valuation_step

std.elementwise.valuation_step · Level L4

Where p divides m, divide it out once and count it. The body padic_valuation runs.

(m, k) → (m/p, k + 1) where p | m

Signature

valuation_step(m: i64[s], k: i64[s], p: 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 m % p == 0: m // p, k + 1 in exact rational arithmetic, on all 40 test cases.
All 358 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

—

Called by

padic_valuation

sha256:f828b4e8bcf4dd831d725ac0bec8b41c27b4d15c7183526f4be016fc97d92f5a

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.valuation_step · Ω:valuation_step
Pins: sha256:b29def97ee9bc102bb19119bc61ed980dcaed2e82d32e762817e85f84b6fa402this graph alone
Evidence: sha256:2bed540bac50a66a5afefc8accfdd40adc33f4b2360cfa1df7c903cf2de4f768the 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.