Add, Subtract, Sum of Elements, Sum

Add or subtract inputs

Library:
Simulink / Math Operations
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 i^th element of input u
One input port	The input port sign is –	y = 0.0 – e[0] – e[1] – e[2] ... – e[m]	`e[i]` is the i^th element of input u
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 i^th input port
Two or more input ports	The k^th 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]	`u[i]` is the input to the i^th input port

Ports

Inputs

expand all

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

`Port_1` — First input operand signal
scalar | vector | matrix

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.

`Port_n` — `n`th input operand signal
scalar | vector | matrix

nth 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.

Output

expand all

`Port_1` — Output signal
scalar | vector | matrix

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

Parameters

expand all

Main

`Icon shape` — Block icon shape
rectangular (default) | round

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'

`List of signs` — Operations performed on inputs
`++` (default) | `+` | `-` | `|` | `integer`

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: '++'

`Sum over` — Dimensions for operations on a single vector input
All dimensions (default) | Specified dimension

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'

`Dimension` — Dimension for summation on vector input
`1` (default) | `integer`

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:

$Y = \sum_{i = 1}^{2} U (i, j)$
Setting Dimension to 2 results in the output Y being computed as:

$Y = \sum_{j = 1}^{3} U (i, j)$

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'

`Sample time` — Specify sample time as a value other than `-1`
`-1` (default) | scalar | vector

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 Show data type assistant 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.

`Require all inputs to have the same data type` — Require that all inputs have the same data type
`off` (default) | `on`

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'

`Accumulator data type` — Data type of the accumulator
`Inherit: Inherit via internal rule` (default) | `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)` | `<data type expression>`

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'

'<data type
                                                  expression>'

Default:

'Inherit: Inherit via internal
                                                  rule'

`Output minimum` — Minimum output value for range checking
`[]` (default) | scalar

Lower value of the output range that Simulink checks.

Simulink uses the minimum to perform:

Parameter range checking (see Specify Minimum and Maximum Values for Block Parameters) for some blocks.
Simulation range checking (see Specify Signal Ranges and Enable Simulation Range Checking).
Automatic scaling of fixed-point data types.
Optimization of the code that you generate from the model. This optimization can remove algorithmic code and affect the results of some simulation modes such as SIL or external mode. For more information, see Optimize using the specified minimum and maximum values (Embedded Coder).

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: '[ ]'

`Output maximum` — Maximum output value for range checking
`[]` (default) | scalar

Upper value of the output range that Simulink checks.

Simulink uses the maximum value to perform:

Parameter range checking (see Specify Minimum and Maximum Values for Block Parameters) for some blocks.
Simulation range checking (see Specify Signal Ranges and Enable Simulation Range Checking).
Automatic scaling of fixed-point data types.
Optimization of the code that you generate from the model. This optimization can remove algorithmic code and affect the results of some simulation modes such as SIL or external mode. For more information, see Optimize using the specified minimum and maximum values (Embedded Coder).

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: '[ ]'

`Output data type` — Specify the output data type
`Inherit: Inherit via internal rule` (default) | `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)` | `<data type expression>`

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.
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'

'<data
                                        type expression>'

Default:

'Inherit:
                                        Inherit via internal rule'

`Lock data type settings against changes by the fixed-point tools` — Prevent fixed-point tools from overriding data types
`off` (default) | `on`

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'

`Integer rounding mode` — Rounding mode for fixed-point operations
`Floor` (default) | `Ceiling` | `Convergent` | `Nearest` | `Round` | `Simplest` | `Zero`

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'

`Saturate on integer overflow` — Method of overflow action
`off` (default) | `on`

Specify whether overflows saturate or wrap.

Action Rationale Impact on Overflows Example

Action	Rationale	Impact on Overflows	Example
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.

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'

Model Examples

Sum Block Reorders Inputs

How the Sum block reorders inputs.

Open Model

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`

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

HDL Code Generation
Generate Verilog and VHDL code for FPGA and ASIC designs using HDL Coder™.

HDL Coder™ provides additional configuration options that affect HDL implementation and synthesized logic.

HDL Architecture of Sum, Add, and Subtract Blocks

The default Linear architecture generates a chain of N operations (adders) for N inputs.

HDL Architecture of Sum of Elements Block

For the Sum of Elements block, HDL Coder supports Tree and Cascade architectures for Sum of Elements blocks that have a single vector input with multiple elements.

This block has multi-cycle implementations that introduce additional latency in the generated code. To see the added latency, view the generated model or validation model. See Generated Model and Validation Model (HDL Coder).

Architecture Additional cycles of latency Description

Architecture	Additional cycles of latency	Description
`Linear`	0	Generates a linear chain of adders to compute the sum of products.
`Tree`	0	Generates a tree structure of adders to compute the sum of products.
`Cascade`	1, when block has a single vector input port.	This implementation optimizes latency * area and is faster than the `Tree` implementation. It computes partial sums and cascades adders. See Cascade Architecture Best Practices (HDL Coder).

Linear

Generates a linear chain of adders to compute the sum of products.

Tree

Generates a tree structure of adders to compute the sum of products.

Cascade

1, when block has a single vector input port.

This implementation optimizes latency * area and is faster than the Tree implementation. It computes partial sums and cascades adders.

