The R Project SVN – R – Diff – /trunk/src/include/Mathlib.h


/*
 *  Mathlib : A C Library of Special Functions
 *  Copyright (C) 1998 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., 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) */
 
/* 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	/* 1/pi */
#endif
 
#ifndef M_2_SQRTPI
#define M_2_SQRTPI	1.128379167095512573896158903122	/* 1/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 */
/* Note there are some repeats of values above */
/* Needs a cleanup */
 
#ifndef M_1_SQRT_2
#define M_1_SQRT_2	0.707106781186547524400844362105	/* 1/sqrt(2) */
#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_PI_half
#define M_PI_half	1.570796326794896619231321691640	/* pi/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
 
# 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	(DBL_MIN * DBL_MIN)
#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
#undef trunc
#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

Rev 3865	Rev 4562
1	`/*`	1	`/*`
2	`* Mathlib : A C Library of Special Functions`	2	`* Mathlib : A C Library of Special Functions`
3	`* Copyright (C) 1998 R Core Team`	3	`* Copyright (C) 1998 R Development Core Team`
4	`*`	4	`*`
5	`* This program is free software; you can redistribute it and/or modify`	5	`* This program is free software; you can redistribute it and/or modify`
6	`* it under the terms of the GNU General Public License as published by`	6	`* it under the terms of the GNU General Public License as published by`
7	`* the Free Software Foundation; either version 2 of the License, or`	7	`* the Free Software Foundation; either version 2 of the License, or`
8	`* (at your option) any later version.`	8	`* (at your option) any later version.`
9	`*`	9	`*`
10	`* This program is distributed in the hope that it will be useful,`	10	`* This program is distributed in the hope that it will be useful,`
11	`* but WITHOUT ANY WARRANTY; without even the implied warranty of`	11	`* but WITHOUT ANY WARRANTY; without even the implied warranty of`
12	`* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the`	12	`* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the`
13	`* GNU General Public License for more details.`	13	`* GNU General Public License for more details.`
14	`*`	14	`*`
15	`* You should have received a copy of the GNU General Public License`	15	`* You should have received a copy of the GNU General Public License`
16	`* along with this program; if not, write to the Free Software`	16	`* along with this program; if not, write to the Free Software`
17	`* Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.`	17	`* Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.`
18	`*`	18	`*`
19		19
20	* Mathlib.h should contain ALL headers from R's C code in `src/nmath'	20	* Mathlib.h should contain ALL headers from R's C code in `src/nmath'
21	--------- such that ``the Math library'' can be used by simply	21	--------- such that ``the Math library'' can be used by simply
22		22
23	``#include "Mathlib.h" ''	23	``#include "Mathlib.h" ''
24		24
25	`and nothing else.`	25	`and nothing else.`
26	`*/`	26	`*/`
27	`#ifndef MATHLIB_H`	27	`#ifndef MATHLIB_H`
28	`#define MATHLIB_H`	28	`#define MATHLIB_H`
29		29
30	`/-- Mathlib as part of R -- undefine this for standalone : /`	30	`/-- Mathlib as part of R -- undefine this for standalone : /`
31	`#define MATHLIB_IN_R`	31	`#define MATHLIB_IN_R`
32		32
33	`#include "Arith.h"`	33	`#include "Arith.h"`
34	`#include "Random.h"`	34	`#include "Random.h"`
35		35
36	`#ifdef FORTRAN_H`	36	`#ifdef FORTRAN_H`
37	`#error __MUST__include "Mathlib.h" _before_ "Fortran.h"`	37	`#error __MUST__include "Mathlib.h" _before_ "Fortran.h"`
