common-math/library.h

#ifndef COMMON_MATH_LIBRARY_H
#define COMMON_MATH_LIBRARY_H

#define TAYLOR_SERIES_DEGREE 34
#define SQRT_NEWTON_ITERATIONS 26
#define INV_SQRT_NEWTON_STEPS 2

const float PI = 3.1415926535897932384626433f;

/**
 * Computes the sign of the parameter x.
 * Returns 1 if x >= 0 and -1 if x < 0
 * @param x
 * @return
 */
float sgn(float x);

/**
 * Computes the signum of the parameter x.
 * Returns 1 if x > 0, 0 if x equals 0 and -1 if x < 0
 * @param x
 * @return
 */
float signum(float x);

/**
 * Compute the factorial of parameter x.
 * This function only properly works on natural numbers.
 * The implementation is an iterative one and is only limited by the size
 * of the type used in the calculation.
 * @param x the factorial of x or 1 if x < 0
 * @return the factorial for x
 */
long long fac(long long x);

/**
 * Computes the n-th element of the fibonacci sequence.
 * This function only properly works on natural numbers.
 * The implementation is an iterative one and is only limited by the size
 * of the type used in the calculation.
 * @param n the n-th element to compute
 * @return the n-th fibonacci number
 */
long long fib(long long n);

/**
 * Truncates the parameter x.
 * In other words this function will cut of the fraction part of the number x.
 * @param x
 * @return trunc(x)
 */
inline float trunc(float x);

/**
 * Computes the fraction of x.
 * In other words this function will only keep the fractional part and cut of the integral.
 * @param x
 * @return fract(x)
 */
inline float fract(float x);

/**
 * Computes the floor of x.
 * In other words this function will round x towards negative infinity.
 * This is effectively the same as trunc(x)
 * @param x
 * @return floor(x)
 */
inline float floor(float x);

/**
 * Computes the ceil of x.
 * In other words this function will round x towards positive infinity
 * @param x
 * @return ceil(x)
 */
inline float ceil(float x);

/**
 * Round the number x.
 * In other words this function will round x towards negative infinity if x the fraction of x is smaller than 0.5 and else
 * towards positive infinity
 * @param x
 * @return round(x)
 */
inline float round(float x);

/**
 * Compute the modulo division of x and y.
 * @param x
 * @param y
 * @return mod(x,y)
 */
float mod(float x, float y);

/**
 * Computes the result of e raised to the power of x.
 * This function only performs an approximation based on the famous taylor series for e^x.
 * @param x the exponent of e^x
 * @return approximation of e^x
 */
float exp(float x);

/**
 * Approximate the sqrt of x using the newton's method.
 * Precision an be optimized via SQRT_NEWTON_ITERATIONS
 * @param x
 * @return sqrt(x)
 */
float sqrt(float x);

/**
 * Approximate the hypotenuse of x and y (sqrt(x²+y²)) using the babylonian method.
 * @param x
 * @param y
 * @return sqrt(x²+y²)
 */
float hypot(float x, float y);

/**
 * Computes the sine of x.
 * @param x
 * @return sin(x)
 */
float sin(float x);

/**
 * Computes the cosine of x.
 * @param x
 * @return cos(x)
 */
float cos(float x);

/**
 * Computes the tangent of x.
 * @param x
 * @return tan(x)
 */
float tan(float x);

/**
 * Computes an approximation of the cosecant of parameter x.
 * @param x
 * @return csc(x)
 */
float csc(float x);

/**
 * Computes an approximation of the secant of parameter x.
 * @param x
 * @return sec(x)
 */
float sec(float x);

/**
 * Computes an approximation of the cotangent of parameter x.
 * @param x
 * @return cot(x)
 */
float cot(float x);

/**
 * Approximates the inverse of the tangent of x
 * @param x
 * @return
 */
float atan(float x);

/**
 * Approximates the inverse of the sine of x
 * @param x
 * @return
 */
float asin(float x);

/**
 * Approximates the inverse of the cosine of x
 * @param x
 * @return
 */
float acos(float x);

/**
 * Approximates the inverse of the cotangent of x
 * @param x
 * @return
 */
float acot(float x);

/**
 * Approximates the inverse of the cosecant of x
 * @param x
 * @return
 */
float acsc(float x);

/**
 * Approximates the inverse of the secant of x
 * @param x
 * @return
 */
float asec(float x);

/**
 * Approximate the inverse square root.
 * This implementation is based on the algorithm introduced in the Quake game with
 * various improvements.
 * @param x
 * @return 1/sqrt(x)
 */
float inv_sqrt(float x);

#endif //COMMON_MATH_LIBRARY_H