math.h

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/* (c) Magnus Auvinen. See licence.txt in the root of the distribution for more information. */
/* If you are missing that file, acquire a complete release at teeworlds.com.                */
#ifndef BASE_MATH_H
#define BASE_MATH_H
 
#include <cmath>
#include <concepts>
#include <cstdlib>
#include <limits>
 
template<typename T>
concept Numeric = std::integral<T> || std::floating_point<T>;
 
constexpr float pi = 3.1415926535897932384626433f;
constexpr float normalized_golden_angle = 137.50776f / 360.0f;
 
// NaN and floats outside the int range convert to INT_MIN, a plain cast would be undefined
constexpr int round_truncate(float f)
{
    constexpr float imin = (float)std::numeric_limits<int>::min();
    return f >= imin && f < -imin ? (int)f : std::numeric_limits<int>::min();
}
 
constexpr int round_to_int(float f)
{
    return f > 0 ? round_truncate(f + 0.5f) : round_truncate(f - 0.5f);
}
 
template<typename T, typename TB>
constexpr T mix(const T a, const T b, TB amount)
{
    return a + (b - a) * amount;
}
 
template<typename T, typename TB>
constexpr T bezier(const T p0, const T p1, const T p2, const T p3, TB amount)
{
    // De-Casteljau Algorithm
    const T c10 = mix(p0, p1, amount);
    const T c11 = mix(p1, p2, amount);
    const T c12 = mix(p2, p3, amount);
 
    const T c20 = mix(c10, c11, amount);
    const T c21 = mix(c11, c12, amount);
 
    return mix(c20, c21, amount); // c30
}
 
template<typename T, typename TB>
constexpr T mix_polynomial(const TB time[], const T data[], int samples, TB amount, T init)
{
    T result = init;
    for(int i = 0; i < samples; i++)
    {
        T term = data[i];
        for(int j = 0; j < samples; j++)
            if(j != i)
                term = term * (amount - time[j]) / TB(time[i] - time[j]);
        result += term;
    }
    return result;
}
 
inline float random_float()
{
    return rand() / (float)(RAND_MAX);
}
 
inline float random_float(float min, float max)
{
    return min + random_float() * (max - min);
}
 
inline float random_float(float max)
{
    return random_float(0.0f, max);
}
 
inline float random_angle()
{
    return 2.0f * pi * (rand() / std::nextafter((float)RAND_MAX, std::numeric_limits<float>::max()));
}
 
constexpr int fxpscale = 1 << 10;
 
// float to fixed
constexpr int f2fx(float v)
{
    return round_to_int(v * fxpscale);
}
constexpr float fx2f(int v)
{
    return v / (float)fxpscale;
}
 
// int to fixed
constexpr int i2fx(int v)
{
    return v * fxpscale;
}
constexpr int fx2i(int v)
{
    return v / fxpscale;
}
 
class fxp
{
    int value;
 
public:
    constexpr void set(int v)
    {
        value = v;
    }
    constexpr int get() const
    {
        return value;
    }
    constexpr fxp &operator=(int v)
    {
        value = i2fx(v);
        return *this;
    }
    constexpr fxp &operator=(float v)
    {
        value = f2fx(v);
        return *this;
    }
    constexpr operator int() const
    {
        return fx2i(value);
    }
    constexpr operator float() const
    {
        return fx2f(value);
    }
};
 
template<typename T>
constexpr T absolute(T a)
{
    return a < T(0) ? -a : a;
}
 
template<Numeric T>
constexpr bool in_range(T a, T lower, T upper)
{
    return lower <= a && a <= upper;
}
template<Numeric T>
constexpr bool in_range(T a, T upper)
{
    return in_range(a, 0, upper);
}
 
#endif // BASE_MATH_H