User:Hadseys/Saving effort/Calculations

From Wikipedia, the free encyclopedia

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

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:

{{ #expr: expression }}

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

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

Contents

[edit] Operators

Operator Operation Example
none {{ #expr: 123456789012345 }} = 123456789012340
{{ #expr: 0.000001 }} = 1.0E-6
+ Unary + sign {{ #expr: +30 * +7 }} = 210
- Unary - sign (negation) {{ #expr: -30 * -7 }} = 210
not Unary NOT, logical NOT {{ #expr: not 0 * 7 }} = 7
{{ #expr: not 30 +7 }} = 7
* Multiplication {{ #expr: 30*7 }} = 210
/ Division, same as div {{ #expr: 30/7 }} = 4.2857142857143
div Division, same as /,
no integer division		 {{ #expr: 30 div 7 }} = 4.2857142857143 (should be 4)
{{ #expr: 5 div 2 * 2 + 5 mod 2 }} = 6 (should be 5)
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.		 {{ #expr: 30 mod 7 }} = 2
{{ #expr: -8 mod -3 }} = -2
{{ #expr: -8 mod +3 }} = -2
{{ #expr: 8 mod 2.7 }} = 0 (should be 2.6)
{{ #expr: 8 mod 3.2 }} = 2 (should be 1.6)
{{ #expr: 8.9 mod 3 }} = 2 (should be 2.9)
+ Addition {{ #expr: 30+7 }} = 37
- Subtraction {{ #expr: 30-7 }} = 23
round Rounds off the number on the left to the power of 1/10 given on the right (PHP function round) {{ #expr: 30/7 round 3 }} = 4.286
{{ #expr: 30/7 round 0 }} = 4
{{ #expr: 3456 round -2}} = 3500
= Equality (numerical incl. logical) {{ #expr: 30 = 7 }} = 0
<> Inequality, same as != {{ #expr: 30 <> 7 }} = 1
 != Inequality, same as <>, logical xor {{ #expr: 1 != 0 }} = 1
< Less than {{ #expr: 30 < 7 }} = 0
> Greater than {{ #expr: 30 > 7 }} = 1
<= Less than or equal to {{ #expr: 30 <= 7 }} = 0
>= Greater than or equal to {{ #expr: 30 >= 7 }} = 1
and Logical AND {{ #expr: 4<5 and 4 mod 2 }} = 0
or Logical OR {{ #expr: 4<5 or 4 mod 2 }} = 1

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 {{ #expr: (2 < 3) + 1 }} = 2.

Precedence:

  • {{ #expr: 2 - 3 + 4 / 5 * 6 }} = 3.8

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

  • {{ #expr: 2 = 5 < 3 + 4 }} = 1

(first +, then =, then <).

  • {{ #expr:1.234 + 1.234 round 1 + 1  }} gives 2.47

(first additions, then round)

  • {{ #expr:3 * 4 mod 10 * 10  }} gives 20

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

Parentheses can force a different precedence: {{ #expr: (2 + 3) * 4 }} = 20

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:

  • {{#expr:7mod3}} gives 1 [1]Template:Xpd/
  • {{#expr:7.5round0}} gives 8 [2]Template:Xpd/
  • {{#expr:0and1}} gives 0 [3]Template:Xpd/
  • {{#expr:0or not0}} gives 1 [4]Template:Xpd/
  • {{#expr:0ornot0}} gives Expression error: Unrecognised word "ornot" [5]Template:Xpd/
  • {{#expr:123 456}} gives Expression error: Unexpected number [6]Template:Xpd/
  • {{#expr:not not3}} gives 1 [7]Template:Xpd/
  • {{#expr:notnot3}} gives Expression error: Unrecognised word "notnot" [8]Template:Xpd/
  • {{#expr:---2}} gives -2 [9]Template:Xpd/
  • {{#expr:-+-2}} gives 2 [10]Template:Xpd/
  • {{#expr:2*-3}} gives -6 [11]Template:Xpd/
  • {{#expr:-not-not-not0}} gives -1 [12]Template:Xpd/
  • {{#expr:2*/3}} gives Expression error: Unexpected / operator [13]Template:Xpd/

[edit] 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.

