conv1d_k3

std.seq.conv1d_k3 · Level L2

One-dimensional convolution with a three-tap kernel w, valid positions only — cross-correlation, as deep-learning libraries define it.

yᵢ = w₀xᵢ + w₁xᵢ₊₁ + w₂xᵢ₊₂

Signature

conv1d_k3(x: f64[n], w: f64[3]) → f64[n−2]

Requires: n ≥ 2

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]wf64[3]Slicex0Slicew0Slicex1Slicew1Slicex2Slicew2Multiplyp0Multiplyp1Multiplyp2Addp01Addyyf64[n−2]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size with n ≥ 2.
  • Equal to the reference np.correlate(x, w, "valid") in exact rational arithmetic, on all 40 test cases.
  • All 88 float64 results inside the running error bound; the closest uses 60% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
76%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
1.38

Identity

Calls
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Called by
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sha256:de93c20a6222969daf23ba6ee827d551f31912aa3e473296875b55dbad2c4e25

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