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The functions #expr: and #ifexpr: of MediaWiki extension ParserFunctions evaluate numerical expressions, and also boolean expressions involving numbers and booleans (not strings). The syntax is
: <nowiki>{{ #expr: </nowiki>''expression''<nowiki> }}</nowiki>
Spaces are not needed, except between words (for operators and constants). Inside numbers no grouping separators (spaces, commas, apostrophes) are allowed, the only decimal separator supported is the period (dot, full stop, excluding commas), and currently the only supported digits are the European decimal digits 0-9.

In calculation expressions embedded within templates, be careful when using magic words for date and time elements, such as <code><nowiki>{{CURRENTHOUR}}</nowiki></code> as their return value may be formatted differently on translated pages and will break expressions (instead, use the parser function <code>#time</code> with the appropriate <code>xg</code> flags before each formatting element). Similar errors will occur with some other magic words that return quantities (make sure you include the appropriate ''raw formatting'' flag).

== Operators, numbers, and constants ==
Since literal numbers are of type float, <code>trunc</code> is sometimes used in the examples to construct an integer-type argument, to demonstrate the result of an operator for this case. 

{| class="wikitable sortable"
! ''Operator''
! ''<abbr title="number of arguments">Args</abbr>''
! ''Operation''
! ''PHP''
! ''Data type''
! ''<abbr title="Precedence">Prec</abbr>''
! ''Examples''
|-
| (number) || 0
| unsigned number in ordinary decimal notation (unary plus and minus and e are treated as operators, see elsewhere in this table) || [http://nl.php.net/manual/en/function.floatval.php floatval] || float || n.a.
|
{| class="wikitable"
| {{xpett|1234567890123456789}}
|-
| {{xpett|123456789.0123456789}}
|}

|-
| '''<code>+</code>''' || 1
| [[w:Unary operation#Unary negative and positive|unary '''<code>+</code>''' sign]]
| (nothing) || same as argument || n.a. ||
{| class="wikitable"
{{xpettu|+|1}}
{{xpettu|+|-1}}
{{xpettu|+|trunc1}}
|}

|-
| <code>'''-'''</code> || 1
| [[w:Unary operation#Unary negative and positive|unary '''<code>-</code>''' sign]]  (negation)
| [http://php.net/manual/en/language.operators.arithmetic.php -] || same as argument|| 10 ||
{| class="wikitable"
{{xpettu|-|12}}
{{xpettu|-|trunc12}}
{{xpettu|-|trunc(-2^63)}}
|}

|-
| '''<code>pi</code>''' || 0
| constant [[w:pi|π]] || [http://php.net/manual/en/function.pi.php pi]() || float || n.a.
|
{| class="wikitable"
| {{xpett|pi}}
|}

|-
| '''<code>e</code>''' as subexpression || 0
| constant [[w:e (mathematical constant)|e]] || [http://php.net/manual/en/function.exp.php exp](1) || float || n.a.
|
{| class="wikitable"
| {{xpett|e}}
|}

|-
| '''<code>e</code>''' between subexpressions|| 2 || *10^ || [http://php.net/manual/en/language.operators.arithmetic.php *] [http://php.net/manual/en/function.pow.php pow] (10,..) || float unless the factor on the left is of type integer and the exponent is non-negative and of type integer || 10

|
{| class="wikitable"
{{xpettb|2|e|3}}
{{xpettb|-2.3|e|-4}}
{{xpettb|(trunc2)|e|(trunc-3)}}
{{xpettb|(trunc2)|e|(trunc0)}}
{{xpettb|(trunc2)|e|(trunc18)}}
{{xpettb|(trunc2)|e|(trunc19)}}
{{xpett|6e(5-2)e-2}}
{{xpett|1e.5}}
|}

Wrong:
{| class="wikitable"
|{{xpett|e4}}
|}
|-
| '''<code>exp</code>''' || 1
| [[w:Exponential function|exponential function e<sup>x</sup>]]
| [http://php.net/manual/en/function.exp.php exp] || float || 9 ||
{| class="wikitable"
{{xpettu|exp|43}}
{{xpettu|exp| trunc0}}
{{xpettu|exp|709}}
{{xpettu|exp|-744}}
|}

