Sqrt

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

Function	Description	Mathematical Expression	MATLAB^® Equivalent
`sqrt`	Square root of the input	`u^0.5`	`sqrt`
`signedSqrt`	Square root of the absolute value of the input, multiplied by the sign of the input	`sign(u)*\|u\|^0.5`	—
`rSqrt`	Reciprocal of the square root of the input	`u^-0.5`	—

Ports

Input

`Port_1` — Input signal
scalar | vector | matrix

Input signal to the block to calculate the square root, signed square root, or reciprocal of square root. The sqrt function accepts real or complex inputs, except for complex fixed-point signals. signedSqrt and rSqrt do not accept complex inputs. For the signedSqrt function, the input signal must be a floating point number.

This table summarizes the support for complex types and negative values for floating point, integer, and fixed-point data types for sqrt, rSqrt, and signedSqrt functions.

Function	Data Type	Complex		Negative Values
Function	Data Type	Input	Output	Negative Values
`sqrt`	Floating point	Yes	Yes	Yes
	Integer and fixed-point	No	No	No
`rSqrt`	Floating point	No	No	Yes
	Integer and fixed-point	No	No	No
`signedSqrt`	Floating point	No	Yes	Yes
	Integer and fixed-point	No	No	No

If the input is negative, set the Output signal to complex for all functions except signedSqrt.

Output

expand all

`Port_1` — Output signal
scalar | vector | matrix

Output signal that is the square root, signed square root, or reciprocal of square root of the input signal. When the input is an integer or fixed-point type, the output must be floating point.

Parameters

expand all

Main

`Function` — Function the block performs
`sqrt` (default) | `signedSqrt` | `rSqrt`

Specify the mathematical function that the block calculates. The block icon changes to match the function you select.

Function	Block Icon
`sqrt`
`signedSqrt`
`rSqrt`

Dependency

When this parameter is set to signedSqrt, the Intermediate results data type parameter is disabled.

Programmatic Use

Block Parameter: Operator

Type: character vector

Values: 'sqrt' | 'signedSqrt' | 'rSqrt'

Default: 'sqrt'

`Output signal type` — Output signal type
`auto` (default) | `real` | `complex`

Specify the output signal type of the block.

Function	Input Signal Type	Output Signal Type
Function	Input Signal Type	Auto	Real	Complex
`sqrt`	`real`	`real` for nonnegative inputs `NaN` for negative inputs	`real` for nonnegative inputs `NaN` for negative inputs	`complex`
`sqrt`	`complex`	`complex`	`error`	`complex`
`signedSqrt`	`real`	`real`	`real`	`complex`
`signedSqrt`	`complex`	`error`	`error`	`error`
`rSqrt`	`real`	`real`	`real`	`error`
`rSqrt`	`complex`	`error`	`error`	`error`

Programmatic Use

Block Parameter: OutputSignalType

Type: character vector

Values: 'auto' | 'real' | 'complex'

Default: 'auto'

`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'

Algorithm

`Method` — Method to compute reciprocal of square root
`Exact` (default) | `Newton-Raphson`

Specify the method for computing the reciprocal of a square root. This parameter is only valid for the rSqrt function.

Method	Data Types Supported	When to Use This Method
`Exact`	Floating point	You do not want an approximation. Note The input or output must be floating point.
`Newton-Raphson`	Floating-point, fixed-point, and built-in integer types	You want a fast, approximate calculation.

The Exact method provides results that are consistent with MATLAB computations.

Note

The algorithms for sqrt and signedSqrt are always of Exact type, no matter what selection appears on the block dialog box.

Programmatic Use

Block Parameter: AlgorithmType

Type: character vector

Values: 'Exact' | 'Newton-Raphson'

Default: 'Exact'

`Number of iterations` — Number of iterations used for Newton Raphson algorithm
`3` (default) | integer

Specify the number of iterations to perform the Newton-Raphson algorithm. This parameter is valid with the rSqrt function and the Newton-Raphson value for Method.

Note

If you enter 0, the block output is the initial guess of the Newton-Raphson algorithm.

Programmatic Use

Block Parameter: Iterations

Type: character vector

Values: integer

Default: '3'

Data Types

Click the Show data type assistant button to display the Data Type Assistant, which helps you set the data type attributes. For more information, see Specify Data Types Using Data Type Assistant.

