vandermonde_step

std.linalg.vandermonde_step · Level L0

One more power of x: v ← v·x, elementwise. The body that vandermonde scans; it does not read its sequence element, only counts the steps.

v′ = v·x

Signature

vandermonde_step(v: f64[m], k: f64[], x: f64[m]) → 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.

input
operation
constant
call
output

Verification

Signature proven by NOVA’s shape solver, for every size.
Equal to the reference v * x in exact rational arithmetic, on all 40 test cases.
All 162 float64 results inside the running error bound; the closest uses 87% of it.
Interpreter and NumPy backend return bit-identical results.
At float32 too: the 40 test cases rounded to float32, and 40 of them inside the running error bound at u = 2⁻²⁴; the closest uses 85% of it.

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

vandermonde

sha256:7484d04613c1d33413c1dff4c6fa332a89fddb4b815218a626f8c1cbbb173ea2

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

Control handle

Symbol: Ω:std.linalg.vandermonde_step · Ω:vandermonde_step
Pins: sha256:cb6ee73a99013b5004569dde454ce2e351f36889035eb9f36b45a6f3211db4e0this graph alone
Evidence: sha256:b8451a9c847ae615db2ba735f493e53f65997903cd22f1ad87aa739e5b32740bthe 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.