View source for INF, NAN, and NULL - Exception values

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<code>INF</code> ("infinity"),  <code>NAN</code> ("not a number"), and <code>Null</code> are special-valued system constants that Analytica returns in particular conditions, such as exceptions. These constants can also be used as values in expressions.

:{| class="wikitable"
!Constant
!Meaning
|-
|<code>INF</code>
|Infinity or a real number larger than can be represented, e.g., <code>1/0</code>
|-
|<code>NAN</code>
|An indeterminant number, which is a numeric value that is not well-defined, such as <code>0/0</code>. The code name NAN suffers from an unfortunate historic misnaming in that it stands for "Not A Number"; however, it is considered to be a numeric data type, and hence <code>[[IsNumber]](NAN)</code> is true.
|-
|<code>Null</code>
|The result of an operation where the desired data is not there, such as
<code>X[I = '?']</code>, where index <code>I</code> does not have the value <code>'?'</code>
|}

==INF (infinity) ==
[[INF]] is the result of a numerical calculation that is mathematically infinite, such as:
:<code>1/0 &rarr; INF</code>

[[INF]] is also the result of a calculation that would produce a number larger than <code>1.797 x10+308</code>, which is the largest floating point number that Analytica can represent:
:<code>10^1000 &rarr; INF</code>

[[INF]] can be positive or negative:
:<code>-1 <nowiki>*</nowiki> 10^1000 &rarr; -INF</code>
:<code>-1/0  &rarr; -Inf</code>

So -[[INF]] means negative infinity (or a number below <code>-1.796E308</code>).

You can perform useful, mathematically correct arithmetic with [[INF]], such as:
:<code>INF + 10 &rarr; INF </code>
:<code>INF/0 &rarr; INF</code>
:<code>10 - INF &rarr; -INF </code>
:<code>100/0 <nowiki>=</nowiki> INF &rarr; True</code>

==NAN (Not a Number)==
[[NaN]] is the result of an indeterminate numerical calculation, including numerical functions whose parameter is outside their domain, such as"
:<code>INF - INF &rarr; NAN </code>
:<code>0/0 &rarr; NAN</code> 
:<code>INF/INF &rarr; NAN</code>
:<code>Sqrt(-1) &rarr; NAN </code>
:<code>ArcSin(2) &rarr; NAN</code>

(If you enable [[Complex Numbers]], [[Sqrt]](-1) returns the valid imaginary number, ''1j''.)

It usually gives a warning if you apply a function to a parameter value outside its range, such as the two examples above — unless you have checked “Ignore warnings”.

Any arithmetic operation, comparison, or function applied to [[NaN]] returns [[NaN]]: 
:<code>0/0 <> NAN &rarr; NAN</code>

Analytica’s representation and treatment of [[INF]] and [[NaN]] is consistent with ANSI (Association of National Standards Institutes) standards and IEEE Floating point standards. [[NaN]] stands for “Not A Number,” which is a bit misleading, since [[NaN]] really is a kind of number. You can detect [[NaN]] in an expression using the [[IsNaN]]() function.

Calculations performed with [[INF]] and [[NaN]] follow the laws of mathematics:
:<code>1/INF &rarr; 0</code>
:<code>1/(-INF) &rarr; 0</code>
:<code>INF + INF &rarr; INF</code>
:<code>INF - INF &rarr; NAN</code>

Expressions taking [[NaN]] as an operand or parameter give [[NaN]] as their result unless the expression has a well-defined logical or numerical value for any value of [[NaN]]:
:<code>True OR NAN &rarr; True</code>
:<code>NAN AND False &rarr; False</code>
:<code>IF True THEN 5 ELSE NAN &rarr; 5</code>

==Null ==
<code>[[Null]]</code>is a result that is ill-defined, usually indicating that there is nothing at the location requested, for example a subscript using a value that does not match a value of the index:
:<code>Index I := 1..5 </code>
:<code>X[I = 6] &rarr; Null</code>

Other operations and functions that can return [[Null]] include [[Slice]](), [[Subscript]](), [[Subindex]](), and [[MdTable]](), e.g.
:<code>Index Year := [2015, 2016, 2017]</code>
:<code>Slice(Year, 4)  &rarr; NULL</code>
:<code>Variable X := Array(Year, [20, 23, 28])</code>
:<code>X[Year = 2018] &rarr; NULL</code>

You can test for [[Null]] using the standard <nowiki>=</nowiki> or <> operators, such as:
:<code>X[I = 6] <nowiki>=</nowiki> Null &rarr; True</code>

or you can use <code>[[IsNull]](X[I = 6])</code>. However, <code>x=Null</code> and <code>[[IsNull]](x)</code> are different when <code>x</code> may be an array. <code>x=Null</code> is a cell-level comparison, where each cell is tested for equality to Null, with the result having the same dimensionality as <code>x</code>, whereas <code>[[IsNull]](x)</code> tests whether the entire value is exactly [[Null]]. When <code>x</code> is an array where every cell is equal to Null, <code>[[IsNull]](x)</code> is false.

When [[Null]] appears in scalar operations, it generally produces a warning and evaluates to [[Null]], for example:
:<code>10 + Null &rarr; Null</code>
:<code>Null - 10 &rarr; Null</code>
:<code>1 AND Null &rarr; Null</code>

Array-reducing functions ignore [[Null]].  These examples demonstrate (assume <code>A</code> is indexed by <code>I</code> as indicated).

:<code>variable A :=</code>
:{| class="wikitable"
! colspan="5" style="text-align: left;" ! | I &#9654;
|-
!|1
!|2
!|3
!|4
!|5
|-
|8
|Null
|4
|Null
|0
|}

Then

:<code>[[Sum]](A, I) &rarr; 12</code>
:<code>[[Average]](A, I) &rarr; 4</code>
:<code>[[JoinText]](A, I, ', ') &rarr; "8, 4, 0"</code>

Graphs will simply ignore (not show) any point whose value is [[Null]].

Array-reducing functions include [[Sum]](), [[Min]](), [[Max]](), [[ArgMin]](), [[ArgMax]](), [[Product]](), [[Average]](), [[JoinText]](), [[Irr]](), [[Npv]]().  

Array functions [[Sum]](), [[Min]]() and [[Max]]() also accept an optional parameter «IgnoreNaN» to ignore [[NaN]] values (which otherwise propagate, i.e. return [[NaN]]).

[[Regression]]() also ignores any data points which have <code>Y = Null</code>, which is useful for missing data.

==See Also==
* [[INF, NAN, and Null]]
* [[IsNaN]]
* [[IsNull]]
* [[Numbers]]
* [[Error Messages/42652|Errors resulting from Null values]]


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