set_operations

std.sets.set_operations · Level L1

Union A ∪ B, intersection A ∩ B, difference A \ B and complement U \ A of subsets of one finite universe U, as 0/1 masks. The complement is always taken relative to the stated universe.

A ∪ B, A ∩ B, A \ B, U \ A

Signature

set_operations(A: f64[n], B: f64[n]) → f64[n], f64[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 bitwise or, and, and-not, not in exact rational arithmetic, on all 40 test cases.
All 552 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

—

sha256:824a0936f5f6078b0195d568d61d64d33fe77854ff9d819aded05427d89ed003

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.set_operations · Ω:set_operations
Pins: sha256:62c2e2e8b31e4f1533cad47538fcd644d78aa1f3ae8e38d3c8b3d4efdbfb65e0this graph alone
Evidence: sha256:13b62336fe62f3cfb60682414c5e97c42e379289ca5f442079f3c1d8dd5d72bbthe 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.