product_step

std.sets.product_step · Level L0

One factor of a product: acc·v. The body counting_rules scans.

acc ← acc·v

Signature

product_step(acc: f64[], v: 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 * v in exact rational arithmetic, on all 40 test cases.
All 40 float64 results are exact: the error is zero.
Interpreter and NumPy backend return bit-identical results.
At float32 too: the 40 test cases rounded to float32, and 40 of them exact, with zero error.

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

Identity

Calls

—

Called by

counting_rules

sha256:345c246d784829ac71143f9658ddf17997e3f26d4948fdb74a116b6d31f546e1

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

Control handle

Symbol: Ω:std.sets.product_step · Ω:product_step
Pins: sha256:80182f27e3475ebd2066c3c317566a1c4bd95418d6dc7c9f1b69bf212bc54985this graph alone
Evidence: sha256:4cc1f3cdafda411d80059f70985fe1f94791f75f289620f8e3ba699798b9bffethe 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.