Product
Multiply and divide scalars and nonscalars or multiply and invert
matrices
 Library:
Simulink /
Commonly Used Blocks
Simulink /
Math Operations
HDL Coder /
Commonly Used Blocks
HDL Coder /
HDL Floating Point Operations
HDL Coder /
Math Operations
Description
The Product block outputs the result of multiplying two inputs: two
scalars, a scalar and a nonscalar, or two nonscalars that have the same dimensions. The
default parameter values that specify this behavior are:
This table shows the output of the Product block for example inputs using default block parameter values.
Inputs and Behavior  Example 

Scalar X
Scalar Output the product of the two
inputs. 

Scalar X
Nonscalar Output a nonscalar having the same
dimensions as the input nonscalar. Each element of the output
nonscalar is the product of the input scalar and the corresponding
element of the input nonscalar. 

Nonscalar X
Nonscalar Output a nonscalar having the same
dimensions as the inputs. Each element of the output is the product
of corresponding elements of the inputs. 

The Divide and Product of Elements blocks are variants
of the Product block.
The Product block (or the Divide block or Product
of Elements block, if appropriately configured) can:
Numerically multiply and divide any number of scalar, vector, or matrix
inputs
Perform matrix multiplication and division on any number of matrix
inputs
The Product block performs scalar or matrix multiplication, depending
on the value of the Multiplication parameter. The block
accepts one or more inputs, depending on the Number of
inputs parameter. The Number of inputs
parameter also specifies the operation to perform on each input.
The Product block can input any combination of scalars, vectors, and
matrices for which the operation to perform has a mathematically defined result. The
block performs the specified operations on the inputs, then outputs the result.
The Product block has two modes: Elementwise
mode, which processes nonscalar inputs element by element, and
Matrix mode, which processes nonscalar inputs as
matrices.
ElementWise Mode
When you set Multiplication to
Elementwise(.*)
, the Product block is in
Elementwise mode, in which it operates on the individual
numeric elements of any nonscalar inputs. The MATLAB^{®} equivalent is the .*
operator. In elementwise
mode, the Product block can perform a variety of multiplication,
division, and arithmetic inversion operations.
The value of the Number of inputs parameter
controls both how many inputs exist and whether each is multiplied or divided to
form the output. When the Product block is in elementwise mode and
has only one input, it is functionally equivalent to a Product of Elements block. When the
block has multiple inputs, any nonscalar inputs must have identical dimensions, and
the block outputs a nonscalar with those dimensions. To calculate the output, the
block first expands any scalar input to a nonscalar that has the same dimensions as
the nonscalar inputs.
This table shows the output of the Product block for example inputs, using the indicated values for the Number of inputs parameter.
Parameter Values  Examples 

