factorial_mod_step
std.elementwise.factorial_mod_step · Level L4Where k ≤ n, multiply the running product by k modulo m, and move to k + 1. The body factorial_mod runs.
(k, acc) → (k + 1, acc·k mod m) while k ≤ n
Signature
factorial_mod_step(k: i64[s], acc: i64[s], n: i64[s], m: i64[s]) → i64[s], i64[s]
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
where k <= n: k + 1, acc*k % min exact rational arithmetic, on all 40 test cases. - All 308 int64 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 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
sha256:be898299b181bd8b6836865d3c3ecb83d32fa600f1aa28720c6f25cc50c3b557The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.
Control handle
- Symbol
- Ω:std.elementwise.factorial_mod_step · Ω:factorial_mod_step
- Pins
sha256:fe79cb066def49cf8cd45ffa422042216734524dad03b74d47f0e225b4041ef7this graph alone- Evidence
sha256:18a71fb96a7f2882701cbed0c59ca1dbf882708594a632b884beb3e9569c2745the 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.