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| <noinclude><!-- | | <includeonly>{{#invoke:Math|precision|{{{1|0}}}|check_fraction=true}}</includeonly><noinclude> |
| --============================================================
| | {{documentation}} |
| -- Getprecision - Count decimal digits or in fraction (2+1/3)
| | </noinclude> |
| --============================================================
| |
| -- (see NOTES at bottom)
| |
| --></noinclude>{{
| |
| #expr: ( 0 {{ | |
| #ifexpr: {{{1|0.0000}}}0={{{1|0.0000}}} |<!--see NOTE Z7-->
| |
| -1 + <noinclude><!--see NOTE S5--></noinclude>
| |
| {{#switch: x{{{1|0.0000}}}
| |
| |{{padleft:|6|x{{{1}}}}}=5
| |
| |{{padleft:|5|x{{{1}}}}}=4
| |
| |{{padleft:|7|x{{{1|0.0000}}}}}=6
| |
| |{{padleft:|4|x{{{1}}}}}=3
| |
| |{{padleft:|8|x{{{1}}}}}=7
| |
| |{{padleft:|9|x{{{1}}}}}=8
| |
| |{{padleft:|10|x{{{1}}}}}=9
| |
| |{{padleft:|11|x{{{1}}}}}=10
| |
| |{{padleft:|2|x{{{1}}}}}=1 <!--for "0"-->
| |
| |{{padleft:|12|x{{{1}}}}}=11
| |
| |{{padleft:|13|x{{{1}}}}}=12
| |
| |{{padleft:|14|x{{{1}}}}}=13
| |
| |{{padleft:|15|x{{{1}}}}}=14
| |
| |{{padleft:|16|x{{{1}}}}}=15
| |
| |{{padleft:|17|x{{{1}}}}}=16
| |
| |{{padleft:|18|x{{{1}}}}}=17
| |
| |{{padleft:|19|x{{{1}}}}}=18
| |
| |{{padleft:|20|x{{{1}}}}}=19
| |
| |{{padleft:|21|x{{{1}}}}}=20
| |
| |{{padleft:|3|x{{{1}}}}}=2
| |
| |{{padleft:|22|x{{{1}}}}}=21
| |
| |{{padleft:|23|x{{{1}}}}}=22
| |
| |{{padleft:|24|x{{{1}}}}}=23
| |
| |{{padleft:|25|x{{{1}}}}}=24
| |
| |{{padleft:|26|x{{{1}}}}}=25
| |
| |{{padleft:|27|x{{{1}}}}}=26
| |
| |{{padleft:|28|x{{{1}}}}}=27
| |
| |{{padleft:|29|x{{{1}}}}}=28
| |
| |{{padleft:|30|x{{{1}}}}}=29
| |
| |{{padleft:|31|x{{{1}}}}}=30
| |
| |{{padleft:|32|x{{{1}}}}}=31
| |
| |{{padleft:|33|x{{{1}}}}}=32
| |
| |{{padleft:|34|x{{{1}}}}}=33
| |
| |{{padleft:|35|x{{{1}}}}}=34
| |
| |{{padleft:|36|x{{{1}}}}}=35
| |
| |{{padleft:|37|x{{{1}}}}}=36
| |
| |{{padleft:|38|x{{{1}}}}}=37
| |
| |{{padleft:|39|x{{{1}}}}}=38
| |
| |{{padleft:|40|x{{{1}}}}}=39
| |
| |{{padleft:|41|x{{{1}}}}}=40
| |
| |#default = 41
| |
| }} - floor(
| |
| ln (floor( abs({{{1|0}}}) )+0.99 )/ln10 ) - 1
| |
| {{#ifexpr: floor(abs({{{1|0}}}) )=0 |-1}}
| |
| {{#ifeq: {{{1|0.0000}}}x|0x| + 1}}{{
| |
| #ifexpr: {{{1|500}}}<0| - 1}}<!--For minus sign-->
| |
| |<noinclude><!--else for integers--></noinclude>{{
| |
| #ifexpr:{{{1|500}}}=floor({{{1|500}}}/10)*10|-1}}{{
| |
| #ifexpr:{{{1|500}}}=floor({{{1|500}}}/100)*100|-1}}{{
| |
| #ifexpr:{{{1|500}}}=floor({{{1|500}}}/1E3)*1E3|-1}}{{
| |
| #ifexpr:{{{1|500}}}=floor({{{1|500}}}/1E4)*1E4|-1}}{{
| |
| #ifexpr:{{{1|500}}}=floor({{{1|500}}}/1E5)*1E5|-1}}{{
| |
| #ifexpr:{{{1|500}}}=floor({{{1|500}}}/1E6)*1E6|-1}}{{
| |
