What are the x86-64 memory addressing modes?

A memory operand has the general form D(Rb, Ri, S), computing the address Rb + Ri×S + D — base register, scaled index register, and a constant displacement.

* The effective address is base + index x scale + displacement; the scale (1/2/4/8) equals the element size, and the index can be any register except %rsp. *

This one flexible form is what lets a single instruction reach an array element, a struct field, or a stack slot. You use whichever pieces you need:

The scale S can only be 1, 2, 4, or 8 — not by accident, but because those are exactly the sizes of the primitive data types, so array[i] for any type maps onto one addressing mode. The index register can be any register except %rsp.

8(%rbp)            # a local variable
(%rax,%rcx,4)      # int array: base + index*4
array(,%rdi,8)     # 8-byte element array[i] with no base register

Go deeper:

• Addressing mode (Wikipedia) — the general base + index x scale + displacement computation.