Rmpfr-package: R MPFR - Multiple Precision Floating-Point Reliable

Description Details Author(s) References See Also Examples

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

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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 Rmpfr (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), http://mpfr.org/

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

and see the vignettes mentioned above.

See Also

The R package gmp for big integer and rational numbers (bigrational) on which Rmpfr now depends.

Examples

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## 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")

Example output

Loading required package: gmp

Attaching package: 'gmp'

The following objects are masked from 'package:base':

    %*%, apply, crossprod, matrix, tcrossprod

C code of R package 'Rmpfr': GMP using 64 bits per limb


Attaching package: 'Rmpfr'

The following objects are masked from 'package:stats':

    dbinom, dnorm, dpois, pnorm

The following objects are masked from 'package:base':

    cbind, pmax, pmin, rbind

1 'mpfr' number of precision  256   bits 
[1] 1.25
9 'mpfr' numbers of precision  256   bits 
[1]                                                             1.25
[2]                                                           1.5625
[3]                                                         1.953125
[4]                                                       2.44140625
[5]                                                     3.0517578125
[6]                                                   3.814697265625
[7]                                                 4.76837158203125
[8]                      86.7361737988403547205962240695953369140625
[9] 807.793566946316088741610050849573099185363389551639556884765625
[1] 807.7935669463161048
1 'mpfr' number of precision  256   bits 
[1] 3.490342957461841376130546029672265482651734398762351622499696738335271802605519
 [1] "abs"      "sign"     "sqrt"     "ceiling"  "floor"    "trunc"   
 [7] "cummax"   "cummin"   "cumprod"  "cumsum"   "exp"      "expm1"   
[13] "log"      "log10"    "log2"     "log1p"    "cos"      "cosh"    
[19] "sin"      "sinh"     "tan"      "tanh"     "acos"     "acosh"   
[25] "asin"     "asinh"    "atan"     "atanh"    "cospi"    "sinpi"   
[31] "tanpi"    "gamma"    "lgamma"   "digamma"  "trigamma"
Function: %*% (package base)
x="Mnumber", y="mpfr"
x="mpfr", y="Mnumber"
x="mpfr", y="mpfr"
x="mpfr", y="mpfrMatrix"
x="mpfrMatrix", y="mpfr"

Function: / (package base)
e1="mpfr", e2="numeric"
    (definition from function "Arith")

Function: Arg (package base)
z="mpfr"

Function: Arith (package base)
e1="array", e2="mpfr"
e1="integer", e2="mpfr"
e1="mpfr", e2="array"
e1="mpfr", e2="integer"
e1="mpfr", e2="missing"
e1="mpfr", e2="mpfr"
e1="mpfr", e2="mpfrArray"
e1="mpfr", e2="numeric"
e1="mpfrArray", e2="mpfr"
e1="numeric", e2="mpfr"

Function: Compare (package methods)
e1="array", e2="mpfr"
e1="integer", e2="mpfr"
e1="mpfr", e2="array"
e1="mpfr", e2="integer"
e1="mpfr", e2="mpfr"
e1="mpfr", e2="mpfrArray"
e1="mpfr", e2="numeric"
e1="mpfrArray", e2="mpfr"
e1="numeric", e2="mpfr"

Function: Conj (package base)
z="mpfr"

Function: Im (package base)
z="mpfr"

Function: Logic (package base)
e1="mpfr", e2="mpfr"
e1="mpfr", e2="numeric"
e1="numeric", e2="mpfr"

Function: Math (package base)
x="mpfr"

Function: Math2 (package methods)
x="mpfr"

Function: Mod (package base)
z="mpfr"

Function: Ops (package base)
e1="array", e2="mpfr"
e1="bigq", e2="mpfr"
e1="bigz", e2="mpfr"
e1="mpfr", e2="array"
e1="mpfr", e2="bigq"
e1="mpfr", e2="bigz"
e1="mpfr", e2="vector"
e1="vector", e2="mpfr"

Function: Re (package base)
z="mpfr"

Function: Summary (package base)
x="mpfr"

Function: [ (package base)
x="mpfr", i="ANY", j="missing", drop="missing"
x="mpfr", i="logical", j="missing", drop="missing"
    (inherited from: x="mpfr", i="ANY", j="missing", drop="missing")

Function: [<- (package base)
x="mpfr", i="ANY", j="missing", value="ANY"
x="mpfr", i="ANY", j="missing", value="mpfr"
x="mpfr", i="missing", j="missing", value="ANY"
x="mpfrArray", i="ANY", j="ANY", value="mpfr"
x="mpfrArray", i="ANY", j="missing", value="mpfr"
x="mpfrArray", i="matrix", j="missing", value="mpfr"
x="mpfrArray", i="missing", j="ANY", value="mpfr"
x="mpfrArray", i="missing", j="missing", value="mpfr"

Function: [[ (package base)
x="mpfr"

Function: ^ (package base)
e1="mpfr", e2="numeric"
    (definition from function "Arith")

Function: abs (package base)
x="mpfr"

Function: all.equal (package base)
target="ANY", current="mpfr"
target="mpfr", current="ANY"
target="mpfr", current="mpfr"

Function: as.integer (package base)
x="mpfr"

Function: as.numeric (package base)
x="mpfr"

Function: asNumeric (package gmp)
x="mpfr"

Function: atan2 (package base)
y="ANY", x="mpfr"
y="mpfr", x="ANY"
y="mpfr", x="mpfr"
y="mpfr", x="numeric"
y="numeric", x="mpfr"

Function: beta (package base)
a="ANY", b="mpfr"
a="mpfr", b="ANY"
a="mpfr", b="mpfr"
a="mpfr", b="numeric"
a="numeric", b="mpfr"

