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/*
This file is part of Warzone 2100.
Copyright (C) 1999-2004 Eidos Interactive
Copyright (C) 2005-2020 Warzone 2100 Project
Warzone 2100 is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
Warzone 2100 is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with Warzone 2100; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
*/
/*!
* \file
* \brief Routines to provide simple math helper functions
*/
#ifndef MATH_EXT_H
#define MATH_EXT_H
#include "wzglobal.h"
#include <cmath>
#include <complex>
#include <cstdlib>
#include <math.h>
// Also PERCENT(int,int); // returns a int value 0->100 of the percentage of the first param over the second
#define PERCENT(a,b) (((a)*100)/(b))
#define PERNUM(range,a,b) (((a)*range)/(b))
#ifndef M_PI
# define M_PI 3.14159265358979323846
#endif
#if (!defined(WZ_C99) && !defined(__cplusplus) && !defined(WZ_CC_GNU)) || (defined _MSC_VER)
#if (_MSC_VER <= 1600)
# include <float.h>
static inline int roundf(float x)
{
// Ensure that float truncation results in a proper rounding
if (x < 0.0f)
{
return x - 0.5f;
}
else
{
return x + 0.5f;
}
}
/**
* nearbyint(3) implementation because that function is only available on C99
* compatible C libraries.
*
* This function rounds its argument to an integer value in floating point
* format, using the current rounding direction and without raising an
* @c inexact exception.
*
* @return The rounded integer value. If @c x is integral or infinite, @c x
* itself is returned.
*/
static inline double nearbyint(double x)
{
if (ceil(x + 0.5) == floor(x + 0.5))
{
if ((int)ceil(x) % 2 == 0)
{
return ceil(x);
}
else
{
return floor(x);
}
}
else
{
return floor(x + 0.5);
}
}
// this is already included for MSVC 2010
#if _MSC_VER < 1600
static inline WZ_DECL_CONST float hypotf(float x, float y)
{
return sqrtf(x * x + y * y);
}
#endif
#endif
#endif
/*!
* Clips x to boundaries
* \param x Value to clip
* \param min Lower bound
* \param max Upper bound
*/
template<typename T>
static inline WZ_DECL_CONST T clip(T x, T min, T max)
{
// std::min and std::max not constexpr until C++14.
return x < min ? min : x > max ? max : x;
}
/*!
* Clips x to boundaries
* \param x Value to clip
* \param min Lower bound
* \param max Upper bound
*/
static inline WZ_DECL_CONST float clipf(float x, float min, float max)
{
return x < min ? min : x > max ? max : x;
}
/// Finds change in y and y' after time dt, according to the differential equation y'' = -ay - fy'
static inline void solveDifferential2ndOrder(float *y_, float *dydt_, double acceleration, double friction, double dt)
{
double y = *y_, dydt = *dydt_;
// Solution is y = g_1 exp(h_1 t) + g_2 exp(h_2 t), where h_i are the solutions to h^2 + f h + a = 0, which are -f/2 +- sqrt(f^2/4 - a).
// At t = 0, g_1 = (y' - h_2 y) / (h_1 - h_2) and g_2 = (y' - h_1 y) / (h_2 - h_1).
std::complex<double> d = friction * friction / 4 - acceleration;
std::complex<double> sqd = std::sqrt(d);
std::complex<double> h1 = -friction / 2 + sqd;
std::complex<double> h2 = -friction / 2 - sqd;
std::complex<double> e1 = std::exp(h1 * dt);
std::complex<double> e2 = std::exp(h2 * dt);
std::complex<double> g1 = (dydt - h2 * y) / (h1 - h2);
std::complex<double> g2 = (dydt - h1 * y) / (h2 - h1);
*y_ = static_cast<float>((g1 * e1 + g2 * e2).real()); // .imag() should be 0.
*dydt_ = static_cast<float>((g1 * h1 * e1 + g2 * h2 * e2).real()); // .imag() should be 0.
}
// Windows unfortunately appears to do this, so do this too for compatibility...
using std::abs;
using std::sqrt;
using std::pow;
#endif // MATH_EXT_H
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