cumsum

std.seq.cumsum · Level L2

Running total: element i is the sum of x₀ … xᵢ.

sᵢ = Σⱼ≤ᵢ xⱼ

Signature

cumsum(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]CumSumssf64[n]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Equal to the reference np.cumsum(x) in exact rational arithmetic, on all 40 test cases.
  • All 175 float64 results inside the running error bound; the closest uses 66% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
93%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
1.14

Identity

Calls
—
Called by
—
sha256:ac816c82cc6961031623bb5d52da21a75fd4a86a4711b9fa6e143e8f2cb5bad3

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

Control handle

Symbol
Ω:std.seq.cumsum · Ω:cumsum
Pins
sha256:ab71c6af5a4ecfe4176b6c08450dfaaafd11ef17d67467f4477381ec88725228this graph alone
Evidence
sha256:f1a7a143385d94ea098309cbdb9c4fa6ee059c15c289fa1a9dfadec8b17778e9the 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.