# Really large numbers in R

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This post will discuss ways of handling huge numbers in R using the **gmp** package.

**The gmp package**

The **gmp** package provides us a way of dealing with really large numbers in R. For example, let’s suppose we want to multiple 10^{250} by itself. Mathematically we know the result should be 10^{500}. But if we try this calculation in base R we get Inf for infinity.

num = 10^250 num^2 # Inf

However, we can get around this using the **gmp** package. Here, we can convert the integer 10 to an object of the *bigz* class. This is an implementation that allows us to handle very large numbers. Once we convert an integer to a *bigz* object, we can use it to perform calculations with regular numbers in R (there’s a small caveat coming).

library(gmp) num = as.bigz(10) (num^250) * (num^250) # or directly 10^500 num^500

One note that we need to be careful about is what numbers we use to convert to *bigz* objects. In the example above, we convert the integer 10 to *bigz*. This works fine for our calculations because 10 is not a very large number in itself. However, let’s suppose we had converted 10^{250} to a *bigz* object instead. If we do this, the number 10^{250} becomes a double data type, which causes a loss in precision for such a number. Thus the result we see below isn’t really 10^{250}:

num = 10^250 as.bigz(num) num

A way around this is to input the number we want as a character into *as.bigz*. For example, we know that 10^{250} is the number 1 followed by 250 zeros. We can create a character that represents this number like below:

num = paste0("1", paste(rep("0", 250), collapse = ""))

Thus, we can use this idea to create *bigz* objects:

as.bigz(num)

In case you run into issues with the above line returning an NA value, you might want to try turning scientific notation off. You can do that using the base *options* command.

options(scipen = 999)

If scientific notation is not turned off, you may have cases where the character version of the number looks like below, which results in an NA being returned by *as.bigz*.

**“1e250”**

In general, numbers can be input to **gmp** functions as characters to avoid this or other precision issues.

**Finding the next prime**

The **gmp** package can find the first prime larger than an input number using the *nextprime* function.

num = "100000000000000000000000000000000000000000000000000" nextprime(num)

**Find the GCD of two huge numbers**

We can find the GCD of two large numbers using the *gcd* function:

num = "2452345345234123123178" num2 = "23459023850983290589042" gcd(num, num2) # returns 2

**Factoring numbers into primes**

**gmp** also provides a way to factor numbers into primes. We can do this using the *factorize* function.

num = "2452345345234123123178" factorize(num)

**Matrices of large numbers**

**gmp** also supports creating matrices with *bigz* objects.

num1 <- "1000000000000000000000000000" num2 <- "10000000000000000000000000000000" num3 <- "100000000000000000000000000000000000000" num4 <- "100000000000000000000000000000000000000000000000" nums <- c(as.bigz(num1), as.bigz(num2), as.bigz(num3), as.bigz(num4)) matrix(nums, nrow = 2)

We can also perform typical operations with our matrix, like find its inverse, using base R functions:

solve(m)

**Sampling random (large) numbers uniformly**

We can sample large numbers from a discrete uniform distribution using the *urand.bigz* function.

urand.bigz(nb = 100, size = 5000, seed = 0)

The *nb* parameter represents how many integers we want to sample. Thus, in this example, we’ll get 100 integers returned. *size = 5000* tells the function to sample the integers from the inclusive range of 0 to 2^{5000} – 1. In general you can sample from the range 0 to 2^{size} – 1.

To learn more about **gmp**, click here for its vignette.

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