/* This is MODIFIED version of R's Mathlib */

/* -*- C -*-
 *  Mathlib : A C Library of Special Functions
 *  Copyright (C) 1998-2003  The R Development 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, write to the Free Software
 *  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301  USA
 *

 * 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

#ifdef  __cplusplus
extern "C" {
#endif

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

#define R_VERSION_STRING "2.3.0"

#ifndef HAVE_LOG1P
# define HAVE_LOG1P 1
#endif

#ifndef HAVE_EXPM1
# define HAVE_EXPM1 1
#endif

#ifndef HAVE_WORKING_LOG1P
# define HAVE_WORKING_LOG1P 1
#endif

#ifndef HAVE_WORKING_LOG
# define HAVE_WORKING_LOG 1
#endif

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

#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

#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_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)) */
#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
 #undef FALSE
 #undef TRUE
 typedef enum { FALSE = 0, TRUE } Rboolean;
#else
# include <R_ext/Boolean.h>
#endif


#ifndef MATHLIB_STANDALONE
#define bessel_i	jags_bessel_i
#define bessel_j	jags_bessel_j
#define bessel_k	jags_bessel_k
#define bessel_y	jags_bessel_y
#define beta		jags_beta
#define choose		jags_choose
#define dbeta		jags_dbeta
#define dbinom		jags_dbinom
#define dcauchy		jags_dcauchy
#define dchisq		jags_dchisq
#define dexp		jags_dexp
#define df		jags_df
#define dgamma		jags_dgamma
#define dgeom		jags_dgeom
#define dhyper		jags_dhyper
#define digamma		jags_digamma
#define dlnorm		jags_dlnorm
#define dlogis		jags_dlogis
#define dnbeta		jags_dnbeta
#define dnbinom		jags_dnbinom
#define dnchisq		jags_dnchisq
#define dnf		jags_dnf
#define dnorm4		jags_dnorm4
#define dnt		jags_dnt
#define dpois		jags_dpois
#define dpsifn		jags_dpsifn
#define dsignrank	jags_dsignrank
#define dt		jags_dt
#define dtukey		jags_dtukey
#define dunif		jags_dunif
#define dweibull	jags_dweibull
#define dwilcox		jags_dwilcox
#define fmax2		jags_fmax2
#define fmin2		jags_fmin2
#define fprec		jags_fprec
#define fround		jags_fround
#define ftrunc		jags_ftrunc
#define fsign		jags_fsign
#define gammafn		jags_gammafn
#define imax2		jags_imax2
#define imin2		jags_imin2
#define lbeta		jags_lbeta
#define lchoose		jags_lchoose
#define lgammafn	jags_lgammafn
#define lgamma1p	jags_lgamma1p
#define log1pmx		jags_log1pmx
#define logspace_add	jags_logspace_add
#define logspace_sub	jags_logspace_sub
#define pbeta		jags_pbeta
#define pbeta_raw	jags_pbeta_raw
#define pbinom		jags_pbinom
#define pcauchy		jags_pcauchy
#define pchisq		jags_pchisq
#define pentagamma	jags_pentagamma
#define pexp		jags_pexp
#define pf		jags_pf
#define pgamma		jags_pgamma
#define pgeom		jags_pgeom
#define phyper		jags_phyper
#define plnorm		jags_plnorm
#define plogis		jags_plogis
#define pnbeta		jags_pnbeta
#define pnbinom		jags_pnbinom
#define pnchisq		jags_pnchisq
#define pnf		jags_pnf
#define pnorm5		jags_pnorm5
#define pnorm_both	jags_pnorm_both
#define pnt		jags_pnt
#define ppois		jags_ppois
#define psignrank	jags_psignrank
#define psigamma	jags_psigamma
#define pt		jags_pt
#define ptukey		jags_ptukey
#define punif		jags_punif
#define pythag		jags_pythag
#define pweibull	jags_pweibull
#define pwilcox		jags_pwilcox
#define qbeta		jags_qbeta
#define qbinom		jags_qbinom
#define qcauchy		jags_qcauchy
#define qchisq		jags_qchisq
#define qchisq_appr	jags_qchisq_appr
#define qexp		jags_qexp
#define qf		jags_qf
#define qgamma		jags_qgamma
#define qgeom		jags_qgeom
#define qhyper		jags_qhyper
#define qlnorm		jags_qlnorm
#define qlogis		jags_qlogis
#define qnbeta		jags_qnbeta
#define qnbinom		jags_qnbinom
#define qnchisq		jags_qnchisq
#define qnf		jags_qnf
#define qnorm5		jags_qnorm5
#define qnt		jags_qnt
#define qpois		jags_qpois
#define qsignrank	jags_qsignrank
#define qt		jags_qt
#define qtukey		jags_qtukey
#define qunif		jags_qunif
#define qweibull	jags_qweibull
#define qwilcox		jags_qwilcox
#define rbeta		jags_rbeta
#define rbinom		jags_rbinom
#define rcauchy		jags_rcauchy
#define rchisq		jags_rchisq
#define rexp		jags_rexp
#define rf		jags_rf
#define rgamma		jags_rgamma
#define rgeom		jags_rgeom
#define rhyper		jags_rhyper
#define rlnorm		jags_rlnorm
#define rlogis		jags_rlogis
#define rnbeta		jags_rnbeta
#define rnbinom		jags_rnbinom
#define rnchisq		jags_rnchisq
#define rnf		jags_rnf
#define rnorm		jags_rnorm
#define rnt		jags_rnt
#define rpois		jags_rpois
#define rsignrank	jags_rsignrank
#define rt		jags_rt
#define rtukey		jags_rtukey
#define runif		jags_runif
#define rweibull	jags_rweibull
#define rwilcox		jags_rwilcox
#define sign		jags_sign
#define tetragamma	jags_tetragamma
#define trigamma	jags_trigamma
#endif

