-- Input can also have multiple links in a single name like:
-- U.S. gallon
-- miles per U.S. quart
-- long tons per short ton
-- Assume that links cannot be nested (never like "abc[[defghi]]").
-- This uses a simple and efficient procedure that works for most cases.
-- Some units (if used) would require more, and can later think about
-- adding a method to handle exceptions.
-- The procedure is to replace each space with a hyphen, but
-- not a space after ')' [for "(pre-1954&nbsp;US) nautical mile"], and
-- not spaces immediately before '(' or in '(...)' [for cases like
-- "British thermal unit (ISO)" and "Calorie (International Steam Table)"].
if name:find(' ', 1, true) then
if parts then
local pos
if name:sub(1, 1) == '(' then
pos = name:find(')', 1, true)
if pos then
return name:sub(1, pos+1) .. name:sub(pos+2):gsub(' ', '-')
end
elseif name:sub(-1) == ')' then
pos = name:find('(', 1, true)
if pos then
return name:sub(1, pos-2):gsub(' ', '-') .. name:sub(pos-1)
end
end
return name:gsub(' ', '-')
end
parts = collection
for before, item, after in name:gmatch('([^[]*)(%[%[[^[]*%]%])([^[]*)') do
if item:find(' ', 1, true) then
local prefix
local plen = item:find('|', 1, true)
if plen then
prefix = item:sub(1, plen)
item = item:sub(plen + 1, -3)
else
prefix = item:sub(1, -3) .. '|'
item = item:sub(3, -3)
end
item = prefix .. hyphenated(item, parts) .. ']]'
end
parts:add(before:gsub(' ', '-') .. item .. after:gsub(' ', '-'))
end
if parts.n == 0 then
-- No link like "..." was found in the original name.
parts:add(hyphenated(name, parts))
end
return table.concat(parts)
end
return name
end  
local function hyphenated_maybe(parms, want_name, sep, id, inout)
-- Return s, f where
-- s = id, possibly modified
-- f = true if hyphenated
-- Possible modifications: hyphenate; prepend '-'; append mid text.
if id == nil or id == '' then
return ''
end
local mid = (inout == (parms.opt_flip and 'out' or 'in')) and parms.mid or ''
if want_name then
if parms.opt_adjectival then
return '-' .. hyphenated(id) .. mid, true
end
if parms.opt_add_s and id:sub(-1) ~= 's' then
id = id .. 's' -- for nowiki
end
end
return sep .. id .. mid
end  
local function use_minus(text)
-- Return text with Unicode minus instead of '-', if present.
if text:sub(1, 1) == '-' then
return MINUS .. text:sub(2)
end
return text
end  
local function digit_groups(parms, text, method)
-- Return a numbered table of groups of digits (-to-, in local language).
-- Parameter method is a number or nil:
-- 3 for 3-digit grouping (default), or
-- 2 for 3-then-2 grouping (only for digits before decimal mark).
local len_right
local len_left = text:find('.', 1, true)
if len_left then
len_right = #text - len_left
len_left = len_left - 1
else
len_left = #text
end
local twos = method == 2 and len_left > 5
local groups = collection
local run = len_left
local n
if run < 4 or (run == 4 and parms.opt_comma5) then
if parms.opt_gaps then
n = run
else
n = #text
end
elseif twos then
n = run % 2 == 0 and 1 or 2
else
n = run % 3 == 0 and 3 or run % 3
end
while run > 0 do
groups:add(n)
run = run - n
n = (twos and run > 3) and 2 or 3
end
if len_right then
if groups.n == 0 then
groups:add(0)
end
if parms.opt_gaps and len_right > 3 then
local want4 = not parms.opt_gaps3 -- true gives no gap before trailing single digit
local isfirst = true
run = len_right
while run > 0 do
n = (want4 and run == 4) and 4 or (run > 3 and 3 or run)
if isfirst then
isfirst = false
groups[groups.n] = groups[groups.n] + 1 + n
else
groups:add(n)
end
run = run - n
end
else
groups[groups.n] = groups[groups.n] + 1 + len_right
end
end
local pos = 1
for i, length in ipairs(groups) do
groups[i] = from_en(text:sub(pos, pos + length - 1))
pos = pos + length
end
return groups
end  
function with_separator(parms, text) -- for forward declaration above
-- Input text is a number in en digits with optional '.' decimal mark.
