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.
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 49% of it.
- Interpreter and NumPy backend return bit-identical results.
- 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 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.
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.
Control handle
- Symbol
- Ω:std.stats.quantile · Ω:quantile
- Pins
sha256:10a3c4193692da8fda2546c8fac0e8dcac5988f304e91429697050b3b14ba8d5this graph alone- Evidence
sha256:e8035b24629c7fba0f9a52cf057b7aa93ab243a8497533d19fe4e0701ee4d86fthe 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.