# Sum, Add, Subtract, Sum of Elements

Add or subtract inputs

Math Operations

## Description

The Sum block performs addition or subtraction on its inputs. This block can add or subtract scalar, vector, or matrix inputs. It can also collapse the elements of a signal.

You specify the operations of the block with the List of signs parameter. Plus (+), minus (-), and spacer (|) characters indicate the operations to be performed on the inputs:

• If there are two or more inputs, then the number of + and - characters must equal the number of inputs. For example, "+-+" requires three inputs and configures the block to subtract the second (middle) input from the first (top) input, and then add the third (bottom) input.

• All nonscalar inputs must have the same dimensions. Scalar inputs will be expanded to have the same dimensions as the other inputs.

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

• 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.

• If only addition of all inputs is required, then a numeric parameter value equal to the number of inputs can be supplied instead of "+" characters.

• If only one input port is required, a single "+" or "-" collapses the element via the specified operation.

The Sum block first converts the input data type(s) 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]

## Data Type Support

The Sum block accepts real or complex signals of the following data types:

• Floating point

• Built-in integer

• Fixed point

• Boolean

The inputs can be of different data types, unless you select the Require all inputs to have the same data type parameter. For more information, see Data Types Supported by Simulink in the Simulink® documentation.

## Parameters and Dialog Box

The Main pane of the Sum block dialog box appears as follows:

The Signal Attributes pane of the Sum block dialog box appears as follows:

### Show data type assistant

Display the Data Type Assistant.

#### Settings

The Data Type Assistant helps you set the Output data type parameter.

For more information, see Specify Block Output Data Types.

### Icon shape

Designate the icon shape of the block.

#### Settings

Default: round

rectangular

Designate the icon shape of the block as rectangular.

round

Designate the icon shape of the block as round.

#### Command-Line Information

See Block-Specific Parameters for the command-line information.

### List of signs

Enter plus (+) and minus (-) characters.

#### Settings

Default: |++

• Addition is the default operation, so if you only want to add the inputs, enter the number of input ports.

• For a single vector input, "+" or "-" will collapse the vector using the specified operation.

• Enter as many plus (+) and minus (-) characters as there are inputs.

#### 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.

#### Dependencies

Entering only one element enables the Sum over parameter.

#### Command-Line Information

See Block-Specific Parameters for the command-line information.

### Sum over

Select dimension over which to perform the sum over operation.

#### Settings

Default: All dimensions

All dimensions

Sum all input elements, yielding a scalar.

Specified dimension

Display the Dimension parameter, where you specify the dimension over which to perform the operation.

#### Dependencies

Selecting Specified dimension enables the Dimension parameter.

List of signs (when it has only one element) enables this parameter.

#### Command-Line Information

See Block-Specific Parameters for the command-line information.

### Dimension

Specify the dimension over which to perform the operation.

#### Settings

Default: 1

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.

#### Dependencies

Setting Sum over to Specified dimension enables this parameter.

#### Command-Line Information

See Block-Specific Parameters for the command-line information.

### Sample time

 Note:   This parameter is not visible in the block dialog box unless it is explicitly set to a value other than -1. To learn more, see Blocks for Which Sample Time Is Not Recommended

### Require all inputs to have the same data type

Require that all inputs have the same data type.

#### Settings

Default: Off

On

Require that all inputs have the same data type.

Off

Do not require that all inputs have the same data type.

#### Command-Line Information

See Block-Specific Parameters for the command-line information.

### Lock data type settings against changes by the fixed-point tools

Select to lock data type settings of this block against changes by the Fixed-Point Tool and the Fixed-Point Advisor.

#### Settings

Default: Off

On

Locks all data type settings for this block.

Off

Allows the Fixed-Point Tool and the Fixed-Point Advisor to change data type settings for this block.

#### Command-Line Information

See Block-Specific Parameters for the command-line information.

### Integer rounding mode

Specify the rounding mode for fixed-point operations.

#### Settings

Default: Floor

Ceiling

Rounds both positive and negative numbers toward positive infinity. Equivalent to the MATLAB ceil function.

Convergent

Rounds number to the nearest representable value. If a tie occurs, rounds to the nearest even integer. Equivalent to the Fixed-Point Designer™ convergent function.

Floor

Rounds both positive and negative numbers toward negative infinity. Equivalent to the MATLAB floor function.

Nearest

Rounds number to the nearest representable value. If a tie occurs, rounds toward positive infinity. Equivalent to the Fixed-Point Designer nearest function.

