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/*
 *  Mathlib : A C Library of Special Functions
 *  Copyright (C) 1998-2000  The R Development 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., 59 Temple Place, Suite 330, Boston, MA  02111-1307  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 <Rmath.h> ''

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

/*-- Mathlib as part of R --  define this for standalone : */
/* #undef MATHLIB_STANDALONE */

#ifdef MATHLIB_STANDALONE
# define R_NO_REMAP 1
#endif


#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>

    /* Undo SGI Madness */

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


/* ----- The following constants and entry points are part of the R API ---- */

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

/* SVID & X/Open Constants */
/* Names from Solaris math.h */

#ifndef M_E
#define M_E     2.718281828459045235360287471353    /* e */
#endif

#ifndef M_LOG2E
#define M_LOG2E     1.442695040888963407359924681002    /* log2(e) */
#endif

#ifndef M_LOG10E
#define M_LOG10E    0.434294481903251827651128918917    /* log10(e) */
#endif

#ifndef M_LN2
#define M_LN2       0.693147180559945309417232121458    /* ln(2) */
#endif

#ifndef M_LN10
#define M_LN10      2.302585092994045684017991454684    /* ln(10) */
#endif

#ifndef M_PI
#define M_PI        3.141592653589793238462643383280    /* pi */
#endif

#ifndef M_PI_2
#define M_PI_2      1.570796326794896619231321691640    /* pi/2 */
#endif

#ifndef M_PI_4
#define M_PI_4      0.785398163397448309615660845820    /* pi/4 */
#endif

#ifndef M_1_PI
#define M_1_PI      0.318309886183790671537767526745    /* 1/pi */
#endif

#ifndef M_2_PI
#define M_2_PI      0.636619772367581343075535053490    /* 2/pi */
#endif

#ifndef M_2_SQRTPI
#define M_2_SQRTPI  1.128379167095512573896158903122    /* 2/sqrt(pi) */
#endif

#ifndef M_SQRT2
#define M_SQRT2     1.414213562373095048801688724210    /* sqrt(2) */
#endif

#ifndef M_SQRT1_2
#define M_SQRT1_2   0.707106781186547524400844362105    /* 1/sqrt(2) */
#endif

/* R-Specific Constants */

#ifndef M_SQRT_3
#define M_SQRT_3    1.732050807568877293527446341506    /* sqrt(3) */
#endif

#ifndef M_SQRT_32
#define M_SQRT_32   5.656854249492380195206754896838    /* sqrt(32) */
#endif

#ifndef M_LOG10_2
#define M_LOG10_2   0.301029995663981195213738894724    /* log10(2) */
#endif

#ifndef M_SQRT_PI
#define M_SQRT_PI   1.772453850905516027298167483341    /* sqrt(pi) */
#endif

#ifndef M_1_SQRT_2PI
#define M_1_SQRT_2PI    0.398942280401432677939946059934    /* 1/sqrt(2pi) */
#endif

#ifndef M_SQRT_2dPI
#define M_SQRT_2dPI 0.797884560802865355879892119869    /* sqrt(2/pi) */
#endif


#ifndef M_LN_SQRT_PI
#define M_LN_SQRT_PI    0.572364942924700087071713675677    /* log(sqrt(pi)) */
#endif

#ifndef M_LN_SQRT_2PI
#define M_LN_SQRT_2PI   0.918938533204672741780329736406    /* log(sqrt(2*pi)) */
#endif

#ifndef M_LN_SQRT_PId2
#define M_LN_SQRT_PId2  0.225791352644727432363097614947    /* log(sqrt(pi/2)) */
#endif

#ifdef MATHLIB_STANDALONE
 typedef enum { FALSE = 0, TRUE } Rboolean;
#else
# include "R_ext/Boolean.h"

/* for API back-compatibility -- DEPRECATED since R 1.2 -- */
#define LTRUE  TRUE
#define LFALSE FALSE
#endif



