tutte_step

std.linalg.tutte_step · Level L4

One term of the Tutte–Berge formula: for the vertex set U given by the bits of c, (n + |U| − odd(G − U))/2, where odd counts the components of G − U with an odd number of vertices. Keep the smallest so far, and the first U that gives it. The body of max_matching's first loop.

(n + |U| − odd(G − U))/2

Signature

tutte_step(c: f64[], best: f64[], U: f64[n], A: f64[n, n], pow2: f64[n], total: 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 components of G − U by search; (n + |U| − #odd)/2; keep the first smallest in exact rational arithmetic, on all 40 test cases.
All 179 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

component_labels

Called by

max_matching

sha256:9e7658af7999598ca165f1cbf1f747979d23851d7de585c564fe07fc3db3bb44

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.tutte_step · Ω:tutte_step
Pins: sha256:b5aab08aaddea1ac769b580737c80b7ceeafb1195e3251bc4e67289cfdf98ea8this graph and the 3 it reaches through calls
Evidence: sha256:71231630681a668f2d72b6662e806199650a07647ddd6dccaceaff4c0c7b96eathe 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.