/*

 *  Mathlib : A C Library of Special Functions

 *  Copyright (C) 2013-2022 The R Core Team

 *

 *  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.

 */

#include "nmath.h"

/* HAVE_COSPI etc will not be defined in standalone-use: the

   intention is to make the versions here available in that case.

   The __cospi etc variants are from macOS (and perhaps other BSD-based systems).

*/

#ifdef HAVE_COSPI

#elif defined HAVE___COSPI

double cospi(double x) {

    return __cospi(x);

}

#else

// cos(pi * x)  -- exact when x = k/2  for all integer k

double cospi(double x) {

#ifdef IEEE_754

    /* NaNs propagated correctly */

    if (ISNAN(x)) return x;

#endif

    if(!R_FINITE(x)) ML_WARN_return_NAN;

    x = fmod(fabs(x), 2.);// cos() symmetric; cos(pi(x + 2k)) == cos(pi x) for all integer k

    if(fmod(x, 1.) == 0.5) return 0.;

    if( x == 1.) return -1.;

    if( x == 0.) return  1.;

    // otherwise

    return cos(M_PI * x);

}

#endif

#ifdef HAVE_SINPI

#elif defined HAVE___SINPI

double sinpi(double x) {

    return __sinpi(x);

}

#else

// sin(pi * x)  -- exact when x = k/2  for all integer k

double sinpi(double x) {

#ifdef IEEE_754

    if (ISNAN(x)) return x;

#endif

    if(!R_FINITE(x)) ML_WARN_return_NAN;

    x = fmod(x, 2.); // sin(pi(x + 2k)) == sin(pi x)  for all integer k

    // map (-2,2) --> (-1,1] :

    if(x <= -1) x += 2.; else if (x > 1.) x -= 2.;

    if(x == 0. || x == 1.) return 0.;

    if(x ==  0.5) return  1.;

    if(x == -0.5) return -1.;

    // otherwise

    return sin(M_PI * x);

}

#endif

// tan(pi * x)  -- exact when x = k/4  for all integer k and half-values give NaN

// ----------- e.g. used in ../main/arithmetic.c : 

double Rtanpi(double x)

{

#ifdef IEEE_754

    if (ISNAN(x)) return x;

#endif

    if(!R_FINITE(x)) ML_WARN_return_NAN;

    x = fmod(x, 1.); // tan(pi(x + k)) == tan(pi x)  for all integer k

    // map (-1,1] --> (-1/2, 1/2] :

    if(x <= -0.5) x++; else if(x > 0.5) x--;

    return (x == 0.) ? 0. :

  ((x ==  0.5 ) ? ML_NAN :

  ((x ==  0.25) ?  1. :

  ((x == -0.25) ? -1. :

      tan(M_PI * x)

      )));

}

#if defined(HAVE_TANPI) || defined(HAVE___TANPI)

#else

double tanpi(double x) {

    return Rtanpi(x);

}

#endif

#if !defined(HAVE_TANPI) && defined(HAVE___TANPI)

double tanpi(double x) {

    return __tanpi(x);

}

/* #else tanpi() defined from C standard math lib */

#endif