Compare:
{| class="wikitable"
|{{xpett|e^43}}
|-
|{{xpett|trunc exp43}}
|}
|-
| '''<code>ln</code>''' || 1
| [[w:Natural logarithm|natural logarithm]]
| [http://php.net/manual/en/function.log.php log] || float || 9 ||
{| class="wikitable"
{{xpettu|ln|2}}
{{xpettu|ln| trunc1}}
{{xpettu|ln|8.9e307}}
{{xpettu|ln|.5e-323}}
|}
Hence, the common logarithm of e.g. 2:
{| class="wikitable"
|{{xpett|ln2/ln10}}
|}
|-
| '''<code>abs</code>''' || 1
| [[w:Absolute value|absolute value]]
| [http://php.net/manual/en/function.abs.php abs] || same as argument, but never negative || 9 ||
{| class="wikitable"
{{xpettu|abs|-2}}
{{xpettu|abs| trunc-2}}
{{xpettu|abs| trunc-2^63}}
|}
|-
| '''<code>sqrt</code>''' || 1
| [[w:Square root|square root]]
| [http://php.net/manual/en/function.sqrt.php sqrt] || float || 9 ||
{| class="wikitable"
{{xpettu|sqrt| 4}}
{{xpettu|sqrt| 2}}
{{xpettu|sqrt| 1e19}}
|}
Negative arguments are not permitted:
{| class="wikitable"
{{xpettu|sqrt|-1}}
|}
|-
| '''<code>trunc</code>''' || 1
| [[w:Truncation|truncation]]
| [http://php.net/manual/en/language.types.integer.php#language.types.integer.casting (int)], i.e. [[w:Type conversion|type-casting]] to integer || integer || 9 ||
{| class="wikitable"
{{xpettu|trunc|1.2}}
{{xpettu|trunc|1.8}}
{{xpettu|trunc|-1.2}}
{{xpettu|trunc|(-2^64+1e5)}}
{{xpettu|trunc|(-2^63+1e5)}}
{{xpettu|trunc|(2^63)}}
{{xpettu|trunc|(2^63+1e5)}}
{{xpettu|trunc|(2^64+1e5)}}
|}
|-
| '''<code>floor</code>''' || 1
| [[w:Floor function|floor function]]
| [http://php.net/manual/en/function.floor.php floor] || float || 9 ||
{| class="wikitable"
{{xpettu|floor|1.2}}
{{xpettu|floor|-1.2}}
{{xpettu|floor| trunc3}}
|}
|-
| '''<code>ceil</code>''' || 1
| [[w:Ceiling function|ceiling function]]
| [http://php.net/manual/en/function.ceil.php ceil] || float || 9 ||
{| class="wikitable"
{{xpettu|ceil|1.2}}
{{xpettu|ceil|-1.2}}
{{xpettu|ceil| trunc3}}
|}
|-
| '''<code>sin</code>''' || 1
| [[w:Sine function|sine]]
| [http://php.net/manual/en/function.sin.php sin] || float || 9 ||
{| class="wikitable"
{{xpettu|sin|.1}}
{{xpettu|sin| trunc1}}
|}
With an angle in degrees, e.g. 30°:
{| class="wikitable"
|{{xpett|sin(30*pi/180)}}
|}
|-
| '''<code>cos</code>''' || 1
| [[w:Cosine function|cosine]]
| [http://php.net/manual/en/function.cos.php cos] || float || 9 ||
{| class="wikitable"
{{xpettu|cos|.1}}
{{xpettu|cos| trunc1}}
|}
|-
| '''<code>tan</code>''' || 1
| [[w:Tangent function|tangent]]
| [http://php.net/manual/en/function.tan.php tan] || float || 9 ||
{| class="wikitable"
{{xpettu|tan|.1}}
{{xpettu|tan| trunc1}}
|}
|-
| '''<code>asin</code>''' || 1
| [[w:Arcsine|arcsine]]
