interp_linear

std.seq.interp_linear · Level L3

Piecewise-linear interpolation through the points (xⱼ, yⱼ), x increasing, at each query point xq; beyond either end, the end value. NumPy's np.interp. The segment is found by counting the xⱼ at or below each query, exactly.

yⱼ + (xq − xⱼ)·(yⱼ₊₁ − yⱼ)/(xⱼ₊₁ − xⱼ), xⱼ ≤ xq < xⱼ₊₁

Signature

interp_linear(xq: f64[q], x: f64[n], y: f64[n]) → f64[q]

Requires: n ≥ 2

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 with n ≥ 2.
Equal to the reference np.interp(xq, x, y) in exact rational arithmetic, on all 40 test cases.
All 149 float64 results inside the running error bound; the closest uses 68% 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 75% of it.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 72%
bit-equal to the NumPy formula in float64: 82%
largest error, in units in the last place: 45

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

—

Called by

—

sha256:ea747eb7fd97d0098f3e2e69d6578995c1ca36d1fe1aa0710bb1cc2ac45bf5b8

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.interp_linear · Ω:interp_linear
Pins: sha256:98a1fbee5cd5f5ba6ef8b40a196cd524d8e493483cccd2151260d5459c77ac56this graph alone
Evidence: sha256:5d14e5d587e0dd5f9eed5b8aae68c070db4b0628617ec59e78ee0c6450e559d9the 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.