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/*
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* Mathlib : A C Library of Special Functions
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* Copyright (C) 1998-2003 The R Development Core Team
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ripley |
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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 Lesser General Public License as published by
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* the Free Software Foundation; either version 2.1 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 Lesser General Public License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
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*
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* Rmath.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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ripley |
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``#include <Rmath.h> ''
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and nothing else.
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*/
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#ifndef RMATH_H
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#define RMATH_H
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/*-- Mathlib as part of R -- define this for standalone : */
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/* #undef MATHLIB_STANDALONE */
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#ifndef HAVE_LOG1P
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@RMATH_HAVE_LOG1P@
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#endif
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#ifndef HAVE_EXPM1
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@RMATH_HAVE_EXPM1@
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#endif
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#ifndef HAVE_WORKING_LOG1P
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@RMATH_HAVE_WORKING_LOG1P@
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#endif
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#include <errno.h>
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#include <limits.h>
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#include <float.h>
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#include <math.h>
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#if defined(HAVE_LOG1P) && !defined(HAVE_WORKING_LOG1P)
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/* remap to avoid problems with getting the right entry point */
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double Rlog1p(double);
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#define log1p Rlog1p
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#endif
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#include <stdlib.h>
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/* Undo SGI Madness */
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#ifdef ftrunc
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# undef ftrunc
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#endif
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#ifdef qexp
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# undef qexp
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#endif
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#ifdef qgamma
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# undef qgamma
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#endif
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/* ----- The following constants and entry points are part of the R API ---- */
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/* 30 Decimal-place constants */
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/* Computed with bc -l (scale=32; proper round) */
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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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#define M_LOG10E 0.434294481903251827651128918917 /* log10(e) */
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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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#define M_PI 3.141592653589793238462643383280 /* pi */
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#endif
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#ifndef M_2PI
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#define M_2PI 6.283185307179586476925286766559 /* 2*pi */
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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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#ifndef M_1_PI
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#define M_1_PI 0.318309886183790671537767526745 /* 1/pi */
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#endif
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#ifndef M_2_PI
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#define M_2_PI 0.636619772367581343075535053490 /* 2/pi */
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#endif
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#ifndef M_2_SQRTPI
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#define M_2_SQRTPI 1.128379167095512573896158903122 /* 2/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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/* R-Specific Constants */
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#ifndef M_SQRT_3
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#define M_SQRT_3 1.732050807568877293527446341506 /* sqrt(3) */
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#endif
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#ifndef M_SQRT_32
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#define M_SQRT_32 5.656854249492380195206754896838 /* sqrt(32) */
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#endif
