---
license: apache-2.0
tags:
  - cuda
  - quantization
  - ternary
  - llm-inference
  - kernel
---

# tritllm-kernel

Multiply-free ternary GEMV CUDA kernel for the codec from
**"Balanced Ternary Post-Training Quantization for Large Language Models"** (Stentzel, 2026).

The headline number from the paper: **7.8× speedup** over cuBLAS FP16 GEMV on RTX 4090 in the memory-bound regime, projected to full-model token generation throughput from per-layer benchmarks.

> **These are kernel-only projections, not end-to-end serving throughput.** They exclude attention, KV cache, sampling, and tokenizer overhead. See Section 7 of the paper for methodology.

## What it is

A standalone CUDA shared library (`libtrit_gemv.so` / `.dll`) callable via `ctypes` from any language, with no PyTorch dependency. The same algorithm is also wrapped via PyTorch's pybind11 in `trit_gemv_wrapper.cu` for benchmarking.

The core trick: each ternary weight (-1, 0, +1) reduces a multiply-accumulate to a conditional add/subtract/skip. The kernel uses Ada/Hopper/Blackwell `dp4a` intrinsics on int4-packed weights and pre-interleaved int8 activations to do four ternary-times-int8 dot products per instruction.

## Build

```bash
cd kernel
./build.sh
```

The build script targets SM 70/75/80/86/89/90/100/120 in one fat binary so the `.so` runs on V100, T4, A100, RTX 30/40/50, H100, and B100/B200 without recompilation.

Required: `nvcc` (CUDA 11.8 or newer) and a C++ compiler.

## Performance (Qwen2.5-7B, d=2, 3.47 bpw, 3.3 GB model)

| GPU | L2 cache | Tokens/sec | Speedup vs FP16 cuBLAS | Effective BW |
|---|---|---|---|---|
| RTX 4090 | 72 MB | 588 | 7.8× | 1940 GB/s |
| RTX 3090 | 6 MB | 192 | 3.4× | 633 GB/s |
| RTX 4080 Laptop | 64 MB | 133 | 5.8× | 439 GB/s |
| A100 80GB | 40 MB | 201 | 4.2× | 663 GB/s |

These are per-layer GEMV benchmarks projected to full-model token-generation throughput. The L2-cache size correlates strongly with speedup because each `d=2` layer fits in L2 on the RTX 4090, giving an effective bandwidth roughly 2× HBM bandwidth.

See `kernel/bench_*.py` for the benchmark drivers.

## Launch contract

The kernels in `trit_gemv.cu` and `trit_gemv_standalone.cu` assume:

| Constraint | Why | What happens if violated |
|---|---|---|
| `blockDim.x == 32` (one warp per block) | Kernels use `__shfl_down_sync(0xFFFFFFFF, ...)` and lane-0 reduction | OOB index reads + race on `y[row]` |
| `in_features % 64 == 0` | Group size is fixed at 64 weights | Trailing partial group is silently dropped — incorrect output for that row |
| Weight, scale, and activation buffers are device-resident and properly aligned | Kernel uses `__ldg` for cached loads | UB / device fault |

If your model has `in_features` not divisible by 64, pad the weight matrix to the next multiple of 64 with zero rows before quantizing.

## API surface

C ABI in `trit_gemv_standalone.cu`:

```c
// Best-tested d=2 path (champion for 4090)
void trit_gemv_d2_fast(
    const int32_t* pt,        // [rows * num_groups * 8] int4-packed weights
    const float*   ws,        // [rows * num_groups]     scales
    const int32_t* xt_e,      // [num_groups * 8]        even nibble activations
    const int32_t* xt_o,      // [num_groups * 8]        odd nibble activations
    const float*   xs,        // [num_groups]            activation scales
    float*         y,         // [rows]                  output
    int cols, int rows, int num_groups,
    int use_l2_persist        // 0 = off, 1 = enable L2 persistence
);

// Native-trit packed d=3 (no int4 intermediate)
void trit_gemv_d3_native(
    const int32_t* pt,        // [rows * num_groups * 13] trit-packed
    const float*   sc,
    const float*   x,
    float*         y,
    int cols, int rows, int depth
);

// L2 cache size query (for deciding whether to enable persist)
int  get_l2_cache_bytes();
void get_gpu_name(char* buf, int buflen);
void cuda_sync();
```

## Error reporting

All `extern "C"` entry points return `void`, so per-call status is delivered through a separate channel:

```c
int trit_gemv_get_last_error();
```

Returns `0` on success. Negative values are host-side argument-validation failures (`TRIT_ERR_NULL_PTR`, `TRIT_ERR_BAD_DIM`, `TRIT_ERR_BAD_GROUP`, `TRIT_ERR_BAD_BUFFER`). Positive values are `cudaError_t` codes captured from the most recent kernel launch.

The host-side validator in each entry point checks pointer non-null, positive dimensions, `cols % 64 == 0`, and `cols / 64 == num_groups`. If validation fails, no kernel is launched, the error is recorded, and the call returns silently.

## Known limitations

The educational kernels in `trit_gemv.cu` use a lane-0 scale-and-add reduction that idles 31 lanes per group. This is a deliberate readability tradeoff — the headline 7.8× number is from the deferred-reduction `k_d3_hardened` kernel in `trit_gemv_standalone.cu`. See [KNOWN_ISSUES.md](KNOWN_ISSUES.md) for details and a planned API-cleanup item.

## Citation

```
@article{stentzel2026ternaryptq,
  title  = {Balanced Ternary Post-Training Quantization for Large Language Models},
  author = {Stentzel, Eric},
  year   = 2026,
  note   = {Entrit Systems}
}
```

## License

Apache-2.0.