lognormal_cdf

std.stats.lognormal_cdf · Level L5

The log-normal distribution's cumulative probability: Φ((log x − μ)/σ) for x > 0. Calls normal_cdf.

F(x) = Φ((log x − μ)/σ)

Signature

lognormal_cdf(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 (1 + erf((log x − μ)/(σ√2)))/2 to 80 digits (100-digit arithmetic), on all 40 test cases.
All 143 float64 results inside the running error bound; the closest uses 26% 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 32% of it.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 58%
bit-equal to the NumPy formula in float64: 75%
largest error, in units in the last place: 444

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

normal_cdf

Called by

—

sha256:82c5dee8082020008c110792bd8000bc46f22076acc7af0a98b4fe496863abe9

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_cdf · Ω:lognormal_cdf
Pins: sha256:42af6fb369d77a0ccc7559eb4db09a53c8e24f36a3f70d90e541f440d695f635this graph and the 1 it reaches through calls
Evidence: sha256:a9039990c344578b6fc48c5ababe423fbe32b273926971c17d054313de974668the 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.