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math_tools.c
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math_tools.c
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/**
******************************************************************************
* File Name : math_tools.c
* Author : Xavier Halgand
* Date :
* Description :
******************************************************************************
*/
/*
* 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
* (at your option) 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, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*
*/
#include "math_tools.h"
/*-----------------------------------------------------------------------------------*/
float approx_exp(float x)
{
float y; // exp(x) = lim n->inf (1 + x/n)^n, here we've choosen n = 16
y = 1.f + x/16.f ;
y *= y;
y *= y;
y *= y;
y *= y;
return y ;
}
//------------------------------------------------------------------------------------
// input val in 0 ... 127
// output is an exponential between min and max
float Lin2Exp(uint8_t val, float min, float max)
{
return min * powf(max / min, val / MIDI_MAX);
}
//------------------------------------------------------------------------------------
float tanhXdX(float x)
{
float a = x*x;
// IIRC I got this as Pade-approx for tanh(sqrt(x))/sqrt(x)
x = ((a + 105)*a + 945) / ((15*a + 420)*a + 945);
return x;
}
//------------------------------------------------------------------------------------
float fastTanh(float var)
{
if(var < -1.95f) return -1.0f;
else if(var > 1.95f) return 1.0f;
else return 4.15f*var/(4.29f+var*var);
}
//------------------------------------------------------------------------------------
float softClipTwo(float in)
{
return in * tanhXdX(0.5*in);
}
//------------------------------------------------------------------------------------
float fastTan(float x)
{
float A = -15*x+x*x*x;
float B = 3*(-5+2*x*x);
return A/B;
}