Help:Calculation


 * The accuracy and format of numeric results varies with the server; even on a single Wikimedia page, while for any rendering there is consistency within the page, there is no consistency among renderings.

The MediaWiki extension ParserFunctions enables users to perform simple mathematical computations.

The expr function evaluates numerical expressions, and also boolean expressions involving numbers and booleans (not strings). The syntax is



The spaces are not needed. Inside numbers no spaces are allowed.

The supported operators (roughly in order of precedence) are not, *, /, div, mod, +, -, round</tt>, =</tt>, &lt;&gt;</tt>, !=</tt>, &lt;=</tt>, &gt;=</tt>, and</tt>, and or</tt>.

Operators
{| cellpadding="6px" border=1 style="border:1px solid #C0C0C0; border-collapse:collapse;" ! Operator ! Operation ! Examples
 * none|| none
 * none|| none

Wrong: ! exp

Compare: ! ln
 * Natural logarithm

Hence, the common logarithm of e.g. 2: ! abs

! trunc ! floor

! ceil ! sin With an angle in degrees, e.g. 30°:

! cos ! tan

! asin ! acos

! atan ! + ! -
 * Unary +</tt> sign
 * Unary -</tt> sign (negation)

! not ! ^
 * Unary NOT, logical NOT
 * Power

! *
 * Multiplication

! / ! div not integer division ! mod
 * Division, same as div
 * Division, same as /,
 * "Modulo",&#160;remainder&#160;of&#160;division after truncating both operands to an integer (PHP operator %).

Caveat, div and mod are different from all programming languages. This has been fixed (but needs to be committed), see bugzilla:6068. ! +</tt>
 * Addition

! -</tt> ! round ! =
 * Subtraction
 * Rounds off the number on the left to the power of 1/10 given on the right (PHP function round)
 * Equality (numerical incl. logical)

! &lt;&gt;
 * Inequality, same as !=

!| != ! &lt;
 * Inequality, same as &lt;&gt;, logical xor
 * Less than

! &gt; ! &lt;=
 * Greater than
 * Less than or equal to

! &gt;= ! and ! or
 * Greater than or equal to
 * Logical AND
 * Logical OR


 * }

The boolean operators consider 0 to be false and any other number to be true. An intermediate or final result "true" is identified with 1. Thus. Note that "and" and "or" work with #expr and #ifexpr only; for use with #if, #ifeq, and #ifexist, use 1 as then-text and 0 as else-text, and combine results with "and" and "or" in an outer #expr or #ifexpr. Instead of we can also use }}. For negation, simply subtract from 1 or interchange then- and else-part.

Precedence:

(+ and - have equal precedence, * and / also, both higher than the former two).



(first +, then =, then <).



(first additions, then round)



(mod and multiplication have equal precedence, evaluation from left to right)

Parentheses can force a different precedence:

Blank spaces are good for readability but not needed for working properly, except between not and an adjacent and/div/mod/not/or/round operator, and within numbers not allowed:



Numbers as input
Leading zeros are allowed, as well as a trailing decimal point (for an integer) and trailing zeros in a number with a decimal point.



These equivalences are also relevant for #ifeq and #switch, see below.

In we have define( 'EXPR_NUMBER_CLASS', '0123456789.' ); ... elseif ( false !== strpos( EXPR_NUMBER_CLASS, $char ) ) { // Number if ( $expecting != 'expression' ) {throw new ExprError('unexpected_number');} // Find the rest of it $length = strspn( $expr, EXPR_NUMBER_CLASS, $p ); // Convert it to float, silently removing double decimal points $operands[] = floatval( substr( $expr, $p, $length ) ); $p += $length;$expecting = 'operator';continue;}

Thus the part of the expression representing a number is a sequence of digits and points; due to floatval a second point and any digits and points immediately after it are ignored, and do not give an error message. Group separators are not allowed: a comma is considered an unrecognised punctuation character:

Thus a number can only consist of one or more digits, or zero or more digits, a point, and zero or more digits. (For the purpose of evaluating an expression a plus or minus sign is considered a unary operator instead of part of the number.)