38	`#endif`	38	`#endif`
39		39
40	`#include <errno.h>`	40	`#include <errno.h>`
41	`#include <limits.h>`	41	`#include <limits.h>`
42	`#include <float.h>`	42	`#include <float.h>`
43	`#include <math.h>`	43	`#include <math.h>`
44	`#include <stdlib.h>`	44	`#include <stdlib.h>`
45		45
46	`/* TRUE and FALSE conflict with the Mac --- Fortran.h still defines them... */`	46	`/* TRUE and FALSE conflict with the Mac --- Fortran.h still defines them... */`
47	`#define LTRUE (1)`	47	`#define LTRUE (1)`
48	`#define LFALSE (0)`	48	`#define LFALSE (0)`
49		49
50	`/* 30 Decimal-place constants */`	50	`/* 30 Decimal-place constants */`
51	`/* Computed with bc -l (scale=32; proper round) */`	51	`/* Computed with bc -l (scale=32; proper round) */`
52		52
53	`/* SVID & X/Open Constants */`	53	`/* SVID & X/Open Constants */`
54	`/* Names from Solaris math.h */`	54	`/* Names from Solaris math.h */`
55		55
56	`#ifndef M_E`	56	`#ifndef M_E`
57	`#define M_E 2.718281828459045235360287471353 /* e */`	57	`#define M_E 2.718281828459045235360287471353 /* e */`
58	`#endif`	58	`#endif`
59		59
60	`#ifndef M_LOG2E`	60	`#ifndef M_LOG2E`
61	`#define M_LOG2E 1.442695040888963407359924681002 /* log2(e) */`	61	`#define M_LOG2E 1.442695040888963407359924681002 /* log2(e) */`
62	`#endif`	62	`#endif`
63		63
64	`#ifndef M_LOG10E`	64	`#ifndef M_LOG10E`
65	`#define M_LOG10E 0.434294481903251827651128918917 /* log10(e) */`	65	`#define M_LOG10E 0.434294481903251827651128918917 /* log10(e) */`
66	`#endif`	66	`#endif`
67		67
68	`#ifndef M_LN2`	68	`#ifndef M_LN2`
69	`#define M_LN2 0.693147180559945309417232121458 /* ln(2) */`	69	`#define M_LN2 0.693147180559945309417232121458 /* ln(2) */`
70	`#endif`	70	`#endif`
71		71
72	`#ifndef M_LN10`	72	`#ifndef M_LN10`
73	`#define M_LN10 2.302585092994045684017991454684 /* ln(10) */`	73	`#define M_LN10 2.302585092994045684017991454684 /* ln(10) */`
74	`#endif`	74	`#endif`
75		75
76	`#ifndef M_PI`	76	`#ifndef M_PI`
77	`#define M_PI 3.141592653589793238462643383280 /* pi */`	77	`#define M_PI 3.141592653589793238462643383280 /* pi */`
78	`#endif`	78	`#endif`
79		79
80	`#ifndef M_PI_2`	80	`#ifndef M_PI_2`
81	`#define M_PI_2 1.570796326794896619231321691640 /* pi/2 */`	81	`#define M_PI_2 1.570796326794896619231321691640 /* pi/2 */`
82	`#endif`	82	`#endif`
83		83
84	`#ifndef M_PI_4`	84	`#ifndef M_PI_4`
85	`#define M_PI_4 0.785398163397448309615660845820 /* pi/4 */`	85	`#define M_PI_4 0.785398163397448309615660845820 /* pi/4 */`
86	`#endif`	86	`#endif`
87		87
88	`#ifndef M_1_PI`	88	`#ifndef M_1_PI`
89	`#define M_1_PI 0.318309886183790671537767526745 /* 1/pi */`	89	`#define M_1_PI 0.318309886183790671537767526745 /* 1/pi */`
90	`#endif`	90	`#endif`
91		91
92	`#ifndef M_2_PI`	92	`#ifndef M_2_PI`
93	`#define M_2_PI 0.636619772367581343075535053490 /* 1/pi */`	93	`#define M_2_PI 0.636619772367581343075535053490 /* 1/pi */`
94	`#endif`	94	`#endif`
95		95
96	`#ifndef M_2_SQRTPI`	96	`#ifndef M_2_SQRTPI`
97	`#define M_2_SQRTPI 1.128379167095512573896158903122 /* 1/sqrt(pi) */`	97	`#define M_2_SQRTPI 1.128379167095512573896158903122 /* 1/sqrt(pi) */`
98	`#endif`	98	`#endif`
99		99
100	`#ifndef M_SQRT2`	100	`#ifndef M_SQRT2`
101	`#define M_SQRT2 1.414213562373095048801688724210 /* sqrt(2) */`	101	`#define M_SQRT2 1.414213562373095048801688724210 /* sqrt(2) */`
102	`#endif`	102	`#endif`
103		103
104	`#ifndef M_SQRT1_2`	104	`#ifndef M_SQRT1_2`
105	`#define M_SQRT1_2 0.707106781186547524400844362105 /* 1/sqrt(2) */`	105	`#define M_SQRT1_2 0.707106781186547524400844362105 /* 1/sqrt(2) */`
106	`#endif`	106	`#endif`
107		107
108	`/* Other, R-Specific Constants */`	108	`/* Other, R-Specific Constants */`
109	`/* Note there are some repeats of values above */`	109	`/* Note there are some repeats of values above */`
