| 3279 |
pd |
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/*
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* Mathlib : A C Library of Special Functions
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pd |
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* Copyright (C) 1998 R Development Core Team
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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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* Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
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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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ihaka |
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#ifndef MATHLIB_H
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#define MATHLIB_H
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r |
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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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r |
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#include "Arith.h"
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pd |
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#include "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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ihaka |
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#include <errno.h>
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hornik |
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#include <limits.h>
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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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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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#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_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 /* 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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maechler |
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#define M_1_SQRT_2 0.707106781186547524400844362105 /* 1/sqrt(2) */
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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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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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maechler |
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#endif
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r |
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#ifndef M_PI_half
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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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ihaka |
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#define M_SQRT_PI 1.772453850905516027298167483341 /* sqrt(pi) */
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r |
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#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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maechler |
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#ifndef M_LN_SQRT_PI
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ihaka |
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#define M_LN_SQRT_PI 0.572364942924700087071713675677 /* log(sqrt(pi)) */
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r |
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#endif
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ihaka |
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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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maechler |
148 |
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ihaka |
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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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pd |
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#ifdef MATHLIB_IN_R/* Mathlib in R */
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maechler |
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pd |
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#include "Error.h"
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# 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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pd |
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#else/* Mathlib standalone */
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#include <stdio.h>
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pd |
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# define MATHLIB_ERROR(fmt,x) { printf(fmt,x); exit(1) }
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pd |
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# 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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ihaka |
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#define ME_NONE 0
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pd |
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/* no error */
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ihaka |
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#define ME_DOMAIN 1
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pd |
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/* argument out of domain */
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ihaka |
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#define ME_RANGE 2
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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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ihaka |
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#ifdef IEEE_754
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pd |
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pd |
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# 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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ihaka |
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ihaka |
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extern double m_zero;
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extern double m_one;
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ihaka |
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/* extern double m_tiny; */
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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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ihaka |
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#define ML_UNDERFLOW (DBL_MIN * DBL_MIN)
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maechler |
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#define ML_VALID(x) (!isnan(x))
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pd |
206 |
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#else/*--- NO IEEE: No +/-Inf, NAN,... ---*/
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ihaka |
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#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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maechler |
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#define ML_VALID(x) (errno == 0)
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r |
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#endif
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ihaka |
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/* Splus Compatibility */
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r |
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ihaka |
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#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 |
