Rmpfr: Rmpfr-package – R documentation

Become an expert in R — Interactive courses, Cheat Sheets, certificates and more!

Rmpfr-package

R MPFR - Multiple Precision Floating-Point Reliable

Description

Rmpfr provides S4 classes and methods for arithmetic including transcendental ("special") functions for arbitrary precision floating point numbers, here often called “mpfr - numbers”. To this end, it interfaces to the LGPL'ed MPFR (Multiple Precision Floating-Point Reliable) Library which itself is based on the GMP (GNU Multiple Precision) Library.

Details

Package:	Rmpfr
Title:	R MPFR - Multiple Precision Floating-Point Reliable
Version:	0.8-4
Date:	2021-04-08
DateNote:	Previous CRAN version 0.8-3 on 2021-03-23
Type:	Package
Authors@R:	c(person("Martin","Maechler", role = c("aut","cre"), email = "maechler@stat.math.ethz.ch", comment = c(ORCID="0000-0002-8685-9910")) , person(c("Richard", "M."), "Heiberger", role = "ctb", email="rmh@temple.edu", comment = "formatHex(), Bin, Dec") , person(c("John", "C."), "Nash", role = "ctb", email="nashjc@uottawa.ca", comment = "hjkMpfr(), origin of unirootR()") , person(c("Hans", "W."), "Borchers", role = "ctb", email="hwborchers@googlemail.com", comment = "optimizeR(*, \"GoldenRatio\"); origin of hjkMpfr()") )
Description:	Arithmetic (via S4 classes and methods) for arbitrary precision floating point numbers, including transcendental ("special") functions. To this end, the package interfaces to the 'LGPL' licensed 'MPFR' (Multiple Precision Floating-Point Reliable) Library which itself is based on the 'GMP' (GNU Multiple Precision) Library.
SystemRequirements:	gmp (>= 4.2.3), mpfr (>= 3.0.0), pdfcrop (part of TexLive) is required to rebuild the vignettes.
SystemRequirementsNote:	'MPFR' (MP Floating-Point Reliable Library, https://www.mpfr.org/) and 'GMP' (GNU Multiple Precision library, https://gmplib.org/), see >> README.md
Depends:	gmp (>= 0.6-1), R (>= 3.5.0)
Imports:	stats, utils, methods
Suggests:	MASS, Bessel, polynom, sfsmisc (>= 1.0-20), Matrix
SuggestsNote:	MASS, polynom, sfsmisc: only for vignette; Matrix: test-tools
Enhances:	dfoptim, pracma
EnhancesNote:	mentioned in Rd xrefs
URL:	https://rmpfr.r-forge.r-project.org/
BugReports:	https://r-forge.r-project.org/tracker/?group_id=386
License:	GPL (>= 2)
Encoding:	UTF-8
Author:	Martin Maechler [aut, cre] (<https://orcid.org/0000-0002-8685-9910>), Richard M. Heiberger [ctb] (formatHex(), Bin, Dec), John C. Nash [ctb] (hjkMpfr(), origin of unirootR()), Hans W. Borchers [ctb] (optimizeR(*, "GoldenRatio"); origin of hjkMpfr())
Maintainer:	Martin Maechler <maechler@stat.math.ethz.ch>

Index of help topics:

.bigq2mpfr              Conversion Utilities gmp <-> Rmpfr
Bernoulli               Bernoulli Numbers in Arbitrary Precision
Bessel_mpfr             Bessel functions of Integer Order in multiple
                        precisions
Mnumber-class           Class "Mnumber" and "mNumber" of "mpfr" and
                        regular numbers and arrays from them
Rmpfr-package           R MPFR - Multiple Precision Floating-Point
                        Reliable
array_or_vector-class   Auxiliary Class "array\_or\_vector"
asNumeric-methods       Methods for 'asNumeric(<mpfr>)'
atomicVector-class      Virtual Class "atomicVector" of Atomic Vectors
c.mpfr                  MPFR Number Utilities
cbind                   "mpfr" '...' - Methods for Functions cbind(),
                        rbind()
chooseMpfr              Binomial Coefficients and Pochhammer Symbol aka
                        Rising Factorial
determinant.mpfrMatrix
                        Functions for mpfrMatrix Objects
factorialMpfr           Factorial 'n!'  in Arbitrary Precision
formatHex               Flexibly Format Numbers in Binary, Hex and
                        Decimal Format
formatMpfr              Formatting MPFR (multiprecision) Numbers
getPrec                 Rmpfr - Utilities for Precision Setting,
                        Printing, etc
hjkMpfr                 Hooke-Jeeves Derivative-Free Minimization R
                        (working for MPFR)
igamma                  Incomplete Gamma Function
integrateR              One-Dimensional Numerical Integration - in pure
                        R
is.whole.mpfr           Whole ("Integer") Numbers
log1mexp                Compute f(a) = log(1 +/- exp(-a)) Numerically
                        Optimally
matmult                 (MPFR) Matrix (Vector) Multiplication
mpfr                    Create "mpfr" Numbers (Objects)
mpfr-class              Class "mpfr" of Multiple Precision Floating
                        Point Numbers
mpfrArray               Construct "mpfrArray" almost as by 'array()'
mpfrMatrix-class        Classes "mpfrMatrix" and "mpfrArray"
optimizeR               High Precision One-Dimensional Optimization
outer                   Base Functions etc, as an Rmpfr version
pbetaI                  Accurate Incomplete Beta / Beta Probabilities
                        For Integer Shapes
pmax                    Parallel Maxima and Minima
pnorm                   Distribution Functions etc (MPFR)
roundMpfr               Rounding to Binary bits, "mpfr-internally"
sapplyMpfr              Apply a Function over a "mpfr" Vector
seqMpfr                 "mpfr" Sequence Generation
str.mpfr                Compactly Show STRucture of Rmpfr Number Object
sumBinomMpfr            (Alternating) Binomial Sums via Rmpfr
unirootR                One Dimensional Root (Zero) Finding - in pure R
zeta                    Special Mathematical Functions (MPFR)

