Calculate square root, signed square root, or reciprocal of square root - Simulink - 金宝app,下载188bet金宝搏,金宝搏官方网站

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. Thesqrtfunction accepts real or complex inputs, except for complex fixed-point signals.signedSqrtandrSqrtdo not accept complex inputs. 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 forsqrt,rSqrt, andsignedSqrtfunctions.

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 theOutput signalto complex for all functions exceptsignedSqrt.

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`

依赖ency

When this parameter is set tosignedSqrt, theIntermediate results data typeparameter 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`——指定样本以外的价值`-1`
`-1`(default) | scalar | vector

Specify the sample time as a value other than -1. For more information, seeSpecify Sample Time.

依赖encies

This parameter is not visible unless it is explicitly set to a value other than-1. To learn more, seeBlocks 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 therSqrtfunction.

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.

TheExactmethod provides results that are consistent with MATLAB computations.

Note

The algorithms forsqrtandsignedSqrtare always ofExacttype, 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 therSqrtfunction and theNewton-Raphsonvalue forMethod.

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 theShow data type assistantbuttonto display theData Type Assistant, which helps you set the data type attributes. For more information, seeSpecify Data Types Using Data Type Assistant.

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

Specify the data type for intermediate results when you setFunctiontosqrtorrSqrton theMainpane.

可以inhe类型rited, specified directly, or expressed as a data type object such asSimulink.NumericType.

Note

To avoid overflow, the intermediate data type must be larger than or equal to a data type that can contain the square of the output data type.

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 isnotdouble.	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 setIntermediate results data typeto继承:Inherit from outputwhen:

You selectNewton-Raphsonto 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继承:Inherit from outputyields 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 aData Type Conversionblock in front of the Sqrt block to perform the conversion.

依赖encies

This parameter is disabled when theFunctionparameter is set tosignedSqrt.

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).''

Default:'Inherit: Inherit via internal rule'

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

指定输出数据类型。可以inhe类型rited, specified directly, or expressed as a data type object such asSimulink.NumericType.

依赖encies

When input is a floating-point data type smaller than single precision, the继承:Inherit via internal ruleoutput data type depends on the setting of theInherit floating-point output type smaller than single precisionconfiguration 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,halfandint16are smaller than single precision.

Programmatic Use

Block Parameter:OutDataTypeStr

Type: character vector

Default:'Inherit: Same as first input'

`Minimum`——最小输出值范围检查
`[]`(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, seeSimulink.BusElement.

Simulink uses the minimum to perform:

Parameter range checking (seeSpecify Minimum and Maximum Values for Block Parameters) for some blocks.
Simulation range checking (seeSpecify Signal RangesandEnable 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, seeOptimize using the specified minimum and maximum values(Embedded Coder).

Note

Output minimumdoes not saturate or clip the actual output signal. Use theSaturationblock 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, seeSimulink.BusElement.

Simulink uses the maximum value to perform:

Parameter range checking (seeSpecify Minimum and Maximum Values for Block Parameters) for some blocks.
Simulation range checking (seeSpecify Signal RangesandEnable 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, seeOptimize using the specified minimum and maximum values(Embedded Coder).

Note

Output maximumdoes not saturate or clip the actual output signal. Use theSaturationblock 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, seeRounding(Fixed-Point Designer).

Programmatic Use

Block Parameter:RndMeth

Type:character vector

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, seeUse 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, seeTroubleshoot 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 theint8(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, seeTroubleshoot Signal Range Errors.

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

The maximum value that theint8(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 asint8, which can produce an unintended result. For example, a block result of 130 (binary 1000 0010) expressed asint8, 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`\|`half`\|`integer`\|`single`
Direct Feedthrough	`yes`
多维信号	`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 theSqrtblock withFunctionset tosqrt, the code generator supports various architectures and data types.

Thesqrtfunctionarchitecture supports code generation for fixed-point types and floating-point types. When you use floating-point types, setFloating Point IP Library(HDL Coder)toNative Floating Point. You can specify theLatencyStrategyandCustomLatencyHDL properties to choose from a range of frequency values when targeting your design on the hardware platform.

