# Add, Subtract, Sum of Elements, Sum

• Library:

HDL Coder / HDL Floating Point Operations

HDL Coder / Math Operations

## Description

The Sum block performs addition or subtraction on its inputs. The Add, Subtract, Sum of Elements, and Sum blocks are identical blocks. This block can add or subtract scalar, vector, or matrix inputs. It can also collapse the elements of a signal and perform a summation.

You specify the operations of the block with the List of signs parameter with plus (`+`), minus (`-`), and spacer (`|`).

• The number of `+` and `-` characters equals the number of inputs. For example, `+-+` requires three inputs. The block subtracts the second (middle) input from the first (top) input, and then adds the third (bottom) input.

• A spacer character creates extra space between ports on the block icon.

• If performing only addition, you can use a numerical value equal to the number of inputs.

• If only there is only one input port, a single `+` or `-` adds or subtracts the elements over all dimensions or in the specified dimension.

The Sum block first converts the input data type to its accumulator data type, then performs the specified operations. The block converts the result to its output data type using the specified rounding and overflow modes.

### Calculation of Block Output

Output calculation for the Sum block depends on the number of block inputs and the sign of input ports:

If the Sum block has...And...The formula for output calculation is...Where...

One input port

The input port sign is +

y = e[0] + e[1] + e[2] ... + e[m]

`e[i]` is the ith element of input u

The input port sign is –

y = 0.0 – e[0] – e[1] – e[2] ... – e[m]

Two or more input ports

All input port signs are –

y = 0.0 – u[0] – u[1] – u[2] ... – u[n]

`u[i]` is the input to the ith input port

The kth input port is the first port where the sign is +

y = u[k] – u[0] – u[1] – u[2] – u[k–1] (+/–) u[k+1] ... (+/–) u[n]

## Ports

### Inputs

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The inputs can be of different data types, unless you select the Require all inputs to have the same data type parameter.

Input signal to the addition or subtraction operation. If there is only one input signal, then addition or subtraction is performed on the elements over all dimensions or the specified dimension.

Data Types: `half` | `single` | `double` | `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64` | `Boolean` | `fixed point`

`n`th input signal to the operations. The number of inputs matches the number of signs in the List of signs parameter. The block applies the operations to the inputs in the order listed. You can also use a numerical value equal to the number of input ports as the List of signs parameter. The block creates the input ports and applies addition to all inputs. For example, if you assign `5` for the List of signs parameter, the block creates `5` input ports and adds them together to produce the output.

All nonscalar inputs must have the same dimensions. Scalar inputs are expanded to have the same dimensions as other inputs.

Data Types: `half` | `single` | `double` | `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64` | `Boolean` | `fixed point`

### Output

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Output signal resulting from addition and/or subtraction operations. The output signal has the same dimension as the input signals.

Data Types: `half` | `single` | `double` | `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64` | `Boolean` | `fixed point`

## Parameters

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### Main

Designate the icon shape of the block as rectangular or round.

For a rectangular block, the first input port is the top port. For a round Sum block, the first input port is the port closest to the 12 o'clock position going in a counterclockwise direction around the block. Similarly, other input ports appear in counterclockwise order around the block.

#### Programmatic Use

 Block Parameter: `IconShape` Type: character vector Values: `'rectangular'` | `'round'` Default: `'round'`

Enter addition and subtraction operations performed on the inputs. An input port is created for each operation. A spacer (`|`) creates extra space between the input ports on the block icon. Addition is the default operation. If you only want to add the inputs, enter the number of input ports. The operations are performed in the order listed.

When you enter only one element, the block enables the Sum over parameter. For a single vector input, `+` or `-` adds or subtracts the elements over all dimensions or in the specified dimension.

#### Tips

You can manipulate the positions of the input ports on the block by inserting spacers (`|`) between the signs in the List of signs parameter. For example, “`++|--`” creates an extra space between the second and third input ports.

#### Programmatic Use

 Block Parameter: `Inputs` Type: character vector Values: `'+'` | `'-'` | `|` | integer Default: `'++'`

Select the dimension over which the block performs the sum-over operation.

For All dimensions, all input elements are summed. When you select configuration parameter Use algorithms optimized for row-major array layout, Simulink® enables row-major algorithms for simulation. To generate row-major code, set configuration parameter Array layout (Simulink Coder) to `Row-major` in addition to selecting Use algorithms optimized for row-major array layout. The column-major and row-major algorithms differ only in the summation order. In some cases, due to different operation order on the same data set, you might experience minor numeric differences in the outputs of column-major and row-major algorithms.

