npv

std.seq.npv · Level L2

The net present value of a cash flow c₀, c₁, … at one per period, at rate i per period: Σ cₜ/(1 + i)ᵗ, with c₀ undiscounted. Computed as the discounted return at factor 1/(1 + i), by Horner's rule from the last cash flow back.

NPV = Σₜ cₜ/(1 + i)ᵗ

Signature

npv(c: f64[T], i: f64[]) → 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 sum(c[t] / (1 + i)**t) in exact rational arithmetic, on all 40 test cases.
All 40 float64 results inside the running error bound; the closest uses 47% 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 27% of it.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 73%
bit-equal to the NumPy formula in float64: 65%
largest error, in units in the last place: 17

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

discounted_returns

Called by

—

sha256:31da393c8a9f16100825f5719efc54b2dc198dc50adb6744f364814643041fd8

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.npv · Ω:npv
Pins: sha256:16abd86fba70e48dfe9d0d19fac3875f07bcf58e7cce4fd5f475e7e1496fc977this graph and the 2 it reaches through calls
Evidence: sha256:02fb74fc962d12ec7032a82bd1a98bbc74be151238c58b2297b5bd2524a97229the 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.