growth_step

std.seq.growth_step · Level L0

One step of the discrete exponential model: x ← r·x. The body geometric_growth scans.

xₙ₊₁ = r·xₙ

Signature

growth_step(x: f64[m], t: f64[], rate: 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 rate * x in exact rational arithmetic, on all 40 test cases.
All 173 float64 results inside the running error bound; the closest uses 84% 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 79% 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

max_clique max_matching geometric_growth inclusion_exclusion

sha256:43d3b59d9332e471b3901ac445ff9c4e35243ae4e5825aac08a8fe312cee3915

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.growth_step · Ω:growth_step
Pins: sha256:3f0ac47483b25eba47e762818620cbdfe56a973e5365729c58506731f441e027this graph alone
Evidence: sha256:a7f31f9cb8a1e4168ec65e39e7adb6fb1aaec81f48d62f555bac8bfa96ac7920the 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.