Understanding Floating Point Precision in R

Introduction

Floating point numbers are used to represent decimal values in computers. However, due to the way they are stored and processed, floating point arithmetic can lead to unexpected results when dealing with very large or very small numbers.

In this article, we’ll explore how floating point precision works in R and how to work around the limitations of floating point arithmetic.

What is Floating Point Precision?

Floating point precision refers to the accuracy of a floating point number. When you perform arithmetic operations on floating point numbers, the result is also a floating point number. However, due to the way computers store floating point numbers, there can be small errors in the calculations.

For example, consider the following code:

options(scipen = 999)
x <- 10000000000000000000000000

When you print the value of x, you might expect it to be rounded to a more reasonable value due to floating point magic. However, as we’ll see later, this is not always the case.

The Problem with Rounding Floating Point Numbers

The issue arises when trying to compare floating point numbers for equality. When you use the == operator, R performs a comparison between two floating point numbers using their binary representation, which can lead to incorrect results due to rounding errors.

For example:

x ==  9999999999999998758486016
# [1] FALSE

x ==  9999999999999996611002368
# [1] TRUE

As you can see, even though the numbers look similar, R considers them not equal.

Using Big Integers to Work Around Floating Point Precision Issues

One way to work around this issue is to use big integers instead of floating point numbers. Big integers are whole numbers that can be exactly represented and manipulated without worrying about rounding errors.

In R, you can use the gmp package to work with big integers.

library(gmp)
x <- as.bigz("10000000000000000000000000")

With big integers, you can perform arithmetic operations without worrying about floating point precision issues.

Creating a Faithful dput() Equivalent

The OP is looking for an equivalent of the dput() function that works with any number and returns a string representation of the original value. This would allow them to compare the returned string with the original value using the == operator.

One way to achieve this is by using big integers as mentioned earlier. However, if you want to stick with floating point numbers, you can use the format() function from the utils package in combination with the bigz function from the gmp package.

format(as.bigz("10000000000000000000000000"))

This will return a string representation of the original value.

Using Rmpfr Package

Another option is to use the Rmpfr package, which provides an interface to the GNU Multiple Precision Floating Point Arithmetic Library (GMP). You can install this package using:

install.packages("Rmpfr")

And then use it as follows:

library(Rmpfr)
x <- mpfr("10000000000000000000000000", 50)
format(x)

This will return a string representation of the original value.

Conclusion

Floating point precision issues can be frustrating when working with numbers in R. However, by using big integers or floating point libraries like gmp and Rmpfr, you can work around these issues and achieve more accurate results.

In this article, we’ve explored how floating point precision works in R and how to use different approaches to deal with the limitations of floating point arithmetic. Whether you choose to use big integers or floating point libraries, there are often better alternatives to using built-in functions that rely on floating point precision.

Last modified on 2023-10-01