Help:Calculation

The accuracy and format of numeric results varies with the server; even on a single 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 calculations, for simple arithmetic or for functions as on a scientific calculator, with rounding, floor, logarithms (ln), sine, cosine, or modulo (etc.), plus boolean comparisons with "=" or "<" or ">=" etc.

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

{{ #expr: expression }} - Spaces are not required, but spaces/commas within numbers are not allowed.

The supported operators (roughly in order of precedence) are: not, ^, *, /, div, mod, +, -, round, trunc, =, <>, !=, <=, >=, and, and or. Functions include: abs( ), ceil( ), floor( ), ln( ), sin( ), cos( ), tan( ), etc.

The precision supports 14-digit numbers (pi: {{#expr:pi}}, or longer on some servers) and E-notation ("1.54E17"), but truncation error can cause mismatches on comparisons of very large numbers or tiny decimals, so see below: "Tactics for handling extreme numbers".

Operators

Operator Operation Examples

none

Template:Xpd/wl\|#expr:123456789012345}}}}"	"{{#expr:123456789012345}}" {{#ifeq:	}} [1]
Template:Xpd/wl\|#expr:1.23456789012345}}}}"	"{{#expr:1.23456789012345}}" {{#ifeq:	}} [2]
Template:Xpd/wl\|#expr:.000001}}}}"	"{{#expr:.000001}}" {{#ifeq:	}} [3]
Template:Xpd/wl\|#expr:.00000123456789012345}}}}"	"{{#expr:.00000123456789012345}}" {{#ifeq:	}} [4]
Template:Xpd/wl\|#expr:.123e4}}}}"	"{{#expr:.123e4}}" {{#ifeq:	}} [5]
Template:Xpd/wl\|#expr:123E-2}}}}"	"{{#expr:123E-2}}" {{#ifeq:	}} [6]
Template:Xpd/wl\|#expr:e}}}}"	"{{#expr:e}}" {{#ifeq:	}} [7]
Template:Xpd/wl\|#expr:pi}}}}"	"{{#expr:pi}}" {{#ifeq:	}} [8]

Wrong:

Template:Xpd/wl\|#expr:e4}}}}"	"{{#expr:e4}}" {{#ifeq:				}} [9]

exp

e to the specified power

Template:Xpd/wl\|#expr:exp1.2}}}}"	"{{#expr:exp1.2}}" {{#ifeq:				}} [10]

Compare:

Template:Xpd/wl\|#expr:e^1.2}}}}"	"{{#expr:e^1.2}}" {{#ifeq:				}} [11]

ln

Natural logarithm

Template:Xpd/wl\|#expr:ln2}}}}"	"{{#expr:ln2}}" {{#ifeq:				}} [12]

Hence, the base ten logarithm of e.g. 2:

Template:Xpd/wl\|#expr:ln2/ln10}}}}"	"{{#expr:ln2/ln10}}" {{#ifeq:				}} [13]

abs

Template:Xpd/wl\|#expr:abs-1.2}}}}"	"{{#expr:abs-1.2}}" {{#ifeq:				}} [14]

trunc

Template:Xpd/wl\|#expr:trunc1.2}}}}"	"{{#expr:trunc1.2}}" {{#ifeq:				}} [15]
Template:Xpd/wl\|#expr:trunc-1.2}}}}"	"{{#expr:trunc-1.2}}" {{#ifeq:				}} [16]

floor

Template:Xpd/wl\|#expr:floor1.2}}}}"	"{{#expr:floor1.2}}" {{#ifeq:				}} [17]
Template:Xpd/wl\|#expr:floor-1.2}}}}"	"{{#expr:floor-1.2}}" {{#ifeq:				}} [18]

ceil

Template:Xpd/wl\|#expr:ceil1.2}}}}"	"{{#expr:ceil1.2}}" {{#ifeq:				}} [19]
Template:Xpd/wl\|#expr:ceil-1.2}}}}"	"{{#expr:ceil-1.2}}" {{#ifeq:				}} [20]

sin

Template:Xpd/wl\|#expr:sin.1}}}}"	"{{#expr:sin.1}}" {{#ifeq:				}} [21]

With an angle in degrees, e.g. 30°:

Template:Xpd/wl\|#expr:sin(30*pi/180)}}}}"	"{{#expr:sin(30*pi/180)}}" {{#ifeq:				}} [22]

cos

Template:Xpd/wl\|#expr:cos.1}}}}"	"{{#expr:cos.1}}" {{#ifeq:				}} [23]

tan

Template:Xpd/wl\|#expr:tan.1}}}}"	"{{#expr:tan.1}}" {{#ifeq:				}} [24]

asin

Template:Xpd/wl\|#expr:asin.1}}}}"	"{{#expr:asin.1}}" {{#ifeq:				}} [25]

acos

Template:Xpd/wl\|#expr:acos.1}}}}"	"{{#expr:acos.1}}" {{#ifeq:				}} [26]

atan

Template:Xpd/wl\|#expr:atan.1}}}}"	"{{#expr:atan.1}}" {{#ifeq:				}} [27]

+

Unary + sign

Template:Xpd/wl\|#expr:+12}}}}"	"{{#expr:+12}}" {{#ifeq:	}} [28]
Template:Xpd/wl\|#expr:++12}}}}"	"{{#expr:++12}}" {{#ifeq:	}} [29]
Template:Xpd/wl\|#expr:+-12}}}}"	"{{#expr:+-12}}" {{#ifeq:	}} [30]

-

Unary - sign (negation)

Template:Xpd/wl\|#expr:-12}}}}"	"{{#expr:-12}}" {{#ifeq:	}} [31]
Template:Xpd/wl\|#expr:-+12}}}}"	"{{#expr:-+12}}" {{#ifeq:	}} [32]
Template:Xpd/wl\|#expr:--12}}}}"	"{{#expr:--12}}" {{#ifeq:	}} [33]

not

Unary NOT, logical NOT

Template:Xpd/wl\|#expr:not 0}}}}"	"{{#expr:not 0}}" {{#ifeq:	}} [34]
Template:Xpd/wl\|#expr:not 1}}}}"	"{{#expr:not 1}}" {{#ifeq:	}} [35]
Template:Xpd/wl\|#expr:not 2}}}}"	"{{#expr:not 2}}" {{#ifeq:	}} [36]

^

Power

Template:Xpd/wl\|#expr:2^7}}}}"	"{{#expr:2^7}}" {{#ifeq:	}} [37]
Template:Xpd/wl\|#expr:2^-7}}}}"	"{{#expr:2^-7}}" {{#ifeq:	}} [38]
Template:Xpd/wl\|#expr:(-2)^7}}}}"	"{{#expr:(-2)^7}}" {{#ifeq:	}} [39]
Template:Xpd/wl\|#expr:(-2)^8}}}}"	"{{#expr:(-2)^8}}" {{#ifeq:	}} [40]
Template:Xpd/wl\|#expr:2^1.2}}}}"	"{{#expr:2^1.2}}" {{#ifeq:	}} [41]
Template:Xpd/wl\|#expr:2^.5}}}}"	"{{#expr:2^.5}}" {{#ifeq:	}} [42]
Template:Xpd/wl\|#expr:(-2)^1.2}}}}"	"{{#expr:(-2)^1.2}}" {{#ifeq:	}} [43]
Template:Xpd/wl\|#expr:(-2)^.5}}}}"	"{{#expr:(-2)^.5}}" {{#ifeq:	}} [44]

*

Multiplication

Template:Xpd/wl\|#expr:30*7}}}}"	"{{#expr:30*7}}" {{#ifeq:				}} [45]
Template:Xpd/wl\|#expr:30*-7}}}}"	"{{#expr:30*-7}}" {{#ifeq:				}} [46]

/

Division, same as div

Template:Xpd/wl\|#expr:30/7}}}}"	"{{#expr:30/7}}" {{#ifeq:				}} [47]
Template:Xpd/wl\|#expr:30/-7}}}}"	"{{#expr:30/-7}}" {{#ifeq:				}} [48]

div

Division, same as /,
not integer division

Template:Xpd/wl\|#expr:30 div 7}}}}"	"{{#expr:30 div 7}}" {{#ifeq:				}} [49] (should be 4)

mod

"Modulo", remainder of 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.

