Perform mathematical function

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Libraries:
Simulink / Math Operations
HDL Coder / Math Operations

Description

The Math Function block performs many common mathematical functions.

You can select one of these functions from the Function parameter listin Math Function block.

Function	Description	Mathematical Expression	MATLAB^® Equivalent
`exp`	Exponential	`e^u`	exp
`log`	Natural logarithm	`ln u`	log
`2^u`	Power of base 2	`2^u`	`2.^u` (see power)
`10^u`	Power of base 10	`10^u`	`10.^u` (see power)
`log10`	Common (base 10) logarithm	`log u`	log10
`magnitude^2`	Complex modulus	`\|u\|²`	`real(u).^2 + imag(u).^2` (see real, imag, andpower)
`square`	Power 2	`u²`	`u.^2` (see power)
`pow`	Power	`sign(u)*\|u\|^v`(default, applied only for even-order roots) or`u^v`	power
`conj`	Complex conjugate	`ū`	conj
`reciprocal` with Exact method	Reciprocal	`1/u`	`1./u` (see rdivide)
`reciprocal` with Newton-Raphson method	Reciprocal	See Newton-Raphson Reciprocal Algorithm Method	None
`hypot`	Square root of sum squares	`(u²+v²)^0.5`	hypot
`rem`	Remainder after division	—	rem
`mod`	Modulus after division	—	mod
`transpose`	Transpose	`u^T`	`u.'` (see Array vs. Matrix Operations)
`hermitian`	Complex conjugate transpose	`u^H`	`u'` (see Array vs. Matrix Operations)

Tip

To perform square root calculations, use the Sqrt block.

The block output is the result of the operation of the function on the input or inputs. Thefunctions support these types of operations.

Function	Scalar Operations	Element-Wise Vector and Matrix Operations	Vector and Matrix Operations
`exp`	Yes	Yes	Not applicable
`log`	Yes	Yes	Not applicable
`2^u`	Yes	Yes	Not applicable
`10^u`	Yes	Yes	Not applicable
`log10`	Yes	Yes	Not applicable
`magnitude^2`	Yes	Yes	Not applicable
`square`	Yes	Yes	Not applicable
`pow`	Yes	Yes	Not applicable
`conj`	Yes	Yes	Not applicable
`reciprocal` with Exact method	Yes	Yes	Not applicable
`reciprocal` with Newton-Raphson method	Yes	Yes	Not applicable
`hypot`	Yes, on two inputs	Yes, on two inputs (two vectors or two matrices of the same size, a scalar and avector, or a scalar and a matrix)	—
`rem`	Yes, on two inputs	Yes, on two inputs (two vectors or two matrices of the same size, a scalar and avector, or a scalar and a matrix)	Not applicable
`mod`	Yes, on two inputs	Yes, on two inputs (two vectors or two matrices of the same size, a scalar and avector, or a scalar and a matrix)	Not applicable
`transpose`	Yes	—	Yes
`hermitian`	Yes	—	Yes

The name of the function and the appropriate number of input ports appear on the block.

Tip

Use the Math Function block when you want vector or matrix output.

Newton-Raphson Reciprocal Algorithm Method

The reciprocal function that has the Newton-Raphson algorithm methodcalculates the reciprocal by using the Newton-Raphson approximation method. Thefunction uses recursive approximation to find better approximations to the roots ofa real-value function.

The reciprocal of a real number $a$ is defined as a zero of the function:

$f (x) = \frac{1}{x} - a .$

Simulink^® chooses an initial estimate in the range $0 < x_{0} < \frac{2}{a}$ , because this is the domain of convergence for thefunction.

To successively calculate the roots of the function, specify the Number ofiterations parameter. The process is repeated as follows:

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

$f' (x)$ is the derivative of the function $f (x)$ .

Data Type Support

This table lists the input data types that each function of the block can support.

