Floating-Point Numbers :: Data Types (Programming)

Programming

Floating-Point Numbers

MATLAB represents floating-point numbers in either double-precision or single-precision format. The default is double precision, but you can make any number single precision with a simple conversion function.

This section covers

Double-Precision Floating Point

MATLAB constructs the double data type according to IEEE Standard 754 for double precision. Any value stored as a double requires 64 bits, formatted as shown in the table below:

Bits
Usage

63
Sign (0 = positive, 1 = negative)

62 to 52
Exponent, biased by 1023

51 to 0
Fraction f of the number 1.f

Bits	Usage
`63`	Sign (`0` = positive, `1` = negative)
`62` to `52`	Exponent, biased by `1023`
`51` to `0`	Fraction `f` of the number `1.f`

Maximum and Minimum Double-Precision Values. The MATLAB functions realmax and realmin return the maximum and minimum values that you can represent with the double data type:

str = 'The range for double is:\n\t%g to %g and\n\t %g to  %g';
sprintf(str, -realmax, -realmin, realmin, realmax)

ans =
The range for double is:
   -1.79769e+308 to -2.22507e-308 and
    2.22507e-308 to  1.79769e+308

Numbers larger than realmax or smaller than -realmax are assigned the values of positive and negative infinity respectively:

realmax + .0001e+308
ans =
   Inf

-realmax - .0001e+308
ans =
  -Inf

Creating Double-Precision Data. Since the default numeric type for MATLAB is double, you can create a double with a simple assignment statement:

```
x = 25.783;
```

The whos function shows that MATLAB has created a 1-by-1 array of type double for the value you just stored in x:

whos x
  Name      Size                   Bytes  Class

  x         1x1                        8  double array

Use the isfloat function if you just want to verify that x is a floating-point number:

```
isfloat(x)
ans =
     1
```

The next statement creates a much larger value. This value requires a double; you could not store this using the single-precision data type:

```
x = 5.73 * 10^300;
```

Converting to Double Precision. You can convert other numeric data, characters or strings, and logical data to double precision using the MATLAB function, double. This example converts a signed integer to double-precision floating point:

y = int64(-589324077574);          % Create a 64-bit integer

x = double(y)                      % Convert to double
x =
   -5.8932e+011

whos x
  Name      Size                   Bytes  Class

  x         1x1                        8  double array

Single-Precision Floating Point

MATLAB constructs the single data type according to IEEE Standard 754 for single precision. Any value stored as a single requires 32 bits, formatted as shown in the table below:

Bits
Usage

31
Sign (0 = positive, 1 = negative)

30 to 23
Exponent, biased by 127

22 to 0
Fraction f of the number 1.f

Bits	Usage
`31`	Sign (`0` = positive, `1` = negative)
`30` to `23`	Exponent, biased by `127`
`22` to `0`	Fraction `f` of the number `1.f`

Maximum and Minimum Single-Precision Values. The MATLAB functions realmax and realmin, when called with the argument 'single', return the maximum and minimum values that you can represent with the single data type:

str = 'The range for single is:\n\t%g to %g and\n\t %g to  %g';
sprintf(str, -realmax('single'), -realmin('single'), ...
   realmin('single'), realmax('single'))

ans =
The range for single is:
   -3.40282e+038 to -1.17549e-038 and
    1.17549e-038 to  3.40282e+038

Numbers larger than realmax('single') or smaller than -realmax('single') are assigned the values of positive and negative infinity respectively:

realmax('single') + .0001e+038
ans =
   Inf

-realmax('single') - .0001e+038
ans =
  -Inf

Creating Single-Precision Data. Because MATLAB stores numeric data as a double by default, you need to use the single conversion function to create a single-precision number:

```
x = single(25.783);
```

The whos function shows that MATLAB has created a 1-by-1 array of type single. This value requires only 4 bytes compared with the 8 bytes used to store a double:

whos x
  Name      Size                   Bytes  Class

  x         1x1                        4  single array

Use the isfloat function if you just want to verify that x is a floating-point number:

```
isfloat(x)
ans =
     1
```

Converting to Single Precision. You can convert other numeric data, characters or strings, and logical data to single precision using the MATLAB function, single. This example converts a signed integer to single-precision floating point:

y = int64(-589324077574);          % Create a 64-bit integer

x = single(y)                      % Convert to single
x =
   -5.8932e+011

whos x
  Name      Size                   Bytes  Class

  x         1x1                        4  single array

Floating-Point Functions

See Floating-Point Functions for a list of functions most commonly used with floating-point numbers in MATLAB.

Numeric Types Complex Numbers