// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2016 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/.
// SPDX-License-Identifier: MPL-2.0

#include "main.h"
#include "../Eigen/SpecialFunctions"

template <typename X, typename Y>
void verify_component_wise(const X& x, const Y& y) {
  for (Index i = 0; i < x.size(); ++i) {
    if ((numext::isfinite)(y(i))) {
      VERIFY_IS_APPROX(x(i), y(i));
    } else if ((numext::isnan)(y(i)))
      VERIFY((numext::isnan)(x(i)));
    else
      VERIFY_IS_EQUAL(x(i), y(i));
  }
}

template <typename ArrayType>
void array_bessel_functions() {
  // Test Bessel function i0. Reference results obtained with SciPy.
  {
    ArrayType x(21);
    ArrayType expected(21);
    ArrayType res(21);

    x << -20.0, -18.0, -16.0, -14.0, -12.0, -10.0, -8.0, -6.0, -4.0, -2.0, 0.0, 2.0, 4.0, 6.0, 8.0, 10.0, 12.0, 14.0,
        16.0, 18.0, 20.0;

    expected << 4.35582826e+07, 6.21841242e+06, 8.93446228e+05, 1.29418563e+05, 1.89489253e+04, 2.81571663e+03,
        4.27564116e+02, 6.72344070e+01, 1.13019220e+01, 2.27958530e+00, 1.00000000e+00, 2.27958530e+00, 1.13019220e+01,
        6.72344070e+01, 4.27564116e+02, 2.81571663e+03, 1.89489253e+04, 1.29418563e+05, 8.93446228e+05, 6.21841242e+06,
        4.35582826e+07;

    CALL_SUBTEST(res = bessel_i0(x); verify_component_wise(res, expected););
  }

  // Test Bessel function i0e. Reference results obtained with SciPy.
  {
    ArrayType x(21);
    ArrayType expected(21);
    ArrayType res(21);

    x << -20.0, -18.0, -16.0, -14.0, -12.0, -10.0, -8.0, -6.0, -4.0, -2.0, 0.0, 2.0, 4.0, 6.0, 8.0, 10.0, 12.0, 14.0,
        16.0, 18.0, 20.0;

    expected << 0.0897803118848, 0.0947062952128, 0.100544127361, 0.107615251671, 0.116426221213, 0.127833337163,
        0.143431781857, 0.16665743264, 0.207001921224, 0.308508322554, 1.0, 0.308508322554, 0.207001921224,
        0.16665743264, 0.143431781857, 0.127833337163, 0.116426221213, 0.107615251671, 0.100544127361, 0.0947062952128,
        0.0897803118848;

    CALL_SUBTEST(res = bessel_i0e(x); verify_component_wise(res, expected););
  }

  // Test Bessel function i1. Reference results obtained with SciPy.
  {
    ArrayType x(21);
    ArrayType expected(21);
    ArrayType res(21);

    x << -20.0, -18.0, -16.0, -14.0, -12.0, -10.0, -8.0, -6.0, -4.0, -2.0, 0.0, 2.0, 4.0, 6.0, 8.0, 10.0, 12.0, 14.0,
        16.0, 18.0, 20.0;

    expected << -4.24549734e+07, -6.04313324e+06, -8.65059436e+05, -1.24707259e+05, -1.81413488e+04, -2.67098830e+03,
        -3.99873137e+02, -6.13419368e+01, -9.75946515e+00, -1.59063685e+00, 0.00000000e+00, 1.59063685e+00,
        9.75946515e+00, 6.13419368e+01, 3.99873137e+02, 2.67098830e+03, 1.81413488e+04, 1.24707259e+05, 8.65059436e+05,
        6.04313324e+06, 4.24549734e+07;