Template:Xpd/wl\|#expr:30 mod 7}}}}"	"{{#expr:30 mod 7}}" {{#ifeq:	}} [50]
Template:Xpd/wl\|#expr:30 mod -7}}}}"	"{{#expr:30 mod -7}}" {{#ifeq:	}} [51]
Template:Xpd/wl\|#expr:-30 mod 7}}}}"	"{{#expr:-30 mod 7}}" {{#ifeq:	}} [52]
Template:Xpd/wl\|#expr:-30 mod -7}}}}"	"{{#expr:-30 mod -7}}" {{#ifeq:	}} [53]
Template:Xpd/wl\|#expr:-8 mod -3}}}}"	"{{#expr:-8 mod -3}}" {{#ifeq:	}} [54]
Template:Xpd/wl\|#expr:-8 mod 2.9}}}}"	"{{#expr:-8 mod 2.9}}" {{#ifeq:	}} [55] (should be 2.6)
Template:Xpd/wl\|#expr:-8 mod 3.2}}}}"	"{{#expr:-8 mod 3.2}}" {{#ifeq:	}} [56] (should be 1.6)
Template:Xpd/wl\|#expr:8.9 mod 3}}}}"	"{{#expr:8.9 mod 3}}" {{#ifeq:	}} [57] (should be 2.9)

+

Addition

Template:Xpd/wl\|#expr:30 + 7}}}}"	"{{#expr:30 + 7}}" {{#ifeq:				}} [58]

-

Subtraction

Template:Xpd/wl\|#expr:30 - 7}}}}"	"{{#expr:30 - 7}}" {{#ifeq:				}} [59]

round

Rounds off the number on the left to the power of 1/10 given on the right (PHP function round)

Template:Xpd/wl\|#expr:4.2857 round 3}}}}"	"{{#expr:4.2857 round 3}}" {{#ifeq:	}} [60]
Template:Xpd/wl\|#expr:4.2857 round 0}}}}"	"{{#expr:4.2857 round 0}}" {{#ifeq:	}} [61]
Template:Xpd/wl\|#expr:42857 round -2}}}}"	"{{#expr:42857 round -2}}" {{#ifeq:	}} [62]
Template:Xpd/wl\|#expr:4.5 round 0}}}}"	"{{#expr:4.5 round 0}}" {{#ifeq:	}} [63]
Template:Xpd/wl\|#expr:-4.5 round 0}}}}"	"{{#expr:-4.5 round 0}}" {{#ifeq:	}} [64]

=

Equality (numerical incl. logical)

Template:Xpd/wl\|#expr:3=03.0}}}}"	"{{#expr:3=03.0}}" {{#ifeq:				}} [65]

<>

Inequality, same as !=

Template:Xpd/wl\|#expr:3<>03.0}}}}"	"{{#expr:3<>03.0}}" {{#ifeq:				}} [66]
Template:Xpd/wl\|#expr:3<>4}}}}"	"{{#expr:3<>4}}" {{#ifeq:				}} [67]

!=

Inequality, same as <>, logical xor

Template:Xpd/wl\|#expr:3!=03.0}}}}"	"{{#expr:3!=03.0}}" {{#ifeq:				}} [68]
Template:Xpd/wl\|#expr:3!=4}}}}"	"{{#expr:3!=4}}" {{#ifeq:				}} [69]

<

Less than

Template:Xpd/wl\|#expr:3<2}}}}"	"{{#expr:3<2}}" {{#ifeq:	}} [70]
Template:Xpd/wl\|#expr:3<3}}}}"	"{{#expr:3<3}}" {{#ifeq:	}} [71]
Template:Xpd/wl\|#expr:3<4}}}}"	"{{#expr:3<4}}" {{#ifeq:	}} [72]

>

Greater than

Template:Xpd/wl\|#expr:3>2}}}}"	"{{#expr:3>2}}" {{#ifeq:	}} [73]
Template:Xpd/wl\|#expr:3>3}}}}"	"{{#expr:3>3}}" {{#ifeq:	}} [74]
Template:Xpd/wl\|#expr:3>4}}}}"	"{{#expr:3>4}}" {{#ifeq:	}} [75]

<=

Less than or equal to

Template:Xpd/wl\|#expr:3<=2}}}}"	"{{#expr:3<=2}}" {{#ifeq:	}} [76]
Template:Xpd/wl\|#expr:3<=3}}}}"	"{{#expr:3<=3}}" {{#ifeq:	}} [77]
Template:Xpd/wl\|#expr:3<=4}}}}"	"{{#expr:3<=4}}" {{#ifeq:	}} [78]

>=

Greater than or equal to

Template:Xpd/wl\|#expr:3>=2}}}}"	"{{#expr:3>=2}}" {{#ifeq:	}} [79]
Template:Xpd/wl\|#expr:3>=3}}}}"	"{{#expr:3>=3}}" {{#ifeq:	}} [80]
Template:Xpd/wl\|#expr:3>=4}}}}"	"{{#expr:3>=4}}" {{#ifeq:	}} [81]

and

Logical AND

Template:Xpd/wl\|#expr:3 and 4}}}}"	"{{#expr:3 and 4}}" {{#ifeq:	}} [82]
Template:Xpd/wl\|#expr:0 and 3}}}}"	"{{#expr:0 and 3}}" {{#ifeq:	}} [83]
Template:Xpd/wl\|#expr:-3 and 0}}}}"	"{{#expr:-3 and 0}}" {{#ifeq:	}} [84]
Template:Xpd/wl\|#expr:0 and 0}}}}"	"{{#expr:0 and 0}}" {{#ifeq:	}} [85]

or

Logical OR

Template:Xpd/wl\|#expr:3 or 4}}}}"	"{{#expr:3 or 4}}" {{#ifeq:	}} [86]
Template:Xpd/wl\|#expr:0 or 3}}}}"	"{{#expr:0 or 3}}" {{#ifeq:	}} [87]
Template:Xpd/wl\|#expr:-3 or 0}}}}"	"{{#expr:-3 or 0}}" {{#ifeq:	}} [88]
Template:Xpd/wl\|#expr:0 or 0}}}}"	"{{#expr:0 or 0}}" {{#ifeq:	}} [89]

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 "{{{{#if:|Template:Xpd/wl|#expr: (2 < 3) + 1}}}}" gives "{{#expr: (2 < 3) + 1}}" {{#ifeq:{{{gives}}}||||||}} [90]. 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 {{ #expr: {{#if:{{{a}}}|1|0}} or {{#if:{{{b}}}|1|0}} }} we can also use {{#if:{{{a}}}{{{b}}}|1|0}}}}. For negation, simply subtract from 1 or interchange then- and else-part.

