Absolute value of fi object
c = abs(a)
c = abs(a,T)
c = abs(a,F)
c = abs(a,T,F)
c = abs(a) returns the absolute value of fi object a with
the same numerictype object as a.
Intermediate quantities are calculated using the fimath associated
with a. The output fi object c has
the same local fimath as a.
c = abs(a,T) returns a 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 c has
the same local fimath as a. See Data Type Propagation Rules.
c = abs(a,F) returns a fi object
with a value equal to the absolute value of a and
the same numerictype object as a.
Intermediate quantities are calculated using the fimath object F.
The output fi object c has no
local fimath.
c = abs(a,T,F) returns a 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 c has no
local fimath. See Data Type Propagation Rules.
When the Signedness of the input numerictype object T is Auto,
the abs function always returns an Unsigned fi object.
abs only supports fi objects
with [Slope Bias] scaling when the bias is zero and the fractional
slope is one. abs does not support complex fi objects
of data type Boolean.
When the 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 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 “floating-point data types are propagated.”
This allows you to write code that can be used with both fixed-point
and floating-point inputs.
| Data Type of Input fi Object a | Data Type of numerictype object T | Data Type of Output c |
|---|---|---|
|
| Data type of |
|
|
|
|
|
|
|
|
|
Any |
|
|
Any |
|
|
The following example shows the difference between the absolute
value results for the most negative value representable by a signed
data type when OverflowAction is saturate or wrap.
P = fipref('NumericTypeDisplay','full',... 'FimathDisplay','full'); a = fi(-128) a = -128 DataTypeMode: Fixed-point: binary point scaling Signedness: Signed WordLength: 16 FractionLength: 8 abs(a) ans = 127.9961 DataTypeMode: Fixed-point: binary point scaling Signedness: Signed WordLength: 16 FractionLength: 8 a.OverflowAction = 'Wrap' a = -128 DataTypeMode: Fixed-point: binary point scaling Signedness: Signed WordLength: 16 FractionLength: 8 RoundingMethod: Nearest OverflowAction: Wrap ProductMode: FullPrecision SumMode: FullPrecision abs(a) ans = -128 DataTypeMode: Fixed-point: binary point scaling Signedness: Signed WordLength: 16 FractionLength: 8 RoundingMethod: Nearest OverflowAction: Wrap ProductMode: FullPrecision SumMode: FullPrecision
The following 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 OverflowAction is wrap.
re = fi(-1,1,16,15)
re =
-1
DataTypeMode: Fixed-point: binary point scaling
Signedness: Signed
WordLength: 16
FractionLength: 15
im = fi(0,1,16,15)
im =
0
DataTypeMode: Fixed-point: binary point scaling
Signedness: Signed
WordLength: 16
FractionLength: 15
a = complex(re,im)
a =
-1
DataTypeMode: Fixed-point: binary point scaling
Signedness: Signed
WordLength: 16
FractionLength: 15
abs(a,re.numerictype,fimath('OverflowAction','Wrap'))
ans =
1.0000
DataTypeMode: Fixed-point: binary point scaling
Signedness: Signed
WordLength: 16
FractionLength: 15
abs(re,re.numerictype,fimath('OverflowAction','Wrap'))
ans =
-1
DataTypeMode: Fixed-point: binary point scaling
Signedness: Signed
WordLength: 16
FractionLength: 15
The following 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') a = -1 DataTypeMode: Fixed-point: binary point scaling Signedness: Signed WordLength: 6 FractionLength: 5 RoundingMethod: Nearest OverflowAction: Wrap ProductMode: FullPrecision SumMode: FullPrecision abs(a) ans = -1 DataTypeMode: Fixed-point: binary point scaling Signedness: Signed WordLength: 6 FractionLength: 5 RoundingMethod: Nearest OverflowAction: Wrap ProductMode: FullPrecision SumMode: FullPrecision f = fimath('OverflowAction','Saturate') f = RoundingMethod: Nearest OverflowAction: Wrap ProductMode: FullPrecision SumMode: FullPrecision abs(a,f) ans = 0.9688 DataTypeMode: Fixed-point: binary point scaling Signedness: Signed WordLength: 6 FractionLength: 5 t = numerictype(a.numerictype, 'Signed', false) t = DataTypeMode: Fixed-point: binary point scaling Signedness: Unsigned WordLength: 6 FractionLength: 5 abs(a,t,f) ans = 1 DataTypeMode: Fixed-point: binary point scaling Signedness: Unsigned WordLength: 6 FractionLength: 5
The following example shows how to specify numerictype and fimath objects
as optional arguments to control the result of the abs function
for complex inputs.
a = fi(-1-i,1,16,15,'OverflowAction','Wrap') a = -1.0000 - 1.0000i DataTypeMode: Fixed-point: binary point scaling Signedness: Signed WordLength: 16 FractionLength: 15 RoundingMethod: Nearest OverflowAction: Wrap ProductMode: FullPrecision SumMode: FullPrecision t = numerictype(a.numerictype,'Signed',false) t = DataTypeMode: Fixed-point: binary point scaling Signedness: Unsigned WordLength: 16 FractionLength: 15 abs(a,t) ans = 1.4142 DataTypeMode: Fixed-point: binary point scaling Signedness: Unsigned WordLength: 16 FractionLength: 15 RoundingMethod: Nearest OverflowAction: Wrap ProductMode: FullPrecision SumMode: FullPrecision f = fimath('OverflowAction','Saturate','SumMode',... 'KeepLSB','SumWordLength',a.WordLength,... 'ProductMode','specifyprecision',... 'ProductWordLength',a.WordLength,... 'ProductFractionLength',a.FractionLength) f = RoundingMethod: Nearest OverflowAction: Saturate ProductMode: SpecifyPrecision ProductWordLength: 16 ProductFractionLength: 15 SumMode: KeepLSB SumWordLength: 16 CastBeforeSum: true abs(a,t,f) ans = 1.4142 DataTypeMode: Fixed-point: binary point scaling Signedness: Unsigned WordLength: 16 FractionLength: 15
The absolute value y of a real input a is
defined as follows:
y = a if a >=
0
y = -a if a <
0
The absolute value y of a complex input a is
related to its real and imaginary parts as follows:
y
= sqrt(real(a)*real(a) + imag(a)*imag(a))
The abs function computes the absolute value
of complex inputs as follows:
Calculate the real and imaginary parts of a using
the following equations:
re = real(a)
im
= imag(a)
Compute the squares of re and im using
one of the following objects:
The fimath object F if F is
specified as an argument.
The fimath associated with a if F is
not specified as an argument.
Cast the squares of re and im to
unsigned types if the input is signed.
Add the squares of re and im using
one of the following objects:
The fimath object F if F is
specified as an argument.
The fimath object associated with a if F is
not specified as an argument.
Compute the square root of the sum computed in step
four using the sqrt function with the following
additional arguments:
The numerictype object T if T is
specified, or the numerictype object of a otherwise.
The fimath object F if F is
specified, or the fimath object associated with a otherwise.
Step three 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 five.