abs
Absolute value of fi
object
Description
returns the
absolute value of y
= abs(a
)fi
object a
with the same
numerictype
object as a
. Intermediate quantities
are calculated using the fimath
associated with a
.
The output fi
object, y
, has the same local
fimath
as a
.
returns a y
= abs(a
,T
)fi
object with a value equal to the absolute value of
a
and numerictype
object T
.
Intermediate quantities are calculated using the fimath
associated with
a
and the output fi
object y
has the same local fimath
as a
. See Data Type Propagation Rules.
returns a y
= abs(a
,T
,F
)fi
object with a value equal to the absolute value of
a
and the numerictype
object
T
. Intermediate quantities are calculated using the
fimath
object F
. The output fi
object, y
, has no local fimath
. See Data Type Propagation Rules.
Examples
Absolute Value of Most Negative Representable Value
This example shows the difference between the absolute value results
for the most negative value representable by a signed data type when the
'OverflowAction'
property is set to 'Saturate'
or
'Wrap'
.
Calculate the absolute value when the 'OverflowAction'
is set to
the default value 'Saturate'
.
P = fipref('NumericTypeDisplay','full',... 'FimathDisplay','full'); a = fi(128) y = abs(a)
a = 128 DataTypeMode: Fixedpoint: binary point scaling Signedness: Signed WordLength: 16 FractionLength: 8 y = 127.9961 DataTypeMode: Fixedpoint: binary point scaling Signedness: Signed WordLength: 16 FractionLength: 8
abs
returns 127.9961
, which is a result of
saturation to the maximum positive value.
Calculate the absolute value when the 'OverflowAction'
is set to
'Wrap'
.
a.OverflowAction = 'Wrap'
y = abs(a)
a = 128 DataTypeMode: Fixedpoint: binary point scaling Signedness: Signed WordLength: 16 FractionLength: 8 RoundingMethod: Nearest OverflowAction: Wrap ProductMode: FullPrecision SumMode: FullPrecision y = 128 DataTypeMode: Fixedpoint: binary point scaling Signedness: Signed WordLength: 16 FractionLength: 8 RoundingMethod: Nearest OverflowAction: Wrap ProductMode: FullPrecision SumMode: FullPrecision
abs
returns 128
, which is a result of
wrapping back to the most negative value.
Difference Between Absolute Values for Real and Complex fi
Inputs
This example shows the difference between the absolute value results
for complex and real fi
inputs that have the most negative value
representable by a signed data type when the 'OverflowAction'
property
is set to 'Wrap'
.
Define a complex fi
object.
re = fi(1,1,16,15); im = fi(0,1,16,15); a = complex(re,im)
a = 1.0000 + 0.0000i DataTypeMode: Fixedpoint: binary point scaling Signedness: Signed WordLength: 16 FractionLength: 15
a
is complex, but numerically equal to the real part,
re
.
Calculate the absolute value of the complex fi
object.
y = abs(a,re.numerictype,fimath('OverflowAction','Wrap'))
y = 1.0000 DataTypeMode: Fixedpoint: binary point scaling Signedness: Signed WordLength: 16 FractionLength: 15
Calculate the absolute value of the real fi
object.
y = abs(re,re.numerictype,fimath('OverflowAction','Wrap'))
y = 1 DataTypeMode: Fixedpoint: binary point scaling Signedness: Signed WordLength: 16 FractionLength: 15
Specify numerictype
and fimath
Inputs to Control the Result of abs
for Real Inputs
This example shows how to specify numerictype
and
fimath
objects as optional arguments to control the result of the
abs
function for real inputs. When you specify a
fimath
object as an argument, that fimath
object
is used to compute intermediate quantities, and the resulting fi
object
has no local fimath
.
a = fi(1,1,6,5,'OverflowAction','Wrap'); y = abs(a)
y = 1 DataTypeMode: Fixedpoint: binary point scaling Signedness: Signed WordLength: 6 FractionLength: 5 RoundingMethod: Nearest OverflowAction: Wrap ProductMode: FullPrecision SumMode: FullPrecision
The returned output is identical to the input. This may be undesirable because the absolute value is expected to be positive.
F = fimath('OverflowAction','Saturate'); y = abs(a,F)
y = 0.9688 DataTypeMode: Fixedpoint: binary point scaling Signedness: Signed WordLength: 6 FractionLength: 5
The returned fi
object is saturated to a value of
0.9688
and has the same numerictype
object as
the input.
Because the output of abs
is always expected to be positive, an
unsigned numerictype
may be specified for the output.
T = numerictype(a.numerictype, 'Signed', false);
y = abs(a,T,F)
y = 1 DataTypeMode: Fixedpoint: binary point scaling Signedness: Unsigned WordLength: 6 FractionLength: 5
Specifying an unsigned numerictype
enables better
precision.
Specify numerictype
and fimath
Inputs to Control the Result of abs
for Complex Inputs
This example shows how to specify numerictype
and
fimath
objects as optional arguments to control the result of the
abs
function for complex inputs.
Specify a numerictype
input and calculate the absolute value of
a
.
