#include <iostream>
#include <iomanip>
#include <cmath>

namespace Math {

    #define MATH_PI_025 0.785375
    #define MATH_PI_05 1.57075
    #define MATH_PI 3.1415
    #define MATH_PI_15 4.71225
    #define MATH_PI_2 6.283

    double abs(double a) {
        if(a < 0)
            return -a;

        return a;
    }

    double sin(double a) {
        a = abs(a);

        while(a > MATH_PI_2)
            a -= MATH_PI_2;

        //We map sin to first quadrant.
        bool minAttached = false;

        if(a > MATH_PI_15) {
            a = MATH_PI_2 - a;
            minAttached = true;
        }

        else if(a > MATH_PI) {
            a = a - MATH_PI;
            minAttached = true;
        }

        else if(a > MATH_PI_05)
            a = a - 2 * (a - MATH_PI_05);

        //Its accurate only to 45 deg
        if(a > MATH_PI_025)
            return cos(MATH_PI_05 - a);

        //Polynomal
        double result = a - ((a * a * a) / 6) + ((a * a * a * a * a) / 120);

        if(minAttached)
            return -result;

        return result;
    }

    double cos(double a) {
        a = abs(a);

        while(a > MATH_PI_2)
            a -= MATH_PI_2;

        //We map sin to first quadrant.
        bool minAttached = false;

        if(a > MATH_PI_15)
            a = MATH_PI_2 - a;

        else if(a > MATH_PI) {
            a = a - MATH_PI;
            minAttached = true;
        }

        else if(a > MATH_PI_05) {
            a = a - 2 * (a - MATH_PI_05);
            minAttached = true;
        }

        //It's accurate only to 45 deg
        if(a > MATH_PI_025)
            return sin(MATH_PI_05 - a);

        //Polynomal
        double result = 1 - ((a * a) / 2) + ((a * a * a * a) / 24) - ((a * a * a * a * a * a) / 720);

        if(minAttached)
            return -result;

        return result;
    }

    double sqrt(double a)
    {

    }

}

int main(void)
{
    std::cout << std::fixed << std::setprecision(8) << std::sin(MATH_PI)            << " : " << Math::sin(MATH_PI)              << std::endl;
    std::cout << std::fixed << std::setprecision(8) << std::sin(MATH_PI * 2)        << " : " << Math::sin(MATH_PI * 2)          << std::endl;
    std::cout << std::fixed << std::setprecision(8) << std::sin(MATH_PI * 0.45664)  << " : " << Math::sin(MATH_PI * 0.45664)    << std::endl;
    std::cout << std::fixed << std::setprecision(8) << std::cos(MATH_PI)            << " : " << Math::cos(MATH_PI)              << std::endl;
    std::cout << std::fixed << std::setprecision(8) << std::cos(MATH_PI * 2)        << " : " << Math::cos(MATH_PI * 2)          << std::endl;
    std::cout << std::fixed << std::setprecision(8) << std::cos(MATH_PI * 0.45664)  << " : " << Math::cos(MATH_PI * 0.45664)    << std::endl;

    return 0;
}