  • {{ #expr: +01.20 }} gives 1.2
  • {{ #expr: 12. }} gives 12

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

In [14] 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. Scientific notation and group separators are not allowed: an e or E is considered an unrecognized word after the number, 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:

  • {{ #expr: 123 }} gives 123
  • {{ #expr: 123.456 }} gives 123.456
  • {{ #expr: 0.456 }} gives 0.456
  • {{ #expr: 0 }} gives 0

Accepted, although in some cases more or less odd:

  • {{ #expr: .456 }} gives 0.456
  • {{ #expr: 123. }} gives 123
  • {{ #expr: 000123 }} gives 123
  • {{ #expr: 123.456.789 }} gives 123.456
  • {{ #expr: . }} gives 0

Wrong:

  • {{ #expr: 2e-5 }} gives 2.0E-5
  • {{ #expr: 2E-5 }} gives 2.0E-5
  • {{ #expr: 123,456 }} gives Expression error: Unrecognised punctuation character ","
  • {{ #expr: 123 456 }} gives Expression error: Unexpected number

Due to the specifier R ("raw"), {{NUMBEROFARTICLES:R}} gives 2405487 [15]Template:Xpd/ etc. produce numbers without group separators, which can be used in computations.

[edit] 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). Thus numbers produced include (depending on the operating system of the server):

  • {{ #expr: .000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000123456789012345 }} = 1.2345678901234E-106
  • {{ #expr: .00000123456789012345 }} = 1.2345678901234E-6
  • {{ #expr: .0000123456789012345 }} = 1.2345678901235E-5
  • {{ #expr: .000123456789012345 }} = 0.00012345678901234
  • {{ #expr: 123456789012.345 }} = 123456789012.35
  • {{ #expr: 1234567890123.45 }} = 1234567890123.4
  • {{ #expr: 12345678901234.5 }} = 12345678901234
  • {{ #expr: 123456789012345 }} = 123456789012340
  • {{ #expr: 1234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456 }} = 1.2345678901235E+105

For negative numbers simply a minus sign is prefixed:

  • {{ #expr: -123456789012345 }} = -123456789012340

Since scientific notation is not accepted as input, nested use of #expr may fail in cases where the same composite computation with a single #expr works.

Thus:
{{ #expr: 1/10000 *2 }} = 0.0002,
{{#expr:{{ #expr: 1/10000}} *2}} = 0.0002,
{{ #expr: 1/100000 *2 }} = 2.0E-5, but
{{#expr:{{ #expr: 1/100000}} *2}} = 2.0E-5.
Long YYYYMMDDhhmmss timestamps can run into the same problem:
{{ CURRENTTIMESTAMP }} gives 20080609101634,
{{#expr:{{ CURRENTTIMESTAMP}}}} gives 20080609101634.
Timestamps without seconds are 12 digits, just short enough:
{{ #expr:20080609101634/100 }} gives 200806091016.34

To allow the output of an expression to be used as input, the expression can be replaced by e.g.

  • {{#ifexpr: ''expression''/10000000000 >1 | {{#expr:''expression''/10000000000}} * 10000000000 | ''expression'' }}

Examples:

  • {{#ifexpr: 123456789012345/10000000000 >1 | {{#expr:123456789012345/10000000000}} * 10000000000 | 123456789012345 }} gives 12345.678901234 * 10000000000
  • {{#ifexpr: 12345.6789012345/10000000000 >1 | {{#expr:12345.6789012345/10000000000}} * 10000000000 | 12345.6789012345 }} gives 12345.6789012345

This increases the upper limit by a factor 1e10.

See m:Template:evalint (backlinks, edit) for producing output of large integers in non-scientific notation, suitable as input in another computation. For producing numbers with commas as group separators, see m:Template:csn (backlinks, edit).

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 ):

  • {{ #expr: ( -0.2 round 0 ) }} = -0
  • {{ #expr: 1*(-0.2 round 0) }} = -0
  • {{ #expr: 0+(-0.2 round 0) }} = 0

[edit] Accuracy

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

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

  • {{ #expr:(2/3) }} gives 0.66666666666667
  • {{ #expr:(2/3)*1000000-666666 }} gives 0.66666666662786
  • {{#expr:{{ #expr:(2/3)}} *1000000-666666}} gives 0.66666667000391
  • {{ #expr:1234567890.1234567890-1234567890 }} gives 0.12345671653748 (conclusion: 16 or 17 digits of 1234567890.1234567890 used)
  • {{ #expr:1234567890.1234567890 }} gives 1234567890.1235 (result is rounded to a total of 12 digits)
  • {{#expr:({{ #expr:1234567890.1234567890}} -1234567890)}} gives 0.12350010871887
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):
{{ #expr:1=1+0.00000000000000011102230246251566636831481088739149080826 }} = 0
{{ #expr:1=1+0.00000000000000011102230246251566636831481088739149080825 }} = 1
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:
{{ #expr:1+0.000000000004999889392 }} = 1.000000000005
{{ #expr:1+0.000000000004999889391 }} = 1.000000000005 below about 1 + 5E-12.

