Sqrt
Calculate square root, signed square root, or reciprocal of square root
Libraries:
Simulink /
Math Operations
HDL Coder /
HDL Floating Point Operations
HDL Coder /
Math Operations
Description
The Sqrt block calculates the square root, signed square root, or reciprocal of square root on the input signal. Select one of the following functions from the Function parameter list.
Function  Description  Mathematical Expression  MATLAB^{®} Equivalent 

sqrt
 Square root of the input 

sqrt

signedSqrt
 Square root of the absolute value of the input, multiplied by the sign of the input 
 — 
rSqrt
 Reciprocal of the square root of the input 
 — 
The block icon changes to match the function.
Examples
Square Root of Negative Values
This example shows how to compute the square root of a negativevalued input signal as complexvalued output.
By setting the Function to sqrt
and Output signal type to complex
, the block produces the correct result of 0 + 10i
for an input of 100
. If you change the Output signal type to auto
or real
, the block outputs NaN
.
Signed Square Root of Negative Values
This example shows how to compute the signed square root of a negativevalued input signal.
When the block input is negative and you set the Function to signedSqrt
, the Sqrt block output is the same for any setting of the Output signal type parameter. By setting the Numerica display format of the first Display block to decimal (Stored Integer)
, you can see the value of the imaginary part for the complex output.
rSqrt of FloatingPoint Inputs
This example shows how to compute the rSqrt of a floatingpoint input signal. The Sqrt block has the following settings:
Method =
NewtonRaphson
Number of iterations =
1
Intermediate results data type =
Inherit: Inherit from input
After one iteration of the NewtonRaphson algorithm, the block output is within 0.0004 of the final value (0.4834).
rSqrt of FixedPoint Inputs
This example shows how to compute the rSqrt of a fixedpoint input signal. The Sqrt block has the following settings:
Method =
NewtonRaphson
Number of iterations =
1
Intermediate results data type =
Inherit: Inherit from input
After one iteration of the NewtonRaphson algorithm, the block output is within 0.0459 of the final value (0.4834).
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 fixedpoint signals.
signedSqrt
and rSqrt
do 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 fixedpoint data types for
sqrt
, rSqrt
, and
signedSqrt
functions.
Function  Data Type  Complex  Negative Values  

Input  Output  
sqrt  Floating point  Yes  Yes  Yes 
Integer and fixedpoint  No  No  No  
 Floating point  No  No  Yes 
Integer and fixedpoint  No  No  No  
signedSqrt  Floating point  No  Yes  Yes 
Integer and fixedpoint  No  No  No 
If the input is negative, set the Output signal to complex for all
functions except signedSqrt
.
Data Types: single
 double
 half
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
 fixed point
Output
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 fixedpoint type, the output must be floating point.
Data Types: single
 double
 half
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
 fixed point
Parameters
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  

Auto  Real  Complex  








 








 









Programmatic Use
Block Parameter:
OutputSignalType 
Type: character vector 
Values:
'auto'  'real' 
'complex' 
Default:
'auto' 
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
Block Parameter:
SampleTime 
Type: string scalar or character vector 
Default:
"1" 
Algorithm
Method — Method to compute reciprocal of square root
Exact
(default)  NewtonRaphson
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. 
NewtonRaphson
 Floatingpoint, fixedpoint, and builtin 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' 
'NewtonRaphson' 
Default:
'Exact' 
Number of iterations — Number of iterations used for Newton Raphson algorithm
3
(default)  integer
Specify the number of iterations to perform the NewtonRaphson
algorithm. This parameter is valid with the rSqrt
function and the NewtonRaphson
value for
Method.
Note
If you enter 0, the block output is the initial guess of the NewtonRaphson algorithm.
Programmatic Use
Block Parameter:
Iterations 
Type: character vector 
Values: integer 
Default:
'3' 
Data Types
The Data Type Assistant helps you set data attributes. To use the Data Type Assistant, click . 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
.
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 nonsingle 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
NewtonRaphson
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 floatingpoint to fixedpoint data type. For example, insert a Data Type Conversion block in front of the Sqrt block to perform the conversion.
Dependencies
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
 half
 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
.
Dependencies
When input is a floatingpoint data type smaller than single
precision, the Inherit: Inherit via internal
rule
output data type depends on the setting of
the Inherit floatingpoint 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 singleprecision 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: Inherit via back
propagation'  'Inherit: Same as first
input'  'double' 
'single'  'half' 
'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 fixedpoint 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 fixedpoint 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 fixedpoint operations
Floor
(default)  Ceiling
 Convergent
 Nearest
 Round
 Simplest
 Zero
Specify the rounding mode for fixedpoint operations. For more information, see Rounding (FixedPoint 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 fixedpoint tools — Prevent fixedpoint tools from overriding data types
off
(default)  on
Select to lock the output data type setting of this block against changes by the FixedPoint Tool and the FixedPoint Advisor. For more information, see Use Lock Output Data Type Setting (FixedPoint Designer).
Programmatic Use
Block Parameter:
LockScale 
Type: character vector 
Values:
'off' 
'on' 
Default:
'off' 
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 