-- Return an equivalent, formatted for display:
-- with a custom decimal mark instead of '.', if wanted
-- with thousand separators inserted, if wanted
-- digits in local language
-- The given text is like '123' or '123.' or '12345.6789'.
-- The text has no sign (caller inserts that later, if necessary).
-- When using gaps, they are inserted before and after the decimal mark.
-- Separators are inserted only before the decimal mark.
-- A trailing dot (as in '123.') is removed because their use appears to
-- be accidental, and such a number should be shown as '123' or '123.0'.
-- It is useful for convert to suppress the dot so, for example, '4000.'
-- is a simple way of indicating that all the digits are significant.
if text:sub(-1) == '.' then
text = text:sub(1, -2)
end
if #text < 4 or parms.opt_nocomma or numsep == '' then
return from_en(text)
end
local groups = digit_groups(parms, text, group_method)
if parms.opt_gaps then
if groups.n <= 1 then
return groups[1] or ''
end
local nowrap = '<span>'
local gap = '<span>'
local close = '</span>'
return nowrap .. groups[1] .. gap .. table.concat(groups, close .. gap, 2, groups.n) .. close .. close
end
return table.concat(groups, numsep)
end  
-- An input value like 1.23e12 is displayed using scientific notation (1.23×10¹²).
-- That also makes the output use scientific notation, except for small values.
-- In addition, very small or very large output values use scientific notation.
-- Use format(fmtpower, significand, '10', exponent) where each argument is a string.
local fmtpower = '%s<span>×</span>%s<sup>%s</sup>'  
local function with_exponent(parms, show, exponent)
-- Return wikitext to display the implied value in scientific notation.
-- Input uses en digits; output uses digits in local language.
return format(fmtpower, with_separator(parms, show), from_en('10'), use_minus(from_en(tostring(exponent))))
end  
local function make_sigfig(value, sigfig)
-- Return show, exponent that are equivalent to the result of
-- converting the number 'value' (where value >= 0) to a string,
-- rounded to 'sigfig' significant figures.
-- The returned items are:
-- show: a string of digits; no sign and no dot;
-- there is an implied dot before show.
-- exponent: a number (an integer) to shift the implied dot.
-- Resulting value = tonumber('.' .. show) * 10^exponent.
-- Examples:
-- make_sigfig(23.456, 3) returns '235', 2 (.235 * 10^2).
-- make_sigfig(0.0023456, 3) returns '235', -2 (.235 * 10^-2).
-- make_sigfig(0, 3) returns '000', 1 (.000 * 10^1).
if sigfig <= 0 then
sigfig = 1
elseif sigfig > maxsigfig then
sigfig = maxsigfig
end
if value == 0 then
return string.rep('0', sigfig), 1
end
local exp, fracpart = math.modf(log10(value))
if fracpart >= 0 then
fracpart = fracpart - 1
exp = exp + 1
end
local digits = format('%.0f', 10^(fracpart + sigfig))
if #digits > sigfig then
-- Overflow (for sigfig=3: like 0.9999 rounding to "1000"; need "100").
digits = digits:sub(1, sigfig)
exp = exp + 1
end
assert(#digits == sigfig, 'Bug: rounded number has wrong length')
return digits, exp
end  
-- Fraction output format.
local fracfmt = {
{ -- Like (fraction slash).
'<span role="math">{SIGN}<span>{NUM}</span>&frasl;<span>{DEN}</span></span>', -- 1/2
'<span role="math">{SIGN}{WHOLE}<span>+</span><span>{NUM}</span>&frasl;<span>{DEN}</span></span>', -- 1+2/3,
},
{ -- Like (stacked fraction, that is, horizontal bar).
'<span role="math">{SIGN}<span>{NUM}</span><span>/</span><span>{DEN}</span></span>', -- 1//2
'<span role="math">{SIGN}{WHOLE}<span>+</span><span><span>{NUM}</span><span>/</span><span>{DEN}</span></span></span>', -- 1+2//3,
},
}  
local function format_fraction(parms, inout, negative, wholestr, numstr, denstr, do_spell, style)
-- Return wikitext for a fraction, possibly spelled.
-- Inputs use en digits and have no sign; output uses digits in local language.
local wikitext
if not style then
style = parms.opt_fraction_horizontal and 2 or 1
end
if wholestr == '' then
wholestr = nil
end
local substitute = {
SIGN = negative and MINUS or '',
WHOLE = wholestr and with_separator(parms, wholestr),
NUM = from_en(numstr),