bracket_open

std.func.bracket_open · Level L1

Whether any bisection bracket is still wider than tol, as 1 or 0. The condition bisect loops on.

[ maxᵢ (hiᵢ − loᵢ) > tol ]

Signature

bracket_open(lo: f64[n], hi: f64[n], tol: 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(np.max(hi - lo) > tol) 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

bisect

sha256:16b58ce4ed612af1fab92dddfe7170d8ca42c96b21d476389e0eef9e546c7da9

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

Control handle

Symbol: Ω:std.func.bracket_open · Ω:bracket_open
Pins: sha256:2315849638a2fe9ade6f315bf5d643a4d493425cdc03b0ffd2835c7c3a6b29b9this graph alone
Evidence: sha256:e963b7ba3caaf953acd7259ddd845a2ba842e481c6412b72a375c9bbf84ad5fdthe 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.