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#ifndef M_LOG10_2
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#define M_LOG10_2 0.301029995663981195213738894724 /* log10(2) */
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#endif
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#ifndef M_SQRT_PI
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#define M_SQRT_PI 1.772453850905516027298167483341 /* sqrt(pi) */
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#endif
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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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#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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#ifndef M_LN_SQRT_PI
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#define M_LN_SQRT_PI 0.572364942924700087071713675677 /* log(sqrt(pi)) */
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#endif
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#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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#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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#ifdef MATHLIB_STANDALONE
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typedef enum { FALSE = 0, TRUE } Rboolean;
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#else
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# include <R_ext/Boolean.h>
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/* for API back-compatibility -- DEPRECATED since R 1.2 -- */
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#define LTRUE TRUE
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#define LFALSE FALSE
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#endif
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ripley |
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#ifndef MATHLIB_STANDALONE
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#define bessel_i Rf_bessel_i
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#define bessel_j Rf_bessel_j
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#define bessel_k Rf_bessel_k
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#define bessel_y Rf_bessel_y
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#define beta Rf_beta
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#define choose Rf_choose
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#define dbeta Rf_dbeta
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#define dbinom Rf_dbinom
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#define dcauchy Rf_dcauchy
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#define dchisq Rf_dchisq
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#define dexp Rf_dexp
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#define df Rf_df
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#define dgamma Rf_dgamma
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#define dgeom Rf_dgeom
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#define dhyper Rf_dhyper
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#define digamma Rf_digamma
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#define dlnorm Rf_dlnorm
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#define dlogis Rf_dlogis
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#define dnbeta Rf_dnbeta
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#define dnbinom Rf_dnbinom
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#define dnchisq Rf_dnchisq
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#define dnf Rf_dnf
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#define dnorm4 Rf_dnorm4
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#define dnt Rf_dnt
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#define dpois Rf_dpois
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#define dsignrank Rf_dsignrank
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#define dt Rf_dt
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#define dtukey Rf_dtukey
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#define dunif Rf_dunif
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#define dweibull Rf_dweibull
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#define dwilcox Rf_dwilcox
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#define fmax2 Rf_fmax2
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#define fmin2 Rf_fmin2
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#define fprec Rf_fprec
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#define fround Rf_fround
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#define ftrunc Rf_ftrunc
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#define fsign Rf_fsign
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#define gammafn Rf_gammafn
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#define imax2 Rf_imax2
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#define imin2 Rf_imin2
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#define lbeta Rf_lbeta
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#define lchoose Rf_lchoose
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#define lgammafn Rf_lgammafn
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#define pbeta Rf_pbeta
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#define pbeta_raw Rf_pbeta_raw
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#define pbinom Rf_pbinom
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#define pcauchy Rf_pcauchy
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#define pchisq Rf_pchisq
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#define pentagamma Rf_pentagamma
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#define pexp Rf_pexp
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#define pf Rf_pf
