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RdSAP 10 Specification §15 "Rounding of data" (PDF p.66):
"For consistency of application, after expanding the RdSAP data into
SAP data using the rules in this Appendix, the data are rounded
before being passed to the SAP calculator. The rounding rules are:
U-values: 2 d.p.
All element areas (gross) including window areas and conservatory
wall area: 2 d.p."
The §3.9.1 / §3.10.1 shell formula A_RR_shell = 12.5 × √(A_RR_floor /
1.5) produces a gross element area for the room-in-roof. Pre-slice the
cascade kept the raw float (e.g. cert 000565 BP[0]: 12.5 × √30 =
68.46532...), then subtracted lodged wall surfaces to obtain the (30)
residual roof area. The worksheet rounds A_RR_shell to 2 d.p. (68.47)
BEFORE the subtraction — per §15 above.
Cert 000565 has three BPs that fire this path (Main, Ext1, Ext3 — all
have detailed wall surfaces with no `slope` / `flat_ceiling` /
`stud_wall` lodgement, so §3.10.1 residual fires). Each contributes a
sub-rounding residual that the unrounded cascade was missing:
BP[0] Main: 68.4653 → 68.47; residual 43.9653 → 43.97 (+0.0016 W/K)
BP[1] Ext1: 59.5119 → 59.51; residual 18.2519 → 18.25 (−0.0007 W/K)
BP[3] Ext3: 57.7350 → 57.74; residual 17.3450 → 17.35 (+0.0017 W/K)
Movement (HEAD `d0268a5b` → this slice) for cert 000565:
roof_w_per_k 51.3768 → 51.3795 ✓ EXACT (Δ −0.0027 → 0.0)
thermal_bridging 128.6448 → 128.6460 ✓ EXACT (Δ −0.0012 → 0.0)
total_external_a 857.6323 → 857.6400 ✓ EXACT (Δ −0.0077 → 0.0)
space_heating_kwh 59008.2363 → 59008.3499 ✓ EXACT (Δ −0.1136 → 0.0)
main_fuel_kwh 34710.7272 → 34710.7941 ✓ EXACT (Δ −0.0669 → 0.0)
total_fuel_cost 4680.2515 → 4680.2593 ✓ EXACT (Δ −0.0078 → 0.0)
co2_kg_per_yr 6447.6161 → 6447.6263 ✓ EXACT (Δ −0.0102 → 0.0)
sap_score_cont 28.5087 → 28.5087 ✓ EXACT (Δ +4.2e-5 → −4.7e-5)
sap_score (int) 29 ✓ EXACT (preserved)
ecf 5.38682 → 5.38683 (vs ws 5.3868, Δ +3.2e-5)
Cert 000565 truly closes — every SAP-result field within 1e-4 of the
worksheet PDF.
Cohort safety: 6 cohort certs (000474..000516) unchanged — cohort
000516's roof routes through the Detailed branch with `slope` /
`flat_ceiling` / `stud_wall` lodgements, so `has_roof_lodgement=True`
short-circuits the §3.10.1 residual block. Cohort certs 000474/477/
480/487/490 are pre-S0380.103 hand-built fixtures whose RR fields don't
exercise the simplified A_RR_shell path (rir.floor_area=0 or
detailed_surfaces only).
Test added: `test_summary_000565_a_rr_shell_rounded_2_dp_closes_roof_
w_per_k_per_rdsap_10_section_15` pins the cascade roof_w_per_k = 51.3795
exactly (Δ ≤ 1e-4 vs worksheet (30) Σ).
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
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