110	`/* Needs a cleanup */`	110	`/* Needs a cleanup */`
111		111
112	`#ifndef M_1_SQRT_2`	112	`#ifndef M_1_SQRT_2`
113	`#define M_1_SQRT_2 0.707106781186547524400844362105 /* 1/sqrt(2) */`	113	`#define M_1_SQRT_2 0.707106781186547524400844362105 /* 1/sqrt(2) */`
114	`#endif`	114	`#endif`
115		115
116	`#ifndef M_SQRT_32`	116	`#ifndef M_SQRT_32`
117	`#define M_SQRT_32 5.656854249492380195206754896838 /* sqrt(32) */`	117	`#define M_SQRT_32 5.656854249492380195206754896838 /* sqrt(32) */`
118	`#endif`	118	`#endif`
119		119
120	`#ifndef M_LOG10_2`	120	`#ifndef M_LOG10_2`
121	`#define M_LOG10_2 0.301029995663981195213738894724 /* log10(2) */`	121	`#define M_LOG10_2 0.301029995663981195213738894724 /* log10(2) */`
122	`#endif`	122	`#endif`
123		123
124	`#ifndef M_PI_half`	124	`#ifndef M_PI_half`
125	`#define M_PI_half 1.570796326794896619231321691640 /* pi/2 */`	125	`#define M_PI_half 1.570796326794896619231321691640 /* pi/2 */`
126	`#endif`	126	`#endif`
127		127
128	`#ifndef M_SQRT_PI`	128	`#ifndef M_SQRT_PI`
129	`#define M_SQRT_PI 1.772453850905516027298167483341 /* sqrt(pi) */`	129	`#define M_SQRT_PI 1.772453850905516027298167483341 /* sqrt(pi) */`
130	`#endif`	130	`#endif`
131		131
132	`#ifndef M_1_SQRT_2PI`	132	`#ifndef M_1_SQRT_2PI`
133	`#define M_1_SQRT_2PI 0.398942280401432677939946059934 /* 1/sqrt(2pi) */`	133	`#define M_1_SQRT_2PI 0.398942280401432677939946059934 /* 1/sqrt(2pi) */`
134	`#endif`	134	`#endif`
135		135
136	`#ifndef M_SQRT_2dPI`	136	`#ifndef M_SQRT_2dPI`
137	`#define M_SQRT_2dPI 0.797884560802865355879892119869 /* sqrt(2/pi) */`	137	`#define M_SQRT_2dPI 0.797884560802865355879892119869 /* sqrt(2/pi) */`
138	`#endif`	138	`#endif`
139		139
140		140
141	`#ifndef M_LN_SQRT_PI`	141	`#ifndef M_LN_SQRT_PI`
142	`#define M_LN_SQRT_PI 0.572364942924700087071713675677 /* log(sqrt(pi)) */`	142	`#define M_LN_SQRT_PI 0.572364942924700087071713675677 /* log(sqrt(pi)) */`
143	`#endif`	143	`#endif`
144		144
145	`#ifndef M_LN_SQRT_2PI`	145	`#ifndef M_LN_SQRT_2PI`
146	`#define M_LN_SQRT_2PI 0.918938533204672741780329736406 /* log(sqrt(2pi)) /`	146	`#define M_LN_SQRT_2PI 0.918938533204672741780329736406 /* log(sqrt(2pi)) /`
147	`#endif`	147	`#endif`
148		148
149	`#ifndef M_LN_SQRT_PId2`	149	`#ifndef M_LN_SQRT_PId2`
150	`#define M_LN_SQRT_PId2 0.225791352644727432363097614947 /* log(sqrt(pi/2)) */`	150	`#define M_LN_SQRT_PId2 0.225791352644727432363097614947 /* log(sqrt(pi/2)) */`
151	`#endif`	151	`#endif`
152		152
153		153
154	`#ifdef MATHLIB_IN_R/* Mathlib in R */`	154	`#ifdef MATHLIB_IN_R/* Mathlib in R */`
155		155
156	`#include "Error.h"`	156	`#include "Error.h"`
157	`# define MATHLIB_ERROR(fmt,x) error(fmt,x);`	157	`# define MATHLIB_ERROR(fmt,x) error(fmt,x);`
158	`# define MATHLIB_WARNING(fmt,x) warning(fmt,x)`	158	`# define MATHLIB_WARNING(fmt,x) warning(fmt,x)`
159	`# define MATHLIB_WARNING2(fmt,x,x2) warning(fmt,x,x2)`	159	`# define MATHLIB_WARNING2(fmt,x,x2) warning(fmt,x,x2)`
160	`# define MATHLIB_WARNING3(fmt,x,x2,x3) warning(fmt,x,x2,x3)`	160	`# define MATHLIB_WARNING3(fmt,x,x2,x3) warning(fmt,x,x2,x3)`
161	`# define MATHLIB_WARNING4(fmt,x,x2,x3,x4) warning(fmt,x,x2,x3,x4)`	161	`# define MATHLIB_WARNING4(fmt,x,x2,x3,x4) warning(fmt,x,x2,x3,x4)`
162		162
163	`#else/* Mathlib standalone */`	163	`#else/* Mathlib standalone */`
164		164
165	`#include <stdio.h>`	165	`#include <stdio.h>`
166	`# define MATHLIB_ERROR(fmt,x) { printf(fmt,x); exit(1) }`	166	`# define MATHLIB_ERROR(fmt,x) { printf(fmt,x); exit(1) }`
167	`# define MATHLIB_WARNING(fmt,x) printf(fmt,x)`	167	`# define MATHLIB_WARNING(fmt,x) printf(fmt,x)`
168	`# define MATHLIB_WARNING2(fmt,x,x2) printf(fmt,x,x2)`	168	`# define MATHLIB_WARNING2(fmt,x,x2) printf(fmt,x,x2)`
