Template:Getprecision/doc

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:
 * &rarr;
 * &rarr;
 * &rarr;
 * &rarr;
 * &rarr;
 * &rarr;
 * &rarr;
 * &rarr;
 * &rarr;


 * &rarr;
 * 3 &rarr; 3 [ Getprecision handles negatives, but not {precision} ]


 * &rarr;
 * &rarr;
 * &rarr;
 * &rarr;

Known bugs

 * For numbers in scientific notation, the precision is typically returned as too low by 1 decimal place. Example: &rarr;  (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: {&#123;getprecision|9000000000000}} &rarr; (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 )+0.99 )/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: 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.

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.