Function	Single	Double	Half*	Boolean	Built-In Integer	Fixed Point
`exp`	Yes	Yes	Yes	—	—	—
`log`	Yes	Yes	Yes	—	—	—
`2^u`	Yes	Yes	Yes	—	—	—
`10^u`	Yes	Yes	Yes	—	—	—
`log10`	Yes	Yes	Yes	—	—	—
`magnitude^2`	Yes	Yes	Yes	—	Yes	Yes
`square`	Yes	Yes	Yes	—	Yes	Yes
`pow`	Yes	Yes	Yes	—	—	—
`conj`	Yes	Yes	Yes	—	Yes	Yes
`reciprocal` with Exact method	Yes	Yes	Yes	—	Yes	Yes
`reciprocal` with Newton-Raphson method (for more information,see Output)	Yes	Yes	—	—	Yes	Yes
`hypot`	Yes	Yes	Yes	—	—	—
`rem`	Yes	Yes	Yes	—	Yes	—
`mod`	Yes	Yes	Yes	—	Yes	—
`transpose`	Yes	Yes	Yes	Yes	Yes	Yes
`hermitian`	Yes	Yes	Yes	—	Yes	Yes

For more information on half-precision arithmetic operations, see The Half-Precision Data Type in Simulink (Fixed-Point Designer).

Examples

Bounded Variable-Size Signal Basic OperationsGenerate bounded variable-size signals and illustrates some of the operations using those signals. In this example, you generate variable-size signals using the Selector block and the Switch block. The signals are used in math operations, bus creation, bus selection matrix concatenation, and to implement a discrete filter equation.

Open Model

Ports

Input

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Port_1 — Input signal
scalar | vector | matrix

Input signal specified as a scalar, vector, or matrix. Supported modes accept real andcomplex inputs, except for reciprocal, which does notaccept complex fixed-point inputs. See Description.

Dependencies

Data type support for this block depends on the Function that youselect and the size of the inputs. For more information, see Data Type Support.

Port_2 — Input signal
scalar | vector | matrix

Input signal specified as a scalar, vector, or matrix. Supported modes accept real andcomplex inputs, except for reciprocal, which does notaccept complex fixed-point inputs.

Dependencies

To enable this port, set Function tohypot,rem, ormod.

Data type support for this block depends on the Function that youselect, and the size of the inputs. For more information, see Data Type Support.

Output

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Port_1 — Result of the operation of the function on the input orinputs
scalar | vector | matrix

Output signal specified as a scalar, vector, or matrix. The dimensions of the blockoutput depend on the Function that you select andthe size of the inputs. The block output is real or complex, dependingon what you select for Output signal type. SeeDescription.

`reciprocal` with Newton-Raphson Method

The reciprocal with Newton-Raphson methodoutput data type depends on the input data type:

Input Data Type	Output Data Type
single	single
double	double
built-in integer	built-in integer
built-in fixed-point	built-in fixed-point
`fi`(value, 0,word_length,fraction_length)	`fi`(value, 0,word_length,word_length–fraction_length–1)
`fi`(value, 1,word_length,fraction_length)	`fi`(value, 1,word_length,word_length–fraction_length–2)

Parameters

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Main

Function — Math function
`exp` (default) | `log` | `2^u` | `10^u` | `log10` | `magnitude^2` | `square` | `pow` | `conj` | `reciprocal` | `hypot` | `rem` | `mod` | `transpose` | `hermitian`

Specify the mathematical function. For more information about the options for thisparameter, see Description.

Dependency

Setting Function topow enables the Signedpower parameter.

Programmatic Use

Block Parameter:Operator

Type: charactervector

Values:

'exp' | 'log' | '2^u' | '10^u' | 'log10' |'magnitude^2' | 'square' | 'pow' | 'conj' | 'reciprocal' |'hypot' | 'rem' | 'mod' | 'transpose' |'hermitian'

Default:'exp'

Algorithm method — Algorithm method for `reciprocal` function
`Exact` (default) | `Newton-Raphson`

Algorithm method for reciprocal function, specifiedas Exact orNewton-Raphson. To calculate reciprocalwith the Newton-Raphson approximation method, selectNewton-Raphson. Otherwise, selectExact.

Dependency

Setting Function toreciprocal enables this parameter.

Programmatic Use

Block Parameter:AlgorithmType

Type: charactervector

Values:'Exact' | 'Newton-Raphson'

Default:'Exact'

Signed power — Power signedness
on (default) | off

When calculating power, specified as on or off, take into account sign of the inputsignal.. This parameter applies only for even-order roots, such asu^1/2,u^1/4, and soforth.

on — Calculate power of the absolute value of the input,multiplied by the sign of the input.
off — Calculate power of the actual input value. If the firstinput is negative and the second input is an even-order root,returns nan.

Dependency

Setting Function topow enables this parameter.

Programmatic Use

Block Parameter:SignedPower

Type: charactervector

Values:'on' | 'off' |

Default:'on'

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

Specify the output signal type of the Math Function block asauto, real, orcomplex.

