Meeting C++ 2026 - std::complex Ate My Performances! - Making Faster Hyper-complex Maths

Joel FALCOU

On Day 3 at 11:40 (CET/Berlin) in Track C [Jade Room and online]

We all love the elegance of pure mathematics. Writing complex equations exactly as they appear in textbooks is the dream. But let's be honest: when you hit compile, std::complex often turns that dream into an Array-of-Structures (AoS) performance nightmare. You expect compiler optimisations to save you, but auto-vectorizers take one look at that interleaved data layout, panic, and drown your instruction cache in cross-lane shuffles and horizontal adds. And what happens when you need to go beyond complex numbers? If you need quaternions for 3D rotations, or octonions just to prove you can, the standard library leaves you completely on your own.

We are going to talk about KYOSU, a C++ library providing a unified, SIMD-aware implementation of complex numbers, quaternions, octonions, and general R-Cayley-Dickson algebras. Built on top of EVE, our SIMD wrapper, and KUMI, our tuple replacement, KYOSU delivers over 150 complex domain functions with absolutely zero abstraction penalty.

In this talk, we are going from mathematical textbooks straight down to the bare metal. We will cover:

• Why the historical ABI baggage of std::complex makes compiler optimisations fail miserably, and why you are leaving massive performance on the table. 
• How KYOSU uses EVE and KUMI to enforce strict Structure-of-Arrays (SoA) layouts, flattening the Cayley-Dickson construction to keep your SIMD registers fully fed. 
• Real-world benchmarks and assembly inspection. We will look at the instruction traces and prove that doing exotic math doesn't have to cost you your CPU cycles.

Whether you need to aggressively optimize complex math for signal processing, or you just want to see how to make octonions execute faster than the time you can spell Cayley-Dickson, this talk will give you food for thoughts.

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