| Rmpfr-package {Rmpfr} | R Documentation |
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: | 0.9-5 |
| Date: | 2024-01-20 |
| DateNote: | Previous CRAN version 0.9-4 on 2023-12-04 |
| 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 (>= 3.6.0) |
| Imports: | stats, utils, methods |
| Suggests: | MASS, Bessel, polynom, sfsmisc (>= 1.1-14) |
| SuggestsNote: | MASS, polynom, sfsmisc: only for vignette; |
| Enhances: | dfoptim, pracma, DPQ |
| EnhancesNote: | mentioned in Rd xrefs | used in example |
| 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
frexpMpfr Base-2 Representation and Multiplication of
Mpfr 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 with MPFR Arithmetic
qnormI Gaussian / Normal Quantiles 'qnorm()' via
Inversion
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.
See Also
The R package gmp for big integer gmp
and rational numbers (bigrational) on which Rmpfr
depends.
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")
[Package Rmpfr version 0.9-5 Index]