Round

Rounds number to the nearest representable value. If a tie occurs, rounds positive numbers toward positive infinity and rounds negative numbers toward negative infinity. Equivalent to the Fixed-Point Designer round function.

Simplest

Automatically chooses between round toward floor and round toward zero to generate rounding code that is as efficient as possible.

Zero

Rounds number toward zero. Equivalent to the MATLAB fix function.

#### Command-Line Information

 Parameter: RndMeth Type: string Value: 'Ceiling' | 'Convergent' | 'Floor' | 'Nearest' | 'Round' | 'Simplest' | 'Zero' Default: 'Floor'

#### See Also

For more information, see Rounding in the Fixed-Point Designer documentation.

### Saturate on integer overflow

Specify whether overflows saturate.

#### Settings

Default: Off

On

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

For example, an overflow associated with a signed 8-bit integer can saturate to -128 or 127.

Off

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

For example, the number 130 does not fit in a signed 8-bit integer and wraps to -126.

#### Tips

• Consider selecting this check box when your model has possible overflow and you want explicit saturation protection in the generated code.

• Consider clearing this check box when you want to optimize efficiency of your generated code.

Clearing this check box also helps you avoid overspecifying how a block handles out-of-range signals. For more information, see Checking for Signal Range Errors.

• When you select this check box, saturation applies to every internal operation on the block, not just the output or result.

• In general, the code generation process can detect when overflow is not possible. In this case, the code generator does not produce saturation code.

#### Command-Line Information

 Parameter: SaturateOnIntegerOverflow Type: string Value: 'off' | 'on' Default: 'off'

### Accumulator data type

Specify the accumulator data type.

#### Settings

Default: Inherit: Inherit via internal rule

Inherit: Inherit via internal rule

Use internal rule to determine accumulator data type.

Inherit: Same as first input

Use data type of first input signal.

double

Accumulator data type is double.

single

Accumulator data type is single.

int8

Accumulator data type is int8.

uint8

Accumulator data type is uint8.

int16

Accumulator data type is int16.

uint16

Accumulator data type is uint16.

int32

Accumulator data type is int32.

uint32

Accumulator data type is uint32.

fixdt(1,16,0)

Accumulator data type is fixed point fixdt(1,16,0).

fixdt(1,16,2^0,0)

Accumulator data type is fixed point fixdt(1,16,2^0,0).

<data type expression>

The name of a data type object, for example Simulink.NumericType

#### Command-Line Information

See Block-Specific Parameters for the command-line information.

#### See Also

For more information, see Specify Data Types Using Data Type Assistant.

### Mode

Select the category of accumulator data to specify

#### Settings

Default: Inherit

Inherit

Specifies inheritance rules for data types. Selecting Inherit enables a list of possible values:

• Inherit via internal rule (default)

• Same as first input

Built in

Specifies built-in data types. Selecting Built in enables a list of possible values:

• double (default)

• single

• int8

• uint8

• int16

• uint16

• int32

• uint32

Fixed point

Specifies fixed-point data types.

Expression

Specifies expressions that evaluate to data types. Selecting Expression enables you to enter an expression.

#### Dependency

Clicking the Show data type assistant button for the accumulator data type enables this parameter.

#### Command-Line Information

See Block-Specific Parameters for the command-line information.

### Data type override

Specify data type override mode for this signal.

#### Settings

Default: Inherit

Inherit

Inherits the data type override setting from its context, that is, from the block, Simulink.Signal object or Stateflow® chart in Simulink that is using the signal.

Off

Ignores the data type override setting of its context and uses the fixed-point data type specified for the signal.

#### Tip

The ability to turn off data type override for an individual data type provides greater control over the data types in your model when you apply data type override. For example, you can use this option to ensure that data types meet the requirements of downstream blocks regardless of the data type override setting.

#### Dependency

This parameter appears only when the Mode is Built in or Fixed point.

### Signedness

Specify whether you want the fixed-point data to be signed or unsigned.

#### Settings

Default: Signed

Signed

Specify the fixed-point data to be signed.

Unsigned

Specify the fixed-point data to be unsigned.

#### Dependencies

Selecting Mode > Fixed point for the accumulator data type enables this parameter.

#### Command-Line Information

See Block-Specific Parameters for the command-line information.

#### See Also

See Specifying a Fixed-Point Data Type for more information.

### Word length

Specify the bit size of the word that will hold the quantized integer.

