Module:Convert: Difference between revisions

From Random Island Wiki
Jump to navigation Jump to search
>WOSlinker
(temperature convert)
m (1 revision imported)
 
(157 intermediate revisions by 7 users not shown)
Line 1: Line 1:
--[[
-- Convert a value from one unit of measurement to another.
Start of convert that I hope will be driven from tables.
-- Example: {{convert|123|lb|kg}} --> 123 pounds (56 kg)
Lots to do (first want to fix the default rounding).
-- See [[:en:Template:Convert/Transwiki guide]] if copying to another wiki.
I (enwiki Johnuniq) started this two days ago; it's not ready for release
but I'm dropping it here per BRD to see if others want to work with this.


Testing makes me think these results will occur with current code:
local MINUS = '−'  -- Unicode U+2212 MINUS SIGN (UTF-8: e2 88 92)
{{convert|3.21|kg|lb|2}}    3.21 kg (7.08 lb)
local abs = math.abs
{{convert|212|F|C|2}}        212 F (100.00 C)
local floor = math.floor
{{convert|5|to|10|kg|lb|2}}  5 to 10 kg (11.02 to 22.05 lb)
local format = string.format
{{convert|5|-|10|kg|lb|2}}  5–10 kg (11.02–22.05 lb)
local log10 = math.log10
{{convert|15|ft|m|2}}        15 ft (4.57 m)
local ustring = mw.ustring
{{convert|3.21|kg|m|2}}      Error: Cannot convert mass to length
local ulen = ustring.len
]]--
local usub = ustring.sub


--[[-----BEGIN DATA TABLE-----
-- Configuration options to keep magic values in one location.
Plan to write a program to generate the conversion tables below.
-- Conversion data and message text are defined in separate modules.
The input would be a text file in human-friendly format, and
local config, maxsigfig
the output would be the tables following like length/mass/units.
local numdot  -- must be '.' or ',' or a character which works in a regex
Values from http://en.wikipedia.org/wiki/Conversion_of_units
local numsep, numsep_remove, numsep_remove2
Check with http://en.wikipedia.org/wiki/Template:Convert/list_of_units
local data_code, all_units
]]--
local text_code
local varname        -- can be a code to use variable names that depend on value
local from_en_table  -- to translate an output string of en digits to local language
local to_en_table    -- to translate an input string of digits in local language to en
-- Use translation_table in convert/text to change the following.
local en_default          -- true uses lang=en unless convert has lang=local or local digits
local group_method = 3    -- code for how many digits are in a group
local per_word = 'per'    -- for units like "liters per kilometer"
local plural_suffix = 's' -- only other useful value is probably '' to disable plural unit names
local omitsep              -- true to omit separator before local symbol/name


local function scaled(self, value, in_unit, out_unit)
-- All units should be defined in the data module. However, to cater for quick changes
    -- Return scaled value for a simple convert.
-- and experiments, any unknown unit is looked up in an extra data module, if it exists.
    if out_unit == nil then
-- That module would be transcluded in only a small number of pages, so there should be
        out_unit = self[in_unit][2]
-- little server overhead from making changes, and changes should propagate quickly.
    end
local extra_module  -- name of module with extra units
    return value * (self[in_unit] / self[out_unit])
local extra_units  -- nil or table of extra units from extra_module
 
-- Some options in the invoking template can set variables used later in the module.
local currency_text  -- for a user-defined currency symbol: {{convert|12|$/ha|$=€}} (euro replaces dollar)
 
local function from_en(text)
-- Input is a string representing a number in en digits with '.' decimal mark,
-- without digit grouping (which is done just after calling this).
-- Return the translation of the string with numdot and digits in local language.
if numdot ~= '.' then
text = text:gsub('%.', numdot)
end
if from_en_table then
text = text:gsub('%d', from_en_table)
end
return text
end
end


local length = {
local function to_en(text)
    convert = scaled,
-- Input is a string representing a number in the local language with
    ['NAME'] = 'length',
-- an optional numdot decimal mark and numsep digit grouping.
    ['m'] = 1,
-- Return the translation of the string with '.' mark and en digits,
    ['km'] = 1000,
-- and no separators (they have to be removed here to handle cases like
    ['mi'] = 1609.344,
-- numsep = '.' and numdot = ',' with input "1.234.567,8").
    ['ft'] = 0.3048,
if to_en_table then
text = ustring.gsub(text, '%d', to_en_table)
end
if numsep_remove then
text = text:gsub(numsep_remove, '')
end
if numsep_remove2 then
text = text:gsub(numsep_remove2, '')
end
if numdot ~= '.' then
text = text:gsub(numdot, '.')
end
return text
end
 
local function decimal_mark(text)
-- Return ',' if text probably is using comma for decimal mark, or has no decimal mark.
-- Return '.' if text probably is using dot for decimal mark.
-- Otherwise return nothing (decimal mark not known).
if not text:find('[.,]') then return ',' end
text = text:gsub('^%-', ''):gsub('%+%d+/%d+$', ''):gsub('[Ee]%-?%d+$', '')
local decimal =
text:match('^0?([.,])%d+$') or
text:match('%d([.,])%d?%d?$') or
text:match('%d([.,])%d%d%d%d+$')
if decimal then return decimal end
if text:match('%.%d+%.') then return ',' end
if text:match('%,%d+,') then return '.' end
end
 
local add_warning, with_separator  -- forward declarations
local function to_en_with_check(text, parms)
-- Version of to_en() for a wiki using numdot = ',' and numsep = '.' to check
-- text (an input number as a string) which might have been copied from enwiki.
-- For example, in '1.234' the '.' could be a decimal mark or a group separator.
-- From viwiki.
if to_en_table then
text = ustring.gsub(text, '%d', to_en_table)
end
if decimal_mark(text) == '.' then
local original = text
text = text:gsub(',', '')  -- for example, interpret "1,234.5" as an enwiki value
if parms then
add_warning(parms, 0, 'cvt_enwiki_num', original, with_separator({}, text))
end
else
if numsep_remove then
text = text:gsub(numsep_remove, '')
end
if numsep_remove2 then
text = text:gsub(numsep_remove2, '')
end
if numdot ~= '.' then
text = text:gsub(numdot, '.')
end
end
return text
end
 
local function omit_separator(id)
-- Return true if there should be no separator before id (a unit symbol or name).
-- For zhwiki, there should be no separator if id uses local characters.
-- The following kludge should be a sufficient test.
if omitsep then
if id:sub(1, 2) == '-{' then  -- for "-{...}-" content language variant
return true
end
if id:byte() > 127 then
local first = usub(id, 1, 1)
if first ~= 'Å' and first ~= '°' and first ~= 'µ' then
return true
end
end
end
return id:sub(1, 1) == '/'  -- no separator before units like "/ha"
end
 
local spell_module  -- name of module that can spell numbers
local speller      -- function from that module to handle spelling (set if needed)
local wikidata_module, wikidata_data_module  -- names of Wikidata modules
local wikidata_code, wikidata_data  -- exported tables from those modules (set if needed)
 
local function set_config(args)
-- Set configuration options from template #invoke or defaults.
config = args
maxsigfig = config.maxsigfig or 14  -- maximum number of significant figures
local data_module, text_module
local sandbox = config.sandbox and ('/' .. config.sandbox) or ''
data_module = "Module:Convert/data" .. sandbox
text_module = "Module:Convert/text" .. sandbox
extra_module = "Module:Convert/extra" .. sandbox
wikidata_module = "Module:Convert/wikidata" .. sandbox
wikidata_data_module = "Module:Convert/wikidata/data" .. sandbox
spell_module = "Module:ConvertNumeric"
data_code = mw.loadData(data_module)
text_code = mw.loadData(text_module)
all_units = data_code.all_units
local translation = text_code.translation_table
if translation then
numdot = translation.numdot
numsep = translation.numsep
if numdot == ',' and numsep == '.' then
if text_code.all_messages.cvt_enwiki_num then
to_en = to_en_with_check
end
end
if translation.group then
group_method = translation.group
end
if translation.per_word then
per_word = translation.per_word
end
if translation.plural_suffix then
plural_suffix = translation.plural_suffix
end
varname = translation.varname
from_en_table = translation.from_en
local use_workaround = true
if use_workaround then
-- 2013-07-05 workaround bug by making a copy of the required table.
-- mw.ustring.gsub fails with a table (to_en_table) as the replacement,
-- if the table is accessed via mw.loadData.
local source = translation.to_en
if source then
to_en_table = {}
for k, v in pairs(source) do
to_en_table[k] = v
end
end
else
to_en_table = translation.to_en
end
if translation.lang == 'en default' then
en_default = true  -- for hiwiki
end
omitsep = translation.omitsep  -- for zhwiki
end
numdot = config.numdot or numdot or '.'  -- decimal mark before fractional digits
numsep = config.numsep or numsep or ','  -- group separator for numbers
-- numsep should be ',' or '.' or '' or ' ' or a Unicode character.
-- numsep_remove must work in a regex to identify separators to be removed.
if numsep ~= '' then
numsep_remove = (numsep == '.') and '%.' or numsep
end
if numsep ~= ',' and numdot ~= ',' then
numsep_remove2 = ','  -- so numbers copied from enwiki will work
end
end
 
local function collection()
-- Return a table to hold items.
return {
n = 0,
add = function (self, item)
self.n = self.n + 1
self[self.n] = item
end,
}
end
 
local function divide(numerator, denominator)
-- Return integers quotient, remainder resulting from dividing the two
-- given numbers, which should be unsigned integers.
local quotient, remainder = floor(numerator / denominator), numerator % denominator
if not (0 <= remainder and remainder < denominator) then
-- Floating point limits may need this, as in {{convert|160.02|Ym|ydftin}}.
remainder = 0
end
return quotient, remainder
end
 
local function split(text, delimiter)
-- Return a numbered table with fields from splitting text.
-- The delimiter is used in a regex without escaping (for example, '.' would fail).
-- Each field has any leading/trailing whitespace removed.
local t = {}
text = text .. delimiter  -- to get last item
for item in text:gmatch('%s*(.-)%s*' .. delimiter) do
table.insert(t, item)
end
return t
end
 
local function strip(text)
-- If text is a string, return its content with no leading/trailing
-- whitespace. Otherwise return nil (a nil argument gives a nil result).
if type(text) == 'string' then
return text:match("^%s*(.-)%s*$")
end
end
 
local function table_len(t)
-- Return length (<100) of a numbered table to replace #t which is
-- documented to not work if t is accessed via mw.loadData().
for i = 1, 100 do
if t[i] == nil then
return i - 1
end
end
end
 
local function wanted_category(catkey, catsort, want_warning)
-- Return message category if it is wanted in current namespace,
-- otherwise return ''.
local cat
local title = mw.title.getCurrentTitle()
if title then
local nsdefault = '0'  -- default namespace: '0' = article; '0,10' = article and template
local namespace = title.namespace
for _, v in ipairs(split(config.nscat or nsdefault, ',')) do
if namespace == tonumber(v) then
cat = text_code.all_categories[want_warning and 'warning' or catkey]
if catsort and catsort ~= '' and cat:sub(-2) == ']]' then
cat = cat:sub(1, -3) .. '|' .. mw.text.nowiki(usub(catsort, 1, 20)) .. ']]'
end
break
end
end
end
return cat or ''
end
 
local function message(parms, mcode, is_warning)
-- Return wikitext for an error message, including category if specified
-- for the message type.
-- mcode = numbered table specifying the message:
--    mcode[1] = 'cvt_xxx' (string used as a key to get message info)
--    mcode[2] = 'parm1' (string to replace '$1' if any in message)
--    mcode[3] = 'parm2' (string to replace '$2' if any in message)
--    mcode[4] = 'parm3' (string to replace '$3' if any in message)
local msg
if type(mcode) == 'table' then
if mcode[1] == 'cvt_no_output' then
-- Some errors should cause convert to output an empty string,
-- for example, for an optional field in an infobox.
return ''
end
msg = text_code.all_messages[mcode[1]]
end
parms.have_problem = true
local function subparm(fmt, ...)
local rep = {}
for i, v in ipairs({...}) do
rep['$' .. i] = v
end
return (fmt:gsub('$%d+', rep))
end
if msg then
local parts = {}
local regex, replace = msg.regex, msg.replace
for i = 1, 3 do
local limit = 40
local s = mcode[i + 1]
if s then
if regex and replace then
s = s:gsub(regex, replace)
limit = nil  -- allow long "should be" messages
end
-- Escape user input so it does not break the message.
-- To avoid tags (like {{convert|1<math>23</math>|m}}) breaking
-- the mouseover title, any strip marker starting with char(127) is
-- replaced with '...' (text not needing i18n).
local append
local pos = s:find(string.char(127), 1, true)
if pos then
append = '...'
s = s:sub(1, pos - 1)
end
if limit and ulen(s) > limit then
s = usub(s, 1, limit)
append = '...'
end
s = mw.text.nowiki(s) .. (append or '')
else
s = '?'
end
parts['$' .. i] = s
end
local function ispreview()
-- Return true if a prominent message should be shown.
if parms.test == 'preview' or parms.test == 'nopreview' then
-- For testing, can preview a real message or simulate a preview
-- when running automated tests.
return parms.test == 'preview'
end
local success, revid = pcall(function ()
return (parms.frame):preprocess('{{REVISIONID}}') end)
return success and (revid == '')
end
local want_warning = is_warning and
not config.warnings and  -- show unobtrusive warnings if config.warnings not configured
not msg.nowarn          -- but use msg settings, not standard warning, if specified
local title = string.gsub(msg[1] or 'Missing message', '$%d+', parts)
local text = want_warning and '*' or msg[2] or 'Missing message'
local cat = wanted_category(msg[3], mcode[2], want_warning)
local anchor = msg[4] or ''
local fmtkey = ispreview() and 'cvt_format_preview' or
(want_warning and 'cvt_format2' or msg.format or 'cvt_format')
local fmt = text_code.all_messages[fmtkey] or 'convert: bug'
return subparm(fmt, title:gsub('"', '&quot;'), text, cat, anchor)
end
return 'Convert internal error: unknown message'
end
 
function add_warning(parms, level, key, text1, text2)  -- for forward declaration above
-- If enabled, add a warning that will be displayed after the convert result.
-- A higher level is more verbose: more kinds of warnings are displayed.
-- To reduce output noise, only the first warning is displayed.
if level <= (tonumber(config.warnings) or 1) then
if parms.warnings == nil then
parms.warnings = message(parms, { key, text1, text2 }, true)
end
end
end
 
local function spell_number(parms, inout, number, numerator, denominator)
-- Return result of spelling (number, numerator, denominator), or
-- return nil if spelling is not available or not supported for given text.
-- Examples (each value must be a string or nil):
--  number  numerator  denominator  output
--  ------  ---------  -----------  -------------------
--  "1.23"    nil        nil        one point two three
--    "1"      "2"        "3"        one and two thirds
--    nil      "2"        "3"        two thirds
if not speller then
local function get_speller(module)
return require(module).spell_number
end
local success
success, speller = pcall(get_speller, spell_module)
if not success or type(speller) ~= 'function' then
add_warning(parms, 1, 'cvt_no_spell', 'spell')
return nil
end
end
local case
if parms.spell_upper == inout then
case = true
parms.spell_upper = nil  -- only uppercase first word in a multiple unit
end
local sp = not parms.opt_sp_us
local adj = parms.opt_adjectival
return speller(number, numerator, denominator, case, sp, adj)
end
 
------------------------------------------------------------------------
-- BEGIN: Code required only for built-in units.
-- LATER: If need much more code, move to another module to simplify this module.
local function speed_of_sound(altitude)
-- This is for the Mach built-in unit of speed.
-- Return speed of sound in metres per second at given altitude in feet.
-- If no altitude given, use default (zero altitude = sea level).
-- Table gives speed of sound in miles per hour at various altitudes:
--  altitude = -17,499 to 302,499 feet
-- mach_table[a + 4] = s where
--  a = (altitude / 5000) rounded to nearest integer (-3 to 60)
--  s = speed of sound (mph) at that altitude
-- LATER: Should calculate result from an interpolation between the next
-- lower and higher altitudes in table, rather than rounding to nearest.
-- From: http://www.aerospaceweb.org/question/atmosphere/q0112.shtml
local mach_table = {                                                      -- a =
799.5, 787.0, 774.2, 761.207051,                                      -- -3 to  0
748.0, 734.6, 721.0, 707.0, 692.8, 678.3, 663.5, 660.1, 660.1, 660.1,  --  1 to 10
660.1, 660.1, 660.1, 662.0, 664.3, 666.5, 668.9, 671.1, 673.4, 675.6,  -- 11 to 20
677.9, 683.7, 689.9, 696.0, 702.1, 708.1, 714.0, 719.9, 725.8, 731.6,  -- 21 to 30
737.3, 737.7, 737.7, 736.2, 730.5, 724.6, 718.8, 712.9, 707.0, 701.1,  -- 31 to 40
695.0, 688.9, 682.8, 676.6, 670.4, 664.1, 657.8, 652.9, 648.3, 643.7,  -- 41 to 50
639.1, 634.4, 629.6, 624.8, 620.0, 615.2, 613.2, 613.2, 613.2, 613.5,  -- 51 to 60
}
altitude = altitude or 0
local a = (altitude < 0) and -altitude or altitude
a = floor(a / 5000 + 0.5)
if altitude < 0 then
a = -a
end
if a < -3 then
a = -3
elseif a > 60 then
a = 60
end
return mach_table[a + 4] * 0.44704  -- mph converted to m/s
end
-- END: Code required only for built-in units.
------------------------------------------------------------------------
 
local function add_style(parms, class)
-- Add selected template style to parms if not already present.
parms.templatestyles = parms.templatestyles or {}
if not parms.templatestyles[class] then
parms.templatestyles[class] = parms.frame:extensionTag({
name = 'templatestyles', args = { src = text_code.titles[class] }
})
end
end
 
local function get_styles(parms)
-- Return string of required template styles, empty if none.
if parms.templatestyles then
local t = {}
for _, v in pairs(parms.templatestyles) do
table.insert(t, v)
end
return table.concat(t)
end
return ''
end
 
local function get_range(word)
-- Return a range (string or table) corresponding to word (like "to"),
-- or return nil if not a range word.
local ranges = text_code.ranges
return ranges.types[word] or ranges.types[ranges.aliases[word]]
end
 
local function check_mismatch(unit1, unit2)
-- If unit1 cannot be converted to unit2, return an error message table.
-- This allows conversion between units of the same type, and between
-- Nm (normally torque) and ftlb (energy), as in gun-related articles.
-- This works because Nm is the base unit (scale = 1) for both the
-- primary type (torque), and the alternate type (energy, where Nm = J).
-- A match occurs if the primary types are the same, or if unit1 matches
-- the alternate type of unit2, and vice versa. That provides a whitelist
-- of which conversions are permitted between normally incompatible types.
if unit1.utype == unit2.utype or
(unit1.utype == unit2.alttype and unit1.alttype == unit2.utype) then
return nil
end
return { 'cvt_mismatch', unit1.utype, unit2.utype }
end
 
local function override_from(out_table, in_table, fields)
-- Copy the specified fields from in_table to out_table, but do not
-- copy nil fields (keep any corresponding field in out_table).
for _, field in ipairs(fields) do
if in_table[field] then
out_table[field] = in_table[field]
end
end
end
 
local function shallow_copy(t)
-- Return a shallow copy of table t.
-- Do not need the features and overhead of the Scribunto mw.clone().
local result = {}
for k, v in pairs(t) do
result[k] = v
end
return result
end
 
local unit_mt = {
-- Metatable to get missing values for a unit that does not accept SI prefixes.
-- Warning: The boolean value 'false' is returned for any missing field
-- so __index is not called twice for the same field in a given unit.
__index = function (self, key)
local value
if key == 'name1' or key == 'sym_us' then
value = self.symbol
elseif key == 'name2' then
value = self.name1 .. plural_suffix
elseif key == 'name1_us' then
value = self.name1
if not rawget(self, 'name2_us') then
-- If name1_us is 'foot', do not make name2_us by appending plural_suffix.
self.name2_us = self.name2
end
elseif key == 'name2_us' then
local raw1_us = rawget(self, 'name1_us')
if raw1_us then
value = raw1_us .. plural_suffix
else
value = self.name2
end
elseif key == 'link' then
value = self.name1
else
value = false
end
rawset(self, key, value)
return value
end
}
}


