Randomized trial benchmarks fixed-denominator integer inference in a transformer model, suggesting high precision and efficiency during deployment.
We benchmark a single-block transformer language model implemented in Zig using Q16 fixed-denominator integer arithmetic (D = 2^16 = 65536). The implementation uses no floating-point operations, no heap allocations, and no SIMD intrinsics. On a 2019 laptop (Intel Core i7-10th gen class, single core, scalar execution), the model achieves 688 ns per forward pass, 1,159 ns per training step, and 1.42 million tokens per second for greedy generation. All 5 verification tests pass including bit-identical determinism and exact softmax sum-to-one. From this scalar baseline, we project performance under SIMD vectorization, GPU integer tensor cores, and datacenter-scale deployment, comparing directly against conventional float16/float32 and quantized INT8 inference at each level. The central finding is that VDR Q16 arithmetic maps to the same hardware instructions as quantized integer inference — widening multiply-accumulate with right-shift epilogue — placing it at computational parity with INT8/INT16 quantization while providing stronger precision guarantees.
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Geoffrey Howland (2026) studied this question.
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