Math Function - Perform mathematical function - Simulink (original) (raw)

Perform mathematical function

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 list in 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
square Power 2 _u_2 u.^2 (see power)
pow Power With Signed power selected andOutput signal type set toreal, the expression issign(u)*|u v.With Signed power cleared orOutput signal type set tocomplex, the expression isuv.When Output signal type is set toauto, the expression depends on the complexity type that the software compiles.
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 (_u_2+_v_2)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. The functions 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 a vector, 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 a vector, 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 a vector, 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 method calculates the reciprocal by using the Newton-Raphson approximation method. The function uses recursive approximation to find better approximations to the roots of a real-value function.

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

Simulink® chooses an initial estimate in the range 0<x0<2a, because this is the domain of convergence for the function.

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

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

Ports

Input

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Input signal specified as a scalar, vector, or matrix. Supported modes accept real and complex inputs, except for reciprocal, which does not accept complex fixed-point inputs. See Description.

Dependencies

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

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

Input signal specified as a scalar, vector, or matrix. Supported modes accept real and complex inputs, except for reciprocal, which does not accept 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 you select, and the size of the inputs. For more information, see Data Type Support.

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

Output

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

reciprocal with Newton-Raphson Method

The reciprocal with Newton-Raphson method output 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)

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

Parameters

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Main

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

Dependency

Setting Function topow enables the Signed power parameter.

Programmatic Use

Block Parameter: Operator
Type: character vector
Values: 'exp' | 'log' '2^u' '10^u' 'log10' 'magnitude^2' 'square' 'pow' 'conj' 'reciprocal' 'hypot' 'rem' 'mod' 'transpose' 'hermitian'
Default: 'exp'

Algorithm method for reciprocal function, specified as Exact orNewton-Raphson. To calculate reciprocal with the Newton-Raphson approximation method, selectNewton-Raphson. Otherwise, selectExact.

Dependency

Setting Function toreciprocal enables this parameter.

Programmatic Use

Block Parameter: AlgorithmType
Type: character vector
Values: 'Exact' | 'Newton-Raphson'
Default: 'Exact'

When calculating power, specified as on or off, take into account sign of the input signal. Math Function uses this parameter only when the output signal is real.

Dependency

Setting Function topow enables this parameter.

Programmatic Use

| Block Parameter: SignedPower | | | -------------------------------- | | | Type: character vector | | | Values: 'on' | 'off' | | | Default: 'on' | |

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

Function Input Signal Type Output Signal Type
Auto Real Complex
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

Programmatic Use

Block Parameter: OutputSignalType
Type: character vector
Values: 'auto' | 'real' 'complex'
Default: 'auto'

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

Dependencies

To enable this parameter, set:

Programmatic Use

Block Parameter: Iterations
Type: character vector
Values: '3' | scalar
Default: '3'

Specify the time interval between samples. To inherit the sample time, set this parameter to -1. For more information, see Specify Sample Time.

Dependencies

This parameter is visible only if you set it to a value other than-1. To learn more, see Blocks for Which Sample Time Is Not Recommended.

Programmatic Use

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

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

Signal Attributes

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

The Data Type Assistant helps you set data attributes. To use the Data Type Assistant, click the Show data type assistant button. For more information, see Specify Data Types Using Data Type Assistant.

Dependencies

Programmatic Use

Block Parameter:OutDataTypeStr
Type: character vector
Values: 'Inherit: Inherit via internal rule | 'Inherit: Same as first input' 'Inherit: Inherit via back propagation' 'double' 'single' 'half' 'int8' 'uint8' 'int16' 'uint16' 'int32' 'uint32' 'int64' 'uint64' 'fixdt(1,16)' 'fixdt(1,16,0)' 'fixdt(1,16,2^0,0)' ''
Default: 'Inherit: Same as first input'

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

Dependencies

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

Programmatic Use

Block Parameter: LockScale
Type: character vector
Values: 'off' | 'on'
Default: 'off'

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

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

Dependencies

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

Programmatic Use

Block Parameter: RndMeth
Type: character vector
Values: 'Ceiling' | 'Convergent' 'Floor' 'Nearest' 'Round' 'Simplest' 'Zero'
Default: 'Floor'
Action Rationale Overflows Example
Select Saturate on integer overflow 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 Saturate on integer overflow 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 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 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. The code generation process can detect when overflow is not possible. In this case, the code generator does not produce saturation code.

