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

E = 
       1              2              2            -51           1024          -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 | table | timetable

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

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 | table | timetable
Complex Number Support: Yes

Output Arguments

Y — Base 2 logarithm values

scalar | vector | matrix | multidimensional array | table | timetable

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

F — Mantissa values

scalar | vector | matrix | multidimensional array | table | timetable

Mantissa values, returned as a scalar, vector, matrix, multidimensional array, table, or timetable 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 | table | timetable

Exponent values, returned as a scalar, vector, matrix, multidimensional array, table, or timetable 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.

The log2 function fully supports tall arrays. For more information, see Tall Arrays.

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

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

GPU Arrays

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

The log2 function supports GPU array input with these 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).

Version History

Introduced before R2006a

R2025a: Complex input for two-output syntax will not be accepted

The log2 function issues a warning if you specify a complex input when using the two-output syntax. Support for complex input in this syntax will be removed in a future release. In previous releases, the two-output syntax of log2 ignored the imaginary part of a complex input and processed only the real part.

To preserve the behavior of previous releases, use the real function to extract the real part of a complex input, as shown in this table.

Not Recommended (Warns)	Recommended
X = 2 - 1i; [F,E] = log2(X);	X = 2 - 1i; [F,E] = log2(real(X));

R2023a: Perform calculations directly on tables and timetables

The log2 function can calculate on all variables within a table or timetable without indexing to access those variables. All variables must have data types that support the calculation. For more information, see Direct Calculations on Tables and Timetables.