factorial

std.elementwise.factorial · Level L3

n! for each n ≥ 0, as P(n, n) through permutations. 0! = 1. Exact through 18! = 6.4·10¹⁵ < 2⁵³; 21! overflows int64.

n! = P(n, n), 0! = 1

Signature

factorial(n: 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) in exact rational arithmetic, on all 40 test cases.
All 155 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

permutations

Called by

—

sha256:25cc2b185273685ef93e6247c6f2a6304ed5dd6c905445a50658e7e9aca965eb

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 · Ω:factorial
Pins: sha256:16b54f3a9d6a1ec11075e60d3f8f77e66d07d772a7c5ff5a2644e33bb882d909this graph and the 3 it reaches through calls
Evidence: sha256:884975e6dd04e930416bcfe3a16ae4f80007725d7206f1c60b77ab4bb9ea292fthe 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.