The R Project SVN – R – /branches/R-0-99-patches/src/include/R_ext/Mathlib.h

/*
 *  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 "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 "Rconfig.h"
#include "R_ext/Arith.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) */

/* 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

/* Other, R-Specific Constants */

#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_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
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    (DBL_MIN * DBL_MIN)
#define ML_VALID(x) (!ISNAN(x))

#else/*--- NO IEEE: No +/-Inf, NAN,... ---*/
void ml_error(int n);
#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

#define ML_ERR_return_NAN { ML_ERROR(ME_DOMAIN); return ML_NAN; }

    /* old-R 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
#ifdef qgamma
# undef qgamma
#endif

    /* Name Hiding to Avoid Clashes with Fortran */

#ifdef HIDE_NAMES
# define d1mach c_d1mach
# define i1mach c_i1mach
#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 chebyshev_eval  Rf_chebyshev_eval
#define chebyshev_init  Rf_chebyshev_init
#define choose      Rf_choose
#define d1mach      Rf_d1mach
#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 fastchoose  Rf_fastchoose
#define fcube       Rf_fcube
#define fmax2       Rf_fmax2
#define fmin2       Rf_fmin2
#define fmod        Rf_fmod
#define fprec       Rf_fprec
#define fround      Rf_fround
#define fsign       Rf_fsign
#define fsquare     Rf_fsquare
#define ftrunc      Rf_ftrunc
#define gammafn     Rf_gammafn
#define gammalims   Rf_gammalims
#define gamma_cody  Rf_gamma_cody
#define i1mach      Rf_i1mach
#define imax2       Rf_imax2
#define imin2       Rf_imin2
#define I_bessel    Rf_I_bessel
#define J_bessel    Rf_J_bessel
#define K_bessel    Rf_K_bessel
#define lbeta       Rf_lbeta
#define lchoose     Rf_lchoose
#define lfastchoose Rf_lfastchoose
#define lgammacor   Rf_lgammacor
#define lgammafn    Rf_lgammafn
#define logrelerr   Rf_logrelerr
#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 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
#define Y_bessel    Rf_Y_bessel
#endif

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


    /* Utilities for `dpq' handling (density/probability/quantile) */

/* give_log in "d";  log_p in "p" & "q" : */
#define give_log log_p
                            /* "DEFAULT" */
                            /* --------- */
#define R_D__0  (log_p ? ML_NEGINF : 0.)        /* 0 */
#define R_D__1  (log_p ? 0. : 1.)           /* 1 */
#define R_DT_0  (lower_tail ? R_D__0 : R_D__1)      /* 0 */
#define R_DT_1  (lower_tail ? R_D__1 : R_D__0)      /* 1 */

#define R_D_Lval(p) (lower_tail ? (p) : (1 - (p)))  /*  p  */
#define R_D_Cval(p) (lower_tail ? (1 - (p)) : (p))  /*  1 - p */

#define R_D_val(x)  (log_p  ? log(x) : (x))     /*  x  in pF(x,..) */
#define R_D_qIv(p)  (log_p  ? exp(p) : (p))     /*  p  in qF(p,..) */
#define R_D_exp(x)  (log_p  ?  (x)   : exp(x))  /* exp(x) */
#define R_D_log(p)  (log_p  ?  (p)   : log(p))  /* log(p) */

#define R_DT_val(x) R_D_val(R_D_Lval(x))        /*  x  in pF */
#define R_DT_Cval(x)    R_D_val(R_D_Cval(x))        /*  1 - x */
#define R_DT_qIv(p) R_D_Lval(R_D_qIv(p))        /*  p  in qF ! */
#define R_DT_CIv(p) R_D_Cval(R_D_qIv(p))        /*  1 - p in qF */

#define R_DT_exp(x) R_D_exp(R_D_Lval(x))        /* exp(x) */
#define R_DT_Cexp(x)    R_D_exp(R_D_Cval(x))        /* exp(1 - x) */

#define R_DT_log(p) (lower_tail ? R_D_log(p) :      \
             logrelerr(- (log_p ? exp(p) : p)))/* log(p)    in qF */

#define R_DT_Clog(p)    (lower_tail ?               \
             logrelerr(- (log_p ? exp(p) : p)) :    \
             R_D_log(p))            /* log(1 - p)   in qF */

#define R_Q_P01_check(p)            \
    if ((log_p  && p > 0) ||            \
    (!log_p && (p < 0 || p > 1)) )      \
    ML_ERR_return_NAN


    /* 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);

    /* 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  norm_rand(void);
double  unif_rand(void);
double  exp_rand(void);

    /* Chebyshev Series */

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

    /* Gamma and Related Functions */

double  logrelerr(double); /* = log(1+x) {care for small x} */
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 */

/* These 3 will be re-defined in  ./S_compat.h  (when that is used) : */
#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  dnf(double, double, double, double, int);
double  pnf(double, double, double, double, int, int);
double  qnf(double, double, double, double, int, int);
double  rnf(double, double, double);

    /* 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);
double  rnt(double, double);

    /* Studentized Range Distribution */

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

/* Wilcoxon Rank Sum Distribution */

#define WILCOX_MAX 50
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 */

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

#endif
The R Project SVN R

(root)/branches/R-0-99-patches/src/include/R_ext/Mathlib.h @ 28362 – Rev 8029