a = fi(1i,1,16,15,'OverflowAction','Wrap'); T = numerictype(a.numerictype,'Signed',false); y = abs(a,T)
y = 1.4142 DataTypeMode: Fixedpoint: binary point scaling Signedness: Unsigned WordLength: 16 FractionLength: 15 RoundingMethod: Nearest OverflowAction: Wrap ProductMode: FullPrecision SumMode: FullPrecision
A fi
object is returned with a value of 1.4142
and the specified unsigned numerictype
. The fimath
used for intermediate calculation and the fimath
of the output are
the same as that of the input.
Now specify a fimath
object different from that of
a
.
F = fimath('OverflowAction','Saturate','SumMode',... 'KeepLSB','SumWordLength',a.WordLength,... 'ProductMode','specifyprecision',... 'ProductWordLength',a.WordLength,... 'ProductFractionLength',a.FractionLength); y = abs(a,T,F)
y = 1.4142 DataTypeMode: Fixedpoint: binary point scaling Signedness: Unsigned WordLength: 16 FractionLength: 15
The specified fimath
object is used for intermediate calculation.
The fimath
associated with the output is the default
fimath
.
Input Arguments
a
— Input fi
array
scalar  vector  matrix  multidimensional array
Input fi
array, specified as a scalar, vector, matrix, or
multidimensional array.
abs
only supports fi
objects with trivial
[Slope Bias] scaling, that is, when the bias is 0
and the fractional
slope is 1
.
abs
uses a different algorithm for real and complex inputs. For
more information, see Absolute Value.
Data Types: fi
Complex Number Support: Yes
T
— numerictype
of the output
numerictype
object
numerictype
of the output fi
object
y
, specified as a numerictype
object. For more
information, see Data Type Propagation Rules.
Example: T =
numerictype(0,24,12,'DataType','Fixed')
F
— Fixedpoint math settings to use
fimath
object
Fixedpoint math settings to use for the calculation of absolute value, specified as
a fimath
object.
Example: F =
fimath('OverflowAction','Saturate','RoundingMethod','Convergent')
Algorithms
Absolute Value
The absolute value of a real number is the corresponding nonnegative value that disregards the sign.
For a real input, a
, the absolute value, y
,
is:
y = a if a >=
0  (1) 
y = a if a <
0  (2) 
abs(0)
returns 0
.
Note
When the fi
object a
is real and has a signed
data type, the absolute value of the most negative value is problematic since it is not
representable. In this case, the absolute value saturates to the most positive value
representable by the data type if the 'OverflowAction'
property is set
to 'Saturate'
. If 'OverflowAction'
is
'Wrap'
, the absolute value of the most negative value has no
effect.
For a complex input, a
, the absolute value, y
, is
related to its real and imaginary parts as follows:
y = sqrt(real(a)*real(a) + imag(a)*imag(a))  (3) 
The abs
function computes the absolute value of a complex input,
a
, as follows:
Calculate the real and imaginary parts of
a
.re = real(a)
(4) im = imag(a)
(5) Compute the squares of
re
andim
using one of the following objects:The
fimath
objectF
ifF
is specified as an argument.The
fimath
associated witha
ifF
is not specified as an argument.
If the input is signed, cast the squares of
re
andim
to unsigned types.Add the squares of
re
andim
using one of the following objects:The
fimath
objectF
ifF
is specified as an argument.The
fimath
object associated witha
ifF
is not specified as an argument.
Compute the square root of the sum computed in Step 4 using the
sqrt
function with the following additional arguments:The
numerictype
objectT
ifT
is specified, or thenumerictype
object ofa
otherwise.The
fimath
objectF
ifF
is specified, or thefimath
object associated witha
otherwise.
Note
Step 3 prevents the sum of the squares of the real and imaginary components from
being negative. This is important because if either re
or
im
has the maximum negative value and the
'OverflowAction'
property is set to 'Wrap'
then
an error will occur when taking the square root in Step 5.
Data Type Propagation Rules
For syntaxes for which you specify a numerictype
object
T
, the abs
function follows the data type
propagation rules listed in the following table. In general, these rules can be summarized
as “floatingpoint data types are propagated.” This allows you to write code
that can be used with both fixedpoint and floatingpoint inputs.
Data Type of Input fi Object
a  Data Type of numerictype object
T  Data Type of Output y 


 Data type of 









Any 


Any 


Note
When the Signedness
of the input numerictype
object T
is Auto
, the abs
function always returns an Unsigned
fi
object.
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
HDL Code Generation
Generate VHDL, Verilog and SystemVerilog code for FPGA and ASIC designs using HDL Coder™.
Double and complex data types are not supported.
Version History
Introduced before R2006a
See Also
fi
 fimath
 numerictype
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