gamma

std.elementwise.gamma · Level L5

The gamma function Γ(x) for x > 0, as e^(log Γ(x)): (n − 1)! at the positive integers, √π at ½.

Γ(x) = ∫₀^∞ tˣ⁻¹ e⁻ᵗ dt

Signature

gamma(x: f64[n]) → 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 math.gamma(x) to 80 digits (100-digit arithmetic), on all 40 test cases.
All 162 float64 results inside the running error bound; the closest uses 15% 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 4% of it.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 17%
bit-equal to the NumPy formula in float64: 15%
largest error, in units in the last place: 6.26

Identity

Calls

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Called by

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sha256:e0c891110a956e54517088c49451e77eaf7faeffacba930dbe7221548e3c0265

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

Control handle

Symbol: Ω:std.elementwise.gamma · Ω:gamma
Pins: sha256:49713a60d67a767dd52cca2b5c610a5660e515a5efbf72a4b4f13e437b7d623dthis graph alone
Evidence: sha256:9cc49d108dca69983d1d2be5c8360660f4d90a7c5c94060152333f400501a4c5the 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.