits<half>::infinity(), half(0.0f)) == -(std::numeric_limits<half>::max)());
  VERIFY(numext::nextafter(half(1.0f), std::numeric_limits<half>::infinity()) ==
         half(1.0f) + std::numeric_limits<half>::epsilon());
  VERIFY(numext::nextafter(half(1.0f), -std::numeric_limits<half>::infinity()) ==
         half(1.0f) - std::numeric_limits<half>::epsilon() / half(2.0f));
  VERIFY(numext::nextafter(half(-1.0f), -std::numeric_limits<half>::infinity()) ==
         half(-1.0f) - std::numeric_limits<half>::epsilon());
  VERIFY(numext::nextafter(half(-1.0f), std::numeric_limits<half>::infinity()) ==
         half(-1.0f) + std::numeric_limits<half>::epsilon() / half(2.0f));
  VERIFY(numext::nextafter((std::numeric_limits<half>::max)(), std::numeric_limits<half>::infinity()) ==
         std::numeric_limits<half>::infinity());
  VERIFY(numext::nextafter(-(std::numeric_limits<half>::max)(), -std::numeric_limits<half>::infinity()) ==
         -std::numeric_limits<half>::infinity());
  // The neighbors of ±0 are the smallest subnormals with the sign of the
  // direction, matching std::nextafter (IEEE-754 nextUp/nextDown of zero).
  VERIFY_HALF_BITS_EQUAL(numext::nextafter(half(0.0f), half(1.0f)), 0x0001);
  VERIFY_HALF_BITS_EQUAL(numext::nextafter(half(-0.0f), half(1.0f)), 0x0001);
  VERIFY_HALF_BITS_EQUAL(numext::nextafter(half(0.0f), half(-1.0f)), 0x8001);
  VERIFY_HALF_BITS_EQUAL(numext::nextafter(half(-0.0f), half(-1.0f)), 0x8001);
  // from == to returns to, preserving the sign of zero.
  VERIFY_HALF_BITS_EQUAL(numext::nextafter(half(0.0f), half(-0.0f)), 0x8000);
  VERIFY_HALF_BITS_EQUAL(numext::nextafter(half(-0.0f), half(0.0f)), 0x0000);
  VERIFY_HALF_BITS_EQUAL(numext::nextafter(half(0.0f), half(0.0f)), 0x0000);
  VERIFY_HALF_BITS_EQUAL(numext::nextafter(half(-0.0f), half(-0.0f)), 0x8000);
}

EIGEN_DECLARE_TEST(half_float) {
  CALL_SUBTEST(test_numtraits());
  for (int i = 0; i < g_repeat; i++) {
    CALL_SUBTEST(test_conversion());
    CALL_SUBTEST(test_arithmetic());
    CALL_SUBTEST(test_comparison());
    CALL_SUBTEST(test_basic_functions());
    CALL_SUBTEST(test_trigonometric_functions());
    CALL_SUBTEST(test_array());
    CALL_SUBTEST(test_product());
    CALL_SUBTEST(test_gemm_float_accumulation());
    CALL_SUBTEST(test_nextafter());
  }
}