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/*
 *  Mathlib : A C Library of Special Functions
 *  Copyright (C) 1998 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.
 *
 *  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., 675 Mass Ave, Cambridge, MA 02139, USA.
 *

 * Mathlib.h  should contain ALL headers from R's C code in `src/nmath'
   ---------  such that ``the Math library'' can be used by simply

   ``#include "Mathlib.h" ''

   and nothing else.
*/
#ifndef MATHLIB_H
#define MATHLIB_H

/*-- Mathlib as part of R --  undefine this for standalone : */
#define MATHLIB_IN_R

#include "Arith.h"
#include "Random.h"

#ifdef FORTRAN_H
#error __MUST__include "Mathlib.h"  _before_  "Fortran.h"
#endif

#include <errno.h>
#include <limits.h>
#include <float.h>
#include <math.h>
#include <stdlib.h>

/* TRUE and FALSE conflict with the Mac --- Fortran.h still defines them... */
#define LTRUE   (1)
#define LFALSE  (0)

/* 30 Decimal-place constants computed with bc -l (scale=32; proper round) */

#ifndef M_SQRT_2
#define M_SQRT_2    1.4142135623730950488016887242097
#define M_1_SQRT_2  0.707106781186547524400844362105    /* 1/sqrt(2) */
#define M_SQRT_32   5.656854249492380195206754896838    /* sqrt(32) */
#endif

#ifndef M_LN_2
#define M_LN_2      0.693147180559945309417232121458176568
#define M_LOG10_2   0.301029995663981195213738894724493027
#endif

#ifndef M_PI
#define M_PI        3.141592653589793238462643383279502884197169399375
#endif
#ifndef M_PI_half
#define M_PI_half   1.570796326794896619231321691640
#endif

#ifndef M_SQRT_PI
/* sqrt(pi),  1/sqrt(2pi),  sqrt(2/pi) : */
# define M_SQRT_PI  1.772453850905516027298167483341
# define M_1_SQRT_2PI   0.398942280401432677939946059934
# define M_SQRT_2dPI    0.79788456080286535587989211986876
#endif


#ifndef M_LN_SQRT_PI
/* log(sqrt(pi)) = log(pi)/2 : */
# define M_LN_SQRT_PI   0.5723649429247000870717136756765293558
/* log(sqrt(2*pi)) = log(2*pi)/2 : */
# define M_LN_SQRT_2PI  0.91893853320467274178032973640562
/* log(sqrt(pi/2)) = log(pi/2)/2 : */
# define M_LN_SQRT_PId2 0.225791352644727432363097614947441
#endif


#ifdef MATHLIB_IN_R/* Mathlib in R */

#include "Error.h"
# define MATHLIB_ERROR(fmt,x)       error(fmt,x);
# define MATHLIB_WARNING(fmt,x)     warning(fmt,x)
# define MATHLIB_WARNING2(fmt,x,x2) warning(fmt,x,x2)
# define MATHLIB_WARNING3(fmt,x,x2,x3)  warning(fmt,x,x2,x3)
# define MATHLIB_WARNING4(fmt,x,x2,x3,x4) warning(fmt,x,x2,x3,x4)

#else/* Mathlib standalone */

#include <stdio.h>
# define MATHLIB_ERROR(fmt,x)   { printf(fmt,x); exit(1) }
# define MATHLIB_WARNING(fmt,x)     printf(fmt,x)
# define MATHLIB_WARNING2(fmt,x,x2) printf(fmt,x,x2)
# define MATHLIB_WARNING3(fmt,x,x2,x3)  printf(fmt,x,x2,x3)
# define MATHLIB_WARNING4(fmt,x,x2,x3,x4) printf(fmt,x,x2,x3,x4)
#endif

#define ME_NONE     0
/*  no error */
#define ME_DOMAIN   1
/*  argument out of domain */
#define ME_RANGE    2
/*  value out of range */
#define ME_NOCONV   4
/*  process did not converge */
#define ME_PRECISION    8
/*  does not have "full" precision */
#define ME_UNDERFLOW    16
/*  and underflow occured (important for IEEE)*/


#ifdef IEEE_754

# ifdef HAVE_IEEE754_H
#  include <ieee754.h> /* newer Linuxen */
# else
#  ifdef HAVE_IEEEFP_H
#   include <ieeefp.h> /* others [Solaris 2.5.x], .. */
#  endif
# endif

extern double m_zero;
extern double m_one;
extern double m_tiny;
#define ML_ERROR(x) /* nothing */
#define ML_POSINF   (m_one / m_zero)
#define ML_NEGINF   ((-m_one) / m_zero)
#define ML_NAN      (m_zero / m_zero)
#define ML_UNDERFLOW    (m_tiny * m_tiny)
#define ML_VALID(x) (!isnan(x))

#else/*--- NO IEEE: No +/-Inf, NAN,... ---*/
#define ML_ERROR(x) ml_error(x)
#define ML_POSINF   DBL_MAX
#define ML_NEGINF   (-DBL_MAX)
#define ML_NAN      (-DBL_MAX)
#define ML_UNDERFLOW    0
#define ML_VALID(x) (errno == 0)
#endif

    /* Splus Compatibility */

#define snorm   norm_rand
#define sunif   unif_rand
#define sexp    exp_rand

    /* Undo SGI Madness */

#ifdef ftrunc
#undef ftrunc
#endif
#ifdef qexp
#undef qexp
#endif

    /* Name Hiding to Avoid Clashes with Fortran */

#ifdef HIDE_NAMES
# define d1mach c_d1mach
# define i1mach c_i1mach
#endif

#define rround  fround
#define prec    fprec
#define trunc   ftrunc

    /* Machine Characteristics */

double  d1mach(int);
double  d1mach_(int*);
int i1mach(int);
int i1mach_(int*);