local mass = {
local function prefixed_name(unit, name, index)
    convert = scaled,
-- Return unit name with SI prefix inserted at correct position.
    ['NAME'] = 'mass',
-- index = 1 (name1), 2 (name2), 3 (name1_us), 4 (name2_us).
    ['kg'] = 1,
-- The position is a byte (not character) index, so use Lua's sub().
    ['lb'] = 0.45359237,
local pos = rawget(unit, 'prefix_position')
if type(pos) == 'string' then
pos = tonumber(split(pos, ',')[index])
end
if pos then
return name:sub(1, pos - 1) .. unit.si_name .. name:sub(pos)
end
return unit.si_name .. name
end
 
local unit_prefixed_mt = {
-- Metatable to get missing values for a unit that accepts SI prefixes.
-- Before use, fields si_name, si_prefix must be defined.
-- The unit must define _symbol, _name1 and
-- may define _sym_us, _name1_us, _name2_us
-- (_sym_us, _name2_us may be defined for a language using sp=us
-- to refer to a variant unrelated to U.S. units).
__index = function (self, key)
local value
if key == 'symbol' then
value = self.si_prefix .. self._symbol
elseif key == 'sym_us' then
value = rawget(self, '_sym_us')
if value then
value = self.si_prefix .. value
else
value = self.symbol
end
elseif key == 'name1' then
value = prefixed_name(self, self._name1, 1)
elseif key == 'name2' then
value = rawget(self, '_name2')
if value then
value = prefixed_name(self, value, 2)
else
value = self.name1 .. plural_suffix
end
elseif key == 'name1_us' then
value = rawget(self, '_name1_us')
if value then
value = prefixed_name(self, value, 3)
else
value = self.name1
end
elseif key == 'name2_us' then
value = rawget(self, '_name2_us')
if value then
value = prefixed_name(self, value, 4)
elseif rawget(self, '_name1_us') then
value = self.name1_us .. plural_suffix
else
value = self.name2
end
elseif key == 'link' then
value = self.name1
else
value = false
end
rawset(self, key, value)
return value
end
}
}


local temperature = {
local unit_per_mt = {
    convert = function (self, value, in_unit, out_unit)
-- Metatable to get values for a per unit of form "x/y".
        -- Return scaled value for a temperature convert.
-- This is never called to determine a unit name or link because per units
        if out_unit == nil then
-- are handled as a special case.
            out_unit = self[in_unit][2]
-- Similarly, the default output is handled elsewhere, and for a symbol
        end
-- this is only called from get_default() for default_exceptions.
        return (value - self[in_unit][2]) / self[in_unit][1] * self[out_unit][1] + self[out_unit][2]
__index = function (self, key)
    end,
local value
    ['NAME'] = 'temperature',
if key == 'symbol' then
    ['K'] = {1, -273.15},
local per = self.per
    ['C'] = {1, 0},
local unit1, unit2 = per[1], per[2]
    ['F'] = {1.8, 32},
if unit1 then
    ['°K'] = {1, -273.15},
value = unit1[key] .. '/' .. unit2[key]
    ['°C'] = {1, 0},
else
    ['°F'] = {1.8, 32},
value = '/' .. unit2[key]
end
elseif key == 'sym_us' then
value = self.symbol
elseif key == 'scale' then
local per = self.per
local unit1, unit2 = per[1], per[2]
value = (unit1 and unit1.scale or 1) * self.scalemultiplier / unit2.scale
else
value = false
end
rawset(self, key, value)
return value
end
}
}


local units = {
local function make_per(unitcode, unit_table, ulookup)
    -- Each value is {converter_table, default_out_unit}.
-- Return true, t where t is a per unit with unit codes expanded to unit tables,
    lookup = function (self, unit)
-- or return false, t where t is an error message table.
        -- If unit is known, return its converter_table, default_out_unit.
local result = {
        local t = self[unit]
unitcode = unitcode,
        if t == nil then
utype = unit_table.utype,
            local msg = 'Unit %s not known'
per = {}
            error(msg:format(unit))
}
        end
override_from(result, unit_table, { 'invert', 'iscomplex', 'default', 'link', 'symbol', 'symlink' })
        return t[1], t[2]
result.symbol_raw = (result.symbol or false)  -- to distinguish between a defined exception and a metatable calculation
    end,
local prefix
    ['kg'] = {mass, 'lb'},
for i, v in ipairs(unit_table.per) do
    ['lb'] = {mass, 'kg'},
if i == 1 and v == '' then
    ['m'] = {length, 'ft'},
-- First unit symbol can be empty; that gives a nil first unit table.
    ['km'] = {length, 'mi'},
elseif i == 1 and text_code.currency[v] then
    ['mi'] = {length, 'km'},
prefix = currency_text or v
    ['ft'] = {length, 'm'},
else
    ['K'] = {temperature, 'C'},
local success, t = ulookup(v)
    ['C'] = {temperature, 'F'},
if not success then return false, t end
    ['F'] = {temperature, 'C'},
result.per[i] = t
    ['°K'] = {temperature, '°C'},
end
    ['°C'] = {temperature, '°F'},
end
    ['°F'] = {temperature, '°C'},
local multiplier = unit_table.multiplier
if not result.utype then
-- Creating an automatic per unit.
local unit1 = result.per[1]
local utype = (unit1 and unit1.utype or prefix or '') .. '/' .. result.per[2].utype
local t = data_code.per_unit_fixups[utype]
if t then
if type(t) == 'table' then
utype = t.utype or utype
result.link = result.link or t.link
multiplier = multiplier or t.multiplier
else
utype = t
end
end
result.utype = utype
end
result.scalemultiplier = multiplier or 1
result.vprefix = prefix or false  -- set to non-nil to avoid calling __index
return true, setmetatable(result, unit_per_mt)
end
 
local function lookup(parms, unitcode, what, utable, fails, depth)
-- Return true, t where t is a copy of the unit's converter table,
-- or return false, t where t is an error message table.
-- Parameter 'what' determines whether combination units are accepted:
--  'no_combination'  : single unit only
--  'any_combination' : single unit or combination or output multiple
--  'only_multiple'  : single unit or output multiple only
-- Parameter unitcode is a symbol (like 'g'), with an optional SI prefix (like 'kg').
-- If, for example, 'kg' is in this table, that entry is used;
-- otherwise the prefix ('k') is applied to the base unit ('g').
-- If unitcode is a known combination code (and if allowed by what),
-- a table of output multiple unit tables is included in the result.
-- For compatibility with the old template, an underscore in a unitcode is
-- replaced with a space so usage like {{convert|350|board_feet}} works.
-- Wikignomes may also put two spaces or "&nbsp;" in combinations, so
-- replace underscore, "&nbsp;", and multiple spaces with a single space.
utable = utable or parms.unittable or all_units
fails = fails or {}
depth = depth and depth + 1 or 1
if depth > 9 then
-- There are ways to mistakenly define units which result in infinite
-- recursion when lookup() is called. That gives a long delay and very
-- confusing error messages, so the depth parameter is used as a guard.
return false, { 'cvt_lookup', unitcode }
end
if unitcode == nil or unitcode == '' then
return false, { 'cvt_no_unit' }
end
unitcode = unitcode:gsub('_', ' '):gsub('&nbsp;', ' '):gsub('  +', ' ')
local function call_make_per(t)
return make_per(unitcode, t,
function (ucode) return lookup(parms, ucode, 'no_combination', utable, fails, depth) end
)
end
local t = utable[unitcode]
if t then
if t.shouldbe then
return false, { 'cvt_should_be', t.shouldbe }
end
if t.sp_us then
parms.opt_sp_us = true
end
local target = t.target  -- nil, or unitcode is an alias for this target
if target then
local success, result = lookup(parms, target, what, utable, fails, depth)
if not success then return false, result end
override_from(result, t, { 'customary', 'default', 'link', 'symbol', 'symlink' })
local multiplier = t.multiplier
if multiplier then
result.multiplier = tostring(multiplier)
result.scale = result.scale * multiplier
end
return true, result
end
if t.per then
return call_make_per(t)
end
local combo = t.combination  -- nil or a table of unitcodes
if combo then
local multiple = t.multiple
if what == 'no_combination' or (what == 'only_multiple' and not multiple) then
return false, { 'cvt_bad_unit', unitcode }
end
-- Recursively create a combination table containing the
-- converter table of each unitcode.
local result = { utype = t.utype, multiple = multiple, combination = {} }
local cvt = result.combination
for i, v in ipairs(combo) do
local success, t = lookup(parms, v, multiple and 'no_combination' or 'only_multiple', utable, fails, depth)
if not success then return false, t end
cvt[i] = t
end
return true, result
end
local result = shallow_copy(t)
result.unitcode = unitcode
if result.prefixes then
result.si_name = ''
result.si_prefix = ''
return true, setmetatable(result, unit_prefixed_mt)
end
return true, setmetatable(result, unit_mt)
end
local SIprefixes = text_code.SIprefixes
for plen = SIprefixes[1] or 2, 1, -1 do
-- Look for an SI prefix; should never occur with an alias.
-- Check for longer prefix first ('dam' is decametre).
-- SIprefixes[1] = prefix maximum #characters (as seen by mw.ustring.sub).
local prefix = usub(unitcode, 1, plen)
local si = SIprefixes[prefix]
if si then
local t = utable[usub(unitcode, plen+1)]
if t and t.prefixes then
local result = shallow_copy(t)
result.unitcode = unitcode
result.si_name = parms.opt_sp_us and si.name_us or si.name
result.si_prefix = si.prefix or prefix
result.scale = t.scale * 10 ^ (si.exponent * t.prefixes)
return true, setmetatable(result, unit_prefixed_mt)
end
end
end
-- Accept user-defined combinations like "acre+m2+ha" or "acre m2 ha" for output.
-- If '+' is used, each unit code can include a space, and any error is fatal.
-- If ' ' is used and if each space-separated word is a unit code, it is a combo,
-- but errors are not fatal so the unit code can be looked up as an extra unit.
local err_is_fatal
local combo = collection()
if unitcode:find('+', 1, true) then
err_is_fatal = true
for item in (unitcode .. '+'):gmatch('%s*(.-)%s*%+') do
if item ~= '' then
combo:add(item)
end
end
elseif unitcode:find('%s') then
for item in unitcode:gmatch('%S+') do
combo:add(item)
end
end
if combo.n > 1 then
local function lookup_combo()
if what == 'no_combination' or what == 'only_multiple' then
return false, { 'cvt_bad_unit', unitcode }
end
local result = { combination = {} }
local cvt = result.combination
for i, v in ipairs(combo) do
local success, t = lookup(parms, v, 'only_multiple', utable, fails, depth)
if not success then return false, t end
if i == 1 then
result.utype = t.utype
else
local mismatch = check_mismatch(result, t)
if mismatch then
return false, mismatch
end
end
cvt[i] = t
end
return true, result
end
local success, result = lookup_combo()
if success or err_is_fatal then
return success, result
end
end
-- Accept any unit with an engineering notation prefix like "e6cuft"
-- (million cubic feet), but not chained prefixes like "e3e6cuft",
-- and not if the unit is a combination or multiple,
-- and not if the unit has an offset or is a built-in.
-- Only en digits are accepted.
local exponent, baseunit = unitcode:match('^e(%d+)(.*)')
if exponent then
local engscale = text_code.eng_scales[exponent]
if engscale then
local success, result = lookup(parms, baseunit, 'no_combination', utable, fails, depth)
if success and not (result.offset or result.builtin or result.engscale) then
result.unitcode = unitcode  -- 'e6cuft' not 'cuft'
result.defkey = unitcode  -- key to lookup default exception
result.engscale = engscale
result.scale = result.scale * 10 ^ tonumber(exponent)
return true, result
end
end
end
-- Look for x/y; split on right-most slash to get scale correct (x/y/z is x/y per z).
local top, bottom = unitcode:match('^(.-)/([^/]+)$')
if top and not unitcode:find('e%d') then
-- If valid, create an automatic per unit for an "x/y" unit code.
-- The unitcode must not include extraneous spaces.
-- Engineering notation (apart from at start and which has been stripped before here),
-- is not supported so do not make a per unit if find text like 'e3' in unitcode.
local success, result = call_make_per({ per = {top, bottom} })
if success then
return true, result
end
end
if not parms.opt_ignore_error and not get_range(unitcode) then
-- Want the "what links here" list for the extra_module to show only cases
-- where an extra unit is used, so do not require it if invoked from {{val}}
-- or if looking up a range word which cannot be a unit.
if not extra_units then
local success, extra = pcall(function () return require(extra_module).extra_units end)
if success and type(extra) == 'table' then
extra_units = extra
end
end
if extra_units then
-- A unit in one data table might refer to a unit in the other table, so
-- switch between them, relying on fails or depth to terminate loops.
if not fails[unitcode] then
fails[unitcode] = true
local other = (utable == all_units) and extra_units or all_units
local success, result = lookup(parms, unitcode, what, other, fails, depth)
if success then
return true, result
end
end
end
end
if to_en_table then
-- At fawiki it is common to translate all digits so a unit like "km2" becomes "km۲".
local en_code = ustring.gsub(unitcode, '%d', to_en_table)
if en_code ~= unitcode then
return lookup(parms, en_code, what, utable, fails, depth)
end
end
return false, { 'cvt_unknown', unitcode }
end
 
local function valid_number(num)
-- Return true if num is a valid number.
-- In Scribunto (different from some standard Lua), when expressed as a string,
-- overflow or other problems are indicated with text like "inf" or "nan"
-- which are regarded as invalid here (each contains "n").
if type(num) == 'number' and tostring(num):find('n', 1, true) == nil then
return true
end
end
 
local function hyphenated(name, parts)
-- Return a hyphenated form of given name (for adjectival usage).
-- The name may be linked and the target of the link must not be changed.
-- Hypothetical examples:
--  [[long ton|ton]]        →  [[long ton|ton]]          (no change)
--  [[tonne|long ton]]      →  [[tonne|long-ton]]
--  [[metric ton|long ton]]  →  [[metric ton|long-ton]]
--  [[long ton]]            →  [[long ton|long-ton]]
-- Input can also have multiple links in a single name like:
--  [[United States customary units|U.S.]] [[US gallon|gallon]]
--  [[mile]]s per [[United States customary units|U.S.]] [[quart]]
--  [[long ton]]s per [[short ton]]
-- Assume that links cannot be nested (never like "[[abc[[def]]ghi]]").
-- 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 (left-to-right, 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 style="white-space: nowrap">'
local gap = '<span style="margin-left: 0.25em">'
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 style="margin:0 .15em 0 .25em">×</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 {{frac}} (fraction slash).
'<span class="frac" role="math">{SIGN}<span class="num">{NUM}</span>&frasl;<span class="den">{DEN}</span></span>', -- 1/2
'<span class="frac" role="math">{SIGN}{WHOLE}<span class="sr-only">+</span><span class="num">{NUM}</span>&frasl;<span class="den">{DEN}</span></span>', -- 1+2/3
style = 'frac',
},
{ -- Like {{sfrac}} (stacked fraction, that is, horizontal bar).
'<span class="sfrac tion" role="math">{SIGN}<span class="num">{NUM}</span><span class="sr-only">/</span><span class="den">{DEN}</span></span>',  -- 1//2
'<span class="sfrac" role="math">{SIGN}{WHOLE}<span class="sr-only">+</span><span class="tion"><span class="num">{NUM}</span><span class="sr-only">/</span><span class="den">{DEN}</span></span></span>', -- 1+2//3
style = 'sfrac',
},
}
}
-------END DATA TABLE-----


local function require_number(value, missing, invalid)
local function format_fraction(parms, inout, negative, wholestr, numstr, denstr, do_spell, style)
    -- If value is missing or not a number, throw an error.
-- Return wikitext for a fraction, possibly spelled.
     -- Return value as a number if valid.
-- Inputs use en digits and have no sign; output uses digits in local language.
     if value == nil then error(missing) end
local wikitext
    local number = tonumber(value)
if not style then
    if number == nil then error(invalid:format(value)) end
style = parms.opt_fraction_horizontal and 2 or 1
     return number
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),
DEN = from_en(denstr),
}
wikitext = fracfmt[style][wholestr and 2 or 1]:gsub('{(%u+)}', substitute)
if do_spell then
if negative then
if wholestr then
wholestr = '-' .. wholestr
else
numstr = '-' .. numstr
end
end
local s = spell_number(parms, inout, wholestr, numstr, denstr)
if s then
return s
end
end
add_style(parms, fracfmt[style].style)
return wikitext
end
 
local function format_number(parms, show, exponent, isnegative)
-- Parameter show is a string or a table containing strings.
-- Each string is a formatted number in en digits and optional '.' decimal mark.
-- A table represents a fraction: integer, numerator, denominator;
-- if a table is given, exponent must be nil.
-- Return t where t is a table with fields:
--  show = wikitext formatted to display implied value
--          (digits in local language)
--  is_scientific = true if show uses scientific notation
--  clean = unformatted show (possibly adjusted and with inserted '.')
--          (en digits)
--  sign = '' or MINUS
--  exponent = exponent (possibly adjusted)
-- The clean and exponent fields can be used to calculate the
-- rounded absolute value, if needed.
--
-- The value implied by the arguments is found from:
--  exponent is nil; and
--  show is a string of digits (no sign), with an optional dot;
--  show = '123.4' is value 123.4, '1234' is value 1234.0;
-- or:
--  exponent is an integer indicating where dot should be;
--  show is a string of digits (no sign and no dot);
--  there is an implied dot before show;
--  show does not start with '0';
--  show = '1234', exponent = 3 is value 0.1234*10^3 = 123.4.
--
-- The formatted result:
-- * Is for an output value and is spelled if wanted and possible.
-- * Includes a Unicode minus if isnegative and not spelled.
-- * Uses a custom decimal mark, if wanted.
-- * Has digits grouped where necessary, if wanted.
-- * Uses scientific notation if requested, or for very small or large values
--  (which forces result to not be spelled).
-- * Has no more than maxsigfig significant digits
--  (same as old template and {{#expr}}).
local xhi, xlo  -- these control when scientific notation (exponent) is used
if parms.opt_scientific then
xhi, xlo = 4, 2  -- default for output if input uses e-notation
elseif parms.opt_scientific_always then
xhi, xlo = 0, 0  -- always use scientific notation (experimental)
else
xhi, xlo = 10, 4  -- default
end
local sign = isnegative and MINUS or ''
local maxlen = maxsigfig
local tfrac
if type(show) == 'table' then
tfrac = show
show = tfrac.wholestr
assert(exponent == nil, 'Bug: exponent given with fraction')
end
if not tfrac and not exponent then
local integer, dot, decimals = show:match('^(%d*)(%.?)(.*)')
if integer == '0' or integer == '' then
local zeros, figs = decimals:match('^(0*)([^0]?.*)')
if #figs == 0 then
if #zeros > maxlen then
show = '0.' .. zeros:sub(1, maxlen)
end
elseif #zeros >= xlo then
show = figs
exponent = -#zeros
elseif #figs > maxlen then
show = '0.' .. zeros .. figs:sub(1, maxlen)
end
elseif #integer >= xhi then
show = integer .. decimals
exponent = #integer
else
maxlen = maxlen + #dot
if #show > maxlen then
show = show:sub(1, maxlen)
end
end
end
if exponent then
local function zeros(n)
return string.rep('0', n)
end
if #show > maxlen then
show = show:sub(1, maxlen)
end
if exponent > xhi or exponent <= -xlo or (exponent == xhi and show ~= '1' .. zeros(xhi - 1)) then
-- When xhi, xlo = 10, 4 (the default), scientific notation is used if the
-- rounded value satisfies: value >= 1e9 or value < 1e-4 (1e9 = 0.1e10),
-- except if show is '1000000000' (1e9), for example:
-- {{convert|1000000000|m|m|sigfig=10}} → 1,000,000,000 metres (1,000,000,000 m)
local significand
if #show > 1 then
significand = show:sub(1, 1) .. '.' .. show:sub(2)
else
significand = show
end
return {
clean = '.' .. show,
exponent = exponent,
sign = sign,
show = sign .. with_exponent(parms, significand, exponent-1),
is_scientific = true,
}
end
if exponent >= #show then
show = show .. zeros(exponent - #show)  -- result has no dot
elseif exponent <= 0 then
show = '0.' .. zeros(-exponent) .. show
else
show = show:sub(1, exponent) .. '.' .. show:sub(exponent+1)
end
end
local formatted_show
if tfrac then
show = tostring(tfrac.value)  -- to set clean in returned table
formatted_show = format_fraction(parms, 'out', isnegative, tfrac.wholestr, tfrac.numstr, tfrac.denstr, parms.opt_spell_out)
else
if isnegative and show:match('^0.?0*$') then
sign = ''  -- don't show minus if result is negative but rounds to zero
end
formatted_show = sign .. with_separator(parms, show)
if parms.opt_spell_out then
formatted_show = spell_number(parms, 'out', sign .. show) or formatted_show
end
end
return {
clean = show,
sign = sign,
show = formatted_show,
is_scientific = false,  -- to avoid calling __index
}
end
 