Function Input SignalType Output Signal Type

Auto Real Complex

Function	Input SignalType	Output Signal Type
`exp`, `log`, `2^u`,`10^u`, `log10`,`square`, `pow`,`reciprocal`,`conjugate`,`transpose`,`hermitian`	`real` `complex`	`real` `complex`	`real` `error`	`complex` `complex`
`magnitude squared`	`real` `complex`	`real` `real`	`real` `real`	`complex` `complex`
`hypot`, `rem`,`mod`	`real` `complex`	`real` `error`	`real` `error`	`complex` `error`

exp, log, 2^u,10^u, log10,square, pow,reciprocal,conjugate,transpose,hermitian

real

complex

real

complex

real

error

complex

magnitude squared

real

complex

real

complex

hypot, rem,mod

real

complex

real

error

real

error

complex

error

Programmatic Use

Block Parameter:OutputSignalType

Type: charactervector

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

Default:'auto'

Number of iterations — Number of Newton-Raphson iterations
3 (default) | scalar

Number of Newton-Raphson iterations, specified as a scalar.

Dependencies

To enable this parameter, set:

Function toreciprocal.
Algorithm method toNewton-Raphson.

Programmatic Use

Block Parameter:Iterations

Type: charactervector

Values:'3' | scalar

Default:'3'

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"

Signal Attributes

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

Lower value of the output range that Simulink checks.

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: '[ ]'

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

Upper value of the output range that Simulink checks.

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: '[ ]'

Output data type — Specify the output data type
`Inherit: Same as firstinput` (default) | `Inherit: Inherit via internal rule` | `Inherit: Inherit via back propagation` | `double` | `single` | `half` | `int8` | `uint8` | `int16` | `uint16` | `int32` | `uint32` | `int64` | `uint64` | `fixdt(1,16)` | `fixdt(1,16,0)` | `fixdt(1,16,2^0,0)` | `<data type expression>`

Specify the output data type. You can set it to:

A rule that inherits a data type, for example,Inherit: Inherit via backpropagation
The name of a built-in data type, for example,single
The name of a data type object, for example, aSimulink.NumericType object
An expression that evaluates to a data type, for example,fixdt(1,16,0)

The Data Type Assistant helps you set dataattributes. To use the Data Type Assistant, click . For more information, see Specify Data Types Using Data Type Assistant.

Dependencies

To enable this parameter, set theFunction tomagnitude^2,square, orreciprocal.
For the magnitude^2 andsquare, when input is afloating-point data type smaller than single precision, theInherit: Inherit via internalrule output data type depends on thesetting of the Inherit floating-point output type smaller than single precision configuration parameter. Data types are smaller thansingle-precision when the number of bits needed to encodethe data type is less than the 32 bits needed to encode thesingle precision data type. For example,half and int16 aresmaller than single precision.

Programmatic Use

Block Parameter:OutDataTypeStr

Type: charactervector

Default: 'Inherit:Same as first input'

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

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

Dependencies

To enable this parameter, set the Function tomagnitude^2,square, orreciprocal.

Programmatic Use

Block Parameter:LockScale

Type: charactervector

Values:'off' | 'on'

Default:'off'

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

Rounding mode for fixed-point operations. For more information, seeRounding (Fixed-Point Designer).

Block parameters always round to the nearest representable value. Tocontrol the rounding of a block parameter, enter an expression using aMATLAB rounding function into the mask field.

Dependencies

To enable this parameter, set the Function tomagnitude^2,square, orreciprocal.

Programmatic Use

Block Parameter:RndMeth

Type: charactervector

Default:'Floor'

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

Action Rationale Overflows Example

Action	Rationale	Overflows	Example
Select Saturate on integer overflow checkbox.	Your model has possible overflow and you want explicit saturation protectionin the generated code.	Overflows saturate to either the minimum ormaximum value that the data type canrepresent.	The maximum value that the`int8` (signed, 8-bit integer)data type can represent is 127. Any blockoperation result greater than this maximum valuecauses overflow of the 8-bit integer. With thecheck box selected, the block output saturates at127. Similarly, the block output saturates at aminimum output value of -128.
Do not select Saturate on integer overflowcheck box.	You want to optimize efficiency of yourgenerated code. You want to avoidoverspecifying how a block handles out-of-rangesignals. For more information, see Troubleshoot Signal Range Errors.	Overflows wrap to the appropriate valuethat is representable by the datatype.	The maximum value that the`int8` (signed, 8-bit integer)data type can represent is 127. Any blockoperation result greater than this maximum valuecauses overflow of the 8-bit integer. With thecheck box cleared, the software interprets theoverflow-causing value as `int8`,which can produce an unintended result. Forexample, a block result of 130 (binary 1000 0010)expressed as `int8`, is-126.

