## PLUS Addition Operator

Section: Mathematical Operators

### Usage

Adds two numerical arrays (elementwise) together. There are two forms for its use, both with the same general syntax:

      y = a + b

where `a` and `b` are `n`-dimensional arrays of numerical type. In the first case, the two arguments are the same size, in which case, the output `y` is the same size as the inputs, and is the element-wise the sum of `a` and `b`. In the second case, either `a` or `b` is a scalar, in which case `y` is the same size as the larger argument, and is the sum of the scalar added to each element of the other argument. The type of `y` depends on the types of `a` and `b` using the type promotion rules. The types are ordered as:

1. `uint8` - unsigned, 8-bit integers range `[0,255]`
2. `int8` - signed, 8-bit integers `[-127,128]`
3. `uint16` - unsigned, 16-bit integers `[0,65535]`
4. `int16` - signed, 16-bit integers `[-32768,32767]`
5. `uint32` - unsigned, 32-bit integers `[0,4294967295]`
6. `int32` - signed, 32-bit integers `[-2147483648,2147483647]`
7. `float` - 32-bit floating point
8. `double` - 64-bit floating point
9. `complex` - 32-bit complex floating point
10. `dcomplex` - 64-bit complex floating point

Note that the type promotion and combination rules work similar to `C`. Numerical overflow rules are also the same as `C`.

### Function Internals

There are three formulae for the addition operator, depending on the sizes of the three arguments. In the most general case, in which the two arguments are the same size, the output is computed via:

If `a` is a scalar, then the output is computed via

On the other hand, if `b` is a scalar, then the output is computed via

### Examples

Here are some examples of using the addition operator. First, a straight-forward usage of the plus operator. The first example is straightforward - the `int32` is the default type used for integer constants (same as in `C`), hence the output is the same type:

    --> 3 + 8

    ans =

     11

    -->
    quit

Next, we use the floating point syntax to force one of the arguments to be a `double`, which results in the output being `double`:

    --> 3.1 + 2

    ans =

        5.1000

    -->
    quit

Note that if one of the arguments is complex-valued, the output will be complex also.

    --> a = 3 + 4*i

    a =

        3.0000 +  4.0000i

    --> b = a + 2.0f

    b =

        5.0000 +  4.0000i

    -->
    quit

If a `complex` value is added to a `double`, the result is promoted to `dcomplex`.

    --> b = a + 2.0

    b =

        5.0000 +  4.0000i

    -->
    quit

We can also demonstrate the three forms of the addition operator. First the element-wise version:

    --> a = [1,2;3,4]

    a =

     1 2
     3 4

    --> b = [2,3;6,7]

    b =

     2 3
     6 7

    --> c = a + b

    c =

      3  5
      9 11

    -->
    quit

Then the scalar versions

    --> c = a + 1

    c =

     2 3
     4 5

    --> c = 1 + b

    c =

     3 4
     7 8

    -->
    quit