poisson_quantile_step
std.stats.poisson_quantile_step · Level L5One bisection step for the Poisson quantile, on every element at once: where the bracket [lo, hi] is still open, mid = ⌊(lo + hi)/2⌋ moves lo up to mid + 1 if F(mid) < p, else hi down to mid. F(mid) is Q(mid + 1, λ) below p = ½ and 1 − P(mid + 1, λ) above it. The body that poisson_quantile runs.
Signature
poisson_quantile_step(lohi: i64[2, n], p: f64[n], lam: f64[]) → i64[2, n]
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.
- Agrees with the reference
mid = (lo + hi) // 2; [mid + 1, hi] if exp(-λ)·Σ_{j≤mid} λʲ/j! < p else [lo, mid]to 80 digits (100-digit arithmetic), on all 40 test cases. - All 274 int64 results are exact: the error is zero.
- Interpreter and NumPy backend return bit-identical results.
- correctly rounded (the int64 nearest the exact value)
- 100%
- bit-equal to the NumPy formula in int64
- 100%
- largest error, in units in the last place
- 0
Identity
sha256:e35833e230bdf1b09a1c868f1c02c0616106950cbe63d6cc10616d186f5767faThe semantic hash of the graph. It changes when the program changes, and never when only its documentation does.
Control handle
- Symbol
- Ω:std.stats.poisson_quantile_step · Ω:poisson_quantile_step
- Pins
sha256:bae4f9563b6f5af93b0d2b35fca1fa51e357aedc4ec11948b2fed678eca46d7cthis graph alone- Evidence
sha256:4ed1d7a17b6715dd9211cf6a82d6780dc0576d853f204d0760ca745bf6b17502the 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.