// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// 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/.

#include "main.h"

// Test the corner cases of pow(x, y) for real types.
template <typename Scalar>
void pow_test() {
  const Scalar zero = Scalar(0);
  const Scalar eps = std::numeric_limits<Scalar>::epsilon();
  const Scalar one = Scalar(1);
  const Scalar two = Scalar(2);
  const Scalar three = Scalar(3);
  const Scalar sqrt_half = Scalar(std::sqrt(0.5));
  const Scalar sqrt2 = Scalar(std::sqrt(2));
  const Scalar inf = std::numeric_limits<Scalar>::infinity();
  const Scalar nan = std::numeric_limits<Scalar>::quiet_NaN();
  const Scalar denorm_min = std::numeric_limits<Scalar>::denorm_min();
  const Scalar min = (std::numeric_limits<Scalar>::min)();
  const Scalar max = (std::numeric_limits<Scalar>::max)();
  const Scalar max_exp =
      (static_cast<Scalar>(int(std::numeric_limits<Scalar>::max_exponent)) *
       Scalar(EIGEN_LN2)) /
      eps;

  const static Scalar abs_vals[] = {zero, denorm_min, min, eps,   sqrt_half,
                                    one,  sqrt2,      two, three, max_exp,
                                    max,  inf,        nan};
  const int abs_cases = 13;
  const int num_cases = 2 * abs_cases * 2 * abs_cases;
  // Repeat the same value to make sure we hit the vectorized path.
  const int num_repeats = 32;
  Array<Scalar, Dynamic, Dynamic> x(num_repeats, num_cases);
  Array<Scalar, Dynamic, Dynamic> y(num_repeats, num_cases);
  int count = 0;
  for (int i = 0; i < abs_cases; ++i) {
    const Scalar abs_x = abs_vals[i];
    for (int sign_x = 0; sign_x < 2; ++sign_x) {
      Scalar x_case = sign_x == 0 ? -abs_x : abs_x;
      for (int j = 0; j < abs_cases; ++j) {
        const Scalar abs_y = abs_vals[j];
        for (int sign_y = 0; sign_y < 2; ++sign_y) {
          Scalar y_case = sign_y == 0 ? -abs_y : abs_y;
          for (int repeat = 0; repeat < num_repeats; ++repeat) {
            x(repeat, count) = x_case;
            y(repeat, count) = y_case;
          }
          ++count;
        }
      }
    }
  }

  Array<Scalar, Dynamic, Dynamic> actual = x.pow(y);
  const Scalar tol = test_precision<Scalar>();
  bool all_pass = true;
  for (int i = 0; i < 1; ++i) {
    for (int j = 0; j < num_cases; ++j) {
      Scalar e = static_cast<Scalar>(std::pow(x(i, j), y(i, j)));
      Scalar a = actual(i, j);
      bool fail = !(a == e) && !internal::isApprox(a, e, tol) &&
                  !((numext::isnan)(a) && (numext::isnan)(e));
      all_pass &= !fail;
      if (fail) {
        std::cout << "pow(" << x(i, j) << "," << y(i, j) << ")   =   " << a
                  << " !=  " << e << std::endl;
      }
    }
  }
  VERIFY(all_pass);
}

template <typename ArrayType>
void array(const ArrayType& m) {
  typedef typename ArrayType::Scalar Scalar;
  typedef typename ArrayType::RealScalar RealScalar;
  typedef Array<Scalar, ArrayType::RowsAtCompileTime, 1> ColVectorType;
  typedef Array<Scalar, 1, ArrayType::ColsAtCompileTime> RowVectorType;

  Index rows = m.rows();
  Index cols = m.cols();

  ArrayType m1 = ArrayType::Random(rows, cols),
            m2 = ArrayType::Random(rows, cols), m3(rows, cols);
  ArrayType m4 = m1;  // copy constructor
  VERIFY_IS_APPROX(m1, m4);

  ColVectorType cv1 = ColVectorType::Random(rows);
  RowVectorType rv1 = RowVectorType::Random(cols);

  Scalar s1 = internal::random<Scalar>(), s2 = internal::random<Scalar>();

  // scalar addition
  VERIFY_IS_APPROX(m1 + s1, s1 + m1);
  VERIFY_IS_APPROX(m1 + s1, ArrayType::Constant(rows, cols, s1) + m1);
  VERIFY_IS_APPROX(s1 - m1, (-m1) + s1);
  VERIFY_IS_APPROX(m1 - s1, m1 - ArrayType::Constant(rows, cols, s1));
  VERIFY_IS_APPROX(s1 - m1, ArrayType::Constant(rows, cols, s1) - m1);
  VERIFY_IS_APPROX((m1 * Scalar(2)) - s2,
                   (m1 + m1) - ArrayType::Constant(rows, cols, s2));
  m3 = m1;
  m3 += s2;
  VERIFY_IS_APPROX(m3, m1 + s2);
  m3 = m1;
  m3 -= s1;
  VERIFY_IS_APPROX(m3, m1 - s1);

