lognormal_logpdf

std.stats.lognormal_logpdf · Level L5

The log-normal distribution's log density at x > 0: −log x − log σ − ½log 2π − (log x − μ)²/(2σ²), with π as arccos(−1).

log f(x) = −log(xσ√(2π)) − (log x − μ)²/(2σ²)

Signature

lognormal_logpdf(x: f64[n], mu: f64[], sigma: f64[]) → f64[n]

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.
Agrees with the reference −log x − log σ − log(2π)/2 − ((log x − μ)/σ)²/2 to 80 digits (100-digit arithmetic), on all 40 test cases.
All 166 float64 results inside the running error bound; the closest uses 17% 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 22% of it.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 38%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 20

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

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Called by

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sha256:4dee604687e0f4ac898608e319039d620b999b2770429111be827bbf5291d2cf

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

Control handle

Symbol: Ω:std.stats.lognormal_logpdf · Ω:lognormal_logpdf
Pins: sha256:290d1e5549e5f045180584cadcc6d3e67d9716e68a00a1d163578b4a37915334this graph alone
Evidence: sha256:f799ff7d12af1ef4c2c5911d80657c342ef246d173b1c842ab176646fc132399the 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.