log2

Base 2 logarithm and floating-point number dissection

Syntax

Y = log2(X)

[F,E] = log2(X)

Description

Y = log2(X) computes the base 2 logarithm of the elements of X such that $$2^Y=X$$.

[F,E] = log2(X) returns arrays F and E such that $$X=F\cdot 2^E$$. The values in F are typically in the range 0.5 <= abs(F) < 1.

Examples

Base 2 Logarithm Values

X = [0 1 2 10 Inf NaN];
Y = log2(X)

Y = 1×6

      -Inf         0    1.0000    3.3219       Inf       NaN

Floating-Point Number Dissection

Dissect several numbers into the exponent and mantissa. These operations all follow standard IEEE® arithmetic.

Create a vector X that contains several test values. Calculate the exponent and mantissa for each number.

X = [1 pi -3 eps realmax realmin];
format rat
[F,E] = log2(X)

F = 
  Columns 1 through 5

       1/2          355/452         -3/4            1/2            1       

  Column 6

       1/2     

E = 
  Columns 1 through 5

       1              2              2            -51           1024       

  Column 6

   -1021       

Collect the results in a table. Convert the numbers into character vectors for display purposes.

x = {'1','pi','-3','eps','realmax','realmin'}';
f = strtrim(cellstr(rats(F')));
T = table(x,f,E','VariableNames',{'Value','Mantissa','Exponent'})

T=6×3 table
       Value        Mantissa      Exponent
    ___________    ___________    ________

    {'1'      }    {'1/2'    }         1  
    {'pi'     }    {'355/452'}         2  
    {'-3'     }    {'-3/4'   }         2  
    {'eps'    }    {'1/2'    }       -51  
    {'realmax'}    {'1'      }      1024  
    {'realmin'}    {'1/2'    }     -1021  

The results indicate that, for the first row, $1=\frac{1}{2}\left(2^1\right)$. Similarly, for the fourth row, $\mathrm{eps}=\frac{1}{2}\left(2^{-51}\right)$.

Input Arguments

X — Input matrix

scalar | vector | matrix | multidimensional array

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

For floating-point number dissection [F,E] = log2(X), any zeros in X produce F = 0 and E = 0. Input values of Inf, -Inf, or NaN are returned unchanged in F with a corresponding exponent of E = 0.

Data Types: single | double
Complex Number Support: Yes

Output Arguments

Y — Base 2 logarithm values

scalar | vector | matrix | multidimensional array

Base 2 logarithm values, returned as a scalar, vector, matrix, or multidimensional array of the same size as X.

F — Mantissa values

scalar | vector | matrix | multidimensional array

Mantissa values, returned as a scalar, vector, matrix, or multidimensional array of the same size as X. The values in F and E satisfy X = F.*2.^E.

E — Exponent values

scalar | vector | matrix | multidimensional array

Exponent values, returned as a scalar, vector, matrix, or multidimensional array of the same size as X. The values in F and E satisfy X = F.*2.^E.

Tips

• This function corresponds to the ANSI^® C function frexp() and the IEEE^® floating-point standard function logb(). Any zeros in X produce F = 0 and E = 0.

Extended Capabilities

Tall Arrays

Calculate with arrays that have more rows than fit in memory.

This function fully supports tall arrays. For more information, see Tall Arrays.

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

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Usage notes and limitations:

• The syntax [F,E] = log2(X) is not supported.

• If the output of the function running on the GPU can be complex, then you must explicitly specify its input arguments as complex. For more information, see Work with Complex Numbers on a GPU (Parallel Computing Toolbox).

For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Distributed Arrays

Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

This function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).