Canonical form:

Accepted, although in some cases more or less odd: Wrong:

Due to the specifier R ("raw"), etc., i.e. numbers without group separators, which can be used in computations.

As opposed to ParserFunctions, "" accepts points and commas in numbers and interprets them in a site-language-specific way (depending on $separatorTransformTable in Messagesxx.php); on this site:

(on e.g. the German and the Dutch sites reversed w.r.t. the result on English sites).

However, this can be used instead of #ifeq, #ifexpr or #switch only for distinguishing a few site-language-specific categories of numbers (for English: 1 and "not equal to 1", for French <=1 and >1, etc.). Also, since it is designed for linguistic distinction of singular and plural, in some languages the categories of numbers are numerically less useful.

Numbers as output
A non-integer result has a decimal point in it. Scientific notation is produced for numbers with small absolute value (for Wikimedia: less than 1E-4) and for numbers with large absolute value (for Wikimedia: greater than or equal to 1E+12; however, even within Wikimedia there is no uniformity, larger numbers in non-scientific notation and smaller numbers in scientific notation have been observed as output; the format of the same number can vary from preview to view, and by refreshing the page!). Thus numbers produced include (depending on the operating system of the server):



For negative numbers simply a minus sign is prefixed:


 * Long YYYYMMDDhhmmss</tt> timestamps can run into the same problem&#58;


 * Timestamps without seconds are 12 digits, just short enough&#58;

To avoid these problems and also increase accuracy, unless the result is represented by #expr exactly and in non-scientific notation, such as a not too large integer, do not use #expr in an expression to be evaluated by #expr or #ifexpr. Typically the result of a computational template could be needed in a further computation, so at least one version of such a template needs to give the result in a form suitable for that, e.g. and ; for convenience, for the final result another version can be made simply calling the other one and applying #expr to the result, e.g..

Two methods for representing intermediate results are:

1. The expression resulting from processing the expressions themselves, using #expr for branching only.

For example, produces the power of a number in the form of an expression:

However, the expression can get quite long, for see  Help:Calculation/example 1. Although long expressions are allowed, they give rise to a large post-expand include size and template argument size, for which limits exist.

Applying #expr directly on the linked expression gives, but it can also be used in a further computation, unlike the value just mentioned.

2. Writing numbers splitting off factors which are powers of 10 but written plainly.

Example:

Intermediate results are also in such a form, preventing the growth of the expression like above. Again, #expr can be applied directly, as done in , giving, but the result can also be used in a further computation.

Compare:

This uses the same method, but with intermediate application of #expr, giving an error because of internediate results in scientific notation.

If the result of rounding a negative number is zero, the result is "-0". To avoid that, an expression x can be replaced by 0 + ( x ):

The number output is suitable for many other calculation programs, also the scientific notation. In that sense output like 6E23 is more convenient than 6.

Accuracy

 * The accuracy and format of numeric results varies with the operating system of the server. Some remarks in this section are specific for Wikimedia.

Accuracy of the result of #expr is less than internally used within the computation of an expression:


 * (conclusion: 16 or 17 digits of 1234567890.1234567890 used)
 * (result is rounded to a total of 12 digits)
 * (conclusion: 16 or 17 digits of 1234567890.1234567890 used)
 * (result is rounded to a total of 12 digits)
 * (result is rounded to a total of 12 digits)


 * The macheps or smallest x such that 1+x != 1 appears to be near 0.5^53&#160;+&#160;0.5^106</tt> or 1.1102230246251566636831481088739149080825883E- 16 (see above)&#58;


 * That's the normal behaviour for 64=1+52+11 bits (52 mantissa, 11 exponent). As explained above it is unrelated to the smallest expression result greater than 1&#58;
 * below about 1 + 5E- 12.
 * below about 1 + 5E- 12.

Branching depending on an expression
The function #ifexpr produces one of two specified results, depending on the value of a boolean expression involving numbers and booleans (not strings). Examples:


 * yields  because today is Wednesday and so.

Note that rounding errors can affect a result:

Similarly:

Comparisons

 * 1) The function #ifeq: compares numbers and strings for equality (equal if both represent the same number or both are equal strings).
 * 2) The function #switch: compares one string with multiple others, and correspondingly produces one of multiple specified results.




