Rmath.h

/* -*- C -*-
 *  Mathlib : A C Library of Special Functions
 *  Copyright (C) 1998-2011  The R Core Team
 *  Copyright (C) 2004       The R Foundation
 *
 *  This program is free software; you can redistribute it and/or modify
 *  it under the terms of the GNU Lesser General Public License as published by
 *  the Free Software Foundation; either version 2.1 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 Lesser General Public License for more details.
 *
 *  You should have received a copy of the GNU Lesser General Public License
 *  along with this program; if not, a copy is available at
 *  http://www.r-project.org/Licenses/
 *

 * Rmath.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

/* Note that on some systems we need to include math.h before the
   defines below, to avoid redefining ftrunc */
#ifndef NO_C_HEADERS
# include <math.h>
#endif

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

#define R_VERSION_STRING "2.15.1"

#ifndef HAVE_EXPM1
# define HAVE_EXPM1 1
#endif

#ifndef HAVE_HYPOT
# define HAVE_HYPOT 1
#endif

#ifndef HAVE_LOG1P
# define HAVE_LOG1P 1
#endif

#ifndef HAVE_WORKING_LOG1P
# define HAVE_WORKING_LOG1P 1
#endif

#if defined(HAVE_LOG1P) && !defined(HAVE_WORKING_LOG1P)
/* remap to avoid problems with getting the right entry point */
double  Rlog1p(double);
#define log1p Rlog1p
#endif


        /* 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_2PI
#define M_2PI           6.283185307179586476925286766559        /* 2*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))
                                                                   == log(pi)/2 */
#endif

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

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


#ifdef MATHLIB_STANDALONE
# ifndef R_EXT_BOOLEAN_H_
/* "copy-paste" R_ext/Boolean.h if not already included: */
 #define R_EXT_BOOLEAN_H_
 #undef FALSE
 #undef TRUE
 typedef enum { FALSE = 0, TRUE } Rboolean;
# endif
#else
# include <R_ext/Boolean.h>
#endif


#ifndef MATHLIB_STANDALONE
#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 bessel_i_ex     Rf_bessel_i_ex
#define bessel_j_ex     Rf_bessel_j_ex
#define bessel_k_ex     Rf_bessel_k_ex
#define bessel_y_ex     Rf_bessel_y_ex
#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 dpsifn          Rf_dpsifn
#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 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 lgammafn_sign   Rf_lgammafn_sign
#define lgamma1p        Rf_lgamma1p
#define log1pmx         Rf_log1pmx
#define logspace_add    Rf_logspace_add
#define logspace_sub    Rf_logspace_sub
#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 psigamma        Rf_psigamma
#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 qchisq_appr     Rf_qchisq_appr
#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_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);
void    get_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);

double  log1pmx(double);
double  log1pexp(double); // <-- ../nmath/plogis.c
double  lgamma1p(double);
double  logspace_add(double, double);
double  logspace_sub(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);

        /* 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);

        /* Multnomial Distribution */

void    rmultinom(int, double*, int, int*);

        /* 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);

double  dnbinom_mu(double, double, double, int);
double  pnbinom_mu(double, double, double, int, int);
double  qnbinom_mu(double, double, double, int, int);
double  rnbinom_mu(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  dnf(double, double, double, double, int);
double  pnf(double, double, double, double, int, int);
double  qnf(double, double, double, double, int, int);

        /* Non-central Student t Distribution */

double  dnt(double, double, double, int);
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  lgammafn_sign(double, int*);
void    dpsifn(double, int, int, int, double*, int*, int*);
double  psigamma(double, 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);
double  bessel_i_ex(double, double, double, double *);
double  bessel_j_ex(double, double, double *);
double  bessel_k_ex(double, double, double, double *);
double  bessel_y_ex(double, double, double *);


        /* General Support Functions */

#ifndef HAVE_HYPOT
double  hypot(double, double);
#endif
double  pythag(double, double);
#ifndef HAVE_EXPM1
double  expm1(double); /* = exp(x)-1 {care for small x} */
#endif
#ifndef HAVE_LOG1P
double  log1p(double); /* = log(1+x) {care for small x} */
#endif
int     imax2(int, int);
int     imin2(int, int);
double  fmax2(double, double);
double  fmin2(double, double);
double  sign(double);
double  fprec(double, double);
double  fround(double, double);
double  fsign(double, double);
double  ftrunc(double);

double  log1pmx(double); /* Accurate log(1+x) - x, {care for small x} */
double  lgamma1p(double);/* accurate log(gamma(x+1)), small x (0 < x < 0.5) */

/* Compute the log of a sum or difference from logs of terms, i.e.,
 *
 *     log (exp (logx) + exp (logy))
 * or  log (exp (logx) - exp (logy))
 *
 * without causing overflows or throwing away too much accuracy:
 */
double  logspace_add(double logx, double logy);
double  logspace_sub(double logx, double logy);




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

        /* old-R Compatibility */

#ifdef OLD_RMATH_COMPAT
# define snorm  norm_rand
# define sunif  unif_rand
# define sexp   exp_rand
#endif

#if defined(MATHLIB_STANDALONE) && !defined(MATHLIB_PRIVATE_H)
/* second is defined by nmath.h */

/* If isnan is a macro, as C99 specifies, the C++
   math header will undefine it. This happens on OS X */
# ifdef __cplusplus
  int R_isnancpp(double); /* in mlutils.c */
#  define ISNAN(x)     R_isnancpp(x)
# else
#  define ISNAN(x)     (isnan(x)!=0)
# endif

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

# ifdef WIN32  /* not Win32 as no config information */
#  ifdef RMATH_DLL
#   define R_EXTERN extern __declspec(dllimport)
#  else
#   define R_EXTERN extern
#  endif
R_EXTERN double NA_REAL;
R_EXTERN double R_PosInf;
R_EXTERN double R_NegInf;
R_EXTERN int N01_kind;
#  undef R_EXTERN
#else
extern int N01_kind;
# endif

#endif /* MATHLIB_STANDALONE */

#ifdef  __cplusplus
}
#endif

#endif /* RMATH_H */