Dependencies

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

Programmatic Use

Block Parameter:SaturateOnIntegerOverflow
Type: character vector
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

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

HDL Architecture

Function Architecture Description
conj ComplexConjugate Calculate complex conjugate.
hermitian Hermitian Calculate hermitian.
transpose Transpose Calculate array transpose. See Math Function in the Simulink documentation.
modrem ShiftAdd Perform modulus or remainder operation on a built-in integer types input by using a non-restoring division algorithm that performs multiple shift and add operations to compute the mod andrem operations.ShiftAdd is a pipelined implementation, and it can introduce additional latency in the generated code. Using this architecture, you can also set the latency strategy by setting the LatencyStrategy parameter.

Reciprocal Architecture

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

Architecture Parameters Additional Cycles of Latency Description
ShiftAdd(default) None Signed input: (Input word length + 4) Unsigned input: (Input word length + 4)For floating-point latency of the block, see Latency Values of Floating-Point Operators (HDL Coder). Perform reciprocal operation on a fixed-point or floating point input by using a non-restoring division algorithm that performs multiple shift and add operations to compute the reciprocal. This architecture provides improved accuracy compared to the Newton-Raphson approximation method.When you use fixed-point data types, following criteria must be satisfied for generating the HDL code: Input word length (WL) must be less than or equal to 63.[WL input + Abs(FL Sum)] must be less than or equal to 63. Where, FL Sum is given by,FL sum = FL input + FL output

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 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).

HDL code generation also supports the Newton-Raphson algorithm method forreciprocal function. Select the Algorithm method as Newton-Raphson to use these architectures for reciprocal function in the Math Function block.

Architecture Additional Cycles of Latency Description
ReciprocalNewton (default) Iterations + 1 Use the multirate implementation of the iterative Newton method. Select this option to optimize area for your design.The default value forIterations is 3.The recommended value forIterations is from 2 through 10. If Iterations value is outside the recommended range, HDL Coder displays a message.
ReciprocalNewtonSingleRate (Iterations * 2) + 1 Use the single rate pipelined Newton method. Select this option to optimize speed for your design, or if you want a single rate implementation.The default value for Iterations is 3.The recommended value forIterations is between 2 and 10. If Iterations value is outside the recommended range, HDL Coder displays a message.
ReciprocalRsqrtBasedNewtonSingleRate Signed input: (Iterations * 4) + 8Unsigned input: (Iterations * 4) + 6 Use the single rate pipelined Newton method. Select this option to optimize speed, or if you want a single rate implementation.The default value forIterations is 3.The recommended value forIterations is from 2 through 10. If Iterations is outside the recommended 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 is0. 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 is0. 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 is0. For more details, see OutputPipeline (HDL Coder).
LatencyStrategy To enable this property, set HDL architecture toShiftAdd. Specify whether to map the blocks in your design to MAX,Min, CUSTOM, orZERO latency for fixed-point types. The default is MAX. See alsoLatencyStrategy (HDL Coder).
CustomLatency To enable this property, set HDL architecture toShiftAdd. WhenLatencyStrategy is set toCUSTOM, use this property to specify a custom latency value between ZERO andMAX for fixed-point types. See alsoLatencyStrategy (HDL Coder).
Native Floating Point
CheckResetToZero Use this property for the mod and rem functions of the Math Function block. If you have numbersa and b such that the quotient a/b is close to an integer, this setting treats a as an integral multiple ofb, and rem(a,b) = 0. This result is numerically accurate and matches the simulation results. Calculating this result uses additional resources and increases the area footprint on the target FPGA device. For more information, 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 isinherit. See also HandleDenormals (HDL Coder).
LatencyStrategy Specify whether to map the blocks in your design to inherit,Max, Min, Zero, orCustom for the floating-point operator. The default isinherit. See also LatencyStrategy (HDL Coder).
NFPCustomLatency To specify a value, setLatencyStrategy to Custom. HDL Coder adds latency equal to the value that you specify for theNFPCustomLatency setting. See also NFPCustomLatency (HDL Coder).
MaxIterations Use this property for the mod and rem functions of the Math Function block. If you have numbersa and b that are significantly large integers, you can increaseMaxIterations to match the simulation results. Calculating this result uses additional resources and increases the area footprint on the target FPGA device. For more information, see MaxIterations (HDL Coder).
IterationsPerPipeline Use this property for the reciprocal function of theMath Function block. To enable this property, set Algorithm method parameter to Exact. When you setLatencyStrategy toCustom(PerIterations), use this setting to specify the number of iterations per pipeline stages. For more information, see Reciprocal (HDL Coder).

Supported Datatypes and Functions in Native Floating-Point

The Math Function block supports scalar, vector, or matrix data types. This block supports these functions with Native Floating-Point.

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

Restrictions

When you use a reciprocal implementation:

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

Version History

Introduced before R2006a

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