quantile
std.stats.quantile · Level L2The q-quantile with linear interpolation (NumPy's default): sort, then weigh each sorted value by a tent 1 − |i − h| at position h = (n − 1)·q.
Σᵢ x₍ᵢ₎·max(0, 1 − |i − (n − 1)q|)
Signature
quantile(x: f64[n], q: 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
np.quantile(x, q)in exact rational arithmetic, on all 40 test cases. - All 40 float64 results inside the running error bound; the closest uses 17% of it.
- Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
- correctly rounded (the float64 nearest the exact value)
- 75%
- bit-equal to the NumPy formula in float64
- 80%
- largest error, in units in the last place
- 711
Large ulp counts appear only where cancellation drives a result toward zero; the absolute error is still inside the bound.
Note
The tent weights are the whole trick: when h falls between two positions they get 1 − (h − i) and h − i, which is linear interpolation; when h is a position it gets weight 1 alone. No index is ever computed.