  // scalar operators via Maps
  m3 = m1;
  ArrayType::Map(m1.data(), m1.rows(), m1.cols()) -=
      ArrayType::Map(m2.data(), m2.rows(), m2.cols());
  VERIFY_IS_APPROX(m1, m3 - m2);

  m3 = m1;
  ArrayType::Map(m1.data(), m1.rows(), m1.cols()) +=
      ArrayType::Map(m2.data(), m2.rows(), m2.cols());
  VERIFY_IS_APPROX(m1, m3 + m2);

  m3 = m1;
  ArrayType::Map(m1.data(), m1.rows(), m1.cols()) *=
      ArrayType::Map(m2.data(), m2.rows(), m2.cols());
  VERIFY_IS_APPROX(m1, m3 * m2);

  m3 = m1;
  m2 = ArrayType::Random(rows, cols);
  m2 = (m2 == 0).select(1, m2);
  ArrayType::Map(m1.data(), m1.rows(), m1.cols()) /=
      ArrayType::Map(m2.data(), m2.rows(), m2.cols());
  VERIFY_IS_APPROX(m1, m3 / m2);

  // reductions
  VERIFY_IS_APPROX(m1.abs().colwise().sum().sum(), m1.abs().sum());
  VERIFY_IS_APPROX(m1.abs().rowwise().sum().sum(), m1.abs().sum());
  using std::abs;
  VERIFY_IS_MUCH_SMALLER_THAN(abs(m1.colwise().sum().sum() - m1.sum()),
                              m1.abs().sum());
  VERIFY_IS_MUCH_SMALLER_THAN(abs(m1.rowwise().sum().sum() - m1.sum()),
                              m1.abs().sum());
  if (!internal::isMuchSmallerThan(abs(m1.sum() - (m1 + m2).sum()),
                                   m1.abs().sum(), test_precision<Scalar>()))
    VERIFY_IS_NOT_APPROX(((m1 + m2).rowwise().sum()).sum(), m1.sum());
  VERIFY_IS_APPROX(
      m1.colwise().sum(),
      m1.colwise().redux(internal::scalar_sum_op<Scalar, Scalar>()));

  // vector-wise ops
  m3 = m1;
  VERIFY_IS_APPROX(m3.colwise() += cv1, m1.colwise() + cv1);
  m3 = m1;
  VERIFY_IS_APPROX(m3.colwise() -= cv1, m1.colwise() - cv1);
  m3 = m1;
  VERIFY_IS_APPROX(m3.rowwise() += rv1, m1.rowwise() + rv1);
  m3 = m1;
  VERIFY_IS_APPROX(m3.rowwise() -= rv1, m1.rowwise() - rv1);

  // Conversion from scalar
  VERIFY_IS_APPROX((m3 = s1), ArrayType::Constant(rows, cols, s1));
  VERIFY_IS_APPROX((m3 = 1), ArrayType::Constant(rows, cols, 1));
  VERIFY_IS_APPROX((m3.topLeftCorner(rows, cols) = 1),
                   ArrayType::Constant(rows, cols, 1));
  typedef Array<Scalar, ArrayType::RowsAtCompileTime == Dynamic
                            ? 2
                            : ArrayType::RowsAtCompileTime,
                ArrayType::ColsAtCompileTime == Dynamic
                    ? 2
                    : ArrayType::ColsAtCompileTime,
                ArrayType::Options>
      FixedArrayType;
  {
    FixedArrayType f1(s1);
    VERIFY_IS_APPROX(f1, FixedArrayType::Constant(s1));
    FixedArrayType f2(numext::real(s1));
    VERIFY_IS_APPROX(f2, FixedArrayType::Constant(numext::real(s1)));
    FixedArrayType f3((int)100 * numext::real(s1));
    VERIFY_IS_APPROX(f3, FixedArrayType::Constant((int)100 * numext::real(s1)));
    f1.setRandom();
    FixedArrayType f4(f1.data());
    VERIFY_IS_APPROX(f4, f1);
  }
#if EIGEN_HAS_CXX11
  {
    FixedArrayType f1{s1};
    VERIFY_IS_APPROX(f1, FixedArrayType::Constant(s1));
    FixedArrayType f2{numext::real(s1)};
    VERIFY_IS_APPROX(f2, FixedArrayType::Constant(numext::real(s1)));
    FixedArrayType f3{(int)100 * numext::real(s1)};
    VERIFY_IS_APPROX(f3, FixedArrayType::Constant((int)100 * numext::real(s1)));
    f1.setRandom();
    FixedArrayType f4{f1.data()};
    VERIFY_IS_APPROX(f4, f1);
  }
#endif