Number of inputs:
2 

Number of inputs:
*/ 

Number of inputs:
/**/ 

Number of
inputs:** 

Number of inputs:
*/* 

Matrix Mode
When the value of the Multiplication parameter is
Matrix(*)
, the Product block is in
Matrix mode, in which it processes nonscalar inputs as
matrices. The MATLAB equivalent is the *
operator. In Matrix mode, the
Product block can invert a single square matrix, or multiply and
divide any number of matrices that have dimensions for which the result is
mathematically defined.
The value of the Number of inputs parameter
controls both how many inputs exist and whether each input matrix is multiplied or
divided to form the output. The syntax of Number of
inputs is the same as in elementwise mode. The difference between
the modes is in the type of multiplication and division that occur.
Expected Differences Between Simulation and Code Generation
For elementwise operations on complex floatingpoint inputs, simulation and code
generation results might differ in nearoverflow cases. Although complex
numbers is selected and nonfinite numbers is
not selected on the > pane of the Configuration Parameters dialog box, the code generator
does not emit special case code for intermediate overflows. This method improves the
efficiency of embedded operations for the general case that does not include extreme
values. If the inputs could include extreme values, you must manage these cases
explicitly.
The generated code might not produce the exact same pattern of
NaN
and inf
values as simulation when
these values are mathematically meaningless. For example, if the simulation output
contains a NaN
, output from the generated code also contains a
NaN
, but not necessarily in the same place.
Ports
Input
expand all
Port_1
— First input to multiply or divide
scalar  vector  matrix  ND array
First input to multiply or divide, provided as a scalar, vector,
matrix, or ND array.
Data Types: single
 double
 int8
 int16
 int32
 uint8
 uint16
 uint32
 Boolean
 fixed point
Port_N
— Nth input to multiply or divide
scalar  vector  matrix  ND array
Nth input to multiply or divide, provided as a scalar, vector, matrix,
or ND array.
Data Types: single
 double
 int8
 int16
 int32
 uint8
 uint16
 uint32
 Boolean
 fixed point
X
— Input signal to multiply
scalar  vector  matrix  ND array
Input signal to be multiplied with other inputs.
Dependencies
To enable one or more X ports, specify one or
more *
characters for the Number of
inputs parameter.
Data Types: single
 double
 int8
 int16
 int32
 uint8
 uint16
 uint32
 Boolean
 fixed point
÷
— Input signal to divide or invert
scalar  vector  matrix  ND array
Input signal for division or inversion operations.
Dependencies
To enable one or more ÷ ports, specify one or
more /
characters for the Number of
inputs parameter.
Data Types: single
 double
 int8
 int16
 int32
 uint8
 uint16
 uint32
 Boolean
 fixed point
Output
expand all
Port_1
— Output computed by multiplying, dividing, or inverting inputs
scalar  vector  matrix  ND array
Output computed by multiplying, dividing, or inverting inputs.
Data Types: single
 double
 int8
 int16
 int32
 uint8
 uint16
 uint32
 Boolean
 fixed point
Parameters
expand all
Main
Number of inputs
— Control number of inputs and type of operation
2
(default)  scalar  *
or /
for each input
port
Control two properties of the block:
When you specify:
1
or
*
or
/
The block has one input port. In elementwise mode, the block
processes the input as described for the Product of
Elements block. In matrix mode, if the parameter
value is 1
or *
, the block
outputs the input value. If the value is /
,
the input must be a square matrix (including a scalar as a
degenerate case) and the block outputs the matrix inverse. See
ElementWise Mode and Matrix Mode for more
information.
Integer value > 1
The block has the number of inputs given by the integer value.
The inputs are multiplied together in elementwise mode or
matrix mode, as specified by the Multiplication parameter. See ElementWise Mode and Matrix Mode for more
information.
Unquoted string of two or more
*
and /
characters
The block has the number of inputs given by the length of the
character vector. Each input that corresponds to a
*
character is multiplied into the
output. Each input that corresponds to a /
character is divided into the output. The operations occur in
elementwise mode or matrix mode, as specified by the Multiplication parameter. See ElementWise Mode and Matrix Mode for more
information.
Programmatic Use
Block Parameter:
Inputs 
Type: character
vector 
Values:
'2'  '**'  '*/'  '*/*'  ... 
Default:
'2' 
Multiplication
— Elementwise (.*) or Matrix (*) multiplication
Elementwise(.*)
(default)  Matrix(*)
Specify whether the block performs Elementwise(.*)
or
Matrix(*)
multiplication.
Programmatic Use
Block Parameter:
Multiplication 
Type: character vector 
Values:
'Elementwise(.*)'  'Matrix(*)' 
Default:
'Elementwise(.*)' 
Multiply over
— All dimensions or specified dimension
All dimensions
(default)  Specified dimension
Specify the dimension to multiply over as All dimensions
, or
Specified dimension
. When you select
Specified dimension
, you can specify the
Dimension as 1
or
2
.
Dependencies
To enable this parameter, set Number of inputs to *
and Multiplication to Elementwise (.*)
.
Programmatic Use
Block Parameter: CollapseMode 
Type: character vector 
Values: 'All dimensions'  'Specified dimension' 
Default: 'All dimensions' 
Dimension
— Dimension to multiply over
1
(default)  2
 ...
 N
Specify the dimension to multiply over as an integer less than or equal to the number of dimensions of the input signal.
Dependencies
To enable this parameter, set:
Programmatic Use
Block Parameter: CollapseDim 
Type: character vector 
Values:
'1'  '2'  ... 
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
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' 
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:
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:
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: Match scaling
 Inherit: Inherit via back
propagation
 Inherit: Same as first input
 double
 single
 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
. For more information, see
Control Signal Data Types.
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. If you change
the embedded target settings, the data type selected by the
internal rule might change. For example, if the block multiplies
an input of type int8
by a gain of
int16
and
ASIC/FPGA
is specified as the
targeted hardware type, the output data type is
sfix24
. If Unspecified
(assume 32bit Generic)
, in other words, a
generic 32bit microprocessor, is specified as the target
hardware, the output data type is int32
. If
none of the word lengths provided by the target microprocessor
can accommodate the output range, Simulink software displays an error in the Diagnostic
Viewer.
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, deselect the
Saturate on integer overflow
parameter.
This rule never produces overflows.
Inherit: Match scaling
– Simulink chooses a data type whose scaling matches the
scaling of the input types. If the full range of the type does
not fit on the embedded target hardware, the range is reduced
yielding a type appropriate for the embedded target hardware.
This rule can produce overflows. This rule does not support
multiplication between complex signals
The Inherit: Keep MSB
and
Inherit: Match scaling
rules do
not support multiplication between complex signals or signals
with nonzero bias. The rules support only multiplication and
division ('**'
, '*/'
,
'/*'
) between two inputs, matrix
multiplication of two inputs, and collapsing product of two
elements of a vector.
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 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, 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.
Inherit: Inherit via back
propagation
— Use data type of the driving
block.
Inherit: Same as first input
— Use
data type of first input signal.
Programmatic Use
Block Parameter:
OutDataTypeStr 
Type: character
vector 
Values: 'Inherit:
Inherit via internal rule  'Inherit:
Keep MSB'  'Inherit: Match
scaling'  'Inherit: Same as first
input'  'Inherit: Inherit via back
propagation'  'double' 
'single'  'int8' 
'uint8'  'int16' 
'uint16'  'int32' 
'uint32' 
'uint64' 'int64' 'fixdt(1,16)'
 'fixdt(1,16,0)' 
'fixdt(1,16,2^0,0)'  '<data
type expression>' 
Default: 'Inherit:
Inherit via internal rule' 
Lock output data type setting against changes by the fixedpoint tools
— Prevent fixedpoint tools from overriding Output data type
off
(default)  on
Select this parameter to prevent the fixedpoint tools from overriding the
Output data type you specify on the block. For more
information, see Use Lock Output Data Type Setting (FixedPoint Designer).
Programmatic Use
Block Parameter:
LockScale 
Type: character vector 
Values:
'off'  'on' 
Default:
'off' 
Integer rounding mode
— Rounding mode for fixedpoint operations
Floor
(default)  Ceiling
 Convergent
 Nearest
 Round
 Simplest
 Zero
Select the rounding mode for fixedpoint operations. You can select:
Ceiling
Rounds 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 FixedPoint
Designer™
convergent
function.
Floor
Rounds positive and negative numbers toward negative infinity. Equivalent
to theMATLAB
floor
function.
Nearest
Rounds number to the nearest representable value. If a tie occurs, rounds
toward positive infinity. Equivalent to the FixedPoint
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 FixedPoint
Designer
round
function.
Simplest
Chooses between rounding toward floor and rounding toward zero to generate
rounding code that is as efficient as possible.
Zero
Rounds number toward zero. Equivalent to the MATLAB
fix
function.
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 (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,
8bit integer) data type can represent is 127. Any block
operation result greater than this maximum value causes overflow
of the 8bit 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
outofrange signals. For more information, see Check for Signal Range Errors.