When you select Specified dimensions, another parameter Dimension appears. Choose the specific dimension for summing the vector input.

#### Dependency

Enabled when you list only one sign in the List of signs parameter.

#### Programmatic Use

 Block Parameter: `CollapseMode` Type: character vector Values: ```'All dimensions'``` | ```'Specified dimension'``` Default: ```'All dimensions'```

When you choose Specified dimension for the Sum over parameter, specify the dimension over which to perform the operation.

The block follows the same summation rules as the MATLAB® `sum` function.

Suppose that you have a 2-by-3 matrix U.

• Setting Dimension to `1` results in the output Y being computed as:

`$Y={\sum }_{i=1}^{2}U\left(i,j\right)$`

• Setting Dimension to `2` results in the output Y being computed as:

`$Y={\sum }_{j=1}^{3}U\left(i,j\right)$`

If the specified dimension is greater than the dimension of the input, an error message appears.

#### Dependency

Enabled when you choose ```Specified dimension``` for the Sum over parameter.

#### Programmatic Use

 Block Parameter: `CollapseDim` Type: character vector Value: `integer` Default: `'1'`

Specify the sample time as a value other than -1. For more information, see Specify Sample Time.

#### Dependencies

This parameter is not visible unless it is explicitly set to a value other than `-1`. To learn more, see Blocks for Which Sample Time Is Not Recommended.

#### Programmatic Use

 Block Parameter: `SampleTime` Type: character vector Values: scalar or vector Default: `'-1'`

### Signal Attributes

Click the button to display the Data Type Assistant, which helps you set the data type attributes. For more information, see Specify Data Types Using Data Type Assistant.

Specify if input signals must all have the same data type. If you enable this parameter, then an error occurs during simulation if the input signal types are different.

#### Programmatic Use

 Block Parameter: `InputSameDT` Type: character vector Values: `'off' | 'on'` Default: `'off'`

Choose the data type of the accumulator. The type can be inherited, specified directly, or expressed as a data type object such as `Simulink.NumericType`. When you choose ```Inherit: Inherit via internal rule```, Simulink chooses a data type to balance numerical accuracy, performance, and generated code size, while taking into account the properties of the embedded target hardware.

#### Programmatic Use

 Block Parameter: ` AccumDataTypeStr` Type: character vector Values: ```'Inherit: Inherit via internal rule``` | ```'Inherit: Same as first input'``` | `'double'``'single'` | `'half'` | `'int8'` | `'uint8'` | `'int16'` | `'uint16'`, `'int32'` | `'uint32'` | `'int64'` | `'uint64'` | `'fixdt(1,16)'` | `'fixdt(1,16,0)'` | `'fixdt(1,16,2^0,0)'` | ```''``` Default: ```'Inherit: Inherit via internal rule'```

Lower value of the output range that Simulink checks.

Simulink uses the minimum to perform:

Note

Output minimum does not saturate or clip the actual output signal. Use the Saturation block instead.

#### Programmatic Use

 Block Parameter: `OutMin` Type: character vector Values: `'[ ]'`| scalar Default: `'[ ]'`

Upper value of the output range that Simulink checks.

Simulink uses the maximum value to perform:

Note

Output maximum does not saturate or clip the actual output signal. Use the Saturation block instead.

#### Programmatic Use

 Block Parameter: `OutMax` Type: character vector Values: `'[ ]'`| scalar Default: `'[ ]'`

Choose the data type for the output. The type can be inherited, specified directly, or expressed as a data type object such as `Simulink.NumericType`.

When you select an inherited option, the block behaves as follows:

• ```Inherit: Inherit via internal rule```—Simulink chooses a data type to balance numerical accuracy, performance, and generated code size, while taking into account the properties of the embedded target hardware.

Note

The accumulator internal rule favors greater numerical accuracy, possibly at the cost of less efficient generated code. To get the same accuracy for the output, set the output data type to ```Inherit: Inherit same as accumulator```.

Note

When input is a floating-point data type smaller than single precision, the ```Inherit: Inherit via internal rule``` output data type depends on the setting of the Inherit floating-point output type smaller than single precision configuration parameter. Data types are smaller than single precision when the number of bits needed to encode the data type is less than the 32 bits needed to encode the single-precision data type. For example, `half` and `int16` are smaller than single precision.

• `Inherit: Keep MSB`– Simulink chooses a data type that maintains the full range of the operation, then reduces the precision of the output to a size appropriate for the embedded target hardware.

Tip

For more efficient generated code, set the Accumulator data type to ```Inherit: Inherit via internal rule```, and deselect the Saturate on integer overflow parameter.

