#include "library.h"

long long fac(const long long x) {
    long long prod = 1;
    for (long long i = 2; i <= x; i++) {
        prod *= i;
    }
    return prod;
}

inline float trunc(const float x) {
    return (float)(int)(x);
}

inline float fract(const float x) {
    return x - trunc(x);
}

inline float floor(const float x) {
    return trunc(x);
}

inline float ceil(const float x) {
    return trunc(x + 1);
}

inline float round(const float x) {
    return trunc(x + 0.5f);
}

inline float mod(const float x, const float y) {
    const float xs = x/y;
    return (xs - floor(xs)) * 4;
}

float exp(const float x) {
    float sum = 0;
    // iterative counter for computing x^i
    float xpown = 1;
    // iterative counter for factorial operation i!
    float prod = 1;

    // iterate taylor series
    for (int i = 1; i < TAYLOR_SERIES_DEGREE; i++) {
        prod *= (float) i;
        sum += xpown / prod;
        xpown *= x;
    }
    return sum;
}

float sin(const float x) {
    float sign = -1;
    float prod = 1;
    float xpown = mod(x, 2 * PI);
    float sum = 0;

    for (int i = 1; i < TAYLOR_SERIES_DEGREE; i++) {
        sign *= -1;
        prod *= (float) i * (float) (i - 1);
        xpown *= x * x;

        sum += sign * xpown / prod;
    }

    return sum;
}

inline float cos(const float x) {
    return sin(x + PI * 0.5f);
}

inline float tan(const float x) {
    return sin(x)/cos(x);
}