 * Note that #ifeq: unlike #expr: accepts exponential notation on input.
 * Numerical comparisons don't depend on the output format, compare:
 * Note that #ifeq: unlike #expr: accepts exponential notation on input.
 * Numerical comparisons don't depend on the output format, compare:
 * Numerical comparisons don't depend on the output format, compare:
 * Numerical comparisons don't depend on the output format, compare:
 * Numerical comparisons don't depend on the output format, compare:
 * Numerical comparisons don't depend on the output format, compare:
 * Numerical comparisons don't depend on the output format, compare:

ifeq: allows to compare strings containing equal signs:

Length of expressions
To find the absolute value of a numeric expression x without using a separate template at least doubles the length of the expression: (The first is not only shorter but has also the advantage that for substitution one less "subst:" or is needed.)
 * x*(1-2*(</tt>x<0))</tt>
 * x*

Do not use for long expressions as it triples the length.

Similarly do not use mod to round or conversely, because it doubles the length of the expression.

Also providing a leading zero for the result of an expression if it is less than 10 doubles its length:
 * x

This "exponential" growth of expressions, with much repetition, is due to the lack of variables (in the computer programming sense); however, see also VariablesExtension.

Templates (subroutines) provide some of the functionality that variables offer: a template name is comparable with a variable name, while its content is comparable with the value of the variable. Alternatively, a template parameter can be assigned a value which can be used for multiple occurrences of the same parameter in the template. Thus e.g. x*(1-2*(x<0)) with a long expression x can be evaluated avoiding duplication of that expression, in two ways:
 * put the expression x in a template (multiple calls of the same template)
 * put x*(1-2*(x<0)) in a template with parameter x (use of a template with multiple occurrences of the same parameter)

For the the first method does not help, but the second does.

If the number of possible results of a long expression is small, a switch allows arbitrary conversion, including the absolute value and providing a leading zero, etc., without repeating the expression.

Error messages
Examples for all known #expr: and #ifexpr: error messages. The error texts are within the tags &lt;strong class="error">..&lt;/strong>. Note that with the old preprocessor the "=" in "class=error" disturbs the numbering of unnamed parameters, if one of them produces an error message: gives.

Note: copies a given string, here parts of an expression, for the specified times (max. 120), this help page shown on other projects actually evaluate its substituted output like 102 factors "1000" times "180" to get INF (infinity). Wikitext without error message from the parser functions, but typically an error while using or attempting to use them:


 * A crude but informative "unrecognised word" error message can be generated intentionally. Only the first identified error is shown&#58;
 * {&#123;<tt> #expr: 2*</tt>{&#123;<tt> #ifexpr: 3*4>10|toolarge|3*4 </tt>&#125;} &#125;} gives
 * {&#123;<tt> #expr: 2*</tt>{&#123;<tt> #ifexpr: 3*4>10|too large|3*4 </tt>&#125;} &#125;} gives
 * {&#123;<tt> #expr: 2*</tt>{&#123;<tt> #ifexpr: 3*4>10|too large|3*4 </tt>&#125;} &#125;} gives

See also #iferror.

Minus sign
Only the  works as minus sign:

Also many other calculation programs require a hyphen. Therefore, in order to be able to copy rendered numbers and expressions to the edit box or input them through a copy operation into other calculation programs, displayed minus signs also need to be hyphens.

Displaying numbers and numeric expressions
Guidelines such as focus on number display as end product. However, a point of consideration can also be the possibility to apply the rendered output to #expr or #ifexpr, or to input it without conversion into other calculation programs. This would require the following:
 * use digits, not words
 * as mentioned above, use the hyphen as minus sign
 * use *, <=, and >=, not ×, ≤, or ≥
 * do not use thousands separators (however, some programs allow them)
 * use output like 6E23 or 6e23 rather than 6

Examples:

If the number is the result of a computation by MediaWiki and unsuitable for use in a new computation due to application of a formatting function such as #formatnum or a formatting template, one can copy the wikitext and apply the additional computation before the formatting. However, when templates are used, and copying is done to another wiki, these templates have to be copied too, or substituted.