count_running

std.elementwise.count_running · Level L1

Whether some counter i is still at most k, as 1 or 0. The condition the permutation and binomial loops test.

[some i ≤ k]

Signature

count_running(i: i64[s], acc: i64[s], n: i64[s], k: i64[s]) → f64[]

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 float(any(i <= k)) in exact rational arithmetic, on all 40 test cases.
All 40 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

binomial permutations

sha256:902497bfe852f17952c943d7484adc3b0ec8790cc1da9a9c55b1797e0ee4a8c9

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

Control handle

Symbol: Ω:std.elementwise.count_running · Ω:count_running
Pins: sha256:e8fcfa5836dcaa89e236734067987845bc9f814dffb7d0e3b47f1126522b8768this graph alone
Evidence: sha256:1e64bebc5bf3287f78d61da279dd399abd84f7d6437f828123371f1b7e3fd171the 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.