euclid_step

std.elementwise.euclid_step · Level L4

One step of Euclid's algorithm on pairs stored as two rows: (a, b) becomes (b, a mod b); a finished pair, with b = 0, stays as it is. gcd repeats it.

(a, b) → (b, a mod b)

Signature

euclid_step(state: i64[2, n]) → i64[2, 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.

statei64[2, n]SliceaSliceb0Equaldone1Wherea2Whereb_safeModrWhereb2Concatstate2state2i64[2, n]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Equal to the reference (b, a % b), or (a, 0) when b = 0 in exact rational arithmetic, on all 40 test cases.
  • All 310 int64 results are exact: the error is zero.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the int64 nearest the exact value)
100%
bit-equal to the NumPy formula in int64
100%
largest error, in units in the last place
0

Identity

Calls
—
Called by
gcd
sha256:09315c6a2bbd36442eb8ab42aaade56b9ceba5671c69906c5a4f22d4eff1db5b

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

Control handle

Symbol
Ω:std.elementwise.euclid_step · Ω:euclid_step
Pins
sha256:c2809cfcfaa3295a0f9aef4a9ed1c71c9a1e5c2512941914c578bf0385064ca1this graph alone
Evidence
sha256:f10227af3d0240796d048d755606f7adfbf71c7ec071b73fc48655cba203b2adthe 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.