word_step

std.stats.word_step · Level L0

One factor of a Bernoulli cylinder probability: acc·p for a 1, acc·(1 − p) for a 0. The body bernoulli_word scans.

acc·(w·p + (1 − w)(1 − p))

Signature

word_step(acc: f64[], w: f64[], prob: f64[]) → f64[]

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 acc times p or 1 − p in exact rational arithmetic, on all 40 test cases.
All 40 float64 results inside the running error bound; the closest uses 98% 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 74% 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

bernoulli_word

sha256:8af9494f2e7a771eb564471e12870d26a6d55dd56134033c36d0020d73798c0f

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.word_step · Ω:word_step
Pins: sha256:93c80572669b557e123258b5cfa587e88a66a1e2c6e5c2bf64280d6c1d27a4fcthis graph alone
Evidence: sha256:1c3622f4d631d45bae72593e1c0553574a921e35ca8e453188edc17f5f856bc5the 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.