  // pow
  VERIFY_IS_APPROX(m1.pow(2), m1.square());
  VERIFY_IS_APPROX(pow(m1, 2), m1.square());
  VERIFY_IS_APPROX(m1.pow(3), m1.cube());
  VERIFY_IS_APPROX(pow(m1, 3), m1.cube());
  VERIFY_IS_APPROX((-m1).pow(3), -m1.cube());
  VERIFY_IS_APPROX(pow(2 * m1, 3), 8 * m1.cube());
  ArrayType exponents = ArrayType::Constant(rows, cols, RealScalar(2));
  VERIFY_IS_APPROX(Eigen::pow(m1, exponents), m1.square());
  VERIFY_IS_APPROX(m1.pow(exponents), m1.square());
  VERIFY_IS_APPROX(Eigen::pow(2 * m1, exponents), 4 * m1.square());
  VERIFY_IS_APPROX((2 * m1).pow(exponents), 4 * m1.square());
  VERIFY_IS_APPROX(Eigen::pow(m1, 2 * exponents), m1.square().square());
  VERIFY_IS_APPROX(m1.pow(2 * exponents), m1.square().square());
  VERIFY_IS_APPROX(Eigen::pow(m1(0, 0), exponents),
                   ArrayType::Constant(rows, cols, m1(0, 0) * m1(0, 0)));

  // Check possible conflicts with 1D ctor
  typedef Array<Scalar, Dynamic, 1> OneDArrayType;
  {
    OneDArrayType o1(rows);
    VERIFY(o1.size() == rows);
    OneDArrayType o2(static_cast<int>(rows));
    VERIFY(o2.size() == rows);
  }
#if EIGEN_HAS_CXX11
  {
    OneDArrayType o1{rows};
    VERIFY(o1.size() == rows);
    OneDArrayType o4{int(rows)};
    VERIFY(o4.size() == rows);
  }
#endif
  // Check possible conflicts with 2D ctor
  typedef Array<Scalar, Dynamic, Dynamic> TwoDArrayType;
  typedef Array<Scalar, 2, 1> ArrayType2;
  {
    TwoDArrayType o1(rows, cols);
    VERIFY(o1.rows() == rows);
    VERIFY(o1.cols() == cols);
    TwoDArrayType o2(static_cast<int>(rows), static_cast<int>(cols));
    VERIFY(o2.rows() == rows);
    VERIFY(o2.cols() == cols);

    ArrayType2 o3(rows, cols);
    VERIFY(o3(0) == Scalar(rows) && o3(1) == Scalar(cols));
    ArrayType2 o4(static_cast<int>(rows), static_cast<int>(cols));
    VERIFY(o4(0) == Scalar(rows) && o4(1) == Scalar(cols));
  }
#if EIGEN_HAS_CXX11
  {
    TwoDArrayType o1{rows, cols};
    VERIFY(o1.rows() == rows);
    VERIFY(o1.cols() == cols);
    TwoDArrayType o2{int(rows), int(cols)};
    VERIFY(o2.rows() == rows);
    VERIFY(o2.cols() == cols);

    ArrayType2 o3{rows, cols};
    VERIFY(o3(0) == Scalar(rows) && o3(1) == Scalar(cols));
    ArrayType2 o4{int(rows), int(cols)};
    VERIFY(o4(0) == Scalar(rows) && o4(1) == Scalar(cols));
  }
#endif
}

template <typename ArrayType>
void comparisons(const ArrayType& m) {
  using std::abs;
  typedef typename ArrayType::Scalar Scalar;
  typedef typename NumTraits<Scalar>::Real RealScalar;

  Index rows = m.rows();
  Index cols = m.cols();

  Index r = internal::random<Index>(0, rows - 1),
        c = internal::random<Index>(0, cols - 1);

  ArrayType m1 = ArrayType::Random(rows, cols),
            m2 = ArrayType::Random(rows, cols), m3(rows, cols), m4 = m1;

  m4 = (m4.abs() == Scalar(0)).select(1, m4);

  VERIFY(((m1 + Scalar(1)) > m1).all());
  VERIFY(((m1 - Scalar(1)) < m1).all());
  if (rows * cols > 1) {
    m3 = m1;
    m3(r, c) += 1;
    VERIFY(!(m1 < m3).all());
    VERIFY(!(m1 > m3).all());
  }
  VERIFY(!(m1 > m2 && m1 < m2).any());
  VERIFY((m1 <= m2 || m1 >= m2).all());

  // comparisons array to scalar
  VERIFY((m1 != (m1(r, c) + 1)).any());
  VERIFY((m1 > (m1(r, c) - 1)).any());
  VERIFY((m1 < (m1(r, c) + 1)).any());
  VERIFY((m1 == m1(r, c)).any());

  // comparisons scalar to array
  VERIFY(((m1(r, c) + 1) != m1).any());
  VERIFY(((m1(r, c) - 1) < m1).any());
  VERIFY(((m1(r, c) + 1) > m1).any());
  VERIFY((m1(r, c) == m1).any());