| [http://php.net/manual/en/function.asin.php asin] || float || 9 ||
{| class="wikitable"
{{xpettu|asin|.1}}
{{xpettu|asin| trunc1}}
|}
|-
| '''<code>acos</code>''' || 1
| [[w:Arccosine|arccosine]]
| [http://php.net/manual/en/function.acos.php acos] || float || 9 ||
{| class="wikitable"
{{xpettu|acos|.1}}
{{xpettu|acos| trunc1}}
{{xpettu|2*|acos 0}}
|}
|-
| '''<code>atan</code>''' || 1
| [[w:Arctangent|arctangent]]
| [http://php.net/manual/en/function.atan.php atan] || float || 9 ||
{| class="wikitable"
{{xpettu|atan|.1}}
{{xpettu|atan| trunc1}}
{{xpettu|4*|atan 1}} 
|}
|-
| '''<code>not</code>''' || 1
| [[w:Negation|negation]], logical NOT
| [http://www.php.net/manual/en/language.operators.logical.php !] || integer (1 or 0) || 9 ||
{| class="wikitable"
{{xpettu|not|0}}
{{xpettu|not|1}}
{{xpettu|not|2}}
{{xpettu|not| trunc1}}
|}
|-
| '''<code>^</code>''' || 2
| [[w:Exponentiation|exponentiation]] (power)
| [http://php.net/manual/en/function.pow.php pow] || float unless the base is of type integer and the exponent is non-negative and of type integer || 8 ||
{| class="wikitable"
{{xpettb|2|^|3}}
{{xpettb|-2|^|3}}
{{xpettb|-2|^|4}}
{{xpettb|(trunc2)|^|(trunc-3)}}
{{xpettb|(trunc2)|^|(trunc0)}}
{{xpettb|(trunc2)|^|(trunc62)}}
{{xpettb|(trunc2)|^|(trunc63)}}
{{xpettb|(-2)|^|1.2}}
{{xpettb|(-2)|^|.5}}
|}
|-
| '''<code>*</code>''' || 2
| [[w:Multiplication|multiplication]]
| [http://php.net/manual/en/language.operators.arithmetic.php *] || integer if both arguments are integer, otherwise float || 7 ||
{| class="wikitable"
{{xpettb|2|*|3}}
{{xpettb|(trunc2)|*|3}}
{{xpettb|2|*|trunc3}}
{{xpettb|(trunc2)|*|trunc3}}
{{xpettb|(trunc1e10)|*|trunc1e9}}
|}
|-
| '''<code>/</code>''' (also written '''div''') || 2
|| [[w:Division (mathematics)|division]] (div is not integer division<ref name="divmod">'''<code>div</code>''' and '''<code>mod</code>''' are different from all programming languages, see [[phab:T8068]]</ref>)
| [http://php.net/manual/en/language.operators.arithmetic.php /] || float, unless both arguments are integer and the mathematical result is an integer || 7 ||
{| class="wikitable"
{{xpettb|6|/|3}}
{{xpettb|(trunc6)|/|3}}
{{xpettb|2|/|trunc6}}
{{xpettb|(trunc6)|/|trunc3}}
{{xpettb|(trunc6)|/|trunc4}}
|}
|-
| '''<code>mod</code>''' || 2
| [[w:Modulo operation|modulo]] operation,&#160;remainder&#160;of&#160;division after truncating both operands to an integer.<ref name="divmod"/>
| [http://php.net/manual/en/language.operators.arithmetic.php %] || integer || 7 ||
{| class="wikitable"
{{xpettb|30|mod|7}}
{{xpettb|-30|mod|7}}
{{xpettb|30|mod|-7}}
{{xpettb|-30|mod|-7}}
{{xpettb|30.5|mod|7.9}}
|}