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 
Do not select this check box. 
You want to optimize efficiency of your generated code. You want to avoid overspecifying how a block handles outofrange 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 
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' 
Block Characteristics
Data Types 

Direct Feedthrough 

Multidimensional Signals 

VariableSize Signals 

ZeroCrossing Detection 

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.
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
fixedpoint types and floatingpoint types. When you use floatingpoint types,
set the floating point IP library parameters 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
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  FixedPoint  Native FloatingPoint  HandleDenormals  LatencyStrategy 

sqrtfunction  ✓  ✓  ✓  ✓ 
sqrtnewton  ✓  —  —  — 
sqrtnewtonsinglerate  ✓  —  —  — 
recipsqrtnewton  ✓  —  —  — 
recipsqrtnewtonsinglerate  ✓  —  —  — 
This block has multicycle 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) 
 Depends on parameter choices, output word length, and input and output fraction lengths.  To specify this architecture, set Function to
Compute the square root by using a pipelined shift/addition algorithm or multiplicationbased algorithm. The
To see the latency calculation, see HDLMathLib Sqrt (HDL Coder). Improve design frequency and
reduce resource utilization by setting the
UseMultiplier to

SqrtNewton  Iterations  Iterations + 3  To specify this architecture, set Function to
Use the iterative Newton method. Select this option to optimize area. The default value for
The
recommended value for 
SqrtNewtonSingleRate  Iterations  (Iterations * 4) + 6  To specify this architecture, set Function to
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
The
recommended value for 
RecipSqrtNewton  Iterations  Iterations + 2  To specify this architecture, set Function to
Use the iterative Newton method. Select this option to optimize area. 
RecipSqrtNewtonSingleRate  Iterations  (Iterations * 4) + 5  To specify this architecture, set Function to
Use the single rate pipelined Newton method. Select this option to optimize speed, or if you want a single rate implementation. 
The NewtonRaphson iterative method:
$${x}_{i+1}={x}_{i}\frac{f({x}_{i})}{f\text{'}({x}_{i})}={x}_{i}(1.50.5a{x}_{i}{}^{2})$$
ReciprocalRsqrtBasedNewton
and
ReciprocalRsqrtBasedNewtonSingleRate
implement
the NewtonRaphson method with:
$$f(x)=\frac{1}{{x}^{2}}1$$
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

Iterations  Number of iterations for

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

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

UseMultiplier  Select algorithm for Increase design frequency and
reduce resource utilization by setting the
UseMultiplier to

LatencyStrategy  Specify whether to map the blocks in your design to Increase design frequency and reduce
resource utilization by setting the
UseMultiplier to

CustomLatency  When LatencyStrategy is set to 
Native Floating Point  

HandleDenormals  Specify whether you want HDL Coder to insert additional logic to handle denormal numbers in your design.
Denormal numbers are numbers that have magnitudes less than the smallest floatingpoint
number that can be represented without leading zeros in the mantissa. The default is

Input must be an unsigned scalar value.
Output is a fixedpoint scalar value.
PLC Code Generation
Generate Structured Text code using Simulink® PLC Coder™.
FixedPoint Conversion
Design and simulate fixedpoint systems using FixedPoint Designer™.
Version History
Introduced in R2010a
See Also
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