local function extract_fraction(parms, text, negative)
-- If text represents a fraction, return
--  value, altvalue, show, denominator
-- where
--  value is a number (value of the fraction in argument text)
--  altvalue is an alternate interpretation of any fraction for the hands
--        unit where "12.1+3/4" means 12 hands 1.75 inches
--  show is a string (formatted text for display of an input value,
--        and is spelled if wanted and possible)
--  denominator is value of the denominator in the fraction
-- Otherwise, return nil.
-- Input uses en digits and '.' decimal mark (input has been translated).
-- Output uses digits in local language and local decimal mark, if any.
------------------------------------------------------------------------
-- Originally this function accepted x+y/z where x, y, z were any valid
-- numbers, possibly with a sign. For example '1.23e+2+1.2/2.4' = 123.5,
-- and '2-3/8' = 1.625. However, such usages were found to be errors or
-- misunderstandings, so since August 2014 the following restrictions apply:
--  x (if present) is an integer or has a single digit after decimal mark
--  y and z are unsigned integers
--  e-notation is not accepted
-- The overall number can start with '+' or '-' (so '12+3/4' and '+12+3/4'
-- and '-12-3/4' are valid).
-- Any leading negative sign is removed by the caller, so only inputs
-- like the following are accepted here (may have whitespace):
--  negative = false      false        true (there was a leading '-')
--  text    = '2/3'      '+2/3'      '2/3'
--  text    = '1+2/3'    '+1+2/3'    '1-2/3'
--  text    = '12.3+1/2'  '+12.3+1/2'  '12.3-1/2'
-- Values like '12.3+1/2' are accepted, but are intended only for use
-- with the hands unit (not worth adding code to enforce that).
------------------------------------------------------------------------
local leading_plus, prefix, numstr, slashes, denstr =
text:match('^%s*(%+?)%s*(.-)%s*(%d+)%s*(/+)%s*(%d+)%s*$')
if not leading_plus then
-- Accept a single U+2044 fraction slash because that may be pasted.
leading_plus, prefix, numstr, denstr =
text:match('^%s*(%+?)%s*(.-)%s*(%d+)%s*⁄%s*(%d+)%s*$')
slashes = '/'
end
local numerator = tonumber(numstr)
local denominator = tonumber(denstr)
if numerator == nil or denominator == nil or (negative and leading_plus ~= '') then
return nil
end
local whole, wholestr
if prefix == '' then
wholestr = ''
whole = 0
else
-- Any prefix must be like '12+' or '12-' (whole number and fraction sign);
-- '12.3+' and '12.3-' are also accepted (single digit after decimal point)
-- because '12.3+1/2 hands' is valid (12 hands 3½ inches).
local num1, num2, frac_sign = prefix:match('^(%d+)(%.?%d?)%s*([+%-])$')
if num1 == nil then return nil end
if num2 == '' then  -- num2 must be '' or like '.1' but not '.' or '.12'
wholestr = num1
else
if #num2 ~= 2 then return nil end
wholestr = num1 .. num2
end
if frac_sign ~= (negative and '-' or '+') then return nil end
whole = tonumber(wholestr)
if whole == nil then return nil end
end
local value = whole + numerator / denominator
if not valid_number(value) then return nil end
local altvalue = whole + numerator / (denominator * 10)
local style = #slashes  -- kludge: 1 or 2 slashes can be used to select style
if style > 2 then style = 2 end
local wikitext = format_fraction(parms, 'in', negative, leading_plus .. wholestr, numstr, denstr, parms.opt_spell_in, style)
return value, altvalue, wikitext, denominator
end
 
local function extract_number(parms, text, another, no_fraction)
-- Return true, info if can extract a number from text,
-- where info is a table with the result,
-- or return false, t where t is an error message table.
-- Input can use en digits or digits in local language and can
-- have references at the end. Accepting references is intended
-- for use in infoboxes with a field for a value passed to convert.
-- Parameter another = true if the expected value is not the first.
-- Before processing, the input text is cleaned:
-- * Any thousand separators (valid or not) are removed.
-- * Any sign is replaced with '-' (if negative) or '' (otherwise).
--  That replaces Unicode minus with '-'.
-- If successful, the returned info table contains named fields:
--  value    = a valid number
--  altvalue = a valid number, usually same as value but different
--              if fraction used (for hands unit)
--  singular = true if value is 1 or -1 (to use singular form of units)
--  clean    = cleaned text with any separators and sign removed
--              (en digits and '.' decimal mark)
--  show     = text formatted for output, possibly with ref strip markers
--              (digits in local language and custom decimal mark)
-- The resulting show:
-- * Is for an input value and is spelled if wanted and possible.
-- * Has a rounded value, if wanted.
-- * Has digits grouped where necessary, if wanted.
-- * If negative, a Unicode minus is used; otherwise the sign is
--  '+' (if the input text used '+'), or is '' (if no sign in input).
text = strip(text or '')
local reference
local pos = text:find('\127', 1, true)
if pos then
local before = text:sub(1, pos - 1)
local remainder = text:sub(pos)
local refs = {}
while #remainder > 0 do
local ref, spaces
ref, spaces, remainder = remainder:match('^(\127[^\127]*UNIQ[^\127]*%-ref[^\127]*\127)(%s*)(.*)')
if ref then
table.insert(refs, ref)
else
refs = {}
break
end
end
if #refs > 0 then
text = strip(before)
reference = table.concat(refs)
end
end
local clean = to_en(text, parms)
if clean == '' then
return false, { another and 'cvt_no_num2' or 'cvt_no_num' }
end
local isnegative, propersign = false, ''  -- most common case
local singular, show, denominator
local value = tonumber(clean)
local altvalue
if value then
local sign = clean:sub(1, 1)
if sign == '+' or sign == '-' then
propersign = (sign == '+') and '+' or MINUS
clean = clean:sub(2)
end
if value < 0 then
isnegative = true
value = -value
end
else
local valstr
for _, prefix in ipairs({ '-', MINUS, '&minus;' }) do
-- Including '-' sets isnegative in case input is a fraction like '-2-3/4'.
local plen = #prefix
if clean:sub(1, plen) == prefix then
valstr = clean:sub(plen + 1)
if valstr:match('^%s') then  -- "- 1" is invalid but "-1 - 1/2" is ok
return false, { 'cvt_bad_num', text }
end
break
end
end
if valstr then
isnegative = true
propersign = MINUS
clean = valstr
value = tonumber(clean)
end
if value == nil then
if not no_fraction then
value, altvalue, show, denominator = extract_fraction(parms, clean, isnegative)
end
if value == nil then
return false, { 'cvt_bad_num', text }
end
if value <= 1 then
singular = true  -- for example, "½ mile" or "one half mile" (singular unit)
end
end
end
if not valid_number(value) then  -- for example, "1e310" may overflow
return false, { 'cvt_invalid_num' }
end
if show == nil then
-- clean is a non-empty string with no spaces, and does not represent a fraction,
-- and value = tonumber(clean) is a number >= 0.
-- If the input uses e-notation, show will be displayed using a power of ten, but
-- we use the number as given so it might not be normalized scientific notation.
-- The input value is spelled if specified so any e-notation is ignored;
-- that allows input like 2e6 to be spelled as "two million" which works
-- because the spell module converts '2e6' to '2000000' before spelling.
local function rounded(value, default, exponent)
local precision = parms.opt_ri
if precision then
local fmt = '%.' .. format('%d', precision) .. 'f'
local result = fmt:format(tonumber(value) + 2e-14)  -- fudge for some common cases of bad rounding
if not exponent then
singular = (tonumber(result) == 1)
end
return result
end
return default
end
singular = (value == 1)
local scientific
local significand, exponent = clean:match('^([%d.]+)[Ee]([+%-]?%d+)')
if significand then
show = with_exponent(parms, rounded(significand, significand, exponent), exponent)
scientific = true
else
show = with_separator(parms, rounded(value, clean))
end
show = propersign .. show
if parms.opt_spell_in then
show = spell_number(parms, 'in', propersign .. rounded(value, clean)) or show
scientific = false
end
if scientific then
parms.opt_scientific = true
end
end
if isnegative and (value ~= 0) then
value = -value
altvalue = -(altvalue or value)
end
return true, {
value = value,
altvalue = altvalue or value,
singular = singular,
clean = clean,
show = show .. (reference or ''),
denominator = denominator,
}
end
 
local function get_number(text)
-- Return v, f where:
--  v = nil (text is not a number)
-- or
--  v = value of text (text is a number)
--  f = true if value is an integer
-- Input can use en digits or digits in local language,
-- but no separators, no Unicode minus, and no fraction.
if text then
local number = tonumber(to_en(text))
if number then
local _, fracpart = math.modf(number)
return number, (fracpart == 0)
end
end
end
 
local function gcd(a, b)
-- Return the greatest common denominator for the given values,
-- which are known to be positive integers.
if a > b then
a, b = b, a
end
if a <= 0 then
return b
end
local r = b % a
if r <= 0 then
return a
end
if r == 1 then
return 1
end
return gcd(r, a)
end
 
local function fraction_table(value, denominator)
-- Return value as a string or a table:
-- * If result is a string, there is no fraction, and the result
--  is value formatted as a string of en digits.
-- * If result is a table, it represents a fraction with named fields:
--  wholestr, numstr, denstr (strings of en digits for integer, numerator, denominator).
-- The result is rounded to the nearest multiple of (1/denominator).
-- If the multiple is zero, no fraction is included.
-- No fraction is included if value is very large as the fraction would
-- be unhelpful, particularly if scientific notation is required.
-- Input value is a non-negative number.
-- Input denominator is a positive integer for the desired fraction.
if value <= 0 then
return '0'
end
if denominator <= 0 or value > 1e8 then
return format('%.2f', value)
end
local integer, decimals = math.modf(value)
local numerator = floor((decimals * denominator) +
0.5 + 2e-14)  -- add fudge for some common cases of bad rounding
if numerator >= denominator then
integer = integer + 1
numerator = 0
end
local wholestr = tostring(integer)
if numerator > 0 then
local div = gcd(numerator, denominator)
if div > 1 then
numerator = numerator / div
denominator = denominator / div
end
return {
wholestr = (integer > 0) and wholestr or '',
numstr = tostring(numerator),
denstr = tostring(denominator),
value = value,
}
end
return wholestr
end
 
local function preunits(count, preunit1, preunit2)
-- If count is 1:
--    ignore preunit2
--     return p1
-- else:
--    preunit1 is used for preunit2 if the latter is empty
--    return p1, p2
-- where:
--    p1 is text to insert before the input unit
--    p2 is text to insert before the output unit
--    p1 or p2 may be nil to mean "no preunit"
-- Using '+' gives output like "5+ feet" (no space before, but space after).
local function withspace(text, wantboth)
-- Return text with space before and, if wantboth, after.
-- However, no space is added if there is a space or '&nbsp;' or '-'
-- at that position ('-' is for adjectival text).
-- There is also no space if text starts with '&'
-- (e.g. '&deg;' would display a degree symbol with no preceding space).
local char = text:sub(1, 1)
if char == '&' then
return text  -- an html entity can be used to specify the exact display
end
if not (char == ' ' or char == '-' or char == '+') then
text = ' ' .. text
end
if wantboth then
char = text:sub(-1, -1)
if not (char == ' ' or char == '-' or text:sub(-6, -1) == '&nbsp;') then
text = text .. ' '
end
end
return text
end
local PLUS = '+ '
preunit1 = preunit1 or ''
local trim1 = strip(preunit1)
if count == 1 then
if trim1 == '' then
return nil
end
if trim1 == '+' then
return PLUS
end
return withspace(preunit1, true)
end
preunit1 = withspace(preunit1)
preunit2 = preunit2 or ''
local trim2 = strip(preunit2)
if trim1 == '+' then
if trim2 == '' or trim2 == '+' then
return PLUS, PLUS
end
preunit1 = PLUS
end
if trim2 == '' then
if trim1 == '' then
return nil, nil
end
preunit2 = preunit1
elseif trim2 == '+' then
preunit2 = PLUS
elseif trim2 == '&#32;' then  -- trick to make preunit2 empty
preunit2 = nil
else
preunit2 = withspace(preunit2)
end
return preunit1, preunit2
end
 
local function range_text(range, want_name, parms, before, after, inout)
-- Return before .. rtext .. after
-- where rtext is the text that separates two values in a range.
local rtext, adj_text, exception
if type(range) == 'table' then
-- Table must specify range text for ('off' and 'on') or ('input' and 'output'),
-- and may specify range text for 'adj=on',
-- and may specify exception = true.
rtext = range[want_name and 'off' or 'on'] or
range[((inout == 'in') == (parms.opt_flip == true)) and 'output' or 'input']
adj_text = range['adj']
exception = range['exception']
else
rtext = range
end
if parms.opt_adjectival then
if want_name or (exception and parms.abbr_org == 'on') then
rtext = adj_text or rtext:gsub(' ', '-'):gsub('&nbsp;', '-')
end
end
if rtext == '–' and after:sub(1, #MINUS) == MINUS then
rtext = '&nbsp;– '
end
return before .. rtext .. after
end
 
local function get_composite(parms, iparm, in_unit_table)
-- Look for a composite input unit. For example, {{convert|1|yd|2|ft|3|in}}
-- would result in a call to this function with
--  iparm = 3 (parms[iparm] = "2", just after the first unit)
--  in_unit_table = (unit table for "yd"; contains value 1 for number of yards)
-- Return true, iparm, unit where
--  iparm = index just after the composite units (7 in above example)
--  unit = composite unit table holding all input units,
-- or return true if no composite unit is present in parms,
-- or return false, t where t is an error message table.
local default, subinfo
local composite_units, count = { in_unit_table }, 1
local fixups = {}
local total = in_unit_table.valinfo[1].value
local subunit = in_unit_table
while subunit.subdivs do  -- subdivs is nil or a table of allowed subdivisions
local subcode = strip(parms[iparm+1])
local subdiv = subunit.subdivs[subcode] or subunit.subdivs[(all_units[subcode] or {}).target]
if not subdiv then
break
end
local success
success, subunit = lookup(parms, subcode, 'no_combination')
if not success then return false, subunit end  -- should never occur
success, subinfo = extract_number(parms, parms[iparm])
if not success then return false, subinfo end
iparm = iparm + 2
subunit.inout = 'in'
subunit.valinfo = { subinfo }
-- Recalculate total as a number of subdivisions.
-- subdiv[1] = number of subdivisions per previous unit (integer > 1).
total = total * subdiv[1] + subinfo.value
if not default then  -- set by the first subdiv with a default defined
default = subdiv.default
end
count = count + 1
composite_units[count] = subunit
if subdiv.unit or subdiv.name then
fixups[count] = { unit = subdiv.unit, name = subdiv.name, valinfo = subunit.valinfo }
end
end
if count == 1 then
return true  -- no error and no composite unit
end
for i, fixup in pairs(fixups) do
local unit = fixup.unit
local name = fixup.name
if not unit or (count > 2 and name) then
composite_units[i].fixed_name = name
else
local success, alternate = lookup(parms, unit, 'no_combination')
if not success then return false, alternate end  -- should never occur
alternate.inout = 'in'
alternate.valinfo = fixup.valinfo
composite_units[i] = alternate
end
end
return true, iparm, {
utype = in_unit_table.utype,
scale = subunit.scale,  -- scale of last (least significant) unit
valinfo = { { value = total, clean = subinfo.clean, denominator = subinfo.denominator } },
composite = composite_units,
default = default or in_unit_table.default
}
end
 
local function translate_parms(parms, kv_pairs)
-- Update fields in parms by translating each key:value in kv_pairs to terms
-- used by this module (may involve translating from local language to English).
-- Also, checks are performed which may display warnings, if enabled.
-- Return true if successful or return false, t where t is an error message table.
currency_text = nil  -- local testing can hold module in memory; must clear globals
local accept_any_text = {
input = true,
qid = true,
qual = true,
stylein = true,
styleout = true,
tracking = true,
}
if kv_pairs.adj and kv_pairs.sing then
-- For enwiki (before translation), warn if attempt to use adj and sing
-- as the latter is a deprecated alias for the former.
if kv_pairs.adj ~= kv_pairs.sing and kv_pairs.sing ~= '' then
add_warning(parms, 1, 'cvt_unknown_option', 'sing=' .. kv_pairs.sing)
end
kv_pairs.sing = nil
end
kv_pairs.comma = kv_pairs.comma or config.comma  -- for plwiki who want default comma=5
for loc_name, loc_value in pairs(kv_pairs) do
local en_name = text_code.en_option_name[loc_name]
if en_name then
local en_value
if en_name == '$' or en_name == 'frac' or en_name == 'sigfig' then
if loc_value == '' then
add_warning(parms, 2, 'cvt_empty_option', loc_name)
elseif en_name == '$' then
-- Value should be a single character like "€" for the euro currency symbol, but anything is accepted.
currency_text = (loc_value == 'euro') and '€' or loc_value
else
local minimum
local number, is_integer = get_number(loc_value)
if en_name == 'frac' then
minimum = 2
if number and number < 0 then
parms.opt_fraction_horizontal = true
number = -number
end
else
minimum = 1
end
if number and is_integer and number >= minimum then
en_value = number
else
add_warning(parms, 1, (en_name == 'frac' and 'cvt_bad_frac' or 'cvt_bad_sigfig'), loc_name .. '=' .. loc_value)
end
end
elseif accept_any_text[en_name] then
en_value = loc_value ~= '' and loc_value or nil  -- accept non-empty user text with no validation
if en_name == 'input' then
-- May have something like {{convert|input=}} (empty input) if source is an infobox
-- with optional fields. In that case, want to output nothing rather than an error.
parms.input_text = loc_value  -- keep input because parms.input is nil if loc_value == ''
end
else
en_value = text_code.en_option_value[en_name][loc_value]
if en_value and en_value:sub(-1) == '?' then
en_value = en_value:sub(1, -2)
add_warning(parms, -1, 'cvt_deprecated', loc_name .. '=' .. loc_value)
end
if en_value == nil then
if loc_value == '' then
add_warning(parms, 2, 'cvt_empty_option', loc_name)
else
add_warning(parms, 1, 'cvt_unknown_option', loc_name .. '=' .. loc_value)
end
elseif en_value == '' then
en_value = nil  -- an ignored option like adj=off
elseif type(en_value) == 'string' and en_value:sub(1, 4) == 'opt_' then
for _, v in ipairs(split(en_value, ',')) do
local lhs, rhs = v:match('^(.-)=(.+)$')
if rhs then
parms[lhs] = tonumber(rhs) or rhs
else
parms[v] = true
end
end
en_value = nil
end
end
parms[en_name] = en_value
else
add_warning(parms, 1, 'cvt_unknown_option', loc_name .. '=' .. loc_value)
end
end
local abbr_entered = parms.abbr
local cfg_abbr = config.abbr
if cfg_abbr then
-- Don't warn if invalid because every convert would show that warning.
if cfg_abbr == 'on always' then
parms.abbr = 'on'
elseif cfg_abbr == 'off always' then
parms.abbr = 'off'
elseif parms.abbr == nil then
if cfg_abbr == 'on default' then
parms.abbr = 'on'
elseif cfg_abbr == 'off default' then
parms.abbr = 'off'
end
end
end
if parms.abbr then
if parms.abbr == 'unit' then
parms.abbr = 'on'
parms.number_word = true
end
parms.abbr_org = parms.abbr  -- original abbr, before any flip
elseif parms.opt_hand_hh then
parms.abbr_org = 'on'
parms.abbr = 'on'
else
parms.abbr = 'out'  -- default is to abbreviate output only (use symbol, not name)
end
if parms.opt_order_out then
-- Disable options that do not work in a useful way with order=out.
parms.opt_flip = nil  -- override adj=flip
parms.opt_spell_in = nil
parms.opt_spell_out = nil
parms.opt_spell_upper = nil
end
if parms.opt_spell_out and not abbr_entered then
parms.abbr = 'off'  -- should show unit name when spelling the output value
end
if parms.opt_flip then
local function swap_in_out(option)
local value = parms[option]
if value == 'in' then
parms[option] = 'out'
elseif value == 'out' then
parms[option] = 'in'
end
end
swap_in_out('abbr')
swap_in_out('lk')
if parms.opt_spell_in and not parms.opt_spell_out then
-- For simplicity, and because it does not appear to be needed,
-- user cannot set an option to spell the output only.
parms.opt_spell_in = nil
parms.opt_spell_out = true
end
end
if parms.opt_spell_upper then
parms.spell_upper = parms.opt_flip and 'out' or 'in'
end
if parms.opt_table or parms.opt_tablecen then
if abbr_entered == nil and parms.lk == nil then
parms.opt_values = true
end
parms.table_align = parms.opt_table and 'right' or 'center'
end
if parms.table_align or parms.opt_sortable_on then
parms.need_table_or_sort = true
end
local disp_joins = text_code.disp_joins
local default_joins = disp_joins['b']
parms.join_between = default_joins[3] or '; '
local disp = parms.disp
if disp == nil then  -- special case for the most common setting
parms.joins = default_joins
elseif disp == 'x' then
-- Later, parms.joins is set from the input parameters.
else
-- Old template does this.
local abbr = parms.abbr
if disp == 'slash' then
if abbr_entered == nil then
disp = 'slash-nbsp'
elseif abbr == 'in' or abbr == 'out' then
disp = 'slash-sp'
else
disp = 'slash-nosp'
end
elseif disp == 'sqbr' then
if abbr == 'on' then
disp = 'sqbr-nbsp'
else
disp = 'sqbr-sp'
end
end
parms.joins = disp_joins[disp] or default_joins
parms.join_between = parms.joins[3] or parms.join_between
parms.wantname = parms.joins.wantname
end
if (en_default and not parms.opt_lang_local and (parms[1] or ''):find('%d')) or parms.opt_lang_en then
from_en_table = nil
end
if en_default and from_en_table then
-- For hiwiki: localized symbol/name is defined with the US symbol/name field,
-- and is used if output uses localized numbers.
parms.opt_sp_us = true
end
return true
end
 
