circle_position

std.geometry.circle_position · Level L1

Where each point lies relative to the circle with centre O and radius r ≥ 0: −1 inside, 0 on the circle, 1 outside, from the squared distance against r². No square root is taken, so for exact inputs the decision is exact. r = 0 is the degenerate circle {O}.

sign(|P − O|² − r²)

Signature

circle_position(pts: f64[n, 2], center: f64[2], r: 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.
Equal to the reference sign(|p − O|² − r²) in exact rational arithmetic, on all 40 test cases.
All 149 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

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Called by

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sha256:f422de93a751e40c791a1eaedbb568c4dd7693f6fdef827e6f938c0442f6dae8

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

Control handle

Symbol: Ω:std.geometry.circle_position · Ω:circle_position
Pins: sha256:9035173cfa087139192dd3855eef62fc5411f9a8036b5361879db14ee927a90dthis graph alone
Evidence: sha256:00c6fdad8de47de0eece693ae3235d8689d3741ec38bd29c10b9ce025721c327the 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.