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ihaka |
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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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ihaka |
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/* Name Hiding to Avoid Clashes with Fortran */
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r |
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ihaka |
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#ifdef HIDE_NAMES
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pd |
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# define d1mach c_d1mach
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# define i1mach c_i1mach
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ihaka |
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#endif
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r |
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ihaka |
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#define rround fround
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#define prec fprec
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ihaka |
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#undef trunc
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ihaka |
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#define trunc ftrunc
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r |
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ihaka |
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/* Machine Characteristics */
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r |
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ihaka |
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double d1mach(int);
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double d1mach_(int*);
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int i1mach(int);
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int i1mach_(int*);
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r |
249 |
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ihaka |
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/* General Support Functions */
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r |
251 |
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ihaka |
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int imax2(int, int);
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int imin2(int, int);
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double fmax2(double, double);
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double fmin2(double, double);
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double fmod(double, double);
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double fprec(double, double);
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double fround(double, double);
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double ftrunc(double);
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pd |
260 |
double sign(double);
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ihaka |
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double fsign(double, double);
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double fsquare(double);
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double fcube(double);
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r |
264 |
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ihaka |
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/* Random Number Generators */
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r |
266 |
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ihaka |
267 |
double snorm(void);
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double sunif(void);
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double sexp(void);
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r |
270 |
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ihaka |
271 |
/* Chebyshev Series */
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r |
272 |
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ihaka |
273 |
int chebyshev_init(double*, int, double);
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274 |
double chebyshev_eval(double, double *, int);
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| 2 |
r |
275 |
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ihaka |
276 |
/* Gamma and Related Functions */
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r |
277 |
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ihaka |
278 |
double logrelerr(double);
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279 |
void gammalims(double*, double*);
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280 |
double lgammacor(double);
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maechler |
281 |
double gammafn(double);
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maechler |
282 |
double gamma_cody(double);
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| 2278 |
maechler |
283 |
double lgammafn(double);
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| 571 |
ihaka |
284 |
void dpsifn(double, int, int, int, double*, int*, int*);
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285 |
double digamma(double);
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286 |
double trigamma(double);
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287 |
double tetragamma(double);
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288 |
double pentagamma(double);
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| 2 |
r |
289 |
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ihaka |
290 |
double choose(double, double);
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291 |
double lchoose(double, double);
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292 |
double fastchoose(double, double);
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293 |
double lfastchoose(double, double);
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| 2 |
r |
294 |
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| 2629 |
maechler |
295 |
/* Bessel Functions of All Kinds */
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296 |
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| 3786 |
pd |
297 |
double bessel_i(double, double, double);
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298 |
double bessel_j(double, double);
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299 |
double bessel_k(double, double, double);
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300 |
double bessel_y(double, double);
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301 |
void I_bessel(double*, double*, long*, long*, double*, long*);
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302 |
void J_bessel(double*, double*, long*, double*, long*);
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303 |
void K_bessel(double*, double*, long*, long*, double*, long*);
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304 |
void Y_bessel(double*, double*, long*, double*, long*);
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| 2629 |
maechler |
305 |
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| 571 |
ihaka |
306 |
/* Beta and Related Functions */
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| 2 |
r |
307 |
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ihaka |
308 |
double beta(double, double);
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309 |
double lbeta(double, double);
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| 2 |
r |
310 |
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ihaka |
311 |
/* Normal Distribution */
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| 2 |
r |
312 |
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ihaka |
