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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 1 - Linked List Matrices

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.

Inplace Field Operations Comparisons

Linked List Matrix - Closed Inplace Operations

addition

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integer

float16

float32

---

subtraction

  Click to Expand

integer

float16

float32

---

multiplication

  Click to Expand

integer

float16

float32

Inplace Scalar Operations Comparisons

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.

addition

  Click to Expand

integer

float16

float32

---

subtraction

  Click to Expand

integer

float16

float32

---

multiplication

  Click to Expand

integer

float16

float32

---

mod

  Click to Expand

integer

float16

float32

---

power

  Click to Expand

integer

float16

float32

---

floordiv

  Click to Expand

integer

float16

float32

---

 

Conjecture 2 - Scalar dtype Conversion Decorators

 

Conjecture 3