Search code examples
rubybinaryinteger64-bitlargenumber

How does Ruby store large numbers?

Ruby can store extremely large numbers. Now that I think about it though, I don't even know how that's possible.

Computers store data in a series of two digits (0s and 1s). This is referred to as binary notation. However, there is a limit to the size of numbers they can store.

Most current Operating Systems these days run at 64 bits. That means the highest allocatable address space for a variable is 64 bits.

Integers are stored in a base 2 system, which means the highest value a computer should be able to store is

1111111111111111111111111111111111111111111111111111111111111111

Since computers can only read 2 possible values, this means the above number can be represented as

2 ^ 64

This means that the highest value an integer can read should be at most 18,446,744,073,709,551,615

I honestly don't even understand how it's possible to store integer values higher than that.

Solution

  • Ruby uses Bignum objects to store number larger than 2^64. You can see here a description of how this works:

    class_diagram

    On the left, you can see RBignum contains an inner structure called RBasic, which contains internal, technical values used by all Ruby objects. Below that I show values specific to Bignum objects: digits and len. digits is a pointer to an array of 32-bit values that contain the actual big integer’s bits grouped into sets of 32. len records how many 32-bit groups are in the digits array. Since there can be any number of groups in the digits array, Ruby can represent arbitrarily large integers using RBignum.