`Intermediate results data type` — Data type of intermediate results
`Inherit:Inherit via internal rule` (default) | `Inherit: Inherit from input` | `Inherit: Inherit from output` | `double` | `single` | `int8` | `uint8` | `int16` | `uint16` | `int32` | `uint32` | `int64` | `uint64` | `fixdt(1,16,,0)` | `fixdt(1,16,2^0,0)` | `<data type expression>`

Specify the data type for intermediate results when you set Function to sqrt or rSqrt on the Main pane.

The type can be inherited, specified directly, or expressed as a data type object such as Simulink.NumericType.

Follow these guidelines on setting an intermediate data type explicitly for the square root function, sqrt:

Input and Output Data Types	Intermediate Data Type
Input or output is double.	Use double.
Input or output is single, and any non-single data type is not double.	Use single or double.
Input and output are fixed point.	Use fixed point.

Follow these guidelines on setting an intermediate data type explicitly for the reciprocal square root function, rSqrt:

Input and Output Data Types	Intermediate Data Type
Input is double and output is not single.	Use double.
Input is not single and output is double.	Use double.
Input and output are fixed point.	Use fixed point.

Caution

Do not set Intermediate results data type to Inherit:Inherit from output when:

You select Newton-Raphson to compute the reciprocal of a square root.
The input data type is floating point.
The output data type is fixed point.

Under these conditions, selecting Inherit:Inherit from output yields suboptimal performance and produces an error.

To avoid this error, convert the input signal from a floating-point to fixed-point data type. For example, insert a Data Type Conversion block in front of the Sqrt block to perform the conversion.

Dependency

This parameter is disabled when the Function parameter is set to signedSqrt.

Programmatic Use

Block Parameter: IntermediateResultsDataTypeStr

Type: character vector

Values:

'Inherit: Inherit via internal
										rule'

|

'Inherit: Inherit from
										input'

|

'Inherit: Inherit from
										output'

| 'double' | 'single', 'int8', 'uint8', int16, 'uint16', 'int32', 'uint32', 'int64', 'uint64', fixdt(1,16,0), fixdt(1,16,2^0,0).

'<data
										type expression>'

Default:

'Inherit:
										Inherit via internal rule'

`Output` — Output data type
`Inherit: Same as first input` (default) | `Inherit: Inherit via internal rule` | `Inherit: Inherit via back propagation` | `double` | `single` | `int8` | `int32` | `uint32` | `int64` | `uint64` | `fixdt(1,16,2^0,0)` | `<data type expression>` | ...

Specify the output data type. The type can be inherited, specified directly, or expressed as a data type object such as Simulink.NumericType.

Programmatic Use

Block Parameter: OutDataTypeStr

Type: character vector

Values:

'Inherit: Inherit via internal
										rule'

|

'Inherit: Inherit via back
										propagation'

|

'Inherit: Same as first
										input'

| 'double' | 'single', 'int8', 'uint8', int16, 'uint16', 'int32', 'uint32', 'int64', 'uint64', fixdt(1,16,0), fixdt(1,16,2^0,0), fixdt(1,16,2^0,0).

'<data
										type expression>'

Default:

'Inherit:
										Same as first input'

`Minimum` — Minimum output value for range checking
`[]` (default) | scalar

Specify the lower value of the output range that Simulink^® checks as a finite, real, double, scalar value.

Note

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

Simulink uses the minimum to perform:

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).

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:

'[
										]'

`Maximum` — Maximum output value for range checking
`[]` (default) | scalar

Specify the upper value of the output range that Simulink checks as a finite, real, double, scalar value.

Note

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

Simulink uses the maximum value to perform:

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).

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:

'[
										]'

`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 (Fixed-Point Designer).

Programmatic Use

Block Parameter: RndMeth

Type: character vector

Values:

'Ceiling' | 'Convergent' | 'Floor' |
                                                  'Nearest' | 'Round' | 'Simplest' |
                                                  'Zero'

Default: 'Floor'

`Lock output data type setting against changes by the fixed-point tools` — Prevent fixed-point tools from overriding data types
`off` (default) | `on`

Select to lock the output data type setting of this block against changes by the Fixed-Point Tool and the Fixed-Point Advisor. For more information, see Use Lock Output Data Type Setting (Fixed-Point Designer).

