Rmpfr (version 0.8-2)

# mpfr: Create "mpfr" Numbers (Objects)

## Description

Create multiple (i.e. typically high) precision numbers, to be used in arithmetic and mathematical computations with R.

## Usage

mpfr(x, precBits, …)
# S3 method for default
mpfr(x, precBits, base = 10,
rnd.mode = c("N","D","U","Z","A"), scientific = NA, …)Const(name = c("pi", "gamma", "catalan", "log2"), prec = 120L,
rnd.mode = c("N","D","U","Z","A"))is.mpfr(x)

## Arguments

x

a numeric, '>mpfr, bigz, bigq, or character vector or array.

precBits, prec

a number, the maximal precision to be used, in bits; i.e. 53 corresponds to double precision. Must be at least 2. If missing, getPrec(x) determines a default precision.

base

(only when x is character) the base with respect to which x[i] represent numbers; base $$b$$ must fulfill $$2 \le b \le 62$$.

rnd.mode

a 1-letter string specifying how rounding should happen at C-level conversion to MPFR, see details.

scientific

(used only when x is the result of formatBin(), i.e., of class "Bcharacter":) logical indicating that the binary representation of x is in scientific notation. When TRUE, mpfr() will substitute 0 for _; when NA, mpfr() will guess, and use TRUE when finding a "p" in x; see also formatBin.

name

a string specifying the mpfrlib - internal constant computation. "gamma" is Euler's gamma $$(\gamma)$$, and "catalan" Catalan's constant.

potentially further arguments passed to and from methods.

## Value

an object of (S4) class '>mpfr, or for mpfr(x) when x is an array, '>mpfrMatrix, or '>mpfrArray which the user should just as a normal numeric vector or array.

is.mpfr() returns TRUE or FALSE.

## Details

The "'>mpfr" method of mpfr() is a simple wrapper around roundMpfr().

MPFR supports the following rounding modes,

GMP_RNDN:

round to nearest (roundTiesToEven in IEEE 754-2008).

GMP_RNDZ:

round toward zero (roundTowardZero in IEEE 754-2008).

GMP_RNDU:

round toward plus infinity (“Up”, roundTowardPositive in IEEE 754-2008).

GMP_RNDD:

round toward minus infinity (“Down”, roundTowardNegative in IEEE 754-2008).

GMP_RNDA:

round away from zero (new since MPFR 3.0.0).

The ‘round to nearest’ ("N") mode, the default here, works as in the IEEE 754 standard: in case the number to be rounded lies exactly in the middle of two representable numbers, it is rounded to the one with the least significant bit set to zero. For example, the number 5/2, which is represented by (10.1) in binary, is rounded to (10.0)=2 with a precision of two bits, and not to (11.0)=3. This rule avoids the "drift" phenomenon mentioned by Knuth in volume 2 of The Art of Computer Programming (Section 4.2.2).

When x is character, mpfr() will detect the precision of the input object.

## References

The MPFR team. (201x). GNU MPFR -- The Multiple Precision Floating-Point Reliable Library; see https://www.mpfr.org/mpfr-current/#doc or directly https://www.mpfr.org/mpfr-current/mpfr.pdf.

The class documentation '>mpfr contains more details. Use asNumeric to transform back to double precision ("numeric").

## Examples

Run this code
# NOT RUN {
mpfr(pi, 120) ## the double-precision pi "translated" to 120-bit precision

pi. <- Const("pi", prec = 260) # pi "computed" to correct 260-bit precision
pi. # nicely prints 80 digits [260 * log10(2) ~= 78.3 ~ 80]

Const("gamma",   128L) # 0.5772...
Const("catalan", 128L) # 0.9159...

x <- mpfr(0:7, 100)/7 # a more precise version of  k/7, k=0,..,7
x
1 / x

## character input :
mpfr("2.718281828459045235360287471352662497757") - exp(mpfr(1, 150))
## ~= -4 * 10^-40
## Also works for  NA, NaN, ... :
cx <- c("1234567890123456", 345, "NA", "NaN", "Inf", "-Inf")
mpfr(cx)

## with some 'base' choices :
print(mpfr("111.1111", base=2)) * 2^4

mpfr("af21.01020300a0b0c", base=16)
##  68 bit prec.  44833.00393694653820642

mpfr("ugi0", base = 32) == 10^6   ## TRUE

## --- Large integers from package 'gmp':
Z <- as.bigz(7)^(1:200)
## mfpr(Z) by default chooses the correct *maximal* default precision:
mZ. <- mpfr(Z)
## more efficiently chooses precision individually
m.Z <- mpfr(Z, precBits = frexpZ(Z)\$exp)
## the precBits chosen are large enough to keep full precision:
stopifnot(identical(cZ <- as.character(Z),
as(mZ.,"character")),
identical(cZ, as(m.Z,"character")))

## compare mpfr-arithmetic with exact rational one:
stopifnot(all.equal(mpfr(as.bigq(355,113), 99),
mpfr(355, 99) / 113,	tol = 2^-98))

## look at different "rounding modes":
sapply(c("N", "D","U","Z","A"), function(RND)
mpfr(c(-1,1)/5, 20, rnd.mode = RND), simplify=FALSE)

symnum(sapply(c("N", "D","U","Z","A"),
function(RND) mpfr(0.2, prec = 5:15, rnd.mode = RND) < 0.2 ))
# }


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