May give unexpected results for some values of the second argument (see [[#Limitations and workarounds|this section]]):
{| class="wikitable"
{{xpettb|123|mod|2^64}}
|}
|-
| '''<code>fmod</code>''' || 2
| [[w:Modulo operation|modulo]] operation, floating point.  Returns first argument after subtracting an integer multiple of the second argument.
| [https://www.php.net/manual/en/function.fmod.php fmod] || float|| 7 ||
{| class="wikitable"
{{xpettb|5.7|fmod|1.3}}
{{xpettb|99.9|fmod|60}}
{{xpettb|2.99|fmod|1}}
{{xpettb|-2.99|fmod|1}}
{{xpettb|2.99|fmod|-1}}
{{xpettb|-2.99|fmod|-1}}
|}
|-
| '''<code>+</code>''' || 2
|| [[w:Addition|addition]]
| [http://php.net/manual/en/language.operators.arithmetic.php +] || integer if both arguments are integer, otherwise float || 6 ||
{| class="wikitable"
{{xpettb|2|+|3}}
{{xpettb|(trunc2)|+|3}}
{{xpettb|2|+|trunc3}}
{{xpettb|(trunc2)|+|trunc3}}
{{xpettb|(trunc7e18)|+|trunc4e18}}
|}
|-
| '''<code>-</code>''' || 2
|| [[w:Subtraction|subtraction]]
| [http://php.net/manual/en/language.operators.arithmetic.php -] || integer if both arguments are integer, otherwise float || 6 ||
{| class="wikitable"
{{xpettb|3|-|2}}
{{xpettb|(trunc3)|-|2}}
{{xpettb|2|-|trunc2}}
{{xpettb|(trunc3)|-|trunc2}}
{{xpettb|(trunc-7e18)|-|trunc4e18}}
|}
|-
| '''<code>round</code>''' || 2
|| [[w:rounding|rounds off]] the number on the left to a multiple of 1/10 raised to a power, with the exponent equal to the truncated value of the number given on the right 
| [http://php.net/manual/en/function.round.php round] || float || 5 ||
{| class="wikitable"
{{xpettb|9.876|round|2}}
{{xpettb|(trunc1234)|round| trunc-2}}
{{xpettb|4.5|round|0}}
{{xpettb|-4.5|round|0}}
{{xpettb|46.857|round|1.8}}
{{xpettb|46.857|round|-1.8}}
|}
|-
| '''<code>=</code>''' || 2
|| [[w:Equality (mathematics)|equality]] (numerical incl. logical, not for strings)
| [http://php.net/manual/en/language.operators.comparison.php ==] || integer (1 or 0) || 4 ||
{| class="wikitable"
{{xpettb|3.0|{{=}}|3}}
{{xpettb|3.1|{{=}}|3}}
{{xpettb|3.0|{{=}}|trunc3}}
{{xpettb|3.1|{{=}}|trunc3}}
{{xpettb|1e16|{{=}}|trunc(1e16)}}
{{xpettb|1e16|{{=}}|trunc(1e16)+trunc1}}
{{xpettb|trunc(1e16)|{{=}}|trunc(1e16)+trunc1}}
|}