#ifndef R_NO_REMAP
#define bessel_i    Rf_bessel_i
#define bessel_j    Rf_bessel_j
#define bessel_k    Rf_bessel_k
#define bessel_y    Rf_bessel_y
#define beta        Rf_beta
#define choose      Rf_choose
#define dbeta       Rf_dbeta
#define dbinom      Rf_dbinom
#define dcauchy     Rf_dcauchy
#define dchisq      Rf_dchisq
#define dexp        Rf_dexp
#define df      Rf_df
#define dgamma      Rf_dgamma
#define dgeom       Rf_dgeom
#define dhyper      Rf_dhyper
#define digamma     Rf_digamma
#define dlnorm      Rf_dlnorm
#define dlogis      Rf_dlogis
#define dnbeta      Rf_dnbeta
#define dnbinom     Rf_dnbinom
#define dnchisq     Rf_dnchisq
#define dnf     Rf_dnf
#define dnorm4      Rf_dnorm4
#define dnt     Rf_dnt
#define dpois       Rf_dpois
#define dsignrank   Rf_dsignrank
#define dt      Rf_dt
#define dtukey      Rf_dtukey
#define dunif       Rf_dunif
#define dweibull    Rf_dweibull
#define dwilcox     Rf_dwilcox
#define fmax2       Rf_fmax2
#define fmin2       Rf_fmin2
#define fmod        Rf_fmod
#define fprec       Rf_fprec
#define fround      Rf_fround
#define ftrunc      Rf_ftrunc
#define fsign       Rf_fsign
#define gammafn     Rf_gammafn
#define imax2       Rf_imax2
#define imin2       Rf_imin2
#define lbeta       Rf_lbeta
#define lchoose     Rf_lchoose
#define lgammafn    Rf_lgammafn
#define log1p       Rf_log1p
#define pbeta       Rf_pbeta
#define pbeta_raw   Rf_pbeta_raw
#define pbinom      Rf_pbinom
#define pcauchy     Rf_pcauchy
#define pchisq      Rf_pchisq
#define pentagamma  Rf_pentagamma
#define pexp        Rf_pexp
#define pf      Rf_pf
#define pgamma      Rf_pgamma
#define pgeom       Rf_pgeom
#define phyper      Rf_phyper
#define plnorm      Rf_plnorm
#define plogis      Rf_plogis
#define pnbeta      Rf_pnbeta
#define pnbinom     Rf_pnbinom
#define pnchisq     Rf_pnchisq
#define pnf     Rf_pnf
#define pnorm5      Rf_pnorm5
#define pnorm_both  Rf_pnorm_both
#define pnt     Rf_pnt
#define ppois       Rf_ppois
#define psignrank   Rf_psignrank
#define pt      Rf_pt
#define ptukey      Rf_ptukey
#define punif       Rf_punif
#define pythag      Rf_pythag
#define pweibull    Rf_pweibull
#define pwilcox     Rf_pwilcox
#define qbeta       Rf_qbeta
#define qbinom      Rf_qbinom
#define qcauchy     Rf_qcauchy
#define qchisq      Rf_qchisq
#define qexp        Rf_qexp
#define qf      Rf_qf
#define qgamma      Rf_qgamma
#define qgeom       Rf_qgeom
#define qhyper      Rf_qhyper
#define qlnorm      Rf_qlnorm
#define qlogis      Rf_qlogis
#define qnbeta      Rf_qnbeta
#define qnbinom     Rf_qnbinom
#define qnchisq     Rf_qnchisq
#define qnf     Rf_qnf
#define qnorm5      Rf_qnorm5
#define qnt     Rf_qnt
#define qpois       Rf_qpois
#define qsignrank   Rf_qsignrank
#define qt      Rf_qt
#define qtukey      Rf_qtukey
#define qunif       Rf_qunif
#define qweibull    Rf_qweibull
#define qwilcox     Rf_qwilcox
#define rbeta       Rf_rbeta
#define rbinom      Rf_rbinom
#define rcauchy     Rf_rcauchy
#define rchisq      Rf_rchisq
#define rexp        Rf_rexp
#define rf      Rf_rf
#define rgamma      Rf_rgamma
#define rgeom       Rf_rgeom
#define rhyper      Rf_rhyper
#define rlnorm      Rf_rlnorm
#define rlogis      Rf_rlogis
#define rnbeta      Rf_rnbeta
#define rnbinom     Rf_rnbinom
#define rnchisq     Rf_rnchisq
#define rnf     Rf_rnf
#define rnorm       Rf_rnorm
#define rnt     Rf_rnt
#define rpois       Rf_rpois
#define rsignrank   Rf_rsignrank
#define rt      Rf_rt
#define rtukey      Rf_rtukey
#define runif       Rf_runif
#define rweibull    Rf_rweibull
#define rwilcox     Rf_rwilcox
#define sign        Rf_sign
#define tetragamma  Rf_tetragamma
#define trigamma    Rf_trigamma
#endif

