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The Template:Getprecision 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).

Examples

Some examples:

  • {{getprecision| 0}} → 1
  • {{getprecision| 1}} → 0
  • {{getprecision| 22.45}} → 3
  • {{getprecision| 22.12345}} → 6
  • {{getprecision| 22}} → 0
  • {{getprecision| 22000}} → -3
  • {{getprecision| -15.275}} → 4
  • {{getprecision| -15.2500}} → 5
  • {{Getprecision |23000222000111.432}} → 3
  • {{getprecision| -15.123}} → 4
{{precision| -15.123}} → {{precision| -15.123}} (Nota bene*  Template:Getprecision handles negatives, but not Template:Precision)
  • {{getprecision|0.09}} → 2
  • {{getprecision|0.88}} → 2
  • {{getprecision|880000}} → -4
  • {{getprecision|90000000}} → -7

Known bugs

  • For numbers in scientific notation, the precision is typically returned as too low by 1 decimal place. Example: {{getprecision |7.1234E+06}} → -2 (should be precision as 4 decimal digits, not 3).
  • Large numbers are limited to 11 trailing zeroes, so even larger numbers still report precision as being -11, such as 9 trillion: {{getprecision|9000000000000}} → -12 (should be: -12).

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 size is logarithm of denominator divided by log 10: (..prior...)*0 + floor(logn denom / logn 10 - .01) + 1.
  • 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 by natural 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 logn div logn10, 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, Template: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.

History

  • 15Aug10 Created to get precision even if large or negative.
  • 15Aug10 Put NOTES comments to explain template coding.
  • 15Aug10 Put HISTORY comments to log major changes.
  • 18Aug10 Fixed to handle zero: 0 as 0, 0.000 as 3, etc.
  • 04Sep10 Fixed to handle decimals between 0~1 (by round 0).
  • 04Sep10 Updated NOTES to explain the check appending 0 or 1.
  • 03Jan11 Fix integer end-zeroes: 50 as -1, 500 as -2, 5000 -3.
  • 03Jan11 Omit {Order of Magnitude} for 2 levels less nesting.
  • 03Jan11 Omit {Str_len} for 8 fewer levels of 40-nest limit.
  • 03Jan11 Put "noinclude" around all inter-line HTML comments.
  • 03Jan11 Allow fraction "/": floor(logn denom/logn 10 -.01)+1.

See also

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