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	`e^u`	`exp`
`log`	Natural logarithm	`ln u`	`log`
`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`	`(abs(u)).^2` (see `abs` and `power`)
`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`	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	`u^T`	`u.'` (see Array vs. Matrix Operations)
`hermitian`	Complex conjugate transpose	`u^H`	`u'` (see Array vs. Matrix Operations)

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 when you want vector or matrix output.

Data Type Support

This table shows 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	—	—	—
`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`	Yes	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).

Ports

Input

expand all

`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.

`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.

Output

expand all

`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.

Parameters

expand all

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.

Dependency

Setting Function to pow enables the Signed power 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'

`Signed power` — Power signedness
on (default) | off

Take into account sign of the input signal when calculating power, specified as on or off. 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, return 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

Function	Input Signal Type	Output Signal Type
`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`

exp, log, 10u, 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: character vector

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

Default: 'auto'

`Sample time` — Specify sample time as a 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: character vector

Values: scalar or 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)

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'

'<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

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 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.

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 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. 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` \| `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

You can generate HDL code for the Math architecture of the block for single-precision data types in native floating-point mode.

Architecture	Description
`ComplexConjugate`	Compute complex conjugate.
`Hermitian`	Compute hermitian.
`Transpose`	Compute array transpose. See Math Function in the Simulink documentation.

Reciprocal Architecture

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).

Architecture Parameters Additional Cycles of Latency Description

Reciprocal None 0 Compute reciprocal as 1/N, using the HDL divide (/) operator to implement the division.

ReciprocalRsqrtBasedNewton

Architecture	Parameters	Additional Cycles of Latency	Description
Reciprocal	None	0	Compute 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.

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.

The Newton-Raphson iterative method:

$x_{i + 1} = x_{i} - \frac{f (x_{i})}{f' (x_{i})} = x_{i} (1.5 - 0.5 a x_{i}^{2})$

ReciprocalRsqrtBasedNewton and ReciprocalRsqrtBasedNewtonSingleRate implement the Newton-Raphson method with:

$f (x) = \frac{1}{x^{2}} - 1$

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. However, computing 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. However, computing this result uses additional resources and increases the area footprint on the target FPGA device. For more information, see MaxIterations (HDL Coder).

Complex Data Support

The conj, hermitian, and transpose functions support complex data.

Restrictions

Function set to Square is not supported.

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.

Documentation

Math Function

Description

Data Type Support

Ports

Input

Port_1 — Input signal scalar | vector | matrix

Dependencies

Port_2 — Input signal scalar | vector | matrix

Dependencies

Output

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

Parameters

Main

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

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

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

Model Examples

Variable-Size Signal Basic Operations

Block Characteristics

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™.

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

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

See Also

Topics

Simulink Documentation

Support

`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 or inputs
scalar | vector | matrix

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

`Signed power` — Power signedness
on (default) | off

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

`Sample time` — Specify sample time as a value other than `-1`
`-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 Verilog and VHDL 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™.