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floor

Round toward negative infinity

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Syntax

y = floor(a)

Description

y = floor(a) rounds fi object a to the nearest integer in the direction of negative infinity and returns the result in fi object y.

example

Examples

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Open Live Script

The following example demonstrates how the floor 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 = floor(a)
y = 
     3

          DataTypeMode: Fixed-point: binary point scaling
            Signedness: Signed
            WordLength: 5
        FractionLength: 0

The following example demonstrates how the floor 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 = floor(a)
y = 
     0

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

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 to the nearest integer toward zero.

  • The floor function rounds values to the nearest integer toward negative infinity.

This example illustrates these differences for a given fi input object a.

a = fi([-2.5,-1.75,-1.25,-0.5,0.5,1.25,1.75,2.5]');
y = [a ceil(a) fix(a) floor(a)]
y = 
   -2.5000   -2.0000   -2.0000   -3.0000
   -1.7500   -1.0000   -1.0000   -2.0000
   -1.2500   -1.0000   -1.0000   -2.0000
   -0.5000         0         0   -1.0000
    0.5000    1.0000         0         0
    1.2500    2.0000    1.0000    1.0000
    1.7500    2.0000    1.0000    1.0000
    2.5000    3.0000    2.0000    2.0000

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

plot(a,y); legend('a','ceil(a)','fix(a)','floor(a)','location','NW');

Figure contains an axes object. The axes object contains 4 objects of type line. These objects represent a, ceil(a), fix(a), floor(a).

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.

floor 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

Algorithms

  • 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.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

HDL Code Generation
Generate VHDL, Verilog and SystemVerilog code for FPGA and ASIC designs using HDL Coder™.

Version History

Introduced in R2008a

See Also

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