local function get_values(parms)
-- If successful, update parms and return true, v, i where
--  v = table of input values
--  i = index to next entry in parms after those processed here
-- or return false, t where t is an error message table.
local valinfo = collection()  -- numbered table of input values
local range = collection()  -- numbered table of range items (having, for example, 2 range items requires 3 input values)
local had_nocomma  -- true if removed "nocomma" kludge from second parameter (like "tonocomma")
local parm2 = strip(parms[2])
if parm2 and parm2:sub(-7, -1) == 'nocomma' then
parms[2] = strip(parm2:sub(1, -8))
parms.opt_nocomma = true
had_nocomma = true
end
local function extractor(i)
-- If the parameter is not a value, try unpacking it as a range ("1-23" for "1 to 23").
-- However, "-1-2/3" is a negative fraction (-1⅔), so it must be extracted first.
-- Do not unpack a parameter if it is like "3-1/2" which is sometimes incorrectly
-- used instead of "3+1/2" (and which should not be interpreted as "3 to ½").
-- Unpacked items are inserted into the parms table.
-- The tail recursion allows combinations like "1x2 to 3x4".
local valstr = strip(parms[i])  -- trim so any '-' as a negative sign will be at start
local success, result = extract_number(parms, valstr, i > 1)
if not success and valstr and i < 20 then  -- check i to limit abuse
local lhs, sep, rhs = valstr:match('^(%S+)%s+(%S+)%s+(%S.*)')
if lhs and not (sep == '-' and rhs:match('/')) then
if sep:find('%d') then
return success, result  -- to reject {{convert|1 234 567|m}} with a decent message (en only)
end
parms[i] = rhs
table.insert(parms, i, sep)
table.insert(parms, i, lhs)
return extractor(i)
end
if not valstr:match('%-.*/') then
for _, sep in ipairs(text_code.ranges.words) do
local start, stop = valstr:find(sep, 2, true)  -- start at 2 to skip any negative sign for range '-'
if start then
parms[i] = valstr:sub(stop + 1)
table.insert(parms, i, sep)
table.insert(parms, i, valstr:sub(1, start - 1))
return extractor(i)
end
end
end
end
return success, result
end
local i = 1
local is_change
while true do
local success, info = extractor(i)  -- need to set parms.opt_nocomma before calling this
if not success then return false, info end
i = i + 1
if is_change then
info.is_change = true  -- value is after "±" and so is a change (significant for range like {{convert|5|±|5|°C}})
is_change = nil
end
valinfo:add(info)
local range_item = get_range(strip(parms[i]))
if not range_item then
break
end
i = i + 1
range:add(range_item)
if type(range_item) == 'table' then
-- For range "x", if append unit to some values, append it to all.
parms.in_range_x = parms.in_range_x or range_item.in_range_x
parms.out_range_x = parms.out_range_x or range_item.out_range_x
parms.abbr_range_x = parms.abbr_range_x or range_item.abbr_range_x
is_change = range_item.is_range_change
end
end
if range.n > 0 then
if range.n > 30 then  -- limit abuse, although 4 is a more likely upper limit
return false, { 'cvt_invalid_num' }  -- misleading message but it will do
end
parms.range = range
elseif had_nocomma then
return false, { 'cvt_unknown', parm2 }
end
return true, valinfo, i
end
 
local function simple_get_values(parms)
-- If input is like "{{convert|valid_value|valid_unit|...}}",
-- return true, i, in_unit, in_unit_table
-- i = index in parms of what follows valid_unit, if anything.
-- The valid_value is not negative and does not use a fraction, and
-- no options requiring further processing of the input are used.
-- Otherwise, return nothing or return false, parm1 for caller to interpret.
-- Testing shows this function is successful for 96% of converts in articles,
-- and that on average it speeds up converts by 8%.
local clean = to_en(strip(parms[1] or ''), parms)
if parms.opt_ri or parms.opt_spell_in or #clean > 10 or not clean:match('^[0-9.]+$') then
return false, clean
end
local value = tonumber(clean)
if not value then return end
local info = {
value = value,
altvalue = value,
singular = (value == 1),
clean = clean,
show = with_separator(parms, clean),
}
local in_unit = strip(parms[2])
local success, in_unit_table = lookup(parms, in_unit, 'no_combination')
if not success then return end
in_unit_table.valinfo = { info }
return true, 3, in_unit, in_unit_table
end
 
local function wikidata_call(parms, operation, ...)
-- Return true, s where s is the result of a Wikidata operation,
-- or return false, t where t is an error message table.
local function worker(...)
wikidata_code = wikidata_code or require(wikidata_module)
wikidata_data = wikidata_data or mw.loadData(wikidata_data_module)
return wikidata_code[operation](wikidata_data, ...)
end
local success, status, result = pcall(worker, ...)
if success then
return status, result
end
if parms.opt_sortable_debug then
-- Use debug=yes to crash if an error while accessing Wikidata.
error('Error accessing Wikidata: ' .. status, 0)
end
return false, { 'cvt_wd_fail' }
end
 
local function get_parms(parms, args)
-- If successful, update parms and return true, unit where
--  parms is a table of all arguments passed to the template
--        converted to named arguments, and
--  unit is the input unit table;
-- or return false, t where t is an error message table.
-- For special processing (not a convert), can also return
-- true, wikitext where wikitext is the final result.
-- The returned input unit table may be for a fake unit using the specified
-- unit code as the symbol and name, and with bad_mcode = message code table.
-- MediaWiki removes leading and trailing whitespace from the values of
-- named arguments. However, the values of numbered arguments include any
-- whitespace entered in the template, and whitespace is used by some
-- parameters (example: the numbered parameters associated with "disp=x").
local kv_pairs = {}  -- table of input key:value pairs where key is a name; needed because cannot iterate parms and add new fields to it
for k, v in pairs(args) do
if type(k) == 'number' or k == 'test' then  -- parameter "test" is reserved for testing and is not translated
parms[k] = v
else
kv_pairs[k] = v
end
end
if parms.test == 'wikidata' then
local ulookup = function (ucode)
-- Use empty table for parms so it does not accumulate results when used repeatedly.
return lookup({}, ucode, 'no_combination')
end
return wikidata_call(parms, '_listunits', ulookup)
end
local success, msg = translate_parms(parms, kv_pairs)
if not success then return false, msg end
if parms.input then
success, msg = wikidata_call(parms, '_adjustparameters', parms, 1)
if not success then return false, msg end
end
local success, i, in_unit, in_unit_table = simple_get_values(parms)
if not success then
if type(i) == 'string' and i:match('^NNN+$') then
-- Some infoboxes have examples like {{convert|NNN|m}} (3 or more "N").
-- Output an empty string for these.
return false, { 'cvt_no_output' }
end
local valinfo
success, valinfo, i = get_values(parms)
if not success then return false, valinfo end
in_unit = strip(parms[i])
i = i + 1
success, in_unit_table = lookup(parms, in_unit, 'no_combination')
if not success then
in_unit = in_unit or ''
if parms.opt_ignore_error then  -- display given unit code with no error (for use with {{val}})
in_unit_table = ''  -- suppress error message and prevent processing of output unit
end
in_unit_table = setmetatable({
symbol = in_unit, name2 = in_unit, utype = in_unit,
scale = 1, default = '', defkey = '', linkey = '',
bad_mcode = in_unit_table }, unit_mt)
end
in_unit_table.valinfo = valinfo
end
if parms.test == 'msg' then
-- Am testing the messages produced when no output unit is specified, and
-- the input unit has a missing or invalid default.
-- Set two units for testing that.
-- LATER: Remove this code.
if in_unit == 'chain' then
in_unit_table.default = nil  -- no default
elseif in_unit == 'rd' then
in_unit_table.default  = "ft!X!m"  -- an invalid expression
end
end
in_unit_table.inout = 'in'  -- this is an input unit
if not parms.range then
local success, inext, composite_unit = get_composite(parms, i, in_unit_table)
if not success then return false, inext end
if composite_unit then
in_unit_table = composite_unit
i = inext
end
end
if in_unit_table.builtin == 'mach' then
-- As with old template, a number following Mach as the input unit is the altitude,
-- and there is no way to specify an altitude for the output unit.
-- Could put more code in this function to get any output unit and check for
-- an altitude following that unit.
local success, info = extract_number(parms, parms[i], false, true)
if success then
i = i + 1
in_unit_table.altitude = info.value
end
end
local word = strip(parms[i])
i = i + 1
local precision, is_bad_precision
local function set_precision(text)
local number, is_integer = get_number(text)
if number then
if is_integer then
precision = number
else
precision = text
is_bad_precision = true
end
return true  -- text was used for precision, good or bad
end
end
if word and not set_precision(word) then
parms.out_unit = parms.out_unit or word
if set_precision(strip(parms[i])) then
i = i + 1
end
end
if parms.opt_adj_mid then
word = parms[i]
i = i + 1
if word then  -- mid-text words
if word:sub(1, 1) == '-' then
parms.mid = word
else
parms.mid = ' ' .. word
end
end
end
if parms.opt_one_preunit then
parms[parms.opt_flip and 'preunit2' or 'preunit1'] = preunits(1, parms[i])
i = i + 1
end
if parms.disp == 'x' then
-- Following is reasonably compatible with the old template.
local first = parms[i] or ''
local second = parms[i+1] or ''
i = i + 2
if strip(first) == '' then  -- user can enter '&#32;' rather than ' ' to avoid the default
first = ' [&nbsp;' .. first
second = '&nbsp;]' .. second
end
parms.joins = { first, second }
elseif parms.opt_two_preunits then
local p1, p2 = preunits(2, parms[i], parms[i+1])
i = i + 2
if parms.preunit1 then
-- To simplify documentation, allow unlikely use of adj=pre with disp=preunit
-- (however, an output unit must be specified with adj=pre and with disp=preunit).
parms.preunit1 = parms.preunit1 .. p1
parms.preunit2 = p2
else
parms.preunit1, parms.preunit2 = p1, p2
end
end
if precision == nil then
if set_precision(strip(parms[i])) then
i = i + 1
end
end
if is_bad_precision then
add_warning(parms, 1, 'cvt_bad_prec', precision)
else
parms.precision = precision
end
for j = i, i + 3 do
local parm = parms[j]  -- warn if find a non-empty extraneous parameter
if parm and parm:match('%S') then
add_warning(parms, 1, 'cvt_unknown_option', parm)
break
end
end
return true, in_unit_table
end
 
local function record_default_precision(parms, out_current, precision)
-- If necessary, adjust parameters and return a possibly adjusted precision.
-- When converting a range of values where a default precision is required,
-- that default is calculated for each value because the result sometimes
-- depends on the precise input and output values. This function may cause
-- the entire convert process to be repeated in order to ensure that the
-- same default precision is used for each individual convert.
-- If that were not done, a range like 1000 to 1000.4 may give poor results
-- because the first output could be heavily rounded, while the second is not.
-- For range 1000.4 to 1000, this function can give the second convert the
-- same default precision that was used for the first.
if not parms.opt_round_each then
local maxdef = out_current.max_default_precision
if maxdef then
if maxdef < precision then
parms.do_convert_again = true
out_current.max_default_precision = precision
else
precision = out_current.max_default_precision
end
else
out_current.max_default_precision = precision
end
end
return precision
end
 
local function default_precision(parms, invalue, inclean, denominator, outvalue, in_current, out_current, extra)
-- Return a default value for precision (an integer like 2, 0, -2).
-- If denominator is not nil, it is the value of the denominator in inclean.
-- Code follows procedures used in old template.
local fudge = 1e-14  -- {{Order of magnitude}} adds this, so we do too
local prec, minprec, adjust
local subunit_ignore_trailing_zero
local subunit_more_precision  -- kludge for "in" used in input like "|2|ft|6|in"
local composite = in_current.composite
if composite then
subunit_ignore_trailing_zero = true  -- input "|2|st|10|lb" has precision 0, not -1
if composite[#composite].exception == 'subunit_more_precision' then
subunit_more_precision = true  -- do not use standard precision with input like "|2|ft|6|in"
end
end
if denominator and denominator > 0 then
prec = math.max(log10(denominator), 1)
else
-- Count digits after decimal mark, handling cases like '12.345e6'.
local exponent
local integer, dot, decimals, expstr = inclean:match('^(%d*)(%.?)(%d*)(.*)')
local e = expstr:sub(1, 1)
if e == 'e' or e == 'E' then
exponent = tonumber(expstr:sub(2))
end
if dot == '' then
prec = subunit_ignore_trailing_zero and 0 or -integer:match('0*$'):len()
else
prec = #decimals
end
if exponent then
-- So '1230' and '1.23e3' both give prec = -1, and '0.00123' and '1.23e-3' give 5.
prec = prec - exponent
end
end
if in_current.istemperature and out_current.istemperature then
-- Converting between common temperatures (°C, °F, °R, K); not keVT.
-- Kelvin value can be almost zero, or small but negative due to precision problems.
-- Also, an input value like -300 C (below absolute zero) gives negative kelvins.
-- Calculate minimum precision from absolute value.
adjust = 0
local kelvin = abs((invalue - in_current.offset) * in_current.scale)
if kelvin < 1e-8 then  -- assume nonzero due to input or calculation precision problem
minprec = 2
else
minprec = 2 - floor(log10(kelvin) + fudge)  -- 3 sigfigs in kelvin
end
else
if invalue == 0 or outvalue <= 0 then
-- We are never called with a negative outvalue, but it might be zero.
-- This is special-cased to avoid calculation exceptions.
return record_default_precision(parms, out_current, 0)
end
if out_current.exception == 'integer_more_precision' and floor(invalue) == invalue then
-- With certain output units that sometimes give poor results
-- with default rounding, use more precision when the input
-- value is equal to an integer. An example of a poor result
-- is when input 50 gives a smaller output than input 49.5.
-- Experiment shows this helps, but it does not eliminate all
-- surprises because it is not clear whether "50" should be
-- interpreted as "from 45 to 55" or "from 49.5 to 50.5".
adjust = -log10(in_current.scale)
elseif subunit_more_precision then
-- Conversion like "{{convert|6|ft|1|in|cm}}" (where subunit is "in")
-- has a non-standard adjust value, to give more output precision.
adjust = log10(out_current.scale) + 2
else
adjust = log10(abs(invalue / outvalue))
end
adjust = adjust + log10(2)
-- Ensure that the output has at least two significant figures.
minprec = 1 - floor(log10(outvalue) + fudge)
end
if extra then
adjust = extra.adjust or adjust
minprec = extra.minprec or minprec
end
return record_default_precision(parms, out_current, math.max(floor(prec + adjust), minprec))
end
 
local function convert(parms, invalue, info, in_current, out_current)
-- Convert given input value from one unit to another.
-- Return output_value (a number) if a simple convert, or
-- return f, t where
--  f = true, t = table of information with results, or
--  f = false, t = error message table.
local inscale = in_current.scale
local outscale = out_current.scale
if not in_current.iscomplex and not out_current.iscomplex then
return invalue * (inscale / outscale)  -- minimize overhead for most common case
end
if in_current.invert or out_current.invert then
-- Inverted units, such as inverse length, inverse time, or
-- fuel efficiency. Built-in units do not have invert set.
if (in_current.invert or 1) * (out_current.invert or 1) < 0 then
return 1 / (invalue * inscale * outscale)
end
return invalue * (inscale / outscale)
elseif in_current.offset then
-- Temperature (there are no built-ins for this type of unit).
if info.is_change then
return invalue * (inscale / outscale)
end
return (invalue - in_current.offset) * (inscale / outscale) + out_current.offset
else
-- Built-in unit.
local in_builtin = in_current.builtin
local out_builtin = out_current.builtin
if in_builtin and out_builtin then
if in_builtin == out_builtin then
return invalue
end
-- There are no cases (yet) where need to convert from one
-- built-in unit to another, so this should never occur.
return false, { 'cvt_bug_convert' }
end
if in_builtin == 'mach' or out_builtin == 'mach' then
local adjust
if in_builtin == 'mach' then
inscale = speed_of_sound(in_current.altitude)
adjust = outscale / 0.1
else
outscale = speed_of_sound(out_current.altitude)
adjust = 0.1 / inscale
end
return true, {
outvalue = invalue * (inscale / outscale),
adjust = log10(adjust) + log10(2),
}
elseif in_builtin == 'hand' then
-- 1 hand = 4 inches; 1.2 hands = 6 inches.
-- Decimals of a hand are only defined for the first digit, and
-- the first fractional digit should be a number of inches (1, 2 or 3).
-- However, this code interprets the entire fractional part as the number
-- of inches / 10 (so 1.75 inches would be 0.175 hands).
-- A value like 12.3 hands is exactly 12*4 + 3 inches; base default precision on that.
local integer, fracpart = math.modf(invalue)
local inch_value = 4 * integer + 10 * fracpart  -- equivalent number of inches
local factor = inscale / outscale
if factor == 4 then
-- Am converting to inches: show exact result, and use "inches" not "in" by default.
if parms.abbr_org == nil then
out_current.usename = true
end
local show = format('%g', abs(inch_value))  -- show and clean are unsigned
if not show:find('e', 1, true) then
return true, {
invalue = inch_value,
outvalue = inch_value,
clean = show,
show = show,
}
end
end
local outvalue = (integer + 2.5 * fracpart) * factor
local fracstr = info.clean:match('%.(.*)') or ''
local fmt
if fracstr == '' then
fmt = '%.0f'
else
fmt = '%.' .. format('%d', #fracstr - 1) .. 'f'
end
return true, {
invalue = inch_value,
clean = format(fmt, inch_value),
outvalue = outvalue,
minprec = 0,
}
end
end
return false, { 'cvt_bug_convert' }  -- should never occur
end
 
