Add, Subtract, Sum of Elements, Sum
Add or subtract inputs
Libraries:
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:
Number of Sum Block Input Ports  Input Port Signs  Block Output Calculation Formula  Output Formula Variables 

One input port 
The input port sign is + 
y = e[0] + e[1] + e[2] ... + e[m] 

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] 

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] 
Examples
Sum Block Reorders Inputs
This example shows how the Sum block reorders inputs. If you use a 
sign as the first operation, the block reorders the inputs, if possible, to use a +
operation. For example, in the expression output = ab+c
, the Sum block reorders the input so that output = cab
. 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 fixedpoint data types. In that case, the output value differs from the result of accumulating the values for a
, b
, and c
.
Both the constant inputs use int8
data types The Sum block also uses int8
for the accumulator and output data types and has Saturate on integer overflow turned on. The Sum block reorders the inputs to give the ideal result of 127
.
Reorders inputs from
(Input1 + Input2)
to(Input2  Input1)
.Initializes the accumulator by using the first
+
input port.Accumulator = int8(1) = 1
Continues to accumulate values.
Accumulator = Accumulator  int8(128) = 127
Calculates the block output.
Output = int8(127) = 127
If the Sum block does not reorder the inputs, then you get the nonideal result of 126
.
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.Continues to accumulate values.
Accumulator = Accumulator + int8(1) = 126
Calculates the block output.
Output = int8(126) = 126
To explicitly specify a unary minus operation for output = ab+c
, you can use the Unary Minus block in the Math Operations library.
Ports
Inputs
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.
Data Types: half
 single
 double
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
 Boolean
 fixed point
Port_n — nth 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.
Data Types: half
 single
 double
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
 Boolean
 fixed point
Output
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.
Data Types: half
 single
 double
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
 Boolean
 fixed point
Parameters
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:
'++' 
Apply over — How to apply function along specified dimensions
All dimensions
(default)  Specified dimension
Specify how to apply function along specified dimensions.
All dimensions
— Apply function for all input values for all dimensions.For example, in this model, List of signals is set to
+
, and Apply over is set toAll dimensions
. The block returns the sum of all input values from all dimensions.When you select configuration parameter Use algorithms optimized for rowmajor array layout, Simulink^{®} enables rowmajor algorithms for simulation. To generate rowmajor code, set the configuration parameter Array layout (Simulink Coder) to
Rowmajor
, and select Use algorithms optimized for rowmajor array layout. The columnmajor and rowmajor 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 columnmajor and rowmajor algorithms.Specified dimensions
— Apply function for all input values for specified dimension.
Dependencies
To enable this parameter, enter 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 along which to apply summation
1
(default)  positive integer
Specify the dimension along which to apply the summation as a positive integer.
The block follows the same summation rules as the MATLAB^{®}
sum
function. For more information, see Algorithms.
For example, in this model, List of signals is
set to +
, Apply over is set to
Specified dimension
, and
Dimension is set to 2
. The
block returns the sum of the input values of each row.
If the specified dimension is greater than the dimension of the input, an error message appears.
Dependencies
To enable this parameter, set Apply over to
Specified dimension
.
Programmatic Use
Block Parameter:
CollapseDim 
Type: character vector 
Value:
integer 
Default:
'1' 
Sample time (1 for inherited) — Interval between samples
1
(default)  scalar  vector
Specify the time interval between samples. To inherit the sample time, set this
parameter to 1
. For more information, see Specify Sample Time.
Dependencies
This parameter is visible only if you set it to a value other than
1
. To learn more, see Blocks for Which Sample Time Is Not Recommended.
Programmatic Use
Block Parameter:
SampleTime 
Type: string scalar or character vector 
Default:
"1" 
Signal Attributes
The Data Type Assistant helps you set data attributes. To use the Data Type Assistant, click . For more information, see Specify Data Types Using Data Type Assistant.
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 fixedpoint 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 fixedpoint 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
.Note
When input is a floatingpoint data type smaller than single precision, the
Inherit: Inherit via internal rule
output data type depends on the setting of the Inherit floatingpoint 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 singleprecision data type. For example,half
andint16
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 FixedPoint Tool to propose data types for your model. For more information, seefxptdlg
(FixedPoint 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)'  '<data
type expression>' 
Default: 'Inherit:
Inherit via internal rule' 
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' 
'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>' 
Default:
'Inherit: Inherit via internal
rule' 
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' 
Lock data type settings against changes by the fixedpoint tools — Prevent fixedpoint tools from overriding data types
off
(default)  on
Select to lock data type settings of this block against changes by the FixedPoint Tool and the FixedPoint Advisor. For more information, see Lock the Output Data Type Setting (FixedPoint Designer).
Programmatic Use
Block Parameter:
LockScale 
Values:
'off'  'on' 
Default:
'off' 
Integer rounding mode — Rounding mode for fixedpoint operations
Floor
(default)  Ceiling
 Convergent
 Nearest
 Round
 Simplest
 Zero
Specify the rounding mode for fixedpoint operations. For more information, see Rounding (FixedPoint 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 

Select this check box ( 
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 
Do not select this check box ( 
You want to optimize efficiency of your generated code. You want to avoid overspecifying how a block handles outofrange 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 
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 

Direct Feedthrough 

Multidimensional Signals 

VariableSize Signals 

ZeroCrossing Detection 

Algorithms
The block follows the same summation rules as the MATLAB
sum
function.
Suppose that you have a 2by3 matrix U.
Setting Dimension to
1
results in the output Y being computed as:$$Y={\displaystyle {\sum}_{i=1}^{2}U(i,j)}$$
Setting Dimension to
2
results in the output Y being computed as:$$Y={\displaystyle {\sum}_{j=1}^{3}U(i,j)}$$
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.
HDL Code Generation
Generate VHDL, Verilog and SystemVerilog code for FPGA and ASIC designs using HDL Coder™.
HDL Coder™ provides additional configuration options that affect HDL implementation and synthesized logic.
The default Linear
architecture generates a chain
of N operations (adders) for N inputs.
For the Sum of Elements block, HDL Coder supports Tree
architectures for Sum of
Elements blocks that have a single vector input with multiple elements.
This block has multicycle 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 

Linear  0  Generates a linear chain of adders to compute the sum of products. For multiple inputs that have
different bit widths, the 
Tree  0  Generates a tree structure of adders to compute the sum of products. 
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

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

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

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 
NFPCustomLatency  To specify a value, set
LatencyStrategy to 
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.
To generate HDL code for multiinput Sum block that has mixed scalar and vector inputs, you must specify vector input at one of the first two inputs of the Sum block.
PLC Code Generation
Generate Structured Text code using Simulink® PLC Coder™.
FixedPoint Conversion
Design and simulate fixedpoint systems using FixedPoint Designer™.
Version History
Introduced before R2006aR2024a: Sum, Sum of Elements, Subtract, and Add Blocks Have New Parameter Name
The Sum over parameter has been renamed to Apply over for the Sum, Sum of Elements, Subtract, and Add blocks.
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