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

#ifdef  __cplusplus
extern "C" {
#endif

    /* R's versions with !R_FINITE checks */

double R_log(double x);
double R_pow(double x, double y);
double R_pow_di(double, int);

    /* Random Number Generators */

double  norm_rand(void);
double  unif_rand(void);
double  exp_rand(void);
#ifdef MATHLIB_STANDALONE
void    set_seed(unsigned int, unsigned int);
#endif

    /* Normal Distribution */

#define pnorm pnorm5
#define qnorm qnorm5
#define dnorm dnorm4

double  dnorm(double, double, double, int);
double  pnorm(double, double, double, int, int);
double  qnorm(double, double, double, int, int);
double  rnorm(double, double);
void    pnorm_both(double, double *, double *, int, int);/* both tails */

    /* Uniform Distribution */

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

    /* Gamma Distribution */

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

    /* Beta Distribution */

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

    /* Lognormal Distribution */

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

    /* Chi-squared Distribution */

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

    /* Non-central Chi-squared Distribution */

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

    /* F Distibution */

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

    /* Student t Distibution */

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

    /* Binomial Distribution */

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

    /* Cauchy Distribution */

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

    /* Exponential Distribution */

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

    /* Geometric Distribution */

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

    /* Hypergeometric Distibution */

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

    /* Negative Binomial Distribution */

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

    /* Poisson Distribution */

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

    /* Weibull Distribution */

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

    /* Logistic Distribution */

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

    /* Non-central Beta Distribution */

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

    /* Non-central F Distribution */

double  pnf(double, double, double, double, int, int);
double  qnf(double, double, double, double, int, int);

    /* Non-central Student t Distribution */

double  pnt(double, double, double, int, int);
double  qnt(double, double, double, int, int);

    /* Studentized Range Distribution */

double  ptukey(double, double, double, double, int, int);
double  qtukey(double, double, double, double, int, int);

    /* Wilcoxon Rank Sum Distribution */

double dwilcox(double, double, double, int);
double pwilcox(double, double, double, int, int);
double qwilcox(double, double, double, int, int);
double rwilcox(double, double);

    /* Wilcoxon Signed Rank Distribution */

double dsignrank(double, double, int);
double psignrank(double, double, int, int);
double qsignrank(double, double, int, int);
double rsignrank(double);

    /* Gamma and Related Functions */
double  gammafn(double);
double  lgammafn(double);
double  digamma(double);
double  trigamma(double);
double  tetragamma(double);
double  pentagamma(double);

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

double  choose(double, double);
double  lchoose(double, double);

    /* Bessel Functions */

double  bessel_i(double, double, double);
double  bessel_j(double, double);
double  bessel_k(double, double, double);
double  bessel_y(double, double);


    /* General Support Functions */

double  pythag(double, double);
double  log1p(double); /* = log(1+x) {care for small x} */
int imax2(int, int);
int imin2(int, int);
double  fmax2(double, double);
double  fmin2(double, double);
double  sign(double);
double  fmod(double, double);
double  fprec(double, double);
double  fround(double, double);
double  fsign(double, double);
double  ftrunc(double);


/* ----------------- Private part of the header file ------------------- */

    /* old-R Compatibility */

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

#ifdef MATHLIB_PRIVATE
#define d1mach      Rf_d1mach
#define gamma_cody  Rf_gamma_cody

double  d1mach(int);
double  gamma_cody(double);

#endif /* MATHLIB_PRIVATE */

#ifdef MATHLIB_STANDALONE
#ifndef MATHLIB_PRIVATE_H

#define ISNAN(x)       R_IsNaNorNA(x)
#define R_FINITE(x)    R_finite(x)
int R_IsNaNorNA(double);
int R_finite(double);

#ifdef WIN32
# define NA_REAL (*_imp__NA_REAL)
# define R_NegInf (*_imp__R_NegInf)
# define R_PosInf (*_imp__R_PosInf)
# define N01_kind (*_imp__N01_kind)
# endif

#endif /* not MATHLIB_PRIVATE_H */
#endif /* MATHLIB_STANDALONE */

#ifdef MATHLIB_STANDALONE
# define REprintf fprintf(stderr,
#else
# ifndef PRTUTIL_H_
void REprintf(char*, ...);
# endif
#endif

#ifdef  __cplusplus
}
#endif

#endif /* RMATH_H */