The Missing Fourth Term for the Emulation Tensor Memory Equilibrium (TME) Model: The Residue Deconstruction Cost

Harun Bayraktar, John Gunnels, Peter Caday

The Tensor-Memory Equilibrium (TME) model of "FP8 is All You Need (Part 1)" calculates the execution time of Ozaki Scheme II emulation of fp64 as the maximum of a tensor-core term and a High-Bandwidth Memory (HBM) traffic term, plus a per-output reconstruction term. However, it omits the per-input deconstruction cost: every streamed fp64 operand must be scaled, rounded, and reduced modulo each of the $r$ moduli on SIMT pipes before any matrix multiply can issue. In this note we add this fourth term, calibrate its constant from the cuBLAS emulation path, and derive a closed-form operational-intensity threshold $\mathrm{OI}^{*} = c_q r P_{\mathrm{fp64}}/(8P_{\mathrm{int}})$ below which emulation cannot match native fp64 regardless of tensor-core throughput. On the NVIDIA B300 GPU the threshold is $\mathrm{OI}^{*}\approx 0.56$ FLOP/B. As a result, GEMV, SpMV, and low-batch GEMV, which are the memory-bound kernels the original paper claims to accelerate, are limited to 0.3-0.9x of native performance, and the 7-point stencil to 1.8x rather than the claimed 3.1x. Dense GEMM is unaffected as expected. We also show that precomputing and storing the residues moves the same cost into the…