euler_step

std.seq.euler_step · Level L0

One forward-Euler step of the linear system x′ = A·x over a time step dt. The body that euler_linear scans.

x′ = x + dt·A·x

Signature

euler_step(x: f64[k], dt: f64[], A: f64[k, k]) → f64[k]

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[k]Af64[k, k]dtf64[]ReshapexcMatMulAxcReshapeAxMultiplymoveAddx2x2f64[k]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Equal to the reference x + dt * (A @ x) in exact rational arithmetic, on all 40 test cases.
  • All 155 float64 results inside the running error bound; the closest uses 57% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
74%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
32

Large ulp counts appear where a result is tiny next to the numbers it is computed from (after cancellation, for example), so one unit in the last place is tiny too; the absolute error is still inside the bound. Results within their own error of zero are not counted.

Identity

Calls
—
Called by
euler_linear
sha256:4d39a13df3db5cbd64dcc929948c3db29f0871b3ad7d8cae4e4e78ab371cec0e

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.euler_step · Ω:euler_step
Pins
sha256:56c584a87247f5d7c42445cedc742c0dc8e9cee8e2ed579210007a27d101a6fcthis graph alone
Evidence
sha256:32472a0f590e428609286d33667403847c965927abdb18f26742d2fb03b5757cthe 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.