See Cascade Architecture Best Practices (HDL Coder).

HDL Block Properties

Note

To use the LatencyStrategy setting in the Native Floating Point tab of the HDL Block Properties dialog box, specify Linear or Tree as the HDL Architecture.

General
ConstrainedOutputPipeline	Number of registers to place at the outputs by moving existing delays within your design. Distributed pipelining does not redistribute these registers. The default is `0`. For more details, see ConstrainedOutputPipeline (HDL Coder).
InputPipeline	Number of input pipeline stages to insert in the generated code. Distributed pipelining and constrained output pipelining can move these registers. The default is `0`. For more details, see InputPipeline (HDL Coder).
OutputPipeline	Number of output pipeline stages to insert in the generated code. Distributed pipelining and constrained output pipelining can move these registers. The default is `0`. For more details, see OutputPipeline (HDL Coder).

Note

The Sum of Elements block does not support HDL code generation with double data types in the Native Floating Point mode.

Native Floating Point
LatencyStrategy	Specify whether to map the blocks in your design to `inherit`, `Max`, `Min`, `Zero`, or `Custom` for the floating-point operator. The default is `inherit`. See also LatencyStrategy (HDL Coder).
NFPCustomLatency	To specify a value, set LatencyStrategy to `Custom`. HDL Coder adds latency equal to the value that you specify for the NFPCustomLatency setting. See also NFPCustomLatency (HDL Coder).

Complex Data Support

The default Linear implementation supports complex data.

The Tree implementation supports complex data with + for the List of signs block parameter. With native floating point support, the Tree implementation supports complex data with both + and - for List of signs.

Documentation

Add, Subtract, Sum of Elements, Sum

Description

Calculation of Block Output

Ports

Inputs

Port_1 — First input operand signal scalar | vector | matrix

Port_n — nth input operand signal scalar | vector | matrix

Output

Port_1 — Output signal scalar | vector | matrix

Parameters

Main

Icon shape — Block icon shape rectangular (default) | round

Programmatic Use

List of signs — Operations performed on inputs ++ (default) | + | - | | | integer

Tips

Programmatic Use

Sum over — Dimensions for operations on a single vector input All dimensions (default) | Specified dimension

Dependency

Programmatic Use

Dimension — Dimension for summation on vector input 1 (default) | integer

Dependency

Programmatic Use

Sample time — Specify sample time as a value other than -1 -1 (default) | scalar | vector

Dependencies

Programmatic Use

Signal Attributes

Require all inputs to have the same data type — Require that all inputs have the same data type off (default) | on

Programmatic Use

Accumulator data type — Data type of the accumulator Inherit: Inherit via internal rule (default) | 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) | <data type expression>

Programmatic Use

Output minimum — Minimum output value for range checking [] (default) | scalar

Programmatic Use

Output maximum — Maximum output value for range checking [] (default) | scalar

Programmatic Use

Programmatic Use

Lock data type settings against changes by the fixed-point tools — Prevent fixed-point tools from overriding data types off (default) | on

Programmatic Use

Integer rounding mode — Rounding mode for fixed-point operations Floor (default) | Ceiling | Convergent | Nearest | Round | Simplest | Zero

Programmatic Use

Saturate on integer overflow — Method of overflow action off (default) | on

Programmatic Use

Model Examples

Sum Block Reorders Inputs

Block Characteristics

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using Simulink® Coder™.

HDL Code Generation Generate Verilog and VHDL code for FPGA and ASIC designs using HDL Coder™.

PLC Code Generation Generate Structured Text code using Simulink® PLC Coder™.

Fixed-Point Conversion Design and simulate fixed-point systems using Fixed-Point Designer™.

See Also

Topics

Simulink Documentation

Support

`Port_1` — First input operand signal
scalar | vector | matrix

`Port_n` — `n`th input operand signal
scalar | vector | matrix

`Port_1` — Output signal
scalar | vector | matrix

`Icon shape` — Block icon shape
rectangular (default) | round

`List of signs` — Operations performed on inputs
`++` (default) | `+` | `-` | `|` | `integer`

`Sum over` — Dimensions for operations on a single vector input
All dimensions (default) | Specified dimension

`Dimension` — Dimension for summation on vector input
`1` (default) | `integer`

`Sample time` — Specify sample time as a value other than `-1`
`-1` (default) | scalar | vector

`Require all inputs to have the same data type` — Require that all inputs have the same data type
`off` (default) | `on`

`Output minimum` — Minimum output value for range checking
`[]` (default) | scalar

`Output maximum` — Maximum output value for range checking
`[]` (default) | scalar

`Lock data type settings against changes by the fixed-point tools` — Prevent fixed-point tools from overriding data types
`off` (default) | `on`

`Integer rounding mode` — Rounding mode for fixed-point operations
`Floor` (default) | `Ceiling` | `Convergent` | `Nearest` | `Round` | `Simplest` | `Zero`

`Saturate on integer overflow` — Method of overflow action
`off` (default) | `on`

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

HDL Code Generation
Generate Verilog and VHDL code for FPGA and ASIC designs using HDL Coder™.

PLC Code Generation
Generate Structured Text code using Simulink® PLC Coder™.

Fixed-Point Conversion
Design and simulate fixed-point systems using Fixed-Point Designer™.