Gain

Multiply input by constant

• 

Libraries:
Simulink / Commonly Used Blocks
Simulink / Math Operations
HDL Coder / Commonly Used Blocks
HDL Coder / HDL Floating Point Operations
HDL Coder / Math Operations

Description

The Gain block multiplies the input by a constant value, or gain. The input and the gain can each be a scalar, vector, or matrix.

You specify the value of gain in the Gain parameter. The Multiplication parameter lets you specify element-wise or matrix multiplication. For matrix multiplication, this parameter also lets you indicate the order of the multiplicands.

The gain is converted from doubles to the data type specified in the block mask offline using round-to-nearest and saturation. The input and gain are then multiplied, and the result is converted to the output data type using the specified rounding and overflow modes.

Examples

Multiply Constant by Gain

Open and simulate the model named SimpleGain.

mdl = "SimpleGain";
open_system(mdl)
sim(mdl);

This model represents the equation:

$$2*5=10$$

The Constant block provides a constant value of 2 to the Gain block.

The Gain block multiplies its input by 5.

The Display block displays the result of the multiplication.

Extended Examples

Simulation of Bouncing Ball

Uses two models of a bouncing ball to show different approaches to modeling hybrid dynamic systems with Zeno behavior. Zeno behavior is informally characterized by an infinite number of events occurring in a finite time interval for certain hybrid systems. As the ball loses energy, the ball collides with the ground in successively smaller intervals of time.

• Open Model

Model Stick-Slip Friction and Hard Stops in Mass-Spring-Damper System

One way you can incorporate hard stops and friction changes from stick-slip motion into a mass-spring-damper model.

• Open Live Script

Engine Timing Model with Closed Loop Control

Develop and implement a closed loop control algorithm for the open loop engine model described in Model Engine Timing Using Triggered Subsystems. In this example, the model sldemo_enginewc contains a controller that regulates engine speed using a fast throttle actuator such that changes in load torque have minimal effect. The controller is implemented using a discrete PI controller.

• Open Model

Ports

Input

Port_1 — Input signal

scalar | vector | matrix

The Gain block accepts real or complex-valued scalar, vector, or matrix input. The Gain block supports fixed-point data types. If the input of the Gain block is real and gain is complex, the output is complex.

Data Types: half | single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | Boolean | fixed point
Complex Number Support: Yes

Output

Port_1 — Input multiplied by gain

scalar | vector | matrix

The Gain block outputs the input multiplied by a constant gain value. When the input to the Gain block is real and gain is complex, the output is complex.

Data Types: half | single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | Boolean | fixed point
Complex Number Support: Yes

Parameters

To edit block parameters interactively, use the Property Inspector. From the Simulink^® Toolstrip, on the Simulation tab, in the Prepare gallery, select Property Inspector.

Main

Gain — Value by which to multiply the input

1 (default) | real or complex-valued scalar, vector, or matrix

Specify the value by which to multiply the input. The gain can be a real or complex-valued scalar, vector, or matrix.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

Parameter:	Gain
Values:	'1' (default) | real or complex-valued scalar, vector, or matrix in quotes

Multiplication — Specify the multiplication mode

Element-wise(K.*u) (default) | Matrix(K*u) | Matrix(u*K) | Matrix(K*u) (u vector)

Specify one of these multiplication modes:

• Element-wise(K.*u) — Each element of the input is multiplied by each element of the gain. The block performs expansions, if necessary, so that the input and gain have the same dimensions.

• Matrix(K*u) — The input and gain are matrix-multiplied with the input as the second operand.

• Matrix(u*K) — The input and gain are matrix-multiplied with the input as the first operand.

• Matrix(K*u) (u vector) — The input and gain are matrix multiplied with the input as the second operand. This mode is identical to Matrix(K*u), except for how dimensions are determined.

  Suppose that K is an m-by-n matrix. Matrix(K*u)(u vector) sets the input to a vector of length n and the output to a vector of length m. In contrast, Matrix(K*u) uses propagation to determine dimensions for the input and output. For an m-by-n gain matrix, the input can propagate to an n-by-q matrix, and the output becomes an m-by-q matrix.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

Parameter:	Multiplication
Values:	'Element-wise(K.*u)' (default) | 'Matrix(K*u)' | 'Matrix(u*K)' | 'Matrix(K*u) (u vector)'

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

To set the block parameter value programmatically, use the set_param function.

Parameter:	SampleTime
Values:	"-1" (default) | scalar or vector in quotes

Signal Attributes

Output minimum — Minimum output value for range checking

[] (default) | scalar

Lower value of the output range that the software checks.

The software 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).

