Manuscript VIII-C@3 · VIII-C-v3.tex · section · 3b070436

Permission and register arithmetic

Exact algebraic and resource checks › Permission and register arithmetic · lines 2432–2463

The permission trace is

(1, 1) \to (1, 1) \to (1, 0) \to (1, 0) \to (0, 0) \to (0, 0) .

Only $S_{tab}$ consumes source permission, and only $E_{3 - 6}$ consumes incidence permission.

The exact slice range $j \in [- 2^{d}, 2^{d}]$ fits in $d + 2$ signed bits. The table-index range fits in the allocated $q + 2$ signed bits. Unused signed words are off-domain.

Summing the hybrid fields,

H = 3 + 1 + (r_{G} + r_{src}) + (d + 2) + 3 + (q + 2) + (q + 2) + 11 + 24 (b + 4) = 24 b + d + 2 q + r_{G} + r_{src} + 120.

Consequently,

8 H - 2 + 12 n = 192 b + 8 d + 16 q + 8 r_{G} + 8 r_{src} + 958 + 12 n .

At $q = 6, d = 1, r_{G} = r_{src} = 1$ ,

H = 24 b + 135, K_{6} = 1, T_{6} = 3, Q_{m a x} = 36.

These are exact mathematical arithmetic checks, not reported software execution.

Displayed formulas in this passage

unlabeled · line 2446
$H = 3 + 1 + (r_{G} + r_{src}) + (d + 2) + 3 + (q + 2) + (q + 2) + 11 + 24 (b + 4) = 24 b + d + 2 q + r_{G} + r_{src} + 120.$
unlabeled · line 2435
$(1, 1) \to (1, 1) \to (1, 0) \to (1, 0) \to (0, 0) \to (0, 0) .$
unlabeled · line 2453
$8 H - 2 + 12 n = 192 b + 8 d + 16 q + 8 r_{G} + 8 r_{src} + 958 + 12 n .$
unlabeled · line 2458
$H = 24 b + 135, K_{6} = 1, T_{6} = 3, Q_{m a x} = 36.$