wrong:
{| class="wikitable"
|{{xpett|a{{=}}a}}
|}
|-
| '''<code>&lt;&gt;</code>''' (also written '''!=''') || 2
| [[w:Inequality|inequality]], logical ''xor'';  not for strings  (negation of =)
| [http://php.net/manual/en/language.operators.comparison.php !=] || integer (1 or 0) || 4 ||
{| class="wikitable"
{{xpettb|3|<>|3}}
{{xpettb|3|<>|4}}
|}

|-
| '''<code>&lt;</code>''' || 2
|| [[w:Inequality (mathematics)|less than]] (not for ordering of strings)
| [http://php.net/manual/en/language.operators.comparison.php <] || integer (1 or 0) || 4 ||
{| class="wikitable"
{{xpettb|3|<|3}}
{{xpettb|3|<|4}}
{{xpettb|2.9|<|3}}
{{xpettb|3.0|<|3}}
{{xpettb|2.9|<|trunc3}}
{{xpettb|3.0|<|trunc3}}
{{xpettb|1e16|<|trunc(1e16)+trunc1}}
|}

wrong:
{| class="wikitable"
{{xpettb|a|<|b}}
|}
|-
| '''<code>&gt;</code>''' || 2
|| [[w:Inequality (mathematics)|greater than]] (same as <, with arguments reversed)
| [http://php.net/manual/en/language.operators.comparison.php >] || integer (1 or 0) || 4 ||
{| class="wikitable"
{{xpettb|4|>|3}}
{{xpettb|3|>|3}}
|}
|-
| '''<code>&lt;=</code>''' || 2
| [[w:Inequality (mathematics)|less than or equal to]] (same as >=, with arguments reversed)
| [http://php.net/manual/en/language.operators.comparison.php <=] || integer (1 or 0) || 4 ||
{| class="wikitable"
{{xpettb|3|<{{=}}|4}}
{{xpettb|3|<{{=}}|3}}
|}
|-
| '''<code>&gt;=</code>''' || 2
| [[w:Inequality (mathematics)|greater than or equal to]] (negation of <)
| [http://php.net/manual/en/language.operators.logical.php >=] || integer (1 or 0) || 4 ||
{| class="wikitable"
{{xpettb|4|>{{=}}|3}}
{{xpettb|3|>{{=}}|3}}
|}
|-
| '''<code>and</code>''' || 2
| [[w:Logical conjunction|logical AND]]
| [http://php.net/manual/en/language.operators.logical.php &&] || integer (1 or 0) || 3 ||
{| class="wikitable"
{{xpettb|3|and|4}}
{{xpettb|-3|and|0}}
{{xpettb|0|and|4}}
{{xpettb|0|and|0}}
|}
|-
| '''<code>or</code>''' || 2
| [[w:Logical disjunction|logical OR]]
| [http://php.net/manual/en/language.operators.logical.php <nowiki>||</nowiki>] || integer (1 or 0) || 2 ||
{| class="wikitable"
{{xpettb|3|or|4}}
{{xpettb|-3|or|0}}
{{xpettb|0|or|4}}
{{xpettb|0|or|0}}
|}
|}

The logical operators <code>and</code>, <code>or</code>, and <code>not</code> interpret an input value of 0 as false and any other number as true, and return 0 for a false result and 1 for true. These output values also apply to the relation operators; thus <code><nowiki>{{#expr: (2 < 3) + 1}}</nowiki></code> gives {{#expr: (2 < 3) + 1}}.

To use <code>and</code>, <code>or</code>, and <code>not</code> in <code>#if</code>, <code>#ifeq</code>, or <code>#ifexist</code> contexts, one can use 1 as then-text (true case) and 0 as else-text (false case), then combine the results with the logical operators provided by <code>#expr</code> or <code>#ifexpr</code>. Note that negation can also be achieved by subtracting the result from 1 (inside of <code>#expr</code> or <code>#ifexpr</code>) or by simply switching the then- and else-text(s) of <code>#if</code> <code>#ifeq</code> <code>#ifexists</code> or <code>#ifexpr</code>. Also, note that the construct <code><nowiki>{{#expr: {{#if:{{{a|}}}|1|0}} or {{#if:{{{b|}}}|1|0}} }}</nowiki></code> is equivalent to the simpler <code><nowiki>{{#if:{{{a|}}}{{{b|}}}|1|0}}}}</nowiki></code>.

Precedence is indicated in the "Prec" column above, a higher number means that the operator is applied earlier. Examples (">" refers to going before, "~" means application from left to right):
* <code>e</code> > <code>floor</code>, <code>not</code>, etc.: {{xpsoc|#expr:floor1.5e1}}, {{xpsoc|#expr:not0e1}} 
* <code>floor</code> > <code>^</code>: {{xpsoc|#expr:floor1.5^2}} 
* <code>^</code> > <code>*</code>: {{xpsoc|#expr:2*3^2}} 
* <code>*</code> ~ <code>/</code> ~ <code>mod</code>: {{xpsoc|#expr:12/3*2}}, {{xpsoc|#expr:111/3mod10}}, {{xpsoc|#expr:358mod10*2}}, 
* <code>*</code> > <code>+</code>, <code>-</code>: {{xpsoc|#expr:2+3*4}}, {{xpsoc|#expr:2-3*4}}
* <code>+</code> ~ <code>-</code>: {{xpsoc|#expr:6-2+3}}, {{xpsoc|#expr:-2+3}}
* <code>+</code>, <code>-</code> > <code>round</code>: {{xpsoc|#expr:1.234round2-1}}
* <code>round</code> > <code>=</code> etc.: {{xpsoc|1=#expr:1.23=1.234round2}}
* <code>=</code> etc. > <code>and</code>: {{xpsoc|1=#expr:1 and 2=1}}
* <code>and</code> > <code>or</code>: {{xpsoc|1=#expr:1 or 1 and 0}}

