CppCon 2026

Floating point has a reputation for betrayal. Change the thread count, vector width, compiler flags, reduction tree, or target architecture, and the low bits can move. Parallel algorithms make this worse: the standard often specifies the operation, but not the numerical expression whose result must be reproduced. This talk asks a provocative question: what if reproducible numerics did not have to be slow?

We will show reproducible, deterministic implementations of reduce and scan that exhibit better error behavior on hostile floating-point workloads and can match or beat conventional standard-library implementations on realistic workloads. The trick is not to freeze the execution schedule. It is to specify the expression being computed, then let the implementation use SIMD, threading, blocking, tiling, and platform-specific strategies to compute that expression efficiently.

The key idea, developed through C++ standardization work such as P4016R0 and P4229R0, is reproducibility by reproducing the computation. Instead of asking the implementation to promise a particular schedule, we give the calculation a named expression. Once that expression is chosen, changing the thread count, vector width, chunking, or blocking strategy does not silently change the answer.

A reproducible scan makes this harder than reduce because it does not expose only one final value. It exposes every prefix. A reproducible final sum is not enough if the intermediate results still drift. We will show how expression and observation contracts make those prefixes reproducible without forcing the computation back into a slow sequential order.

Then we go below the algorithm layer, to the places where bits usually escape: FMA contraction, denormals, floating-point environment choices, math-library approximations, and vectorized transcendental functions. The goal is not to get the same answer by turning off the hardware. We will show reproducible vectorized primitives, including transcendental functions, running at speeds comparable to established vector math libraries while preserving a cross-platform numerical contract.

Finally, we put the whole stack under stress: a heterogeneous numerical pipeline across x86-64, Apple Silicon, and CUDA. The data is deliberately hostile, with high cancellation rates and fragile intermediate states. The aim is not to pass friendly benchmark cases, but to reproduce the specified computation, including the same intermediate failures, not just the same final answer, bit for bit, across CPUs, GPUs, and toolchains.