Precedence:

"{{{{#if:|Template:Xpd/wl|#expr: 2 - 3 + 4 / 5 * 6}}}}" gives "{{#expr: 2 - 3 + 4 / 5 * 6}}" {{#ifeq:{{{gives}}}||||||}} [91]

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

"{{{{#if:|Template:Xpd/wl|#expr: 2 = 5 < 3 + 4}}}}" gives "{{#expr: 2 = 5 < 3 + 4}}" {{#ifeq:{{{gives}}}||||||}} [92]

(first +, then =, then <).

"{{{{#if:|Template:Xpd/wl|#expr:1.234 + 1.234 round 1 + 1 }}}}" gives "{{#expr:1.234 + 1.234 round 1 + 1 }}" {{#ifeq:{{{gives}}}||||||}} [93]

(first additions, then round)

"{{{{#if:|Template:Xpd/wl|#expr:3 * 4 mod 10 * 10 }}}}" gives "{{#expr:3 * 4 mod 10 * 10 }}" {{#ifeq:{{{gives}}}||||||}} [94]

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

Parentheses can force a different precedence: "{{{{#if:|Template:Xpd/wl|#expr: (2 + 3) * 4}}}}" gives "{{#expr: (2 + 3) * 4}}" {{#ifeq:{{{gives}}}||||||}} [95]

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:

"{{{{#if:|Template:Xpd/wl|#expr:7mod3}}}}" gives "{{#expr:7mod3}}" {{#ifeq:{{{gives}}}||||||}} [96]
"{{{{#if:|Template:Xpd/wl|#expr:7.5round0}}}}" gives "{{#expr:7.5round0}}" {{#ifeq:{{{gives}}}||||||}} [97]
"{{{{#if:|Template:Xpd/wl|#expr:0and1}}}}" gives "{{#expr:0and1}}" {{#ifeq:{{{gives}}}||||||}} [98]
"{{{{#if:|Template:Xpd/wl|#expr:0or not0}}}}" gives "{{#expr:0or not0}}" {{#ifeq:{{{gives}}}||||||}} [99]
"{{{{#if:|Template:Xpd/wl|#expr:0ornot0}}}}" gives "{{#expr:0ornot0}}" {{#ifeq:{{{gives}}}||||||}} [100]
"{{{{#if:|Template:Xpd/wl|#expr:123 456}}}}" gives "{{#expr:123 456}}" {{#ifeq:{{{gives}}}||||||}} [101]
"{{{{#if:|Template:Xpd/wl|#expr:not not3}}}}" gives "{{#expr:not not3}}" {{#ifeq:{{{gives}}}||||||}} [102]
"{{{{#if:|Template:Xpd/wl|#expr:notnot3}}}}" gives "{{#expr:notnot3}}" {{#ifeq:{{{gives}}}||||||}} [103]

"{{{{#if:|Template:Xpd/wl|#expr:---2}}}}" gives "{{#expr:---2}}" {{#ifeq:{{{gives}}}||||||}} [104]
"{{{{#if:|Template:Xpd/wl|#expr:-+-2}}}}" gives "{{#expr:-+-2}}" {{#ifeq:{{{gives}}}||||||}} [105]
"{{{{#if:|Template:Xpd/wl|#expr:2*-3}}}}" gives "{{#expr:2*-3}}" {{#ifeq:{{{gives}}}||||||}} [106]
"{{{{#if:|Template:Xpd/wl|#expr:-not-not-not0}}}}" gives "{{#expr:-not-not-not0}}" {{#ifeq:{{{gives}}}||||||}} [107]
"{{{{#if:|Template:Xpd/wl|#expr:2*/3}}}}" gives "{{#expr:2*/3}}" {{#ifeq:{{{gives}}}||||||}} [108]
"{{{{#if:|Template:Xpd/wl|#expr:sinln1.1}}}}" gives "{{#expr:sinln1.1}}" {{#ifeq:{{{gives}}}||||||}} [109]
"{{{{#if:|Template:Xpd/wl|#expr:sin ln1.1}}}}" gives "{{#expr:sin ln1.1}}" {{#ifeq:{{{gives}}}||||||}} [110]

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.

"{{{{#if:|Template:Xpd/wl|#expr: +01.20}}}}" gives "{{#expr: +01.20}}" {{#ifeq:{{{gives}}}||||||}} [111]
"{{{{#if:|Template:Xpd/wl|#expr: 12.}}}}" gives "{{#expr: 12.}}" {{#ifeq:{{{gives}}}||||||}} [112]

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

In [113] 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:

"{{{{#if:|Template:Xpd/wl|#expr: 123}}}}" gives "{{#expr: 123}}" {{#ifeq:{{{gives}}}||||||}} [114]
"{{{{#if:|Template:Xpd/wl|#expr: 123.456}}}}" gives "{{#expr: 123.456}}" {{#ifeq:{{{gives}}}||||||}} [115]
"{{{{#if:|Template:Xpd/wl|#expr: 0.456}}}}" gives "{{#expr: 0.456}}" {{#ifeq:{{{gives}}}||||||}} [116]
"{{{{#if:|Template:Xpd/wl|#expr: 0}}}}" gives "{{#expr: 0}}" {{#ifeq:{{{gives}}}||||||}} [117]
"{{{{#if:|Template:Xpd/wl|#expr: 2.0E-5}}}}" gives "{{#expr: 2.0E-5}}" {{#ifeq:{{{gives}}}||||||}} [118]

Accepted, although in some cases more or less odd:

"{{{{#if:|Template:Xpd/wl|#expr: .456}}}}" gives "{{#expr: .456}}" {{#ifeq:{{{gives}}}||||||}} [119]
"{{{{#if:|Template:Xpd/wl|#expr: 123.}}}}" gives "{{#expr: 123.}}" {{#ifeq:{{{gives}}}||||||}} [120]
"{{{{#if:|Template:Xpd/wl|#expr: 000123}}}}" gives "{{#expr: 000123}}" {{#ifeq:{{{gives}}}||||||}} [121]
"{{{{#if:|Template:Xpd/wl|#expr: 123.456.789}}}}" gives "{{#expr: 123.456.789}}" {{#ifeq:{{{gives}}}||||||}} [122]
"{{{{#if:|Template:Xpd/wl|#expr: .}}}}" gives "{{#expr: .}}" {{#ifeq:{{{gives}}}||||||}} [123]
"{{{{#if:|Template:Xpd/wl|#expr: 2e-5}}}}" gives "{{#expr: 2e-5}}" {{#ifeq:{{{gives}}}||||||}} [124]
"{{{{#if:|Template:Xpd/wl|#expr: 2E-5}}}}" gives "{{#expr: 2E-5}}" {{#ifeq:{{{gives}}}||||||}} [125]
"{{{{#if:|Template:Xpd/wl|#expr: E}}}}" gives "{{#expr: E}}" {{#ifeq:{{{gives}}}||||||}} [126]
"{{{{#if:|Template:Xpd/wl|#expr: e}}}}" gives "{{#expr: e}}" {{#ifeq:{{{gives}}}||||||}} [127]
"{{{{#if:|Template:Xpd/wl|#expr: E-5}}}}" gives "{{#expr: E-5}}" {{#ifeq:{{{gives}}}||||||}} [128]
"{{{{#if:|Template:Xpd/wl|#expr: e-5}}}}" gives "{{#expr: e-5}}" {{#ifeq:{{{gives}}}||||||}} [129]
"{{{{#if:|Template:Xpd/wl|#expr: 1e-5}}}}" gives "{{#expr: 1e-5}}" {{#ifeq:{{{gives}}}||||||}} [130]