    CALL_SUBTEST(res = bessel_i1(x); verify_component_wise(res, expected););
  }

  // Test Bessel function i1e. Reference results obtained with SciPy.
  {
    ArrayType x(21);
    ArrayType expected(21);
    ArrayType res(21);

    x << -20.0, -18.0, -16.0, -14.0, -12.0, -10.0, -8.0, -6.0, -4.0, -2.0, 0.0, 2.0, 4.0, 6.0, 8.0, 10.0, 12.0, 14.0,
        16.0, 18.0, 20.0;

    expected << -0.0875062221833, -0.092036796872, -0.0973496147565, -0.103697667463, -0.11146429929, -0.121262681384,
        -0.134142493293, -0.152051459309, -0.178750839502, -0.215269289249, 0.0, 0.215269289249, 0.178750839502,
        0.152051459309, 0.134142493293, 0.121262681384, 0.11146429929, 0.103697667463, 0.0973496147565, 0.092036796872,
        0.0875062221833;

    CALL_SUBTEST(res = bessel_i1e(x); verify_component_wise(res, expected););
  }

  // Test Bessel function j0. Reference results obtained with SciPy.
  {
    ArrayType x(77);
    ArrayType expected(77);
    ArrayType res(77);

    x << -38., -37., -36., -35., -34., -33., -32., -31., -30., -29., -28., -27., -26., -25., -24., -23., -22., -21.,
        -20., -19., -18., -17., -16., -15., -14., -13., -12., -11., -10., -9., -8., -7., -6., -5., -4., -3., -2., -1.,
        0., 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23.,
        24., 25., 26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36., 37., 38.;

    expected << 0.11433274, 0.01086237, -0.10556738, -0.12684568, -0.03042119, 0.09727067, 0.13807901, 0.05120815,
        -0.08636798, -0.14784876, -0.07315701, 0.07274192, 0.15599932, 0.09626678, -0.05623027, -0.16241278,
        -0.12065148, 0.03657907, 0.16702466, 0.14662944, -0.01335581, -0.16985425, -0.17489907, -0.01422447, 0.17107348,
        0.2069261, 0.04768931, -0.1711903, -0.24593576, -0.09033361, 0.17165081, 0.30007927, 0.15064526, -0.17759677,
        -0.39714981, -0.26005195, 0.22389078, 0.76519769, 1., 0.76519769, 0.22389078, -0.26005195, -0.39714981,
        -0.17759677, 0.15064526, 0.30007927, 0.17165081, -0.09033361, -0.24593576, -0.1711903, 0.04768931, 0.2069261,
        0.17107348, -0.01422447, -0.17489907, -0.16985425, -0.01335581, 0.14662944, 0.16702466, 0.03657907, -0.12065148,
        -0.16241278, -0.05623027, 0.09626678, 0.15599932, 0.07274192, -0.07315701, -0.14784876, -0.08636798, 0.05120815,
        0.13807901, 0.09727067, -0.03042119, -0.12684568, -0.10556738, 0.01086237, 0.11433274;

    CALL_SUBTEST(res = bessel_j0(x); verify_component_wise(res, expected););
  }

  // Test Bessel function j1. Reference results obtained with SciPy.
  {
    ArrayType x(81);
    ArrayType expected(81);
    ArrayType res(81);

    x << -40., -39., -38., -37., -36., -35., -34., -33., -32., -31., -30., -29., -28., -27., -26., -25., -24., -23.,
        -22., -21., -20., -19., -18., -17., -16., -15., -14., -13., -12., -11., -10., -9., -8., -7., -6., -5., -4., -3.,
        -2., -1., 0., 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13., 14., 15., 16., 17., 18., 19., 20., 21.,
        22., 23., 24., 25., 26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36., 37., 38., 39., 40.;