  // test Select
  VERIFY_IS_APPROX((m1 < m2).select(m1, m2), m1.cwiseMin(m2));
  VERIFY_IS_APPROX((m1 > m2).select(m1, m2), m1.cwiseMax(m2));
  Scalar mid =
      (m1.cwiseAbs().minCoeff() + m1.cwiseAbs().maxCoeff()) / Scalar(2);
  for (int j = 0; j < cols; ++j)
    for (int i = 0; i < rows; ++i)
      m3(i, j) = abs(m1(i, j)) < mid ? 0 : m1(i, j);
  VERIFY_IS_APPROX((m1.abs() < ArrayType::Constant(rows, cols, mid))
                       .select(ArrayType::Zero(rows, cols), m1),
                   m3);
  // shorter versions:
  VERIFY_IS_APPROX(
      (m1.abs() < ArrayType::Constant(rows, cols, mid)).select(0, m1), m3);
  VERIFY_IS_APPROX(
      (m1.abs() >= ArrayType::Constant(rows, cols, mid)).select(m1, 0), m3);
  // even shorter version:
  VERIFY_IS_APPROX((m1.abs() < mid).select(0, m1), m3);

  // count
  VERIFY(((m1.abs() + 1) > RealScalar(0.1)).count() == rows * cols);

  // and/or
  VERIFY((m1 < RealScalar(0) && m1 > RealScalar(0)).count() == 0);
  VERIFY((m1 < RealScalar(0) || m1 >= RealScalar(0)).count() == rows * cols);
  RealScalar a = m1.abs().mean();
  VERIFY((m1 < -a || m1 > a).count() == (m1.abs() > a).count());

  typedef Array<Index, Dynamic, 1> ArrayOfIndices;

  // TODO allows colwise/rowwise for array
  VERIFY_IS_APPROX(((m1.abs() + 1) > RealScalar(0.1)).colwise().count(),
                   ArrayOfIndices::Constant(cols, rows).transpose());
  VERIFY_IS_APPROX(((m1.abs() + 1) > RealScalar(0.1)).rowwise().count(),
                   ArrayOfIndices::Constant(rows, cols));
}

template <typename ArrayType>
void array_real(const ArrayType& m) {
  using std::abs;
  using std::sqrt;
  typedef typename ArrayType::Scalar Scalar;
  typedef typename NumTraits<Scalar>::Real RealScalar;

  Index rows = m.rows();
  Index cols = m.cols();

  ArrayType m1 = ArrayType::Random(rows, cols),
            m2 = ArrayType::Random(rows, cols), m3(rows, cols), m4 = m1;

  m4 = (m4.abs() == Scalar(0)).select(Scalar(1), m4);

  Scalar s1 = internal::random<Scalar>();

  // these tests are mostly to check possible compilation issues with
  // free-functions.
  VERIFY_IS_APPROX(m1.sin(), sin(m1));
  VERIFY_IS_APPROX(m1.cos(), cos(m1));
  VERIFY_IS_APPROX(m1.tan(), tan(m1));
  VERIFY_IS_APPROX(m1.asin(), asin(m1));
  VERIFY_IS_APPROX(m1.acos(), acos(m1));
  VERIFY_IS_APPROX(m1.atan(), atan(m1));
  VERIFY_IS_APPROX(m1.sinh(), sinh(m1));
  VERIFY_IS_APPROX(m1.cosh(), cosh(m1));
  VERIFY_IS_APPROX(m1.tanh(), tanh(m1));
#if EIGEN_HAS_CXX11_MATH
  VERIFY_IS_APPROX(m1.tanh().atanh(), atanh(tanh(m1)));
  VERIFY_IS_APPROX(m1.sinh().asinh(), asinh(sinh(m1)));
  VERIFY_IS_APPROX(m1.cosh().acosh(), acosh(cosh(m1)));
#endif
  VERIFY_IS_APPROX(m1.logistic(), logistic(m1));

  VERIFY_IS_APPROX(m1.arg(), arg(m1));
  VERIFY_IS_APPROX(m1.round(), round(m1));
  VERIFY_IS_APPROX(m1.rint(), rint(m1));
  VERIFY_IS_APPROX(m1.floor(), floor(m1));
  VERIFY_IS_APPROX(m1.ceil(), ceil(m1));
  VERIFY((m1.isNaN() == (Eigen::isnan)(m1)).all());
  VERIFY((m1.isInf() == (Eigen::isinf)(m1)).all());
  VERIFY((m1.isFinite() == (Eigen::isfinite)(m1)).all());
  VERIFY_IS_APPROX(m4.inverse(), inverse(m4));
  VERIFY_IS_APPROX(m1.abs(), abs(m1));
  VERIFY_IS_APPROX(m1.abs2(), abs2(m1));
  VERIFY_IS_APPROX(m1.square(), square(m1));
  VERIFY_IS_APPROX(m1.cube(), cube(m1));
  VERIFY_IS_APPROX(cos(m1 + RealScalar(3) * m2),
                   cos((m1 + RealScalar(3) * m2).eval()));
  VERIFY_IS_APPROX(m1.sign(), sign(m1));
  VERIFY((m1.sqrt().sign().isNaN() == (Eigen::isnan)(sign(sqrt(m1)))).all());

