segment_sum

std.stats.segment_sum · Level L3

Add each value into its segment: x[k] goes to base[seg[k]], and segments that repeat accumulate. A ScatterAdd.

outⱼ = baseⱼ + Σ{ xₖ : segₖ = j }

Signature

segment_sum(base: f64[m], seg: i64[n], x: f64[n]) → f64[m]

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.

basef64[m]segi64[n]xf64[n]ScatterAddoutoutf64[m]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Equal to the reference out = base.copy(); np.add.at(out, seg, x) in exact rational arithmetic, on all 40 test cases.
  • All 148 float64 results inside the running error bound; the closest uses 90% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
97%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
1.00

Identity

Calls
—
Called by
—
sha256:3ab76686537716121303cc8b84df5b74f0e9d3489e7900659a351d9362f9e016

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.segment_sum · Ω:segment_sum
Pins
sha256:9a36299891700e542afad8bf51b96c297c48750894b650d70417932b16511c6fthis graph alone
Evidence
sha256:af79067bb51f80830f29a890d7e63a90530c52ab58c2e39305ea075c33c1ceb2the 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.