logistic_step

std.seq.logistic_step · Level L0

One step of the discrete logistic model: x ← x + r·x·(1 − x/K). The body logistic_growth scans.

xₙ₊₁ = xₙ + r·xₙ(1 − xₙ/K)

Signature

logistic_step(x: f64[m], t: f64[], rate: f64[m], K: 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 x + rate*x*(1 - x/K) in exact rational arithmetic, on all 40 test cases.
All 142 float64 results inside the running error bound; the closest uses 56% 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 88% of it.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 75%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 14

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

logistic_growth

sha256:eefa50fcc3c83f9e2e599cc67a41509a78f744237e1d7e0224fa6c8b2bad1077

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.logistic_step · Ω:logistic_step
Pins: sha256:ccc9f5ec6b2dbb811d70fc3e6fefd161c88eacbc1dbed09cf2119fa6775afbbethis graph alone
Evidence: sha256:562054eaed27e771856a2c009c4b2132fb60772b15d376f82b3a61f6eeba246fthe 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.