| 3279 |
pd |
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/*
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* Mathlib : A C Library of Special Functions
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| 5458 |
ripley |
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* Copyright (C) 1998-1999 R Development Core Team
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| 3279 |
pd |
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 2 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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| 5458 |
ripley |
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* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
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| 3279 |
pd |
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*
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* Mathlib.h should contain ALL headers from R's C code in `src/nmath'
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--------- such that ``the Math library'' can be used by simply
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``#include "Mathlib.h" ''
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and nothing else.
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*/
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| 571 |
ihaka |
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#ifndef MATHLIB_H
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#define MATHLIB_H
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r |
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| 3279 |
pd |
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/*-- Mathlib as part of R -- undefine this for standalone : */
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#define MATHLIB_IN_R
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pd |
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| 7108 |
ripley |
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#include "R_ext/Rver.h" /* for IEEE_754 */
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| 7003 |
ripley |
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#include "R_ext/Arith.h"
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/*#include "R_ext/Random.h"*/
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r |
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maechler |
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#ifdef FORTRAN_H
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#error __MUST__include "Mathlib.h" _before_ "Fortran.h"
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#endif
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| 571 |
ihaka |
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#include <errno.h>
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| 2737 |
hornik |
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#include <limits.h>
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| 571 |
ihaka |
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#include <float.h>
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r |
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#include <math.h>
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#include <stdlib.h>
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maechler |
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/* TRUE and FALSE conflict with the Mac --- Fortran.h still defines them... */
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#define LTRUE (1)
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#define LFALSE (0)
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| 3244 |
ihaka |
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/* 30 Decimal-place constants */
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/* Computed with bc -l (scale=32; proper round) */
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r |
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ihaka |
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/* SVID & X/Open Constants */
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/* Names from Solaris math.h */
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#ifndef M_E
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#define M_E 2.718281828459045235360287471353 /* e */
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#endif
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#ifndef M_LOG2E
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#define M_LOG2E 1.442695040888963407359924681002 /* log2(e) */
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#endif
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#ifndef M_LOG10E
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maechler |
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#define M_LOG10E 0.434294481903251827651128918917 /* log10(e) */
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ihaka |
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#endif
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#ifndef M_LN2
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#define M_LN2 0.693147180559945309417232121458 /* ln(2) */
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#endif
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#ifndef M_LN10
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#define M_LN10 2.302585092994045684017991454684 /* ln(10) */
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#endif
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#ifndef M_PI
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maechler |
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#define M_PI 3.141592653589793238462643383280 /* pi */
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ihaka |
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#endif
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#ifndef M_PI_2
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#define M_PI_2 1.570796326794896619231321691640 /* pi/2 */
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#endif
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#ifndef M_PI_4
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#define M_PI_4 0.785398163397448309615660845820 /* pi/4 */
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#endif
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maechler |
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#ifndef M_1_PI
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ihaka |
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#define M_1_PI 0.318309886183790671537767526745 /* 1/pi */
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#endif
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maechler |
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#ifndef M_2_PI
