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.

Arguments

Author

Martin Maechler

Details

tools:::Rd_package_DESCRIPTION("Rmpfr") tools:::Rd_package_indices("Rmpfr")

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)

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

Run this code

## 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")