path_arclength

std.geometry.path_arclength · Level L2

Arc length along the polyline at every point, starting from 0: the running sum of the segment lengths. Calls segment_lengths.

s₀ = 0, sᵢ = Σⱼ<ᵢ ‖Pⱼ₊₁ − Pⱼ‖

Signature

path_arclength(P: f64[n, d]) → 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.

Pf64[n, d]segment_lengthsLCumSumrun[0.0]Concatssf64[n]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Agrees with the reference np.concatenate([[0], np.cumsum(segment lengths)]) to 80 digits (100-digit arithmetic), on all 40 test cases.
  • All 150 float64 results inside the running error bound; the closest uses 35% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
85%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
1.33

Identity

Calls
segment_lengths
Called by
—
sha256:b1cc8a27f66b6cc1b6b4b6c19b5e4405c9db57cc334be130998c916340db27ea

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