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ihaka |
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#define M_2_PI 0.636619772367581343075535053490 /* 1/pi */
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#endif
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#ifndef M_2_SQRTPI
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#define M_2_SQRTPI 1.128379167095512573896158903122 /* 1/sqrt(pi) */
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#endif
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#ifndef M_SQRT2
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#define M_SQRT2 1.414213562373095048801688724210 /* sqrt(2) */
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#endif
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#ifndef M_SQRT1_2
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#define M_SQRT1_2 0.707106781186547524400844362105 /* 1/sqrt(2) */
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#endif
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/* Other, R-Specific Constants */
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/* Note there are some repeats of values above */
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/* Needs a cleanup */
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#ifndef M_1_SQRT_2
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| 777 |
maechler |
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#define M_1_SQRT_2 0.707106781186547524400844362105 /* 1/sqrt(2) */
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| 3244 |
ihaka |
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#endif
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#ifndef M_SQRT_32
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maechler |
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#define M_SQRT_32 5.656854249492380195206754896838 /* sqrt(32) */
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r |
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#endif
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| 3244 |
ihaka |
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#ifndef M_LOG10_2
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#define M_LOG10_2 0.301029995663981195213738894724 /* log10(2) */
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| 777 |
maechler |
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#endif
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r |
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#ifndef M_PI_half
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| 3244 |
ihaka |
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#define M_PI_half 1.570796326794896619231321691640 /* pi/2 */
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r |
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#endif
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#ifndef M_SQRT_PI
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| 3244 |
ihaka |
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#define M_SQRT_PI 1.772453850905516027298167483341 /* sqrt(pi) */
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r |
131 |
#endif
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ihaka |
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#ifndef M_1_SQRT_2PI
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#define M_1_SQRT_2PI 0.398942280401432677939946059934 /* 1/sqrt(2pi) */
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#endif
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r |
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ihaka |
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#ifndef M_SQRT_2dPI
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#define M_SQRT_2dPI 0.797884560802865355879892119869 /* sqrt(2/pi) */
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#endif
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| 777 |
maechler |
142 |
#ifndef M_LN_SQRT_PI
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| 3244 |
ihaka |
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#define M_LN_SQRT_PI 0.572364942924700087071713675677 /* log(sqrt(pi)) */
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| 2 |
r |
144 |
#endif
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| 3244 |
ihaka |
146 |
#ifndef M_LN_SQRT_2PI
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#define M_LN_SQRT_2PI 0.918938533204672741780329736406 /* log(sqrt(2*pi)) */
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#endif
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| 777 |
maechler |
149 |
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| 3244 |
ihaka |
150 |
#ifndef M_LN_SQRT_PId2
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#define M_LN_SQRT_PId2 0.225791352644727432363097614947 /* log(sqrt(pi/2)) */
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#endif
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| 3076 |
pd |
155 |
#ifdef MATHLIB_IN_R/* Mathlib in R */
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| 777 |
maechler |
156 |
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| 7007 |
ripley |
157 |
#include "R_ext/Error.h"
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| 3076 |
pd |
158 |
# define MATHLIB_ERROR(fmt,x) error(fmt,x);
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# define MATHLIB_WARNING(fmt,x) warning(fmt,x)
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# define MATHLIB_WARNING2(fmt,x,x2) warning(fmt,x,x2)
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# define MATHLIB_WARNING3(fmt,x,x2,x3) warning(fmt,x,x2,x3)
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# define MATHLIB_WARNING4(fmt,x,x2,x3,x4) warning(fmt,x,x2,x3,x4)
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r |
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| 3076 |
pd |
164 |
#else/* Mathlib standalone */
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#include <stdio.h>
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| 3786 |
pd |
167 |
# define MATHLIB_ERROR(fmt,x) { printf(fmt,x); exit(1) }
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| 3076 |
pd |
168 |
# define MATHLIB_WARNING(fmt,x) printf(fmt,x)
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# define MATHLIB_WARNING2(fmt,x,x2) printf(fmt,x,x2)
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# define MATHLIB_WARNING3(fmt,x,x2,x3) printf(fmt,x,x2,x3)
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# define MATHLIB_WARNING4(fmt,x,x2,x3,x4) printf(fmt,x,x2,x3,x4)
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#endif
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| 571 |
ihaka |
174 |
#define ME_NONE 0
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| 3786 |
