bisect_step

std.func.bisect_step · Level L1

One bisection step for a root of f in each bracket [lo, hi]: halve it at the midpoint and keep the half where f changes sign. The body bisect loops on; it takes the loop's tolerance and does not use it. A template over f.

m = (lo + hi)/2; [m, hi] if f(lo) and f(m) have one sign, else [lo, m]

Signature

bisect_step(lo: f64[n], hi: f64[n], tol: 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.
Agrees with the reference witness f = silu: mid = (lo + hi)/2; [mid, hi] where f(lo) > 0 equals f(mid) > 0, else [lo, mid] to 80 digits (100-digit arithmetic), on all 40 test cases.
All 292 float64 results inside the running error bound; the closest uses 49% 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 49% of it.

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: 0.50

Identity

Calls

—

Called by

bisect

sha256:9e4652f3fb005e76d4f9982ab53559bd5496ac537e014dc6cbfaac418bcdddd8

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.bisect_step[f=std.elementwise.silu]
Pins: sha256:0c7338c9bede014c24c15cdcae88844d79fb83ee4b7f4a5b3bfb0713a9275d0ethis graph and the 1 it reaches through calls
Evidence: sha256:07a1740fd336117965fa25c3a5e1a7b41af1f440eb20299cf30102288a7f1c88the 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.