Infinity and NaN

Infinity

MATLAB® represents infinity by the special value inf. Infinity results from operations like division by zero and overflow, which lead to results too large to represent as conventional floating-point values. MATLAB also provides a function called inf that returns the IEEE® arithmetic representation for positive infinity as a double scalar value.

Several examples of statements that return positive or negative infinity in MATLAB are shown here.

x = 1/0
x =
Inf

x = 1.e1000
x =
   Inf

x = exp(1000)
x =
   Inf

x = log(0)
x =
   -Inf

Use the isinf function to verify that x is positive or negative infinity:

x = log(0);

isinf(x)
ans =
     1

NaN

MATLAB represents values that are not real or complex numbers with a special value called NaN, which stands for “Not a Number”. Expressions like 0/0 and inf/inf result in NaN, as do any arithmetic operations involving a NaN:

x = 0/0
x =

   NaN

You can also create NaNs by:

x = NaN;

whos x
  Name      Size                   Bytes  Class

  x         1x1                        8  double

The NaN function returns one of the IEEE arithmetic representations for NaN as a double scalar value. The exact bit-wise hexadecimal representation of this NaN value is,

format hex
x = NaN

x =

   fff8000000000000

Always use the isnan function to verify that the elements in an array are NaN:

isnan(x)
ans =

     1

MATLAB preserves the “Not a Number” status of alternate NaN representations and treats all of the different representations of NaN equivalently. However, in some special cases (perhaps due to hardware limitations), MATLAB does not preserve the exact bit pattern of alternate NaN representations throughout an entire calculation, and instead uses the canonical NaN bit pattern defined above.

Logical Operations on NaN

Because two NaNs are not equal to each other, logical operations involving NaN always return false, except for a test for inequality, (NaN ~= NaN):

NaN > NaN
ans =
     0

NaN ~= NaN 
ans =
     1
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