  // avoid inf and NaNs so verification doesn't fail
  m3 = m4.abs();
  VERIFY_IS_APPROX(m3.sqrt(), sqrt(abs(m3)));
  VERIFY_IS_APPROX(m3.rsqrt(), Scalar(1) / sqrt(abs(m3)));
  VERIFY_IS_APPROX(rsqrt(m3), Scalar(1) / sqrt(abs(m3)));
  VERIFY_IS_APPROX(m3.log(), log(m3));
  VERIFY_IS_APPROX(m3.log1p(), log1p(m3));
  VERIFY_IS_APPROX(m3.log10(), log10(m3));
  VERIFY_IS_APPROX(m3.log2(), log2(m3));

  VERIFY((!(m1 > m2) == (m1 <= m2)).all());

  VERIFY_IS_APPROX(sin(m1.asin()), m1);
  VERIFY_IS_APPROX(cos(m1.acos()), m1);
  VERIFY_IS_APPROX(tan(m1.atan()), m1);
  VERIFY_IS_APPROX(sinh(m1), Scalar(0.5) * (exp(m1) - exp(-m1)));
  VERIFY_IS_APPROX(cosh(m1), Scalar(0.5) * (exp(m1) + exp(-m1)));
  VERIFY_IS_APPROX(tanh(m1), (Scalar(0.5) * (exp(m1) - exp(-m1))) /
                                 (Scalar(0.5) * (exp(m1) + exp(-m1))));
  VERIFY_IS_APPROX(logistic(m1), (Scalar(1) / (Scalar(1) + exp(-m1))));
  VERIFY_IS_APPROX(arg(m1), ((m1 < Scalar(0)).template cast<Scalar>()) *
                                Scalar(std::acos(Scalar(-1))));
  VERIFY((round(m1) <= ceil(m1) && round(m1) >= floor(m1)).all());
  VERIFY((rint(m1) <= ceil(m1) && rint(m1) >= floor(m1)).all());
  VERIFY(((ceil(m1) - round(m1)) <= Scalar(0.5) ||
          (round(m1) - floor(m1)) <= Scalar(0.5))
             .all());
  VERIFY(((ceil(m1) - round(m1)) <= Scalar(1.0) &&
          (round(m1) - floor(m1)) <= Scalar(1.0))
             .all());
  VERIFY(((ceil(m1) - rint(m1)) <= Scalar(0.5) ||
          (rint(m1) - floor(m1)) <= Scalar(0.5))
             .all());
  VERIFY(((ceil(m1) - rint(m1)) <= Scalar(1.0) &&
          (rint(m1) - floor(m1)) <= Scalar(1.0))
             .all());
  VERIFY((Eigen::isnan)((m1 * Scalar(0)) / Scalar(0)).all());
  VERIFY((Eigen::isinf)(m4 / Scalar(0)).all());
  VERIFY(((Eigen::isfinite)(m1) &&
          (!(Eigen::isfinite)(m1 * Scalar(0) / Scalar(0))) &&
          (!(Eigen::isfinite)(m4 / Scalar(0))))
             .all());
  VERIFY_IS_APPROX(inverse(inverse(m4)), m4);
  VERIFY((abs(m1) == m1 || abs(m1) == -m1).all());
  VERIFY_IS_APPROX(m3, sqrt(abs2(m3)));
  VERIFY_IS_APPROX(m1.absolute_difference(m2),
                   (m1 > m2).select(m1 - m2, m2 - m1));
  VERIFY_IS_APPROX(m1.sign(), -(-m1).sign());
  VERIFY_IS_APPROX(m1 * m1.sign(), m1.abs());
  VERIFY_IS_APPROX(m1.sign() * m1.abs(), m1);

  VERIFY_IS_APPROX(
      numext::abs2(numext::real(m1)) + numext::abs2(numext::imag(m1)),
      numext::abs2(m1));
  VERIFY_IS_APPROX(
      numext::abs2(Eigen::real(m1)) + numext::abs2(Eigen::imag(m1)),
      numext::abs2(m1));
  if (!NumTraits<Scalar>::IsComplex) VERIFY_IS_APPROX(numext::real(m1), m1);

  // shift argument of logarithm so that it is not zero
  Scalar smallNumber = NumTraits<Scalar>::dummy_precision();
  VERIFY_IS_APPROX((m3 + smallNumber).log(), log(abs(m3) + smallNumber));
  VERIFY_IS_APPROX((m3 + smallNumber + Scalar(1)).log(),
                   log1p(abs(m3) + smallNumber));