In the case of equal precedence number, evaluation is from left to right:
*{{xpsoc|#expr:12/2*3}}
*{{xpsoc|#expr:3^3^3}}

Parentheses can force a different precedence: {{xpsoc|#expr:(2+3)*4}}

Blank spaces are good for readability but not needed for working properly, except between words (including "<code>e</code>"), and not allowed within numbers:
*{{xpd0|d=|#expr:7mod3}}
*{{xpd0|d=|#expr:7.5round0}}
*{{xpd0|d=|#expr:0and1}}
*{{xpd0|d=|#expr:0or not0}}
*{{xpd0|d=|#expr:0ornot0}}
*{{xpd0|d=|#expr:123 456}}
*{{xpd0|d=|#expr:not not3}}
*{{xpd0|d=|#expr:notnot3}}

*{{xpd0|d=|#expr:---2}}
*{{xpd0|d=|#expr:-+-2}}
*{{xpd0|d=|#expr:2*-3}}
*{{xpd0|d=|#expr:-not-not-not0}}
*{{xpd0|d=|#expr:2*/3}}
*{{xpd0|d=|#expr:sinln1.1}}
*{{xpd0|d=|#expr:sin ln1.1}}

For scientific notation <code>e</code> is treated as an operator. An <code>e</code> between subexpressions works just like <code>*10^</code>, except that together with the unary minus it has the highest precedence (e.g., before a separate <code>^</code>), and that the implicit 10 is of type integer, not float. An <code>e</code> as subexpression (i.e., with each side either nothing or an operator) is [[w:Euler's constant|Euler's constant]]. An <code>e</code> with nothing or an operator on one side and a subexpression on the other gives an error message.

=== Rounding operators ===
{{hatnote|See also [[Manual:Rounding numbers]] for some more examples}}
The following rounding operators are supported:

* Uniformly distributed around 0 and [[w:Strict|non-strictly]] [[w:monotonic|monotonic function]]:
** ceil
** floor

* Symmetric with respect to 0 and non-strictly monotonic on each side of 0:
** trunc
** round

* Otherwise related to 0 and periodic on each side of 0:
** mod

==== Trunc ====
Trunc converts a float to an integer by cutting off the decimal part. For values in the range <code>2^63 ≤ x ≤ 2^64</code>, it returns <code>x - 2^64</code>. Values larger than <code>2^64</code> returns <code>0</code>, and values less than <code>-2^63</code> returns <code>-2^63</code>.

See the below examples:
*{{xpsoc|#expr:trunc(-2*2^63-2^12)}}
*{{xpsoc|#expr:trunc(-2*2^63+2^12)}}
*{{xpsoc|#expr:trunc(-1*2^63-2^12)}}
*{{xpsoc|#expr:trunc(-1*2^63+2^12)}}
*{{xpsoc|#expr:trunc(0*2^63-2^12)}}
*{{xpsoc|#expr:trunc(0*2^63+2^12)}}
*{{xpsoc|#expr:trunc(1*2^63-2^12)}}
*{{xpsoc|#expr:trunc(1*2^63+2^12)}}
*{{xpsoc|#expr:trunc(2*2^63-2^12)}}
*{{xpsoc|#expr:trunc(2*2^63+2^12)}}
*{{xpsoc|#expr:trunc(2^64+1024)}}
*{{xpsoc|#expr:trunc(3*2^63-2^12)}}
*{{xpsoc|#expr:trunc(3*2^63+2^12)}}

Converting a number to an integer type ensures precise display without rounding to 14 decimal places.

x is truncated, <code>x = trunc x</code>, if it is an integer or a floating-point number representing an integer value.

