---
layout: post
title: "Is there hardware support for 128-bit integers in modern processors?"
permalink: /extras/hardware-support-for-128-bit-integers-in-modern-processors.html
---

**Let’s break this down in two parts:**
* What do we mean by “hardware support for 128-bit integers”?
* How do modern CPUs (particularly x86-64) handle 128-bit values?

## 1. What do we mean by “hardware support for 128-bit integers”?

* **Native 128-bit integer operations:** If a CPU has true 128-bit registers in its general-purpose register file, it would include single-instruction operations such as 128-bit addition or 128-bit subtraction. This is what we typically mean by “native” support.
* **Partial 128-bit hardware support:** Many architectures offer a subset of 128-bit functionality. For instance, an instruction that multiplies two 64-bit values and yields a 128-bit result (stored in two 64-bit registers) is often considered partial hardware support for 128-bit integers.
* **SIMD registers:** On several modern architectures (including **x86-64**), there are vector/SIMD registers of 128 bits or more (**SSE**, **AVX**, or **AVX-512**). While these registers can handle 128-bit or wider integer operations, they are typically optimized for parallel processing of smaller-element vectors rather than acting like a single 128-bit general-purpose integer register.

## 2. How do modern CPUs (particularly x86-64) handle 128-bit values?

* **64-bit × 64-bit → 128-bit multiplication**
    * **x86-64** has single-instruction multiply variants (`mul` for unsigned, `imul` for signed) that produce a 128-bit result in **RDX:RAX**. This is convenient since it handles the entire 128-bit product in one go.
    * Other architectures may not offer this in a single instruction, necessitating multiple “partial” operations to get the full 128-bit result.

* **Other 128-bit integer operations (add, subtract, logical operations, etc.)**
    * In **x86-64’s** general-purpose register file, most instructions top out at 64-bit operands. Doing a full 128-bit addition or subtraction requires combining instructions (e.g., one 64-bit add followed by an add-with-carry instruction).
    * If performance or code density is a concern, compilers will emit sequences of multiple instructions to emulate 128-bit operations.

* **SIMD/AVX registers for 128-bit or wider integers**
    * Modern **x86-64** processors have **SSE** (128-bit), **AVX** (256-bit), and **AVX-512** (512-bit) registers. These can perform integer operations on concurrently packed data elements. However, they are typically used as vector registers rather than as single “general-purpose” 128-bit integer registers with a full set of integer instructions (like add, sub, mul, div) in the same sense as 64-bit GPRs.

### I was thinking along these lines:

The **x86-64** instruction set can do 64-bit × 64-bit to 128-bit using a single instruction. Specifically, you have the `mul` instruction for unsigned multiplication and the `imul` instruction for signed multiplication (each taking one operand from `RAX` and the other as an explicit register/value). In effect, you can say that to some degree there is support for 128-bit integer arithmetic because the hardware can produce a full 128-bit result in `RDX:RAX` from two 64-bit operands.

If an architecture does not provide such an instruction, you would need multiple steps to emulate 64-bit × 64-bit to 128-bit multiplication. This efficiency is one reason why 128-bit to 128-bit operations can be performed with a relatively small number of instructions on **x86-64**.

For example, if we look at a simple function in C/C++ that multiplies two 128-bit numbers:

```c++
__int128 mul(__int128 a, __int128 b) {
  return a * b;
}
```

GCC may generate assembly like this:

```assembly
imulq   %rdx, %rsi
movq    %rdi, %rax
imulq   %rdi, %rcx
mulq    %rdx
addq    %rsi, %rcx
addq    %rcx, %rdx
```

Here, one of those lines (for instance `mulq %rdx`) is a 64-bit × 64-bit → 128-bit instruction. The others handle the partial products, storing them in temporary registers, and properly summing them into the final 128-bit value. You’ll notice two additional 64-bit multiplication instructions (`imulq`) that produce lower 64-bit results and two 64-bit additions (`addq`). Even so, the presence of a single 64-bit × 64-bit → 128-bit instruction streamlines the process considerably compared to a pure software approach that must work in smaller chunks with no hardware multiply support at all.

**Final Answer**

Modern **x86-64** processors do not provide full native 128-bit general-purpose registers with a comprehensive set of integer operations (add, subtract, multiply, etc. as single instructions). However, they do offer partial hardware support in the form of a single-instruction 64×64 → 128 multiply (`mul`/`imul`), and they can handle 128-bit data in **SSE/AVX** registers, albeit as vectors. So while you can’t say they have complete 128-bit integer hardware support (like they do for 32 or 64 bits), the existence of 64×64 → 128 multiplication instructions and SIMD capabilities make 128-bit arithmetic more efficient than purely software-based emulation.