pd |
175 |
/* no error */
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| 571 |
ihaka |
176 |
#define ME_DOMAIN 1
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| 3786 |
pd |
177 |
/* argument out of domain */
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| 571 |
ihaka |
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#define ME_RANGE 2
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| 3786 |
pd |
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/* value out of range */
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#define ME_NOCONV 4
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/* process did not converge */
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#define ME_PRECISION 8
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/* does not have "full" precision */
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#define ME_UNDERFLOW 16
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/* and underflow occured (important for IEEE)*/
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| 571 |
ihaka |
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#ifdef IEEE_754
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| 7108 |
ripley |
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#ifdef OLD
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pd |
190 |
# ifdef HAVE_IEEE754_H
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# include <ieee754.h> /* newer Linuxen */
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# else
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# ifdef HAVE_IEEEFP_H
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# include <ieeefp.h> /* others [Solaris 2.5.x], .. */
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# endif
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# endif
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| 7108 |
ripley |
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#endif
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| 995 |
ihaka |
198 |
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| 571 |
ihaka |
199 |
extern double m_zero;
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extern double m_one;
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| 3548 |
ihaka |
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/* extern double m_tiny; */
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| 571 |
ihaka |
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#define ML_ERROR(x) /* nothing */
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#define ML_POSINF (m_one / m_zero)
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#define ML_NEGINF ((-m_one) / m_zero)
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#define ML_NAN (m_zero / m_zero)
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| 3548 |
ihaka |
206 |
#define ML_UNDERFLOW (DBL_MIN * DBL_MIN)
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| 777 |
maechler |
207 |
#define ML_VALID(x) (!isnan(x))
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pd |
208 |
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#else/*--- NO IEEE: No +/-Inf, NAN,... ---*/
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| 7016 |
ripley |
210 |
void ml_error(int n);
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| 571 |
ihaka |
211 |
#define ML_ERROR(x) ml_error(x)
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#define ML_POSINF DBL_MAX
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#define ML_NEGINF (-DBL_MAX)
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#define ML_NAN (-DBL_MAX)
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#define ML_UNDERFLOW 0
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| 777 |
maechler |
216 |
#define ML_VALID(x) (errno == 0)
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r |
217 |
#endif
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| 571 |
ihaka |
219 |
/* Splus Compatibility */
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r |
220 |
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| 571 |
ihaka |
221 |
#define snorm norm_rand
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#define sunif unif_rand
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#define sexp exp_rand
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r |
224 |
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| 1394 |
ihaka |
225 |
/* Undo SGI Madness */
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#ifdef ftrunc
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| 5408 |
hornik |
228 |
# undef ftrunc
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| 1394 |
ihaka |
229 |
#endif
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230 |
#ifdef qexp
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| 5408 |
hornik |
231 |
# undef qexp
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| 1394 |
ihaka |
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#endif
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| 5408 |
hornik |
233 |
#ifdef qgamma
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# undef qgamma
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#endif
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| 1394 |
ihaka |
236 |
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| 571 |
ihaka |
237 |
/* Name Hiding to Avoid Clashes with Fortran */
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r |
238 |
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| 571 |
ihaka |
239 |
#ifdef HIDE_NAMES
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| 3076 |
pd |
240 |
# define d1mach c_d1mach
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# define i1mach c_i1mach
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| 571 |
ihaka |
242 |
#endif
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r |
243 |
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| 571 |
ihaka |
244 |
#define rround fround
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245 |
#define prec fprec
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| 3244 |
ihaka |
246 |
#undef trunc
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| 571 |
ihaka |
247 |
#define trunc ftrunc
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| 2 |
r |
248 |
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| 4835 |
maechler |
249 |
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250 |
/* Utilities for `dpq' handling (density/probability/quantile) */
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251 |
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252 |
#define R_D__0 (give_log ? ML_NEGINF : 0.)
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253 |
#define R_D__1 (give_log ? 0. : 1.)
