Memory Alignment and Hardware Constraints in C++

Overview

This note presents a structured view of how memory alignment and hardware-level constraints interact with the C++ object model and compiler guarantees. It connects the requirements of modern hardware architectures with language-level semantics.

Memory Model

C++ programs operate in a virtual memory space divided into regions for code, static data, stack, and heap. Dynamic allocation (new, malloc) reserves space on the heap, returning a pointer satisfying platform alignment guarantees.

Each allocation unit is defined in bytes. For example:

unsigned char* buffer = new unsigned char[1024];

The returned address obeys alignof(std::max_align_t), typically 8 or 16 bytes on 64-bit systems.

Alignment Definition

Let an address $ A $ and alignment $ k \in \mathbb{N} $.
$ A $ is k-aligned if and only if

$$ A \bmod k = 0. $$

Alignment ensures that the address of an object satisfies the boundary constraints required by the underlying hardware.

Hardware Considerations

Processors read and write memory through buses that operate on fixed-size chunks. These transfer units determine the natural alignment requirements.

If an object crosses one of these boundaries, multiple transfers or traps may occur.

Misalignment

A misaligned access occurs when the address of a load or store does not satisfy its alignment. Its effect is architecture-dependent.

Aligned access guarantees that a load/store fits entirely within one bus transaction.

C++ Language Rules

C++ enforces that every object’s address satisfies its alignment requirement:

$$ \text{address} \bmod \text{alignof}(T) = 0. $$

The alignment requirement ( \text{alignof}(T) ) is a compile-time constant depending on the target ABI (Application Binary Interface).

Over-Alignment

Manual over-alignment is declared using alignas(N). It enforces that the object’s address is a multiple of $ N $. Example:

struct alignas(64) Vec4 {
    float data[4];
};

Motivation

• SIMD (Single Instruction Multiple Data) operations (AVX/AVX-512)
• Cache-line isolation in concurrent programs
• DMA and accelerator interfaces requiring aligned buffers

If the requested alignment exceeds hardware capability, the compiler inserts sufficient padding to maintain correctness. This is a compile-time guarantee; performance behavior depends on the target architecture.

Relationship Between Size and Alignment

$$ \text{alignof}(T) \leq \text{sizeof}(T). $$

Equality is common for primitive types. Structs and arrays may have $ \text{alignof}(T) < \text{sizeof}(T) $ due to internal padding. The C++ standard only enforces address correctness, not divisibility between size and alignment.

Misalignment Visualization

Proper Alignment (8-byte double)

Bus boundary: ─────────┬────────┬────────
                       0x1000   0x1008   0x1010
Aligned: [0x1008–0x100F] → one 8B transaction

Misalignment (starts at 0x100A)

Bus boundary: ─────────┬────────┬────────
                       0x1000   0x1008   0x1010
Misaligned: [0x100A–0x1011] → spans two transactions

Byte-Aligned (char)

No restriction: alignment = 1

Key Properties

Summary

1. Alignment guarantees that memory accesses conform to hardware transfer boundaries.
2. Misaligned loads or stores can incur penalties or hardware traps.
3. $ \text{alignof}(T) $ defines the minimum alignment for a type.
4. alignas(N) allows manual over-alignment beyond natural alignment.
5. The compiler ensures $\text{alignof}(T) \leq \text{hardware_max_alignment}$.

This document provides a compact reference linking hardware design, compiler layout rules, and C++ alignment guarantees.