diff

std.seq.diff · Level L2

First differences: each element minus the one before it. One element shorter than x.

dᵢ = xᵢ₊₁ − xᵢ

Signature

diff(x: f64[n]) → 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.

xf64[n]SlicelaterSliceearlierSubtractddf64[n−1]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Equal to the reference np.diff(x) in exact rational arithmetic, on all 40 test cases.
  • All 146 float64 results inside the running error bound; the closest uses 93% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
100%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
0.50

Identity

Calls
—
Called by
trapezoid_xy
sha256:f1eeca7a3d9ad56364c01f33ec472e3ad6edc34fd76efade702b8ccdf80e7412

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.diff · Ω:diff
Pins
sha256:87236799bd54d0eaae1a73413d11273d4296fb66cfce527fdbdd0871c7d18442this graph alone
Evidence
sha256:68065d0c275a23f9743dcc39288b63d97a6df94915e5104dce4fd3cf44086842the 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.