  VERIFY_IS_APPROX(m1.exp() * m2.exp(), exp(m1 + m2));
  VERIFY_IS_APPROX(m1.exp(), exp(m1));
  VERIFY_IS_APPROX(m1.exp() / m2.exp(), (m1 - m2).exp());

  VERIFY_IS_APPROX(m1.expm1(), expm1(m1));
  VERIFY_IS_APPROX((m3 + smallNumber).exp() - Scalar(1),
                   expm1(abs(m3) + smallNumber));

  VERIFY_IS_APPROX(m3.pow(RealScalar(0.5)), m3.sqrt());
  VERIFY_IS_APPROX(pow(m3, RealScalar(0.5)), m3.sqrt());

  VERIFY_IS_APPROX(m3.pow(RealScalar(-0.5)), m3.rsqrt());
  VERIFY_IS_APPROX(pow(m3, RealScalar(-0.5)), m3.rsqrt());

  // Avoid inf and NaN.
  m3 = (m1.square() < NumTraits<Scalar>::epsilon()).select(Scalar(1), m3);
  VERIFY_IS_APPROX(m3.pow(RealScalar(-2)), m3.square().inverse());
  pow_test<Scalar>();

  VERIFY_IS_APPROX(log10(m3), log(m3) / numext::log(Scalar(10)));
  VERIFY_IS_APPROX(log2(m3), log(m3) / numext::log(Scalar(2)));

  // scalar by array division
  const RealScalar tiny = sqrt(std::numeric_limits<RealScalar>::epsilon());
  s1 += Scalar(tiny);
  m1 += ArrayType::Constant(rows, cols, Scalar(tiny));
  VERIFY_IS_APPROX(s1 / m1, s1 * m1.inverse());

  // check inplace transpose
  m3 = m1;
  m3.transposeInPlace();
  VERIFY_IS_APPROX(m3, m1.transpose());
  m3.transposeInPlace();
  VERIFY_IS_APPROX(m3, m1);
}

template <typename ArrayType>
void array_complex(const ArrayType& m) {
  typedef typename ArrayType::Scalar Scalar;
  typedef typename NumTraits<Scalar>::Real RealScalar;

  Index rows = m.rows();
  Index cols = m.cols();

  ArrayType m1 = ArrayType::Random(rows, cols), m2(rows, cols), m4 = m1;

  m4.real() =
      (m4.real().abs() == RealScalar(0)).select(RealScalar(1), m4.real());
  m4.imag() =
      (m4.imag().abs() == RealScalar(0)).select(RealScalar(1), m4.imag());

  Array<RealScalar, -1, -1> m3(rows, cols);

  for (Index i = 0; i < m.rows(); ++i)
    for (Index j = 0; j < m.cols(); ++j) m2(i, j) = sqrt(m1(i, j));

  // these tests are mostly to check possible compilation issues with
  // free-functions.
  VERIFY_IS_APPROX(m1.sin(), sin(m1));
  VERIFY_IS_APPROX(m1.cos(), cos(m1));
  VERIFY_IS_APPROX(m1.tan(), tan(m1));
  VERIFY_IS_APPROX(m1.sinh(), sinh(m1));
  VERIFY_IS_APPROX(m1.cosh(), cosh(m1));
  VERIFY_IS_APPROX(m1.tanh(), tanh(m1));
  VERIFY_IS_APPROX(m1.logistic(), logistic(m1));
  VERIFY_IS_APPROX(m1.arg(), arg(m1));
  VERIFY((m1.isNaN() == (Eigen::isnan)(m1)).all());
  VERIFY((m1.isInf() == (Eigen::isinf)(m1)).all());
  VERIFY((m1.isFinite() == (Eigen::isfinite)(m1)).all());
  VERIFY_IS_APPROX(m4.inverse(), inverse(m4));
  VERIFY_IS_APPROX(m1.log(), log(m1));
  VERIFY_IS_APPROX(m1.log10(), log10(m1));
  VERIFY_IS_APPROX(m1.log2(), log2(m1));
  VERIFY_IS_APPROX(m1.abs(), abs(m1));
  VERIFY_IS_APPROX(m1.abs2(), abs2(m1));
  VERIFY_IS_APPROX(m1.sqrt(), sqrt(m1));
  VERIFY_IS_APPROX(m1.square(), square(m1));
  VERIFY_IS_APPROX(m1.cube(), cube(m1));
  VERIFY_IS_APPROX(cos(m1 + RealScalar(3) * m2),
                   cos((m1 + RealScalar(3) * m2).eval()));
  VERIFY_IS_APPROX(m1.sign(), sign(m1));

  VERIFY_IS_APPROX(m1.exp() * m2.exp(), exp(m1 + m2));
  VERIFY_IS_APPROX(m1.exp(), exp(m1));
  VERIFY_IS_APPROX(m1.exp() / m2.exp(), (m1 - m2).exp());

