std

std.stats.std · Level L1

Population standard deviation. Calls variance.

√((1/n)·Σᵢ (xᵢ − x̄)²)

Signature

std(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]variancevSqrtssf64[]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Agrees with the reference np.std(x) to 80 digits (100-digit arithmetic), on all 40 test cases.
  • All 40 float64 results inside the running error bound; the closest uses 19% 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
1.51

Identity

sha256:6ba69dae4d6215805a108df5211f8cf6e6493b615e82c1e31a3af325a35e1ce7

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

Control handle

Symbol
Ω:std.stats.std · Ω:std
Pins
sha256:0754380d418ef017f9ed66972f6eaf5ac9ee7e6b81349f7687d9e73e5c91926dthis graph and the 1 it reaches through calls
Evidence
sha256:a66d0c47f4f036f62effe9f3acb479924859efbd4dc491fa3c99f8464e6a5103the 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.