x86-64 Big Integer Representation?

Question

How do hig-performance native big-integer libraries on x86-64 represent a big integer in memory? (or does it vary? Is there a most common way?)

Naively I was think

Answer 1

I would think it would be as an array lowest value to highest. I implemented addition of arbitrary sized numbers in assembler. The CPU provides the carry flag that allows you to easily perform these sorts of operations. You write a loop that performs the operation in byte size chunks. The carry flag is included in the next operation using the "Add with carry" instruction (ADC opcode).