polyline_length

std.geometry.polyline_length · Level L2

Total length of the polyline through the points P. Calls segment_lengths.

Σᵢ ‖Pᵢ₊₁ − Pᵢ‖

Signature

polyline_length(P: f64[n, d]) → 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.

Pf64[n, d]segment_lengthsLReduceSumlengthlengthf64[]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Agrees with the reference np.sum(np.sqrt(np.sum(np.diff(P, axis=0) ** 2, axis=1))) to 80 digits (100-digit arithmetic), on all 40 test cases.
  • All 40 float64 results inside the running error bound; the closest uses 47% 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
0.91

Identity

Calls
segment_lengths
Called by
—
sha256:0559dfe15921ab7277cb2dae614e8597c3683143dda992d2f4963ea719323822

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

Control handle

Symbol
Ω:std.geometry.polyline_length · Ω:polyline_length
Pins
sha256:5ea81e1bcd47269a2e4f33c50b31593a9b38016842924b3c0c7b856f0db5a34dthis graph and the 1 it reaches through calls
Evidence
sha256:1692ad30362777eac42af9a0bc45628eb8bc0f5cba355aadd411390bb1d4e94athe 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.