dimension_ops

std.elementwise.dimension_ops · Level L1

Dimensional analysis with the base dimensions L, M and T, each quantity's dimension an exponent vector (a, b, c) for L^a M^b T^c: the dimension of a product (exponents add), of a quotient (they subtract), of the k-th power (they scale by k), and whether u and v have the same dimension, which an equality or a sum of the two quantities needs, as 1 or 0. Consistent dimensions are necessary for a physical equation, not sufficient.

[QR] = [Q] + [R], [Q/R] = [Q] − [R], [Qᵏ] = k[Q]

Signature

dimension_ops(u: f64[3], v: f64[3], k: f64[]) → f64[3], f64[3], f64[3], 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 exponent arithmetic in exact rational arithmetic, on all 40 test cases.
All 400 float64 results are exact: the error is zero.
Interpreter and NumPy backend return bit-identical results.
At float32 too: the 40 test cases rounded to float32, and 40 of them exact, with zero error.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 100%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 0

Identity

Calls

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Called by

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sha256:7336efd2dc0e5a36cf342eda8103928ba807488c232bb19fc0d8e767335ec754

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.dimension_ops · Ω:dimension_ops
Pins: sha256:82f5b6d280c61b1fb470ed5977ea37a9b6b5229a7b493921afb8d1ab3446787bthis graph alone
Evidence: sha256:2c7fa841881af55a39b130cfe3e104c2d5903e7c0b2cb807ac92e2cdc3587784the 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.