poly_definite_integral

std.seq.poly_definite_integral · Level L2

The fundamental theorem of calculus for a polynomial f (coefficients highest degree first): an antiderivative F with F(0) = 0, and the directed integral ∫_a^b f = F(b) − F(a); reversed limits change its sign and equal ones give 0.

∫_a^b f = F(b) − F(a), F′ = f

Signature

poly_definite_integral(c: f64[m], a: f64[], b: f64[]) → f64[m+1], 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 term-by-term antiderivative in exact arithmetic in exact rational arithmetic, on all 40 test cases.
All 199 float64 results inside the running error bound; the closest uses 50% 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): 96%
bit-equal to the NumPy formula in float64: 97%
largest error, in units in the last place: 3.49

Identity

Calls

horner poly_integral

Called by

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sha256:ba83ec13a9df6e189b7f87eef8cadceb59da5476f244ce9e0735e01d3e192853

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_definite_integral · Ω:poly_definite_integral
Pins: sha256:eec208d4a44f4b86f7c02f85b4cf76dc7edd6d137f3b4d9170c8e0c12e93fec6this graph and the 3 it reaches through calls
Evidence: sha256:4ae769897876e786e1db60f53dc836ae4d08ff2efbd56c8fd10d619d5c8a08bethe 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.