169	`# define MATHLIB_WARNING3(fmt,x,x2,x3) printf(fmt,x,x2,x3)`	169	`# define MATHLIB_WARNING3(fmt,x,x2,x3) printf(fmt,x,x2,x3)`
170	`# define MATHLIB_WARNING4(fmt,x,x2,x3,x4) printf(fmt,x,x2,x3,x4)`	170	`# define MATHLIB_WARNING4(fmt,x,x2,x3,x4) printf(fmt,x,x2,x3,x4)`
171	`#endif`	171	`#endif`
172		172
173	`#define ME_NONE 0`	173	`#define ME_NONE 0`
174	`/* no error */`	174	`/* no error */`
175	`#define ME_DOMAIN 1`	175	`#define ME_DOMAIN 1`
176	`/* argument out of domain */`	176	`/* argument out of domain */`
177	`#define ME_RANGE 2`	177	`#define ME_RANGE 2`
178	`/* value out of range */`	178	`/* value out of range */`
179	`#define ME_NOCONV 4`	179	`#define ME_NOCONV 4`
180	`/* process did not converge */`	180	`/* process did not converge */`
181	`#define ME_PRECISION 8`	181	`#define ME_PRECISION 8`
182	`/* does not have "full" precision */`	182	`/* does not have "full" precision */`
183	`#define ME_UNDERFLOW 16`	183	`#define ME_UNDERFLOW 16`
184	`/* and underflow occured (important for IEEE)*/`	184	`/* and underflow occured (important for IEEE)*/`
185		185
186		186
187	`#ifdef IEEE_754`	187	`#ifdef IEEE_754`
188		188
189	`# ifdef HAVE_IEEE754_H`	189	`# ifdef HAVE_IEEE754_H`
190	`# include <ieee754.h> /* newer Linuxen */`	190	`# include <ieee754.h> /* newer Linuxen */`
191	`# else`	191	`# else`
192	`# ifdef HAVE_IEEEFP_H`	192	`# ifdef HAVE_IEEEFP_H`
193	`# include <ieeefp.h> /* others [Solaris 2.5.x], .. */`	193	`# include <ieeefp.h> /* others [Solaris 2.5.x], .. */`
194	`# endif`	194	`# endif`
195	`# endif`	195	`# endif`
196		196
197	`extern double m_zero;`	197	`extern double m_zero;`
198	`extern double m_one;`	198	`extern double m_one;`
199	`/* extern double m_tiny; */`	199	`/* extern double m_tiny; */`
200	`#define ML_ERROR(x) /* nothing */`	200	`#define ML_ERROR(x) /* nothing */`
201	`#define ML_POSINF (m_one / m_zero)`	201	`#define ML_POSINF (m_one / m_zero)`
202	`#define ML_NEGINF ((-m_one) / m_zero)`	202	`#define ML_NEGINF ((-m_one) / m_zero)`
203	`#define ML_NAN (m_zero / m_zero)`	203	`#define ML_NAN (m_zero / m_zero)`
204	`#define ML_UNDERFLOW (DBL_MIN * DBL_MIN)`	204	`#define ML_UNDERFLOW (DBL_MIN * DBL_MIN)`
205	`#define ML_VALID(x) (!isnan(x))`	205	`#define ML_VALID(x) (!isnan(x))`
206		206
207	`#else/--- NO IEEE: No +/-Inf, NAN,... ---/`	207	`#else/--- NO IEEE: No +/-Inf, NAN,... ---/`
208	`#define ML_ERROR(x) ml_error(x)`	208	`#define ML_ERROR(x) ml_error(x)`
209	`#define ML_POSINF DBL_MAX`	209	`#define ML_POSINF DBL_MAX`
210	`#define ML_NEGINF (-DBL_MAX)`	210	`#define ML_NEGINF (-DBL_MAX)`
211	`#define ML_NAN (-DBL_MAX)`	211	`#define ML_NAN (-DBL_MAX)`
212	`#define ML_UNDERFLOW 0`	212	`#define ML_UNDERFLOW 0`
213	`#define ML_VALID(x) (errno == 0)`	213	`#define ML_VALID(x) (errno == 0)`
214	`#endif`	214	`#endif`
215		215
216	`/* Splus Compatibility */`	216	`/* Splus Compatibility */`
217		217
218	`#define snorm norm_rand`	218	`#define snorm norm_rand`
219	`#define sunif unif_rand`	219	`#define sunif unif_rand`
220	`#define sexp exp_rand`	220	`#define sexp exp_rand`
221		221
222	`/* Undo SGI Madness */`	222	`/* Undo SGI Madness */`
223		223
224	`#ifdef ftrunc`	224	`#ifdef ftrunc`
225	`#undef ftrunc`	225	`#undef ftrunc`
226	`#endif`	226	`#endif`
227	`#ifdef qexp`	227	`#ifdef qexp`
228	`#undef qexp`	228	`#undef qexp`
229	`#endif`	229	`#endif`
230		230
231	`/* Name Hiding to Avoid Clashes with Fortran */`	231	`/* Name Hiding to Avoid Clashes with Fortran */`
232		232
233	`#ifdef HIDE_NAMES`	233	`#ifdef HIDE_NAMES`
234	`# define d1mach c_d1mach`	234	`# define d1mach c_d1mach`
235	`# define i1mach c_i1mach`	235	`# define i1mach c_i1mach`
236	`#endif`	236	`#endif`
237		237
