is_member

std.sets.is_member · Level L3

Whether x ∈ A for a subset A of a finite universe, as 1 or 0.

[x ∈ A]

Signature

is_member(A: f64[n], x: i64[]) → 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 A[x] 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

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sha256:e83d0905c07b5c27d3d668b9e81148c636cb03b541ab291da9544dd3f3a1bdb5

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.is_member · Ω:is_member
Pins: sha256:c0cb24c4d97f8b50214f69cb93096c14339939d1ac6fb4d1597a38fdb494f76dthis graph alone
Evidence: sha256:a883737a176f5ad9b577708fe52f13db9d76277c209c68c513a372ace971b623the 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.