fixed_point_step

std.func.fixed_point_step · Level L0

One step of fixed-point (Picard) iteration: x ← g(x), elementwise. The body fixed_point loops on; it takes the loop's tolerance and does not use it. A template over g.

x′ = g(x)

Signature

fixed_point_step(x: f64[n], tol: f64[]) → 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.
Agrees with the reference witness g = sigmoid: sigmoid(x) to 80 digits (100-digit arithmetic), on all 40 test cases.
All 139 float64 results inside the running error bound; the closest uses 15% of it.
Interpreter and NumPy backend return bit-identical results.
At float32 too: the 40 test cases rounded to float32, and 40 of them inside the running error bound at u = 2⁻²⁴; the closest uses 19% of it.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 72%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 1.31

Identity

Calls

—

Called by

fixed_point

sha256:e0353a529bf000f503630b942b7951cbe38c3e9316fa74351594753d6164c510

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

Control handle

Symbol: Ω:std.func.fixed_point_step[g=std.elementwise.sigmoid]
Pins: sha256:27b8175b8d8bfce5dd8b031cc2916eeb7fbd06ef05bc1f3ebc103cccbfa6a0c0this graph and the 1 it reaches through calls
Evidence: sha256:b53243ba1608494803b86a61abb066b27ad98e4ddeb4ef74955aa12d7576105ethe 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.