norm

std.linalg.norm · Level L1

Euclidean norm. Calls norm_sq.

‖x‖ = √(x·x)

Signature

norm(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]norm_sqsqSqrtssf64[]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Agrees with the reference np.linalg.norm(x) to 80 digits (100-digit arithmetic), on all 40 test cases.
  • All 40 float64 results inside the running error bound; the closest uses 79% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
93%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
0.71

Identity

sha256:b9f21d1977e15d2d7731748462f3cdc15cfd2e0663a81c5474943be5d277d6ea

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 · Ω:norm
Pins
sha256:8c37166844e29e4f3f0cb18663125f10d8d2453519f09bf9d5adea1e80c0d9dbthis graph and the 2 it reaches through calls
Evidence
sha256:34b5bfaef13b0eb06b76024284901510de294831f1b5517e3527cacbcdbd4a9dthe 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.