    expected << -0.12603832, -0.0640561, 0.05916189, 0.13058004, 0.08232981, -0.04399094, -0.13297118, -0.10061965,
        0.02658903, 0.13302432, 0.11875106, -0.0069342, -0.13055149, -0.13658472, -0.01504573, 0.12535025, 0.15403807,
        0.03951932, -0.11717779, -0.17112027, -0.06683312, 0.10570143, 0.18799489, 0.09766849, -0.09039718, -0.20510404,
        -0.13337515, 0.07031805, 0.2234471, 0.1767853, -0.04347275, -0.24531179, -0.23463635, 0.00468282, 0.27668386,
        0.32757914, 0.06604333, -0.33905896, -0.57672481, -0.44005059, 0., 0.44005059, 0.57672481, 0.33905896,
        -0.06604333, -0.32757914, -0.27668386, -0.00468282, 0.23463635, 0.24531179, 0.04347275, -0.1767853, -0.2234471,
        -0.07031805, 0.13337515, 0.20510404, 0.09039718, -0.09766849, -0.18799489, -0.10570143, 0.06683312, 0.17112027,
        0.11717779, -0.03951932, -0.15403807, -0.12535025, 0.01504573, 0.13658472, 0.13055149, 0.0069342, -0.11875106,
        -0.13302432, -0.02658903, 0.10061965, 0.13297118, 0.04399094, -0.08232981, -0.13058004, -0.05916189, 0.0640561,
        0.12603832;

    CALL_SUBTEST(res = bessel_j1(x); verify_component_wise(res, expected););
  }
  // Test Bessel function k0e. Reference results obtained with SciPy.
  {
    ArrayType x(42);
    ArrayType expected(42);
    ArrayType res(42);

    x << 0.25, 0.5, 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13., 14., 15., 16., 17., 18., 19., 20., 21., 22.,
        23., 24., 25., 26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36., 37., 38., 39., 40.;

    expected << 1.97933385, 1.52410939, 1.14446308, 0.84156822, 0.6977616, 0.60929767, 0.54780756, 0.50186313,
        0.4658451, 0.43662302, 0.41229555, 0.39163193, 0.3737955, 0.35819488, 0.34439865, 0.33208364, 0.32100235,
        0.31096159, 0.30180802, 0.29341821, 0.28569149, 0.27854488, 0.2719092, 0.26572635, 0.25994703, 0.25452917,
        0.2494366, 0.24463801, 0.24010616, 0.23581722, 0.23175022, 0.22788667, 0.22421014, 0.22070602, 0.21736123,
        0.21416406, 0.21110397, 0.20817141, 0.20535778, 0.20265524, 0.20005668, 0.19755558;

    CALL_SUBTEST(res = bessel_k0e(x); verify_component_wise(res, expected););
  }

  // Test Bessel function k0. Reference results obtained with SciPy.
  {
    ArrayType x(42);
    ArrayType expected(42);
    ArrayType res(42);

    x << 0.25, 0.5, 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13., 14., 15., 16., 17., 18., 19., 20., 21., 22.,
        23., 24., 25., 26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36., 37., 38., 39., 40.;

    expected << 1.54150675, 0.92441907, 4.21024438e-01, 1.13893873e-01, 3.47395044e-02, 1.11596761e-02, 3.69109833e-03,
        1.24399433e-03, 4.24795742e-04, 1.46470705e-04, 5.08813130e-05, 1.77800623e-05, 6.24302055e-06, 2.20082540e-06,
        7.78454386e-07, 2.76137082e-07, 9.81953648e-08, 3.49941166e-08, 1.24946640e-08, 4.46875334e-09, 1.60067129e-09,
        5.74123782e-10, 2.06176797e-10, 7.41235161e-11, 2.66754511e-11, 9.60881878e-12, 3.46416156e-12, 1.24987740e-12,
        4.51286453e-13, 1.63053459e-13, 5.89495073e-14, 2.13247750e-14, 7.71838266e-15, 2.79505752e-15, 1.01266123e-15,
        3.67057597e-16, 1.33103515e-16, 4.82858338e-17, 1.75232770e-17, 6.36161716e-18, 2.31029936e-18, 8.39286110e-19;

