Round toward zero
y = fix(a)
y = fix(a) rounds fi object a to
the nearest integer in the direction of zero and returns the result
in fi object y.
y and a have the same fimath object
and DataType property.
When the DataType property of a is single, double,
or boolean, the numerictype of y is
the same as that of a.
When the fraction length of a is zero or
negative, a is already an integer, and the numerictype of y is
the same as that of a.
When the fraction length of a is positive,
the fraction length of y is 0,
its sign is the same as that of a, and its word
length is the difference between the word length and the fraction
length of a. If a is signed,
then the minimum word length of y is 2.
If a is unsigned, then the minimum word length
of y is 1.
For complex fi objects, the imaginary and
real parts are rounded independently.
fix does not support fi objects
with nontrivial slope and bias scaling. Slope and bias scaling is
trivial when the slope is an integer power of 2 and the bias is 0.
The following example demonstrates how the fix function
affects the numerictype properties of a signed fi object
with a word length of 8 and a fraction length of 3.
a = fi(pi, 1, 8, 3)
a =
3.1250
DataTypeMode: Fixed-point: binary point scaling
Signedness: Signed
WordLength: 8
FractionLength: 3
y = fix(a)
y =
3
DataTypeMode: Fixed-point: binary point scaling
Signedness: Signed
WordLength: 5
FractionLength: 0
The following example demonstrates how the fix function
affects the numerictype properties of a signed fi object
with a word length of 8 and a fraction length of 12.
a = fi(0.025,1,8,12)
a =
0.0249
DataTypeMode: Fixed-point: binary point scaling
Signedness: Signed
WordLength: 8
FractionLength: 12
y = fix(a)
y =
0
DataTypeMode: Fixed-point: binary point scaling
Signedness: Signed
WordLength: 2
FractionLength: 0
The functions ceil, fix,
and floor differ in the way they round fi objects:
The ceil function rounds values
to the nearest integer toward positive infinity
The fix function rounds values
toward zero
The floor function rounds values
to the nearest integer toward negative infinity
The following table illustrates these differences for
a given fi object a.
| a | ceil(a) | fix(a) | floor(a) |
|---|---|---|---|
| – 2.5 | –2 | –2 | –3 |
| –1.75 | –1 | –1 | –2 |
| –1.25 | –1 | –1 | –2 |
| –0.5 | 0 | 0 | –1 |
| 0.5 | 1 | 0 | 0 |
| 1.25 | 2 | 1 | 1 |
| 1.75 | 2 | 1 | 1 |
| 2.5 | 3 | 2 | 2 |
ceil | convergent | floor | nearest | round