Matlab Floating Point Precision

Numeric class in MATLAB includes signed and unsigned integers, single-precision floating-point numbers, and double-precision floating-point numbers. Generally, MATLAB stores all numeric values as double-precision floating-point.Floating Point Numbers in MATLAB are stored in two forms:

1. Single Precision Floating point
2. Double Precision Floating point

MATLAB keeps the double precision floating point as the default floating point representation however, it can be changed to single by a very simple function.

Single Precision Floating Point:

The single precision floating point number requires 32 bits for representation by the standards of IEE®. These 32 bits are formatted as following.

Bit Number/Range	Bits’ Functionality
31	Sign: – 0 for positive. 1 for negative.
30-23	exponent part; biased by 127
22-0	mantissa of the number; 1.f

Where exponent and mantissa are the components of exponential/scientific notation of a number.

Double Precision Floating Point:

The double precision floating point number requires 64 bits for representation by the standards of IEE®. These 64 bits are formatted as following.

Bit Number/Range	Bits’ Functionality
63	Sign: – 0 for positive. 1 for negative.
62-52	exponent part; biased by 1023
51-0	mantissa of the number; 1.f

Creating Single Floating Point and Double Floating Point in MATLAB:

Single Precision:

As MATLAB creates double precision floating point number by default, we use single() function to create single precision floating point number.

Example 1:

Matlab

% MATLAB code for creating single precision floating point
num = single(123.45);

% verifying the attributes of num by whose function
whose("num")

Output:

Double Precision:

Double precision floating point numbers can be created by ordinary assignment or using the double function.

Example 2:

Matlab

% MATLAB code for creating number by double function
num = double(123.45);

% Creating number by ordinary assignment
num_assignment = 678.9;

% Checking the attributes of both variables
whose("num","num_assignment")

Output:

As it can be seen, both num and num_assignment variables have same attributes of double type.