math - 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 thinking about storing them as 0-terminated strings of numbers in base 2⁶⁴.

For example suppose X is in memory as:

[8 bytes] Dn
.
.
[8 bytes] D2
[8 bytes] D1
[8 bytes] D0
[8 bytes] 0

Let B = 2⁶⁴

Then

X = D_n * Bⁿ + ... + D₂ * B² + D₁ * B¹ + D₀

The empty string (i.e. 8 bytes of zero) means zero.

Is this a reasonable way? What are the pros and cons of this way? Is there a better way?

How would you handle signedness? Does 2's complement work with this variable length value?

(Found this: http://gmplib.org/manual/Integer-Internals.html Whats a limb?)

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).