Function: coerce (package methods)
from="array", to="mpfr"
from="bigq", to="mpfr"
from="bigz", to="mpfr"
from="character", to="mpfr"
from="integer", to="mpfr"
from="logical", to="mpfr"
from="mpfr", to="bigz"
from="mpfr", to="character"
from="mpfr", to="integer"
from="mpfr", to="mNumber"
from="mpfr", to="mpfr1"
from="mpfr", to="numeric"
from="mpfr1", to="mpfr"
from="numeric", to="mpfr"
from="raw", to="mpfr"

Function: coerce<- (package methods)
from="mpfr", to="list"

Function: crossprod (package gmp)
x="Mnumber", y="mpfr"
x="mpfr", y="Mnumber"
x="mpfr", y="missing"
x="mpfr", y="mpfr"
x="mpfr", y="mpfrMatrix"
x="mpfrMatrix", y="mpfr"

Function: dim (package base)

Function: dim<- (package base)
x="mpfr"

Function: exp (package base)
x="mpfr"
    (definition from function "Math")

Function: factorial (package base)
x="mpfr"

Function: format (package base)
x="mpfr"

Function: initialize (package methods)
.Object="mpfr"
    (inherited from: .Object="ANY")

Function: is.finite (package base)
x="mpfr"

Function: is.infinite (package base)
x="mpfr"

Function: is.na (package base)
x="mpfr"

Function: is.nan (package base)
x="mpfr"

Function: lbeta (package base)
a="ANY", b="mpfr"
a="mpfr", b="ANY"
a="mpfr", b="mpfr"
a="mpfr", b="numeric"
a="numeric", b="mpfr"

Function: log (package base)
x="mpfr"

Function: mean (package base)
x="mpfr"

Function: median (package stats)
x="mpfr"

Function: quantile (package stats)
x="mpfr"

Function: show (package methods)
object="mpfr"

Function: sign (package base)
x="mpfr"

Function: t (package base)
x="mpfr"

Function: tcrossprod (package gmp)
x="Mnumber", y="mpfr"
x="mpfr", y="Mnumber"
x="mpfr", y="missing"
x="mpfr", y="mpfr"
x="mpfr", y="mpfrMatrix"
x="mpfrMatrix", y="mpfr"

Function: unique (package base)
x="mpfr", incomparables="missing"

Function: which.max (package base)
x="mpfr"

Function: which.min (package base)
x="mpfr"

Function: Arith (package base)
e1="mpfr", e2="mpfrArray"
e1="mpfrArray", e2="mpfr"
e1="mpfrArray", e2="mpfrArray"
e1="mpfrArray", e2="numeric"
e1="numeric", e2="mpfrArray"

Function: Compare (package methods)
e1="mpfr", e2="mpfrArray"
e1="mpfrArray", e2="mpfr"
e1="mpfrArray", e2="numeric"
e1="numeric", e2="mpfrArray"

Function: [ (package base)
x="mpfrArray", i="ANY", j="ANY", drop="ANY"
x="mpfrArray", i="ANY", j="missing", drop="missing"
x="mpfrArray", i="matrix", j="missing", drop="missing"

Function: [<- (package base)
x="mpfrArray", i="ANY", j="ANY", value="ANY"
x="mpfrArray", i="ANY", j="ANY", value="mpfr"
x="mpfrArray", i="ANY", j="missing", value="ANY"
x="mpfrArray", i="ANY", j="missing", value="mpfr"
x="mpfrArray", i="matrix", j="missing", value="ANY"
x="mpfrArray", i="matrix", j="missing", value="mpfr"
x="mpfrArray", i="missing", j="ANY", value="ANY"
x="mpfrArray", i="missing", j="ANY", value="mpfr"
x="mpfrArray", i="missing", j="missing", value="ANY"
x="mpfrArray", i="missing", j="missing", value="mpfr"

Function: aperm (package base)
a="mpfrArray"

Function: apply (package gmp)
X="mpfrArray"

Function: as.vector (package base)
x="mpfrArray"

Function: asNumeric (package gmp)
x="mpfrArray"

Function: atan2 (package base)
y="ANY", x="mpfrArray"
y="mpfrArray", x="ANY"
y="mpfrArray", x="mpfrArray"

Function: beta (package base)
a="ANY", b="mpfrArray"
a="mpfrArray", b="ANY"
a="mpfrArray", b="mpfrArray"

Function: coerce (package methods)
from="mpfrArray", to="array"
from="mpfrArray", to="matrix"
from="mpfrArray", to="vector"

Function: coerce<- (package methods)
from="mpfrArray", to="vector"

Function: colMeans (package base)
x="mpfrArray"

Function: colSums (package base)
x="mpfrArray"

Function: dim (package base)
x="mpfrArray"

Function: dimnames (package base)
x="mpfrArray"

Function: dimnames<- (package base)
x="mpfrArray"

Function: initialize (package methods)
.Object="mpfrArray"

Function: is.finite (package base)
x="mpfrArray"

Function: is.infinite (package base)
x="mpfrArray"

Function: is.na (package base)
x="mpfrArray"

Function: is.nan (package base)
x="mpfrArray"

Function: lbeta (package base)
a="ANY", b="mpfrArray"
a="mpfrArray", b="ANY"
a="mpfrArray", b="mpfrArray"

Function: rowMeans (package base)
x="mpfrArray"

Function: rowSums (package base)
x="mpfrArray"

Function: show (package methods)
object="mpfrArray"

Function: sign (package base)
x="mpfrArray"

Rmpfr documentation built on Aug. 19, 2018, 3 a.m.