segment_lengths

std.geometry.segment_lengths · Level L2

Lengths of the segments of a polyline through the points P, in order.

Lᵢ = ‖Pᵢ₊₁ − Pᵢ‖

Signature

segment_lengths(P: f64[n, d]) → f64[n−1]

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]SlicelaterSliceearlierSubtractstepMultiplysqReduceSumssSqrtLLf64[n−1]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Agrees with the reference np.sqrt(np.sum(np.diff(P, axis=0) ** 2, axis=1)) to 80 digits (100-digit arithmetic), on all 40 test cases.
  • All 113 float64 results inside the running error bound; the closest uses 61% 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
1.44

Identity

sha256:f4e1eb03663d6aac10b6ddeaf011e4a851a4edb37d25eca2c560e18e9a78850d

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.segment_lengths · Ω:segment_lengths
Pins
sha256:dede73e18aad29b8122cc3303c3aadf9442cacabc09d41105961cd2f88147188this graph alone
Evidence
sha256:94cec96f7c5819e98a2e6538238c4f7758c4a0631c8c32687d7f674d9733721fthe 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.