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254 |
#define R_DT_0 (lower_tail ? R_D__0 : R_D__1)
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255 |
#define R_DT_1 (lower_tail ? R_D__1 : R_D__0)
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256 |
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257 |
#define R_D_val(x) (give_log ? log(x) : x) /* x */
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258 |
#define R_D_log(x) (give_log ? x : exp(x)) /* log(x) */
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259 |
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260 |
#define R_DT_val(x) R_D_val(lower_tail ? x : 1. - x) /* x */
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261 |
#define R_DT_Cval(x) R_D_val(lower_tail ? 1. - x : x) /* 1 - x */
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262 |
#define R_DT_log(x) R_D_log(lower_tail ? x : 1. - x) /* log(x) */
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263 |
#define R_DT_Clog(x) R_D_log(lower_tail ? 1. - x : x) /* log(1 - x) */
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264 |
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265 |
#define R_D_give_log(dd) (((int)dd) >> 1) /* Extract ``give_log'' flag */
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266 |
#define R_D_lower_tail(dd) (((int)dd) % 2) /* Extract ``lower_tail'' flag */
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267 |
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268 |
/* R's version of C functions: */
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269 |
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270 |
double R_log(double x);
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271 |
double R_pow(double x, double y);
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272 |
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| 571 |
ihaka |
273 |
/* Machine Characteristics */
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| 2 |
r |
274 |
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| 571 |
ihaka |
275 |
double d1mach(int);
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276 |
double d1mach_(int*);
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277 |
int i1mach(int);
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278 |
int i1mach_(int*);
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| 2 |
r |
279 |
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| 571 |
ihaka |
280 |
/* General Support Functions */
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| 2 |
r |
281 |
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| 571 |
ihaka |
282 |
int imax2(int, int);
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283 |
int imin2(int, int);
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284 |
double fmax2(double, double);
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285 |
double fmin2(double, double);
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286 |
double fmod(double, double);
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287 |
double fprec(double, double);
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288 |
double fround(double, double);
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289 |
double ftrunc(double);
|
| 3076 |
pd |
290 |
double sign(double);
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| 571 |
ihaka |
291 |
double fsign(double, double);
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292 |
double fsquare(double);
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293 |
double fcube(double);
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| 2 |
r |
294 |
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| 571 |
ihaka |
295 |
/* Random Number Generators */
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| 2 |
r |
296 |
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| 571 |
ihaka |
297 |
double snorm(void);
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298 |
double sunif(void);
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299 |
double sexp(void);
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| 2 |
r |
300 |
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| 571 |
ihaka |
301 |
/* Chebyshev Series */
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| 2 |
r |
302 |
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| 571 |
ihaka |
303 |
int chebyshev_init(double*, int, double);
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304 |
double chebyshev_eval(double, double *, int);
