poly_integral

std.seq.poly_integral · Level L2

The antiderivative of a polynomial that is 0 at t = 0, coefficients from the highest degree down: cₖ/(n − k), then a zero constant term. NumPy's np.polyint.

∫₀ᵗ Σₖ cₖ·sⁿ⁻¹⁻ᵏ ds = Σₖ cₖ/(n − k)·tⁿ⁻ᵏ

Signature

poly_integral(c: f64[n]) → f64[n+1]

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.polyint(c) in exact rational arithmetic, on all 40 test cases.
All 210 float64 results inside the running error bound; the closest uses 70% 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 74% of it.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 100%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 0.43

Identity

Calls

—

Called by

poly_definite_integral

sha256:aba533e2e13ec42f6544fced741dbd21e847b71b97abab47a85958316791d498

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

Control handle

Symbol: Ω:std.seq.poly_integral · Ω:poly_integral
Pins: sha256:a803c50d03211bf602a62073799144c138aa10d2a704b4ae9bb1874120fa980dthis graph alone
Evidence: sha256:3742b50a080e07b3754961cf67cfc7fa313d129cd67c8bcbddd09e3a79b84956the 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.