#### Settings

Default: 16

Minimum: 0

Maximum: 32

Large word sizes represent large values with greater precision than small word sizes.

#### Dependencies

Selecting Mode > Fixed point for the accumulator data type enables this parameter.

#### Command-Line Information

See Block-Specific Parameters for the command-line information.

#### See Also

See Specifying a Fixed-Point Data Type for more information.

### Scaling

Specify the method for scaling your fixed-point data to avoid overflow conditions and minimize quantization errors.

#### Settings

Default: Binary point

Binary point

Specify binary point location.

Slope and bias

Enter slope and bias.

#### Dependencies

Selecting Mode > Fixed point for the accumulator data type enables this parameter.

Selecting Binary point enables:

• Fraction length

Selecting Slope and bias enables:

• Slope

• Bias

#### Command-Line Information

See Block-Specific Parameters for the command-line information.

#### See Also

See Specifying a Fixed-Point Data Type for more information.

### Fraction length

Specify fraction length for fixed-point data type.

#### Settings

Default: 0

Binary points can be positive or negative integers.

#### Dependencies

Selecting Scaling > Binary point for the accumulator data type enables this parameter.

#### Command-Line Information

See Block-Specific Parameters for the command-line information.

#### See Also

See Specifying a Fixed-Point Data Type for more information.

### Slope

Specify slope for the fixed-point data type.

#### Settings

Default: 2^0

Specify any positive real number.

#### Dependencies

Selecting Scaling > Slope and bias for the accumulator data type enables this parameter.

#### Command-Line Information

See Block-Specific Parameters for the command-line information.

#### See Also

See Specifying a Fixed-Point Data Type for more information.

### Bias

Specify bias for the fixed-point data type.

#### Settings

Default: 0

Specify any real number.

#### Dependencies

Selecting Scaling > Slope and bias for the accumulator data type enables this parameter.

#### Command-Line Information

See Block-Specific Parameters for the command-line information.

#### See Also

See Specifying a Fixed-Point Data Type for more information.

### Output minimum

Lower value of the output range that Simulink checks.

#### Settings

Default: [] (unspecified)

Specify this number as a finite, real, double, scalar value.

 Note:   If you specify a bus object as the data type for this block, do not set the minimum value for bus data on the block. Simulink ignores this setting. Instead, set the minimum values for bus elements of the bus object specified as the data type. For information on the Minimum parameter for a bus element, see Simulink.BusElement.

Simulink uses the minimum to perform:

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

#### Command-Line Information

 Parameter: OutMin Type: string Value: '[ ]' Default: '[ ]'

### Output maximum

Upper value of the output range that Simulink checks.

#### Settings

Default: [] (unspecified)

Specify this number as a finite, real, double, scalar value.

 Note:   If you specify a bus object as the data type for this block, do not set the maximum value for bus data on the block. Simulink ignores this setting. Instead, set the maximum values for bus elements of the bus object specified as the data type. For information on the Maximum parameter for a bus element, see Simulink.BusElement.

Simulink uses the maximum value to perform:

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

#### Command-Line Information

 Parameter: OutMax Type: string Value: '[ ]' Default: '[ ]'

### Output data type

Specify the output data type.

#### Settings

Default: Inherit: Inherit via internal rule

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. If you change the embedded target settings, the data type selected by the internal rule might change. It is not always possible for the software to optimize code efficiency and numerical accuracy at the same time. If the internal rule doesn't 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.

• 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.

 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: Inherit via back propagation

Use data type of the driving block.

Inherit: Same as first input

Use data type of first input signal.

Inherit: Same as accumulator

Output data type is the same as accumulator data type.

double

Output data type is double.

single

Output data type is single.

int8

Output data type is int8.

uint8

Output data type is uint8.

int16

Output data type is int16.

uint16

Output data type is uint16.

int32

Output data type is int32.

uint32

Output data type is uint32.

fixdt(1,16,0)

Output data type is fixed point fixdt(1,16,0).

fixdt(1,16,2^0,0)

Output data type is fixed point fixdt(1,16,2^0,0).

<data type expression>

Use a data type object, for example, Simulink.NumericType.

#### Command-Line Information

See Block-Specific Parameters for the command-line information.

#### See Also

For more information, see Specify Block Output Data Types.

### Mode

Select the category of data to specify.

