bracket_unconverged

std.seq.bracket_unconverged · Level L2

Whether a bisection bracket is still too wide: hi − lo above 10⁻¹²·(|a| + 1), as 1 or 0. The condition cbrt_bisect loops on.

[ hi − lo > 10⁻¹²·(|a| + 1) ]

Signature

bracket_unconverged(lohi: f64[2], a: 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.

lohif64[2]af64[]SliceloSlicehiNegatenaSubtractw11.0Maximumabs_aReshapewidthAddscale1.000e-12MultiplylimGreatergogof64[]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Equal to the reference float(hi - lo > 1e-12 * (abs(a) + 1)) 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.
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
cbrt_bisect
sha256:208351c1095b50b175be1df29aaeee0e0c0f68f89633065f87ea9708fe0ee785

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