triangle_check

std.geometry.triangle_check · Level L3

Whether three points A, B, C of the plane (the rows of P) form a non-degenerate triangle, as 1 or 0: they are distinct and not collinear, which is (B − A) × (C − A) ≠ 0; and that cross product, twice the signed area (positive when A, B, C run counterclockwise). Exact for integer coordinates.

(B − A) × (C − A) ≠ 0

Signature

triangle_check(P: f64[3, 2]) → 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.
Equal to the reference the cross product in exact arithmetic in exact rational arithmetic, on all 40 test cases.
All 80 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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sha256:73130f721b7f6ad497b023800807f32e1db52343c1dca7d3a415d1999693e315

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.triangle_check · Ω:triangle_check
Pins: sha256:83a88a3423583c164ac511edb2dd34af90a93e136fd030c0b3619ed4c3b937dcthis graph alone
Evidence: sha256:7b04deda797892bf16f431919827e8500881b7f061050a2431ee61ed0a79e0bathe 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.