Math Function

Perform mathematical function

• Library:

• Simulink / Math Operations

  HDL Coder / Math Operations

Description

The Math Function block performs numerous common mathematical functions.

Tip

To perform square root calculations, use the Sqrt block.

You can select one of these functions from the Function parameter list.

Function	Description	Mathematical Expression	MATLAB® Equivalent
exp	Exponential	eu	exp
log	Natural logarithm	ln u	log
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	(abs(u)).^2 (see abs and power)
square	Power 2	u2	u.^2 (see power)
pow	Power	uv	power
conj	Complex conjugate	ū	conj
reciprocal	Reciprocal	1/u	1./u (see rdivide)
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 (MATLAB))
hermitian	Complex conjugate transpose	uH	u' (see Array vs. Matrix Operations (MATLAB))

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	—
log	Yes	Yes	—
10^u	Yes	Yes	—
log10	Yes	Yes	—
magnitude^2	Yes	Yes	—
square	Yes	Yes	—
pow	Yes	Yes	—
conj	Yes	Yes	—
reciprocal	Yes	Yes	—
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)	—
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)	—
transpose	Yes	—	Yes
hermitian	Yes	—	Yes

The name of the function appears on the block. The appropriate number of input ports appears automatically.

Tip

Use the Math Function block instead of the Fcn block when you want vector or matrix output because the Fcn block produces only scalar output.

Data Type Support

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

Function	single	double	boolean	built-in integer	fixed point
exp	Yes	Yes	—	—	—
log	Yes	Yes	—	—	—
10^u	Yes	Yes	—	—	—
log10	Yes	Yes	—	—	—
magnitude^2	Yes	Yes	—	Yes	Yes
square	Yes	Yes	—	Yes	Yes
pow	Yes	Yes	—	—	—
conj	Yes	Yes	—	Yes	Yes
reciprocal	Yes	Yes	—	Yes	Yes
hypot	Yes	Yes	—	—	—
rem	Yes	Yes	—	Yes	—
mod	Yes	Yes	—	Yes	—
transpose	Yes	Yes	Yes	Yes	Yes
hermitian	Yes	Yes	—	Yes	Yes

Ports

Input

Port_1 — Input signal

scalar | vector | matrix

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

Dependencies

Data type support for this block depends on the Function you select and the size of the input(s). For more information, see Data Type Support.

Data Types: single | double | int8 | int16 | int32 | uint8 | uint16 | uint32 | Boolean | fixed point | bus

Port_2 — Input signal

scalar | vector | matrix

Input signal specified as a scalar, vector, or matrix. All supported modes accept both 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 you select, and the size of the input(s). For more information, see Data Type Support.

Data Types: single | double | int8 | int16 | int32 | uint8 | uint16 | uint32 | Boolean | fixed point | bus

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 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 for more information.

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

Parameters

Main

Function — Math function

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

Specify the mathematical function. See Description for more information about the options for this parameter.

Programmatic Use

Block Parameter: Operator

Type: character vector

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

Default: 'exp'

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, 10u, 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'

Sample time — Specify sample time as a value other than -1

-1 (default) | scalar

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: character vector

Values: scalar

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 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 (Simulink 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 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 (Simulink 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 | 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)

Click the Show data type assistant button to display the Data Type Assistant, which helps you set the data type attributes. 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.

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' | '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	Reasons for Taking This Action	What Happens for Overflows	Example
Select this check box.	Your model has possible overflow, and you want explicit saturation protection in the generated code.	Overflows saturate to either the minimum or maximum value that the data type can represent.	The maximum value that the int8 (signed, 8-bit integer) data type can represent is 127. Any block operation result greater than this maximum value causes overflow of the 8-bit integer. With the check box selected, the block output saturates at 127. Similarly, the block output saturates at a minimum output value of -128.
Do not select this check box.	You want to optimize efficiency of your generated code. You want to avoid overspecifying how a block handles out-of-range signals. For more information, see Check for 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. Usually, 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'

Model Examples

Variable-Size Signal Basic Operations

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

Open Model

Block Characteristics

Data Types	Boolean | double | fixed point | integer | single
Direct Feedthrough	no
Multidimensional Signals	no
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™.

The Math Function block has HDL code generation restrictions when you set the Function to reciprocal. For more information, see Math Function.

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

Fixed-Point Conversion

Convert floating-point algorithms to fixed point using Fixed-Point Designer™.

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