/*
 * Copyright Nick Thompson, 2021
 * Use, modification and distribution are subject to the
 * Boost Software License, Version 1.0. (See accompanying file
 * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
 */

#include "math_unit_test.hpp"
#include <boost/math/tools/cubic_roots.hpp>
#include <random>
#include <cmath>
#include <cfloat>
#ifdef BOOST_HAS_FLOAT128
#include <boost/multiprecision/float128.hpp>
using boost::multiprecision::float128;
#endif

using boost::math::tools::cubic_root_condition_number;
using boost::math::tools::cubic_root_residual;
using boost::math::tools::cubic_roots;
using std::cbrt;
using std::abs;

template <class Real> void test_zero_coefficients() {
    Real a = 0;
    Real b = 0;
    Real c = 0;
    Real d = 0;
    auto roots = cubic_roots(a, b, c, d);
    CHECK_EQUAL(roots[0], Real(0));
    CHECK_EQUAL(roots[1], Real(0));
    CHECK_EQUAL(roots[2], Real(0));

    a = 1;
    roots = cubic_roots(a, b, c, d);
    CHECK_EQUAL(roots[0], Real(0));
    CHECK_EQUAL(roots[1], Real(0));
    CHECK_EQUAL(roots[2], Real(0));

    a = 1;
    d = 1;
    // x^3 + 1 = 0:
    roots = cubic_roots(a, b, c, d);
    CHECK_EQUAL(roots[0], Real(-1));
    CHECK_NAN(roots[1]);
    CHECK_NAN(roots[2]);
    d = -1;
    // x^3 - 1 = 0:
    roots = cubic_roots(a, b, c, d);
    CHECK_EQUAL(roots[0], Real(1));
    CHECK_NAN(roots[1]);
    CHECK_NAN(roots[2]);

    d = -2;
    // x^3 - 2 = 0
    roots = cubic_roots(a, b, c, d);
    CHECK_ULP_CLOSE(roots[0], cbrt(Real(2)), 2);
    CHECK_NAN(roots[1]);
    CHECK_NAN(roots[2]);

    d = -8;
    roots = cubic_roots(a, b, c, d);
    CHECK_EQUAL(roots[0], Real(2));
    CHECK_NAN(roots[1]);
    CHECK_NAN(roots[2]);

    // (x-1)(x-2)(x-3) = x^3 - 6x^2 + 11x - 6
    roots = cubic_roots(Real(1), Real(-6), Real(11), Real(-6));
    CHECK_ULP_CLOSE(roots[0], Real(1), 2);
    CHECK_ULP_CLOSE(roots[1], Real(2), 2);
    CHECK_ULP_CLOSE(roots[2], Real(3), 2);

    // Double root:
    // (x+1)^2(x-2) = x^3 - 3x - 2:
    // Note: This test is unstable wrt to perturbations!
    roots = cubic_roots(Real(1), Real(0), Real(-3), Real(-2));
    CHECK_ULP_CLOSE(Real(-1), roots[0], 2);
    CHECK_ULP_CLOSE(Real(-1), roots[1], 2);
    CHECK_ULP_CLOSE(Real(2), roots[2], 2);

    std::uniform_real_distribution<Real> dis(-2, 2);
    std::mt19937 gen(12345);
    // Expected roots
    std::array<Real, 3> r;
    int trials = 10;
    for (int i = 0; i < trials; ++i) {
        // Mathematica:
        // Expand[(x - r0)*(x - r1)*(x - r2)]
        // - r0 r1 r2 + (r0 r1 + r0 r2 + r1 r2) x
        // - (r0 + r1 + r2) x^2 + x^3
        for (auto &root : r) {
            root = static_cast<Real>(dis(gen));
        }
        std::sort(r.begin(), r.end());
        Real a = 1;
        Real b = -(r[0] + r[1] + r[2]);
        Real c = r[0] * r[1] + r[0] * r[2] + r[1] * r[2];
        Real d = -r[0] * r[1] * r[2];

        auto roots = cubic_roots(a, b, c, d);
        // I could check the condition number here, but this is fine right?
        if (!CHECK_ULP_CLOSE(r[0], roots[0], (std::numeric_limits<Real>::digits > 100 ? 120 : 25))) {
            std::cerr << "  Polynomial x^3 + " << b << "x^2 + " << c << "x + "
                      << d << " has roots {";
            std::cerr << r[0] << ", " << r[1] << ", " << r[2]
                      << "}, but the computed roots are {";
            std::cerr << roots[0] << ", " << roots[1] << ", " << roots[2]
                      << "}\n";
        }
        CHECK_ULP_CLOSE(r[1], roots[1], 25);
        CHECK_ULP_CLOSE(r[2], roots[2], (std::numeric_limits<Real>::digits > 100 ? 120 : 25));
        for (auto root : roots) {
            auto res = cubic_root_residual(a, b, c, d, root);
            CHECK_LE(abs(res[0]), res[1]);
        }
    }
}

void test_ill_conditioned() {
    // An ill-conditioned root reported by SATovstun:
    // "Exact" roots produced with a high-precision calculation on Wolfram Alpha:
    // NSolve[x^3 + 10000*x^2 + 200*x +1==0,x]
    std::array<double, 3> expected_roots{-9999.97999997,
                                         -0.010010015026300100757327057,
                                         -0.009990014973799899662674923};
    auto roots = cubic_roots<double>(1, 10000, 200, 1);
    CHECK_ABSOLUTE_ERROR(expected_roots[0], roots[0],
                         std::numeric_limits<double>::epsilon());

    if (!(boost::math::isnan)(roots[1]))
    {
       // This test is so ill-conditioned, that we can't always get here.
       // Test case is Clang C++20 mode on MacOS Arm.  Best guess is that
       // fma is behaving differently there...
       CHECK_ABSOLUTE_ERROR(expected_roots[1], roots[1], 1.01e-5);
       CHECK_ABSOLUTE_ERROR(expected_roots[2], roots[2], 1.01e-5);
       double cond =
          cubic_root_condition_number<double>(1, 10000, 200, 1, roots[1]);
       double r1 = expected_roots[1];
       // The factor of 10 is a fudge factor to make the test pass.
       // Nonetheless, it does show this is basically correct:
       CHECK_LE(abs(r1 - roots[1]) / abs(r1),
          10 * std::numeric_limits<double>::epsilon() * cond);

       cond = cubic_root_condition_number<double>(1, 10000, 200, 1, roots[2]);
       double r2 = expected_roots[2];
       // The factor of 10 is a fudge factor to make the test pass.
       // Nonetheless, it does show this is basically correct:
       CHECK_LE(abs(r2 - roots[2]) / abs(r2),
          10 * std::numeric_limits<double>::epsilon() * cond);
    }
    else
    {
       CHECK_NAN(roots[2]);
    }
    // See https://github.com/boostorg/math/issues/757:
    // The polynomial is ((x+1)^2+1)*(x+1) which has roots -1, and two complex
    // roots:
    roots = cubic_roots<double>(1, 3, 4, 2);
    CHECK_ULP_CLOSE(roots[0], -1.0, 3);
    CHECK_NAN(roots[1]);
    CHECK_NAN(roots[2]);
    return;
}

int main() {
    test_zero_coefficients<float>();
    test_zero_coefficients<double>();
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
    test_zero_coefficients<long double>();
#endif
    test_ill_conditioned();
#ifdef BOOST_HAS_FLOAT128
    // For some reason, the quadmath is way less accurate than the
    // float/double/long double:
    // test_zero_coefficients<float128>();
#endif

    return boost::math::test::report_errors();
}
