round

Syntax

R = round(x)

R = round(x,n)

R = round(x,n,'type')

Inputs

x

The values to round.

Type: double

Dimension: scalar | matrix

n

The number of places to round.

See 'type' for the options.

Type: integer

Dimension: scalar

'type'

The type of rounding to perform.

The available options are:

'decimal' (default)

Round to n digits (base 10) to the right of the decimal for positive n, and to the left for negative n (default: 0).

'significant'

Round to n significant digits (base 10). A positive integer is required.

'binary'

Round to n bits to the right of the decimal for positive n, and to the left for negative n (default: 0).

'sigbits'

Round to n significant bits. A positive integer is required.

Type: string

Outputs

R

The rounded values.

Type: double

Dimension: scalar | matrix

Examples

R = round(0.5)
        R = 1
        

R = round([0.437, 16.605, 0.570, -8.749, -0.594, -0.621], 2, 'decimal')
        R = [Matrix] 1 x 6
          0.44000  16.61000  0.57000  -8.75000  -0.59000  -0.62000
        

a1 = 2048 * (3 * 0.1)
        a2 = 2048 * 0.3
        delta1 = a1 - a2    % rounding difference
        bits = -log2(abs(delta1)) - 1
        r1 = round(a1, bits, 'binary')
        r2 = round(a2, bits, 'binary')
        delta2 = r1 - r2    % no rounding difference
        
          a1 = 614.4
          a2 = 614.4
          delta1 = 1.13687e-13
          bits = 42
          r1 = 614.4
          r2 = 614.4
          delta2 = 0
        

Comments

When x is complex, the rounding is applied to the real and imaginary components.

It should be understood that results from rounding in base 10 are constrained by binary limitations. A value such as 0.1 (base 10) does not have a finite precision representation in base 2 because it has a repeating bit pattern.

The 'binary' and 'sigbits' options are useful when analyzing values whose differences are too small to be observed in base 10.

Double precision (64 bit) values in IEEE 754 have 53 explicit bits, with the leading bit being an implied 1. The 'sigbits' option treats the implied leading bit as significant.