Wrong:

"{{{{#if:|Template:Xpd/wl|#expr: 123,456}}}}" gives "{{#expr: 123,456}}" {{#ifeq:{{{gives}}}||||||}} [131]
"{{{{#if:|Template:Xpd/wl|#expr: 123 456}}}}" gives "{{#expr: 123 456}}" {{#ifeq:{{{gives}}}||||||}} [132]

As opposed to ParserFunctions, "plural" 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 ( less than 1E-4) and for numbers with large absolute value ( greater than or equal to 1E+12; however, even within MediaWiki 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):

{{xpd/w{{#if:|l}}|"}}{{xpd/w{{#if:|l}}|{}}{{xpd/w{{#if:|l}}|{}}{{xpd/w{{#if:|l}}|#expr: .000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000123456789012345}}{{xpd/w{{#if:|l}}|}}}{{xpd/w{{#if:|l}}|}}}{{xpd/w{{#if:|l}}|{{{{{#switch:pq|p q=2|p

{{xpd/w{{#if:|l}}|"}}{{xpd/w{{#if:|l}}|{}}{{xpd/w{{#if:|l}}|{}}{{xpd/w{{#if:|l}}|#expr: .00000123456789012345}}{{xpd/w{{#if:|l}}|}}}{{xpd/w{{#if:|l}}|}}}{{xpd/w{{#if:|l}}|{{{{{#switch:pq|p q=2|p

{{xpd/w{{#if:|l}}|"}}{{xpd/w{{#if:|l}}|{}}{{xpd/w{{#if:|l}}|{}}{{xpd/w{{#if:|l}}|#expr: .0000123456789012345}}{{xpd/w{{#if:|l}}|}}}{{xpd/w{{#if:|l}}|}}}{{xpd/w{{#if:|l}}|{{{{{#switch:pq|p q=2|p

{{xpd/w{{#if:|l}}|"}}{{xpd/w{{#if:|l}}|{}}{{xpd/w{{#if:|l}}|{}}{{xpd/w{{#if:|l}}|#expr: .000123456789012345}}{{xpd/w{{#if:|l}}|}}}{{xpd/w{{#if:|l}}|}}}{{xpd/w{{#if:|l}}|{{{{{#switch:pq|p q=2|p

{{xpd/w{{#if:|l}}|"}}{{xpd/w{{#if:|l}}|{}}{{xpd/w{{#if:|l}}|{}}{{xpd/w{{#if:|l}}|#expr: 123456789012.345}}{{xpd/w{{#if:|l}}|}}}{{xpd/w{{#if:|l}}|}}}{{xpd/w{{#if:|l}}|{{{{{#switch:pq|p q=2|p

{{xpd/w{{#if:|l}}|"}}{{xpd/w{{#if:|l}}|{}}{{xpd/w{{#if:|l}}|{}}{{xpd/w{{#if:|l}}|#expr: 1234567890123.45}}{{xpd/w{{#if:|l}}|}}}{{xpd/w{{#if:|l}}|}}}{{xpd/w{{#if:|l}}|{{{{{#switch:pq|p q=2|p

{{xpd/w{{#if:|l}}|"}}{{xpd/w{{#if:|l}}|{}}{{xpd/w{{#if:|l}}|{}}{{xpd/w{{#if:|l}}|#expr: 12345678901234.5}}{{xpd/w{{#if:|l}}|}}}{{xpd/w{{#if:|l}}|}}}{{xpd/w{{#if:|l}}|{{{{{#switch:pq|p q=2|p

{{xpd/w{{#if:|l}}|"}}{{xpd/w{{#if:|l}}|{}}{{xpd/w{{#if:|l}}|{}}{{xpd/w{{#if:|l}}|#expr: 123456789012345}}{{xpd/w{{#if:|l}}|}}}{{xpd/w{{#if:|l}}|}}}{{xpd/w{{#if:|l}}|{{{{{#switch:pq|p q=2|p

{{xpd/w{{#if:|l}}|"}}{{xpd/w{{#if:|l}}|{}}{{xpd/w{{#if:|l}}|{}}{{xpd/w{{#if:|l}}|#expr: 1234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456}}{{xpd/w{{#if:|l}}|}}}{{xpd/w{{#if:|l}}|}}}{{xpd/w{{#if:|l}}|{{{{{#switch:pq|p q=2|p

{{xpd/w{{#if:|l}}|"}}{{xpd/w{{#if:|l}}|{}}{{xpd/w{{#if:|l}}|{}}{{xpd/w{{#if:|l}}|#expr: 1.234e4}}{{xpd/w{{#if:|l}}|}}}{{xpd/w{{#if:|l}}|}}}{{xpd/w{{#if:|l}}|{{{{{#switch:pq|p q=2|p

{{xpd/w{{#if:|l}}|"}}{{xpd/w{{#if:|l}}|{}}{{xpd/w{{#if:|l}}|{}}{{xpd/w{{#if:|l}}|#expr: 1.234e-4}}{{xpd/w{{#if:|l}}|}}}{{xpd/w{{#if:|l}}|}}}{{xpd/w{{#if:|l}}|{{{{{#switch:pq|p q=2|p

For negative numbers simply a minus sign is prefixed:

{{xpd/w{{#if:|l}}|"}}{{xpd/w{{#if:|l}}|{}}{{xpd/w{{#if:|l}}|{}}{{xpd/w{{#if:|l}}|#expr: -123456789012345}}{{xpd/w{{#if:|l}}|}}}{{xpd/w{{#if:|l}}|}}}{{xpd/w{{#if:|l}}|{{{{{#switch:pq|p q=2|p

Long YYYYMMDDhhmmss timestamps can run into the same problem: {{xpd/w{{#if:|l}}|"}}{{xpd/w{{#if:|l}}|{}}{{xpd/w{{#if:|l}}|{}}{{xpd/w{{#if:|l}}|CURRENTTIMESTAMP}}{{xpd/w{{#if:|l}}|}}}{{xpd/w{{#if:|l}}|}}}{{xpd/w{{#if:|l}}|{{{{{#switch:pq|p q=2|p

Template:Xpdoocc.
Timestamps without seconds are 12 digits, just short enough: {{xpd/w{{#if:|l}}|"}}{{xpd/w{{#if:|l}}|{}}{{xpd/w{{#if:|l}}|{}}{{xpd/w{{#if:|l}}|#expr:20241127064211/100}}{{xpd/w{{#if:|l}}|}}}{{xpd/w{{#if:|l}}|}}}{{xpd/w{{#if:|l}}|{{{{{#switch:pq|p q=2|p

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. Template:roote and Template:rooteval; for convenience, for the final result another version can be made simply calling the other one and applying #expr to the result, e.g. Template:rootfineval.