local function user_style(parms, i)
-- Return text for a user-specified style for a table cell, or '' if none,
-- given i = 1 (input style) or 2 (output style).
local style = parms[(i == 1) and 'stylein' or 'styleout']
if style then
style = style:gsub('"', '')
if style ~= '' then
if style:sub(-1) ~= ';' then
style = style .. ';'
end
return style
end
end
return ''
end
 
local function make_table_or_sort(parms, invalue, info, in_current, scaled_top)
-- Set options to handle output for a table or a sort key, or both.
-- The text sort key is based on the value resulting from converting
-- the input to a fake base unit with scale = 1, and other properties
-- required for a conversion derived from the input unit.
-- For other modules, return the sort key in a hidden span element, and
-- the scaled value used to generate the sort key.
-- If scaled_top is set, it is the scaled value of the numerator of a per unit
-- to be combined with this unit (the denominator) to make the sort key.
-- Scaling only works with units that convert with a factor (not temperature).
local sortkey, scaled_value
if parms.opt_sortable_on then
local base = {  -- a fake unit with enough fields for a valid convert
scale = 1,
invert = in_current.invert and 1,
iscomplex = in_current.iscomplex,
offset = in_current.offset and 0,
}
local outvalue, extra = convert(parms, invalue, info, in_current, base)
if extra then
outvalue = extra.outvalue
end
if in_current.istemperature then
-- Have converted to kelvin; assume numbers close to zero have a
-- rounding error and should be zero.
if abs(outvalue) < 1e-12 then
outvalue = 0
end
end
if scaled_top and outvalue ~= 0 then
outvalue = scaled_top / outvalue
end
scaled_value = outvalue
if not valid_number(outvalue) then
if outvalue < 0 then
sortkey = '1000000000000000000'
else
sortkey = '9000000000000000000'
end
elseif outvalue == 0 then
sortkey = '5000000000000000000'
else
local mag = floor(log10(abs(outvalue)) + 1e-14)
local prefix
if outvalue > 0 then
prefix = 7000 + mag
else
prefix = 2999 - mag
outvalue = outvalue + 10^(mag+1)
end
sortkey = format('%d', prefix) .. format('%015.0f', floor(outvalue * 10^(14-mag)))
end
end
local sortspan
if sortkey and not parms.table_align then
sortspan = parms.opt_sortable_debug and
'<span data-sort-value="' .. sortkey .. '♠"><span style="border:1px solid">' .. sortkey .. '♠</span></span>' or
'<span data-sort-value="' .. sortkey .. '♠"></span>'
parms.join_before = sortspan
end
if parms.table_align then
local sort
if sortkey then
sort = ' data-sort-value="' .. sortkey .. '"'
if parms.opt_sortable_debug then
parms.join_before = '<span style="border:1px solid">' .. sortkey .. '</span>'
end
else
sort = ''
end
local style = 'style="text-align:' .. parms.table_align .. ';'
local joins = {}
for i = 1, 2 do
joins[i] = (i == 1 and '' or '\n|') .. style .. user_style(parms, i) .. '"' .. sort .. '|'
end
parms.table_joins = joins
end
return sortspan, scaled_value
end
 
local cvt_to_hand
 
local function cvtround(parms, info, in_current, out_current)
-- Return true, t where t is a table with the conversion results; fields:
--  show = rounded, formatted string with the result of converting value in info,
--      using the rounding specified in parms.
--  singular = true if result (after rounding and ignoring any negative sign)
--      is "1", or like "1.00", or is a fraction with value < 1;
--  (and more fields shown below, and a calculated 'absvalue' field).
-- or return false, t where t is an error message table.
-- Input info.clean uses en digits (it has been translated, if necessary).
-- Output show uses en or non-en digits as appropriate, or can be spelled.
if out_current.builtin == 'hand' then
return cvt_to_hand(parms, info, in_current, out_current)
end
local invalue = in_current.builtin == 'hand' and info.altvalue or info.value
local outvalue, extra = convert(parms, invalue, info, in_current, out_current)
if parms.need_table_or_sort then
parms.need_table_or_sort = nil  -- process using first input value only
make_table_or_sort(parms, invalue, info, in_current)
end
if extra then
if not outvalue then return false, extra end
invalue = extra.invalue or invalue
outvalue = extra.outvalue
end
if not valid_number(outvalue) then
return false, { 'cvt_invalid_num' }
end
local isnegative
if outvalue < 0 then
isnegative = true
outvalue = -outvalue
end
local precision, show, exponent
local denominator = out_current.frac
if denominator then
show = fraction_table(outvalue, denominator)
else
precision = parms.precision
if not precision then
if parms.sigfig then
show, exponent = make_sigfig(outvalue, parms.sigfig)
elseif parms.opt_round then
local n = parms.opt_round
if n == 0.5 then
local integer, fracpart = math.modf(floor(2 * outvalue + 0.5) / 2)
if fracpart == 0 then
show = format('%.0f', integer)
else
show = format('%.1f', integer + fracpart)
end
else
show = format('%.0f', floor((outvalue / n) + 0.5) * n)
end
else
local inclean = info.clean
if extra then
inclean = extra.clean or inclean
show = extra.show
end
if not show then
precision = default_precision(parms, invalue, inclean, info.denominator, outvalue, in_current, out_current, extra)
end
end
end
end
if precision then
if precision >= 0 then
local fudge
if precision <= 8 then
-- Add a fudge to handle common cases of bad rounding due to inability
-- to precisely represent some values. This makes the following work:
-- {{convert|-100.1|C|K}} and {{convert|5555000|um|m|2}}.
-- Old template uses #expr round, which invokes PHP round().
-- LATER: Investigate how PHP round() works.
fudge = 2e-14
else
fudge = 0
end
local fmt = '%.' .. format('%d', precision) .. 'f'
local success
success, show = pcall(format, fmt, outvalue + fudge)
if not success then
return false, { 'cvt_big_prec', tostring(precision) }
end
else
precision = -precision  -- #digits to zero (in addition to any digits after dot)
local shift = 10 ^ precision
show = format('%.0f', outvalue/shift)
if show ~= '0' then
exponent = #show + precision
end
end
end
local t = format_number(parms, show, exponent, isnegative)
if type(show) == 'string' then
-- Set singular using match because on some systems 0.99999999999999999 is 1.0.
if exponent then
t.singular = (exponent == 1 and show:match('^10*$'))
else
t.singular = (show == '1' or show:match('^1%.0*$'))
end
else
t.fraction_table = show
t.singular = (outvalue <= 1)  -- cannot have 'fraction == 1', but if it were possible it would be singular
end
t.raw_absvalue = outvalue  -- absolute value before rounding
return true, setmetatable(t, {
__index = function (self, key)
if key == 'absvalue' then
-- Calculate absolute value after rounding, if needed.
local clean, exponent = rawget(self, 'clean'), rawget(self, 'exponent')
local value = tonumber(clean)  -- absolute value (any negative sign has been ignored)
if exponent then
value = value * 10^exponent
end
rawset(self, key, value)
return value
end
end })
end
 
function cvt_to_hand(parms, info, in_current, out_current)
-- Convert input to hands, inches.
-- Return true, t where t is a table with the conversion results;
-- or return false, t where t is an error message table.
if parms.abbr_org == nil then
out_current.usename = true  -- default is to show name not symbol
end
local precision = parms.precision
local frac = out_current.frac
if not frac and precision and precision > 1 then
frac = (precision == 2) and 2 or 4
end
local out_next = out_current.out_next
if out_next then
-- Use magic knowledge to determine whether the next unit is inches without requiring i18n.
-- The following ensures that when the output combination "hand in" is used, the inches
-- value is rounded to match the hands value. Also, displaying say "61½" instead of 61.5
-- is better as 61.5 implies the value is not 61.4.
if out_next.exception == 'subunit_more_precision' then
out_next.frac = frac
end
end
-- Convert to inches; calculate hands from that.
local dummy_unit_table = { scale = out_current.scale / 4, frac = frac }
local success, outinfo = cvtround(parms, info, in_current, dummy_unit_table)
if not success then return false, outinfo end
local tfrac = outinfo.fraction_table
local inches = outinfo.raw_absvalue
if tfrac then
inches = floor(inches)  -- integer part only; fraction added later
else
inches = floor(inches + 0.5)  -- a hands measurement never shows decimals of an inch
end
local hands, inches = divide(inches, 4)
outinfo.absvalue = hands + inches/4  -- supposed to be the absolute rounded value, but this is close enough
local inchstr = tostring(inches)  -- '0', '1', '2' or '3'
if precision and precision <= 0 then  -- using negative or 0 for precision rounds to nearest hand
hands = floor(outinfo.raw_absvalue/4 + 0.5)
inchstr = ''
elseif tfrac then
-- Always show an integer before fraction (like "15.0½") because "15½" means 15-and-a-half hands.
inchstr = numdot .. format_fraction(parms, 'out', false, inchstr, tfrac.numstr, tfrac.denstr)
else
inchstr = numdot .. from_en(inchstr)
end
outinfo.show = outinfo.sign .. with_separator(parms, format('%.0f', hands)) .. inchstr
return true, outinfo
end
 
local function evaluate_condition(value, condition)
-- Return true or false from applying a conditional expression to value,
-- or throw an error if invalid.
-- A very limited set of expressions is supported:
--    v < 9
--    v * 9 < 9
-- where
--    'v' is replaced with value
--    9 is any number (as defined by Lua tonumber)
--      only en digits are accepted
--    '<' can also be '<=' or '>' or '>='
-- In addition, the following form is supported:
--    LHS and RHS
-- where
--    LHS, RHS = any of above expressions.
local function compare(value, text)
local arithop, factor, compop, limit = text:match('^%s*v%s*([*]?)(.-)([<>]=?)(.*)$')
if arithop == nil then
error('Invalid default expression', 0)
elseif arithop == '*' then
factor = tonumber(factor)
if factor == nil then
error('Invalid default expression', 0)
end
value = value * factor
end
limit = tonumber(limit)
if limit == nil then
error('Invalid default expression', 0)
end
if compop == '<' then
return value < limit
elseif compop == '<=' then
return value <= limit
elseif compop == '>' then
return value > limit
elseif compop == '>=' then
return value >= limit
end
error('Invalid default expression', 0)  -- should not occur
end
local lhs, rhs = condition:match('^(.-%W)and(%W.*)')
if lhs == nil then
return compare(value, condition)
end
return compare(value, lhs) and compare(value, rhs)
end
 
local function get_default(value, unit_table)
-- Return true, s where s = name of unit's default output unit,
-- or return false, t where t is an error message table.
-- Some units have a default that depends on the input value
-- (the first value if a range of values is used).
-- If '!' is in the default, the first bang-delimited field is an
-- expression that uses 'v' to represent the input value.
-- Example: 'v < 120 ! small ! big ! suffix' (suffix is optional)
-- evaluates 'v < 120' as a boolean with result
-- 'smallsuffix' if (value < 120), or 'bigsuffix' otherwise.
-- Input must use en digits and '.' decimal mark.
local default = data_code.default_exceptions[unit_table.defkey or unit_table.symbol] or unit_table.default
if not default then
local per = unit_table.per
if per then
local function a_default(v, u)
local success, ucode = get_default(v, u)
if not success then
return '?'  -- an unlikely error has occurred; will cause lookup of default to fail
end
-- Attempt to use only the first unit if a combination or output multiple.
-- This is not bulletproof but should work for most cases.
-- Where it does not work, the convert will need to specify the wanted output unit.
local t = all_units[ucode]
if t then
local combo = t.combination
if combo then
-- For a multiple like ftin, the "first" unit (ft) is last in the combination.
local i = t.multiple and table_len(combo) or 1
ucode = combo[i]
end
else
-- Try for an automatically generated combination.
local item = ucode:match('^(.-)%+') or ucode:match('^(%S+)%s')
if all_units[item] then
return item
end
end
return ucode
end
local unit1, unit2 = per[1], per[2]
local def1 = (unit1 and a_default(value, unit1) or unit_table.vprefix or '')
local def2 = a_default(1, unit2)  -- 1 because per unit of denominator
return true, def1 .. '/' .. def2
end
return false, { 'cvt_no_default', unit_table.symbol }
end
if default:find('!', 1, true) == nil then
return true, default
end
local t = split(default, '!')
if #t == 3 or #t == 4 then
local success, result = pcall(evaluate_condition, value, t[1])
if success then
default = result and t[2] or t[3]
if #t == 4 then
default = default .. t[4]
end
return true, default
end
end
return false, { 'cvt_bad_default', unit_table.symbol }
end
 
local linked_pages  -- to record linked pages so will not link to the same page more than once
 
local function unlink(unit_table)
-- Forget that the given unit has previously been linked (if it has).
-- That is needed when processing a range of inputs or outputs when an id
-- for the first range value may have been evaluated, but only an id for
-- the last value is displayed, and that id may need to be linked.
linked_pages[unit_table.unitcode or unit_table] = nil
end
 
local function make_link(link, id, unit_table)
-- Return wikilink "[[link|id]]", possibly abbreviated as in examples:
--  [[Mile|mile]]  --> [[mile]]
--  [[Mile|miles]] --> [[mile]]s
-- However, just id is returned if:
-- * no link given (so caller does not need to check if a link was defined); or
-- * link has previously been used during the current convert (to avoid overlinking).
local link_key
if unit_table then
link_key = unit_table.unitcode or unit_table
else
link_key = link
end
if not link or link == '' or linked_pages[link_key] then
return id
end
linked_pages[link_key] = true
-- Following only works for language en, but it should be safe on other wikis,
-- and overhead of doing it generally does not seem worthwhile.
local l = link:sub(1, 1):lower() .. link:sub(2)
if link == id or l == id then
return '[[' .. id .. ']]'
elseif link .. 's' == id or l .. 's' == id then
return '[[' .. id:sub(1, -2) .. ']]s'
else
return '[[' .. link .. '|' .. id .. ']]'
end
end
 
local function variable_name(clean, unit_table)
-- For slwiki, a unit name depends on the value.
-- Parameter clean is the unsigned rounded value in en digits, as a string.
-- Value            Source    Example for "m"
-- integer 1:        name1    meter  (also is the name of the unit)
-- integer 2:        var{1}    metra
-- integer 3 and 4:  var{2}    metri
-- integer else:     var{3}    metrov (0 and 5 or more)
-- real/fraction:    var{4}    metra
-- var{i} means the i'th field in unit_table.varname if it exists and has
-- an i'th field, otherwise name2.
-- Fields are separated with "!" and are not empty.
-- A field for a unit using an SI prefix has the prefix name inserted,
-- replacing '#' if found, or before the field otherwise.
local vname
if clean == '1' then
vname = unit_table.name1
elseif unit_table.varname then
local i
if clean == '2' then
i = 1
elseif clean == '3' or clean == '4' then
i = 2
elseif clean:find('.', 1, true) then
i = 4
else
i = 3
end
if i > 1 and varname == 'pl' then
i = i - 1
end
vname = split(unit_table.varname, '!')[i]
end
if vname then
local si_name = rawget(unit_table, 'si_name') or ''
local pos = vname:find('#', 1, true)
if pos then
vname = vname:sub(1, pos - 1) .. si_name .. vname:sub(pos + 1)
else
vname = si_name .. vname
end
return vname
end
return unit_table.name2
end
 
local function linked_id(parms, unit_table, key_id, want_link, clean)
-- Return final unit id (symbol or name), optionally with a wikilink,
-- and update unit_table.sep if required.
-- key_id is one of: 'symbol', 'sym_us', 'name1', 'name1_us', 'name2', 'name2_us'.
local abbr_on = (key_id == 'symbol' or key_id == 'sym_us')
if abbr_on and want_link then
local symlink = rawget(unit_table, 'symlink')
if symlink then
return symlink  -- for exceptions that have the linked symbol built-in
end
end
local multiplier = rawget(unit_table, 'multiplier')
local per = unit_table.per
if per then
local paren1, paren2 = '', ''  -- possible parentheses around bottom unit
local unit1 = per[1]  -- top unit_table, or nil
local unit2 = per[2]  -- bottom unit_table
if abbr_on then
if not unit1 then
unit_table.sep = ''  -- no separator in "$2/acre"
end
if not want_link then
local symbol = unit_table.symbol_raw
if symbol then
return symbol  -- for exceptions that have the symbol built-in
end
end
if (unit2.symbol):find('⋅', 1, true) then
paren1, paren2 = '(', ')'
end
end
local key_id2  -- unit2 is always singular
if key_id == 'name2' then
key_id2 = 'name1'
elseif key_id == 'name2_us' then
key_id2 = 'name1_us'
else
key_id2 = key_id
end
local result
if abbr_on then
result = '/'
elseif omitsep then
result = per_word
elseif unit1 then
result = ' ' .. per_word .. ' '
else
result = per_word .. ' '
end
if want_link and unit_table.link then
if abbr_on or not varname then
result = (unit1 and linked_id(parms, unit1, key_id, false, clean) or '') .. result .. linked_id(parms, unit2, key_id2, false, '1')
else
result = (unit1 and variable_name(clean, unit1) or '') .. result .. variable_name('1', unit2)
end
if omit_separator(result) then
unit_table.sep = ''
end
return make_link(unit_table.link, result, unit_table)
end
if unit1 then
result = linked_id(parms, unit1, key_id, want_link, clean) .. result
if unit1.sep then
unit_table.sep = unit1.sep
end
elseif omitsep then
unit_table.sep = ''
end
return result .. paren1 .. linked_id(parms, unit2, key_id2, want_link, '1') .. paren2
end
if multiplier then
-- A multiplier (like "100" in "100km") forces the unit to be plural.
multiplier = from_en(multiplier)
if not omitsep then
multiplier = multiplier .. (abbr_on and '&nbsp;' or ' ')
end
if not abbr_on then
if key_id == 'name1' then
key_id = 'name2'
elseif key_id == 'name1_us' then
key_id = 'name2_us'
end
end
else
multiplier = ''
end
local id = unit_table.fixed_name or ((varname and not abbr_on) and variable_name(clean, unit_table) or unit_table[key_id])
if omit_separator(id) then
unit_table.sep = ''
end
if want_link then
local link = data_code.link_exceptions[unit_table.linkey or unit_table.symbol] or unit_table.link
if link then
local before = ''
local i = unit_table.customary
if i == 1 and parms.opt_sp_us then
i = 2  -- show "U.S." not "US"
end
if i == 3 and abbr_on then
i = 4  -- abbreviate "imperial" to "imp"
end
local customary = text_code.customary_units[i]
if customary then
-- LATER: This works for language en only, but it's esoteric so ignore for now.
local pertext
if id:sub(1, 1) == '/' then
-- Want unit "/USgal" to display as "/U.S. gal", not "U.S. /gal".
pertext = '/'
id = id:sub(2)
elseif id:sub(1, 4) == 'per ' then
-- Similarly want "per U.S. gallon", not "U.S. per gallon" (but in practice this is unlikely to be used).
pertext = 'per '
id = id:sub(5)
else
pertext = ''
end
-- Omit any "US"/"U.S."/"imp"/"imperial" from start of id since that will be inserted.
local removes = (i < 3) and { 'US&nbsp;', 'US ', 'U.S.&nbsp;', 'U.S. ' } or { 'imp&nbsp;', 'imp ', 'imperial ' }
for _, prefix in ipairs(removes) do
local plen = #prefix
if id:sub(1, plen) == prefix then
id = id:sub(plen + 1)
break
end
end
before = pertext .. make_link(customary.link, customary[1]) .. ' '
end
id = before .. make_link(link, id, unit_table)
end
end
return multiplier .. id
end
end


