orbit_step

std.sets.orbit_step · Level L3

One step of following every point's forward orbit under a self-map f of a finite set at once: pw(x) ← f(pw(x)), so after k steps from x it is fᵏ(x); a point that first returns to itself at step k gets period k. The body orbit_periods scans.

pw ← f(pw); first fᵏ(x) = x: period k

Signature

orbit_step(pw: f64[n], period: f64[n], k: f64[], f: i64[n]) → f64[n], 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 f applied to every current point, and the first return in exact rational arithmetic, on all 40 test cases.
All 338 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

—

Called by

orbit_periods

sha256:0a23ac268a473a787f161c740d580d3a33b64b078066c779862eae27f50423ca

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

Control handle

Symbol: Ω:std.sets.orbit_step · Ω:orbit_step
Pins: sha256:c0ce395c5ed9302201282fece02e56037c66895070806c68ada6afad233a685athis graph alone
Evidence: sha256:d3ccfd37355a59a4565604e31148859af8a2da2036fb7868815a789c12657520the 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.