prob_AC_COGRIG_cos

#include <stdio.h>
#include <math.h>

double calculateK(unsigned int n){
    double k = 1.0;
    int i = 0;
    unsigned long power = 1;
    for(; i < n; i++){
        k*=sqrt(1.0 + 1.0/power);
    }
    return k;
}
double codrig(double theta, unsigned int n){
    double x = 1.0/calculateK(n);
    double x_old = x;
    double y = 0;
    double z = theta;
    double power = 1.0;

    for(int i = 0; i < n; i++, power/= 2.0){
        if(z>=0){
            x = x - (y * power) ;
            y = y + (x_old * power) ;
            z = z - atan(power);
        }
        else {
            x = x + (y * power) ;
            y = y - (x_old * power) ;
            z = z + atan(power);
        }
        x_old = x;
        }
    return x;
}
void printCODRIG(double theta, char* thetaSTR, unsigned int n){
    double cos_cordig = codrig(theta, n);
    double cos_library = cos(theta);
    double error = cos_cordig - cos_library;
    unsigned int noEqualBits = 0;
    if(thetaSTR == NULL) thetaSTR = "theta";
        printf(" n = %2d | cos_cordig(%s) = %+.10f | cos_library(%s) = %+.10f | error = %+.15f | equal_bits = %2d\n",
                            n, thetaSTR, cos_cordig, thetaSTR, cos_library, error, noEqualBits);
}
int main()
{
    double theta = 0;
    char* thetaSTR = NULL;
    unsigned int n = 0;
    theta = M_PI/6;
    n = 31;
    thetaSTR = "pi/6";
    printCODRIG(theta, thetaSTR, n);

    return 0;
}
//sau aslta varianta
#include <stdio.h>
#include <math.h>

/*double calculateK(unsigned int n){
    double k = 1.0;
    int i = 0;
    unsigned long power = 1;
    for(; i < n; i++){
        k*=sqrt(1.0 + 1.0/power);
    }
    return k;
}
double codrig(double theta, unsigned int n){
    double x = 1.0/calculateK(n);
    double x_old = x;
    double y = 0;
    double z = theta;
    double power = 1.0;

    for(int i = 0; i < n; i++, power/= 2.0){
        if(z>=0){
            x = x - (y * power) ;
            y = y + (x_old * power) ;
            z = z - atan(power);
        }
        else {
            x = x + (y * power) ;
            y = y - (x_old * power) ;
            z = z + atan(power);
        }
        x_old = x;
        }
    return x;
}*/
double codrig(float theta, unsigned int n){
    double x,y,z,alpha;
    double k = 1;
    for(int i = 0; i < n; i++){
        k*=sqrt(1+pow(2, -2*i));
    }
    printf("k = %f.8\n", k);
    x = 1/k;
    y = 0;
    z = theta;
    for (int i = 0; i< n; i ++){
        alpha = atan(pow(2,-i));
        if(z>0){
            float x_temp = x;
            float y_temp = y;
            x = x - pow(2, -i) * y_temp;
            y = y + pow(2, -i) * x_temp;
            z = z - alpha;
        }
        else {
            float x_temp = x;
            float y_temp = y;
            x = x + pow(2, -i) * y_temp;
            y = y - pow(2, -i) * x_temp;
            z = z + alpha;
        }
        printf("z = %.8f  y = %.8f  x = %.8f  alpha = %.8f\n", z, y, x, alpha);
    }
    return x;
}
void printCODRIG(double theta, char* thetaSTR, unsigned int n){
    double cos_cordig = codrig(theta, n);
    double cos_library = cos(theta);
    double error = cos_cordig - cos_library;
    unsigned int noEqualBits = 0;
    if(thetaSTR == NULL) thetaSTR = "theta";
        printf(" n = %2d | cos_cordig(%s) = %+.10f | cos_library(%s) = %+.10f | error = %+.15f | equal_bits = %2d\n",
                            n, thetaSTR, cos_cordig, thetaSTR, cos_library, error, noEqualBits);
}
int main()
{
    double theta = 0;
    char* thetaSTR = NULL;
    unsigned int n = 0;
    theta = M_PI/6;
    n = 31;
    thetaSTR = "pi/6";
    printCODRIG(theta, thetaSTR, n);

    return 0;
}