Tips

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

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

Parameter:	OutMin
Values:	'[]' (default) | scalar in quotes

Output maximum — Maximum output value for range checking

[] (default) | scalar

Upper value of the output range that the software checks.

The software 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).

Tips

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

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

Parameter:	OutMax
Values:	'[]' (default) | scalar in quotes

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 input | double | single | half | int8 | uint8 | int16 | uint16 | int32 | int64 | uint64 | uint32 | 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 exhibits these behaviors:

• Inherit: Inherit via internal rule — The software 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 32-bit Generic), in other words, a generic 32-bit 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, the software displays an error in the Diagnostic Viewer.

• Inherit: Keep MSB– The software 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, clear Saturate on integer overflow.

  This rule never produces overflows.

• Inherit: Match scaling – The software 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.

  It is not always possible for the software to optimize code efficiency and numerical accuracy at the same time. If these internal 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 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 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 the data type of the driving block.

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

Dependencies

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

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

Parameter:	OutDataTypeStr
Values:	'Inherit: Inherit via internal rule' (default) | 'Inherit: Keep MSB' | 'Inherit: Match scaling' | 'Inherit: Inherit via back propagation' | 'Inherit: Same as 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>'

Lock output data type setting against changes by the fixed-point tools — Option to prevent fixed-point tools from overriding Output data type

off (default) | on

Select this parameter to prevent the fixed-point tools from overriding the Output data type you specify on the block. For more information, see Use Lock Output Data Type Setting (Fixed-Point Designer).

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

Parameter:	LockScale
Values:	'off' (default) | 'on'

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 Modes (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

To set the block parameter value programmatically, use the set_param function.

Parameter:	RndMeth
Values:	'Floor' (default) | 'Ceiling' | 'Convergent' | 'Nearest' | 'Round' | 'Simplest' | 'Zero'

Saturate on integer overflow — Method of overflow action

off (default) | on

Specify whether overflows saturate or wrap.

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

• off — Overflows wrap to the appropriate value that the data type can represent.

For example, the maximum value that the signed 8-bit integer int8 can represent is 127. Any block operation result greater than this maximum value causes overflow of the 8-bit integer.

• With this parameter selected, the block output saturates at 127. Similarly, the block output saturates at a minimum output value of -128.

• With this parameter 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.

Tips

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

• Consider clearing this parameter when you want to optimize efficiency of your generated code. Clearing this parameter also helps you to avoid overspecifying how a block handles out-of-range signals. For more information, see Troubleshoot Signal Range Errors.

• When you select this parameter, 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.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

Parameter:	SaturateOnIntegerOverflow
Values:	'off' (default) | 'on'

Mode — Select data type mode

Inherit (default) | Built in | Fixed Point

Select the category of data to specify.

• Inherit — Inheritance rules for data types. Selecting Inherit enables a second menu/text box to the right where you can select the inheritance mode.

• Built in — Built-in data types. Selecting Built in enables a second menu/text box to the right where you can select a built-in data type.

• Fixed point — Fixed-point data types. Selecting Fixed point enables additional parameters that you can use to specify a fixed-point data type.

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

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

Dependencies

To enable this parameter, click the Show data type assistant button .

Data type override — Specify data type override mode for this signal

Inherit | Off

Select the data type override mode for this signal.

• When you select Inherit, Simulink 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.

• When you select Off, Simulink ignores the data type override setting of its context and uses the fixed-point data type specified for the signal.

For more information, see Specify Data Types Using Data Type Assistant in the Simulink documentation.

Dependencies

To enable this parameter, set Mode to Built in or Fixed point.

Tips

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.

Signedness — Specify signed or unsigned

Signed (default) | Unsigned

Specify whether the fixed-point data is signed or unsigned. Signed data can represent positive and negative values, but unsigned data represents positive values only.

• Signed, specifies the fixed-point data as signed.

• Unsigned, specifies the fixed-point data as unsigned.

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

Dependencies

To enable this parameter, set the Mode to Fixed point.

Word length — Bit size of the word that holds the quantized integer

16 (default) | integer from 0 to 32

Specify the bit size of the word that holds the quantized integer. For more information, see Specifying a Fixed-Point Data Type.

Dependencies

To enable this parameter, set Mode to Fixed point.

Scaling — Method for scaling fixed-point data

Best precision (default) | Binary point | Slope and bias

Specify the method for scaling your fixed-point data to avoid overflow conditions and minimize quantization errors. For more information, see Specifying a Fixed-Point Data Type.

Dependencies

To enable this parameter, set Mode to Fixed point.

Slope — Specify slope for the fixed-point data type

2^0 (default) | positive, real-valued scalar

Specify slope for the fixed-point data type. For more information, see Specifying a Fixed-Point Data Type.

