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.

Control handle

Symbol
Ω:std.seq.sqrt_unconverged · Ω:sqrt_unconverged
Pins
sha256:6ed8873114948a8ef2eef2ef887262efaf8306009223c2046613a0a6fb5f7d80this graph alone
Evidence
sha256:cd789ee5182e58c841b7f8a2f7f245f597fb904edda5a7eb6cff2fb3310e3644the 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.