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 only where cancellation drives a result toward zero; the absolute error is still inside the bound.

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.