313 |
double dnorm(double, double, double);
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314 |
double pnorm(double, double, double);
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315 |
double qnorm(double, double, double);
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316 |
double rnorm(double, double);
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| 2 |
r |
317 |
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| 571 |
ihaka |
318 |
/* Uniform Distribution */
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| 2 |
r |
319 |
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| 571 |
ihaka |
320 |
double dunif(double, double, double);
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321 |
double punif(double, double, double);
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322 |
double qunif(double, double, double);
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323 |
double runif(double, double);
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| 2 |
r |
324 |
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| 571 |
ihaka |
325 |
/* Gamma Distribution */
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| 2 |
r |
326 |
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| 571 |
ihaka |
327 |
double dgamma(double, double, double);
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328 |
double pgamma(double, double, double);
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329 |
double qgamma(double, double, double);
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330 |
double rgamma(double, double);
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| 2 |
r |
331 |
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| 571 |
ihaka |
332 |
/* Beta Distribution */
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| 2 |
r |
333 |
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| 571 |
ihaka |
334 |
double dbeta(double, double, double);
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335 |
double pbeta(double, double, double);
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|
336 |
double pbeta_raw(double, double, double);
|
|
|
337 |
double qbeta(double, double, double);
|
|
|
338 |
double rbeta(double, double);
|
| 2 |
r |
339 |
|
| 571 |
ihaka |
340 |
/* Lognormal Distribution */
|
| 2 |
r |
341 |
|
| 571 |
ihaka |
342 |
double dlnorm(double, double, double);
|
|
|
343 |
double plnorm(double, double, double);
|
|
|
344 |
double qlnorm(double, double, double);
|
|
|
345 |
double rlnorm(double, double);
|
| 2 |
r |
346 |
|
| 571 |
ihaka |
347 |
/* Chi-squared Distribution */
|
| 2 |
r |
348 |
|
| 571 |
ihaka |
349 |
double dchisq(double, double);
|
|
|
350 |
double pchisq(double, double);
|
|
|
351 |
double qchisq(double, double);
|
|
|
352 |
double rchisq(double);
|
| 2 |
r |
353 |
|
| 571 |
ihaka |
354 |
/* Non-central Chi-squared Distribution */
|
| 2 |
r |
355 |
|
| 605 |
ihaka |
356 |
double dnchisq(double, double, double);
|
| 571 |
ihaka |
357 |
double pnchisq(double, double, double);
|
|
|
358 |
double qnchisq(double, double, double);
|
| 605 |
ihaka |
359 |
double rnchisq(double, double);
|
| 571 |
ihaka |
360 |
|
|
|
361 |
/* F Distibution */
|
|
|
362 |
|
|
|
363 |
double df(double, double, double);
|
|
|
364 |
double pf(double, double, double);
|
|
|
365 |
double qf(double, double, double);
|
|
|
366 |
double rf(double, double);
|
|
|
367 |
|
|
|
368 |
/* Student t Distibution */
|
|
|
369 |
|
|
|
370 |
double dt(double, double);
|
|
|
371 |
double pt(double, double);
|
|
|
372 |
double qt(double, double);
|
|
|
373 |
double rt(double);
|
|
|
374 |
|
|
|
375 |
/* Binomial Distribution */
|
|
|
376 |
|
|
|
377 |
double dbinom(double, double, double);
|
|
|
378 |
double pbinom(double, double, double);
|
|
|
379 |
double qbinom(double, double, double);
|
|
|
380 |
double rbinom(double, double);
|
|
|
381 |
|
|
|
382 |
/* Cauchy Distribution */
|
|
|
383 |
|
|
|
384 |
double dcauchy(double, double, double);
|
|
|
385 |
double pcauchy(double, double, double);
|
|
|
386 |
double qcauchy(double, double, double);
|
|
|
387 |
double rcauchy(double, double);
|
|
|
388 |
|
|
|
389 |
/* Exponential Distribution */
|
|
|
390 |
|
|
|
391 |
double dexp(double, double);
|
|
|
392 |
double pexp(double, double);
|
|
|
393 |
double qexp(double, double);
|
|
|
394 |
double rexp(double);
|
|
|
395 |
|
|
|
396 |
/* Geometric Distribution */
|
|
|
397 |
|
|
|
398 |
double dgeom(double, double);
|
|
|
399 |
double pgeom(double, double);
|
|
|
400 |
double qgeom(double, double);
|
|
|
401 |
double rgeom(double);
|
|
|
402 |
|
|
|
403 |
/* Hypergeometric Distibution */
|
|
|
404 |
|
|
|
405 |
double dhyper(double, double, double, double);
|
|
|
406 |
double phyper(double, double, double, double);
|
|
|
407 |
double qhyper(double, double, double, double);
|
|
|
408 |
double rhyper(double, double, double);
|
|
|
409 |
|
|
|
410 |
/* Negative Binomial Distribution */
|
|
|
411 |
|
|
|
412 |
double dnbinom(double, double, double);
|
|
|
413 |
double pnbinom(double, double, double);
|
|
|
414 |
double qnbinom(double, double, double);
|
|
|
415 |
double rnbinom(double, double);
|
|
|
416 |
|
|
|
417 |
/* Poisson Distribution */
|
|
|
418 |
|
|
|
419 |
double dpois(double, double);
|
|
|
420 |
double ppois(double, double);
|
|
|
421 |
double qpois(double, double);
|
|
|
422 |
double rpois(double);
|
|
|
423 |
|
|
|
424 |
/* Weibull Distribution */
|
|
|
425 |
|
|
|
426 |
double dweibull(double, double, double);
|
|
|
427 |
double pweibull(double, double, double);
|
|
|
428 |
double qweibull(double, double, double);
|
|
|
429 |
double rweibull(double, double);
|
|
|
430 |
|
|
|
431 |
/* Logistic Distribution */
|
|
|
432 |
|
|
|
433 |
double dlogis(double, double, double);
|
|
|
434 |
double plogis(double, double, double);
|
|
|
435 |
double qlogis(double, double, double);
|
|
|
436 |
double rlogis(double, double);
|
|
|
437 |
|
| 602 |
ihaka |
438 |
/* Non-central Beta Distribution */
|
|
|
439 |
|
|
|
440 |
double dnbeta(double, double, double, double);
|
|
|
441 |
double pnbeta(double, double, double, double);
|
|
|
442 |
double qnbeta(double, double, double, double);
|
|
|
443 |
double rnbeta(double, double, double);
|
|
|
444 |
|
|
|
445 |
/* Non-central F Distribution */
|
|
|
446 |
|
|
|
447 |
double dnf(double, double, double, double);
|
|
|
448 |
double pnf(double, double, double, double);
|
|
|
449 |
double qnf(double, double, double, double);
|
|
|
450 |
double rnf(double, double, double);
|
|
|
451 |
|
|
|
452 |
/* Non-central Student t Distribution */
|
|
|
453 |
|
|
|
454 |
double dnt(double, double, double);
|
|
|
455 |
double pnt(double, double, double);
|
|
|
456 |
double qnt(double, double, double);
|
|
|
457 |
double rnt(double, double);
|
|
|
458 |
|
| 624 |
ihaka |
459 |
/* Studentized Range Distribution */
|
|
|
460 |
|
|
|
461 |
double dtukey(double, double, double, double);
|
|
|
462 |
double ptukey(double, double, double, double);
|
|
|
463 |
double qtukey(double, double, double, double);
|
|
|
464 |
double rtukey(double, double, double);
|
|
|
465 |
|
| 2235 |
hornik |
466 |
/* Wilcoxon Rank Sum Distribution */
|
| 1276 |
hornik |
467 |
|
| 3865 |
pd |
468 |
#define WILCOX_MAX 50
|
| 1276 |
hornik |
469 |
double dwilcox(double, double, double);
|
|
|
470 |
double pwilcox(double, double, double);
|
|
|
471 |
double qwilcox(double, double, double);
|
|
|
472 |
double rwilcox(double, double);
|
|
|
473 |
|
| 2235 |
hornik |
474 |
/* Wilcoxon Signed Rank Distribution */
|
|
|
475 |
|
| 3865 |
pd |
476 |
#define SIGNRANK_MAX 50
|
| 2235 |
hornik |
477 |
double dsignrank(double, double);
|
|
|
478 |
double psignrank(double, double);
|
|
|
479 |
double qsignrank(double, double);
|
|
|
480 |
double rsignrank(double);
|
|
|
481 |
|
| 2 |
r |
482 |
#endif
|
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