convergent - Round toward nearest integer with ties rounding to nearest even integer

Syntax

y = convergent(a) y = convergent(x)

Description

y = convergent(a) rounds fi object a to the nearest integer. In the case of a tie, convergent(a) rounds to the nearest even integer.

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.

convergent 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.

y = convergent(x) rounds the elements of x to the nearest integer. In the case of a tie, convergent(x) rounds to the nearest even integer.

Examples

Example 1

The following example demonstrates how the convergent 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 = convergent(a) 

y =
 
     3

          DataTypeMode: Fixed-point: binary point scaling
            Signedness: Signed
            WordLength: 6
        FractionLength: 0

Example 2

The following example demonstrates how the convergent 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 = convergent(a) 

y =
 
     0

          DataTypeMode: Fixed-point: binary point scaling
            Signedness: Signed
            WordLength: 2
        FractionLength: 0

Example 3

The 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