# Extended floating point precision in R with Rmpfr

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I learnt from a recent post on John Cook’s excellent blog that it’s really easy to do extended floating point computations in R using the `Rmpfr`

package. `Rmpfr`

is R’s wrapper around the C library MPFR, which stands for “**M**ultiple **P**recision **F**loating-point **R**eliable”.

The main function that users will interact with is the `mpfr`

function: it converts numeric values into (typically) high-precision numbers, which can then be used for computation. The function’s first argument is the numeric value(s) to be converted, and the second argument, `precBits`

, represents the maximal precision to be used in numbers of bits. For example, `precBits = 53`

corresponds to double precision.

In his blog post, Cook gives an example of computing to 100 decimal places by multiplying the arctangent of 1 by 4 (recall that , so ):

4 * atan(mpfr(1, 333)) # 1 'mpfr' number of precision 333 bits # [1] 3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706807

* Why does he set the precision to 333 bits?* This link suggests that with bits, we get decimal digits of precision. (Reality for floating point numbers is not quite as straightforward as that: see this for a discussion. But for our purposes, this approximation will do.) Hence, to get 100 decimal places, we need around bits, so he rounds it up to 333 bits.

The first argument to `mpfr`

can be a vector as well:

mpfr(1:10, 5) # 10 'mpfr' numbers of precision 5 bits # [1] 1 2 3 4 5 6 7 8 9 10

As the next code snippet shows, R does NOT consider the output of a call to `mpfr`

a numeric variable.

x <- sin(mpfr(1, 100)) x # 1 'mpfr' number of precision 100 bits # [1] 0.84147098480789650665250232163005 is.numeric(x) # [1] FALSE

We can use the `asNumeric`

function to convert it to a numeric:

y <- asNumeric(x) y # [1] 0.841471 is.numeric(y) # [1] TRUE

** Can we use the more familiar as.numeric instead?** According to the function’s documentation,

`as.numeric`

coerces to both “numeric” and to a vector, whereas `asNumeric()`

should keep dim (and other) attributes. We can see this through a small example:x <- mpfr(matrix(1:4, nrow = 2), 10) x # 'mpfrMatrix' of dim(.) = (2, 2) of precision 10 bits # [,1] [,2] # [1,] 1.0000 3.0000 # [2,] 2.0000 4.0000 asNumeric(x) # [,1] [,2] # [1,] 1 3 # [2,] 2 4 as.numeric(x) # [1] 1 2 3 4

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