ie_open

std.sets.ie_open · Level L1

Whether the index-set counter c is still below 2^s, as 1 or 0. The condition inclusion_exclusion loops on.

[c < 2^s]

Signature

ie_open(c: f64[], total: f64[], S: f64[s, m], pow2: f64[s], count: f64[]) → 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(c < count) 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

inclusion_exclusion

sha256:831f397b7ae0056e08c991307aafdcfcaa607a5a8da0bbadfc144c5a1ec83d65

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.ie_open · Ω:ie_open
Pins: sha256:80683d46c41a7b82deadd804007c391f63436850f2076b26e0d6b19ee04cc500this graph alone
Evidence: sha256:c1d0c0ab424ea499437bc102b6439eb7f0853c878918665082a31a720bb9e904the 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.