Two methods for representing intermediate results are:

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

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

Template:Xpd2

However, the expression can get quite long, for Template:roote 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 a linked expression gives {{#expr:Template:Roote}}, 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:

Template:Xpd1

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 Template:rootfineval, giving Template:Fineval, but the result can also be used in a further computation.

Compare:

"{{{{#if:|Template:Xpd/wl|#expr:(.0000000000001)^(1/2)}}}}" gives "{{#expr:(.0000000000001)^(1/2)}}" {{#ifeq:{{{gives}}}||||||}} [133]

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 ):

"{{{{#if:|Template:Xpd/wl|#expr: ( -0.2 round 0 )}}}}" gives "{{#expr: ( -0.2 round 0 )}}" {{#ifeq:{{{gives}}}||||||}} [134]
"{{{{#if:|Template:Xpd/wl|#expr: 1*(-0.2 round 0)}}}}" gives "{{#expr: 1*(-0.2 round 0)}}" {{#ifeq:{{{gives}}}||||||}} [135]
"{{{{#if:|Template:Xpd/wl|#expr: 0+(-0.2 round 0)}}}}" gives "{{#expr: 0+(-0.2 round 0)}}" {{#ifeq:{{{gives}}}||||||}} [136]

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{{#if:23

|×10^{{{#switch:{{{2}}}
 |#default={{#switch:{{#if:23|{{#ifeq:23|{{#if:{{#ifexpr:{{#expr:23}}}}|(23)|{{#expr:23}}}}|true|{{#ifeq:23|+{{#if:{{#ifexpr:{{#expr:23}}}}|(23)|{{#expr:23}}}}|true|{{#ifeq:23|({{#if:{{#ifexpr:{{#expr:23}}}}|(23)|{{#expr:23}}}})|true|false}}}}}}}}
  |#default={{#switch:{{{2}}}
   |plus=+{{#ifexpr:(231)=(23)|Template:FormattingError|{{#ifexpr:23<0|−}}{{#ifexpr:abs(231)>10*abs(23)|{{#expr:abs(23)}}|{{#expr:trunc(abs(23))}}.{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>14|Template:FormattingError|{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=1|{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E1mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=2|{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E2mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=3|{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E3mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=4|{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>4|}}{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E4mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=5|{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E5mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=6|{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E6mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=7|{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>7|}}{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E7mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=8|{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E8mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=9|{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E9mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=10|{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>10|}}{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E10mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=11|{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E11mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=12|{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E12mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=13|{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>13|}}{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E13mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=14|{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E14mod10}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
   |#default={{#ifexpr:(231)=(23)|Template:FormattingError|{{#ifexpr:23<0|−}}{{#ifexpr:abs(231)>10*abs(23)|{{#expr:abs(23)}}|{{#expr:trunc(abs(23))}}.{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>14|Template:FormattingError|{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=1|{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E1mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=2|{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E2mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=3|{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E3mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=4|{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>4|}}{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E4mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=5|{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E5mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=6|{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E6mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=7|{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>7|}}{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E7mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=8|{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E8mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=9|{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E9mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=10|{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>10|}}{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E10mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=11|{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E11mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=12|{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E12mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=13|{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>13|}}{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E13mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=14|{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E14mod10}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
  }}
  |false=23
 }}
 |text=23
}}}
|^e

}}.

Accuracy

The accuracy and format of numeric results varies with the operating system of the server.

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

{{xpd/w{{#if:|l}}|"}}{{xpd/w{{#if:|l}}|{}}{{xpd/w{{#if:|l}}|{}}{{xpd/w{{#if:|l}}|#expr:(2/3)}}{{xpd/w{{#if:|l}}|}}}{{xpd/w{{#if:|l}}|}}}{{xpd/w{{#if:|l}}|{{{{{#switch:pq|p q=2|p

{{xpd/w{{#if:|l}}|"}}{{xpd/w{{#if:|l}}|{}}{{xpd/w{{#if:|l}}|{}}{{xpd/w{{#if:|l}}|#expr:(2/3)*1000000-666666}}{{xpd/w{{#if:|l}}|}}}{{xpd/w{{#if:|l}}|}}}{{xpd/w{{#if:|l}}|{{{{{#switch:pq|p q=2|p

Template:Xpdoocc
{{xpd/w{{#if:|l}}|"}}{{xpd/w{{#if:|l}}|{}}{{xpd/w{{#if:|l}}|{}}{{xpd/w{{#if:|l}}|#expr:1234567890.1234567890-1234567890}}{{xpd/w{{#if:|l}}|}}}{{xpd/w{{#if:|l}}|}}}{{xpd/w{{#if:|l}}|{{{{{#switch:pq|p q=2|p

{{xpd/w{{#if:|l}}|"}}{{xpd/w{{#if:|l}}|{}}{{xpd/w{{#if:|l}}|{}}{{xpd/w{{#if:|l}}|#expr:1234567890.1234567890}}{{xpd/w{{#if:|l}}|}}}{{xpd/w{{#if:|l}}|}}}{{xpd/w{{#if:|l}}|{{{{{#switch:pq|p q=2|p

Template:Xpdoocc

The macheps or smallest x such that 1+x != 1 appears to be near 0.5^53 + 0.5^106 or 1.1102230246251566636831481088739149080825883E-16 (see above)
{{xpd/w{{#if:|l}}|"}}{{xpd/w{{#if:|l}}|{}}{{xpd/w{{#if:|l}}|{}}{{xpd/w{{#if:|l}}|#expr:1=1+0.00000000000000011102230246251566636831481088739149080826}}{{xpd/w{{#if:|l}}|}}}{{xpd/w{{#if:|l}}|}}}{{xpd/w{{#if:|l}}|{{{{{#switch:pq|p q=2|p

{{xpd/w{{#if:|l}}|"}}{{xpd/w{{#if:|l}}|{}}{{xpd/w{{#if:|l}}|{}}{{xpd/w{{#if:|l}}|#expr:1=1+0.00000000000000011102230246251566636831481088739149080825}}{{xpd/w{{#if:|l}}|}}}{{xpd/w{{#if:|l}}|}}}{{xpd/w{{#if:|l}}|{{{{{#switch:pq|p q=2|p

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
{{xpd/w{{#if:|l}}|"}}{{xpd/w{{#if:|l}}|{}}{{xpd/w{{#if:|l}}|{}}{{xpd/w{{#if:|l}}|#expr:1+0.000000000004999889392}}{{xpd/w{{#if:|l}}|}}}{{xpd/w{{#if:|l}}|}}}{{xpd/w{{#if:|l}}|{{{{{#switch:pq|p q=2|p

{{xpd/w{{#if:|l}}|"}}{{xpd/w{{#if:|l}}|{}}{{xpd/w{{#if:|l}}|{}}{{xpd/w{{#if:|l}}|#expr:1+0.000000000004999889391}}{{xpd/w{{#if:|l}}|}}}{{xpd/w{{#if:|l}}|}}}{{xpd/w{{#if:|l}}|{{{{{#switch:pq|p q=2|p

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:

{{#ifexpr: {{CURRENTDOW}} = 0 or {{CURRENTDOW}} = 6 | weekEND | weekDAY}} yields {{#ifexpr: 3 = 0 or 3 = 6|weekEND|weekDAY}} because today is Wednesday and so "{{{{#if:|Template:Xpd/wl|CURRENTDOW}}}}" is "3" {{#ifeq: is||||||}} [137].

