normalize

std.linalg.normalize · Level L1

Scale a non-zero vector to unit length. Calls norm.

x / ‖x‖

Signature

normalize(x: f64[n]) → f64[n]

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]normlenDivideuuf64[n]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Agrees with the reference x / np.linalg.norm(x) to 80 digits (100-digit arithmetic), on all 40 test cases.
  • All 147 float64 results inside the running error bound; the closest uses 48% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
73%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
1.36

Identity

Calls
norm
Called by
—
sha256:447f30f25fe3d26effa7a14a064696a686cb20c591dab70ea36ac2f91326b73a

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.normalize · Ω:normalize
Pins
sha256:5a8a380441b603f0b386cb643d9a4d5c65a405225aac77b290b283786ce94016this graph and the 3 it reaches through calls
Evidence
sha256:440863c76c4eb0a3f06d292553254dd2efee6fcdd587fd59e063ef275c8f4737the 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.