power_step

std.algebra.power_step · Level L3

One step of computing every element's powers at once: pw(g) ← pw(g)·g, so after k steps from e it is gᵏ; an element whose power first returns to e at this step k gets order k. The body element_orders scans.

pw(g) ← pw(g)·g; first pw(g) = e at step k: ord(g) = k

Signature

power_step(pw: f64[n], order: f64[n], k: f64[], T: i64[n, n], e: f64[]) → f64[n], f64[n]

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 T[pw(g), g] for each g; order k where it first meets e in exact rational arithmetic, on all 40 test cases.
All 254 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

Calls

—

Called by

element_orders

sha256:78ad752a86e47d46151c59138bc3e83718b0e562915cfcebad96c7642b2c0c03

The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.

Control handle

Symbol: Ω:std.algebra.power_step · Ω:power_step
Pins: sha256:81d21969d060e03b36afef83e257665d1cd9f72be74b85668aa57208a85496abthis graph alone
Evidence: sha256:b526f50fa3514c026ec83c3f51c912bb85110a7489df75f83aed2da8fc77efe8the 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.