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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> |
| − | --============================================================
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| − | -- (see NOTES at bottom)
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| − | --></noinclude>{{
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| − | #expr: ( 0 {{ | |
| − | #ifexpr: {{{1|0.0000}}}0={{{1|0.0000}}} |<!--see NOTE Z7-->
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| − | -1 + <noinclude><!--see NOTE S5--></noinclude>
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| − | {{#switch: x{{{1|0.0000}}}
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| − | |{{padleft:|6|x{{{1}}}}}=5
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| − | |{{padleft:|5|x{{{1}}}}}=4
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| − | |{{padleft:|7|x{{{1|0.0000}}}}}=6
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| − | |{{padleft:|4|x{{{1}}}}}=3
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| − | |{{padleft:|8|x{{{1}}}}}=7
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| − | |{{padleft:|9|x{{{1}}}}}=8
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| − | |{{padleft:|10|x{{{1}}}}}=9
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| − | |{{padleft:|11|x{{{1}}}}}=10
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| − | |{{padleft:|2|x{{{1}}}}}=1 <!--for "0"-->
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| − | |{{padleft:|12|x{{{1}}}}}=11
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| − | |{{padleft:|13|x{{{1}}}}}=12
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| − | |{{padleft:|14|x{{{1}}}}}=13
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| − | |{{padleft:|15|x{{{1}}}}}=14
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| − | |{{padleft:|16|x{{{1}}}}}=15
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| − | |{{padleft:|17|x{{{1}}}}}=16
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| − | |{{padleft:|18|x{{{1}}}}}=17
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| − | |{{padleft:|19|x{{{1}}}}}=18
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| − | |{{padleft:|20|x{{{1}}}}}=19
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| − | |{{padleft:|21|x{{{1}}}}}=20
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| − | |{{padleft:|3|x{{{1}}}}}=2
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| − | |{{padleft:|22|x{{{1}}}}}=21
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| − | |{{padleft:|23|x{{{1}}}}}=22
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| − | |{{padleft:|24|x{{{1}}}}}=23
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| − | |{{padleft:|25|x{{{1}}}}}=24
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| − | |{{padleft:|26|x{{{1}}}}}=25
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| − | |{{padleft:|27|x{{{1}}}}}=26
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| − | |{{padleft:|28|x{{{1}}}}}=27
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| − | |{{padleft:|29|x{{{1}}}}}=28
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| − | |{{padleft:|30|x{{{1}}}}}=29
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| − | |{{padleft:|31|x{{{1}}}}}=30
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| − | |{{padleft:|32|x{{{1}}}}}=31
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| − | |{{padleft:|33|x{{{1}}}}}=32
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| − | |{{padleft:|34|x{{{1}}}}}=33
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| − | |{{padleft:|35|x{{{1}}}}}=34
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| − | |{{padleft:|36|x{{{1}}}}}=35
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| − | |{{padleft:|37|x{{{1}}}}}=36
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| − | |{{padleft:|38|x{{{1}}}}}=37
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| − | |{{padleft:|39|x{{{1}}}}}=38
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| − | |{{padleft:|40|x{{{1}}}}}=39
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| − | |{{padleft:|41|x{{{1}}}}}=40
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| − | |#default = 41
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| − | }} - floor(
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| − | ln (floor( abs({{{1|0}}}) )+0.99 )/ln10 ) - 1
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| − | {{#ifexpr: floor(abs({{{1|0}}}) )=0 |-1}}
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| − | {{#ifeq: {{{1|0.0000}}}x|0x| + 1}}{{
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| − | #ifexpr: {{{1|500}}}<0| - 1}}<!--For minus sign-->
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| − | |<noinclude><!--else for integers--></noinclude>{{
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| − | #ifexpr:{{{1|500}}}=floor({{{1|500}}}/10)*10|-1}}{{
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| − | #ifexpr:{{{1|500}}}=floor({{{1|500}}}/100)*100|-1}}{{
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| − | #ifexpr:{{{1|500}}}=floor({{{1|500}}}/1E3)*1E3|-1}}{{
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| − | #ifexpr:{{{1|500}}}=floor({{{1|500}}}/1E4)*1E4|-1}}{{
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| − | #ifexpr:{{{1|500}}}=floor({{{1|500}}}/1E5)*1E5|-1}}{{
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| − | #ifexpr:{{{1|500}}}=floor({{{1|500}}}/1E6)*1E6|-1}}{{
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| − | #ifexpr:{{{1|500}}}=floor({{{1|500}}}/1E7)*1E7|-1}}{{
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| − | #ifexpr:{{{1|500}}}=floor({{{1|500}}}/1E8)*1E8|-1}}{{