Further information is available in the following vignettes:

`Maechler_useR_2011-abstr`	useR-2011-abstract (source)
`Rmpfr-pkg`	Arbitrarily Accurate Computation with R Package Rmpfr (source)
`log1mexp-note`	Accurately Computing log(1 - exp(.)) -- Assessed by Rmpfr (source)

The following (help pages) index does not really mention that we provide many methods for mathematical functions, including gamma, digamma, etc, namely, all of R's (S4) Math group (with the only exception of trigamma), see the list in the examples. Additionally also pnorm, the “error function”, and more, see the list in zeta, and further note the first vignette (below).

Partial index:

`mpfr`	Create "mpfr" Numbers (Objects)
`mpfrArray`	Construct "mpfrArray" almost as by `array()`
`mpfr-class`	Class "mpfr" of Multiple Precision Floating Point Numbers
`mpfrMatrix-class`	Classes "mpfrMatrix" and "mpfrArray"

`Bernoulli`	Bernoulli Numbers in Arbitrary Precision
`Bessel_mpfr`	Bessel functions of Integer Order in multiple precisions
`c.mpfr`	MPFR Number Utilities
`cbind`	"mpfr" `...` - Methods for Functions cbind(), rbind()
`chooseMpfr`	Binomial Coefficients and Pochhammer Symbol aka
	Rising Factorial
`factorialMpfr`	Factorial 'n!' in Arbitrary Precision
`formatMpfr`	Formatting MPFR (multiprecision) Numbers
`getPrec`	Rmpfr - Utilities for Precision Setting, Printing, etc
`roundMpfr`	Rounding to Binary bits, "mpfr-internally"
`seqMpfr`	"mpfr" Sequence Generation
`sumBinomMpfr`	(Alternating) Binomial Sums via Rmpfr
`zeta`	Special Mathematical Functions (MPFR)

`integrateR`	One-Dimensional Numerical Integration - in pure R
`unirootR`	One Dimensional Root (Zero) Finding - in pure R
`optimizeR`	High Precisione One-Dimensional Optimization
`hjkMpfr`	Hooke-Jeeves Derivative-Free Minimization R (working for MPFR)

Further information is available in the following vignettes:

`Rmpfr-pkg`	Arbitrarily Accurate Computation with R: The 'Rmpfr' package (source, pdf)
`log1mexp-note`	Acccurately Computing log(1 - exp(.)) -- Assessed by Rmpfr (source, pdf)

Author(s)

Martin Maechler

References

MPFR (MP Floating-Point Reliable Library), https://www.mpfr.org/

GMP (GNU Multiple Precision library), https://gmplib.org/

and see the vignettes mentioned above.

Examples

## Using  "mpfr" numbers instead of regular numbers...
n1.25 <- mpfr(5, precBits = 256)/4
n1.25

## and then "everything" just works with the desired chosen precision:hig
n1.25 ^ c(1:7, 20, 30) ## fully precise; compare with
print(1.25 ^ 30, digits=19)

exp(n1.25)

## Show all math functions which work with "MPFR" numbers (1 exception: trigamma)
getGroupMembers("Math")

## We provide *many* arithmetic, special function, and other methods:
showMethods(classes = "mpfr")
showMethods(classes = "mpfrArray")

Rmpfr

R MPFR - Multiple Precision Floating-Point Reliable

v0.8-4

GPL (>= 2)

Authors

Martin Maechler [aut, cre] (<https://orcid.org/0000-0002-8685-9910>), Richard M. Heiberger [ctb] (formatHex(), *Bin, *Dec), John C. Nash [ctb] (hjkMpfr(), origin of unirootR()), Hans W. Borchers [ctb] (optimizeR(*, "GoldenRatio"); origin of hjkMpfr())

Initial release

2021-04-08