162 lines
4.2 KiB
C++
162 lines
4.2 KiB
C++
/*
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This file is part of Warzone 2100.
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Copyright (C) 1999-2004 Eidos Interactive
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Copyright (C) 2005-2013 Warzone 2100 Project
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Warzone 2100 is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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Warzone 2100 is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with Warzone 2100; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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*/
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/*!
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* \file
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* \brief Routines to provide simple math helper functions
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*/
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#ifndef MATH_EXT_H
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#define MATH_EXT_H
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#include "wzglobal.h"
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#include <cmath>
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#include <complex>
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#include <cstdlib>
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#include <math.h>
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// Also PERCENT(int,int); // returns a int value 0->100 of the percentage of the first param over the second
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#define PERCENT(a,b) (((a)*100)/(b))
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#define PERNUM(range,a,b) (((a)*range)/(b))
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#ifndef M_PI
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# define M_PI 3.14159265358979323846
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#endif
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#if (!defined(WZ_C99) && !defined(__cplusplus) && !defined(WZ_CC_GNU)) || (defined _MSC_VER)
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# include <float.h>
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static inline int roundf(float x)
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{
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// Ensure that float truncation results in a proper rounding
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if (x < 0.0f)
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return x - 0.5f;
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else
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return x + 0.5f;
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}
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/**
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* nearbyint(3) implementation because that function is only available on C99
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* compatible C libraries.
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*
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* This function rounds its argument to an integer value in floating point
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* format, using the current rounding direction and without raising an
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* @c inexact exception.
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*
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* @return The rounded integer value. If @c x is integral or infinite, @c x
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* itself is returned.
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*/
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static inline double nearbyint(double x)
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{
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if (ceil(x + 0.5) == floor(x + 0.5))
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{
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if ((int)ceil(x) % 2 == 0)
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{
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return ceil(x);
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}
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else
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{
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return floor(x);
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}
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}
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else
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{
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return floor(x + 0.5);
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}
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}
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// this is already included for MSVC 2010
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#if _MSC_VER < 1600
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static inline WZ_DECL_CONST float hypotf(float x, float y)
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{
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return sqrtf(x * x + y * y);
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}
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#endif
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#endif
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/*!
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* Moves x into the range 0.0f - max
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* \param x Value to clip
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* \param max Upper range
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* \return Value in the range 0.0f - max
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*/
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static inline WZ_DECL_CONST float wrapf(float x, float max)
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{
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while(x < 0.0f) x += max;
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while(x >= max) x -= max;
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return x;
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}
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/*!
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* Clips x to boundaries
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* \param x Value to clip
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* \param min Lower bound
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* \param max Upper bound
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*/
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static inline WZ_DECL_CONST int clip(int x, int min, int max)
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{
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if (x < min) return min;
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if (x > max) return max;
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return x;
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}
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/*!
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* Clips x to boundaries
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* \param x Value to clip
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* \param min Lower bound
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* \param max Upper bound
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*/
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static inline WZ_DECL_CONST float clipf(float x, float min, float max)
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{
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if (x < min) return min;
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if (x > max) return max;
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return x;
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}
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/// Finds change in y and y' after time dt, according to the differential equation y'' = -ay - fy'
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static inline void solveDifferential2ndOrder(float *y_, float *dydt_, double acceleration, double friction, double dt)
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{
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double y = *y_, dydt = *dydt_;
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// 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).
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// At t = 0, g_1 = (y' - h_2 y) / (h_1 - h_2) and g_2 = (y' - h_1 y) / (h_2 - h_1).
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std::complex<double> d = friction*friction/4 - acceleration;
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std::complex<double> sqd = std::sqrt(d);
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std::complex<double> h1 = -friction/2 + sqd;
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std::complex<double> h2 = -friction/2 - sqd;
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std::complex<double> e1 = std::exp(h1*dt);
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std::complex<double> e2 = std::exp(h2*dt);
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std::complex<double> g1 = (dydt - h2 * y) / (h1 - h2);
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std::complex<double> g2 = (dydt - h1 * y) / (h2 - h1);
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*y_ = (g1*e1 + g2*e2).real(); // .imag() should be 0.
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*dydt_ = (g1*h1*e1 + g2*h2*e2).real(); // .imag() should be 0.
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}
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// Windows unfortunately appears to do this, so do this too for compatibility...
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using std::abs;
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using std::sqrt;
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using std::pow;
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#endif // MATH_EXT_H
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