order_running
std.elementwise.order_running · Level L4Whether some power aᵏ mod n has not yet returned to 1, as 1 or 0. The condition multiplicative_order loops on.
[some aᵏ ≢ 1 (mod n)]
Signature
order_running(k: i64[s], pw: i64[s], a: i64[s], n: i64[s]) → 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(pw != 1 % n))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:a0c177cc236122002f4ff74c470e96d6ea8a334bd44c878626f071859a8e6df0The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.
Control handle
- Symbol
- Ω:std.elementwise.order_running · Ω:order_running
- Pins
sha256:b69b3aeca7567edc90b08e504315aa098d57a8bb2beed636d1648ce78ebdf37athis graph alone- Evidence
sha256:beda7b477a45129fc436cff8f9c5e863b23227adaba5ce4e1abeef0a80eb8174the 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.