Select Saturate on integer overflow checkbox.

Your model has possible overflow and you want explicit saturation protectionin the generated code.

Overflows saturate to either the minimum ormaximum value that the data type canrepresent.

The maximum value that theint8 (signed, 8-bit integer)data type can represent is 127. Any blockoperation result greater than this maximum valuecauses overflow of the 8-bit integer. With thecheck box selected, the block output saturates at127. Similarly, the block output saturates at aminimum output value of -128.

Do not select Saturate on integer overflowcheck box.

You want to optimize efficiency of yourgenerated code.

You want to avoidoverspecifying how a block handles out-of-rangesignals. For more information, see Troubleshoot Signal Range Errors.

Overflows wrap to the appropriate valuethat is representable by the datatype.

The maximum value that theint8 (signed, 8-bit integer)data type can represent is 127. Any blockoperation result greater than this maximum valuecauses overflow of the 8-bit integer. With thecheck box cleared, the software interprets theoverflow-causing value as int8,which can produce an unintended result. Forexample, 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 theblock, not just the output or result. The code generation process candetect when overflow is not possible. In this case, the code generatordoes not produce saturation code.

Dependencies

To enable this parameter, set the Function tomagnitude^2,square,conj,reciprocal, orhermitian.

Programmatic Use

Block Parameter:SaturateOnIntegerOverflow

Type: charactervector

Value:'off' | 'on'

Default:'on'

Block Characteristics

Data Types	`Boolean` \| `double` \| `fixed point` \| `half` \| `integer` \| `single`
Direct Feedthrough	`yes`
Multidimensional Signals	`yes`
Variable-Size Signals	`yes`
Zero-Crossing Detection	`no`

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

HDL Code Generation
Generate VHDL, Verilog and SystemVerilog code for FPGA and ASIC designs using HDL Coder™.

HDL Coder™ provides additional configuration options that affect HDLimplementation and synthesized logic.

HDL Architecture

Function	Architecture	Description
`conj`	`ComplexConjugate`	Calculate complex conjugate.
`hermitian`	`Hermitian`	Calculate hermitian.
`transpose`	`Transpose`	Calculate array transpose. See Math Functionin the Simulink documentation.
`mod` `rem`	`ShiftAdd`	Perform modulus or remainder operation on a built-ininteger types input by using a non-restoring divisionalgorithm that performs multiple shift and add operations tocompute the `mod` and`rem`operations. `ShiftAdd`is a pipelined implementation, and it can introduceadditional latency in the generated code. Using thisarchitecture, you can also set the latency strategy bysetting the LatencyStrategyparameter.

Reciprocal Architecture

You can generate HDL code for single-precision floating-point data types in nativefloating-point mode by using Math architecture forreciprocal function. Thereciprocal function in the Math Functionblock also supports the architectures listed in the table.

When you set the Algorithm method toExact, you can select this options in HDL Blockproperties of this block.

Architecture Parameters Additional Cycles of Latency Description

Architecture	Parameters	Additional Cycles of Latency	Description
`ShiftAdd`	None	Signed input: (Input word length + 4) Unsigned input: (Input wordlength + 4)	Perform reciprocal operation on a fixed-point input by using a non-restoringdivision algorithm that performs multiple shift and addoperations to compute the reciprocal. This architectureprovides improved accuracy compared to the Newton-Raphsonapproximation method. When you use fixed-pointdata types, following criteria must be satisfied forgenerating the HDL code: Input word length (`WL`) must beless than or equal to 63. `[WL input + Abs(FL Sum)]` mustbe less than or equal to 63. Where, `FLSum` is given by, `FL sum = FL input + FLoutput`

ShiftAdd

None

Signed input: (Input word length + 4)

Unsigned input: (Input wordlength + 4)

Perform reciprocal operation on a fixed-point input by using a non-restoringdivision algorithm that performs multiple shift and addoperations to compute the reciprocal. This architectureprovides improved accuracy compared to the Newton-Raphsonapproximation method.