238	`#define rround fround`	238	`#define rround fround`
239	`#define prec fprec`	239	`#define prec fprec`
240	`#undef trunc`	240	`#undef trunc`
241	`#define trunc ftrunc`	241	`#define trunc ftrunc`
242		242
243	`/* Machine Characteristics */`	243	`/* Machine Characteristics */`
244		244
245	`double d1mach(int);`	245	`double d1mach(int);`
246	`double d1mach_(int*);`	246	`double d1mach_(int*);`
247	`int i1mach(int);`	247	`int i1mach(int);`
248	`int i1mach_(int*);`	248	`int i1mach_(int*);`
249		249
250	`/* General Support Functions */`	250	`/* General Support Functions */`
251		251
252	`int imax2(int, int);`	252	`int imax2(int, int);`
253	`int imin2(int, int);`	253	`int imin2(int, int);`
254	`double fmax2(double, double);`	254	`double fmax2(double, double);`
255	`double fmin2(double, double);`	255	`double fmin2(double, double);`
256	`double fmod(double, double);`	256	`double fmod(double, double);`
257	`double fprec(double, double);`	257	`double fprec(double, double);`
258	`double fround(double, double);`	258	`double fround(double, double);`
259	`double ftrunc(double);`	259	`double ftrunc(double);`
260	`double sign(double);`	260	`double sign(double);`
261	`double fsign(double, double);`	261	`double fsign(double, double);`
262	`double fsquare(double);`	262	`double fsquare(double);`
263	`double fcube(double);`	263	`double fcube(double);`
264		264
265	`/* Random Number Generators */`	265	`/* Random Number Generators */`
266		266
267	`double snorm(void);`	267	`double snorm(void);`
268	`double sunif(void);`	268	`double sunif(void);`
269	`double sexp(void);`	269	`double sexp(void);`
270		270
271	`/* Chebyshev Series */`	271	`/* Chebyshev Series */`
272		272
273	`int chebyshev_init(double*, int, double);`	273	`int chebyshev_init(double*, int, double);`
274	`double chebyshev_eval(double, double *, int);`	274	`double chebyshev_eval(double, double *, int);`
275		275
276	`/* Gamma and Related Functions */`	276	`/* Gamma and Related Functions */`
277		277
278	`double logrelerr(double);`	278	`double logrelerr(double);`
279	`void gammalims(double, double);`	279	`void gammalims(double, double);`
280	`double lgammacor(double);`	280	`double lgammacor(double);`
281	`double gammafn(double);`	281	`double gammafn(double);`
282	`double gamma_cody(double);`	282	`double gamma_cody(double);`
283	`double lgammafn(double);`	283	`double lgammafn(double);`
284	`void dpsifn(double, int, int, int, double, int, int*);`	284	`void dpsifn(double, int, int, int, double, int, int*);`
285	`double digamma(double);`	285	`double digamma(double);`
286	`double trigamma(double);`	286	`double trigamma(double);`
287	`double tetragamma(double);`	287	`double tetragamma(double);`
288	`double pentagamma(double);`	288	`double pentagamma(double);`
289		289
290	`double choose(double, double);`	290	`double choose(double, double);`
291	`double lchoose(double, double);`	291	`double lchoose(double, double);`
292	`double fastchoose(double, double);`	292	`double fastchoose(double, double);`
293	`double lfastchoose(double, double);`	293	`double lfastchoose(double, double);`
294		294
295	`/* Bessel Functions of All Kinds */`	295	`/* Bessel Functions of All Kinds */`
296		296
297	`double bessel_i(double, double, double);`	297	`double bessel_i(double, double, double);`
298	`double bessel_j(double, double);`	298	`double bessel_j(double, double);`
299	`double bessel_k(double, double, double);`	299	`double bessel_k(double, double, double);`
300	`double bessel_y(double, double);`	300	`double bessel_y(double, double);`
301	`void I_bessel(double, double, long, long, double, long);`	301	`void I_bessel(double, double, long, long, double, long);`
302	`void J_bessel(double, double, long, double, long*);`	302	`void J_bessel(double, double, long, double, long*);`
