Function dense_gemm_router 

pub fn dense_gemm_router(
    gpu: &dyn GpuBackend,
    kernel: KernelHandle,
    input: DevicePtr,
    weight: &DenseWeight,
    output: DevicePtr,
    m: u32,
    n: u32,
    k: u32,
    stream: u64,
) -> Result<()>

Order-preserving register-blocked BF16 GEMM (kernel dense_gemm_bf16_router).

Same math AND the same per-output FP32 accumulation order (strict k = 0..K-1) as the scalar dense_gemm — bit-identical output under the kernel dir’s --fmad=false build (verified 0 differing elements at the router shapes M=4510/M=2255, [M,2048]x[2048,256]) — at ~2x the speed via register blocking + vectorized smem staging. This is the ONLY fast GEMM that satisfies the 2026-08-12 router-numerics pin (see router_gate_gemm_dense); tensor-core kernels reassociate and stay forbidden there.

Grid: (ceil(N/64), ceil(M/16), 1) Block: (16, 16, 1)