convergent

Round toward nearest integer with ties rounding to nearest even integer

Description

example

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.

example

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

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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

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

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.

This example illustrates these differences for a given input, a.

a = fi([-3.5:3.5]');
y = [a convergent(a) nearest(a) round(a)]
y =
-3.5000   -4.0000   -3.0000   -4.0000
-2.5000   -2.0000   -2.0000   -3.0000
-1.5000   -2.0000   -1.0000   -2.0000
-0.5000         0         0   -1.0000
0.5000         0    1.0000    1.0000
1.5000    2.0000    2.0000    2.0000
2.5000    2.0000    3.0000    3.0000
3.5000    3.9999    3.9999    3.9999

DataTypeMode: Fixed-point: binary point scaling
Signedness: Signed
WordLength: 16
FractionLength: 13

Input Arguments

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Input fi array, specified as scalar, vector, matrix, or multidimensional array.

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.

Data Types: fi
Complex Number Support: Yes

Input array, specified as a scalar, vector, matrix, or multidimensional array.

For complex inputs, the real and imaginary parts are rounded independently.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64
Complex Number Support: Yes

Algorithms

• y and a have the same fimath object and DataType property.

• When the DataType property of a is single, or double, 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.

Extended Capabilities

HDL Code GenerationGenerate Verilog and VHDL code for FPGA and ASIC designs using HDL Coder™. 