sqrt_unconverged

std.seq.sqrt_unconverged · Level L1

Whether a square-root guess still misses: |s² − a| above 10⁻¹² of a, as 1 or 0. The condition sqrt_newton loops on.

[ |s² − a| > 10⁻¹²·a ]

Signature

sqrt_unconverged(s: f64[], 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.

sf64[]af64[]1.000e-12MultiplyssMultiplylimSubtractrNegatenrMaximumarGreatergogof64[]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Equal to the reference float(abs(s * s - a) > 1e-12 * a) 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
sqrt_newton
sha256:a8f9ec0c8f291bb3ff843b296fb9aa6b149c8adc1bed09bb76ec4a95a1a16568

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