local function require_integer(value, missing, invalid)
local function make_id(parms, which, unit_table)
    -- If value is missing or not an integer, throw an error.
-- Return id, f where
    -- Return value as a number if valid.
--   id = unit name or symbol, possibly modified
    local number = require_number(value, missing, invalid)
--  f = true if id is a name, or false if id is a symbol
    if number ~= math.floor(number) then
-- using the value for index 'which', and for 'in' or 'out' (unit_table.inout).
        error(invalid:format(value))
-- Result is '' if no symbol/name is to be used.
    end
-- In addition, set unit_table.sep = ' ' or '&nbsp;' or ''
    return number
-- (the separator that caller will normally insert before the id).
if parms.opt_values then
unit_table.sep = ''
return ''
end
local inout = unit_table.inout
local info = unit_table.valinfo[which]
local abbr_org = parms.abbr_org
local adjectival = parms.opt_adjectival
local lk = parms.lk
local want_link = (lk == 'on' or lk == inout)
local usename = unit_table.usename
local singular = info.singular
local want_name
if usename then
want_name = true
else
if abbr_org == nil then
if parms.wantname then
want_name = true
end
if unit_table.usesymbol then
want_name = false
end
end
if want_name == nil then
local abbr = parms.abbr
if abbr == 'on' or abbr == inout or (abbr == 'mos' and inout == 'out') then
want_name = false
else
want_name = true
end
end
end
local key
if want_name then
if lk == nil and unit_table.builtin == 'hand' then
want_link = true
end
if parms.opt_use_nbsp then
unit_table.sep = '&nbsp;'
else
unit_table.sep = ' '
end
if parms.opt_singular then
local value
if inout == 'in' then
value = info.value
else
value = info.absvalue
end
if value then  -- some unusual units do not always set value field
value = abs(value)
singular = (0 < value and value < 1.0001)
end
end
if unit_table.engscale then
-- engscale: so "|1|e3kg" gives "1 thousand kilograms" (plural)
singular = false
end
key = (adjectival or singular) and 'name1' or 'name2'
if parms.opt_sp_us then
key = key .. '_us'
end
else
if unit_table.builtin == 'hand' then
if parms.opt_hand_hh then
unit_table.symbol = 'hh'  -- LATER: might want i18n applied to this
end
end
unit_table.sep = '&nbsp;'
key = parms.opt_sp_us and 'sym_us' or 'symbol'
end
return linked_id(parms, unit_table, key, want_link, info.clean), want_name
end
end


local function get_parms(pframe)
local function decorate_value(parms, unit_table, which, number_word)
    -- Return table with all arguments passed by template converted to
-- If needed, update unit_table so values will be shown with extra information.
    -- named arguments. The numeric args are used to add named args:
-- For consistency with the old template (but different from fmtpower),
    --   in_text, in_text2 (strings given for value, value2)
-- the style to display powers of 10 includes "display:none" to allow some
    --   value, in_unit, out_unit, value2, range, round_to
-- browsers to copy, for example, "10³" as "10^3", rather than as "103".
    -- (except for range, which is nil or a table, the named args that are
local info
    -- added here could be provided by the user of the template).
local engscale = unit_table.engscale
    local range_types = { -- text to separate input, output ranges
local prefix = unit_table.vprefix
        ['and'] = {' and ', ' and '},
if engscale or prefix then
        ['by'] = {' by ', ' by '},
info = unit_table.valinfo[which]
        ['to'] = {' to ', ' to '},
if info.decorated then
        ['-'] = {'–', '–'},
return -- do not redecorate if repeating convert
        ['to(-)'] = {' to ', '–'},
end
        ['x'] = {' by ', ' × '},
info.decorated = true
        ['+/-'] = {' ± ', ' ± '},
if engscale then
    }
local inout = unit_table.inout
    local args = {}                        -- arguments passed to template
local abbr = parms.abbr
    for k,v in pframe:argumentPairs() do
if (abbr == 'on' or abbr == inout) and not parms.number_word then
        args[k] = v
info.show = info.show ..
    end
'<span style="margin-left:0.2em">×<span style="margin-left:0.1em">' ..
    args.in_text = args[1]
from_en('10') ..
    args.value = require_number(args.in_text, 'Need value', 'Value "%s" must be a number')
'</span></span><s style="display:none">^</s><sup>' ..
    local in_unit = args[2]
from_en(tostring(engscale.exponent)) .. '</sup>'
    local i = 3
elseif number_word then
    local range = range_types[in_unit]
local number_id
    if range ~= nil then
local lk = parms.lk
        args.in_text2 = args[3]
if lk == 'on' or lk == inout then
        args.value2 = require_number(args.in_text2, 'Need second value', 'Second value "%s" must be a number')
number_id = make_link(engscale.link, engscale[1])
        in_unit = args[4]
else
        i = 5
number_id = engscale[1]
    end
end
    local out_unit = args[i]
-- WP:NUMERAL recommends "&nbsp;" in values like "12 million".
    local round_to = args[i+1]
info.show = info.show .. (parms.opt_adjectival and '-' or '&nbsp;') .. number_id
    if in_unit == nil then error('Need input unit') end
end
    args.in_unit = in_unit
end
    args.out_unit = out_unit
if prefix then
    args.range = range
info.show = prefix .. info.show
    args.round_to = round_to
end
    return args
end
end
end


local function converter(parms)
local function process_input(parms, in_current)
    -- If we can convert from given in to out unit, return the table
-- Processing required once per conversion.
    -- that handles the two given unit types.
-- Return block of text to represent input (value/unit).
    -- If no out_unit, change it to the default for the in_unit.
if parms.opt_output_only or parms.opt_output_number_only or parms.opt_output_unit_only then
    local t1, outdefault = units:lookup(parms.in_unit)
parms.joins = { '', '' }
    if parms.out_unit == nil then           -- need to catch empty string also?
return ''
        parms.out_unit = outdefault
end
    end
local first_unit
    local t2 = units:lookup(parms.out_unit)
local composite = in_current.composite  -- nil or table of units
    if t1 ~= t2 then
if composite then
        local msg = 'Cannot convert %s to %s'
first_unit = composite[1]
        error(msg:format(t1.NAME, t2.NAME))
else
    end
first_unit = in_current
    return t1
end
local id1, want_name = make_id(parms, 1, first_unit)
local sep = first_unit.sep  -- separator between value and unit, set by make_id
local preunit = parms.preunit1
if preunit then
sep = ''  -- any separator is included in preunit
else
preunit = ''
end
if parms.opt_input_unit_only then
parms.joins = { '', '' }
if composite then
local parts = { id1 }
for i, unit in ipairs(composite) do
if i > 1 then
table.insert(parts, (make_id(parms, 1, unit)))
end
end
id1 = table.concat(parts, ' ')
end
if want_name and parms.opt_adjectival then
return preunit .. hyphenated(id1)
end
return  preunit .. id1
end
if parms.opt_also_symbol and not composite and not parms.opt_flip then
local join1 = parms.joins[1]
if join1 == ' (' or join1 == ' [' then
parms.joins = { ' [' .. first_unit[parms.opt_sp_us and 'sym_us' or 'symbol'] .. ']' .. join1 , parms.joins[2] }
end
end
if in_current.builtin == 'mach' and first_unit.sep ~= '' then  -- '' means omitsep with non-enwiki name
local prefix = id1 .. '&nbsp;'
local range = parms.range
local valinfo = first_unit.valinfo
local result = prefix .. valinfo[1].show
if range then
-- For simplicity and because more not needed, handle one range item only.
local prefix2 = make_id(parms, 2, first_unit) .. '&nbsp;'
result = range_text(range[1], want_name, parms, result, prefix2 .. valinfo[2].show, 'in')
end
return preunit .. result
end
if composite then
-- Simplify: assume there is no range, and no decoration.
local mid = (not parms.opt_flip) and parms.mid or ''
local sep1 = '&nbsp;'
local sep2 = ' '
if parms.opt_adjectival and want_name then
sep1 = '-'
sep2 = '-'
end
if omitsep and sep == '' then
-- Testing the id of the most significant unit should be sufficient.
sep1 = ''
sep2 = ''
end
local parts = { first_unit.valinfo[1].show .. sep1 .. id1 }
for i, unit in ipairs(composite) do
if i > 1 then
table.insert(parts, unit.valinfo[1].show .. sep1 .. (make_id(parms, 1, unit)))
end
end
return table.concat(parts, sep2) .. mid
end
local add_unit = (parms.abbr == 'mos') or
parms[parms.opt_flip and 'out_range_x' or 'in_range_x'] or
(not want_name and parms.abbr_range_x)
local range = parms.range
if range and not add_unit then
unlink(first_unit)
end
local id = range and make_id(parms, range.n + 1, first_unit) or id1
local extra, was_hyphenated = hyphenated_maybe(parms, want_name, sep, id, 'in')
if was_hyphenated then
add_unit = false
end
local result
local valinfo = first_unit.valinfo
if range then
for i = 0, range.n do
local number_word
if i == range.n then
add_unit = false
number_word = true
end
decorate_value(parms, first_unit, i+1, number_word)
local show = valinfo[i+1].show
if add_unit then
show = show .. first_unit.sep .. (i == 0 and id1 or make_id(parms, i+1, first_unit))
end
if i == 0 then
result = show
else
result = range_text(range[i], want_name, parms, result, show, 'in')
end
end
else
decorate_value(parms, first_unit, 1, true)
result = valinfo[1].show
end
return result .. preunit .. extra
end
end


local function cvtround(invalue, parms, cvt)
local function process_one_output(parms, out_current)
    -- Convert given invalue using parms, cvt (return '' if invalue == nil).
-- Processing required for each output unit.
    -- Return rounded, formatted string for result, using rounding
-- Return block of text to represent output (value/unit).
    -- specified in parms.
local inout = out_current.inout  -- normally 'out' but can be 'in' for order=out
    -- This code combines convert/round because some rounding requires
local id1, want_name = make_id(parms, 1, out_current)
    -- knowledge of what we are converting.
local sep = out_current.sep  -- set by make_id
    -- TODO Fix!
local preunit = parms.preunit2
    local text = ''
if preunit then
    if invalue == nil then return text end
sep = ''  -- any separator is included in preunit
    local outvalue = cvt:convert(invalue, parms.in_unit, parms.out_unit)
else
    local round_to = parms.round_to
preunit = ''
    local sigfig = parms.sigfig
end
    local disp = parms.disp
if parms.opt_output_unit_only then
    if round_to then
if want_name and parms.opt_adjectival then
        -- Ignore sigfig, disp.
return preunit .. hyphenated(id1)
        round_to = require_integer(round_to, 'Need value', 'round_to "%s" must be an integer')
end
        if round_to >= 0 then
return preunit .. id1
            local fmt = '%.' .. string.format('%.0f', round_to) .. 'f'
end
            text = string.format(fmt, outvalue)
if out_current.builtin == 'mach' and out_current.sep ~= '' then  -- '' means omitsep with non-enwiki name
        else
local prefix = id1 .. '&nbsp;'
            factor = 10^(-round_to)
local range = parms.range
            zeroes = string.sub(tonumber(factor), 2)
local valinfo = out_current.valinfo
            text = string.format('%.0f', outvalue/factor) .. zeroes
local result = prefix .. valinfo[1].show
        end
if range then
    elseif sigfig then
-- For simplicity and because more not needed, handle one range item only.
        -- Ignore disp.
result = range_text(range[1], want_name, parms, result, prefix .. valinfo[2].show, inout)
        sigfig = require_integer(sigfig, 'Need value', 'sigfig "%s" must be an integer')
end
        if sigfig <= 0 then
return preunit .. result
            msg = 'sigfig "%s" must be positive'
end
            error(msg:format(parms.sigfig))
local add_unit = (parms[parms.opt_flip and 'in_range_x' or 'out_range_x'] or
        end
(not want_name and parms.abbr_range_x)) and
        local fmt = '%.' .. string.format('%.0f', sigfig) .. 'g'
not parms.opt_output_number_only
        text = string.format(fmt, outvalue)
local range = parms.range
    elseif disp == '5' then
if range and not add_unit then
        local negative = false
unlink(out_current)
        if outvalue < 0 then
end
            negative = true
local id = range and make_id(parms, range.n + 1, out_current) or id1
            outvalue = -outvalue
local extra, was_hyphenated = hyphenated_maybe(parms, want_name, sep, id, inout)
        end
if was_hyphenated then
        outvalue = math.floor((outvalue / 5) + 0.5) * 5
add_unit = false
        if negative then
end
            outvalue = -outvalue
local result
        end
local valinfo = out_current.valinfo
        text = string.format('%.0f', outvalue)
if range then
    else
for i = 0, range.n do
        -- Default rounding.
local number_word
        text = outvalue .. 'TODO: default rounding'
if i == range.n then
    end
add_unit = false
    return text
number_word = true
end
decorate_value(parms, out_current, i+1, number_word)
local show = valinfo[i+1].show
if add_unit then
show = show .. out_current.sep .. (i == 0 and id1 or make_id(parms, i+1, out_current))
end
if i == 0 then
result = show
else
result = range_text(range[i], want_name, parms, result, show, inout)
end
end
else
decorate_value(parms, out_current, 1, true)
result = valinfo[1].show
end
if parms.opt_output_number_only then
return result
end
return result .. preunit .. extra
end
end


local disp_single = {
local function make_output_single(parms, in_unit_table, out_unit_table)
    ['or'] = '%s %s or %s %s',
-- Return true, item where item = wikitext of the conversion result
    ['sqbr'] = '%s %s [%s %s]',
-- for a single output (which is not a combination or a multiple);
    ['comma'] = '%s %s, %s %s',
-- or return false, t where t is an error message table.
    ['b'] = '%s %s (%s %s)',
if parms.opt_order_out and in_unit_table.unitcode == out_unit_table.unitcode then
}
out_unit_table.valinfo = in_unit_table.valinfo
else
out_unit_table.valinfo = collection()
for _, v in ipairs(in_unit_table.valinfo) do
local success, info = cvtround(parms, v, in_unit_table, out_unit_table)
if not success then return false, info end
out_unit_table.valinfo:add(info)
end
end
return true, process_one_output(parms, out_unit_table)
end


local disp_double = {
local function make_output_multiple(parms, in_unit_table, out_unit_table)
    ['or'] = '%s%s%s %s or %s%s%s %s',
-- Return true, item where item = wikitext of the conversion result
    ['sqbr'] = '%s%s%s %s [%s%s%s %s]',
-- for an output which is a multiple (like 'ftin');
    ['comma'] = '%s%s%s %s, %s%s%s %s',
-- or return false, t where t is an error message table.
    ['b'] = '%s%s%s %s (%s%s%s %s)',
local inout = out_unit_table.inout  -- normally 'out' but can be 'in' for order=out
}
local multiple = out_unit_table.multiple  -- table of scaling factors (will not be nil)
local combos = out_unit_table.combination  -- table of unit tables (will not be nil)
local abbr = parms.abbr
local abbr_org = parms.abbr_org
local disp = parms.disp
local want_name = (abbr_org == nil and (disp == 'or' or disp == 'slash')) or
not (abbr == 'on' or abbr == inout or abbr == 'mos')
local want_link = (parms.lk == 'on' or parms.lk == inout)
local mid = parms.opt_flip and parms.mid or ''
local sep1 = '&nbsp;'
local sep2 = ' '
if parms.opt_adjectival and want_name then
sep1 = '-'
sep2 = '-'
end
local do_spell = parms.opt_spell_out
parms.opt_spell_out = nil  -- so the call to cvtround does not spell the value
local function make_result(info, isfirst)
local fmt, outvalue, sign
local results = {}
for i = 1, #combos do
local tfrac, thisvalue, strforce
local out_current = combos[i]
out_current.inout = inout
local scale = multiple[i]
if i == 1 then  -- least significant unit ('in' from 'ftin')
local decimals
out_current.frac = out_unit_table.frac
local success, outinfo = cvtround(parms, info, in_unit_table, out_current)
if not success then return false, outinfo end
if isfirst then
out_unit_table.valinfo = { outinfo }  -- in case output value of first least significant unit is needed
end
sign = outinfo.sign
tfrac = outinfo.fraction_table
if outinfo.is_scientific then
strforce = outinfo.show
decimals = ''
elseif tfrac then
decimals = ''
else
local show = outinfo.show  -- number as a string in local language
local p1, p2 = show:find(numdot, 1, true)
decimals = p1 and show:sub(p2 + 1) or ''  -- text after numdot, if any
end
fmt = '%.' .. ulen(decimals) .. 'f'  -- to reproduce precision
if decimals == '' then
if tfrac then
outvalue = floor(outinfo.raw_absvalue)  -- integer part only; fraction added later
else
outvalue = floor(outinfo.raw_absvalue + 0.5)  -- keep all integer digits of least significant unit
end
else
outvalue = outinfo.absvalue
end
end
if scale then
outvalue, thisvalue = divide(outvalue, scale)
else
thisvalue = outvalue
end
local id
if want_name then
if varname then
local clean
if strforce or tfrac then
clean = '.1' -- dummy value to force name for floating point
else
clean = format(fmt, thisvalue)
end
id = variable_name(clean, out_current)
else
local key = 'name2'
if parms.opt_adjectival then
key = 'name1'
elseif tfrac then
if thisvalue == 0 then
key = 'name1'
end
elseif parms.opt_singular then
if 0 < thisvalue and thisvalue < 1.0001 then
key = 'name1'
end
else
if thisvalue == 1 then
key = 'name1'
end
end
id = out_current[key]
end
else
id = out_current['symbol']
end
if i == 1 and omit_separator(id) then
-- Testing the id of the least significant unit should be sufficient.
sep1 = ''
sep2 = ''
end
if want_link then
local link = out_current.link
if link then
id = make_link(link, id, out_current)
end
end
local strval
local spell_inout = (i == #combos or outvalue == 0) and inout or '' -- trick so the last value processed (first displayed) has uppercase, if requested
if strforce and outvalue == 0 then
sign = ''  -- any sign is in strforce
strval = strforce  -- show small values in scientific notation; will only use least significant unit
elseif tfrac then
local wholestr = (thisvalue > 0) and tostring(thisvalue) or nil
strval = format_fraction(parms, spell_inout, false, wholestr, tfrac.numstr, tfrac.denstr, do_spell)
else
strval = (thisvalue == 0) and from_en('0') or with_separator(parms, format(fmt, thisvalue))
if do_spell then
strval = spell_number(parms, spell_inout, strval) or strval
end
end
table.insert(results, strval .. sep1 .. id)
if outvalue == 0 then
break
end
fmt = '%.0f'  -- only least significant unit can have a non-integral value
end
local reversed, count = {}, #results
for i = 1, count do
reversed[i] = results[count + 1 - i]
end
return true, sign .. table.concat(reversed, sep2)
end
local valinfo = in_unit_table.valinfo
local success, result = make_result(valinfo[1], true)
if not success then return false, result end
local range = parms.range
if range then
for i = 1, range.n do
local success, result2 = make_result(valinfo[i+1])
if not success then return false, result2 end
result = range_text(range[i], want_name, parms, result, result2, inout)
end
end
return true, result .. mid
end


