clique_step

std.linalg.clique_step · Level L4

Test one vertex subset, the bits of c: it is a clique when every pair in it is adjacent, which is bitsᵀ·A·bits = k(k − 1) for k vertices. Keep the largest clique found so far, the first of its size in counter order, and count the cliques of that size. The body max_clique runs.

clique ⇔ bitsᵀ A bits = k(k − 1)

Signature

clique_step(c: f64[], best: f64[], count: f64[], wit: f64[n], A: f64[n, n], pow2: f64[n], total: f64[]) → f64[], f64[], f64[], f64[n]

Structure

The function as NOVA stores it: one box per input, operation and output, and arrows that carry values. A double border marks another library function this one runs — called once, or by Scan once per element; select it to open that function.

input
operation
constant
call
output

Verification

Signature proven by NOVA’s shape solver, for every size.
Equal to the reference the bits of c; every pair adjacent; keep the first largest, count its ties in exact rational arithmetic, on all 40 test cases.
All 265 float64 results are exact: the error is zero.
Interpreter and NumPy backend return bit-identical results.
At float32 too: the 40 test cases rounded to float32, and 40 of them exact, with zero error.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 100%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 0

Identity

Calls

dot vecmat

Called by

max_clique

sha256:1f7eab788afab92484947b689ba1a7409356134ea123ab615b7eb3cbd995e0dc

The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.

Control handle

Symbol: Ω:std.linalg.clique_step · Ω:clique_step
Pins: sha256:238c1021c78a4dec4f81ba907b0c99efdc13bcefdea2136047e858d6bace4a5bthis graph and the 2 it reaches through calls
Evidence: sha256:141764077d4b850bf3f888f0e22741f2856f8e8f32897ba83486ce22b7503852the hash of its verification record
Needs: no capability: a pure function

Through NOVA’s control layer, the symbol launches this function only while the program still matches what it pins: a change to this graph, or to any graph it reaches, needs a migration first.