Divide

Divide one input by another

• 

Libraries:
Simulink / Math Operations
HDL Coder / HDL Floating Point Operations
HDL Coder / Math Operations

Description

The Divide block outputs the result of dividing its first input by its second. The inputs can be scalars, a scalar and a nonscalar, or two nonscalars that have the same dimensions. This block supports only complex input values at division ports when all ports have the same single or double data type.

The Divide block is functionally a Product block that has two block parameter values preset:

• Multiplication — Element-wise(.*)

• Number of Inputs — */

Setting nondefault values for either of those parameters can change a Divide block to be functionally equivalent to a Product block or a Product of Elements block.

Examples

Divide Inputs of Different Dimensions Using the Divide Block

This example shows how to perform element-wise (.*) division of two inputs using the Divide block. In this example, the Divide block divides two scalars, a vector by a scalar, a scalar by a vector, and two matrices.

Ports

Input

X — Input signal to multiply

scalar | vector | matrix | N-D 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 and set the Multiplication parameter to Element-wise(.*).

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

÷ — Input signal to divide or invert

scalar | vector | matrix | N-D 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 and set the Multiplication parameter to Element-wise(.*).

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

Port_1 — First input to multiply or divide

scalar | vector | matrix | N-D array

First input to multiply or divide, provided as a scalar, vector, matrix, or N-D array.

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

Port_N — Nth input to multiply or divide

scalar | vector | matrix | N-D array

Nth input to multiply or divide, provided as a scalar, vector, matrix, or N-D array.

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

* — Input signal to multiply

scalar | vector | matrix | N-D array

Input signal to be multiplied with other inputs.

Dependencies

To enable one or more * ports, specify one or more * characters for the Number of inputs parameter and set the Multiplication parameter to Matrix(*).

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

Inv — Input signal to divide or invert

scalar | vector | matrix | N-D array

Input signal for division or inversion operations.

Dependencies

To enable one or more Inv ports, specify one or more / characters for the Number of inputs parameter and set the Multiplication parameter to Matrix(*).

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

Output

Port_1 — Output computed by multiplying, dividing, or inverting inputs

scalar | vector | matrix | N-D array

Output computed by multiplying, dividing, or inverting inputs.

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

Parameters

Main

Number of inputs — Control number of inputs and type of operation

*/ (default) | positive integer scalar | * or / for each input port

Control two properties of the block:

• The number of input ports on the block

• Whether each input is multiplied or divided into the output

When you specify:

• 1 or * or /

  The block has one input port. In element-wise 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 Element-Wise 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 element-wise mode or matrix mode, as specified by the Multiplication parameter. See Element-Wise 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 element-wise mode or matrix mode, as specified by the Multiplication parameter. See Element-Wise Mode and Matrix Mode for more information.

Programmatic Use

Block Parameter: Inputs

Type: character vector

Values: '2' | '*' | '**' | '*/' | '*/*' | ...

Default: '*/'

Multiplication — Element-wise (.*) or Matrix (*) multiplication

Element-wise(.*) (default) | Matrix(*)

Specify whether the block performs Element-wise(.*) or Matrix(*) multiplication.

Programmatic Use

Block Parameter: Multiplication

Type: character vector

Values: 'Element-wise(.*)' | 'Matrix(*)'

Default: 'Element-wise(.*)'

Apply over — How to apply function along specified dimensions

All dimensions (default) | Specified dimension

Specify how to apply the function along specified dimensions.

• All dimensions — Apply function for all input values for all dimensions.

• Specified dimension — Apply function for all input values for specified dimension.

For example, in this model, Multiplication is set to Element-wise(.*), and Apply over is set to All dimensions. The block returns the product of all values from all dimensions.

Dependencies

To enable this parameter, set Number of inputs to * and Multiplication to Element-wise (.*).

