gamma_sf

std.stats.gamma_sf · Level L5

The gamma distribution's upper tail with shape a and rate b: Q(a, b·x).

P(X > x; a, b) = Q(a, b·x)

Signature

gamma_sf(x: f64[n], shape: f64[], rate: f64[]) → f64[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 scipy.special.gammaincc(a, b·x) to 80 digits (100-digit arithmetic), on all 40 test cases.
All 152 float64 results inside the running error bound; the closest uses 26% of it.
Interpreter and NumPy backend return bit-identical results.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 21%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 25

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:e5635eeb696d471a67b74ef9c8713fdf2ec51242c84af20d011651c615fdaea2

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

Control handle

Symbol: Ω:std.stats.gamma_sf · Ω:gamma_sf
Pins: sha256:58e1e6bed81317ebcf7a5b3ffb0058ebbbe38acd487aa108af27244ab16eacb1this graph alone
Evidence: sha256:a14342fa6b0cc27311b9803ae561fe0a33757b3140512c7c2115f4723d32e904the 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.