SIMD Math Optimization

High-performance math library using SIMD instructions for vector and matrix operations in game engines.

Context

School project GTech3, optimization competition, 4 weeks. Individual project.

Implementing math operations with SIMD intrinsics to achieve maximum throughput.

School Requirements

• Implement SIMD vector operations
• Benchmark vs scalar, minimum 4x speedup
• x86 intrinsics (no inline asm), SSE4.2 minimum

My Implementation

Beyond the required vectors:

• Complete hierarchy: Vec2, Vec3, Vec4, Mat4, Quaternion
• AVX in addition to SSE: 8 floats vs 4
• SIMD Quaternions: optimized rotations
• Optimized data layouts: SoA support
• Runtime dispatch: automatic CPU detection

Links

Code available on request.

SIMD Architecture

Type hierarchy with runtime dispatch:

┌─────────────────────────────────────────┐
│         Runtime CPU Detection           │
│    (SSE4.2 / AVX / AVX2 available?)     │
└──────────────┬──────────────────────────┘
               │
     ┌─────────┴─────────┐
     ▼                   ▼
┌─────────┐         ┌─────────┐
│  SSE    │         │  AVX    │
│ 128-bit │         │ 256-bit │
│ 4 floats│         │ 8 floats│
└─────────┘         └─────────┘

Tech Stack

Tech	Version	Role
C++	17	Core language
SSE4.2	x86 intrinsics	128-bit registers
AVX/AVX2	x86 intrinsics	256-bit registers
CMake	3.x	Build system

Types Implemented

• Vec2, Vec3, Vec4 (SIMD)
• Mat4 (SIMD)
• Quaternion (SIMD)
• SoA (Structure of Arrays) support for batch

Optimization Techniques

• Memory alignment (16/32 bytes)
• Data layout SoA vs AoS
• Cache-friendly patterns
• Branch elimination
• Runtime SSE/AVX dispatch

Benchmarks

Operation	Scalar	SIMD	Speedup
Vec4 dot	4 ops	1 op	~4x
Mat4 mul	64 ops	16 ops	~4x
Batch transform	N ops	N/4 ops	~4x