Template:Xpd2

Note that rounding errors can affect a result:

"{{{{#if:|Template:Xpd/wl|#expr:sin pi}}}}" gives "{{#expr:sin pi}}" {{#ifeq:{{{gives}}}||||||}} [138]
Template:Xpd2
Template:Xpd2

Similarly:

"{{{{#if:|Template:Xpd/wl|#expr:sin pi=0}}}}" gives "{{#expr:sin pi=0}}" {{#ifeq:{{{gives}}}||||||}} [139]
"{{{{#if:|Template:Xpd/wl|#expr:abs sin pi<1e-15}}}}" gives "{{#expr:abs sin pi<1e-15}}" {{#ifeq:{{{gives}}}||||||}} [140]

Comparisons

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

Template:Xpdopepepec

Note that #ifeq: unlike #expr: accepts exponential notation on input.

{{#ifexpr:0.00003456 = 3.456E-05|1|0}} gives "{{#ifexpr:0.00003456 = 3.456E-05|1|0}}"

Template:Xpd3
Template:Xpd3
Template:Xpd3
Template:Xpd3
Numerical comparisons don't depend on the output format, compare:
"{{{{#if:|Template:Xpd/wl|#expr:1234567890123}}}}" gives "{{#expr:1234567890123}}" {{#ifeq:{{{gives}}}||||||}} [141]
"{{{{#if:|Template:Xpd/wl|#expr:1234567890120}}}}" gives "{{#expr:1234567890120}}" {{#ifeq:{{{gives}}}||||||}} [142]

#ifeq: allows to compare strings containing equal signs:

#switch form	#ifeq form
{{`{{{1n}}}`}}`}}{{#ifeq:+\|-\|\|-1=okay\|fail\|\|{{#ifeq:fail\|fail\|\|-1=okay\|fail\|{{#ifeq:-1=okay\|-1=okay\|\|-1=okay\|}}}}}}`}} </td><td> {{#ifeq:-\|+\|{{#switch:-1.0\|-1=okay\|fail\|}}\|{{#ifeq:fail\|fail\|{{#switch:-1.0\|-1=okay\|fail}}\|{{#ifeq:-1=okay\|-1=okay\|{{#switch:-1.0\|-1=okay}}\|{{#switch:-1.0}}}}}}}}	{{`{{{1n}}}`}}`}}{{#ifeq:fail\|fail\|\|-1\|okay\|fail\|{{#ifeq:okay\|okay\|\|-1\|okay\|{{#ifeq:-1\|-1\|\|-1\|}}}}}}`}} </td><td> {{#ifeq:fail\|fail\|{{#ifeq:-1.0\|-1\|okay\|fail}}\|{{#ifeq:okay\|okay\|{{#ifeq:-1.0\|-1\|okay}}\|{{#ifeq:-1\|-1\|{{#ifeq:-1.0\|-1}}\|{{#ifeq:-1.0}}}}}}}}
-1=okay\|fail}}"
{{`{{{1n}}}`}}`}}{{#ifeq:+\|-\|\|a=b=okay\|fail\|\|{{#ifeq:fail\|fail\|\|a=b=okay\|fail\|{{#ifeq:a=b=okay\|a=b=okay\|\|a=b=okay\|}}}}}}`}} </td><td> {{#ifeq:-\|+\|{{#switch:a=b\|a=b=okay\|fail\|}}\|{{#ifeq:fail\|fail\|{{#switch:a=b\|a=b=okay\|fail}}\|{{#ifeq:a=b=okay\|a=b=okay\|{{#switch:a=b\|a=b=okay}}\|{{#switch:a=b}}}}}}}}	{{`{{{1n}}}`}}`}}{{#ifeq:fail\|fail\|\|a=b\|okay\|fail\|{{#ifeq:okay\|okay\|\|a=b\|okay\|{{#ifeq:a=b\|a=b\|\|a=b\|}}}}}}`}} </td><td> {{#ifeq:fail\|fail\|{{#ifeq:a=b\|a=b\|okay\|fail}}\|{{#ifeq:okay\|okay\|{{#ifeq:a=b\|a=b\|okay}}\|{{#ifeq:a=b\|a=b\|{{#ifeq:a=b\|a=b}}\|{{#ifeq:a=b}}}}}}}}
{{`{{{1n}}}`}}`}}{{#ifeq:+\|-\|\|a=b=fail\|okay\|\|{{#ifeq:okay\|okay\|\|a=b=fail\|okay\|{{#ifeq:a=b=fail\|a=b=fail\|\|a=b=fail\|}}}}}}`}} </td><td> {{#ifeq:-\|+\|{{#switch:a=c\|a=b=fail\|okay\|}}\|{{#ifeq:okay\|okay\|{{#switch:a=c\|a=b=fail\|okay}}\|{{#ifeq:a=b=fail\|a=b=fail\|{{#switch:a=c\|a=b=fail}}\|{{#switch:a=c}}}}}}}}	{{`{{{1n}}}`}}`}}{{#ifeq:okay\|okay\|\|a=b\|fail\|okay\|{{#ifeq:fail\|fail\|\|a=b\|fail\|{{#ifeq:a=b\|a=b\|\|a=b\|}}}}}}`}} </td><td> {{#ifeq:okay\|okay\|{{#ifeq:a=c\|a=b\|fail\|okay}}\|{{#ifeq:fail\|fail\|{{#ifeq:a=c\|a=b\|fail}}\|{{#ifeq:a=b\|a=b\|{{#ifeq:a=c\|a=b}}\|{{#ifeq:a=c}}}}}}}}

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:

x*(1-2*(x<0))
x*{{#ifexpr:x>0|1|-1}}

(The first is not only shorter but has also the advantage that for substitution one less "subst:" or {{{subst|}}} is needed.)

Do not use

{{#ifexpr:x>0|x|-x}}

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:

{{#ifexpr:x<10|0}}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 pre-expand include size maximum 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 <strong class="error">..</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: {{t1|{{#expr:1/0}}}} gives Template:T1.

