quadrant

std.geometry.quadrant · Level L3

The quadrant of each point (x, y) of the coordinate plane: 1 for x > 0 and y > 0, 2 for x < 0 and y > 0, 3 for both negative, 4 for x > 0 and y < 0, and 0 on an axis (y = 0 is the x-axis, x = 0 the y-axis, meeting at the origin).

sign(x), sign(y) ↦ 1 … 4, 0 on an axis

Signature

quadrant(pts: f64[m, 2]) → f64[m]

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 signs of the coordinates in exact rational arithmetic, on all 40 test cases.
All 151 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:b5a5fe1c17a5500f40456af24a15811d9b30f1fe07cdb7d8ac22010f8b367934

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.quadrant · Ω:quadrant
Pins: sha256:99848cef8bd2d10fa9bcec7fc6965e41b756cd2570e701696322ff89f631934bthis graph alone
Evidence: sha256:2d1e1f6a17509471c7a9426bc346f6aa341884665e0201dfe31a80175d2dbf3cthe 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.