bezout_running
std.elementwise.bezout_running · Level L1Whether the extended Euclidean algorithm still has a pair to reduce: some remainder r1 above 0, as 1 or 0. The condition bezout loops on.
[max r₁ > 0]
Signature
bezout_running(r0: i64[n], r1: i64[n], s0: i64[n], s1: i64[n], t0: i64[n], t1: i64[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.
- input
- operation
- constant
- call
- output
Verification
- Signature proven by NOVA’s shape solver, for every size.
- Equal to the reference
float(any(r1 > 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.
- 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
sha256:de711c456b4b9099ac5b4849f9abf5d507bd138543c8d7c87939c641dfd78c50The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.
Control handle
- Symbol
- Ω:std.elementwise.bezout_running · Ω:bezout_running
- Pins
sha256:0e64be125ad2294f2c811242595a8f98b5b1c6502b84ae7f4bc7feeeb4bf910dthis graph alone- Evidence
sha256:4fd5f57edbd009e1f330e531526a9dae50b70a4426cc1253a8808ac916e33270the 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.