analytical-viz: roofline tab — 'How hyperscalers pick GPU count' section

New section at the bottom of the Chip Roofline tab implementing the
three-axis GPU count decision:

  N_GPUs = max(capacity_floor, KV_headroom, throughput_SLO) × N_replicas

Interactive inputs: concurrent users, avg context/user, TPOT SLO.
Four KPI cards report each axis + the recommended total, with a
'binds:' delta chip showing which axis is the bottleneck.

  - Axis A (capacity):  PEs to hold weights alone
  - Axis B (KV):        PEs to hold weights + all KV of one replica's users
  - Axis C (throughput): replicas needed at B_at_SLO users each
  - Total: max(A,B) × N_replicas

Contextual caption explains what to do about the binding axis. If SLO
is infeasible (even B=1 exceeds SLO), an error block explains the
options (loosen SLO, shorten context, or scale up FLOPs/BW knobs).

Plus three collapsed expanders explaining the hybrid deployment
pattern hyperscalers use:
  - Layer 1: one elastic pool + PagedAttention + continuous batching
  - Layer 2: length-tier routing (standard vs long-context)
  - Layer 3: disaggregated prefill/decode (DistServe, Splitwise)

Pure additions in chip_roofline.py:
- max_batch_within_slo(machine, model, s_kv, slo_s) — analytical
  inverse of step_latency to find the largest per-replica B under SLO
- size_deployment(machine, model, n_users, avg_ctx, slo_s) — returns
  GpuSizingResult with all three axes + binding info

6 new tests cover: capacity scales with model size, KV grows with
users/context, binding axis flips with workload shape, tight SLO
shrinks max batch, weight-time-exceeds-SLO returns 0, total ==
per-replica × replicas.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

tests/analytical_visualization/test_chip_roofline.py

@@ -15,9 +15,11 @@ from tests.analytical_visualization.chip_roofline import (
     good_context,
     knee_batch,
     kv_bytes_per_token,
+    max_batch_within_slo,
     memory_budget_curve_vs_batch,
     memory_budget_curve_vs_skv,
     per_token_latency_curve,
+    size_deployment,
     step_latency_curve,
     t_com,
     t_mem_long,
@@ -430,6 +432,79 @@ def test_ai_sensitivity_bad_axis_raises():
                               [1.0], axis="bogus")
 
 
+# ── GPU sizing (three-axis) ────────────────────────────────────────
+
+
+def test_capacity_floor_scales_with_model_size():
+    """A model with 2× params needs ~2× PEs for weights alone (axis A)."""
+    m = MachineParams()
+    small = PRESETS["Llama 3 8B"].model
+    big = PRESETS["Llama 3 70B"].model
+    r_small = size_deployment(m, small, n_users=1, avg_ctx=1024,
+                                tpot_slo_s=1.0)
+    r_big = size_deployment(m, big, n_users=1, avg_ctx=1024,
+                              tpot_slo_s=1.0)
+    ratio = r_big.pes_axis_a_capacity / r_small.pes_axis_a_capacity
+    # 70B / 8B ≈ 8.75× params — allow generous tolerance
+    assert 5 < ratio < 12, (ratio, r_small, r_big)
+
+
+def test_kv_headroom_scales_with_users_and_context():
+    """Doubling n_users OR avg_ctx grows KV load roughly linearly."""
+    m = MachineParams()
+    model = PRESETS["Llama 3 8B"].model
+    base = size_deployment(m, model, n_users=64, avg_ctx=4096,
+                             tpot_slo_s=1.0)
+    twice_users = size_deployment(m, model, n_users=128, avg_ctx=4096,
+                                    tpot_slo_s=1.0)
+    twice_ctx = size_deployment(m, model, n_users=64, avg_ctx=8192,
+                                  tpot_slo_s=1.0)
+    # KV bytes doubled either way → axis-B PE count must strictly grow.
+    assert twice_users.pes_axis_b_kv > base.pes_axis_b_kv
+    assert twice_ctx.pes_axis_b_kv > base.pes_axis_b_kv
+
+
+def test_binding_axis_flips_with_workload():
+    """Huge N_users + short ctx → throughput binds.
+    Huge ctx + few users → kv (or capacity) binds."""
+    m = MachineParams()
+    model = PRESETS["Llama 3 8B"].model
+    big_users = size_deployment(m, model, n_users=10_000, avg_ctx=1024,
+                                  tpot_slo_s=0.05)
+    long_ctx = size_deployment(m, model, n_users=1, avg_ctx=500_000,
+                                 tpot_slo_s=1.0)
+    assert big_users.binding_axis == "throughput", big_users
+    assert long_ctx.binding_axis in ("kv", "capacity"), long_ctx
+
+
+def test_max_batch_shrinks_with_shorter_slo():
+    """Tighter SLO → smaller B fits."""
+    m = MachineParams()
+    model = PRESETS["Llama 3 8B"].model
+    loose = max_batch_within_slo(m, model, s_kv=1024, tpot_slo_s=1.0)
+    tight = max_batch_within_slo(m, model, s_kv=1024, tpot_slo_s=0.05)
+    assert tight < loose, (tight, loose)
+
+
+def test_max_batch_returns_zero_when_weight_time_exceeds_slo():
+    """If weight-fetch alone > SLO, no batch fits."""
+    m = MachineParams()
+    model = PRESETS["Llama 3 70B"].model
+    # 70B in BF16 = 140 GB. Reading at 256 GB/s takes ~547 ms.
+    # SLO of 100 ms cannot be met.
+    assert max_batch_within_slo(m, model, s_kv=100,
+                                  tpot_slo_s=0.1) == 0
+
+
+def test_total_pes_equals_per_replica_times_replicas():
+    """Sanity: total_pes = pes_per_replica × n_replicas."""
+    m = MachineParams()
+    model = PRESETS["Llama 3 8B"].model
+    r = size_deployment(m, model, n_users=500, avg_ctx=4096,
+                          tpot_slo_s=0.1)
+    assert r.total_pes == r.pes_per_replica * r.n_replicas
+
+
 # ── App wiring: tab exists on the Streamlit app ────────────────────