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#define pgamma Rf_pgamma
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#define pgeom Rf_pgeom
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#define phyper Rf_phyper
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#define plnorm Rf_plnorm
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#define plogis Rf_plogis
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#define pnbeta Rf_pnbeta
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#define pnbinom Rf_pnbinom
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#define pnchisq Rf_pnchisq
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#define pnf Rf_pnf
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#define pnorm5 Rf_pnorm5
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#define pnorm_both Rf_pnorm_both
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#define pnt Rf_pnt
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#define ppois Rf_ppois
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#define psignrank Rf_psignrank
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#define pt Rf_pt
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#define ptukey Rf_ptukey
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#define punif Rf_punif
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#define pythag Rf_pythag
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#define pweibull Rf_pweibull
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#define pwilcox Rf_pwilcox
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#define qbeta Rf_qbeta
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#define qbinom Rf_qbinom
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#define qcauchy Rf_qcauchy
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#define qchisq Rf_qchisq
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#define qexp Rf_qexp
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#define qf Rf_qf
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#define qgamma Rf_qgamma
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#define qgeom Rf_qgeom
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#define qhyper Rf_qhyper
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#define qlnorm Rf_qlnorm
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#define qlogis Rf_qlogis
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#define qnbeta Rf_qnbeta
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#define qnbinom Rf_qnbinom
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#define qnchisq Rf_qnchisq
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#define qnf Rf_qnf
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#define qnorm5 Rf_qnorm5
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#define qnt Rf_qnt
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#define qpois Rf_qpois
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#define qsignrank Rf_qsignrank
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#define qt Rf_qt
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#define qtukey Rf_qtukey
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#define qunif Rf_qunif
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#define qweibull Rf_qweibull
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#define qwilcox Rf_qwilcox
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#define rbeta Rf_rbeta
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#define rbinom Rf_rbinom
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#define rcauchy Rf_rcauchy
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#define rchisq Rf_rchisq
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#define rexp Rf_rexp
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#define rf Rf_rf
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#define rgamma Rf_rgamma
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#define rgeom Rf_rgeom
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#define rhyper Rf_rhyper
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#define rlnorm Rf_rlnorm
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#define rlogis Rf_rlogis
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#define rnbeta Rf_rnbeta
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#define rnbinom Rf_rnbinom
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#define rnchisq Rf_rnchisq
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#define rnf Rf_rnf
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#define rnorm Rf_rnorm
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#define rnt Rf_rnt
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#define rpois Rf_rpois
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#define rsignrank Rf_rsignrank
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#define rt Rf_rt
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#define rtukey Rf_rtukey
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#define runif Rf_runif
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#define rweibull Rf_rweibull
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#define rwilcox Rf_rwilcox
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#define sign Rf_sign
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#define tetragamma Rf_tetragamma
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#define trigamma Rf_trigamma
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#endif
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#define rround fround
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#define prec fprec
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#undef trunc
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#define trunc ftrunc
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#ifdef __cplusplus