Programmatic Use

Block Parameter: LockScale

Type: character vector

Values: 'off' | 'on'

Default: 'off'

`Saturate on integer overflow` — Choose the behavior when integer overflow occurs
`off` (default) | `on`

Action Reasons for Taking This Action What Happens for Overflows Example

Action	Reasons for Taking This Action	What Happens for 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 `int8` (signed, 8-bit integer) data type can represent is 127. Any block operation result greater than this maximum value causes overflow of the 8-bit 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.	You want to optimize efficiency of your generated code. You want to avoid overspecifying how a block handles out-of-range 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 `int8` (signed, 8-bit integer) data type can represent is 127. Any block operation result greater than this maximum value causes overflow of the 8-bit integer. With the check box 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.

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 int8 (signed, 8-bit integer) data type can represent is 127. Any block operation result greater than this maximum value causes overflow of the 8-bit 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.

You want to optimize efficiency of your generated code.

You want to avoid overspecifying how a block handles out-of-range 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 int8 (signed, 8-bit integer) data type can represent is 127. Any block operation result greater than this maximum value causes overflow of the 8-bit integer. With the check box 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.

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: DoSatur

Type: character vector

Value: 'off' | 'on'

Default: 'off'

Model Examples

Square Root of Negative Values

Compute the square root of a negative-valued input signal as complex-valued output.

Open Model

Signed Square Root of Negative Values

Compute the signed square root of a negative-valued input signal.

Open Model

rSqrt of Floating-Point Inputs

Compute the rSqrt of a floating-point input signal.

Open Model

rSqrt of Fixed-Point Inputs

Compute the rSqrt of a fixed-point input signal.

Open Model

Block Characteristics

Data Types	`double` \| `fixed point` \| `integer` \| `single`
Direct Feedthrough	`no`
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 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.

Sqrt Function Modes

For the Sqrt block with Function set to sqrt, the code generator supports various architectures and data types.

The sqrtfunction architecture supports code generation for fixed-point types and floating-point types. When you use floating-point types, set Floating Point IP Library (HDL Coder) to Native Floating Point. You can specify the LatencyStrategy and CustomLatency HDL properties to choose from a range of frequency values when targeting your design on the hardware platform.

Use the UseMultiplier HDL block property in combination with the LatencyStrategy and CustomLatency properties to specify whether to compute the square root by using a pipelined shift and add or multiplication algorithm

Native Floating Point Settings for Different Modes

For this architecture, you can specify the HandleDenormals and LatencyStrategy settings from the Native Floating Point tab in the HDL Block Properties dialog box.

Architecture	Fixed-Point	Native Floating-Point	HandleDenormals	LatencyStrategy
`sqrtfunction`	✓	✓	✓	✓
`sqrtnewton`	✓	—	—	—
`sqrtnewtonsinglerate`	✓	—	—	—
`recipsqrtnewton`	✓	—	—	—
`recipsqrtnewtonsinglerate`	✓	—	—	—

HDL Architecture

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).

Architecture	Parameter	Additional cycles of latency	Description
`SqrtFunction` (default)	`UseMultiplier` `LatencyStrategy` `CustomLatency`	Depends on parameter choices, output word length, and input and output fraction lengths.	To specify this architecture, set Function to `sqrt` or `rSqrt`. Compute the square root by using a pipelined shift/addition algorithm or multiplication-based algorithm. The `SqrtFunction` architecture has a maximum latency that is determined by the output word length, and input and output fraction lengths, for fixed-point data. For example, the maximum latency is `11` for output word length of `17`. To see the latency calculation, at the MATLAB command prompt, enter: HDLMathLib
`SqrtNewton`	`Iterations`	`Iterations` + 3	To specify this architecture, set Function to `sqrt`. Use the iterative Newton method. Select this option to optimize area. The default value for `Iterations` is 3. The recommended value for `Iterations` is from 2 through 10. If `Iterations` is outside the recommended range, HDL Coder generates a message.
`SqrtNewtonSingleRate`	`Iterations`	(`Iterations` * 4) + 6	To specify this architecture, set Function to `sqrt`. Use the single rate pipelined Newton method. Select this option to optimize speed, or if you want a single rate implementation. The default value for `Iterations` is 3. The recommended value for `Iterations` is from 2 through 10. If `Iterations` is outside the recommended range, the coder generates a message.
`RecipSqrtNewton`	`Iterations`	`Iterations` + 2	To specify this architecture, set Function to `rSqrt`. Use the iterative Newton method. Select this option to optimize area.
`RecipSqrtNewtonSingleRate`	`Iterations`	(`Iterations` * 4) + 5	To specify this architecture, set Function to `rSqrt`. Use the single rate pipelined Newton method. Select this option to optimize speed, or if you want a single rate implementation.