    CALL_SUBTEST(res = bessel_k0(x); verify_component_wise(res, expected););
  }

  // Test Bessel function k1. Reference results obtained with SciPy.
  {
    ArrayType x(42);
    ArrayType expected(42);
    ArrayType res(42);

    x << 0.25, 0.5, 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13., 14., 15., 16., 17., 18., 19., 20., 21., 22.,
        23., 24., 25., 26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36., 37., 38., 39., 40.;

    expected << 3.74702597, 1.65644112, 6.01907230e-01, 1.39865882e-01, 4.01564311e-02, 1.24834989e-02, 4.04461345e-03,
        1.34391972e-03, 4.54182487e-04, 1.55369212e-04, 5.36370164e-05, 1.86487735e-05, 6.52086067e-06, 2.29075746e-06,
        8.07858841e-07, 2.85834365e-07, 1.01417294e-07, 3.60715712e-08, 1.28570417e-08, 4.59124963e-09, 1.64226697e-09,
        5.88305797e-10, 2.11029922e-10, 7.57898116e-11, 2.72493059e-11, 9.80699893e-12, 3.53277807e-12, 1.27369078e-12,
        4.59568940e-13, 1.65940011e-13, 5.99574032e-14, 2.16773200e-14, 7.84189960e-15, 2.83839927e-15, 1.02789171e-15,
        3.72416929e-16, 1.34991783e-16, 4.89519373e-17, 1.77585196e-17, 6.44478588e-18, 2.33973340e-18, 8.49713195e-19;

    CALL_SUBTEST(res = bessel_k1(x); verify_component_wise(res, expected););
  }

  // Test Bessel function k1e. Reference results obtained with SciPy.
  {
    ArrayType x(42);
    ArrayType expected(42);
    ArrayType res(42);

    x << 0.25, 0.5, 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13., 14., 15., 16., 17., 18., 19., 20., 21., 22.,
        23., 24., 25., 26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36., 37., 38., 39., 40.;

    expected << 4.81127659, 2.73100971, 1.63615349, 1.03347685, 0.80656348, 0.68157595, 0.60027386, 0.54217591,
        0.49807158, 0.46314909, 0.43462525, 0.41076657, 0.39043094, 0.37283175, 0.35740757, 0.34374563, 0.33153489,
        0.32053597, 0.31056123, 0.30146131, 0.29311559, 0.2854255, 0.27830958, 0.27169987, 0.26553913, 0.25977879,
        0.25437733, 0.249299, 0.24451285, 0.23999191, 0.2357126, 0.23165413, 0.22779816, 0.22412841, 0.22063036,
        0.21729103, 0.21409878, 0.21104314, 0.20811462, 0.20530466, 0.20260547, 0.20000997;

    CALL_SUBTEST(res = bessel_k1e(x); verify_component_wise(res, expected););
  }

  // Test Bessel function y0. Reference results obtained with SciPy.
  {
    ArrayType x(42);
    ArrayType expected(42);
    ArrayType res(42);

    x << 0.25, 0.5, 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13., 14., 15., 16., 17., 18., 19., 20., 21., 22.,
        23., 24., 25., 26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36., 37., 38., 39., 40.;

    expected << -0.93157302, -0.44451873, 0.08825696, 0.51037567, 0.37685001, -0.01694074, -0.30851763, -0.28819468,
        -0.02594974, 0.22352149, 0.2499367, 0.05567117, -0.16884732, -0.22523731, -0.07820786, 0.12719257, 0.2054643,
        0.095811, -0.0926372, -0.18755216, -0.10951969, 0.0626406, 0.17020176, 0.1198876, -0.03598179, -0.15283403,
        -0.12724943, 0.01204463, 0.13521498, 0.13183647, 0.00948116, -0.11729573, -0.13383266, -0.02874248, 0.09913483,
        0.13340405, 0.04579799, -0.08085609, -0.13071488, -0.06066076, 0.06262353, 0.12593642;

