present_value

std.elementwise.present_value · Level L5

The present value of an amount F due n periods ahead, at rate i per period: F/(1 + i)ⁿ, computed as F·exp(−n·log1p(i)). It inverts compound_balance.

PV = F/(1 + i)ⁿ

Signature

present_value(F: f64[m], i: f64[m], n: f64[m]) → f64[m]

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 F / (1 + i)**n to 80 digits (100-digit arithmetic), on all 40 test cases.
All 152 float64 results inside the running error bound; the closest uses 13% 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 25% of it.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 59%
bit-equal to the NumPy formula in float64: 47%
largest error, in units in the last place: 6.24

Identity

Calls

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Called by

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sha256:701226d6d7503422eeaad5dd11dfa5279cb2b126fc9d879edb5340e5cce664ff

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.present_value · Ω:present_value
Pins: sha256:7987a84690dea27928b1811ed6256d6b345a6aefd399dcfaf41160693708f347this graph alone
Evidence: sha256:0f844a6246f6c0c07d2ad67297ddc680c06929f7531b4ee693e039b61180efbbthe 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.