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

```
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)

precBits, prec

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

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.

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`

.

The `"'>mpfr"`

method of `mpfr()`

is a simple
wrapper around `roundMpfr()`

.

MPFR supports the following rounding modes,

- GMP_RND
**N**: round to

**n**earest (roundTiesToEven in IEEE 754-2008).- GMP_RND
**Z**: round toward

**z**ero (roundTowardZero in IEEE 754-2008).- GMP_RND
**U**: round toward plus infinity (“Up”, roundTowardPositive in IEEE 754-2008).

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

- GMP_RND
**A**: round

**a**way 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.

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`

").

# 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) head(Z, 40) ## 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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