    CALL_SUBTEST(res = bessel_y0(x); verify_component_wise(res, expected););
  }

  // Test Bessel function y1. Reference results obtained with SciPy.
  {
    ArrayType x(42);
    ArrayType expected(42);
    ArrayType res(42);

    x << 0.25, 0.5, 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13., 14., 15., 16., 17., 18., 19., 20., 21., 22.,
        23., 24., 25., 26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36., 37., 38., 39., 40.;

    expected << -2.70410523, -1.47147239, -0.78121282, -0.10703243, 0.32467442, 0.39792571, 0.14786314, -0.17501034,
        -0.30266724, -0.15806046, 0.10431458, 0.24901542, 0.16370554, -0.05709922, -0.21008141, -0.16664484, 0.02107363,
        0.17797517, 0.16720504, 0.00815513, -0.14956011, -0.16551161, -0.03253926, 0.12340586, 0.1616692, 0.05305978,
        -0.09882996, -0.15579655, -0.07025124, 0.07552213, 0.14803412, 0.08442557, -0.05337283, -0.13854483,
        -0.09578012, 0.03238588, 0.12751273, 0.10445477, -0.01262946, -0.11514066, -0.11056411, -0.00579351;

    CALL_SUBTEST(res = bessel_y1(x); verify_component_wise(res, expected););
  }
}

// exp(|x|) overflows above |x| ~ 88.7228 (float) / ~709.7827 (double), while i0/i1 stay finite up to
// |x| ~ 91.9008 / ~713.9869, so these arguments exercise the intermediate-overflow path.
// Reference values computed with mpmath at 40 digits.
template <typename ArrayType>
void test_bessel_i_large_finite(const typename ArrayType::Scalar (&x_val)[2],
                                const typename ArrayType::Scalar (&i0_truth)[2],
                                const typename ArrayType::Scalar (&i1_truth)[2]) {
  ArrayType x(4);
  x << x_val[0], -x_val[0], x_val[1], -x_val[1];
  ArrayType i0_res = bessel_i0(x);
  ArrayType i1_res = bessel_i1(x);
  for (Index i = 0; i < x.size(); ++i) {
    VERIFY((numext::isfinite)(i0_res(i)));
    VERIFY((numext::isfinite)(i1_res(i)));
    // The vectorized and scalar paths must agree.
    VERIFY_IS_APPROX(numext::bessel_i0(x(i)), i0_res(i));
    VERIFY_IS_APPROX(numext::bessel_i1(x(i)), i1_res(i));
  }
  // i0 is even, i1 is odd.
  VERIFY_IS_APPROX(i0_res(0), i0_truth[0]);
  VERIFY_IS_APPROX(i0_res(1), i0_truth[0]);
  VERIFY_IS_APPROX(i0_res(2), i0_truth[1]);
  VERIFY_IS_APPROX(i0_res(3), i0_truth[1]);
  VERIFY_IS_APPROX(i1_res(0), i1_truth[0]);
  VERIFY_IS_APPROX(i1_res(1), -i1_truth[0]);
  VERIFY_IS_APPROX(i1_res(2), i1_truth[1]);
  VERIFY_IS_APPROX(i1_res(3), -i1_truth[1]);
}

void test_bessel_i_large_finite_float() {
  const float x[2] = {90.0f, 91.0f};
  const float i0_truth[2] = {5.1392383455086638e+37f, 1.3892714060989622e+38f};
  const float i1_truth[2] = {5.1106068152565982e+37f, 1.3816168414593216e+38f};
  test_bessel_i_large_finite<ArrayXf>(x, i0_truth, i1_truth);
}

void test_bessel_i_large_finite_double() {
  const double x[2] = {712.0, 713.0};
  const double i0_truth[2] = {2.4684110577627524e+307, 6.7051282636709964e+307};
  const double i1_truth[2] = {2.4666770135246152e+307, 6.7004245591864022e+307};
  test_bessel_i_large_finite<ArrayXd>(x, i0_truth, i1_truth);
}

EIGEN_DECLARE_TEST(bessel_functions) {
  CALL_SUBTEST_1(array_bessel_functions<ArrayXf>());
  CALL_SUBTEST_1(test_bessel_i_large_finite_float());
  CALL_SUBTEST_2(array_bessel_functions<ArrayXd>());
  CALL_SUBTEST_2(test_bessel_i_large_finite_double());
}