Rotate. Accumulate.
Why It Matters
Modern AI runs on a single operation repeated trillions of times: multiply-accumulate. RAC reframes that operation as a degenerate one-dimensional projection of a richer primitive — geometric rotation. By routing tensor workloads through the CORDIC hardware already present in every modern GPU's Special Function Units — idle roughly 95% of the time under MAC-heavy code — RAC delivers the same mathematical result with a fundamentally more efficient energy profile.
How It Works
RAC is not a simulator, an emulator, or a research toy. It is a production-grade primitive library that ships with CUDA and HIP backends, PyTorch-native modules, and on-device benchmarks. Every capability below is implemented and verified against float32 tolerance.
Every operation is built on CORDIC — the 1959 algorithm that resolves multiplication, division, trigonometry, and roots through pure rotation. Same mathematical answers. Fundamentally different physics underneath.
Modern GPUs contain idle Special Function Units that execute trig and division in four cycles. RAC redirects tensor workloads through these underutilized cores instead of the multiplier-heavy tensor pipeline.
Attention, softmax, LayerNorm, RMSNorm, RoPE — every transformer operation maps to a native CORDIC mode. RoPE in particular is literally a Givens rotation; RAC executes it natively rather than emulating it through multiplication.
CORDIC adds one bit of precision per iteration. That becomes a first-class control knob: 24 iterations for fp32-matched training, 16 for default inference, 8 for edge and quantized deployment. No other architecture exposes this control.
Production CUDA and HIP/ROCm backends. NVIDIA Ampere, Hopper, and AMD CDNA/RDNA architectures supported out of the box. Benchmark harness and correctness tests ship with the source.
Drop-in RACLinear, RACRoPEAttention, RACLayerNorm, and RACLlamaBlock modules. Every operation routes through CORDIC; nothing else in your training loop has to change.
Inside the Library
Every primitive in the library reduces to rotation. Grouped by purpose, they cover the full surface area of modern AI and DSP workloads.
rotate · rotate_raw · compensate · project
polar · norm · normalize
dot · coherence
complex_mul · dct
exp · tanh · softmax
rotate_batch · inner · outer · matmul
Key insight
Rotary position embeddings, the backbone of modern attention, are literally Givens rotations. Every other accelerator emulates them using multipliers. RAC executes them natively — one rotation per embedding-dimension pair.
Primary Use Cases
Attention, RoPE, normalization, and feed-forward layers all route through native CORDIC primitives — the entire transformer stack on one execution model.
Inference at hyperscale, on-prem deployments under thermal limits, and any environment where joules-per-token is the binding metric.
Eight-iteration CORDIC delivers good-enough precision for edge inference at a fraction of the energy budget — and the same code scales back up for the data center.
Complex multiplication, DCT, and polar conversion are native rotation operations — no emulation, no MAC fallback.
Rotate your vision. Accumulate what matters.
