Two new evaluation plots for §3 GEMM, both using the composite window
as the denominator (the up-front tl.load of A in load_ref is therefore
excluded — only HBM traffic and compute inside the composite count):
- gemm_hbm_bw_util.png: per-PE HBM bandwidth utilization against the
256 GB/s per-PE ceiling. Answers "is this workload memory-bound on
this configuration?" — small/single-tile shapes sit at 22–46%
(pipeline-fill-limited), large or output-write-dominated shapes
saturate (≥85%).
- gemm_per_pe_tflops.png: per-PE GEMM throughput against the 8 TFLOP/s
engine peak. The deep-K K=3072 load_ref case lands at
7.18 TFLOP/s (~90% of peak) — the configuration's clean win.
ref_ref at the same shape drops to 3.83 TFLOP/s because the second
operand doubles HBM pressure and the kernel hits the BW ceiling.
The variant gap on this chart is the operational cost of NOT
pre-staging the activation.
Both charts compare two operand-staging variants on every shape:
load_ref ("activation pre-staged", weight-only HBM streaming) and
ref_ref (both A and W streamed from HBM). load_load is omitted —
with both operands pre-staged the composite carries no HBM traffic
and the BW metric collapses to 0.
Analytic / measured peak unified to the single hardware spec
(8.0 TFLOP/s = 8000 flops/ns). T_STAGE is now derived as
tile_flops / peak (= 16.384 ns for the 32×64×32 tile) rather than
the previous hardcoded 16 ns, so MAC efficiency and per-PE TFLOPS%
share the same denominator and never disagree. Side effect: max
analytic-vs-measured gap tightens from 2.2 ppt to 1.4 ppt across
the sweep.
§3 Results restructured: lead with the two new evaluation plots
(BW saturation, achieved throughput), then the MAC-utilization
analytic-vs-measured chart serves as the validation step, then the
per-stage engine wall-clock as the supporting diagnostic. §3
Analysis updated to use the load_ref / ref_ref contrast as the
hardware-software boundary line that motivates the GQA kernel of §5.
§2.4 Accuracy claim updated to match: GEMM analytic-vs-measured
agreement is now "within 1.4 ppt across every swept shape", from
~7.7% at single-tile up to ~90% at K=3072. Subtitle/title vertical
stacking glitch in the matplotlib charts fixed in passing.
Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