303	`void K_bessel(double, double, long, long, double, long);`	303	`void K_bessel(double, double, long, long, double, long);`
304	`void Y_bessel(double, double, long, double, long*);`	304	`void Y_bessel(double, double, long, double, long*);`
305		305
306	`/* Beta and Related Functions */`	306	`/* Beta and Related Functions */`
307		307
308	`double beta(double, double);`	308	`double beta(double, double);`
309	`double lbeta(double, double);`	309	`double lbeta(double, double);`
310		310
311	`/* Normal Distribution */`	311	`/* Normal Distribution */`
312		312
313	`double dnorm(double, double, double);`	313	`double dnorm(double, double, double);`
314	`double pnorm(double, double, double);`	314	`double pnorm(double, double, double);`
315	`double qnorm(double, double, double);`	315	`double qnorm(double, double, double);`
316	`double rnorm(double, double);`	316	`double rnorm(double, double);`
317		317
318	`/* Uniform Distribution */`	318	`/* Uniform Distribution */`
319		319
320	`double dunif(double, double, double);`	320	`double dunif(double, double, double);`
321	`double punif(double, double, double);`	321	`double punif(double, double, double);`
322	`double qunif(double, double, double);`	322	`double qunif(double, double, double);`
323	`double runif(double, double);`	323	`double runif(double, double);`
324		324
325	`/* Gamma Distribution */`	325	`/* Gamma Distribution */`
326		326
327	`double dgamma(double, double, double);`	327	`double dgamma(double, double, double);`
328	`double pgamma(double, double, double);`	328	`double pgamma(double, double, double);`
329	`double qgamma(double, double, double);`	329	`double qgamma(double, double, double);`
330	`double rgamma(double, double);`	330	`double rgamma(double, double);`
331		331
332	`/* Beta Distribution */`	332	`/* Beta Distribution */`
333		333
334	`double dbeta(double, double, double);`	334	`double dbeta(double, double, double);`
335	`double pbeta(double, double, double);`	335	`double pbeta(double, double, double);`
336	`double pbeta_raw(double, double, double);`	336	`double pbeta_raw(double, double, double);`
337	`double qbeta(double, double, double);`	337	`double qbeta(double, double, double);`
338	`double rbeta(double, double);`	338	`double rbeta(double, double);`
339		339
340	`/* Lognormal Distribution */`	340	`/* Lognormal Distribution */`
341		341
342	`double dlnorm(double, double, double);`	342	`double dlnorm(double, double, double);`
343	`double plnorm(double, double, double);`	343	`double plnorm(double, double, double);`
344	`double qlnorm(double, double, double);`	344	`double qlnorm(double, double, double);`
345	`double rlnorm(double, double);`	345	`double rlnorm(double, double);`
346		346
347	`/* Chi-squared Distribution */`	347	`/* Chi-squared Distribution */`
348		348
349	`double dchisq(double, double);`	349	`double dchisq(double, double);`
350	`double pchisq(double, double);`	350	`double pchisq(double, double);`
351	`double qchisq(double, double);`	351	`double qchisq(double, double);`
352	`double rchisq(double);`	352	`double rchisq(double);`
353		353
354	`/* Non-central Chi-squared Distribution */`	354	`/* Non-central Chi-squared Distribution */`
355		355
356	`double dnchisq(double, double, double);`	356	`double dnchisq(double, double, double);`
357	`double pnchisq(double, double, double);`	357	`double pnchisq(double, double, double);`
358	`double qnchisq(double, double, double);`	358	`double qnchisq(double, double, double);`
359	`double rnchisq(double, double);`	359	`double rnchisq(double, double);`
360		360
361	`/* F Distibution */`	361	`/* F Distibution */`
362		362
363	`double df(double, double, double);`	363	`double df(double, double, double);`
