# Missing operators implementations
###### tags: `archive`

## Bitwise operations

Negation through the use of `tilde` (~)

def bitwise_negation(cond: boolean, inp0: Field, inp1: Field):
    result = inp0 if ~cond else inp1
    return result

Implementationg of XOR with use of `apostrophe` (^)

def bitwise_xor(cond1: boolean, cond2: boolean, inp0: Field, inp1: Field):
    result = inp0 if cond1^cond2 else inp1
    return result

HV: For field of booleans only, right? Makes sense.

NF: Correct, booleans or fields of booleans

## Basic trigonometric operations - all already implemented (it seems)

Most importantly: sin, cosin, tan

def sin_imp(inp1: Field):
    return sin(inp1)

HV: here is the list we want to support https://github.com/GridTools/gt4py/blob/adec0c3bf36fd2660ee766ec38114733672150ad/src/gt4py/gtscript.py#L39

NF: Good point! I didn't think about including this list in the doc

## Implement tests for all math builtins

A lot of math builtins such as log and exp are not tested anywhere

## Augmented assignments

This should work for primary BinaryOperators: +=, -=, *=, /=

def aug_add(inp1: Field):
    inp1 += 1
    return inp1

HV: In general, we don't want to support them because it obfuscates the functional language. Augmented assigns look like you are updating the left hand side, but all we can do is return a new object with the result of `inp1 + 1`.

NF: makes sense
## Logarithmic operators

This should include log2 and log10

def log2_imp(inp1: Field):
    return log2(inp1)

def log10_imp(inp1: Field):
    return log10(inp1)

HV: That means adding them to the frontend as syntax sugar, right?

NF: Yes, it does

## Matrix multiplication operator

Basic Python (from 3.5 onwards) uses the `at` (@) for matrix multiplication:

A = np.asarray([[1, 2], [3, 4]])

B = np.asarray([[11, 12], [13, 14]])

A @ B = array([[1 * 11 + 2 * 13, 1 * 12 + 2 * 14],
[3 * 11 + 4 * 13, 3 * 12 + 4 * 14]])

A @ B = array([[37, 40],
[85, 92]])

Likewise in gt4py:

def matrix_mult(inp0: Field, inp1: Field):
    return inp0@inp1

Here fields need to have the same dimensions

HV: I don't think we want this in the way you describe, but instead we want to add matrix/vector operations acting on (matrix/vector-valued) elements of the field.

NF: Ok, we can discuss this further once it's time
## Neighbor reductions

As extensions of neighbor_sum, this would include neighbor reductions functions for primary BinaryOperators:

@field_operator
def sum_cells(inp0: Field[[CellDim], float]) -> Field[[EdgeDim], float]:
    return neighbor_sum(inp0(E2C), axis=E2CDim)

Likewise, we may want:

neighbor_sub, neighbor_mult, neighbor_div

HV: Yes, we want a general reduce and then we can implement all of this as library functions. There are open issues we want to resolve before we start that https://github.com/GridTools/gt4py/issues/827.

NF: Good point, I should have checked the already existing issues. Thanks for pointing it out