fixed_point_open

std.func.fixed_point_open · Level L1

Whether some |g(x) − x| is still above tol, as 1 or 0. The condition fixed_point loops on. A template over g.

[ maxᵢ |g(xᵢ) − xᵢ| > tol ]

Signature

fixed_point_open(x: f64[n], tol: f64[]) → f64[]

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: float(np.max(np.abs(sigmoid(x) - x)) > tol) to 80 digits (100-digit arithmetic), on all 40 test cases.
All 40 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

fixed_point

sha256:0344c5e3364b07c4a9dcc07547b68e09652921231742885d0750219de92b5dbf

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_open[g=std.elementwise.sigmoid]
Pins: sha256:5de750c3688b074c20611270bd07ae3164e00ce0868a1a1b56773174c25cfcedthis graph and the 1 it reaches through calls
Evidence: sha256:4e5698d5afd964e163cc2ff220481d2b2af5955b54856e52b50606270db5d343the 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.