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


/* log(1 - exp(x))  in stable form: */
#define R_Log1_Exp(x)   ((x) > -M_LN2 ? log(-expm1(x)) : log1p(-exp(x)))

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

#if defined(MATHLIB_STANDALONE) && defined(HAVE_WORKING_LOG)
#define R_log log
#else
double R_log(double x);
#endif
double R_pow(double x, double y);
double R_pow_di(double, int);

	/* Random Number Generators */

typedef struct RNG RNG;
double	norm_rand(RNG*);
double	unif_rand(RNG*);
double	exp_rand(RNG*);

	/* 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, RNG*); 
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, RNG*);

	/* 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, RNG*);

double  log1pmx(double);
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, RNG*);

	/* 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, RNG*);

	/* Chi-squared Distribution */

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

	/* 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, RNG*);

	/* 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, RNG*); 

	/* Student t Distibution */

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

	/* 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, RNG*);

	/* Multnomial Distribution */

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

	/* 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, RNG*);

	/* Exponential Distribution */

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

	/* Geometric Distribution */

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

	/* 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, RNG*);

	/* 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, RNG*);

	/* Poisson Distribution */

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

	/* 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, RNG*);

	/* 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, RNG*);

	/* 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, RNG*);

	/* 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	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, RNG*); 

	/* Wilcoxon Signed Rank Distribution */

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

	/* Gamma and Related Functions */
double	gammafn(double);
double	lgammafn(double);
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);


	/* General Support Functions */

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 */

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

#ifdef MATHLIB_PRIVATE
#define d1mach		jags_d1mach
#define i1mach          jags_i1mach
#define gamma_cody	jags_gamma_cody

double	gamma_cody(double); /* used in arithmetic.c */

#endif /* MATHLIB_PRIVATE */

double  jags_d1mach(int); /* used in port.c in package stats */
int     jags_i1mach(int); /* used in port.c in package stats */

#ifdef MATHLIB_STANDALONE
#ifndef MATHLIB_PRIVATE_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


/* We don't have config information available to do anything else */
#define R_FINITE(x)    R_finite(x)
int R_finite(double);

#ifdef WIN32  /* not Win32 as no config information */
# 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 */

#ifndef R_EXT_PRINT_H_
void REprintf(char const*, ...);
#endif

#ifdef  __cplusplus
}
#endif

#endif /* RMATH_H */
