Round toward nearest integer with ties rounding toward positive infinity
y = nearest(a)
y = nearest(a) rounds fi object a to
the nearest integer or, in case of a tie, to the nearest integer in
the direction of positive infinity, 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, plus one bit. 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.
nearest 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 nearest 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 = nearest(a)
y =
3
DataTypeMode: Fixed-point: binary point scaling
Signedness: Signed
WordLength: 6
FractionLength: 0The following example demonstrates how the nearest 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 = nearest(a)
y =
0
DataTypeMode: Fixed-point: binary point scaling
Signedness: Signed
WordLength: 2
FractionLength: 0The functions convergent, nearest and round differ
in the way they treat values whose least significant digit is 5:
The convergent function rounds
ties to the nearest even integer
The nearest function rounds ties
to the nearest integer toward positive infinity
The round function rounds ties
to the nearest integer with greater absolute value
The following table illustrates these differences for a given fi object a.
| a | convergent(a) | nearest(a) | round(a) |
|---|---|---|---|
| –3.5 | –4 | –3 | –4 |
| –2.5 | –2 | –2 | –3 |
| –1.5 | –2 | –1 | –2 |
| –0.5 | 0 | 0 | –1 |
| 0.5 | 0 | 1 | 1 |
| 1.5 | 2 | 2 | 2 |
| 2.5 | 2 | 3 | 3 |
| 3.5 | 4 | 4 | 4 |
ceil | convergent | fix | floor | round