newton_sqrt_step

std.seq.newton_sqrt_step · Level L0

One step of Newton's method for √a: average the guess with a divided by it. The body that sqrt_newton runs.

s′ = (s + a/s)/2

Signature

newton_sqrt_step(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[]DivideqAddt0.5Multiplys2s2f64[]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Equal to the reference (s + a / s) / 2 in exact rational arithmetic, on all 40 test cases.
  • All 40 float64 results inside the running error bound; the closest uses 41% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
88%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
0.70

Identity

Calls
—
Called by
sqrt_newton
sha256:93ba544f4caf9a8c83730a27ada64499105d311622a7869131034f16c424efa2

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.newton_sqrt_step · Ω:newton_sqrt_step
Pins
sha256:31235063f07ecfed58c4e232ca248e6118bf4f7076f448bed5ed6d253b0e16d1this graph alone
Evidence
sha256:41dc5677260d0c133135c5bb9490966015f0269cb5d8e87eb9cded9ca815eb0dthe 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.