Expression	Error message
Template:Xpd1
Template:Xpd1
Template:Xpd1
Template:Xpd1
Template:Xpd1
Template:Xpd1
Template:Xpd1
Template:Xpd1
Template:Xpd1
Template:Xpd1
Template:Xpd1
Template:Xpd1
{{ `#expr:`{{ `x\|102\|1000`}} `18` }} gives {{#ifeq:TrainzOnline\|Meta\|{{#expr:Template:X18}}\|{{#expr:100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000*18}}}}
{{ `#expr:`{{ `x\|102\|1000`}} `179` }} gives {{#ifeq:TrainzOnline\|Meta\|{{#expr:Template:X179}}\|{{#expr:100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000*179}}}}
{{ `#expr:`{{ `x\|102\|1000`}} `180` }} gives {{#ifeq:TrainzOnline\|Meta\|{{#expr:Template:X180}}\|{{#expr:100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000*180}}}} ( "INF", but depending on the operating system of the server it may also be e.g. "1.#INF")
{{ `#expr:`{{ `x\|33\|(1+(`}} `1` {{ `x\|33\|))`}} }} gives {{#ifeq:TrainzOnline\|Meta\|{{#expr:Template:X1Template:X}}\|{{#expr:(1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+(1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))}}}}
{{ `#expr:`{{ `x\|34\|(1+(`}} `1` {{ `x\|34\|))`}} }} gives {{#ifeq:TrainzOnline\|Meta\|{{#expr:Template:X1Template:X}}\|{{#expr:(1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+((1+(1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))}}}}
`"{{{{#if:\|Template:Xpd/wl\|#expr:3.4.5.6}}}}"` gives "{{#expr:3.4.5.6}}" {{#ifeq:{{{gives}}}		}} [143] (no feature, only an oddity)

Note: Template:Links-small 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:

{{{#expr:2*3}}}	{{{#expr:2*3}}}	(triple braces, the whole is interpreted as parameter tag with parameter name "#expr:2*3")
{{#expr:2*3}}}	{{#expr:2*3}}}	(one closing brace too many; the last of the three is interpreted as plain text, so that the rest works fine)
{{{#expr:2*3}}	{{{#expr:2*3}}	(one opening brace too many; the first of the three is interpreted as plain text, so that the rest works fine)
{{#expr:2*3}	{{#expr:2*3}	(too few braces, the whole is interpreted as plain text)

A crude but informative "unrecognised word" error message can be generated intentionally. Only the first identified error is shown

{{ #expr: 2*{{ #ifexpr: 3*4>10|toolarge|3*4 }} }} gives

{{#expr:2*{{#ifexpr:3*4>10|toolarge|3*4}}}},

{{ #expr: 2*{{ #ifexpr: 3*4>10|too large|3*4 }} }} gives

{{#expr:2*{{#ifexpr:3*4>10|too large|3*4}}}}.

Minus sign

Only the ASCII hyphen (hyphen-minus) and minus signs work as minus signs; dashes are not permitted. The output, however, will always be in the form of a hyphen-minus:

hyphen-minus	Template:Xpd/wl\|#expr:-12}}}}"	"{{#expr:-12}}" {{#ifeq:	}} [144]
Unicode hyphen (U+2010, ‐)	`"{{#expr:‐12}}"`	"{{#expr:‐12}}"
minus sign produced by −	`"{{#expr:−12}}"`	"{{#expr:−12}}"
−	`"{{#expr:−12}}"`	"{{#expr:−12}}"
em dash produced by —	`"{{#expr:—12}}"`	"{{#expr:—12}}"
—	`"{{#expr:—12}}"`	"{{#expr:—12}}"
en dash produced by –	`"{{#expr:–12}}"`	"{{#expr:–12}}"
–	`"{{#expr:–12}}"`	"{{#expr:–12}}"

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 WP:Manual of Style (dates and numbers)#Numbers 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{{#if:23

|×10^{{{#switch:{{{2}}}
 |#default={{#switch:{{#if:23|{{#ifeq:23|{{#if:{{#ifexpr:{{#expr:23}}}}|(23)|{{#expr:23}}}}|true|{{#ifeq:23|+{{#if:{{#ifexpr:{{#expr:23}}}}|(23)|{{#expr:23}}}}|true|{{#ifeq:23|({{#if:{{#ifexpr:{{#expr:23}}}}|(23)|{{#expr:23}}}})|true|false}}}}}}}}
  |#default={{#switch:{{{2}}}
   |plus=+{{#ifexpr:(231)=(23)|Template:FormattingError|{{#ifexpr:23<0|−}}{{#ifexpr:abs(231)>10*abs(23)|{{#expr:abs(23)}}|{{#expr:trunc(abs(23))}}.{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>14|Template:FormattingError|{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=1|{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E1mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=2|{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E2mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=3|{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E3mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=4|{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>4|}}{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E4mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=5|{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E5mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=6|{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E6mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=7|{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>7|}}{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E7mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=8|{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E8mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=9|{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E9mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=10|{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>10|}}{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E10mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=11|{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E11mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=12|{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E12mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=13|{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>13|}}{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E13mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=14|{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E14mod10}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
   |#default={{#ifexpr:(231)=(23)|Template:FormattingError|{{#ifexpr:23<0|−}}{{#ifexpr:abs(231)>10*abs(23)|{{#expr:abs(23)}}|{{#expr:trunc(abs(23))}}.{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>14|Template:FormattingError|{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=1|{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E1mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=2|{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E2mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=3|{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E3mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=4|{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>4|}}{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E4mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=5|{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E5mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=6|{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E6mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=7|{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>7|}}{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E7mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=8|{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E8mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=9|{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E9mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=10|{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>10|}}{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E10mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=11|{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E11mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=12|{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E12mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=13|{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>13|}}{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E13mod10}}{{#ifexpr:{{#expr:(-ln(abs(231)-abs(23))/ln10round 0)-1}}>=14|{{#expr:{{#expr:abs(231)-trunc(abs(231))}}*1E14mod10}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
  }}
  |false=23
 }}
 |text=23
}}}
|^e

}}

Examples:

"{{{{#if:|Template:Xpd/wl|#expr:three}}}}" gives "{{#expr:three}}" {{#ifeq:{{{gives}}}||||||}} [145]
"{{{{#if:|Template:Xpd/wl|#expr:2<3}}}}" gives "{{#expr:2<3}}" {{#ifeq:{{{gives}}}||||||}} [146]
"{{{{#if:|Template:Xpd/wl|#expr:2≤3}}}}" gives "{{#expr:2≤3}}" {{#ifeq:{{{gives}}}||||||}} [147]
"{{{{#if:|Template:Xpd/wl|#expr:2<=3}}}}" gives "{{#expr:2<=3}}" {{#ifeq:{{{gives}}}||||||}} [148]
"{{{{#if:|Template:Xpd/wl|#expr:2>3}}}}" gives "{{#expr:2>3}}" {{#ifeq:{{{gives}}}||||||}} [149]
"{{{{#if:|Template:Xpd/wl|#expr:2≥3}}}}" gives "{{#expr:2≥3}}" {{#ifeq:{{{gives}}}||||||}} [150]
"{{{{#if:|Template:Xpd/wl|#expr:2>=3}}}}" gives "{{#expr:2>=3}}" {{#ifeq:{{{gives}}}||||||}} [151]
"{{{{#if:|Template:Xpd/wl|#expr:2*3}}}}" gives "{{#expr:2*3}}" {{#ifeq:{{{gives}}}||||||}} [152]
"{{{{#if:|Template:Xpd/wl|#expr:2×3}}}}" gives "{{#expr:2×3}}" {{#ifeq:{{{gives}}}||||||}} [153]
"{{{{#if:|Template:Xpd/wl|#expr:2,300}}}}" gives "{{#expr:2,300}}" {{#ifeq:{{{gives}}}||||||}} [154]
"{{{{#if:|Template:Xpd/wl|#expr:6E23}}}}" gives "{{#expr:6E23}}" {{#ifeq:{{{gives}}}||||||}} [155]

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.

