# fimath

Set fixed-point math settings

## Description

example

F = fimath creates a fimath object with the default fimath property settings.

example

F = fimath(Name,Value) specifies the properties of a fimath object by using one or more name-value pair arguments. All properties not specified in the constructor use default values.

## Examples

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This example shows how to create a fimath object with the default property settings.

F = fimath
F =
RoundingMethod: Nearest
OverflowAction: Saturate
ProductMode: FullPrecision
SumMode: FullPrecision

Set the properties of a fimath object at the time of object creation by using name-value pairs. For example, set the overflow action to saturate and the rounding method to convergent.

F = fimath('OverflowAction','Saturate','RoundingMethod','Convergent')
F =
RoundingMethod: Convergent
OverflowAction: Saturate
ProductMode: FullPrecision
SumMode: FullPrecision

## Input Arguments

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### Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: F = fimath('OverflowAction','Saturate','RoundingMethod','Floor')

Whether both operands are cast to the sum data type before addition, specified as a numeric or logical 1 (true) or 0 (false).

Note

This property is hidden when the SumMode is set to FullPrecision.

Example: F = fimath('CastBeforeSum',true)

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical

Maximum allowable word length for the product data type, specified as a positive integer.

Example: F = fimath('MaxProductWordLength',16)

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Maximum allowable word length for the sum data type, specified as a positive integer.

Example: F = fimath('MaxSumWordLength',16)

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Action to take on overflow, specified as one of these values:

• 'Saturate' – Saturate to the maximum or minimum value of the fixed-point range on overflow.

• 'Wrap' – Wrap on overflow. This mode is also known as two's complement overflow.

Example: F = fimath('OverflowAction','Wrap')

Data Types: char

Bias of the product data type, specified as a floating-point number.

Example: F = fimath('ProductBias',1)

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Fixed exponent of the product data type, specified as a nonzero integer.

Note

The ProductFractionLength is the negative of the ProductFixedExponent. Changing one property changes the other.

Example: F = fimath('ProductFixedExponent',-20)

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Fraction length, in bits, of the product data type, specified as a nonzero integer.

Note

The ProductFractionLength is the negative of the ProductFixedExponent. Changing one property changes the other.

Example: F = fimath('ProductFractionLength',20)

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

How the product data type is determined, specified as one of these values:

• 'FullPrecision' – The full precision of the result is kept.

• 'KeepLSB' – Keep the least significant bits. Specify the product word length. The fraction length is set to maintain the least significant bits of the product.

• 'KeepMSB' – Keep the most significant bits. Specify the product word length. The fraction length is set to maintain the most significant bits of the product.

• 'SpecifyPrecision' – Specify the word and fraction lengths or slope and bias of the product.

Example: F = fimath('ProductMode','KeepLSB')

Data Types: char

Slope of the product data type, specified as a finite, positive floating-point number.

Note

$ProductSlope=ProductSlopeAdjustmentFactor×{2}^{ProductFixedExponent}$

Changing one of these properties affects the others.

Example: F = fimath('ProductSlope',9.3132e-10)

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Slope adjustment factor of the product data type, specified as a floating-point number greater than or equal to 1 and less than 2.

Note

$ProductSlope=ProductSlopeAdjustmentFactor×{2}^{ProductFixedExponent}$

Changing one of these properties affects the others.

Example: F = fimath('ProductSlopeAdjustmentFactor',1)

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Word length, in bits, of the product data type, specified as a positive integer.

Example: F = fimath('ProductWordLength',64)

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Rounding method to use, specified as one of these values:

• 'Nearest' – Round toward nearest. Ties round toward positive infinity.

• 'Ceiling' – Round toward positive infinity.

• 'Convergent' – Round toward nearest. Ties round to the nearest even stored integer (least biased).

• 'Zero' – Round toward zero.

• 'Floor' – Round toward negative infinity.

• 'Round' – Round toward nearest. Ties round toward negative infinity for negative numbers, and toward positive infinity for positive numbers.

Example: F = fimath('RoundingMethod','Convergent')

Data Types: char

Bias of the sum data type, specified as a floating-point number.

Example: F = fimath('SumBias',0)

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Fixed exponent of the sum data type, specified as a nonzero integer.

Note

The SumFractionLength is the negative of the SumFixedExponent. Changing one property changes the other.

Example: F = fimath('SumFixedExponent',-20)

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Fraction length, in bits, of the sum data type, specified as a nonzero integer.

Note

The SumFractionLength is the negative of the SumFixedExponent. Changing one property changes the other.

Example: F = fimath('SumFractionLength',20)

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

How the sum data type is determined, specified as one of these values:

• 'FullPrecision' – The full precision of the result is kept.

• 'KeepLSB' – Keep least significant bits. Specify the sum data type word length. The fraction length is set to maintain the least significant bits of the sum.

• 'KeepMSB' – Keep most significant bits. Specify the sum data type word length. The fraction length is set to maintain the most significant bits of the sum and no more fractional bits than necessary.

• 'SpecifyPrecision' – Specify the word and fraction lengths or slope and bias of the sum data type.

Example: F = fimath('SumMode','KeepLSB')

Data Types: char

Slope of the sum data type, specified as a floating-point number.

Note

$SumSlope=SumSlopeAdjustmentFactor×{2}^{SumFixedExponent}$

Changing one of these properties affects the others.

Example: F = fimath('SumSlope',9.3132e-10)

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Slope adjustment factor of the sum data type, specified as a floating-point number greater than or equal to 1 and less than 2.

Note

$SumSlope=SumSlopeAdjustmentFactor×{2}^{SumFixedExponent}$

Changing one of these properties affects the others.

Example: F = fimath('SumSlopeAdjustmentFactor',1)

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Word length, in bits, of the sum data type, specified as a positive integer.

Example: F = fimath('SumWordLength',64)

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

## Version History

Introduced before R2006a

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