gcd_unfinished

std.elementwise.gcd_unfinished · Level L2

Whether any pair still has a non-zero second number, for pairs stored as two rows of non-negative integers: 1 or 0. The condition gcd's loop tests.

maxᵢ [bᵢ > 0]

Signature

gcd_unfinished(state: i64[2, n]) → 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.

statei64[2, n]Sliceb0GreaterleftReduceMaxgogof64[]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Equal to the reference float(any(b > 0)) 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.
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
gcd
sha256:a3642714b9b45b741ce96f8aec362bbc49396096c85ff79a18f41d22e9400dce

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.gcd_unfinished · Ω:gcd_unfinished
Pins
sha256:ebf3096c7f7aab2c2a9fd9196a512e1455bfdd9f7b594600384cc539a4e765d9this graph alone
Evidence
sha256:7400815340e4547d1c8d8d5fc1d739d8d36e1597ed9af35542447fb97c282e62the 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.