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| − | #ifexpr:{{{1|500}}}=floor({{{1|500}}}/1E9)*1E9|-1}}{{
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| − | #ifexpr:{{{1|500}}}=floor({{{1|500}}}/1E10)*1E10|-1}}{{
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| − | #ifexpr:{{{1|500}}}=floor({{{1|500}}}/1E11)*1E11|-1}}{{
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| − | #ifexpr:{{{1|500}}}=floor({{{1|500}}}/1E12)*1E12|-1}}{{
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| − | #ifexpr:{{{1|500}}}=floor({{{1|500}}}/1E13)*1E13|-1}}{{
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| − | #ifexpr:{{{1|500}}}=floor({{{1|500}}}/1E14)*1E14|-1
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| − | }}}}<noinclude><!--endif {1}0={1}
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| − | --------------------------------------------------------
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| − | Check for fraction "/" to use logn of denominator, by
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| − | clearing prior count: (..prior..)*0 + (logn denom / logn 10).
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| − | (see NOTE A1). The whole expression ends with close ")".
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| − | --></noinclude>{{
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| − | #if: {{#titleparts:{{{1|6+3~8}}}|1|2}}| )*0 + (
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| − | (ln {{#titleparts:{{{1|6+3/8}}}|1|2}} / ln10)
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| − | }}<noinclude><!--endif fraction
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| − | --></noinclude> ) }}<noinclude><!--endexpr# (close paren.)
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| − | --
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| − | --------------------------------------------------------------
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| − | --NOTES:
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| − | -- [ These comments are skipped by <noinclude> and not send
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| − | -- inside formatted Internet pages, only during edit. ]
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| − | --
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| − | --NOTE A1: This template determines the precision of decimals
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| − | -- by counting the length of the numeric string (in a
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| − | -- #switch comparing lengths of padded strings), then
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| − | -- subtracting integer length, minus the decimal point,
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| − | -- and minus 1 if negative. For integers, 1 place is
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| − | -- subtracted for each trailing 0 on the integer.
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| − | -- For fractions, any prior count is cleared x 0, then
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| − | -- size is logarithm of denominator divided by logn 10:
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| − | -- (..prior...)*0 + floor(logn denom / logn 10 - .01) + 1.
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| − | --
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| − | --NOTE D2: The check, for whole integers, compares the amount
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| − | -- versus appending "0" at the end: when the amount is a
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| − | -- decimal, then the value is unchanged by appending 0 at
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| − | -- the end: so 5.23 = 5.230 is true, whereas for whole
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| − | -- integers, it would be: 5 = 50 as false, due to values
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| − | -- becoming n*10 for integer n. So, for integer n, the
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| − | -- check rejects: n = n0 as false; hence n is integer.
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| − | --
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| − | --NOTE M3: The magnitude of the integer portion is calculated
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| − | -- by logarithm of the floor of absolute value (divided by
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| − | -- [[natural logarithm]] of 10 to adjust for e=2.71828*),
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| − | -- as: ln (floor( abs({{{1|-0.050067}}}) )+0.99 )/ln10
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| − | -- Function floor(x) trims the decimal part, to leave the
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| − | -- whole count: 0-9 yield 0, 10-19 as 1, 1000-1999 as 3.
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| − | -- The abs(x) avoids floor of negatives, floor(-0.1)= -1,
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| − | -- hence using abs(x) ensures -0.1 floors to 0 not -1.
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| − | -- Near zero, the +0.99 avoids invalid log of 0, but does
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| − | -- not round-up any decimals, already floored as nnn.00.
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| − | -- Complexity is 6 operations: floor of abs( {1} ) +0.99
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| − | -- then logn div logn10, then floor that logarithm ratio.
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| − | -- Decimals -1 < x < 1 yield -1, avoiding log 0.001 = -3.