364	`double pf(double, double, double);`	364	`double pf(double, double, double);`
365	`double qf(double, double, double);`	365	`double qf(double, double, double);`
366	`double rf(double, double);`	366	`double rf(double, double);`
367		367
368	`/* Student t Distibution */`	368	`/* Student t Distibution */`
369		369
370	`double dt(double, double);`	370	`double dt(double, double);`
371	`double pt(double, double);`	371	`double pt(double, double);`
372	`double qt(double, double);`	372	`double qt(double, double);`
373	`double rt(double);`	373	`double rt(double);`
374		374
375	`/* Binomial Distribution */`	375	`/* Binomial Distribution */`
376		376
377	`double dbinom(double, double, double);`	377	`double dbinom(double, double, double);`
378	`double pbinom(double, double, double);`	378	`double pbinom(double, double, double);`
379	`double qbinom(double, double, double);`	379	`double qbinom(double, double, double);`
380	`double rbinom(double, double);`	380	`double rbinom(double, double);`
381		381
382	`/* Cauchy Distribution */`	382	`/* Cauchy Distribution */`
383		383
384	`double dcauchy(double, double, double);`	384	`double dcauchy(double, double, double);`
385	`double pcauchy(double, double, double);`	385	`double pcauchy(double, double, double);`
386	`double qcauchy(double, double, double);`	386	`double qcauchy(double, double, double);`
387	`double rcauchy(double, double);`	387	`double rcauchy(double, double);`
388		388
389	`/* Exponential Distribution */`	389	`/* Exponential Distribution */`
390		390
391	`double dexp(double, double);`	391	`double dexp(double, double);`
392	`double pexp(double, double);`	392	`double pexp(double, double);`
393	`double qexp(double, double);`	393	`double qexp(double, double);`
394	`double rexp(double);`	394	`double rexp(double);`
395		395
396	`/* Geometric Distribution */`	396	`/* Geometric Distribution */`
397		397
398	`double dgeom(double, double);`	398	`double dgeom(double, double);`
399	`double pgeom(double, double);`	399	`double pgeom(double, double);`
400	`double qgeom(double, double);`	400	`double qgeom(double, double);`
401	`double rgeom(double);`	401	`double rgeom(double);`
402		402
403	`/* Hypergeometric Distibution */`	403	`/* Hypergeometric Distibution */`
404		404
405	`double dhyper(double, double, double, double);`	405	`double dhyper(double, double, double, double);`
406	`double phyper(double, double, double, double);`	406	`double phyper(double, double, double, double);`
407	`double qhyper(double, double, double, double);`	407	`double qhyper(double, double, double, double);`
408	`double rhyper(double, double, double);`	408	`double rhyper(double, double, double);`
409		409
410	`/* Negative Binomial Distribution */`	410	`/* Negative Binomial Distribution */`
411		411
412	`double dnbinom(double, double, double);`	412	`double dnbinom(double, double, double);`
413	`double pnbinom(double, double, double);`	413	`double pnbinom(double, double, double);`
414	`double qnbinom(double, double, double);`	414	`double qnbinom(double, double, double);`
415	`double rnbinom(double, double);`	415	`double rnbinom(double, double);`
416		416
417	`/* Poisson Distribution */`	417	`/* Poisson Distribution */`
418		418
419	`double dpois(double, double);`	419	`double dpois(double, double);`
420	`double ppois(double, double);`	420	`double ppois(double, double);`
421	`double qpois(double, double);`	421	`double qpois(double, double);`
422	`double rpois(double);`	422	`double rpois(double);`
423		423
424	`/* Weibull Distribution */`	424	`/* Weibull Distribution */`
425		425
426	`double dweibull(double, double, double);`	426	`double dweibull(double, double, double);`
