Template:Precision

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This template is used onapproximately 5,900 pages and changes may be widely noticed. Test changes in the template's/sandbox or/testcases subpages, or in your ownuser subpage. Consider discussing changes on thetalk page before implementing them.

This template usesLua:

Module:Math (sandbox)

TheTemplate:Precision determines the precision (as a count of decimal digits) for any amount, large or negative, using a fast algorithm. It can also handle a trailing decimal point (such as "15." or "-41.") or trailing zeroes (such as "15.34000" having precision as 5 decimal digits). For fractional input it returns the base ten logarithm of the numerator.

Examples

`{{Precision\|1111.123456789}}`	9
`{{Precision\|1111.12345678}}`	8
`{{Precision\|1111.1234567}}`	7
`{{Precision\|1111.123456}}`	6
`{{Precision\|1111.12345}}`	5
`{{Precision\|1111111111.12345678}}`	8
`{{Precision\|1111111111.1234567}}`	7
`{{Precision\|1111111111.123456}}`	6
`{{Precision\|1111111111.12345}}`	5
`{{Precision\|1111111111.1234}}`	4
`{{Precision\|1111111111.123}}`	3
`{{Precision\|1111111111.12}}`	2
`{{Precision\|1111111111.1}}`	1
`{{Precision\|1111111111.10}}`	2
`{{Precision\|1111111111.100}}`	3
`{{Precision\|1111111111.1000}}`	4
`{{Precision\|1111111111.10000}}`	5
`{{Precision\|1111111111}}`	0
`{{Precision\|1111111110}}`	-1
`{{Precision\|1111111100}}`	-2
`{{Precision\|1111111000}}`	-3
`{{Precision\|1111110000}}`	-4
`{{Precision\|1111100000}}`	-5
`{{Precision\|1111000000}}`	-6
`{{Precision\|1110000000}}`	-7
`{{Precision\|1100000000}}`	-8
`{{Precision\|0}}`	0
`{{Precision\|1}}`	0
`{{Precision\|22.45}}`	2
`{{Precision\|22.12345}}`	5
`{{Precision\|22}}`	0
`{{Precision\|22000}}`	-3
`{{Precision\|-15.275}}`	3
`{{Precision\|-15.2500}}`	4
`{{Precision\|23000222000111.432}}`	3
`{{Precision\|-15.123}}`	3
`{{Precision\|0.09}}`	2
`{{Precision\|0.88}}`	2
`{{Precision\|880000}}`	-4
`{{Precision\|90000000}}`	-7

Known bugs

For numbers in scientific notation, the precision is typically returned as too low by 1 decimal place. Example: {{precision |7.1234E+06}} → -2 (should be precision as 4 decimal digits, not 3).

Technical notes

NOTE A1: This template determines the precision of decimals by counting the length of the numeric string (in a #switch comparing lengths of padded strings), then subtracting integer length, minus the decimal point, and minus 1 if negative. For integers, 1 place is subtracted for each trailing 0 on the integer. For fractions, any prior count is cleared x 0, then returns the base ten logarithm of denominator: (..prior...)*0 + (ln denom / ln 10).
NOTE D2: The check, for whole integers, compares the amount versus appending "0" at the end: when the amount is a decimal, then the value is unchanged by appending 0 at the end: so 5.23 = 5.230 is true, whereas for whole integers, it would be: 5 = 50 as false, due to values becoming n*10 for integer n. So, for integer n, the check rejects: n = n0 as false; hence n is integer.
NOTE M3: The magnitude of the integer portion is calculated by logarithm of the floor of absolute value (divided bynatural logarithm of 10 to adjust for e=2.71828*), as: ln (floor( abs(-0.050067) )+0.99 )/ln10 Function floor(x) trims the decimal part, to leave the whole count: 0-9 yield 0, 10-19 as 1, 1000-1999 as 3. The abs(x) avoids floor of negatives, floor(-0.1)= -1, hence using abs(x) ensures -0.1 floors to 0 not -1. Near zero, the +0.99 avoids invalid log of 0, but does not round-up any decimals, already floored as nnn.00. Complexity is 6 operations: floor of abs( {1} ) +0.99 then log₁₀x (lnx ÷ ln10), then floor that logarithm ratio. Decimals -1 < x < 1 yield -1, avoiding log 0.001 = -3.
NOTE N4: Nesting of if-else and nested templates is kept to a minimum, due to the MediaWiki 1.6 limit of 40 levels of if-logic for all nested templates used together. Template {ordomag} was omitted to avoid 2 more levels of nested templates. Template {Precision} had 8 levels, and this template was trimmed to only 5 levels.
NOTE S5: The #switch is run with "x" prepended in front of the amount, otherwise a #switch will compare as numeric where "2" would match "2.0" even though "2" is length 1 so "x2" no longer matches with "x2.0" as non-numeric. The #switch will exit on the first match, so smaller lengths are compared first, to avoid extra comparisons for more rare, longer numeric strings up to 41 long.
NOTE W6: The check for integers with whole end-zeroes uses typical n=n/10*10, for each power of 10, where whole millions match: {{#ifexpr: {1}=floor( {1}/1E6 )*1E6| }} Previously, {Precision} had tried to use "round" to detect end-zeroes but "round" loses precision at -5, so, n00000 round -5 differs from n00000 slightly, and comparisons to exact rounded amounts failed to match some numbers when 6 or more zeroes "n000000".
NOTE Z7: The check on zero for any .00000 compares adding 1 to the amount, versus appending "1" at the end: if the amount is a decimal, then adding 1 will be larger than appending 1 at the end: 0.00 + 1 > 0.001, whereas for whole zero, it would be: 0+1 > 01 as false, due to the value being the same. So, for integer 0, the check rejects: 0+1 > 01 as false; hence whole 0 is integer.