When you use fixed-pointdata types, following criteria must be satisfied forgenerating the HDL code:

Input word length (WL) must beless than or equal to 63.
[WL input + Abs(FL Sum)] mustbe less than or equal to 63. Where, FLSum is given by,
FL sum = FL input + FLoutput

You can apply sharing optimization for Math Function Reciprocal block inShiftAdd architecture. For more information, seeResource Sharing (HDL Coder).

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

HDL code generation also supports the Newton-Raphson algorithm method forreciprocal function. Select the Algorithmmethod as Newton-Raphson to use thesearchitectures for reciprocal function in the MathFunction block.

Architecture Additional Cycles of Latency Description

Architecture	Additional Cycles of Latency	Description
`ReciprocalNewton`(default)	`Iterations` + 1	Use the multirate implementation of the iterativeNewton method. Select this option to optimize area foryour design. The default value for`Iterations` is3. The recommended value for`Iterations` is from 2 through10. If `Iterations` value is outsidethe recommended range, HDL Coder displays a message.
`ReciprocalNewtonSingleRate`	(`Iterations` * 2) + 1	Use the single rate pipelined Newton method. Selectthis option to optimize speed for your design, or if youwant a single rate implementation. Thedefault value for `Iterations` is3. The recommended value for`Iterations` is between 2 and 10.If `Iterations` value is outside therecommended range, HDL Coder displays a message.
ReciprocalRsqrtBasedNewtonSingleRate	Signed input: (`Iterations` * 4)+ 8 Unsigned input:(`Iterations` * 4) +6	Use the single rate pipelined Newton method. Selectthis option to optimize speed, or if you want a singlerate implementation. The default value for`Iterations` is3. The recommended value for`Iterations` is from 2 through10. If `Iterations` is outside therecommended range, the coder generates a message.

ReciprocalNewton(default)

Iterations + 1

Use the multirate implementation of the iterativeNewton method. Select this option to optimize area foryour design.

The default value forIterations is3.

The recommended value forIterations is from 2 through10. If Iterations value is outsidethe recommended range, HDL Coder displays a message.

ReciprocalNewtonSingleRate

(Iterations * 2) + 1

Use the single rate pipelined Newton method. Selectthis option to optimize speed for your design, or if youwant a single rate implementation.

Thedefault value for Iterations is3.

The recommended value forIterations is between 2 and 10.If Iterations value is outside therecommended range, HDL Coder displays a message.

ReciprocalRsqrtBasedNewtonSingleRate

Signed input: (Iterations * 4)+ 8

Unsigned input:(Iterations * 4) +6

Use the single rate pipelined Newton method. Selectthis option to optimize speed, or if you want a singlerate implementation.

The default value forIterations is3.

The recommended value forIterations is from 2 through10. If Iterations is outside therecommended range, the coder generates a message.

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 tomap the blocks in your design to `MAX`,`Min`, `CUSTOM`, or`ZERO` latency for fixed-point types.The default is `MAX`. See alsoLatencyStrategy (HDL Coder).
CustomLatency	To enable this property, set HDL architecture to`ShiftAdd`. WhenLatencyStrategy is set to`CUSTOM`, use this property to specifya custom latency value between `ZERO` and`MAX` for fixed-point types. See alsoLatencyStrategy (HDL Coder).

Native Floating Point
CheckResetToZero	Use this property for the `mod` and `rem` functionsof the Math Function block. If you have numbers`a` and `b` such that thequotient `a/b` is close to an integer, thissetting treats `a` as an integral multiple of`b`, and `rem(a,b)` = 0.This result is numerically accurate and matches the simulationresults. Calculating this result uses additional resources andincreases the area footprint on the target FPGA device. For moreinformation, see CheckResetToZero (HDL Coder).
HandleDenormals	Specify whether you want HDL Coder to insert additional logic to handle denormal numbers in your design. Denormal numbers are numbers that have magnitudes less than the smallest floating-point number that can be represented without leading zeros in the mantissa. The default is `inherit`. See also HandleDenormals (HDL Coder).
LatencyStrategy	Specify whether to map the blocks in your design to `inherit`, `Max`, `Min`, `Zero`, or `Custom` for the floating-point operator. The default is `inherit`. See also LatencyStrategy (HDL Coder).
NFPCustomLatency	To specify a value, set LatencyStrategy to `Custom`. HDL Coder adds latency equal to the value that you specify for the NFPCustomLatency setting. See also NFPCustomLatency (HDL Coder).
MaxIterations	Use this property for the `mod` and `rem` functionsof the Math Function block. If you have numbers`a` and `b` that aresignificantly large integers, you can increaseMaxIterations to match the simulationresults. Calculating this result uses additional resources andincreases the area footprint on the target FPGA device. For moreinformation, see MaxIterations (HDL Coder).