[edit] 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). Example:

{{#ifexpr: {{CURRENTDOW}} = 0 or {{CURRENTDOW}} = 6 | weekend | Mo-Fr}} yields Mo-Fr because today is Monday with {{CURRENTDOW}} gives 1 [16]Template:Xpd/.

[edit] 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.
  • {{#switch:FR|UK=London|FR=Paris|NL=Amsterdam}} gives NL=Amsterdam [17]Template:Xpd/
  • {{#switch:UK|UK|GB=London|FR=Paris}} gives FR=Paris [18]Template:Xpd/
  • {{#switch:ZZ|UK=London|FR=Paris|no match}} gives no match [19]Template:Xpd/
  • {{#ifeq:3|3.0|1|0}} gives 1 [20]Template:Xpd/
  • {{#ifeq:3|03|1|0}} gives 1 [21]Template:Xpd/
  • {{#ifeq:0.00003456|3.456E-05|1|0}} gives 1 [22]Template:Xpd/
    Note that #ifeq: unlike #expr: accepts exponential notation on input.
  • {{#ifeq:1234567890123|1234567890120|1|0}} gives 0 [23]Template:Xpd/
  • {{#ifeq:1234567890123|1.23456789012E+12|1|0}} gives 0 [24]Template:Xpd/
  • {{#ifeq:1234567890120|1.23456789012E+12|1|0}} gives 1 [25]Template:Xpd/
  • {{#ifeq:1.234567890120E12|1.23456789012E+12|1|0}} gives 1 [26]Template:Xpd/
    Numerical comparisons don't depend on the output format, compare:
  • {{#expr:1234567890123}} gives 1234567890123 [27]Template:Xpd/
  • {{#expr:1234567890120}} gives 1234567890120 [28]Template:Xpd/

#ifeq: allows to compare strings containing equal signs:

#switch: result #ifeq: result
"{{#switch:-1.0|-1=okay|fail}}" "fail" [29]Template:Xpd/ {{#ifeq:-1.0|-1|okay|fail}} gives okay [30]Template:Xpd/
"{{#switch:a=b|a=b=okay|fail}}" "fail" [31]Template:Xpd/ {{#ifeq:a=b|a=b|okay|fail}} gives okay [32]Template:Xpd/
"{{#switch:a=c|a=b=fail|okay}}" "okay" [33]Template:Xpd/ {{#ifeq:a=c|a=b|fail|okay}} gives okay [34]Template:Xpd/


[edit] 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)

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.

[edit] Error messages

Examples for all known #expr: and #ifexpr: error messages
Expression Error message
{{ #expr:1/0 }} Expression error: Division by zero
{{ #expr:2* }} Expression error: Missing operand for *
{{ #expr:1 2 }} Expression error: Unexpected number
{{ #ifexpr:1*/2 }} Expression error: Unexpected / operator
{{ #expr: 1 (2) }} Expression error: Unexpected ( operator
{{ #expr: (1  }} Expression error: Unclosed bracket
{{ #expr: 1)  }} Expression error: Unexpected closing bracket
{{ #expr:2*123,456 }}     Expression error: Unrecognised punctuation character ","
{{ #expr:{{{a}}} }} Expression error: Unrecognised punctuation character "{"
{{ #ifexpr:3%2 }} Expression error: Unrecognised punctuation character "%"
{{ #ifexpr:abc }} Expression error: Unrecognised word "abc"
{{ #expr:abc.def }} Expression error: Unrecognised word "abc"
{{ #expr:{{ x|102|1000*}} 18 }} gives 1.8E+307
{{ #expr:{{ x|102|1000*}} 179 }} gives 1.79E+308
{{ #expr:{{ x|102|1000*}} 180 }} gives INF (on Wikimedia "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 Expression error: Unclosed bracket
{{ #expr:{{ x|34|(1+(}} 1 {{ x|34|))}} }} gives Expression error: Stack exhausted
{{ #expr:3.4.5.6 }} gives 3.4   (no feature, only an oddity)

Note: m:Template:x (backlinks, edit) 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}}} 6} (one closing brace too many; the last of the three is interpreted as plain text, so that the rest works fine)
{{{#expr:2*3}} {6 (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
Expression error: Unrecognised word "toolarge",
{{ #expr: 2*{{ #ifexpr: 3*4>10|too large|3*4 }} }} gives
Expression error: Unrecognised word "too".

[edit] See also

Template:H:f User