Programmatic Use

Block Parameter: CollapseMode

Type: character vector

Values: 'All dimensions' | 'Specified dimension'

Default: 'All dimensions'

Dimension — Dimension along which to multiply

1 (default) | positive integer

Specify the dimension along which to multiply, as a positive integer. For example, for a 2-D matrix, 1 applies the function to each column, and 2 applies the function to each row.

For example, in this model, Multiplication is set to Element-wise(.*), Apply over is set to Specified dimension, and Dimension is set to 2. The block returns the product of all values from each row.

Dependencies

To enable this parameter:

• Set Number of inputs to *

• Set Multiplication to Element-wise (.*)

• Set Apply over to Specified dimension

Programmatic Use

Block Parameter: CollapseDim

Type: character vector

Values: '1' | '2' | ...

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

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

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

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 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: 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 Data Types of Signals.

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 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, Simulink software displays an error in the Diagnostic Viewer.

  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 Fixed-Point Tool to propose data types for your model. For more information, see fxptdlg (Fixed-Point Designer).

  • To specify your own inheritance rule, use Inherit: Inherit via back propagation and then use a Data Type Propagation block. Examples of how to use this block are available in the Signal Attributes library Data Type Propagation Examples block.

• Inherit: Inherit via back propagation — Use data type of the driving block.

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

Dependencies

When 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

Block Parameter: OutDataTypeStr

Type: character vector

Values: 'Inherit: Inherit via internal rule | 'Inherit: Same as first input' | 'Inherit: Inherit via back propagation' | '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>'

Default: 'Inherit: Inherit via internal rule'

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

Select the rounding mode for fixed-point 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 Fixed-Point Designer™ convergent function.

Floor

Rounds 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

Chooses between rounding toward floor and rounding toward zero to generate rounding code that is as efficient as possible. This rounding mode is affected by these configuration parameters on the Hardware Implementation pane.

• If the Signed integer division rounds to parameter is set to Zero or Undefined, Simplest resolves to zero.

• If the Signed integer division rounds to parameter is set to Floor, Simplest resolves to floor.

Zero

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

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

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.

• 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.

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.

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.

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™.

Expected Differences Between Simulation and Code Generation

These conditions may yield different results between simulation and the generated code:

• The Divide block inputs contain a NaN or inf value

• The Divide block generates NaN or inf during execution

This difference is due to the nonfinite NaN or inf values. In such cases, inspect your model configuration and eliminate the conditions that produce NaN or inf.

Code Optimizations

The Simulink Coder™ build process provides efficient code for matrix inverse and division operations. This table describes the benefits and when each benefit is available.

Benefit	Small Matrices (2-by-2 to 5-by-5)	Medium Matrices (6-by-6 to 20-by-20)	Large Matrices (larger than 20-by-20)
Faster code execution time, compared to R2011a and earlier releases	Yes	No	Yes
Reduced ROM and RAM usage, compared to R2011a and earlier releases	Yes, for real values	Yes, for real values	Yes, for real values
Reuse of variables	Yes	Yes	Yes
Dead code elimination	Yes	Yes	Yes
Constant folding	Yes	Yes	Yes
Expression folding	Yes	Yes	Yes
Consistency with MATLAB Coder results	Yes	Yes	Yes

For blocks that have three or more inputs of different dimensions, the code might include an extra buffer to store temporary variables for intermediate results.

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.

Note

When you deploy the generated HDL code onto the target hardware, make sure that you set the signed integer division rounds to parameter in the Hardware Implementation pane of the Configuration Parameters dialog box to Zero or Floor.

To perform an HDL-optimized divide operation, connect a Product block to a Divide block in reciprocal mode.

HDL Architecture

The Divide block is the same as a Product block with Number of Inputs set to */.

