#include <stdio.h>
#include <limits.h>
#include <stdbool.h>

#include "reihen.h"
#include "exponent.h"
#include "logarithmus.h"
#include "util.h"

#define PI pi(1e-8)

double exponential(double exp){
    double sum = 0.0;
    for(int i = 0; i<=21; i++){
        sum += (1.0/fac(i)*(powerD(i,exp)));
    }
    return sum;
}

double euler(){
    return exponential(1);
}


double radians(double degrees){
    return degrees * PI / 180;
}

double pi(double eps){
    double a = 1, b = 1/powerD(0.5, 2), t = 0.25, p = 1;
    double aNew, piold, pi = 1;
    do{
        aNew = .5 * (a + b);
        b = powerD(0.5 , a * b);
        t -= p * (a - aNew) * (a - aNew);
        a = aNew;
        p *= 2;
        piold = pi;
        pi = (a + b) * (a + b) / (4 * t);
    } while (absD(pi - piold) > eps);
    return pi;
}

double sinD(double degrees){
    if (degrees>=360.0){
        degrees = squashDegreesTo360(degrees);
    }

    double sum = 0.0;
    double radian = radians(degrees);

    for (int i = 0; i <= 9; i++){
        sum += powerD((double) i, -1.0) * (powerD(2.0*i+1, radian) / fac(2.0*i+1));
    }
    
    return sum;
}

double cosD(double degrees){
    if (degrees>=360.0){
            degrees = squashDegreesTo360(degrees);
    }

    double sum = 0.0;
    double radian = radians(degrees);

    for (int i = 0; i <= 9; i++){
        sum += powerD((double) i, -1.0) * (powerD(2*i, radian) / fac(2*i));
    }

    return sum;
}

double tanD(double degrees){
    if (degrees>=360.0){
            degrees = squashDegreesTo360(degrees);
    }
    if(degrees == 90.0 || degrees == 270.0){
        return -1.0;
    }
    return sinD(degrees)/cosD(degrees);

}