Math Function

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	eu	exp
log	Natural logarithm	ln u	log
2^u	Power of base 2	2u	2.^u (see power)
10^u	Power of base 10	10u	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, and power)
square	Power 2	u2	u.^2 (see power)
pow	Power	sign(u)*|u|v (default, applied only for even-order roots) or uv	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	uT	u.' (see Array vs. Matrix Operations)
hermitian	Complex conjugate transpose	uH	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:

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

Simulink^® chooses an initial estimate in the range $$0<x_0<\frac{2}{a}$$, because this is the domain of convergence for the function.

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

$$x_{i+1}=x_i-\frac{f\left(x_i\right)}{f\text{'}\left(x_i\right)}=x_i+(x_i-a{x}_i{}^2)=x_i.(2-a{x}_i)$$

$$f\text{'}(x)$$ 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

Variable-Size Signal Basic Operations

How variable-size signals can be generated. It also illustrates some of the operations that can be applied to them. The purpose of this example is to introduce the basic operations associated with variable-size signals.

Open Model

Ports

Input

Port_1 — Input signal

scalar | vector | matrix

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

Port_2 — Input signal

scalar | vector | matrix

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 to hypot, rem, or mod.

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

Port_1 — Result of the operation of the function on the input or inputs

scalar | vector | matrix

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. See Description.

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

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 this parameter, see Description.

Dependency

Setting Function to pow 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 — Algorithm method for reciprocal function

Exact (default) | Newton-Raphson

Algorithm method for reciprocal function, specified as Exact or Newton-Raphson. To calculate reciprocal with the Newton-Raphson approximation method, select Newton-Raphson. Otherwise, select Exact.

Dependency

Setting Function to reciprocal enables this parameter.

Programmatic Use

Block Parameter: AlgorithmType

Type: character vector

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 input signal.. This parameter applies only for even-order roots, such as u^1/2, u^1/4, and so forth.

• 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 first input is negative and the second input is an even-order root, returns nan.

Dependency

Setting Function to pow enables this parameter.

Programmatic Use

Block Parameter: SignedPower

Type: character vector

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 as auto, real, or complex.

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 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 to reciprocal.

• Algorithm method to Newton-Raphson.

Programmatic Use

Block Parameter: Iterations

Type: character vector

Values: '3' | scalar

Default: '3'

Sample time — Sample time value other than -1

-1 (default) | scalar | vector

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

Dependencies

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

Programmatic Use

Block Parameter: SampleTime

Type: 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 first input (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 back propagation

• The name of a built-in data type, for example, single

• The name of a data type object, for example, a Simulink.NumericType object

• An expression that evaluates to a data type, for example, fixdt(1,16,0)

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

Dependencies

• To enable this parameter, set the Function to magnitude^2, square, or reciprocal.

• For the magnitude^2 and square, when input is a floating-point data type smaller than single precision, the Inherit: Inherit via internal rule output data type depends on the setting of the Inherit floating-point 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 single precision 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: 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)' | '<data type expression>'

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 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 to magnitude^2, square, or reciprocal.

Programmatic Use

Block Parameter: LockScale

Type: character vector

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, see Rounding (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 to magnitude^2, square, or reciprocal.

Programmatic Use

Block Parameter: RndMeth

Type: character vector

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

Default: 'Floor'

Saturate on integer overflow — Choose the behavior when integer overflow occurs

on (default) | boolean

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 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 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 the int8 (signed, 8-bit integer) data type can represent is 127. Any block operation result greater than this maximum value causes overflow of the 8-bit integer. With the check box cleared, the software interprets the overflow-causing value as int8, which can produce an unintended result. For example, a block result of 130 (binary 1000 0010) expressed as int8, is -126.

When you select this check box, saturation applies to every internal operation on the block, not just the output or result. 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 to magnitude^2, square, conj, reciprocal, or hermitian.

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

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.

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.

Reciprocal Architecture

You can generate HDL code for single-precision floating-point data types in native floating-point mode by using Math architecture for reciprocal function. The reciprocal function in the Math Function block also supports the architectures listed in the table.

Architecture	Parameters	Additional Cycles of Latency	Description
Reciprocal	None	0	Calculate reciprocal as 1/N, using the HDL divide (/) operator to implement the division.
ReciprocalRsqrtBasedNewton	Iterations	Signed input: Iterations + 5 Unsigned input: Iterations + 3	Use the iterative Newton method. Select this option to optimize area. The default value for Iterations is 3. The recommended value for Iterations is from 2 through 10. If Iterations is outside the recommended range, HDL Coder generates a message.
ReciprocalRsqrtBasedNewtonSingleRate	Iterations	Signed input: (Iterations * 4) + 8 Unsigned 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 for Iterations is 3. The recommended value for Iterations is from 2 through 10. If Iterations is outside the recommended range, the coder generates a message.
ShiftAdd	UsePipelines	Signed input: (Input word length + 4) Unsigned input: (Input word length + 4)	Perform reciprocal operation on a fixed-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 this architecture, to achieve a higher maximum clock frequency on the target FPGA device, leave the UsePipelines HDL block property to on. 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

When you set the algorithm method to Exact, you can select these options in HDL Block properties of this block.

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 for reciprocal 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 for Iterations is 3. The recommended value for Iterations 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 for Iterations is between 2 and 10. If Iterations value is outside the recommended range, HDL Coder displays 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).

Native Floating Point
CheckResetToZero	Use this property for the mod and rem functions of the Math Function block. If you have numbers a and b such that the quotient a/b is close to an integer, this setting treats a as an integral multiple of b, 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 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 functions of the Math Function block. If you have numbers a and b that are significantly large integers, you can increase MaxIterations 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).

Supported Datatypes and Functions in Native Floating-Point

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

Math Functions	Supported Floating-Point Datatypes			Complex Data Support
	Half	Single	Double
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 or unsigned) data type.

• The output must be scalar and have integer or fixed-point (signed or unsigned) data type.

• Only the Zero rounding mode is supported.

• The Saturate on integer overflow option on the block 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 certain configurations. For more information, see the Block Support Table.

Version History

Introduced before R2006a

R2023a: Math Function Block Supports 2^u

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