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extern "C" {
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#endif
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/* R's versions with !R_FINITE checks */
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double R_log(double x);
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double R_pow(double x, double y);
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double R_pow_di(double, int);
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/* Random Number Generators */
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double norm_rand(void);
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double unif_rand(void);
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double exp_rand(void);
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331 |
#ifdef MATHLIB_STANDALONE
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332 |
void set_seed(unsigned int, unsigned int);
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ripley |
333 |
void get_seed(unsigned int *, unsigned int *);
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ripley |
334 |
#endif
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335 |
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336 |
/* Normal Distribution */
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#define pnorm pnorm5
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#define qnorm qnorm5
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340 |
#define dnorm dnorm4
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341 |
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342 |
double dnorm(double, double, double, int);
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343 |
double pnorm(double, double, double, int, int);
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344 |
double qnorm(double, double, double, int, int);
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345 |
double rnorm(double, double);
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void pnorm_both(double, double *, double *, int, int);/* both tails */
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347 |
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348 |
/* Uniform Distribution */
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349 |
|
|
|
350 |
double dunif(double, double, double, int);
|
|
|
351 |
double punif(double, double, double, int, int);
|
|
|
352 |
double qunif(double, double, double, int, int);
|
|
|
353 |
double runif(double, double);
|
|
|
354 |
|
|
|
355 |
/* Gamma Distribution */
|
|
|
356 |
|
|
|
357 |
double dgamma(double, double, double, int);
|
|
|
358 |
double pgamma(double, double, double, int, int);
|
|
|
359 |
double qgamma(double, double, double, int, int);
|
|
|
360 |
double rgamma(double, double);
|
|
|
361 |
|
|
|
362 |
/* Beta Distribution */
|
|
|
363 |
|
|
|
364 |
double dbeta(double, double, double, int);
|
|
|
365 |
double pbeta(double, double, double, int, int);
|
|
|
366 |
double qbeta(double, double, double, int, int);
|
|
|
367 |
double rbeta(double, double);
|
|
|
368 |
double pbeta_raw(double, double, double, int);
|
|
|
369 |
|
|
|
370 |
/* Lognormal Distribution */
|
|
|
371 |
|
|
|
372 |
double dlnorm(double, double, double, int);
|
|
|
373 |
double plnorm(double, double, double, int, int);
|
|
|
374 |
double qlnorm(double, double, double, int, int);
|
|
|
375 |
double rlnorm(double, double);
|
|
|
376 |
|
|
|
377 |
/* Chi-squared Distribution */
|
|
|
378 |
|
|
|
379 |
double dchisq(double, double, int);
|
|
|
380 |
double pchisq(double, double, int, int);
|
|
|
381 |
double qchisq(double, double, int, int);
|
|
|
382 |
double rchisq(double);
|
|
|
383 |
|
|
|
384 |
/* Non-central Chi-squared Distribution */
|
|
|
385 |
|
|
|
386 |
double dnchisq(double, double, double, int);
|
|
|
387 |
double pnchisq(double, double, double, int, int);
|
|
|
388 |
double qnchisq(double, double, double, int, int);
|
|
|
389 |
double rnchisq(double, double);
|
|
|
390 |
|
|
|
391 |
/* F Distibution */
|
|
|
392 |
|
|
|
393 |
double df(double, double, double, int);
|
|
|
394 |
double pf(double, double, double, int, int);
|
|
|
395 |
double qf(double, double, double, int, int);
|
|
|
396 |
double rf(double, double);
|
|
|
397 |
|
|
|
398 |
/* Student t Distibution */
|
|
|
399 |
|
|
|
400 |
double dt(double, double, int);
|
|
|
401 |
double pt(double, double, int, int);
|
|
|
402 |
double qt(double, double, int, int);
|
|
|
403 |
double rt(double);
|
|
|
404 |
|
|
|
405 |
/* Binomial Distribution */
|
|
|
406 |
|
|
|
407 |
double dbinom(double, double, double, int);
|
|
|
408 |
double pbinom(double, double, double, int, int);
|
|
|
409 |
double qbinom(double, double, double, int, int);
|
|
|
410 |
double rbinom(double, double);
|
|
|
411 |
|
| 22959 |
maechler |
412 |
/* Multnomial Distribution */
|
|
|
413 |
|
|
|
414 |
void rmultinom(int, double*, int, int*);
|
|
|
415 |
|
| 22860 |
ripley |
416 |
/* Cauchy Distribution */
|
|
|
417 |
|
|
|
418 |
double dcauchy(double, double, double, int);
|
|
|
419 |
double pcauchy(double, double, double, int, int);
|
|
|
420 |
double qcauchy(double, double, double, int, int);
|
|
|
421 |
double rcauchy(double, double);
|
|
|
422 |
|
|
|
423 |
/* Exponential Distribution */
|
|
|
424 |
|
|
|
425 |
double dexp(double, double, int);
|
|
|
426 |
double pexp(double, double, int, int);
|
|
|
427 |
double qexp(double, double, int, int);
|
|
|
428 |
double rexp(double);
|
|
|
429 |
|
|
|
430 |
/* Geometric Distribution */
|
|
|
431 |
|
|
|
432 |
double dgeom(double, double, int);
|
|
|
433 |
double pgeom(double, double, int, int);
|
|
|
434 |
double qgeom(double, double, int, int);
|
|
|
435 |
double rgeom(double);
|
|
|
436 |
|
|
|
437 |
/* Hypergeometric Distibution */
|
|
|
438 |
|
|
|
439 |
double dhyper(double, double, double, double, int);
|
|
|
440 |
double phyper(double, double, double, double, int, int);
|
|
|
441 |
