dot

std.linalg.dot · Level L0

Inner product of two vectors.

Σᵢ xᵢ·yᵢ

Signature

dot(x: f64[n], y: f64[n]) → 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.

xf64[n]yf64[n]MultiplyxyReduceSumssf64[]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Equal to the reference np.dot(x, y) in exact rational arithmetic, on all 40 test cases.
  • All 40 float64 results inside the running error bound; the closest uses 76% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
90%
bit-equal to the NumPy formula in float64
98%
largest error, in units in the last place
1.75

Identity

sha256:f475eae3aede46aeed8fb40e4d4f68964acfcf7bbd5c7eb60549aff318a3f2cd

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.dot · Ω:dot
Pins
sha256:7c2fb5b0df67240592264ceb63d6506b5331ce8715b0c076d7075814c7261550this graph alone
Evidence
sha256:36ccc15125ff45afcf18708af2cd52df7d1365dc3c3cc5eef6d6efd3376e39abthe 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.