norm_sq

std.linalg.norm_sq · Level L0

Squared Euclidean norm. Calls dot.

‖x‖² = x·x

Signature

norm_sq(x: f64[n]) → 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.

xf64[n]dotssf64[]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Equal to the reference np.sum(x * x) in exact rational arithmetic, on all 40 test cases.
  • All 40 float64 results inside the running error bound; the closest uses 39% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
95%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
1.03

Identity

Calls
dot
Called by
sqdistnorm
sha256:eefaa4b542a4467d5d143b46c4ec5f333d282904eeb923855ce43f249d4e371a

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

Control handle

Symbol
Ω:std.linalg.norm_sq · Ω:norm_sq
Pins
sha256:8e8ad32d34e36a2b4da059f138acc5efb8f938570f5f396350e3975acd2930d5this graph and the 1 it reaches through calls
Evidence
sha256:926948e43dee22e80716784e66903266bedf1fe6c34a4b70028c5072d12415d9the 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.