View source for Template:Rndpad

<noinclude><!--
-=============================================================
- Template:Rndpad - round 11-digit billions & pad end zeroes
-=============================================================
--                              (see NOTES at bottom)
--></noinclude>{{
  #ifexpr: abs( {{{1|0}}} ) > 84999999999 <!--85 billion
-->  or abs( {{{1|7.58}}} ) < 1E-7  <!--tiny below 0.00000001
--then just use-->|{{rnd|{{{1|89730000006.40}}}<!--
  -->|{{{2|-7}}} }}<!--over 85 billion, allow scientific notation

--else-->|<!--round up to 85 billion as split 11-digit form...
-->{{#ifexpr:({{{1|7.58}}}) round ({{{2|-5}}}) > 99999 |<!--
--then-show-digits-above-99,999-->{{#expr:
  floor( ( ({{{1|7.58}}}) round ({{{2|-5}}}) )/100000
   + 1E-9 ) }}<!--add to unbug floor(x) & truncate, see NOTE F3

--show-each-zero-above-rounded-remainder-->{{
#ifexpr:(( {{{1|7.58}}} round {{{2|-5}}})+1E-9) mod 1E5 < 10000|<!--then show "0"-->0}}{{
#ifexpr:(( {{{1|7.58}}} round {{{2|-5}}})+1E-9) mod 1E5 < 1000|<!--then show "0"-->0}}{{
#ifexpr:(( {{{1|7.58}}} round {{{2|-5}}})+1E-9) mod 1E5 < 100|<!--then show "0"-->0}}{{
#ifexpr:(( {{{1|7.58}}} round {{{2|-5}}})+1E-9) mod 1E5 < 10|<!--then show "0"-->0}}<!--

--round remainder-->{{
  #ifexpr: {{{2|-5}}} < 1
  |<!--then round remainder simply
  -->{{#expr:(( {{{1|7.58}}} round {{{2|-5}}})+1E-9) mod 1E5}}
  |<!--else use {rnd/-}-->{{rnd/-|{{#expr: ( {{{1|7.58}}}
         round {{{2|-5}}})+1E-9) mod 1E5
         }}|{{{2|-5}}} }}<!--end {rnd/-}
  -->}}<!--endifexpr {2} < 1

 --else-round below 100thousand
 -->|{{rnd/-|{{#expr:({{{1|80561.4503}}}) round ({{{2|3}}}) }}|{{#expr:{{{2|3}}} }} }}<!--end rnd/-

 -->}}<!--endif-{1}>100thousand

-->}}<!--endif {1}>85billion or {2}< -4 --
--><noinclude><!--
-=============================================================
-
-NOTES:
-  This Template:Rndpad rounds to 85 billion in 11-digit form,
-  and pads any trailing zeroes for round>0. If amount exceeds
-  85 billion or rounding exceeds 100-thousands (< -5) then
-  this template invokes [[Template:Rnd]] & allows scientific
-  notation for amounts above 85 billion. Otherwise, it rounds
-  amounts very quicky, using only the 1 subtemplate {{rnd/-}},
-  which ensures pad with trailing zeros in decimals (x.x00).
-  The expansion depth is 4 of the 40 expansion depth limit,
-  for amounts < 85 billion.
-
- NOTE L1: The limit to upper rounding is -11 for hundreds of
-   billions. The max number to still allow padded end-zeroes
-   "000" is 85 billion, due to scientific notation being shown
-   for the upper half of the digits when more than 85 billion.
-   Numbers >99,999 are split by modulo: {1} round {2} mod 1E5.
-
- NOTE N2: For smaller numbers & {2} < 1, {{rndpad}} will use
--  template {{rnd/-}} to pad any trailing decimal zeroes.
--  But, for amounts over 85 billion, using {{rndpad}} will
-   invoke up to 9 subtemplates, among the following:
-       Template:Order_of_magnitude (view source) (protected)
-       Template:Order_of_magnitude/x (view source) (protected)
-       Template:Rnd (view source) (protected)
-       Template:Rnd/- (view source) (protected)
-       Template:Rnd/b1 (view source) (protected)
-       Template:Rnd/b-1 (view source) (protected)
-       Template:Rnd/c6dec0 (view source) (protected)
-       Template:Rnd/c8dec0 (view source) (protected)
-       Template:Rnd/d (view source) (protected)
-       Template:Rnd/e+ (view source) (protected)
-   Those subtemplates might exceed the template-nesting limit,
-   such as inside nested infoboxes with 3-level nested-if
-   expressions (assuming limit of 40 nested if-expressions).
-
- NOTE F3: The adjustment adds 0.000000001 to fix floor(x).
-   The math function floor(x) experiences a bug whenever
-   numbers are close to a whole digit, yet floor to 1 less:
-   {{#expr: ({{{1|180333}}}round{{{2|-5}}})/100000 }} = 2
-   but floor ( ({{{1|180333}}}round{{{2|-5}}})/100000) = 1.
-   Even though an amount rounded -5 as 200 thousand & divided
-   by 100 thousand, shows as "2", floor of that can be "1".
-   That is why 1E-9 (0.000000001) is added to fix floor(x).
-   Exact: 2 - (180333 round -5)/10E5 = 2.2204460492503E-16
-
- NOTE R4: Rounding by a rounded count: Parentheses are used
-   around the round-digit count to allow an expression, such
-   as "( {{{2|0.5 round 0}}} )" to be a rounded count. The
-   parentheses ensure the "round 0" will apply to 0.5 as 1,
-   rather than have 0.5 enter into the nearby calculation, as
-   "4.16 round 0.5 round 0" versus "4.16 round (0.5 round 0)".
-   Otherwise, the 1st round has precedence: "4.16 round 0.5".
-
-=============================================================
-HISTORY:
-11Mar10 Created to round to 10 billion as 10 digits, pad end 0.
-11Mar10 Put NOTES comments to explain template coding.
-11Mar10 Put HISTORY comments to log major changes.
-11Mar10 Changed to use {rnd} when round less than -4.
-11Mar10 Changed to round 11-digit form, up to 85 billion.
-20Nov10 Changed to allow round -5 up to xx,951,000 of million.
-11Jan11 Fixed rounded-up portions >999,999 to use {{rnd}}.
-11Jan11 Fixed to split digits >99,999 only after rounding.
-11Jan11 Fixed to put 5 zeroes if any portion rounds > 99,999.
-11Jan11 Fixed to put 5 zeroes if rounding count < -4.
-11Jan11 Fixed floor(x) math bug by adding 1E-9 (0.000000001).
-16Jan11 Fixed for negative exponents, abs(x) < 0.0000001.
-18Jan11 Removed use of {formatnum:} to avoid commas.
-19Jan11 Put many parentheses "()" to round by an expression.
-20Jan11 Put #expr in {rnd/-} parms to cut argument size 60%.
-18Feb11 Fixed for whole billions to allow round -6 to -11.
-20Feb11 Numbers >99,999 are split by: {1} round {2} mod 1E5.
-20Feb11 Fixed rounding bug by: ({1} round {2})+1E-9 mod 1E5.
-20Feb11 Fixed whole 100-thousands "00000" by rounding first.
-20Feb11 Used quick {doc_short} rather than {documentation}.
-
-->{{documentation}}
</noinclude>