axpby

std.linalg.axpby · Level L0

Linear combination of two vectors with scalar weights.

a·x + b·y

Signature

axpby(a: f64[], x: f64[n], b: f64[], y: f64[n]) → f64[n]

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.

af64[]xf64[n]bf64[]yf64[n]MultiplyaxMultiplybyAddzzf64[n]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Equal to the reference a * x + b * y in exact rational arithmetic, on all 40 test cases.
  • All 174 float64 results inside the running error bound; the closest uses 66% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
78%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
39

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
—
sha256:2968a70a35c9ff19496b61e43129a5e1f4e5ee31cbf3c05d3406bf0cdf241617

The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.

Control handle

Symbol
Ω:std.linalg.axpby · Ω:axpby
Pins
sha256:d9975f08db7e4a817ff6de273164775aa316ae542d4217b165a9ae6de64f93bfthis graph alone
Evidence
sha256:b403d04f2aae4dabc3f75bcb169601b240a8ab8076c144d03b0081e313856b54the 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.