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).
Iterations	Number of iterations for `SqrtNewton` or `SqrtNewtonSingleRate` implementation.
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).
UseMultiplier	Select algorithm for `SqrtFunction` implementation. By default, this property is set to `off`, and the block computes square root by using the shift-add algorithm. When the property is set to `on`, the square root is computed by using multipliers.
LatencyStrategy	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 `MAX`. The block settings for floating-point types overrides the model-level settings. For fixed-point types, the block-level setting determines the latency strategy. See also LatencyStrategy (HDL Coder).
CustomLatency	When LatencyStrategy is set to `CUSTOM` and if you use fixed-point types, use this property to specify a custom latency value between `ZERO` and `MAX` for fixed-point types. For floating-point types, this value becomes the custom latency of the operator. See also NFPCustomLatency (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).

Restrictions

Input must be an unsigned scalar value.
Output is a fixed-point scalar value.

Documentation

Sqrt

Description

Ports

Input

Port_1 — Input signal scalar | vector | matrix

Output

Port_1 — Output signal scalar | vector | matrix

Parameters

Main

Function — Function the block performs sqrt (default) | signedSqrt | rSqrt

Dependency

Programmatic Use

Output signal type — Output signal type auto (default) | real | complex

Programmatic Use

Sample time — Specify sample time as a value other than -1 -1 (default) | scalar | vector

Dependencies

Programmatic Use

Algorithm

Method — Method to compute reciprocal of square root Exact (default) | Newton-Raphson

Programmatic Use

Number of iterations — Number of iterations used for Newton Raphson algorithm 3 (default) | integer

Programmatic Use

Data Types

Dependency

Programmatic Use

Output — Output data type Inherit: Same as first input (default) | Inherit: Inherit via internal rule | Inherit: Inherit via back propagation | double | single | int8 | int32 | uint32 | int64 | uint64 | fixdt(1,16,2^0,0) | <data type expression> | ...

Programmatic Use

Minimum — Minimum output value for range checking [] (default) | scalar

Programmatic Use

Maximum — Maximum output value for range checking [] (default) | scalar

Programmatic Use

Integer rounding mode — Rounding mode for fixed-point operations Floor (default) | Ceiling | Convergent | Nearest | Round | Simplest | Zero

Programmatic Use

Lock output data type setting against changes by the fixed-point tools — Prevent fixed-point tools from overriding data types off (default) | on

Programmatic Use

Saturate on integer overflow — Choose the behavior when integer overflow occurs off (default) | on

Programmatic Use

Model Examples

Square Root of Negative Values

Signed Square Root of Negative Values

rSqrt of Floating-Point Inputs

rSqrt of Fixed-Point Inputs

Block Characteristics

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™.

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

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

See Also

Simulink Documentation

Support

`Port_1` — Input signal
scalar | vector | matrix

`Port_1` — Output signal
scalar | vector | matrix

`Function` — Function the block performs
`sqrt` (default) | `signedSqrt` | `rSqrt`

`Output signal type` — Output signal type
`auto` (default) | `real` | `complex`

`Sample time` — Specify sample time as a value other than `-1`
`-1` (default) | scalar | vector

`Method` — Method to compute reciprocal of square root
`Exact` (default) | `Newton-Raphson`

`Number of iterations` — Number of iterations used for Newton Raphson algorithm
`3` (default) | integer

`Output` — Output data type
`Inherit: Same as first input` (default) | `Inherit: Inherit via internal rule` | `Inherit: Inherit via back propagation` | `double` | `single` | `int8` | `int32` | `uint32` | `int64` | `uint64` | `fixdt(1,16,2^0,0)` | `<data type expression>` | ...

`Minimum` — Minimum output value for range checking
`[]` (default) | scalar

`Maximum` — Maximum output value for range checking
`[]` (default) | scalar

`Integer rounding mode` — Rounding mode for fixed-point operations
`Floor` (default) | `Ceiling` | `Convergent` | `Nearest` | `Round` | `Simplest` | `Zero`

`Lock output data type setting against changes by the fixed-point tools` — Prevent fixed-point tools from overriding data types
`off` (default) | `on`

`Saturate on integer overflow` — Choose the behavior when integer overflow occurs
`off` (default) | `on`

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™.

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

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