double qhyper(double, double, double, double, int, int);
|
|
|
442 |
double rhyper(double, double, double);
|
|
|
443 |
|
|
|
444 |
/* Negative Binomial Distribution */
|
|
|
445 |
|
|
|
446 |
double dnbinom(double, double, double, int);
|
|
|
447 |
double pnbinom(double, double, double, int, int);
|
|
|
448 |
double qnbinom(double, double, double, int, int);
|
|
|
449 |
double rnbinom(double, double);
|
|
|
450 |
|
|
|
451 |
/* Poisson Distribution */
|
|
|
452 |
|
|
|
453 |
double dpois(double, double, int);
|
|
|
454 |
double ppois(double, double, int, int);
|
|
|
455 |
double qpois(double, double, int, int);
|
|
|
456 |
double rpois(double);
|
|
|
457 |
|
|
|
458 |
/* Weibull Distribution */
|
|
|
459 |
|
|
|
460 |
double dweibull(double, double, double, int);
|
|
|
461 |
double pweibull(double, double, double, int, int);
|
|
|
462 |
double qweibull(double, double, double, int, int);
|
|
|
463 |
double rweibull(double, double);
|
|
|
464 |
|
|
|
465 |
/* Logistic Distribution */
|
|
|
466 |
|
|
|
467 |
double dlogis(double, double, double, int);
|
|
|
468 |
double plogis(double, double, double, int, int);
|
|
|
469 |
double qlogis(double, double, double, int, int);
|
|
|
470 |
double rlogis(double, double);
|
|
|
471 |
|
|
|
472 |
/* Non-central Beta Distribution */
|
|
|
473 |
|
|
|
474 |
double dnbeta(double, double, double, double, int);
|
|
|
475 |
double pnbeta(double, double, double, double, int, int);
|
|
|
476 |
double qnbeta(double, double, double, double, int, int);
|
|
|
477 |
double rnbeta(double, double, double);
|
|
|
478 |
|
|
|
479 |
/* Non-central F Distribution */
|
|
|
480 |
|
|
|
481 |
double pnf(double, double, double, double, int, int);
|
|
|
482 |
double qnf(double, double, double, double, int, int);
|
|
|
483 |
|
|
|
484 |
/* Non-central Student t Distribution */
|
|
|
485 |
|
| 25788 |
maechler |
486 |
double dnt(double, double, double, int);
|
| 22860 |
ripley |
487 |
double pnt(double, double, double, int, int);
|
|
|
488 |
double qnt(double, double, double, int, int);
|
|
|
489 |
|
|
|
490 |
/* Studentized Range Distribution */
|
|
|
491 |
|
|
|
492 |
double ptukey(double, double, double, double, int, int);
|
|
|
493 |
double qtukey(double, double, double, double, int, int);
|
|
|
494 |
|
|
|
495 |
/* Wilcoxon Rank Sum Distribution */
|
|
|
496 |
|
|
|
497 |
double dwilcox(double, double, double, int);
|
|
|
498 |
double pwilcox(double, double, double, int, int);
|
|
|
499 |
double qwilcox(double, double, double, int, int);
|
|
|
500 |
double rwilcox(double, double);
|
|
|
501 |
|
|
|
502 |
/* Wilcoxon Signed Rank Distribution */
|
|
|
503 |
|
|
|
504 |
double dsignrank(double, double, int);
|
|
|
505 |
double psignrank(double, double, int, int);
|
|
|
506 |
double qsignrank(double, double, int, int);
|
|
|
507 |
double rsignrank(double);
|
|
|
508 |
|
|
|
509 |
/* Gamma and Related Functions */
|
|
|
510 |
double gammafn(double);
|
|
|
511 |
double lgammafn(double);
|
|
|
512 |
double digamma(double);
|
|
|
513 |
double trigamma(double);
|
|
|
514 |
double tetragamma(double);
|
|
|
515 |
double pentagamma(double);
|
|
|
516 |
|
|
|
517 |
double beta(double, double);
|
|
|
518 |
double lbeta(double, double);
|
|
|
519 |
|
|
|
520 |
double choose(double, double);
|
|
|
521 |
double lchoose(double, double);
|
|
|
522 |
|
|
|
523 |
/* Bessel Functions */
|
|
|
524 |
|
|
|
525 |
double bessel_i(double, double, double);
|
|
|
526 |
double bessel_j(double, double);
|
|
|
527 |
double bessel_k(double, double, double);
|
|
|
528 |
double bessel_y(double, double);
|
|
|
529 |
|
|
|
530 |
|
|
|
531 |
/* General Support Functions */
|
|
|
532 |
|
|
|
533 |
double pythag(double, double);
|
|
|
534 |
#ifndef HAVE_EXPM1
|
|
|
535 |
double expm1(double); /* = exp(x)-1 {care for small x} */
|
|
|
536 |
#endif
|
|
|
537 |
#ifndef HAVE_LOG1P
|
|
|
538 |
double log1p(double); /* = log(1+x) {care for small x} */
|
|
|
539 |
#endif
|
|
|
540 |
int imax2(int, int);
|
|
|
541 |
int imin2(int, int);
|
|
|
542 |
double fmax2(double, double);
|
|
|
543 |
double fmin2(double, double);
|
|
|
544 |
double sign(double);
|
|
|
545 |
double fprec(double, double);
|
|
|
546 |
double fround(double, double);
|
|
|
547 |
double fsign(double, double);
|
|
|
548 |
double ftrunc(double);
|
|
|
549 |
|
|
|
550 |
|
|
|
551 |
/* ----------------- Private part of the header file ------------------- */
|
|
|
552 |
|
|
|
553 |
/* old-R Compatibility */
|
|
|
554 |
|
|
|
555 |
#define snorm norm_rand
|
|
|
556 |
#define sunif unif_rand
|
|
|
557 |
#define sexp exp_rand
|
|
|
558 |
|
|
|
559 |
#ifdef MATHLIB_PRIVATE
|
|
|
560 |
#define d1mach Rf_d1mach
|
|
|
561 |
#define gamma_cody Rf_gamma_cody
|
|
|
562 |
|
|
|
563 |
double d1mach(int);
|
|
|
564 |
double gamma_cody(double);
|
|
|
565 |
|
|
|
566 |
#endif /* MATHLIB_PRIVATE */
|
|
|
567 |
|
|
|
568 |
#ifdef MATHLIB_STANDALONE
|
|
|
569 |
#ifndef MATHLIB_PRIVATE_H
|
|
|
570 |
|
| 25128 |
luke |
571 |
#ifdef IEEE_754
|
|
|
572 |
# define ISNAN(x) (isnan(x)!=0)
|
|
|
573 |
#else
|
|
|
574 |
# define ISNAN(x) R_IsNaNorNA(x)
|
|
|
575 |
#endif
|
| 22860 |
ripley |
576 |
#define R_FINITE(x) R_finite(x)
|
|
|
577 |
int R_IsNaNorNA(double);
|
|
|
578 |
int R_finite(double);
|
|
|
579 |
|
|
|
580 |
#ifdef WIN32
|
|
|
581 |
# define NA_REAL (*_imp__NA_REAL)
|
|
|
582 |
# define R_NegInf (*_imp__R_NegInf)
|
|
|
583 |
# define R_PosInf (*_imp__R_PosInf)
|
|
|
584 |
# define N01_kind (*_imp__N01_kind)
|
|
|
585 |
# endif
|
|
|
586 |
|
|
|
587 |
#endif /* not MATHLIB_PRIVATE_H */
|
|
|
588 |
#endif /* MATHLIB_STANDALONE */
|
|
|
589 |
|
|
|
590 |
#ifdef MATHLIB_STANDALONE
|
|
|
591 |
# define REprintf fprintf(stderr,
|
|
|
592 |
#else
|
|
|
593 |
# ifndef PRTUTIL_H_
|
|
|
594 |
void REprintf(char*, ...);
|
|
|
595 |
# endif
|
|
|
596 |
#endif
|
|
|
597 |
|
|
|
598 |
#ifdef __cplusplus
|
|
|
599 |
}
|
|
|
600 |
#endif
|
|
|
601 |
|
|
|
602 |
#endif /* RMATH_H */
|
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