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

The maximum value that the int8 (signed,
8bit integer) data type can represent is 127. Any block
operation result greater than this maximum value causes overflow
of the 8bit integer. With the check box cleared, the software
interprets the overflowcausing 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  integer  single

Direct Feedthrough  yes

Multidimensional Signals  yes

VariableSize Signals  yes

ZeroCrossing 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
The default Linear
implementation generates a chain
of N operations (multipliers) for N inputs.
HDL Block Properties
If you use the block in matrix multiplication mode, you can specify the
DotProductStrategy. This setting determines whether you want to
implement the matrix multiplication by using a tree of adders and multipliers, or use the
MultiplyAccumulate block implementation. The default is Fully Parallel
.
For more information, see DotProductStrategy (HDL Coder).
See also Design Considerations for Matrices and Vectors (HDL Coder).
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).

DSPStyle  Synthesis attributes for multiplier mapping. The default is none .
See also DSPStyle (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).

Native Floating Point 

HandleDenormals  Specify whether you want HDL Coder to insert additional logic to handle denormal numbers in your design.
Denormal numbers are numbers that have magnitudes less than the smallest floatingpoint
number that can be represented without leading zeros in the mantissa. The default is
inherit . See also HandleDenormals (HDL Coder). 
LatencyStrategy  Specify whether to map the blocks in your design to inherit ,
Max , Min , Zero , or
Custom for the floatingpoint operator. The default is
inherit . See also LatencyStrategy (HDL Coder).

NFPCustomLatency  To specify a value, set LatencyStrategy to
Custom . HDL Coderadds latency equal to the value that you specify for the
NFPCustomLatency setting. See also NFPCustomLatency (HDL Coder).

MantissaMultiplyStrategy  Specify how to implement the mantissa multiplication operation during code generation.
By using different settings, you can control the DSP usage on the target FPGA device.
The default is inherit . See also MantissaMultiplyStrategy (HDL Coder). 
Complex Data Support
The default (linear) implementation supports complex data.
Complex division is not supported. For block
implementations of the Product block in divide mode or reciprocal mode, see
HDL Code Generation on the
Divide block reference page.
Restrictions
HDL code generation does not support more than two inputs at the ports of the
block when you use the block in matrix multiplication mode.
PLC Code Generation
Generate Structured Text code using Simulink® PLC Coder™.
FixedPoint Conversion
Design and simulate fixedpoint systems using FixedPoint Designer™.
Introduced before R2006a