local function process(parms)
local function process(parms, in_unit_table, out_unit_table)
    local cvt = converter(parms)
-- Return true, s, outunit where s = final wikitext result,
    local outext = cvtround(parms.value, parms, cvt)
-- or return false, t where t is an error message table.
    local outext2 = cvtround(parms.value2, parms, cvt)
linked_pages = {}
    local intext = parms.in_text
local success, bad_output
    local intext2 = parms.in_text2
local bad_input_mcode = in_unit_table.bad_mcode  -- nil if input unit is a valid convert unit
    local range = parms.range
local out_unit = parms.out_unit
    local disp = parms.disp
if out_unit == nil or out_unit == '' or type(out_unit) == 'function' then
    local wikitext
if bad_input_mcode or parms.opt_input_unit_only then
    if range == nil then
bad_output = ''
        wikitext = disp_single[disp] or disp_single['b']
else
        wikitext = wikitext:format(intext, parms.in_unit, outext, parms.out_unit)
local getdef = type(out_unit) == 'function' and out_unit or get_default
    else
success, out_unit = getdef(in_unit_table.valinfo[1].value, in_unit_table)
        wikitext = disp_double[disp] or disp_double['b']
parms.out_unit = out_unit
        wikitext = wikitext:format(intext, range[1], intext2, parms.in_unit, outext, range[2], outext2, parms.out_unit)
if not success then
    end
bad_output = out_unit
    return wikitext
end
end
end
if not bad_output and not out_unit_table then
success, out_unit_table = lookup(parms, out_unit, 'any_combination')
if success then
local mismatch = check_mismatch(in_unit_table, out_unit_table)
if mismatch then
bad_output = mismatch
end
else
bad_output = out_unit_table
end
end
local lhs, rhs
local flipped = parms.opt_flip and not bad_input_mcode
if bad_output then
rhs = (bad_output == '') and '' or message(parms, bad_output)
elseif parms.opt_input_unit_only then
rhs = ''
else
local combos  -- nil (for 'ft' or 'ftin'), or table of unit tables (for 'm ft')
if not out_unit_table.multiple then  -- nil/false ('ft' or 'm ft'), or table of factors ('ftin')
combos = out_unit_table.combination
end
local frac = parms.frac  -- nil or denominator of fraction for output values
if frac then
-- Apply fraction to the unit (if only one), or to non-SI units (if a combination),
-- except that if a precision is also specified, the fraction only applies to
-- the hand unit; that allows the following result:
-- {{convert|156|cm|in hand|1|frac=2}} → 156 centimetres (61.4 in; 15.1½ hands)
-- However, the following is handled elsewhere as a special case:
-- {{convert|156|cm|hand in|1|frac=2}} → 156 centimetres (15.1½ hands; 61½ in)
if combos then
local precision = parms.precision
for _, unit in ipairs(combos) do
if unit.builtin == 'hand' or (not precision and not unit.prefixes) then
unit.frac = frac
end
end
else
out_unit_table.frac = frac
end
end
local outputs = {}
local imax = combos and #combos or 1  -- 1 (single unit) or number of unit tables
if imax == 1 then
parms.opt_order_out = nil -- only useful with an output combination
end
if not flipped and not parms.opt_order_out then
-- Process left side first so any duplicate links (from lk=on) are suppressed
-- on right. Example: {{convert|28|e9pc|e9ly|abbr=off|lk=on}}
lhs = process_input(parms, in_unit_table)
end
for i = 1, imax do
local success, item
local out_current = combos and combos[i] or out_unit_table
out_current.inout = 'out'
if i == 1 then
if imax > 1 and out_current.builtin == 'hand' then
out_current.out_next = combos[2]  -- built-in hand can influence next unit in a combination
end
if parms.opt_order_out then
out_current.inout = 'in'
end
end
if out_current.multiple then
success, item = make_output_multiple(parms, in_unit_table, out_current)
else
success, item = make_output_single(parms, in_unit_table, out_current)
end
if not success then return false, item end
outputs[i] = item
end
if parms.opt_order_out then
lhs = outputs[1]
table.remove(outputs, 1)
end
local sep = parms.table_joins and parms.table_joins[2] or parms.join_between
rhs = table.concat(outputs, sep)
end
if flipped or not lhs then
local input = process_input(parms, in_unit_table)
if flipped then
lhs = rhs
rhs = input
else
lhs = input
end
end
if parms.join_before then
lhs = parms.join_before .. lhs
end
local wikitext
if bad_input_mcode then
if bad_input_mcode == '' then
wikitext = lhs
else
wikitext = lhs .. message(parms, bad_input_mcode)
end
elseif parms.table_joins then
wikitext = parms.table_joins[1] .. lhs .. parms.table_joins[2] .. rhs
else
wikitext = lhs .. parms.joins[1] .. rhs .. parms.joins[2]
end
if parms.warnings and not bad_input_mcode then
wikitext = wikitext .. parms.warnings
end
return true, get_styles(parms) .. wikitext, out_unit_table
end
end


-- Used by template {{convert2}}.
local function main_convert(frame)
-- We will have to keep old {{convert}} for a long time, and run
-- Do convert, and if needed, do it again with higher default precision.
-- {{convert2}} in parallel with {{convert}} while testing/developing.
local parms = { frame = frame } -- will hold template arguments, after translation
local p = {}
set_config(frame.args)
local success, result = get_parms(parms, frame:getParent().args)
if success then
if type(result) ~= 'table' then
return tostring(result)
end
local in_unit_table = result
local out_unit_table
for _ = 1, 2 do  -- use counter so cannot get stuck repeating convert
success, result, out_unit_table = process(parms, in_unit_table, out_unit_table)
if success and parms.do_convert_again then
parms.do_convert_again = false
else
break
end
end
end
-- If input=x gives a problem, the result should be just the user input
-- (if x is a property like P123 it has been replaced with '').
-- An unknown input unit would display the input and an error message
-- with success == true at this point.
-- Also, can have success == false with a message that outputs an empty string.
if parms.input_text then
if success and not parms.have_problem then
return result
end
local cat
if parms.tracking then
-- Add a tracking category using the given text as the category sort key.
-- There is currently only one type of tracking, but in principle multiple
-- items could be tracked, using different sort keys for convenience.
cat = wanted_category('tracking', parms.tracking)
end
return parms.input_text .. (cat or '')
end
return success and result or message(parms, result)
end


function p.convert(frame)
local function _unit(unitcode, options)
     local pframe = frame:getParent()
-- Helper function for Module:Val to look up a unit.
    local parms = get_parms(pframe)
-- Parameter unitcode must be a string to identify the wanted unit.
    return process(parms)
-- Parameter options must be nil or a table with optional fields:
--  value = number (for sort key; default value is 1)
--  scaled_top = nil for a normal unit, or a number for a unit which is
--                the denominator of a per unit (for sort key)
--  si = { 'symbol', 'link' }
--                (a table with two strings) to make an SI unit
--                that will be used for the look up
--  link = true if result should be [[linked]]
--  sort = 'on' or 'debug' if result should include a sort key in a
--                span element ('debug' makes the key visible)
--  name = true for the name of the unit instead of the symbol
--  us = true for the US spelling of the unit, if any
-- Return nil if unitcode is not a non-empty string.
-- Otherwise return a table with fields:
--  text = requested symbol or name of unit, optionally linked
--  scaled_value = input value adjusted by unit scale; used for sort key
--  sortspan = span element with sort key like that provided by {{ntsh}},
--     calculated from the result of converting value
--    to a base unit with scale 1.
--  unknown = true if the unitcode was not known
unitcode = strip(unitcode)
if unitcode == nil or unitcode == '' then
return nil
end
set_config({})
linked_pages = {}
options = options or {}
local parms = {
abbr = options.name and 'off' or 'on',
lk = options.link and 'on' or nil,
opt_sp_us = options.us and true or nil,
opt_ignore_error = true,  -- do not add pages using this function to 'what links here' for Module:Convert/extra
opt_sortable_on = options.sort == 'on' or options.sort == 'debug',
opt_sortable_debug = options.sort == 'debug',
}
if options.si then
-- Make a dummy table of units (just one unit) for lookup to use.
-- This makes lookup recognize any SI prefix in the unitcode.
local symbol = options.si[1] or '?'
parms.unittable = { [symbol] = {
_name1 = symbol,
_name2 = symbol,
_symbol = symbol,
utype = symbol,
scale = symbol == 'g' and 0.001 or 1,
prefixes = 1,
default = symbol,
link = options.si[2],
}}
end
local success, unit_table = lookup(parms, unitcode, 'no_combination')
if not success then
unit_table = setmetatable({
symbol = unitcode, name2 = unitcode, utype = unitcode,
scale = 1, default = '', defkey = '', linkey = '' }, unit_mt)
end
local value = tonumber(options.value) or 1
local clean = tostring(abs(value))
local info = {
value = value,
altvalue = value,
singular = (clean == '1'),
clean = clean,
show = clean,
}
unit_table.inout = 'in'
unit_table.valinfo = { info }
local sortspan, scaled_value
if options.sort then
sortspan, scaled_value = make_table_or_sort(parms, value, info, unit_table, options.scaled_top)
end
return {
text = make_id(parms, 1, unit_table),
sortspan = sortspan,
scaled_value = scaled_value,
unknown = not success and true or nil,
}
end
end


return p
return { convert = main_convert, _unit = _unit }

Latest revision as of 10:55, 6 September 2021

Documentation for this module may be created at Module:Convert/doc 

-- Convert a value from one unit of measurement to another.
-- Example: {{convert|123|lb|kg}} --> 123 pounds (56 kg)
-- See [[:en:Template:Convert/Transwiki guide]] if copying to another wiki.

local MINUS = '−'  -- Unicode U+2212 MINUS SIGN (UTF-8: e2 88 92)
local abs = math.abs
local floor = math.floor
local format = string.format
local log10 = math.log10
local ustring = mw.ustring
local ulen = ustring.len
local usub = ustring.sub

-- Configuration options to keep magic values in one location.
-- Conversion data and message text are defined in separate modules.
local config, maxsigfig
local numdot  -- must be '.' or ',' or a character which works in a regex
local numsep, numsep_remove, numsep_remove2
local data_code, all_units
local text_code
local varname        -- can be a code to use variable names that depend on value
local from_en_table  -- to translate an output string of en digits to local language
local to_en_table    -- to translate an input string of digits in local language to en
-- Use translation_table in convert/text to change the following.
local en_default           -- true uses lang=en unless convert has lang=local or local digits
local group_method = 3     -- code for how many digits are in a group
local per_word = 'per'     -- for units like "liters per kilometer"
local plural_suffix = 's'  -- only other useful value is probably '' to disable plural unit names
local omitsep              -- true to omit separator before local symbol/name

-- All units should be defined in the data module. However, to cater for quick changes
-- and experiments, any unknown unit is looked up in an extra data module, if it exists.
-- That module would be transcluded in only a small number of pages, so there should be
-- little server overhead from making changes, and changes should propagate quickly.
local extra_module  -- name of module with extra units
local extra_units   -- nil or table of extra units from extra_module

-- Some options in the invoking template can set variables used later in the module.
local currency_text  -- for a user-defined currency symbol: {{convert|12|$/ha|$=€}} (euro replaces dollar)

local function from_en(text)
	-- Input is a string representing a number in en digits with '.' decimal mark,
	-- without digit grouping (which is done just after calling this).
	-- Return the translation of the string with numdot and digits in local language.
	if numdot ~= '.' then
		text = text:gsub('%.', numdot)
	end
	if from_en_table then
		text = text:gsub('%d', from_en_table)
	end
	return text
end

local function to_en(text)
	-- Input is a string representing a number in the local language with
	-- an optional numdot decimal mark and numsep digit grouping.
	-- Return the translation of the string with '.' mark and en digits,
	-- and no separators (they have to be removed here to handle cases like
	-- numsep = '.' and numdot = ',' with input "1.234.567,8").
	if to_en_table then
		text = ustring.gsub(text, '%d', to_en_table)
	end
	if numsep_remove then
		text = text:gsub(numsep_remove, '')
	end
	if numsep_remove2 then
		text = text:gsub(numsep_remove2, '')
	end
	if numdot ~= '.' then
		text = text:gsub(numdot, '.')
	end
	return text
end

local function decimal_mark(text)
	-- Return ',' if text probably is using comma for decimal mark, or has no decimal mark.
	-- Return '.' if text probably is using dot for decimal mark.
	-- Otherwise return nothing (decimal mark not known).
	if not text:find('[.,]') then return ',' end
	text = text:gsub('^%-', ''):gsub('%+%d+/%d+$', ''):gsub('[Ee]%-?%d+$', '')
	local decimal =
		text:match('^0?([.,])%d+$') or
		text:match('%d([.,])%d?%d?$') or
		text:match('%d([.,])%d%d%d%d+$')
	if decimal then return decimal end
	if text:match('%.%d+%.') then return ',' end
	if text:match('%,%d+,') then return '.' end
end

local add_warning, with_separator  -- forward declarations
local function to_en_with_check(text, parms)
	-- Version of to_en() for a wiki using numdot = ',' and numsep = '.' to check
	-- text (an input number as a string) which might have been copied from enwiki.
	-- For example, in '1.234' the '.' could be a decimal mark or a group separator.
	-- From viwiki.
	if to_en_table then
		text = ustring.gsub(text, '%d', to_en_table)
	end
	if decimal_mark(text) == '.' then
		local original = text
		text = text:gsub(',', '')  -- for example, interpret "1,234.5" as an enwiki value
		if parms then
			add_warning(parms, 0, 'cvt_enwiki_num', original, with_separator({}, text))
		end
	else
		if numsep_remove then
			text = text:gsub(numsep_remove, '')
		end
		if numsep_remove2 then
			text = text:gsub(numsep_remove2, '')
		end
		if numdot ~= '.' then
			text = text:gsub(numdot, '.')
		end
	end
	return text
end

local function omit_separator(id)
	-- Return true if there should be no separator before id (a unit symbol or name).
	-- For zhwiki, there should be no separator if id uses local characters.
	-- The following kludge should be a sufficient test.
	if omitsep then
		if id:sub(1, 2) == '-{' then  -- for "-{...}-" content language variant
			return true
		end
		if id:byte() > 127 then
			local first = usub(id, 1, 1)
			if first ~= 'Å' and first ~= '°' and first ~= 'µ' then
				return true
			end
		end
	end
	return id:sub(1, 1) == '/'  -- no separator before units like "/ha"
end

local spell_module  -- name of module that can spell numbers
local speller       -- function from that module to handle spelling (set if needed)
local wikidata_module, wikidata_data_module  -- names of Wikidata modules
local wikidata_code, wikidata_data  -- exported tables from those modules (set if needed)

local function set_config(args)
	-- Set configuration options from template #invoke or defaults.
	config = args
	maxsigfig = config.maxsigfig or 14  -- maximum number of significant figures
	local data_module, text_module
	local sandbox = config.sandbox and ('/' .. config.sandbox) or ''
	data_module = "Module:Convert/data" .. sandbox
	text_module = "Module:Convert/text" .. sandbox
	extra_module = "Module:Convert/extra" .. sandbox
	wikidata_module = "Module:Convert/wikidata" .. sandbox
	wikidata_data_module = "Module:Convert/wikidata/data" .. sandbox
	spell_module = "Module:ConvertNumeric"
	data_code = mw.loadData(data_module)
	text_code = mw.loadData(text_module)
	all_units = data_code.all_units
	local translation = text_code.translation_table
	if translation then
		numdot = translation.numdot
		numsep = translation.numsep
		if numdot == ',' and numsep == '.' then
			if text_code.all_messages.cvt_enwiki_num then
				to_en = to_en_with_check
			end
		end
		if translation.group then
			group_method = translation.group
		end
		if translation.per_word then
			per_word = translation.per_word
		end
		if translation.plural_suffix then
			plural_suffix = translation.plural_suffix
		end
		varname = translation.varname
		from_en_table = translation.from_en
		local use_workaround = true
		if use_workaround then
			-- 2013-07-05 workaround bug by making a copy of the required table.
			-- mw.ustring.gsub fails with a table (to_en_table) as the replacement,
			-- if the table is accessed via mw.loadData.
			local source = translation.to_en
			if source then
				to_en_table = {}
				for k, v in pairs(source) do
					to_en_table[k] = v
				end
			end
		else
			to_en_table = translation.to_en
		end
		if translation.lang == 'en default' then
			en_default = true  -- for hiwiki
		end
		omitsep = translation.omitsep  -- for zhwiki
	end
	numdot = config.numdot or numdot or '.'  -- decimal mark before fractional digits
	numsep = config.numsep or numsep or ','  -- group separator for numbers
	-- numsep should be ',' or '.' or '' or '&nbsp;' or a Unicode character.
	-- numsep_remove must work in a regex to identify separators to be removed.
	if numsep ~= '' then
		numsep_remove = (numsep == '.') and '%.' or numsep
	end
	if numsep ~= ',' and numdot ~= ',' then
		numsep_remove2 = ','  -- so numbers copied from enwiki will work
	end
end

local function collection()
	-- Return a table to hold items.
	return {
		n = 0,
		add = function (self, item)
			self.n = self.n + 1
			self[self.n] = item
		end,
	}
end

local function divide(numerator, denominator)
	-- Return integers quotient, remainder resulting from dividing the two
	-- given numbers, which should be unsigned integers.
	local quotient, remainder = floor(numerator / denominator), numerator % denominator
	if not (0 <= remainder and remainder < denominator) then
		-- Floating point limits may need this, as in {{convert|160.02|Ym|ydftin}}.
		remainder = 0
	end
	return quotient, remainder
end

local function split(text, delimiter)
	-- Return a numbered table with fields from splitting text.
	-- The delimiter is used in a regex without escaping (for example, '.' would fail).
	-- Each field has any leading/trailing whitespace removed.
	local t = {}
	text = text .. delimiter  -- to get last item
	for item in text:gmatch('%s*(.-)%s*' .. delimiter) do
		table.insert(t, item)
	end
	return t
end

local function strip(text)
	-- If text is a string, return its content with no leading/trailing
	-- whitespace. Otherwise return nil (a nil argument gives a nil result).
	if type(text) == 'string' then
		return text:match("^%s*(.-)%s*$")
	end
end

local function table_len(t)
	-- Return length (<100) of a numbered table to replace #t which is
	-- documented to not work if t is accessed via mw.loadData().
	for i = 1, 100 do
		if t[i] == nil then
			return i - 1
		end
	end
end

local function wanted_category(catkey, catsort, want_warning)
	-- Return message category if it is wanted in current namespace,
	-- otherwise return ''.
	local cat
	local title = mw.title.getCurrentTitle()
	if title then
		local nsdefault = '0'  -- default namespace: '0' = article; '0,10' = article and template
		local namespace = title.namespace
		for _, v in ipairs(split(config.nscat or nsdefault, ',')) do
			if namespace == tonumber(v) then
				cat = text_code.all_categories[want_warning and 'warning' or catkey]
				if catsort and catsort ~= '' and cat:sub(-2) == ']]' then
					cat = cat:sub(1, -3) .. '|' .. mw.text.nowiki(usub(catsort, 1, 20)) .. ']]'
				end
				break
			end
		end
	end
	return cat or ''
end

local function message(parms, mcode, is_warning)
	-- Return wikitext for an error message, including category if specified
	-- for the message type.
	-- mcode = numbered table specifying the message:
	--    mcode[1] = 'cvt_xxx' (string used as a key to get message info)
	--    mcode[2] = 'parm1' (string to replace '$1' if any in message)
	--    mcode[3] = 'parm2' (string to replace '$2' if any in message)
	--    mcode[4] = 'parm3' (string to replace '$3' if any in message)
	local msg
	if type(mcode) == 'table' then
		if mcode[1] == 'cvt_no_output' then
			-- Some errors should cause convert to output an empty string,
			-- for example, for an optional field in an infobox.
			return ''
		end
		msg = text_code.all_messages[mcode[1]]
	end
	parms.have_problem = true
	local function subparm(fmt, ...)
		local rep = {}
		for i, v in ipairs({...}) do
			rep['$' .. i] = v
		end
		return (fmt:gsub('$%d+', rep))
	end
	if msg then
		local parts = {}
		local regex, replace = msg.regex, msg.replace
		for i = 1, 3 do
			local limit = 40
			local s = mcode[i + 1]
			if s then
				if regex and replace then
					s = s:gsub(regex, replace)
					limit = nil  -- allow long "should be" messages
				end
				-- Escape user input so it does not break the message.
				-- To avoid tags (like {{convert|1<math>23</math>|m}}) breaking
				-- the mouseover title, any strip marker starting with char(127) is
				-- replaced with '...' (text not needing i18n).
				local append
				local pos = s:find(string.char(127), 1, true)
				if pos then
					append = '...'
					s = s:sub(1, pos - 1)
				end
				if limit and ulen(s) > limit then
					s = usub(s, 1, limit)
					append = '...'
				end
				s = mw.text.nowiki(s) .. (append or '')
			else
				s = '?'
			end
			parts['$' .. i] = s
		end
		local function ispreview()
			-- Return true if a prominent message should be shown.
			if parms.test == 'preview' or parms.test == 'nopreview' then
				-- For testing, can preview a real message or simulate a preview
				-- when running automated tests.
				return parms.test == 'preview'
			end
			local success, revid = pcall(function ()
				return (parms.frame):preprocess('{{REVISIONID}}') end)
			return success and (revid == '')
		end
		local want_warning = is_warning and
			not config.warnings and  -- show unobtrusive warnings if config.warnings not configured
			not msg.nowarn           -- but use msg settings, not standard warning, if specified
		local title = string.gsub(msg[1] or 'Missing message', '$%d+', parts)
		local text = want_warning and '*' or msg[2] or 'Missing message'
		local cat = wanted_category(msg[3], mcode[2], want_warning)
		local anchor = msg[4] or ''
		local fmtkey = ispreview() and 'cvt_format_preview' or
			(want_warning and 'cvt_format2' or msg.format or 'cvt_format')
		local fmt = text_code.all_messages[fmtkey] or 'convert: bug'
		return subparm(fmt, title:gsub('"', '&quot;'), text, cat, anchor)
	end
	return 'Convert internal error: unknown message'
end

function add_warning(parms, level, key, text1, text2)  -- for forward declaration above
	-- If enabled, add a warning that will be displayed after the convert result.
	-- A higher level is more verbose: more kinds of warnings are displayed.
	-- To reduce output noise, only the first warning is displayed.
	if level <= (tonumber(config.warnings) or 1) then
		if parms.warnings == nil then
			parms.warnings = message(parms, { key, text1, text2 }, true)
		end
	end
end

local function spell_number(parms, inout, number, numerator, denominator)
	-- Return result of spelling (number, numerator, denominator), or
	-- return nil if spelling is not available or not supported for given text.
	-- Examples (each value must be a string or nil):
	--   number  numerator  denominator  output
	--   ------  ---------  -----------  -------------------
	--   "1.23"    nil        nil        one point two three
	--    "1"      "2"        "3"        one and two thirds
	--    nil      "2"        "3"        two thirds
	if not speller then
		local function get_speller(module)
			return require(module).spell_number
		end
		local success
		success, speller = pcall(get_speller, spell_module)
		if not success or type(speller) ~= 'function' then
			add_warning(parms, 1, 'cvt_no_spell', 'spell')
			return nil
		end
	end
	local case
	if parms.spell_upper == inout then
		case = true
		parms.spell_upper = nil  -- only uppercase first word in a multiple unit
	end
	local sp = not parms.opt_sp_us
	local adj = parms.opt_adjectival
	return speller(number, numerator, denominator, case, sp, adj)
end