    /* General Support Functions */

int imax2(int, int);
int imin2(int, int);
double  fmax2(double, double);
double  fmin2(double, double);
double  fmod(double, double);
double  fprec(double, double);
double  fround(double, double);
double  ftrunc(double);
double  sign(double);
double  fsign(double, double);
double  fsquare(double);
double  fcube(double);

    /* Random Number Generators */

double  snorm(void);
double  sunif(void);
double  sexp(void);

    /* Chebyshev Series */

int chebyshev_init(double*, int, double);
double  chebyshev_eval(double, double *, int);

    /* Gamma and Related Functions */

double  logrelerr(double);
void    gammalims(double*, double*);
double  lgammacor(double);
double  gammafn(double);
double  gamma_cody(double);
double  lgammafn(double);
void    dpsifn(double, int, int, int, double*, int*, int*);
double  digamma(double);
double  trigamma(double);
double  tetragamma(double);
double  pentagamma(double);

double  choose(double, double);
double  lchoose(double, double);
double  fastchoose(double, double);
double  lfastchoose(double, double);

    /* Bessel Functions of All Kinds */

double  bessel_i(double, double, double);
double  bessel_j(double, double);
double  bessel_k(double, double, double);
double  bessel_y(double, double);
void    I_bessel(double*, double*, long*, long*, double*, long*);
void    J_bessel(double*, double*, long*,    double*, long*);
void    K_bessel(double*, double*, long*, long*, double*, long*);
void    Y_bessel(double*, double*, long*,    double*, long*);

    /* Beta and Related Functions */

double  beta(double, double);
double  lbeta(double, double);

    /* Normal Distribution */

double  dnorm(double, double, double);
double  pnorm(double, double, double);
double  qnorm(double, double, double);
double  rnorm(double, double);

    /* Uniform Distribution */

double  dunif(double, double, double);
double  punif(double, double, double);
double  qunif(double, double, double);
double  runif(double, double);

    /* Gamma Distribution */

double  dgamma(double, double, double);
double  pgamma(double, double, double);
double  qgamma(double, double, double);
double  rgamma(double, double);

    /* Beta Distribution */

double  dbeta(double, double, double);
double  pbeta(double, double, double);
double  pbeta_raw(double, double, double);
double  qbeta(double, double, double);
double  rbeta(double, double);

    /* Lognormal Distribution */

double  dlnorm(double, double, double);
double  plnorm(double, double, double);
double  qlnorm(double, double, double);
double  rlnorm(double, double);

    /* Chi-squared Distribution */

double  dchisq(double, double);
double  pchisq(double, double);
double  qchisq(double, double);
double  rchisq(double);

    /* Non-central Chi-squared Distribution */

double  dnchisq(double, double, double);
double  pnchisq(double, double, double);
double  qnchisq(double, double, double);
double  rnchisq(double, double);

    /* F Distibution */

double  df(double, double, double);
double  pf(double, double, double);
double  qf(double, double, double);
double  rf(double, double);

    /* Student t Distibution */

double  dt(double, double);
double  pt(double, double);
double  qt(double, double);
double  rt(double);

    /* Binomial Distribution */

double  dbinom(double, double, double);
double  pbinom(double, double, double);
double  qbinom(double, double, double);
double  rbinom(double, double);

    /* Cauchy Distribution */

double  dcauchy(double, double, double);
double  pcauchy(double, double, double);
double  qcauchy(double, double, double);
double  rcauchy(double, double);

    /* Exponential Distribution */

double  dexp(double, double);
double  pexp(double, double);
double  qexp(double, double);
double  rexp(double);

    /* Geometric Distribution */

double  dgeom(double, double);
double  pgeom(double, double);
double  qgeom(double, double);
double  rgeom(double);

    /* Hypergeometric Distibution */

double  dhyper(double, double, double, double);
double  phyper(double, double, double, double);
double  qhyper(double, double, double, double);
double  rhyper(double, double, double);

    /* Negative Binomial Distribution */

double  dnbinom(double, double, double);
double  pnbinom(double, double, double);
double  qnbinom(double, double, double);
double  rnbinom(double, double);

    /* Poisson Distribution */

double  dpois(double, double);
double  ppois(double, double);
double  qpois(double, double);
double  rpois(double);

    /* Weibull Distribution */

double  dweibull(double, double, double);
double  pweibull(double, double, double);
double  qweibull(double, double, double);
double  rweibull(double, double);

    /* Logistic Distribution */

double  dlogis(double, double, double);
double  plogis(double, double, double);
double  qlogis(double, double, double);
double  rlogis(double, double);

    /* Non-central Beta Distribution */

double  dnbeta(double, double, double, double);
double  pnbeta(double, double, double, double);
double  qnbeta(double, double, double, double);
double  rnbeta(double, double, double);

    /* Non-central F Distribution */

double  dnf(double, double, double, double);
double  pnf(double, double, double, double);
double  qnf(double, double, double, double);
double  rnf(double, double, double);

    /* Non-central Student t Distribution */

double  dnt(double, double, double);
double  pnt(double, double, double);
double  qnt(double, double, double);
double  rnt(double, double);

    /* Studentized Range Distribution */

double  dtukey(double, double, double, double);
double  ptukey(double, double, double, double);
double  qtukey(double, double, double, double);
double  rtukey(double, double, double);

/* Wilcoxon Rank Sum Distribution */

#define WILCOX_MAX 50
double dwilcox(double, double, double);
double pwilcox(double, double, double);
double qwilcox(double, double, double);
double rwilcox(double, double);

/* Wilcoxon Signed Rank Distribution */

#define SIGNRANK_MAX 50
double dsignrank(double, double);
double psignrank(double, double);
double qsignrank(double, double);
double rsignrank(double);

#endif