# Bitwise reproducibility (2D FDTD)

**Bitwise reproducibility** means corresponding results have identical binary representations. It is stricter than agreement within a floating-point tolerance. In FDTD CUDA, the `exact` build disables multiply-add contraction so the CPU and GPU round separate multiplications and additions separately.

A fused multiply-add rounds once, while separate operations round twice. The build controls this with `-ffp-contract=off` for supported C++ compilers and `--fmad=false` for CUDA. Run the exact configuration with:

```bash
$ make test PRESET=exact
```

The backend tests then require exact equality of finite field values and probe records across the tested variants. There are also checks that repeated CUDA runs produce the same results.

This makes small changes in update ordering easier to detect. The checks establish agreement for the tested builds and inputs; they do not establish reproducibility across arbitrary compilers or hardware. Disabling contraction can affect performance, so the exact preset serves a different purpose from the benchmark presets.