# Documentation

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# Math Function

Perform mathematical function

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 the following functions from the Function parameter list.

FunctionDescriptionMathematical ExpressionMATLAB® 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 the following types of operations.

FunctionScalar OperationsElement-Wise Vector and Matrix OperationsVector 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

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

Functionsingledoublebooleanbuilt-in integerfixed 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

All supported modes accept both real and complex inputs, except for `reciprocal`, which does not accept complex fixed-point inputs.

The block output is real or complex, depending on what you select for Output signal type.

## Parameters

Function

Output signal type

Specify the output signal type of the Math Function block as `auto`, `real`, or `complex`.

FunctionInput Signal TypeOutput Signal Type
AutoRealComplex

`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`

Sample time
 Note:   This parameter is not visible in the block dialog box unless it is explicitly set to a value other than `-1`. To learn more, see Blocks for Which Sample Time Is Not Recommended.
 Note   Some parameters on this pane are available only when the function you select in the Function parameter supports fixed-point data types.
Output minimum

Specify the minimum value that the block can output. The default value is `[]` (unspecified). Simulink® software uses this value to perform:

• Simulation range checking (see Signal Ranges)

• Automatic scaling of fixed-point data types

Output maximum

Specify the maximum value that the block can output. The default value is `[]` (unspecified). Simulink software uses this value to perform:

• Simulation range checking (see Signal Ranges)

• Automatic scaling of fixed-point data types

Output data type

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 Output data type parameter.

Lock output data type setting against changes by the fixed-point tools

Select to lock the output data type setting of this block against changes by the Fixed-Point Tool and the Fixed-Point Advisor. For more information, see Use Lock Output Data Type Setting (Fixed-Point Designer).

Integer rounding mode

Specify the rounding mode for fixed-point operations. For more information, see Rounding (Fixed-Point Designer). in the Fixed-Point Designer™ documentation.

Saturate on integer overflow
ActionReasons for Taking This ActionWhat Happens for OverflowsExample

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.

## Characteristics

 Direct Feedthrough Yes Sample Time Inherited from driving block Scalar Expansion Yes, of the input when the function requires two inputs Dimensionalized Yes Multidimensionalized Yes, for all functions except `hermitian` and `transpose` Zero-Crossing Detection No