factorial_mod

std.elementwise.factorial_mod · Level L4

n! mod m, elementwise, multiplying 1 … n and reducing modulo m at every step, so nothing grows past m·n. Wilson's theorem says (p − 1)! ≡ −1 (mod p) exactly when p is prime.

n! mod m

Signature

factorial_mod(n: i64[s], m: 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 math.factorial(n) % m in exact rational arithmetic, on all 40 test cases.
All 160 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

Calls

factorial_mod_running factorial_mod_step

Called by

—

sha256:27b2ccfaeee314a8f82eea19a0b53b12c66ab8be5f17a5f729475f6cdca93ad1

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.factorial_mod · Ω:factorial_mod
Pins: sha256:e9aa5a5a5ab98f6881c0e5fc60b3aeb0e4ded61fdc7a7d45d004a901f2012db5this graph and the 2 it reaches through calls
Evidence: sha256:48cc2a9b134da6fd1b4d93539c6b5d6ab29fd2cf64251b9f0659bc5b1a4a07dathe 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.