test_polynomial.cpp

// Description: Testing for Polynomial
// DocumentationOf: polynomial.h

#include "test/test_init.h"

#include "pastel/math/polynomial.h"
#include "pastel/sys/rational.h"

namespace
{

    using Real = real;
    using Poly = Polynomial<Real>;

}

TEST_CASE("Basic (Polynomial)")
{
    Poly a;
    REQUIRE(a.size() == 1);
    REQUIRE(a[0] == 0);
    REQUIRE(a.degree() == 0);

    a[0] = 1;
    REQUIRE(a.degree() == 0);

    a.set(1, 0);
    REQUIRE(a.size() == 2);
    REQUIRE(a.degree() == 0);

    a.set(5, 0);
    REQUIRE(a.size() == 6);
    REQUIRE(a.degree() == 0);
    a.set(5, 1);
    REQUIRE(a.size() == 6);
    REQUIRE(a.degree() == 5);

    a.setSize(10);
    REQUIRE(a.size() == 10);
    REQUIRE(a.degree() == 5);

    a.setSize(4);
    REQUIRE(a.size() == 4);
    REQUIRE(a.degree() == 0);
}

TEST_CASE("Operators (Polynomial)")
{
    Poly a;
    a.set(0, 1);

    REQUIRE(a.degree() == 0);
    a <<= 1;
    REQUIRE(a.degree() == 1);
    a <<= 2;
    REQUIRE(a.degree() == 3);

    {
        Poly b;
        b.set(3, 1);
        REQUIRE(a == b);
    }
    a >>= 3;
    {
        Poly b;
        b.set(0, 1);
        REQUIRE(a == b);
    }

    Poly c;
    c.set(0, 3);
    c.set(1, 7);
    c.set(2, 5);

    Poly d;
    d.set(0, 1);
    d.set(1, 5);

    {
        Poly e;
        e.set(0, 3 + 1);
        e.set(1, 7 + 5);
        e.set(2, 5 + 0);

        REQUIRE(e == c + d);
    }
    {
        Poly e;
        e.set(0, 3 - 1);
        e.set(1, 7 - 5);
        e.set(2, 5 - 0);

        REQUIRE(e == c - d);
    }
    {
        Poly e;
        e.set(0, 3);
        e.set(1, 22);
        e.set(2, 40);
        e.set(3, 25);

        REQUIRE(e == c * d);
    }
}

TEST_CASE("Tools (Polynomial)")
{
    {
        Poly a;
        a.set(0, 3);
        a.set(1, 7);
        a.set(2, 5);

        differentiate(a);

        Poly b;
        b.set(0, 7);
        b.set(1, 10);

        REQUIRE(a == b);
    }
    {
        Poly a;
        a.set(0, 3);
        a.set(1, 7);
        a.set(2, 5);

        Poly b;
        b.set(0, 1);
        b.set(1, 5);

        Poly quotient;
        Poly remainder;

        divide(a, b, quotient, remainder);

        Poly c;
        c.set(0, Real(6) / 5);
        c.set(1, 1);

        Poly d;
        d.set(0, Real(9) / 5);

        REQUIRE(c == quotient);
        REQUIRE(d == remainder);
    }
    {
        integer maxDegree = 10;

        integer failings = 0;
        for (integer i = 0;i < 10000;++i)
        {
            Poly poly = randomPolynomial<Real>(randomInteger(maxDegree + 1));
            Poly divider = randomPolynomial<Real>(randomInteger(maxDegree + 1));

            Poly quotient;
            Poly remainder;
            divide(poly, divider, quotient, remainder);

            Poly error = poly - (quotient * divider + remainder);

            if (error.degree() != 0)
            {
                ++failings;
            }
        }

        REQUIRE(failings <= 200);
    }
}