Supported Datatypes and Functions in Native Floating-Point

In the Math Function block, these functions are the supported functions with NativeFloating-Point.

Math Functions	Supported Floating-Point Datatypes			Complex Data Support
Math Functions	Half	Single	Double	Complex Data Support
`exp`	No	Yes	No	No
`log`	No	Yes	Yes	No
`2^u`	No	Yes	No	No
`10^u`	No	Yes	No	No
`log10`	No	Yes	No	No
`magnitude^2`	No	Yes	Yes	Yes
`square`	No	Yes	No	Yes
`pow`	No	Yes	No	No
`conj`	No	Yes	No	Yes
`reciprocal`	Yes	Yes	Yes	No
`hypot`	No	Yes	No	No
`rem`	No	Yes	No	No
`mod`	No	Yes	No	No
`transpose`	Yes	Yes	Yes	Yes
`hermitian`	No	Yes	No	Yes

Restrictions

When you use a reciprocal implementation:

Input must be scalar and must have integer or fixed-point (signed orunsigned) data type.
The output must be scalar and have integer or fixed-point (signed orunsigned) data type.
Only the Zero rounding mode issupported.
The Saturate on integer overflow option on theblock must be selected.

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

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

The Math Function block only supports fixed-point conversion in certainconfigurations. For more information, see the Block Support Table.

Version History

Introduced before R2006a

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R2023a: `Math Function` Block Supports 2^u

The Math Function block now supports the2^u function. The MATLAB equivalent is 2.^u (see power).

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Perform mathematical function - Simulink (2024)

Description

Newton-Raphson Reciprocal Algorithm Method

Data Type Support

Examples

Ports

Input

Port_1 — Input signalscalar | vector | matrix

Dependencies

Port_2 — Input signal scalar | vector | matrix

Dependencies

Output

Port_1 — Result of the operation of the function on the input orinputsscalar | vector | matrix

reciprocal with Newton-Raphson Method

Parameters

Main

Function — Math functionexp (default) | log | 2^u | 10^u | log10 | magnitude^2 | square | pow | conj | reciprocal | hypot | rem | mod | transpose | hermitian

Dependency

Programmatic Use

Algorithm method — Algorithm method for reciprocal function Exact (default) | Newton-Raphson

Dependency

Programmatic Use

Signed power — Power signedness on (default) | off

Dependency

Programmatic Use

Output signal type — Complexity of output signal auto (default) | real | complex

Programmatic Use

Number of iterations — Number of Newton-Raphson iterations 3 (default) | scalar

Dependencies

Programmatic Use

Sample time (-1 for inherited) — Interval between samples -1 (default) | scalar | vector

Dependencies

Programmatic Use

Signal Attributes

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

Programmatic Use

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

Programmatic Use

Dependencies

Programmatic Use

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

Dependencies

Programmatic Use

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

Dependencies

Programmatic Use

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

Dependencies

Programmatic Use

Block Characteristics

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using Simulink® Coder™.

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

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

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

Version History

R2023a: Math Function Block Supports 2^u

See Also

Topics

MATLAB Command

Americas

Europe

Asia Pacific

Port_1 — Input signal
scalar | vector | matrix

Port_2 — Input signal
scalar | vector | matrix

Port_1 — Result of the operation of the function on the input orinputs
scalar | vector | matrix

`reciprocal` with Newton-Raphson Method

Function — Math function
`exp` (default) | `log` | `2^u` | `10^u` | `log10` | `magnitude^2` | `square` | `pow` | `conj` | `reciprocal` | `hypot` | `rem` | `mod` | `transpose` | `hermitian`

Algorithm method — Algorithm method for `reciprocal` function
`Exact` (default) | `Newton-Raphson`

Signed power — Power signedness
on (default) | off

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

Number of iterations — Number of Newton-Raphson iterations
3 (default) | scalar

Sample time (-1 for inherited) — Interval between samples
`-1` (default) | scalar | vector

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

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

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

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

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

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™.

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

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

R2023a: `Math Function` Block Supports 2^u