cross

std.linalg.cross · Level L2

The cross product of 3-vectors, row by row: u × v, perpendicular to both, with length |u||v| sin θ. NumPy's np.cross.

u × v = (u₂v₃ − u₃v₂, u₃v₁ − u₁v₃, u₁v₂ − u₂v₁)

Signature

cross(u: f64[n, 3], v: f64[n, 3]) → f64[n, 3]

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 np.cross(u, v) in exact rational arithmetic, on all 40 test cases.
All 435 float64 results inside the running error bound; the closest uses 83% 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 73% of it.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 80%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 249

Large ulp counts appear where a result is tiny next to the numbers it is computed from (after cancellation, for example), so one unit in the last place is tiny too; the absolute error is still inside the bound. Results within their own error of zero are not counted.

Identity

Calls

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Called by

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sha256:41262839d38e2209375d1175e60a1b122f32c1983bc9641b79128b64911421a6

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

Control handle

Symbol: Ω:std.linalg.cross · Ω:cross
Pins: sha256:ee59bccc339749f635c7ec9df689fb2e08163f7f318166bdb61615f82de3722athis graph alone
Evidence: sha256:e29408960698cfc4c579895b2db876a85b4f715b50a4addd8b4fac64f426989cthe 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.