#include "library.h"
#include <inttypes.h>

float sgn(const float x) {
    return x < 0 ? -1 : 1;
}

float signum(const float x) {
    return x < 0 ? -1.0f : (x == 0.0f ? 0.0f : 1.0f);
}

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

long long fib(const long long n) {
    long long sum = 0;
    long long prev = 0;
    for (long long i = 1LL; i <= n; i++) {
        sum += prev;
        prev = i - 1;
    }
    return sum;
}

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 sqrt(const float x) {
    float a = x;
    for (int i = 0; i < SQRT_NEWTON_ITERATIONS; i++) {
        a = 0.5f * (x/a + a);
    }
    return a;
}

float hypot(const float x, const float y) {
    return x + 0.5f * y * y / x;
}

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);
}

inline float csc(const float x) {
    return 1.0f / sin(x);
}

inline float sec(const float x) {
    return 1.0f / cos(x);
}

inline float cot(const float x) {
    return tan(PI * 0.5f - x);
}

float atan(const float x) {
    const float a = 0.6204500718160764f;
    const float b = 0.6204500718160764f;
    const float c = 0.9031580043522688f;

    return a * x / (b + sqrt(c + x * x));
}

inline float acot(const float x) {
    return PI * 0.5f - atan(x);
}

inline float acsc(const float x) {
    return asin(1/x);
}

inline float asec(const float x) {
    return asin(-1/x) + PI * 0.5f;
}

float asin(const float x) {
    return atan(x * inv_sqrt((1 + x) * (1 - x)));
}

float acos(const float x) {
    return asin(-x) + PI * 0.5f;
}

float inv_sqrt(const float x) {
    union {
        float    f;
        uint32_t i;
    } conv = { .f = x };
    conv.i = 0x5f1ffff9 - (conv.i >> 1);

    for (int k = 0; k < INV_SQRT_NEWTON_STEPS; k++)
        conv.f *= 0.703952253f * (2.38924456f - x * conv.f * conv.f);

    return conv.f;
}