The expression <code>p mod 0</code> results in an error message when used in MediaWiki, not the PHP operator %:

*{{xpsoc|#expr:-27mod0}}

In PHP, when using the % operator, if <code>p % 0</code> is calculated and conditions are met where <code>0 < |q| < 1</code> and <code>q >= 2^64</code>, the result is an empty string.

* <code><nowiki>{{formatnum:{{#expr:-123 mod .9}}}}</nowiki></code> → {{formatnum:{{#expr:-123 mod .9}}}}
* <code><nowiki>{{formatnum:{{#expr:-123 mod -.9}}}}</nowiki></code> → {{formatnum:{{#expr:-123 mod -.9}}}}
* <code><nowiki>{{formatnum:{{#expr:-123 mod (2^64)}}}}</nowiki></code> → {{formatnum:{{#expr:-123 mod (2^64)}}}}
* <code><nowiki>{{formatnum:{{#expr:-123 mod 1e20}}}}</nowki> → {{formatnum:{{#expr:-123 mod 1e20}}}}
* Compare:
** <nowki>{{formatnum:{{#expr:-123 mod (2^64-2048)}}}}</nowiki></code> → {{formatnum:{{#expr:-123 mod (2^64-2048)}}}}

==== Floor and ceil ====
When using '''floor or '''ceil''' with an integer, it's first converted to a floating-point number before the function is applied.

*{{xpsoc|numf|floor (trunc1e17+trunc1)}}
*{{xpsoc|numf|ceil (trunc1e17+trunc1)}}

Use [[Template:Floor]] and [[Template:Ceil]] to get in such a case the integer-type expression for the exact result:

*<code><nowiki>{{numf|{{floortrunc1e17+trunc1}}}}</nowiki></code> → {{numf|{{floor|trunc1e17+trunc1}}}}
*<code><nowiki>{{numf|{{ceil|trunc1e17+trunc1}}}}</nowiki></code> → {{numf|{{ceil|trunc1e17+trunc1}}}}

To check whether the internal result of an expression x is mathematically an integer one can simply test "(x) = floor (x)", or similarly with ceil (not with trunc because for large floats we would get false negatives, and not with round0, because for odd numbers between 2^52 and 2^53, we would get false negatives).

==== Safety margins ====
To round an integer x down to the nearest multiple of 7, you can do the following:

* 7*((x-3)/7 round 0)
* 7*floor((x+.5)/7)
* 7*ceil((x-6.5)/7)

To round x to the nearest multiple of 7, you can do the following:

* 7*((x/7) round 0)
* 7*floor((x+3.5)/7)
* 7*ceil((x-3.5)/7)

In these cases, the sign of x doesn't matter, even for rounding, because the value is never exactly halfway between integers. 
All methods provide the same safety margin of 0.5 in x, or 1/14 after dividing by 7, to allow for rounding errors.

{{Note|type=reminder|text=For any real value of x, the difference between the two problems is equivalent to a shift in x by 3.5. However, in this case with integer x values, the shift is 3.}}

=== Precedence ===
Additions before round:
* {{Xpd|#expr:1.234 + 1.234 round 1 + 1}}

Modulo and multiplication operations have equal precedence and they are evaluated from left-to-right:
* {{Xpd|#expr:3 * 4 mod 10 * 10}}

When using spaces in expressions with precedence, the layout can sometimes be confusing:
* {{Xpd|#expr:23+45 mod 10}}

Instead, you can write:
* {{Xpd|#expr:23 + 45 mod10}}

Or you can parenthesis:
* {{Xpd|#expr:23 + (45 mod 10)}}

== Related ==
* [http://meta.wikimedia.org/wiki/Help:Calculation Meta's Help:Calculation]

== References ==
<references />

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[[Category:Help]]