decdeg	degrees, minutes, and seconds todecimal degrees
deg2dms	decimal degrees to degrees, minutes, and seconds
deg2hms	decimal degrees tohour angle (in hours, minutes, and seconds)
hms2deg	hour angle (in hours, minutes, and seconds) to decimal degrees
inflation	calculate inflation of Consumer Price Index-related prices
pop density	population density in an area
track gauge	railway track gauges

Notation andformatting

bigmath	bigger font to matchTeX`\displaystyle` (standalone formulas only)	math	short text-based formulas
mathcal	[mathematical] calligraphic font; alternative toLaTeX`\mathcal{...}`	tombstone	symbol indicating theend of a proof
mvar	individual italicized maths variables in normal text	val	measurement values, uncertainties and units
overline underline	a line set above/below a sequence of characters	vec	various overarrows, underarrows, etc.
abs	absolute values (paired vertical lines)	langle rangle angbr	angular brackets
bra-ket braket bra ket	bra–ket notation	ldelim rdelim	multiline delimiters (2–5 lines inclusive)
ceil,floor	calculations:mw:Help:#expr; formatting indicators⌈3.14⌉,⌊3.14⌋ (no calculation performed)	pars	parentheses that can be resized(∑)
fraction	slant fractions3⁄5 (not for maths/science articles; usestanding or upright fractions`{{sfrac}}` instead)	sfrac	"standing" or upright fractions⁠3/5⁠ (use in maths/science articles instead of`{{fraction}}`)
intmath	integral symbols	sub sup su	subscripts and superscripts
overset underset	arbitrary characters/diacritics set above/below one another
tmath	WrapTeX in<math> tags

Boxes

`{{Precision\|1111.123456789}}`	9
`{{Precision\|1111.12345678}}`	8
`{{Precision\|1111.1234567}}`	7
`{{Precision\|1111.123456}}`	6
`{{Precision\|1111.12345}}`	5
`{{Precision\|1111111111.12345678}}`	8
`{{Precision\|1111111111.1234567}}`	7
`{{Precision\|1111111111.123456}}`	6
`{{Precision\|1111111111.12345}}`	5
`{{Precision\|1111111111.1234}}`	4
`{{Precision\|1111111111.123}}`	3
`{{Precision\|1111111111.12}}`	2
`{{Precision\|1111111111.1}}`	1
`{{Precision\|1111111111.10}}`	2
`{{Precision\|1111111111.100}}`	3
`{{Precision\|1111111111.1000}}`	4
`{{Precision\|1111111111.10000}}`	5
`{{Precision\|1111111111}}`	0
`{{Precision\|1111111110}}`	-1
`{{Precision\|1111111100}}`	-2
`{{Precision\|1111111000}}`	-3
`{{Precision\|1111110000}}`	-4
`{{Precision\|1111100000}}`	-5
`{{Precision\|1111000000}}`	-6
`{{Precision\|1110000000}}`	-7
`{{Precision\|1100000000}}`	-8
`{{Precision\|0}}`	0
`{{Precision\|1}}`	0
`{{Precision\|22.45}}`	2
`{{Precision\|22.12345}}`	5
`{{Precision\|22}}`	0
`{{Precision\|22000}}`	-3
`{{Precision\|-15.275}}`	3
`{{Precision\|-15.2500}}`	4
`{{Precision\|23000222000111.432}}`	3
`{{Precision\|-15.123}}`	3
`{{Precision\|0.09}}`	2
`{{Precision\|0.88}}`	2
`{{Precision\|880000}}`	-4
`{{Precision\|90000000}}`	-7

Movatterモバイル変換

Examples

Known bugs

Technical notes

See also