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| 2 |
r |
305 |
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| 571 |
ihaka |
306 |
/* Gamma and Related Functions */
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| 2 |
r |
307 |
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| 571 |
ihaka |
308 |
double logrelerr(double);
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309 |
void gammalims(double*, double*);
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310 |
double lgammacor(double);
|
| 2278 |
maechler |
311 |
double gammafn(double);
|
| 2629 |
maechler |
312 |
double gamma_cody(double);
|
| 2278 |
maechler |
313 |
double lgammafn(double);
|
| 571 |
ihaka |
314 |
void dpsifn(double, int, int, int, double*, int*, int*);
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315 |
double digamma(double);
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316 |
double trigamma(double);
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317 |
double tetragamma(double);
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318 |
double pentagamma(double);
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| 2 |
r |
319 |
|
| 571 |
ihaka |
320 |
double choose(double, double);
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321 |
double lchoose(double, double);
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322 |
double fastchoose(double, double);
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|
323 |
double lfastchoose(double, double);
|
| 2 |
r |
324 |
|
| 2629 |
maechler |
325 |
/* Bessel Functions of All Kinds */
|
|
|
326 |
|
| 3786 |
pd |
327 |
double bessel_i(double, double, double);
|
|
|
328 |
double bessel_j(double, double);
|
|
|
329 |
double bessel_k(double, double, double);
|
|
|
330 |
double bessel_y(double, double);
|
|
|
331 |
void I_bessel(double*, double*, long*, long*, double*, long*);
|
|
|
332 |
void J_bessel(double*, double*, long*, double*, long*);
|
|
|
333 |
void K_bessel(double*, double*, long*, long*, double*, long*);
|
|
|
334 |
void Y_bessel(double*, double*, long*, double*, long*);
|
| 2629 |
maechler |
335 |
|
| 571 |
ihaka |
336 |
/* Beta and Related Functions */
|
| 2 |
r |
337 |
|
| 571 |
ihaka |
338 |
double beta(double, double);
|
|
|
339 |
double lbeta(double, double);
|
| 2 |
r |
340 |
|
| 571 |
ihaka |
341 |
/* Normal Distribution */
|
| 2 |
r |
342 |
|
| 571 |
ihaka |
343 |
double dnorm(double, double, double);
|
|
|
344 |
double pnorm(double, double, double);
|
|
|
345 |
double qnorm(double, double, double);
|
|
|
346 |
double rnorm(double, double);
|
| 2 |
r |
347 |
|
| 571 |
ihaka |
348 |
/* Uniform Distribution */
|
| 2 |
r |
349 |
|
| 571 |
ihaka |
350 |
double dunif(double, double, double);
|
|
|
351 |
double punif(double, double, double);
|
|
|
352 |
double qunif(double, double, double);
|
|
|
353 |
double runif(double, double);
|
| 2 |
r |
354 |
|
| 571 |
ihaka |
355 |
/* Gamma Distribution */
|
| 2 |
r |
356 |
|
| 571 |
ihaka |
357 |
double dgamma(double, double, double);
|
|
|
358 |
double pgamma(double, double, double);
|
|
|
359 |
double qgamma(double, double, double);
|
|
|
360 |
double rgamma(double, double);
|
| 2 |
r |
361 |
|
| 571 |
ihaka |
362 |
/* Beta Distribution */
|
| 2 |
r |
363 |
|
| 571 |
ihaka |
364 |
double dbeta(double, double, double);
|
|
|
365 |
double pbeta(double, double, double);
|
|
|
366 |
double pbeta_raw(double, double, double);
|
|
|
367 |
double qbeta(double, double, double);
|
|
|
368 |
double rbeta(double, double);
|
| 2 |
r |
369 |
|
| 571 |
ihaka |
370 |
/* Lognormal Distribution */
|
| 2 |
r |
371 |
|
| 571 |
ihaka |
372 |
double dlnorm(double, double, double);
|
|
|
373 |
double plnorm(double, double, double);
|
|
|
374 |
double qlnorm(double, double, double);
|
|
|
375 |
double rlnorm(double, double);
|
| 2 |
r |
376 |
|
| 571 |
ihaka |
377 |
/* Chi-squared Distribution */
|
| 2 |
r |
378 |
|
| 571 |
ihaka |
379 |
double dchisq(double, double);
|
|
|
380 |
double pchisq(double, double);
|
|
|
381 |
double qchisq(double, double);
|
|
|
382 |
double rchisq(double);
|
| 2 |
r |
383 |
|
| 571 |
ihaka |
384 |
/* Non-central Chi-squared Distribution */
|
| 2 |
r |
385 |
|
| 605 |
ihaka |
386 |
double dnchisq(double, double, double);
|
| 571 |
ihaka |
387 |
double pnchisq(double, double, double);
|
|
|
388 |
double qnchisq(double, double, double);
|
| 605 |
ihaka |
389 |
double rnchisq(double, double);
|
| 571 |
ihaka |
390 |
|
|
|
391 |
/* F Distibution */
|
|
|
392 |
|
|
|
393 |
double df(double, double, double);
|
|
|
394 |
double pf(double, double, double);
