affine_line

std.elementwise.affine_line · Level L1

The affine function f(x) = m·x + b through two points (x₁, y₁) and (x₂, y₂): whether it is defined (x₁ ≠ x₂, as 1 or 0), its slope m = (y₂ − y₁)/(x₂ − x₁), and its intercept b (both 0 when undefined). With m = 0 it is constant; it is linear in the sense of linear algebra only when b = 0.

m = (y₂ − y₁)/(x₂ − x₁), b = y₁ − m·x₁

Signature

affine_line(x1: f64[], y1: f64[], x2: f64[], y2: f64[]) → f64[], 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 the two-point formulas in exact arithmetic in exact rational arithmetic, on all 40 test cases.
All 120 float64 results inside the running error bound; the closest uses 41% 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 48% of it.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 84%
bit-equal to the NumPy formula in float64: 98%
largest error, in units in the last place: 3.3e+5

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

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Called by

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sha256:611c4dba08ce20a488b79a0b15dfe519ca3fb6b3633646979a570f2569f21b36

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.affine_line · Ω:affine_line
Pins: sha256:9bdb25afd5d5ef8d4acd59573bb5465a075e95b48a2e75538468637b49f78635this graph alone
Evidence: sha256:6aab1f8969d87d572245f581d241e6e44dfedd0cbf0688176b12de09ae50b2c7the 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.