#### Settings

Default: Inherit

Inherit

Inheritance rules for data types. Selecting Inherit enables a second menu/text box to the right. Select one of the following choices:

• Inherit via internal rule (default)

• Inherit via back propagation

• Same as first input

• Same as accumulator

Built in

Built-in data types. Selecting Built in enables a second menu/text box to the right. Select one of the following choices:

• double (default)

• single

• int8

• uint8

• int16

• uint16

• int32

• uint32

Fixed point

Fixed-point data types.

Expression

Expressions that evaluate to data types. Selecting Expression enables a second menu/text box to the right, where you can enter the expression.

#### Dependency

Clicking the Show data type assistant button enables this parameter.

#### Command-Line Information

See Block-Specific Parameters for the command-line information.

### Signedness

Specify whether you want the fixed-point data as signed or unsigned.

#### Settings

Default: Signed

Signed

Specify the fixed-point data as signed.

Unsigned

Specify the fixed-point data as unsigned.

#### Dependencies

Selecting Mode > Fixed point enables this parameter.

#### See Also

For more information, see Specifying a Fixed-Point Data Type.

### Word length

Specify the bit size of the word that holds the quantized integer.

Default: 16

Minimum: 0

Maximum: 32

#### Dependencies

Selecting Mode > Fixed point enables this parameter.

#### See Also

For more information, see Specifying a Fixed-Point Data Type.

### Scaling

Specify the method for scaling your fixed-point data to avoid overflow conditions and minimize quantization errors.

#### Settings

Default: Binary point

Binary point

Specify binary point location.

Slope and bias

Enter slope and bias.

#### Dependencies

Selecting Mode > Fixed point enables this parameter.

Selecting Binary point enables:

• Fraction length

• Calculate Best-Precision Scaling

Selecting Slope and bias enables:

• Slope

• Bias

• Calculate Best-Precision Scaling

#### Command-Line Information

See Block-Specific Parameters for the command-line information.

### Fraction length

Specify fraction length for fixed-point data type.

#### Settings

Default: 0

Binary points can be positive or negative integers.

#### Dependencies

Selecting Scaling > Binary point enables this parameter.

#### See Also

For more information, see Specifying a Fixed-Point Data Type.

### Slope

Specify slope for the fixed-point data type.

#### Settings

Default: 2^0

Specify any positive real number.

#### Dependencies

Selecting Scaling > Slope and bias enables this parameter.

#### See Also

For more information, see Specifying a Fixed-Point Data Type.

### Bias

Specify bias for the fixed-point data type.

#### Settings

Default: 0

Specify any real number.

#### Dependencies

Selecting Scaling > Slope and bias enables this parameter.

#### See Also

For more information, see Specifying a Fixed-Point Data Type.

## Examples

### How the Sum Block Reorders Inputs

If you use - on the first input port, the Sum block reorders the inputs so that, if possible, the first input uses a + operation. For example, in the expression output = -a-b+c, the Sum block reorders the inputs so that output = c-a-b. To initialize the accumulator, the Sum block uses the first + input port.

The block avoids performing a unary minus operation on the first operand a because doing so can change the value of a for fixed-point data types. In that case, the output value differs from the result of accumulating the values for a, b, and c.

 Tip   To explicitly specify a unary minus operation for output = -a-b+c, you can use the Unary Minus block in the Math Operations library.

Suppose that you have the following modelmodel:

The following block parameters apply:

• Both Constant blocks, Input1 and Input 2, use int8 for the Output data type.

• The Sum block uses int8 for both Accumulator data type and Output data type.

• The Sum block has Saturate on integer overflow turned on.

The Sum block reorders the inputs so that the following operations occur and you get the ideal result of 127.

StepBlock Operation
1

Reorders inputs from (–Input1 + Input2) to (Input2 – Input1).

2

Initializes the accumulator by using the first + input port:

Accumulator = int8(-1) = -1

3

Continues to accumulate values:

Accumulator = Accumulator – int8(-128) = 127

4

Calculates the block output:

Output = int8(127) = 127

If the Sum block does not reorder the inputs, the following operations occur instead and you get the nonideal result of 126.

StepBlock Operation
1

Initializes the accumulator by using the first input port:

Accumulator = int8(-(-128)) = 127

Because saturation is on, the initial value of the accumulator saturates at 127 and does not wrap.

2

Continues to accumulate values:

Accumulator = Accumulator + int8(-1) = 126

3

Calculates the block output:

Output = int8(126) = 126

## Characteristics

 Direct Feedthrough Yes Sample Time Inherited from driving block Scalar Expansion Yes States 0 Dimensionalized Yes Multidimensionalized Yes, only along the specified dimension Zero-Crossing Detection No

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