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| − | --
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| − | --NOTE N4: Nesting of if-else and nested templates is kept to
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| − | -- a minimum, due to the MediaWiki 1.6 limit of 40 levels
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| − | -- of if-logic for all nested templates used together.
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| − | -- Template {ordomag} was omitted to avoid 2 more levels
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| − | -- of nested templates. Template {Precision} had 8 levels,
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| − | -- and this template was trimmed to only 5 levels.
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| − | --
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| − | --NOTE S5: The #switch is run with "x" prepended in front of
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| − | -- the amount, otherwise a #switch will compare as numeric
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| − | -- where 2 would match "2.0" even though "2" is length 1.
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| − | -- So "x2" won't match "x2.0" in non-numeric comparison.
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| − | -- The #switch will exit on the first match, so smaller
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| − | -- lengths are compared first, to avoid extra comparisons
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| − | -- for more rare, longer numeric strings up to 41 long.
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| − | --
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| − | --NOTE W6: The check for integers with whole end-zeroes uses
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| − | -- typical n=n/10*10, for each power of 10, where whole
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| − | -- millions match: {{#ifexpr: {1}=floor( {1}/1E6 )*1E6| }}
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| − | -- Previously, {Precision} had tried to use "round" to
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| − | -- detect end-zeroes but "round" loses precision at -5,
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| − | -- so, n00000 round -5 differs from n00000 slightly, and
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| − | -- comparisons to exact rounded amounts failed to match
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| − | -- some numbers when 6 or more zeroes "n000000".
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| − | --
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| − | --NOTE Z7: The check on zero for any .00000 compares adding 1
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| − | -- to the amount, versus appending "1" at the end: if the
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| − | -- amount is a decimal, then adding 1 will be larger than
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| − | -- appending 1 at the end: 0.00 + 1 > 0.001, whereas for
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| − | -- whole zero, it would be: 0+1 > 01 as false, due to the
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| − | -- value being the same. So, for integer 0, the check
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| − | -- rejects: 0+1 > 01 as false; hence whole 0 is integer.
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| − | --
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| − | -- WARNING: *** DO NOT DELETE COMMENTS FROM THIS TEMPLATE ***
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| − | -- Unless these comments are readily available, people
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| − | -- might tinker with the coding (or rename templates),
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| − | -- in hopes to clarify operation because these comments
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| − | -- were not nearby to explain the issues. Having these
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| − | -- comments only on a doc-page increases the danger of
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| − | -- explanations no longer matching the current coding.
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| − | -- UPDATE these comments to match changes to the template.
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| − | -- UPDATE the HISTORY during major changes (not typos).
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| − | --
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| − | --------------------------------------------------------------
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| − | --HISTORY:
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| − | --15Aug10 Created to get precision even if large or negative.
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| − | --15Aug10 Put NOTES comments to explain template coding.
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| − | --15Aug10 Put HISTORY comments to log major changes.
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| − | --18Aug10 Fixed to handle zero: 0 as 0, 0.000 as 3, etc.
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| − | --04Sep10 Fixed to handle decimals between 0~1 (by round 0).
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| − | --04Sep10 Updated NOTES to explain the check appending 0 or 1.
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| − | --03Jan11 Fix integer end-zeroes: 50 as -1, 500 as -2, 5000 -3.
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| − | --03Jan11 Omit {Order of Magnitude} for 2 levels less nesting.
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| − | --03Jan11 Omit {Str_len} for 8 fewer levels of 40-nest limit.
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| − | --03Jan11 Put "noinclude" around all inter-line HTML comments.
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| − | --03Jan11 Allow fraction "/": floor(ln denom/ln 10 -.01)+1.
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| − | --08Feb11 Fixed to not count minus sign on negative integers.
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| − | --08Feb11 Extended to handle integers with 14 end-zeroes "0".
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| − | --08Feb11 Ordered length-search by most-likely (rarely 1 or 2).
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| − | --10Feb11 Re-added NOTES/HISTORY to explain logic & changes.
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| − | --22Jun11 Move to Precision: no need to keep all three.
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| − | --22Jun11 No rounding up for fractions (i.e. ln denom/ln 10)
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| − | --
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| − | -->{{documentation}}</noinclude>
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