Tactics for handling extreme numbers

In the digital storage of numbers, the effects of truncation error on numeric precision might cause some extreme decimal numbers (above 1E13 or below 1E-12), or other E-notation numbers, to mismatch during comparisons. There are some tactics which can help, such as comparing results with "#ifeq" rather than "#ifexpr".

Comparing large numbers

The floor function might mismatch the original value of a large number, by a tiny amount, and so comparisons can be made with #ifeq between separate expressions. For example:

{{#ifexpr: floor( 1.36E4 ) = 1.36E4|Equal|Differ}} gives "{{#ifexpr: floor( 1.36E4 ) = 1.36E4|Equal|Differ}}"
{{#ifexpr: floor( 1.33E4 ) = 1.33E4|Equal|Differ}} gives "{{#ifexpr: floor( 1.33E4 ) = 1.33E4|Equal|Differ}}"
{{#ifexpr: floor( 1.52E4 ) = 1.52E4|Equal|Differ}} gives "{{#ifexpr: floor( 1.52E4 ) = 1.52E4|Equal|Differ}}"
{{#ifexpr: floor( 1.36E13 ) = 1.36E13|Equal|Differ}} gives "{{#ifexpr: floor( 1.36E13 ) = 1.36E13|Equal|Differ}}"
{{#ifexpr: trunc( 1.36E13 ) = 1.36E13|Equal|Differ}} gives "{{#ifexpr: trunc( 1.36E13 ) = 1.36E13|Equal|Differ}}"

However, using #ifeq to compare the results of 2 expressions can work:

{{#ifeq: {{#expr:floor(1.33E4) }} | {{#expr:1.33E4}}|Equal|Differ}} gives "{{#ifeq: {{#expr:floor(1.33E4) }} | {{#expr:1.33E4}}|Equal|Differ}}"
{{#ifeq: {{#expr:floor(1.36E13) }} | {{#expr:1.36E13}}|Equal|Differ}} gives "{{#ifeq: {{#expr:floor(1.36E13) }} | {{#expr:1.36E13}}|Equal|Differ}}"
{{#ifeq: {{#expr:trunc(1.36E13) }} | {{#expr:1.36E13}}|Equal|Differ}} gives "{{#ifeq: {{#expr:trunc(1.36E13) }} | {{#expr:1.36E13}}|Equal|Differ}}"

The truncation-error amount can usually be displayed by subtraction:

{{#expr: floor(1.36E4) - 1.36E4 }} gives "{{#expr: floor(1.36E4) - 1.36E4 }}"
{{#expr: floor(13600) - 13600 }} gives "{{#expr: floor(13600) - 13600 }}"
{{#expr: floor(1.36E13) - 1.36E13 }} gives "{{#expr: floor(1.36E13) - 1.36E13 }}"
{{#expr: trunc(1.36E13) - 1.36E13 }} gives "{{#expr: trunc(1.36E13) - 1.36E13 }}"

There are similar workarounds to bypass other limitations due to truncation error in the handling of extreme numbers.

#switch form	#ifeq form
{{`{{{1n}}}`}}`}}{{#ifeq:+\|-\|\|-1=okay\|fail\|\|{{#ifeq:fail\|fail\|\|-1=okay\|fail\|{{#ifeq:-1=okay\|-1=okay\|\|-1=okay\|}}}}}}`}} </td><td> {{#ifeq:-\|+\|{{#switch:-1.0\|-1=okay\|fail\|}}\|{{#ifeq:fail\|fail\|{{#switch:-1.0\|-1=okay\|fail}}\|{{#ifeq:-1=okay\|-1=okay\|{{#switch:-1.0\|-1=okay}}\|{{#switch:-1.0}}}}}}}}	{{`{{{1n}}}`}}`}}{{#ifeq:fail\|fail\|\|-1\|okay\|fail\|{{#ifeq:okay\|okay\|\|-1\|okay\|{{#ifeq:-1\|-1\|\|-1\|}}}}}}`}} </td><td> {{#ifeq:fail\|fail\|{{#ifeq:-1.0\|-1\|okay\|fail}}\|{{#ifeq:okay\|okay\|{{#ifeq:-1.0\|-1\|okay}}\|{{#ifeq:-1\|-1\|{{#ifeq:-1.0\|-1}}\|{{#ifeq:-1.0}}}}}}}}
-1=okay\|fail}}"
{{`{{{1n}}}`}}`}}{{#ifeq:+\|-\|\|a=b=okay\|fail\|\|{{#ifeq:fail\|fail\|\|a=b=okay\|fail\|{{#ifeq:a=b=okay\|a=b=okay\|\|a=b=okay\|}}}}}}`}} </td><td> {{#ifeq:-\|+\|{{#switch:a=b\|a=b=okay\|fail\|}}\|{{#ifeq:fail\|fail\|{{#switch:a=b\|a=b=okay\|fail}}\|{{#ifeq:a=b=okay\|a=b=okay\|{{#switch:a=b\|a=b=okay}}\|{{#switch:a=b}}}}}}}}	{{`{{{1n}}}`}}`}}{{#ifeq:fail\|fail\|\|a=b\|okay\|fail\|{{#ifeq:okay\|okay\|\|a=b\|okay\|{{#ifeq:a=b\|a=b\|\|a=b\|}}}}}}`}} </td><td> {{#ifeq:fail\|fail\|{{#ifeq:a=b\|a=b\|okay\|fail}}\|{{#ifeq:okay\|okay\|{{#ifeq:a=b\|a=b\|okay}}\|{{#ifeq:a=b\|a=b\|{{#ifeq:a=b\|a=b}}\|{{#ifeq:a=b}}}}}}}}
{{`{{{1n}}}`}}`}}{{#ifeq:+\|-\|\|a=b=fail\|okay\|\|{{#ifeq:okay\|okay\|\|a=b=fail\|okay\|{{#ifeq:a=b=fail\|a=b=fail\|\|a=b=fail\|}}}}}}`}} </td><td> {{#ifeq:-\|+\|{{#switch:a=c\|a=b=fail\|okay\|}}\|{{#ifeq:okay\|okay\|{{#switch:a=c\|a=b=fail\|okay}}\|{{#ifeq:a=b=fail\|a=b=fail\|{{#switch:a=c\|a=b=fail}}\|{{#switch:a=c}}}}}}}}	{{`{{{1n}}}`}}`}}{{#ifeq:okay\|okay\|\|a=b\|fail\|okay\|{{#ifeq:fail\|fail\|\|a=b\|fail\|{{#ifeq:a=b\|a=b\|\|a=b\|}}}}}}`}} </td><td> {{#ifeq:okay\|okay\|{{#ifeq:a=c\|a=b\|fail\|okay}}\|{{#ifeq:fail\|fail\|{{#ifeq:a=c\|a=b\|fail}}\|{{#ifeq:a=b\|a=b\|{{#ifeq:a=c\|a=b}}\|{{#ifeq:a=c}}}}}}}}

Help:Calculation

Contents

Operators

Numbers as input

Numbers as output

Accuracy

Branching depending on an expression

Comparisons

Length of expressions

Error messages

Minus sign

Displaying numbers and numeric expressions

Tactics for handling extreme numbers

See also

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