  VERIFY_IS_APPROX(m1.expm1(), expm1(m1));
  VERIFY_IS_APPROX(expm1(m1), exp(m1) - 1.);
  // Check for larger magnitude complex numbers that expm1 matches exp - 1.
  VERIFY_IS_APPROX(expm1(10. * m1), exp(10. * m1) - 1.);

  VERIFY_IS_APPROX(sinh(m1), 0.5 * (exp(m1) - exp(-m1)));
  VERIFY_IS_APPROX(cosh(m1), 0.5 * (exp(m1) + exp(-m1)));
  VERIFY_IS_APPROX(tanh(m1),
                   (0.5 * (exp(m1) - exp(-m1))) / (0.5 * (exp(m1) + exp(-m1))));
  VERIFY_IS_APPROX(logistic(m1), (1.0 / (1.0 + exp(-m1))));

  for (Index i = 0; i < m.rows(); ++i)
    for (Index j = 0; j < m.cols(); ++j)
      m3(i, j) = std::atan2(m1(i, j).imag(), m1(i, j).real());
  VERIFY_IS_APPROX(arg(m1), m3);

  std::complex<RealScalar> zero(0.0, 0.0);
  VERIFY((Eigen::isnan)(m1 * zero / zero).all());
#if EIGEN_COMP_MSVC
  // msvc complex division is not robust
  VERIFY((Eigen::isinf)(m4 / RealScalar(0)).all());
#else
#if EIGEN_COMP_CLANG
  // clang's complex division is notoriously broken too
  if ((numext::isinf)(m4(0, 0) / RealScalar(0))) {
#endif
    VERIFY((Eigen::isinf)(m4 / zero).all());
#if EIGEN_COMP_CLANG
  } else {
    VERIFY((Eigen::isinf)(m4.real() / zero.real()).all());
  }
#endif
#endif  // MSVC

  VERIFY(((Eigen::isfinite)(m1) && (!(Eigen::isfinite)(m1 * zero / zero)) &&
          (!(Eigen::isfinite)(m1 / zero)))
             .all());

  VERIFY_IS_APPROX(inverse(inverse(m4)), m4);
  VERIFY_IS_APPROX(conj(m1.conjugate()), m1);
  VERIFY_IS_APPROX(abs(m1), sqrt(square(m1.real()) + square(m1.imag())));
  VERIFY_IS_APPROX(abs(m1), sqrt(abs2(m1)));
  VERIFY_IS_APPROX(log10(m1), log(m1) / log(10));
  VERIFY_IS_APPROX(log2(m1), log(m1) / log(2));

  VERIFY_IS_APPROX(m1.sign(), -(-m1).sign());
  VERIFY_IS_APPROX(m1.sign() * m1.abs(), m1);

  // scalar by array division
  Scalar s1 = internal::random<Scalar>();
  const RealScalar tiny = std::sqrt(std::numeric_limits<RealScalar>::epsilon());
  s1 += Scalar(tiny);
  m1 += ArrayType::Constant(rows, cols, Scalar(tiny));
  VERIFY_IS_APPROX(s1 / m1, s1 * m1.inverse());

  // check inplace transpose
  m2 = m1;
  m2.transposeInPlace();
  VERIFY_IS_APPROX(m2, m1.transpose());
  m2.transposeInPlace();
  VERIFY_IS_APPROX(m2, m1);
  // Check vectorized inplace transpose.
  ArrayType m5 = ArrayType::Random(131, 131);
  ArrayType m6 = m5;
  m6.transposeInPlace();
  VERIFY_IS_APPROX(m6, m5.transpose());
}

template <typename ArrayType>
void min_max(const ArrayType& m) {
  typedef typename ArrayType::Scalar Scalar;

  Index rows = m.rows();
  Index cols = m.cols();

  ArrayType m1 = ArrayType::Random(rows, cols);

  // min/max with array
  Scalar maxM1 = m1.maxCoeff();
  Scalar minM1 = m1.minCoeff();

  VERIFY_IS_APPROX(ArrayType::Constant(rows, cols, minM1),
                   (m1.min)(ArrayType::Constant(rows, cols, minM1)));
  VERIFY_IS_APPROX(m1, (m1.min)(ArrayType::Constant(rows, cols, maxM1)));

  VERIFY_IS_APPROX(ArrayType::Constant(rows, cols, maxM1),
                   (m1.max)(ArrayType::Constant(rows, cols, maxM1)));
  VERIFY_IS_APPROX(m1, (m1.max)(ArrayType::Constant(rows, cols, minM1)));

  // min/max with scalar input
  VERIFY_IS_APPROX(ArrayType::Constant(rows, cols, minM1), (m1.min)(minM1));
  VERIFY_IS_APPROX(m1, (m1.min)(maxM1));

  VERIFY_IS_APPROX(ArrayType::Constant(rows, cols, maxM1), (m1.max)(maxM1));
  VERIFY_IS_APPROX(m1, (m1.max)(minM1));

