# Tensor Instructions

Compared to JOLT instructions, JOLT Atlas operates on tensors. Most operations on tensors act entry wise, like `ADD`, while others such as `MAX` don't.In particular, each instruction specifies:

* The **program counter (PC)** address of this instruction in the bytecode.
* The **operation code (opcode)** that defines the instruction’s function.
* Three **input tensor operands**, specified as the index of a node in the computation graph. These tensor operands are analogous to registers in RISC-V, as both indicate the source location of an operand.
  * The third input tensor operand, used by special opcodes such as `Select`.
* The **destination tensor index**, i.e. the node index in the computation graph where the result will be stored. It is analogous to **`rd`** in RISC-V, indicating the write destination of the operation result.
* An **immediate value**, if applicable to the instruction.
* The number of **virtual instructions remaining** in a *virtual sequence* (see Section 6.2 of the *Jolt* paper).
* The **dimensions** of the output tensor.

> **Note:** Currently limited to rank-2 tensors; scaling for higher ranks is a planned improvement.

* The **number of active elements** in the output tensor.

#### List of instructions <a href="#list-of-instructions" id="list-of-instructions"></a>

| **Op**            | **Expression / Description**                        |
| ----------------- | --------------------------------------------------- |
| **Input**         | $X(input)$                                          |
| **MatMul**        | A \* B                                              |
| **Relu**          | $max(0, x)$                                         |
| **Sigmoid**       | $1 / (1 + e^{(-x)})$                                |
| **Add**           | $A + B$                                             |
| **EinSum**        | $Cᵢⱼ = ∑ₖ Aᵢₖ Bₖⱼ$                                  |
| **Const**         | $c (const)$                                         |
| **RmAxis**        | $squeeze(X)$                                        |
| **Reshape**       | $reshape(X, new\\\_shape)$                          |
| **Conv**          | $(X \* K)(i, j) = ∑\_{ₘ,ₙ} X(i + m, j + n) K(m, n)$ |
| **MaxPool**       | $Y(i, j) = max\_{ₘ,ₙ ∈ window} X(i + m, j + n)$     |
| **Gather**        | $Y(i) = X(g(i))$                                    |
| **Softmax**       | $yᵢ = e^{(xᵢ)} / ∑ⱼ e^{(xⱼ)}$                       |
| **Reduce**        | $y = ∑ᵢ x$ or $y = (1/n) ∑ᵢ xᵢ$                     |
| **AddAxis**       | $Y = expand\\\_dims(X)$                             |
| **Cast**          | $Y = cast(X, type)$                                 |
| **TypedBinOp**    | $C = A ∘ B$                                         |
| **ElementWiseOp** | $Y = f(X)$                                          |


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