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• Conjecture 1 - Linked List Matrices
  • Inplace Field Operations Comparisons
    • addition
    • subtraction
    • multiplication
  • Inplace Scalar Operations Comparisons
    • addition
    • subtraction
    • multiplication
    • mod
    • power
    • floordiv
• Conjecture 2 - Scalar dtype Conversion Decorators
• Conjecture 3

Conjecture

$\forall A \in X, n(P(A, ⊕) - P(U(A), ⊕)) - T(A) > 0 \implies$ The matrix should be converted to a linked list for $n$ operations.

Linked List Matrix - Closed Inplace Operations

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integer

float16

float32

  Click to Expand

integer

float16

float32

  Click to Expand

integer

float16

float32

To achieve the speedup with scalar operations, scalars are converted to linked list matrices and cached.

Thus, there is added $U(α) \cdot min(c, R)$, where $c$ is the cache size of the conversion method and R is the range of $α$.

$\forall A \in X, n(P(A, ⊕) - P(U(A), ⊕)) - T(A) - U(α) \cdot min(c, R) > 0 \implies$ The matrix should be converted to a linked list for $n$ operations.

  Click to Expand

integer

float16

float32

  Click to Expand

integer

float16

float32

  Click to Expand

integer

float16

float32

  Click to Expand

integer

float16

float32

  Click to Expand

integer

float16

float32

  Click to Expand

integer

float16

float32