Architecture	Parameters	Additional cycles of latency	Description
ShiftAdd(Default)	None	Depends on word-length and fractional-length of input and output. For more information, see HDLMathLib Divide (HDL Coder).	Perform divide operations by using a non-restoring division algorithm that performs multiple shift and add operations to compute the quotient. When you use fixed-point data types, following criteria must be satisfied for generating the HDL code: Inputs word length (WL) must be less than 63. [Max(WL input1, WL input2) + Abs(FL Difference)] must be less than 63. Where, Fractional length (FL) Difference is given by, FL Difference = FL input1 - (FL input2 + FL output)

Reciprocal Mode

When Number of Inputs is set to /, the Divide block is in reciprocal mode.

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

In reciprocal mode, the Divide block has the HDL block implementations described in the following table.

Architectures	Parameters	Additional cycles of latency	Description
ShiftAdd(Default)	None	Depends on word-length and fractional-length of input and output. For more information, see HDLMathLib Reciprocal (HDL Coder).	Perform reciprocal operation by using a non-restoring division algorithm that performs multiple shift and add operations to compute the reciprocal. When you use fixed-point data types, following criteria must be satisfied for generating the HDL code: Input word length (WL) must be less than or equal to 63. [WL input + Abs(FL Sum)] must be less than or equal to 63. Where, FL Sum is given by, FL sum = FL input + FL output

HDL code generation supports different output data types for divide (*/) and reciprocal (/) operations in ShiftAdd. You can use these output data types for the blocks:

• Inherit: Inherit via internal rule

• Inherit: Keep MSB​

• Inherit: Match scaling​

• Inherit: Inherit via back propagation​

• Inherit: Same as first input​

• Integer types (uint8,int8,uint16,int16,uint32,int32,uint64,int64)​

• Fixed point types​

HDL Block Properties

General
ConstrainedOutputPipeline	Number of registers to place at the outputs by moving existing delays within your design. Distributed pipelining does not redistribute these registers. The default is 0. For more details, see ConstrainedOutputPipeline (HDL Coder).
InputPipeline	Number of input pipeline stages to insert in the generated code. Distributed pipelining and constrained output pipelining can move these registers. The default is 0. For more details, see InputPipeline (HDL Coder).
OutputPipeline	Number of output pipeline stages to insert in the generated code. Distributed pipelining and constrained output pipelining can move these registers. The default is 0. For more details, see OutputPipeline (HDL Coder).
LatencyStrategy	To enable this property, set HDL architecture to ShiftAdd. Specify whether to map the blocks in your design to MAX, Min, CUSTOM, or ZERO latency for fixed-point and floating-point types. The default is inherit. See also LatencyStrategy (HDL Coder).
CustomLatency	To enable this property, set HDL architecture to ShiftAdd. When LatencyStrategy is set to CUSTOM, use this property to specify a custom latency value between ZERO and MAX for fixed-point types. See also LatencyStrategy (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 floating-point number that can be represented without leading zeros in the mantissa. The default is inherit. See also HandleDenormals (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).
DivisionAlgorithm	Specify whether to use the Radix-2 or Radix-4 algorithm to perform the floating-point division. The Radix-2 mode offers a tradeoff between latency and frequency. The Radix-4 mode offers a tradeoff between latency and resource usage. For more information, see DivisionAlgorithm (HDL Coder).

Complex Data Support

This block does not support code generation for division with complex signals.

Optimization Support

You can apply the sharing or streaming optimizations for Divide and Reciprocal blocks using ShiftAdd architecture.

Block (Inputs)	Resource Sharing	Streaming
Divide(/* or */)	Yes	Yes
Reciprocal (/)	Yes	No

When you use sharing optimization on these blocks, make sure to enclose the block in the atomic subsystem and set the Default parameter behavior configuration parameter to Inlined.

For more information, see Resource Sharing (HDL Coder) and Streaming (HDL Coder).

Restrictions

When you use the Divide block in reciprocal mode, the following restrictions apply:

• When you use fixed-point types, the input and output must be scalar. To use vector inputs, use floating-point types input and output.

• You must select the Saturate on integer overflow option on the block.

For the Divide block, only the Zero and Simplest rounding modes are supported.

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