Dependencies

To enable this parameter, set Scaling to Slope and bias.

Bias — Specify bias for the fixed-point data type

0 (default) | real-valued scalar

Specify bias for the fixed-point data type as any real number. For more information, see Specifying a Fixed-Point Data Type.

Dependencies

To enable this parameter, set Scaling to Slope and bias.

Fraction length — Specify fraction length for fixed-point data type

0 (default) | scalar integer

Specify fraction length for fixed-point data type as a positive or negative integer. For more information, see Specifying a Fixed-Point Data Type.

Dependencies

To enable this parameter, set Scaling to Binary point.

Parameter Attributes

Parameter minimum — Specify the minimum value of gain

[] (default) | scalar

Specify the minimum value of gain. The default value is [] (unspecified). The software uses this value to perform:

• Parameter range checking (see Specify Minimum and Maximum Values for Block Parameters)

• Automatic scaling of fixed-point data types

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

Parameter:	ParamMin
Values:	'[]' (default) | scalar in quotes

Parameter maximum — Specify the maximum value of gain

[] (default) | scalar

Specify the maximum value of gain. The default value is [] (unspecified). The software uses this value to perform:

• Parameter range checking (see Specify Minimum and Maximum Values for Block Parameters)

• Automatic scaling of fixed-point data types

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

Parameter:	ParamMax
Values:	'[]' (default) | scalar in quotes

Parameter data type — Specify the data type of the Gain parameter

Inherit: Inherit via internal rule (default) | Inherit: Same as input | Inherit: Inherit from 'Gain' | 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>

Specify the data type of the Gain parameter.

Setting Parameter data type to Inherit: Inherit via internal rule lets the Gain block select a data type based on an internal heuristic that looks at the current gain value and provides a full precision data type to represent the current gain value. When you update the diagram, the software deduces a data type to fit the gain value 3 with high precision and no range loss. For example, with this heuristic, if the specified gain value is 3, the Gain block deduces a selected data type of sfix32_En29. Consequently, this deduced data type cannot hold values greater than 4. During simulation, if you tune the gain value to 6, an overflow occurs in the selected data type and the behavior is unexpected.

While tuning a parameter with this Parameter data type setting, specify the Parameter Minimum and Parameter Maximum parameters. These settings tell the software about the range of values you want during the simulation and allows the software to provide a full precision data type with sufficient range to allow safe tuning of the gain value within the specified range.

Programmatic Use

To set the block parameter value programmatically, use the set_param function.

Parameter:	ParamDataTypeStr
Values:	'Inherit: Inherit via internal rule' (default) | 'Inherit: Same as input' | 'Inherit: Inherit from 'Gain'' | '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>'

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 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.

Tunable Parameters

You can use a tunable parameter in a Gain block intended for HDL code generation. For details, see Generate DUT Ports for Tunable Parameters (HDL Coder).

HDL Architecture

ConstMultiplierOptimization	Description
none(Default)	By default, HDL Coder does not perform CSD or FCSD optimizations. Code generated for the Gain block retains multiplier operations.
csd	When you specify this option, the generated code decreases the area used by the model while maintaining or increasing clock speed, using canonical signed digit (CSD) techniques. CSD replaces multiplier operations with add and subtract operations. CSD minimizes the number of addition operations required for constant multiplication by representing binary numbers with a minimum count of nonzero digits.
fcsd	This option uses factored CSD (FCSD) techniques, which replace multiplier operations with shift and add/subtract operations on certain factors of the operands. These factors are generally prime but can also be a number close to a power of 2, which favors area reduction. You can achieve a greater area reduction with FCSD at the cost of decreasing clock speed.
auto	When you specify this option, the coder chooses between the CSD or FCSD optimizations. The coder chooses the optimization that yields the most area-efficient implementation, based on the number of adders required. When you specify auto, the coder does not use multipliers, unless conditions are such that CSD or FCSD optimizations are not possible (for example, if the design uses floating-point arithmetic).

HDL Block Properties

General
ConstMultiplierOptimization	Canonical signed digit (CSD) or factored CSD optimization. The default is none. See also ConstMultiplierOptimization (HDL Coder).
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).

Note

For certain values of the Gain parameter, native floating point implements the algorithm differently instead of using multipliers. For example, if you set the Gain parameter to 1, the generated model uses a wire to pass the input to the output. If you set the Gain parameter to -1, the generated model shows a Unary Minus block that inverts the polarity of the input signal. This implementation reduces the latency and resource usage on the target platform.

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 floating-point 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 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).
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

This block supports code generation for complex signals.

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

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

Version History

Introduced before R2006a