mathutils.h

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/*
 *  The Mana Client
 *  Copyright (C) 2009  The Mana World Development Team
 *  Copyright (C) 2009-2012  The Mana Developers
 *
 *  This file is part of The Mana Client.
 *
 *  This program 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
 *  any later version.
 *
 *  This program 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 this program.  If not, see <http://www.gnu.org/licenses/>.
 */
 
#pragma once
 
/* A very fast function to calculate the approximate inverse square root of a
 * floating point value and a helper function that uses it for getting the
 * normal squareroot. For an explanation of the inverse squareroot function
 * read:
 * http://www.math.purdue.edu/~clomont/Math/Papers/2003/InvSqrt.pdf
 *
 * Unfortunately the original creator of this function seems to be unknown.
 */
 
inline float fastInvSqrt(float x)
{
    union { int i; float x; } tmp;
    float xhalf = 0.5f * x;
    tmp.x = x;
    tmp.i = 0x5f375a86 - (tmp.i >> 1);
    x = tmp.x;
    x = x * (1.5f - xhalf * x * x);
    return x;
}
 
inline float fastSqrt(float x)
{
    return 1.0f / fastInvSqrt(x);
}
 
inline float weightedAverage(float n1, float n2, float w)
{
    if (w < 0.0f)
        return n1;
 
    if (w > 1.0f)
        return n2;
 
    return w * n2 + (1.0f - w) * n1;
}