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/**
* \file mathFuncs.h
* \brief Mathematical functions.
* \copyright Copyright (C) 2006-2022 Ralf Hoppe <ralf.hoppe@dfcgen.de>
*/
#ifndef MATHFUNCS_H
#define MATHFUNCS_H
/* INCLUDE FILES **************************************************************/
#include "base.h" /* includes config.h (include before math.h) */
#include <math.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_sf.h> /* all special functions */
#include <gsl/gsl_errno.h>
#ifdef __cplusplus
extern "C" {
#endif
/* GLOBAL TYPE DECLARATIONS ***************************************************/
/** Decimal normalized double value. The original value is determined by
* \f$m 10^e\f$.
*/
typedef struct
{
double mantissa; /**< mantissa m */
double exponent; /**< exponent e */
} MATH_NORMDBL;
/* GLOBAL CONSTANT DECLARATIONS ***********************************************/
/* GLOBAL VARIABLE DECLARATIONS ***********************************************/
/* GLOBAL MACRO DEFINITIONS ***************************************************/
/** This macro swaps two integers (inline).
*/
#define MATH_SWAP_INT(int1, int2) \
{ \
(int1) ^= (int2); \
(int2) ^= (int1); \
(int1) ^= (int2); \
}
#ifdef HAVE_HYPOT
#define HYPOT(x, y) hypot ((x), (y))
#else
#define HYPOT(x, y) gsl_hypot ((x), (y))
#endif
#ifdef HAVE_POW10 /* pow10() exists? */
#define POW10(x) pow10(x)
#else
#ifdef HAVE_EXP10
#define POW10(x) exp10(x) /**< 10 raised to \p x, means \f$y=10^{x}\f$ */
#else
#define POW10(x) pow(10, (x)) /* fallback to (slow) generic function */
#endif /* HAVE_EXP10 */
#endif /* HAVE_POW10 */
#ifndef HAVE_TRUNC
#define trunc(x) ((GSL_SIGN(x) > 0) ? floor(x) : ceil(x))
#endif
#ifndef HAVE_ROUND
#define round(x) floor((x) + 0.5) /* fallback to (slow) generic */
#endif
/* EXPORTED FUNCTIONS *********************************************************/
/* FUNCTION *******************************************************************/
/** Calculates a normalized value consisting of (decimal) mantissa and exponent.
*
* \param val Value to be converted.
*
* \return Normalized value.
******************************************************************************/
MATH_NORMDBL mathNorm10(double val);
/* FUNCTION *******************************************************************/
/** Denormalizes a decimal value from its mantissa and exponent.
*
* \param val Normalized value to be converted.
*
* \return Denormalized value.
******************************************************************************/
double mathDenorm10(MATH_NORMDBL val);
/* FUNCTION *******************************************************************/
/** Rectangle function
\f[
y = \begin{cases} 0, & \mbox{if} \;\; x<0 \\
0, & \mbox{if} \;\; x>1 \\
1, & \mbox{else} \end{cases}
\f]
*
* \param x Argument \f$x\f$.
*
* \return Result \f$y\f$.
******************************************************************************/
double mathFuncRectangle (double x);
/* FUNCTION *******************************************************************/
/** \e Hamming window function
\f[
y = \begin{cases} 0, & \mbox{if} \;\; x<0 \\
0, & \mbox{if} \;\; x>1 \\
0.54-0.46 \cos(2\pi x), & \mbox{else} \end{cases}
\f]
*
* \param x Argument \f$x\f$.
*
* \return Result \f$y\f$.
******************************************************************************/
double mathFuncHamming (double x);
/* FUNCTION *******************************************************************/
/** \e van \e Hann window function
\f[
y = \begin{cases} 0, & \mbox{if} \;\; x<0 \\
0, & \mbox{if} \;\; x>1 \\
\frac{1}{2}\,[1-\cos(2\pi x)], & \mbox{else} \end{cases}
\f]
*
* \param x Argument \f$x\f$.
*
* \return Result \f$y\f$.
******************************************************************************/
double mathFuncVanHann (double x);
/* FUNCTION *******************************************************************/
/** \e Blackman window function
\f[
y = \begin{cases} 0, & \mbox{if} \;\; x<0 \\
0, & \mbox{if} \;\; x>1 \\
0.42-0.5\cos(2\pi x)+0.08\cos(4\pi x), & \mbox{else}
\end{cases}
\f]
*
* \param x Argument \f$x\f$.
*
* \return Result \f$y\f$.
******************************************************************************/
double mathFuncBlackman (double x);
/* FUNCTION *******************************************************************/
/** \e Kaiser window function
\f[
y = \begin{cases} 0, & \mbox{if} \;\; x<0 \\
0, & \mbox{if} \;\; x>1 \\
\frac{I_0\left(\alpha\sqrt{1-(2 x-1)^2}\right)}
{I_0(\alpha)}, & \mbox{else}
\end{cases}
\f]
*
* \param x Argument \f$x\f$.
* \param alpha Parameter \f$\alpha\f$.
*
* \return Result \f$y\f$ when successful evaluated, else
* GSL_POSINF or GSL_NEGINF. Use the functions gsl_isinf()
* or gsl_finite() for result checking.
******************************************************************************/
double mathFuncKaiser (double x, double alpha);
#ifdef __cplusplus
}
#endif
#endif /* MATHFUNCS_H */
/******************************************************************************/
/* END OF FILE */
/******************************************************************************/
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