| #ifexpr:{{{1|500}}}=floor({{{1|500}}}/1E7)*1E7|-1}}{{
| |
| #ifexpr:{{{1|500}}}=floor({{{1|500}}}/1E8)*1E8|-1}}{{
| |
| #ifexpr:{{{1|500}}}=floor({{{1|500}}}/1E9)*1E9|-1}}{{
| |
| #ifexpr:{{{1|500}}}=floor({{{1|500}}}/1E10)*1E10|-1}}{{
| |
| #ifexpr:{{{1|500}}}=floor({{{1|500}}}/1E11)*1E11|-1}}{{
| |
| #ifexpr:{{{1|500}}}=floor({{{1|500}}}/1E12)*1E12|-1}}{{
| |
| #ifexpr:{{{1|500}}}=floor({{{1|500}}}/1E13)*1E13|-1}}{{
| |
| #ifexpr:{{{1|500}}}=floor({{{1|500}}}/1E14)*1E14|-1
| |
| }}}}<noinclude><!--endif {1}0={1}
| |
| --------------------------------------------------------
| |
| Check for fraction "/" to use logn of denominator, by
| |
| clearing prior count: (..prior..)*0 + (logn denom / logn 10).
| |
| (see NOTE A1). The whole expression ends with close ")".
| |
| --></noinclude>{{
| |
| #if: {{#titleparts:{{{1|6+3~8}}}|1|2}}| )*0 + (
| |
| (ln {{#titleparts:{{{1|6+3/8}}}|1|2}} / ln10)
| |
| }}<noinclude><!--endif fraction
| |
| --></noinclude> ) }}<noinclude><!--endexpr# (close paren.)
| |
| --
| |
| --------------------------------------------------------------
| |
| --NOTES:
| |
| -- [ These comments are skipped by <noinclude> and not send
| |
| -- inside formatted Internet pages, only during edit. ]
| |
| --
| |
| --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 logn 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({{{1|-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" won't match "x2.0" in non-numeric comparison.
| |
| -- 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.
| |
| --
| |
| -- WARNING: *** DO NOT DELETE COMMENTS FROM THIS TEMPLATE ***
| |
| -- Unless these comments are readily available, people
| |
| -- might tinker with the coding (or rename templates),
| |
| -- in hopes to clarify operation because these comments
| |
| -- were not nearby to explain the issues. Having these
| |
| -- comments only on a doc-page increases the danger of
| |
| -- explanations no longer matching the current coding.
| |
| -- UPDATE these comments to match changes to the template.
| |
| -- UPDATE the HISTORY during major changes (not typos).
| |
| --
| |
| --------------------------------------------------------------
| |
| --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(ln denom/ln 10 -.01)+1.
| |
| --08Feb11 Fixed to not count minus sign on negative integers.
| |
| --08Feb11 Extended to handle integers with 14 end-zeroes "0".
| |
| --08Feb11 Ordered length-search by most-likely (rarely 1 or 2).
| |
| --10Feb11 Re-added NOTES/HISTORY to explain logic & changes.
| |
| --22Jun11 Move to Precision: no need to keep all three.
| |
| --22Jun11 No rounding up for fractions (i.e. ln denom/ln 10)
| |
| --
| |
| -->{{documentation}}</noinclude>
| |
Template documentation