Use theUseMultiplierHDL block property in combination with theLatencyStrategyandCustomLatencyproperties 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 theHandleDenormalsandLatencyStrategysettings from theNative Floating Pointtab 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. SeeGenerated Model and Validation Model(HDL Coder).

Architecture	Parameter	Additional cycles of latency	Description
`SqrtFunction`(default)	`UseMultiplier` `LatencyStrategy` `CustomLatency`	依赖s on parameter choices, output word length, and input and output fraction lengths.	To specify this architecture, setFunctionto`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 Improve design frequency and reduce resource utilization by setting theUseMultiplierto`off`andLatencyStrategyto`inherit`.
`SqrtNewton`	`Iterations`	`Iterations`+ 3	To specify this architecture, setFunctionto`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`超出了recommended range, HDL Coder generates a message.
`SqrtNewtonSingleRate`	`Iterations`	(`Iterations`* 4) + 6	To specify this architecture, setFunctionto`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`超出了recommended range, the coder generates a message.
`RecipSqrtNewton`	`Iterations`	`Iterations`+ 2	To specify this architecture, setFunctionto`rSqrt`. Use the iterative Newton method. Select this option to optimize area.
`RecipSqrtNewtonSingleRate`	`Iterations`	(`Iterations`* 4) + 5	To specify this architecture, setFunctionto`rSqrt`. Use the single rate pipelined Newton method. Select this option to optimize speed, or if you want a single rate implementation.

The Newton-Raphson iterative method:

$x_{i + 1} = x_{i} - \frac{f (x_{i})}{f' (x_{i})} = x_{i} (1.5 - 0.5 a x_{i}^{2})$

ReciprocalRsqrtBasedNewtonandReciprocalRsqrtBasedNewtonSingleRateimplement the Newton-Raphson method with:

$f (x) = \frac{1}{x^{2}} - 1$

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, seeConstrainedOutputPipeline(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, seeInputPipeline(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, seeOutputPipeline(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. Increase design frequency and reduce resource utilization by setting theUseMultiplierto`off`andLatencyStrategyto`inherit`.
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 alsoLatencyStrategy(HDL Coder). Increase design frequency and reduce resource utilization by setting theUseMultiplierto`off`andLatencyStrategyto`inherit`.
CustomLatency	WhenLatencyStrategyis 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 alsoNFPCustomLatency(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 alsoHandleDenormals(HDL Coder).

Restrictions

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

Sqrt

Description

Ports

Input

Port_1— Input signalscalar | vector | matrix

Output

Port_1— Output signalscalar | vector | matrix

Parameters

Main

Function— Function the block performssqrt(default) |signedSqrt|rSqrt

依赖ency

Programmatic Use

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

Programmatic Use

Sample time——指定样本以外的价值-1-1(default) | scalar | vector

依赖encies

Programmatic Use

Algorithm

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

Programmatic Use

Number of iterations— Number of iterations used for Newton Raphson algorithm3(default) | integer

Programmatic Use

Data Types

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

依赖encies

Programmatic Use

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

依赖encies

Programmatic Use

Minimum——最小输出值范围检查[](default) | scalar

Programmatic Use

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

Programmatic Use

Integer rounding mode— Rounding mode for fixed-point operationsFloor(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 typesoff(default) |on

Programmatic Use

Saturate on integer overflow— Choose the behavior when integer overflow occursoff(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 GenerationGenerate C and C++ code using Simulink® Coder™.

HDL Code GenerationGenerate Verilog and VHDL code for FPGA and ASIC designs using HDL Coder™.

PLC Code GenerationGenerate Structured Text code using Simulink® PLC Coder™.

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

See Also

Simulink Documentation

金宝app

Model-Based Design for Embedded Control Systems

`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`——指定样本以外的价值`-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

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

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

`Minimum`——最小输出值范围检查
`[]`(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™.