  // min/max with various NaN propagation options.
  if (m1.size() > 1 && !NumTraits<Scalar>::IsInteger) {
    m1(0, 0) = std::numeric_limits<Scalar>::quiet_NaN();
    maxM1 = m1.template maxCoeff<PropagateNaN>();
    minM1 = m1.template minCoeff<PropagateNaN>();
    VERIFY((numext::isnan)(maxM1));
    VERIFY((numext::isnan)(minM1));

    maxM1 = m1.template maxCoeff<PropagateNumbers>();
    minM1 = m1.template minCoeff<PropagateNumbers>();
    VERIFY(!(numext::isnan)(maxM1));
    VERIFY(!(numext::isnan)(minM1));
  }
}

EIGEN_DECLARE_TEST(array_cwise) {
  for (int i = 0; i < g_repeat; i++) {
    CALL_SUBTEST_1(array(Array<float, 1, 1>()));
    CALL_SUBTEST_2(array(Array22f()));
    CALL_SUBTEST_3(array(Array44d()));
    CALL_SUBTEST_4(
        array(ArrayXXcf(internal::random<int>(1, EIGEN_TEST_MAX_SIZE),
                        internal::random<int>(1, EIGEN_TEST_MAX_SIZE))));
    CALL_SUBTEST_5(
        array(ArrayXXf(internal::random<int>(1, EIGEN_TEST_MAX_SIZE),
                       internal::random<int>(1, EIGEN_TEST_MAX_SIZE))));
    CALL_SUBTEST_6(
        array(ArrayXXi(internal::random<int>(1, EIGEN_TEST_MAX_SIZE),
                       internal::random<int>(1, EIGEN_TEST_MAX_SIZE))));
    CALL_SUBTEST_6(array(Array<Index, Dynamic, Dynamic>(
        internal::random<int>(1, EIGEN_TEST_MAX_SIZE),
        internal::random<int>(1, EIGEN_TEST_MAX_SIZE))));
  }
  for (int i = 0; i < g_repeat; i++) {
    CALL_SUBTEST_1(comparisons(Array<float, 1, 1>()));
    CALL_SUBTEST_2(comparisons(Array22f()));
    CALL_SUBTEST_3(comparisons(Array44d()));
    CALL_SUBTEST_5(
        comparisons(ArrayXXf(internal::random<int>(1, EIGEN_TEST_MAX_SIZE),
                             internal::random<int>(1, EIGEN_TEST_MAX_SIZE))));
    CALL_SUBTEST_6(
        comparisons(ArrayXXi(internal::random<int>(1, EIGEN_TEST_MAX_SIZE),
                             internal::random<int>(1, EIGEN_TEST_MAX_SIZE))));
  }
  for (int i = 0; i < g_repeat; i++) {
    CALL_SUBTEST_1(min_max(Array<float, 1, 1>()));
    CALL_SUBTEST_2(min_max(Array22f()));
    CALL_SUBTEST_3(min_max(Array44d()));
    CALL_SUBTEST_5(
        min_max(ArrayXXf(internal::random<int>(1, EIGEN_TEST_MAX_SIZE),
                         internal::random<int>(1, EIGEN_TEST_MAX_SIZE))));
    CALL_SUBTEST_6(
        min_max(ArrayXXi(internal::random<int>(1, EIGEN_TEST_MAX_SIZE),
                         internal::random<int>(1, EIGEN_TEST_MAX_SIZE))));
  }
  for (int i = 0; i < g_repeat; i++) {
    CALL_SUBTEST_1(array_real(Array<float, 1, 1>()));
    CALL_SUBTEST_2(array_real(Array22f()));
    CALL_SUBTEST_3(array_real(Array44d()));
    CALL_SUBTEST_5(
        array_real(ArrayXXf(internal::random<int>(1, EIGEN_TEST_MAX_SIZE),
                            internal::random<int>(1, EIGEN_TEST_MAX_SIZE))));
    CALL_SUBTEST_7(array_real(Array<Eigen::half, 32, 32>()));
    CALL_SUBTEST_8(array_real(Array<Eigen::bfloat16, 32, 32>()));
  }
  for (int i = 0; i < g_repeat; i++) {
    CALL_SUBTEST_4(array_complex(
        ArrayXXcf(internal::random<int>(1, EIGEN_TEST_MAX_SIZE),
                  internal::random<int>(1, EIGEN_TEST_MAX_SIZE))));
  }

  VERIFY((internal::is_same<
          internal::global_math_functions_filtering_base<int>::type,
          int>::value));
  VERIFY((internal::is_same<
          internal::global_math_functions_filtering_base<float>::type,
          float>::value));
  VERIFY((internal::is_same<
          internal::global_math_functions_filtering_base<Array2i>::type,
          ArrayBase<Array2i> >::value));
  typedef CwiseUnaryOp<internal::scalar_abs_op<double>, ArrayXd> Xpr;
  VERIFY((internal::is_same<
          internal::global_math_functions_filtering_base<Xpr>::type,
          ArrayBase<Xpr> >::value));
}