This rule never produces overflows.

• `Inherit: Keep LSB`– Simulink chooses a data type that maintains the precision of the operation, but reduces the range if the full type does not fit on the embedded target hardware.

Tip

For more efficient generated code, set the Accumulator data type to ```Inherit: Inherit via internal rule```, and deselect the Saturate on integer overflow parameter.

This rule can produce overflows.

If you change the embedded target settings, the data type selected by these internal rules might change. It is not always possible for the software to optimize code efficiency and numerical accuracy at the same time. If the rules do not meet your specific needs for numerical accuracy or performance, use one of the following options:

• Specify the output data type explicitly.

• Use the simple choice of ```Inherit: Same as first input```.

• Explicitly specify a default data type such as `fixdt(1,32,16)` and then use the Fixed-Point Tool to propose data types for your model. For more information, see `fxptdlg` (Fixed-Point Designer).

• To specify your own inheritance rule, use ```Inherit: Inherit via back propagation``` and then use a Data Type Propagation block. Examples of how to use this block are available in the Signal Attributes library Data Type Propagation Examples block.

• ```Inherit: Inherit via back propagation``` — Use data type of the driving block.

• `Inherit: Same as first input` — Use data type of the first input signal.

• ```Inherit: Inherit same as accumulator```— Use data type of the accumulator.

#### Programmatic Use

 Block Parameter: `OutDataTypeStr` Type: character vector Values: ```'Inherit: Inherit via internal rule```|```'Inherit: Keep MSB'```|`'Inherit: Keep LSB'` | ```'Inherit: Inherit via back propagation'``````'Inherit: Same as first input'``` | ```'Inherit: Same as accumulator'``` | `'double'` | `'single'` | `'half'` | `'int8'` | `'uint8'` | `'int16'` | `'uint16'`, `'int32'` | `'uint32'` | `'int64'`| `'uint64'`|`'fixdt(1,16)'` | `'fixdt(1,16,0)'` | `'fixdt(1,16,2^0,0)'` | ```''``` Default: ```'Inherit: Inherit via internal rule'```

Select to lock data type settings of this block against changes by the Fixed-Point Tool and the Fixed-Point Advisor. For more information, see Lock the Output Data Type Setting (Fixed-Point Designer).

#### Programmatic Use

 Block Parameter: `LockScale` Values: `'off' | 'on'` Default: `'off'`

Specify the rounding mode for fixed-point operations. For more information, see Rounding (Fixed-Point Designer).

Block parameters always round to the nearest representable value. To control the rounding of a block parameter, enter an expression using a MATLAB rounding function into the mask field.

#### Programmatic Use

 Block Parameter: `RndMeth` Type: character vector Values: ```'Ceiling' | 'Convergent' | 'Floor' | 'Nearest' | 'Round' | 'Simplest' | 'Zero'``` Default: `'Floor'`

Specify whether overflows saturate or wrap.

ActionRationaleImpact on OverflowsExample

Select this check box (`on`).

Your model has possible overflow, and you want explicit saturation protection in the generated code.

Overflows saturate to either the minimum or maximum value that the data type can represent.

The maximum value that the `int8` (signed, 8-bit integer) data type can represent is 127. Any block operation result greater than this maximum value causes overflow of the 8-bit integer. With the check box selected, the block output saturates at 127. Similarly, the block output saturates at a minimum output value of -128.

Do not select this check box (`off`).

You want to optimize efficiency of your generated code.

You want to avoid overspecifying how a block handles out-of-range signals. For more information, see Troubleshoot Signal Range Errors.

Overflows wrap to the appropriate value that is representable by the data type.

The maximum value that the `int8` (signed, 8-bit integer) data type can represent is 127. Any block operation result greater than this maximum value causes overflow of the 8-bit integer. With the check box cleared, the software interprets the overflow-causing value as `int8`, which can produce an unintended result. For example, a block result of 130 (binary 1000 0010) expressed as `int8`, is -126.

When you select this check box, saturation applies to every internal operation on the block, not just the output, or result. Usually, the code generation process can detect when overflow is not possible. In this case, the code generator does not produce saturation code.

#### Programmatic Use

 Block Parameter: `SaturateOnIntegerOverflow` Type: character vector Values: `'off' | 'on'` Default: `'off'`

## Block Characteristics

 Data Types `Boolean` | `double` | `fixed point` | `half` | `integer` | `single` Direct Feedthrough `yes` Multidimensional Signals `yes` Variable-Size Signals `yes` Zero-Crossing Detection `no`