|
|
|
395 |
double qf(double, double, double);
|
|
|
396 |
double rf(double, double);
|
|
|
397 |
|
|
|
398 |
/* Student t Distibution */
|
|
|
399 |
|
|
|
400 |
double dt(double, double);
|
|
|
401 |
double pt(double, double);
|
|
|
402 |
double qt(double, double);
|
|
|
403 |
double rt(double);
|
|
|
404 |
|
|
|
405 |
/* Binomial Distribution */
|
|
|
406 |
|
|
|
407 |
double dbinom(double, double, double);
|
|
|
408 |
double pbinom(double, double, double);
|
|
|
409 |
double qbinom(double, double, double);
|
|
|
410 |
double rbinom(double, double);
|
|
|
411 |
|
|
|
412 |
/* Cauchy Distribution */
|
|
|
413 |
|
|
|
414 |
double dcauchy(double, double, double);
|
|
|
415 |
double pcauchy(double, double, double);
|
|
|
416 |
double qcauchy(double, double, double);
|
|
|
417 |
double rcauchy(double, double);
|
|
|
418 |
|
|
|
419 |
/* Exponential Distribution */
|
|
|
420 |
|
|
|
421 |
double dexp(double, double);
|
|
|
422 |
double pexp(double, double);
|
|
|
423 |
double qexp(double, double);
|
|
|
424 |
double rexp(double);
|
|
|
425 |
|
|
|
426 |
/* Geometric Distribution */
|
|
|
427 |
|
|
|
428 |
double dgeom(double, double);
|
|
|
429 |
double pgeom(double, double);
|
|
|
430 |
double qgeom(double, double);
|
|
|
431 |
double rgeom(double);
|
|
|
432 |
|
|
|
433 |
/* Hypergeometric Distibution */
|
|
|
434 |
|
|
|
435 |
double dhyper(double, double, double, double);
|
|
|
436 |
double phyper(double, double, double, double);
|
|
|
437 |
double qhyper(double, double, double, double);
|
|
|
438 |
double rhyper(double, double, double);
|
|
|
439 |
|
|
|
440 |
/* Negative Binomial Distribution */
|
|
|
441 |
|
|
|
442 |
double dnbinom(double, double, double);
|
|
|
443 |
double pnbinom(double, double, double);
|
|
|
444 |
double qnbinom(double, double, double);
|
|
|
445 |
double rnbinom(double, double);
|
|
|
446 |
|
|
|
447 |
/* Poisson Distribution */
|
|
|
448 |
|
|
|
449 |
double dpois(double, double);
|
|
|
450 |
double ppois(double, double);
|
|
|
451 |
double qpois(double, double);
|
|
|
452 |
double rpois(double);
|
|
|
453 |
|
|
|
454 |
/* Weibull Distribution */
|
|
|
455 |
|
|
|
456 |
double dweibull(double, double, double);
|
|
|
457 |
double pweibull(double, double, double);
|
|
|
458 |
double qweibull(double, double, double);
|
|
|
459 |
double rweibull(double, double);
|
|
|
460 |
|
|
|
461 |
/* Logistic Distribution */
|
|
|
462 |
|
|
|
463 |
double dlogis(double, double, double);
|
|
|
464 |
double plogis(double, double, double);
|
|
|
465 |
double qlogis(double, double, double);
|
|
|
466 |
double rlogis(double, double);
|
|
|
467 |
|
| 602 |
ihaka |
468 |
/* Non-central Beta Distribution */
|
|
|
469 |
|
|
|
470 |
double dnbeta(double, double, double, double);
|
|
|
471 |
double pnbeta(double, double, double, double);
|
|
|
472 |
double qnbeta(double, double, double, double);
|
|
|
473 |
double rnbeta(double, double, double);
|
|
|
474 |
|
|
|
475 |
/* Non-central F Distribution */
|
|
|
476 |
|
|
|
477 |
double dnf(double, double, double, double);
|
|
|
478 |
double pnf(double, double, double, double);
|
|
|
479 |
double qnf(double, double, double, double);
|
|
|
480 |
double rnf(double, double, double);
|
|
|
481 |
|
|
|
482 |
/* Non-central Student t Distribution */
|
|
|
483 |
|
|
|
484 |
double dnt(double, double, double);
|
|
|
485 |
double pnt(double, double, double);
|
|
|
486 |
double qnt(double, double, double);
|
|
|
487 |
double rnt(double, double);
|
|
|
488 |
|
| 624 |
ihaka |
489 |
/* Studentized Range Distribution */
|
|
|
490 |
|
|
|
491 |
double dtukey(double, double, double, double);
|
|
|
492 |
double ptukey(double, double, double, double);
|
|
|
493 |
double qtukey(double, double, double, double);
|
|
|
494 |
double rtukey(double, double, double);
|
|
|
495 |
|
| 2235 |
hornik |
496 |
/* Wilcoxon Rank Sum Distribution */
|
| 1276 |
hornik |
497 |
|
| 3865 |
pd |
498 |
#define WILCOX_MAX 50
|
| 1276 |
hornik |
499 |
double dwilcox(double, double, double);
|
|
|
500 |
double pwilcox(double, double, double);
|
|
|
501 |
double qwilcox(double, double, double);
|
|
|
502 |
double rwilcox(double, double);
|
|
|
503 |
|
| 2235 |
hornik |
504 |
/* Wilcoxon Signed Rank Distribution */
|
|
|
505 |
|
| 3865 |
pd |
506 |
#define SIGNRANK_MAX 50
|
| 2235 |
hornik |
507 |
double dsignrank(double, double);
|
|
|
508 |
double psignrank(double, double);
|
|
|
509 |
double qsignrank(double, double);
|
|
|
510 |
double rsignrank(double);
|
|
|
511 |
|
| 2 |
r |
512 |
#endif
|
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