427	`double pweibull(double, double, double);`	427	`double pweibull(double, double, double);`
428	`double qweibull(double, double, double);`	428	`double qweibull(double, double, double);`
429	`double rweibull(double, double);`	429	`double rweibull(double, double);`
430		430
431	`/* Logistic Distribution */`	431	`/* Logistic Distribution */`
432		432
433	`double dlogis(double, double, double);`	433	`double dlogis(double, double, double);`
434	`double plogis(double, double, double);`	434	`double plogis(double, double, double);`
435	`double qlogis(double, double, double);`	435	`double qlogis(double, double, double);`
436	`double rlogis(double, double);`	436	`double rlogis(double, double);`
437		437
438	`/* Non-central Beta Distribution */`	438	`/* Non-central Beta Distribution */`
439		439
440	`double dnbeta(double, double, double, double);`	440	`double dnbeta(double, double, double, double);`
441	`double pnbeta(double, double, double, double);`	441	`double pnbeta(double, double, double, double);`
442	`double qnbeta(double, double, double, double);`	442	`double qnbeta(double, double, double, double);`
443	`double rnbeta(double, double, double);`	443	`double rnbeta(double, double, double);`
444		444
445	`/* Non-central F Distribution */`	445	`/* Non-central F Distribution */`
446		446
447	`double dnf(double, double, double, double);`	447	`double dnf(double, double, double, double);`
448	`double pnf(double, double, double, double);`	448	`double pnf(double, double, double, double);`
449	`double qnf(double, double, double, double);`	449	`double qnf(double, double, double, double);`
450	`double rnf(double, double, double);`	450	`double rnf(double, double, double);`
451		451
452	`/* Non-central Student t Distribution */`	452	`/* Non-central Student t Distribution */`
453		453
454	`double dnt(double, double, double);`	454	`double dnt(double, double, double);`
455	`double pnt(double, double, double);`	455	`double pnt(double, double, double);`
456	`double qnt(double, double, double);`	456	`double qnt(double, double, double);`
457	`double rnt(double, double);`	457	`double rnt(double, double);`
458		458
459	`/* Studentized Range Distribution */`	459	`/* Studentized Range Distribution */`
460		460
461	`double dtukey(double, double, double, double);`	461	`double dtukey(double, double, double, double);`
462	`double ptukey(double, double, double, double);`	462	`double ptukey(double, double, double, double);`
463	`double qtukey(double, double, double, double);`	463	`double qtukey(double, double, double, double);`
464	`double rtukey(double, double, double);`	464	`double rtukey(double, double, double);`
465		465
466	`/* Wilcoxon Rank Sum Distribution */`	466	`/* Wilcoxon Rank Sum Distribution */`
467		467
468	`#define WILCOX_MAX 50`	468	`#define WILCOX_MAX 50`
469	`double dwilcox(double, double, double);`	469	`double dwilcox(double, double, double);`
470	`double pwilcox(double, double, double);`	470	`double pwilcox(double, double, double);`
471	`double qwilcox(double, double, double);`	471	`double qwilcox(double, double, double);`
472	`double rwilcox(double, double);`	472	`double rwilcox(double, double);`
473		473
474	`/* Wilcoxon Signed Rank Distribution */`	474	`/* Wilcoxon Signed Rank Distribution */`
475		475
476	`#define SIGNRANK_MAX 50`	476	`#define SIGNRANK_MAX 50`
477	`double dsignrank(double, double);`	477	`double dsignrank(double, double);`
478	`double psignrank(double, double);`	478	`double psignrank(double, double);`
479	`double qsignrank(double, double);`	479	`double qsignrank(double, double);`
480	`double rsignrank(double);`	480	`double rsignrank(double);`
481		481
482	`#endif`	482	`#endif`

The R Project SVN R

(root)/trunk/src/include/Mathlib.h @ 4792 – Rev 3865 → 4562