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/*
* $Id$
*
* This source code is part of
*
* G R O M A C S
*
* GROningen MAchine for Chemical Simulations
*
* VERSION 3.2.0
* Written by David van der Spoel, Erik Lindahl, Berk Hess, and others.
* Copyright (c) 1991-2000, University of Groningen, The Netherlands.
* Copyright (c) 2001-2004, The GROMACS development team,
* check out http://www.gromacs.org for more information.
* 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.
*
* If you want to redistribute modifications, please consider that
* scientific software is very special. Version control is crucial -
* bugs must be traceable. We will be happy to consider code for
* inclusion in the official distribution, but derived work must not
* be called official GROMACS. Details are found in the README & COPYING
* files - if they are missing, get the official version at www.gromacs.org.
*
* To help us fund GROMACS development, we humbly ask that you cite
* the papers on the package - you can find them in the top README file.
*
* For more info, check our website at http://www.gromacs.org
*
* And Hey:
* Gromacs Runs On Most of All Computer Systems
*/
#ifndef _maths_h
#define _maths_h
#ifdef HAVE_CONFIG_H
#include <config.h>
#endif
#include <math.h>
#include "types/simple.h"
#include "typedefs.h"
#ifndef M_PI
#define M_PI 3.14159265358979323846
#endif
#ifndef M_PI_2
#define M_PI_2 1.57079632679489661923
#endif
#ifndef M_2PI
#define M_2PI 6.28318530718
#endif
#ifndef M_SQRT2
#define M_SQRT2 sqrt(2.0)
#endif
#ifdef CPLUSPLUS
extern "C" {
#endif
extern int gmx_nint(real a);
extern real sign(real x,real y);
extern real gmx_erf(real x);
extern real gmx_erfc(real x);
/*! \brief Check if two numbers are within a tolerance
*
* This routine checks if the relative difference between two numbers is
* approximately within the given tolerance, defined as
* fabs(f1-f2)<=tolerance*fabs(f1+f2+1.0).
*
* This expression is somewhat based on trial-and-error; the fabs() term on
* the right hand side avoids a division (important if f1==f2==0), and adding
* 1.0 is necessary when comparing a single number vs. 0.0.
*
* To check if two floating-point numbers are almost identical, use this routine
* with the tolerance GMX_REAL_EPS, or GMX_DOUBLE_EPS if the check should be
* done in double regardless of Gromacs precision.
*
* To check if two algorithms produce similar results you will normally need
* to relax the tolerance significantly since many operations (e.g. summation)
* accumulate floating point errors.
*
* \param f1 First number to compare
* \param f2 Second number to compare
* \param tol Tolerance to use
*
* \return 1 if the relative difference is within tolerance, 0 if not.
*/
static int
gmx_within_tol(double f1,
double f2,
double tol)
{
/* The or-equal is important - otherwise we return false if f1==f2==0 */
if( fabs(f1-f2) <= tol*fabs(f1+f2+1.0) )
{
return 1;
}
else
{
return 0;
}
}
/**
* Check if a number is smaller than some preset safe minimum
* value, currently defined as GMX_REAL_MIN/GMX_REAL_EPS.
*
* If a number is smaller than this value we risk numerical overflow
* if any number larger than 1.0/GMX_REAL_EPS is divided by it.
*
* \return 1 if 'almost' numerically zero, 0 otherwise.
*/
static int
gmx_numzero(double a)
{
return gmx_within_tol(a,0.0,GMX_REAL_MIN/GMX_REAL_EPS);
}
#ifdef CPLUSPLUS
}
#endif
#endif /* _maths_h */
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