------------------------------------------------------------------------
-- BEGIN: Code required only for built-in units.
-- LATER: If need much more code, move to another module to simplify this module.
local function speed_of_sound(altitude)
	-- This is for the Mach built-in unit of speed.
	-- Return speed of sound in metres per second at given altitude in feet.
	-- If no altitude given, use default (zero altitude = sea level).
	-- Table gives speed of sound in miles per hour at various altitudes:
	--   altitude = -17,499 to 302,499 feet
	-- mach_table[a + 4] = s where
	--   a = (altitude / 5000) rounded to nearest integer (-3 to 60)
	--   s = speed of sound (mph) at that altitude
	-- LATER: Should calculate result from an interpolation between the next
	-- lower and higher altitudes in table, rather than rounding to nearest.
	-- From: http://www.aerospaceweb.org/question/atmosphere/q0112.shtml
	local mach_table = {                                                       -- a =
		799.5, 787.0, 774.2, 761.207051,                                       -- -3 to  0
		748.0, 734.6, 721.0, 707.0, 692.8, 678.3, 663.5, 660.1, 660.1, 660.1,  --  1 to 10
		660.1, 660.1, 660.1, 662.0, 664.3, 666.5, 668.9, 671.1, 673.4, 675.6,  -- 11 to 20
		677.9, 683.7, 689.9, 696.0, 702.1, 708.1, 714.0, 719.9, 725.8, 731.6,  -- 21 to 30
		737.3, 737.7, 737.7, 736.2, 730.5, 724.6, 718.8, 712.9, 707.0, 701.1,  -- 31 to 40
		695.0, 688.9, 682.8, 676.6, 670.4, 664.1, 657.8, 652.9, 648.3, 643.7,  -- 41 to 50
		639.1, 634.4, 629.6, 624.8, 620.0, 615.2, 613.2, 613.2, 613.2, 613.5,  -- 51 to 60
	}
	altitude = altitude or 0
	local a = (altitude < 0) and -altitude or altitude
	a = floor(a / 5000 + 0.5)
	if altitude < 0 then
		a = -a
	end
	if a < -3 then
		a = -3
	elseif a > 60 then
		a = 60
	end
	return mach_table[a + 4] * 0.44704  -- mph converted to m/s
end
-- END: Code required only for built-in units.
------------------------------------------------------------------------

local function add_style(parms, class)
	-- Add selected template style to parms if not already present.
	parms.templatestyles = parms.templatestyles or {}
	if not parms.templatestyles[class] then
		parms.templatestyles[class] = parms.frame:extensionTag({
			name = 'templatestyles', args = { src = text_code.titles[class] }
		})
	end
end

local function get_styles(parms)
	-- Return string of required template styles, empty if none.
	if parms.templatestyles then
		local t = {}
		for _, v in pairs(parms.templatestyles) do
			table.insert(t, v)
		end
		return table.concat(t)
	end
	return ''
end

local function get_range(word)
	-- Return a range (string or table) corresponding to word (like "to"),
	-- or return nil if not a range word.
	local ranges = text_code.ranges
	return ranges.types[word] or ranges.types[ranges.aliases[word]]
end

local function check_mismatch(unit1, unit2)
	-- If unit1 cannot be converted to unit2, return an error message table.
	-- This allows conversion between units of the same type, and between
	-- Nm (normally torque) and ftlb (energy), as in gun-related articles.
	-- This works because Nm is the base unit (scale = 1) for both the
	-- primary type (torque), and the alternate type (energy, where Nm = J).
	-- A match occurs if the primary types are the same, or if unit1 matches
	-- the alternate type of unit2, and vice versa. That provides a whitelist
	-- of which conversions are permitted between normally incompatible types.
	if unit1.utype == unit2.utype or
		(unit1.utype == unit2.alttype and unit1.alttype == unit2.utype) then
		return nil
	end
	return { 'cvt_mismatch', unit1.utype, unit2.utype }
end

local function override_from(out_table, in_table, fields)
	-- Copy the specified fields from in_table to out_table, but do not
	-- copy nil fields (keep any corresponding field in out_table).
	for _, field in ipairs(fields) do
		if in_table[field] then
			out_table[field] = in_table[field]
		end
	end
end

local function shallow_copy(t)
	-- Return a shallow copy of table t.
	-- Do not need the features and overhead of the Scribunto mw.clone().
	local result = {}
	for k, v in pairs(t) do
		result[k] = v
	end
	return result
end

local unit_mt = {
	-- Metatable to get missing values for a unit that does not accept SI prefixes.
	-- Warning: The boolean value 'false' is returned for any missing field
	-- so __index is not called twice for the same field in a given unit.
	__index = function (self, key)
		local value
		if key == 'name1' or key == 'sym_us' then
			value = self.symbol
		elseif key == 'name2' then
			value = self.name1 .. plural_suffix
		elseif key == 'name1_us' then
			value = self.name1
			if not rawget(self, 'name2_us') then
				-- If name1_us is 'foot', do not make name2_us by appending plural_suffix.
				self.name2_us = self.name2
			end
		elseif key == 'name2_us' then
			local raw1_us = rawget(self, 'name1_us')
			if raw1_us then
				value = raw1_us .. plural_suffix
			else
				value = self.name2
			end
		elseif key == 'link' then
			value = self.name1
		else
			value = false
		end
		rawset(self, key, value)
		return value
	end
}

local function prefixed_name(unit, name, index)
	-- Return unit name with SI prefix inserted at correct position.
	-- index = 1 (name1), 2 (name2), 3 (name1_us), 4 (name2_us).
	-- The position is a byte (not character) index, so use Lua's sub().
	local pos = rawget(unit, 'prefix_position')
	if type(pos) == 'string' then
		pos = tonumber(split(pos, ',')[index])
	end
	if pos then
		return name:sub(1, pos - 1) .. unit.si_name .. name:sub(pos)
	end
	return unit.si_name .. name
end

local unit_prefixed_mt = {
	-- Metatable to get missing values for a unit that accepts SI prefixes.
	-- Before use, fields si_name, si_prefix must be defined.
	-- The unit must define _symbol, _name1 and
	-- may define _sym_us, _name1_us, _name2_us
	-- (_sym_us, _name2_us may be defined for a language using sp=us
	-- to refer to a variant unrelated to U.S. units).
	__index = function (self, key)
		local value
		if key == 'symbol' then
			value = self.si_prefix .. self._symbol
		elseif key == 'sym_us' then
			value = rawget(self, '_sym_us')
			if value then
				value = self.si_prefix .. value
			else
				value = self.symbol
			end
		elseif key == 'name1' then
			value = prefixed_name(self, self._name1, 1)
		elseif key == 'name2' then
			value = rawget(self, '_name2')
			if value then
				value = prefixed_name(self, value, 2)
			else
				value = self.name1 .. plural_suffix
			end
		elseif key == 'name1_us' then
			value = rawget(self, '_name1_us')
			if value then
				value = prefixed_name(self, value, 3)
			else
				value = self.name1
			end
		elseif key == 'name2_us' then
			value = rawget(self, '_name2_us')
			if value then
				value = prefixed_name(self, value, 4)
			elseif rawget(self, '_name1_us') then
				value = self.name1_us .. plural_suffix
			else
				value = self.name2
			end
		elseif key == 'link' then
			value = self.name1
		else
			value = false
		end
		rawset(self, key, value)
		return value
	end
}

local unit_per_mt = {
	-- Metatable to get values for a per unit of form "x/y".
	-- This is never called to determine a unit name or link because per units
	-- are handled as a special case.
	-- Similarly, the default output is handled elsewhere, and for a symbol
	-- this is only called from get_default() for default_exceptions.
	__index = function (self, key)
		local value
		if key == 'symbol' then
			local per = self.per
			local unit1, unit2 = per[1], per[2]
			if unit1 then
				value = unit1[key] .. '/' .. unit2[key]
			else
				value = '/' .. unit2[key]
			end
		elseif key == 'sym_us' then
			value = self.symbol
		elseif key == 'scale' then
			local per = self.per
			local unit1, unit2 = per[1], per[2]
			value = (unit1 and unit1.scale or 1) * self.scalemultiplier / unit2.scale
		else
			value = false
		end
		rawset(self, key, value)
		return value
	end
}

local function make_per(unitcode, unit_table, ulookup)
	-- Return true, t where t is a per unit with unit codes expanded to unit tables,
	-- or return false, t where t is an error message table.
	local result = {
		unitcode = unitcode,
		utype = unit_table.utype,
		per = {}
	}
	override_from(result, unit_table, { 'invert', 'iscomplex', 'default', 'link', 'symbol', 'symlink' })
	result.symbol_raw = (result.symbol or false)  -- to distinguish between a defined exception and a metatable calculation
	local prefix
	for i, v in ipairs(unit_table.per) do
		if i == 1 and v == '' then
			-- First unit symbol can be empty; that gives a nil first unit table.
		elseif i == 1 and text_code.currency[v] then
			prefix = currency_text or v
		else
			local success, t = ulookup(v)
			if not success then return false, t end
			result.per[i] = t
		end
	end
	local multiplier = unit_table.multiplier
	if not result.utype then
		-- Creating an automatic per unit.
		local unit1 = result.per[1]
		local utype = (unit1 and unit1.utype or prefix or '') .. '/' .. result.per[2].utype
		local t = data_code.per_unit_fixups[utype]
		if t then
			if type(t) == 'table' then
				utype = t.utype or utype
				result.link = result.link or t.link
				multiplier = multiplier or t.multiplier
			else
				utype = t
			end
		end
		result.utype = utype
	end
	result.scalemultiplier = multiplier or 1
	result.vprefix = prefix or false  -- set to non-nil to avoid calling __index
	return true, setmetatable(result, unit_per_mt)
end

local function lookup(parms, unitcode, what, utable, fails, depth)
	-- Return true, t where t is a copy of the unit's converter table,
	-- or return false, t where t is an error message table.
	-- Parameter 'what' determines whether combination units are accepted:
	--   'no_combination'  : single unit only
	--   'any_combination' : single unit or combination or output multiple
	--   'only_multiple'   : single unit or output multiple only
	-- Parameter unitcode is a symbol (like 'g'), with an optional SI prefix (like 'kg').
	-- If, for example, 'kg' is in this table, that entry is used;
	-- otherwise the prefix ('k') is applied to the base unit ('g').
	-- If unitcode is a known combination code (and if allowed by what),
	-- a table of output multiple unit tables is included in the result.
	-- For compatibility with the old template, an underscore in a unitcode is
	-- replaced with a space so usage like {{convert|350|board_feet}} works.
	-- Wikignomes may also put two spaces or "&nbsp;" in combinations, so
	-- replace underscore, "&nbsp;", and multiple spaces with a single space.
	utable = utable or parms.unittable or all_units
	fails = fails or {}
	depth = depth and depth + 1 or 1
	if depth > 9 then
		-- There are ways to mistakenly define units which result in infinite
		-- recursion when lookup() is called. That gives a long delay and very
		-- confusing error messages, so the depth parameter is used as a guard.
		return false, { 'cvt_lookup', unitcode }
	end
	if unitcode == nil or unitcode == '' then
		return false, { 'cvt_no_unit' }
	end
	unitcode = unitcode:gsub('_', ' '):gsub('&nbsp;', ' '):gsub('  +', ' ')
	local function call_make_per(t)
		return make_per(unitcode, t,
			function (ucode) return lookup(parms, ucode, 'no_combination', utable, fails, depth) end
		)
	end
	local t = utable[unitcode]
	if t then
		if t.shouldbe then
			return false, { 'cvt_should_be', t.shouldbe }
		end
		if t.sp_us then
			parms.opt_sp_us = true
		end
		local target = t.target  -- nil, or unitcode is an alias for this target
		if target then
			local success, result = lookup(parms, target, what, utable, fails, depth)
			if not success then return false, result end
			override_from(result, t, { 'customary', 'default', 'link', 'symbol', 'symlink' })
			local multiplier = t.multiplier
			if multiplier then
				result.multiplier = tostring(multiplier)
				result.scale = result.scale * multiplier
			end
			return true, result
		end
		if t.per then
			return call_make_per(t)
		end
		local combo = t.combination  -- nil or a table of unitcodes
		if combo then
			local multiple = t.multiple
			if what == 'no_combination' or (what == 'only_multiple' and not multiple) then
				return false, { 'cvt_bad_unit', unitcode }
			end
			-- Recursively create a combination table containing the
			-- converter table of each unitcode.
			local result = { utype = t.utype, multiple = multiple, combination = {} }
			local cvt = result.combination
			for i, v in ipairs(combo) do
				local success, t = lookup(parms, v, multiple and 'no_combination' or 'only_multiple', utable, fails, depth)
				if not success then return false, t end
				cvt[i] = t
			end
			return true, result
		end
		local result = shallow_copy(t)
		result.unitcode = unitcode
		if result.prefixes then
			result.si_name = ''
			result.si_prefix = ''
			return true, setmetatable(result, unit_prefixed_mt)
		end
		return true, setmetatable(result, unit_mt)
	end
	local SIprefixes = text_code.SIprefixes
	for plen = SIprefixes[1] or 2, 1, -1 do
		-- Look for an SI prefix; should never occur with an alias.
		-- Check for longer prefix first ('dam' is decametre).
		-- SIprefixes[1] = prefix maximum #characters (as seen by mw.ustring.sub).
		local prefix = usub(unitcode, 1, plen)
		local si = SIprefixes[prefix]
		if si then
			local t = utable[usub(unitcode, plen+1)]
			if t and t.prefixes then
				local result = shallow_copy(t)
				result.unitcode = unitcode
				result.si_name = parms.opt_sp_us and si.name_us or si.name
				result.si_prefix = si.prefix or prefix
				result.scale = t.scale * 10 ^ (si.exponent * t.prefixes)
				return true, setmetatable(result, unit_prefixed_mt)
			end
		end
	end
	-- Accept user-defined combinations like "acre+m2+ha" or "acre m2 ha" for output.
	-- If '+' is used, each unit code can include a space, and any error is fatal.
	-- If ' ' is used and if each space-separated word is a unit code, it is a combo,
	-- but errors are not fatal so the unit code can be looked up as an extra unit.
	local err_is_fatal
	local combo = collection()
	if unitcode:find('+', 1, true) then
		err_is_fatal = true
		for item in (unitcode .. '+'):gmatch('%s*(.-)%s*%+') do
			if item ~= '' then
				combo:add(item)
			end
		end
	elseif unitcode:find('%s') then
		for item in unitcode:gmatch('%S+') do
			combo:add(item)
		end
	end
	if combo.n > 1 then
		local function lookup_combo()
			if what == 'no_combination' or what == 'only_multiple' then
				return false, { 'cvt_bad_unit', unitcode }
			end
			local result = { combination = {} }
			local cvt = result.combination
			for i, v in ipairs(combo) do
				local success, t = lookup(parms, v, 'only_multiple', utable, fails, depth)
				if not success then return false, t end
				if i == 1 then
					result.utype = t.utype
				else
					local mismatch = check_mismatch(result, t)
					if mismatch then
						return false, mismatch
					end
				end
				cvt[i] = t
			end
			return true, result
		end
		local success, result = lookup_combo()
		if success or err_is_fatal then
			return success, result
		end
	end
	-- Accept any unit with an engineering notation prefix like "e6cuft"
	-- (million cubic feet), but not chained prefixes like "e3e6cuft",
	-- and not if the unit is a combination or multiple,
	-- and not if the unit has an offset or is a built-in.
	-- Only en digits are accepted.
	local exponent, baseunit = unitcode:match('^e(%d+)(.*)')
	if exponent then
		local engscale = text_code.eng_scales[exponent]
		if engscale then
			local success, result = lookup(parms, baseunit, 'no_combination', utable, fails, depth)
			if success and not (result.offset or result.builtin or result.engscale) then
				result.unitcode = unitcode  -- 'e6cuft' not 'cuft'
				result.defkey = unitcode  -- key to lookup default exception
				result.engscale = engscale
				result.scale = result.scale * 10 ^ tonumber(exponent)
				return true, result
			end
		end
	end
	-- Look for x/y; split on right-most slash to get scale correct (x/y/z is x/y per z).
	local top, bottom = unitcode:match('^(.-)/([^/]+)$')
	if top and not unitcode:find('e%d') then
		-- If valid, create an automatic per unit for an "x/y" unit code.
		-- The unitcode must not include extraneous spaces.
		-- Engineering notation (apart from at start and which has been stripped before here),
		-- is not supported so do not make a per unit if find text like 'e3' in unitcode.
		local success, result = call_make_per({ per = {top, bottom} })
		if success then
			return true, result
		end
	end
	if not parms.opt_ignore_error and not get_range(unitcode) then
		-- Want the "what links here" list for the extra_module to show only cases
		-- where an extra unit is used, so do not require it if invoked from {{val}}
		-- or if looking up a range word which cannot be a unit.
		if not extra_units then
			local success, extra = pcall(function () return require(extra_module).extra_units end)
			if success and type(extra) == 'table' then
				extra_units = extra
			end
		end
		if extra_units then
			-- A unit in one data table might refer to a unit in the other table, so
			-- switch between them, relying on fails or depth to terminate loops.
			if not fails[unitcode] then
				fails[unitcode] = true
				local other = (utable == all_units) and extra_units or all_units
				local success, result = lookup(parms, unitcode, what, other, fails, depth)
				if success then
					return true, result
				end
			end
		end
	end
	if to_en_table then
		-- At fawiki it is common to translate all digits so a unit like "km2" becomes "km۲".
		local en_code = ustring.gsub(unitcode, '%d', to_en_table)
		if en_code ~= unitcode then
			return lookup(parms, en_code, what, utable, fails, depth)
		end
	end
	return false, { 'cvt_unknown', unitcode }
end

local function valid_number(num)
	-- Return true if num is a valid number.
	-- In Scribunto (different from some standard Lua), when expressed as a string,
	-- overflow or other problems are indicated with text like "inf" or "nan"
	-- which are regarded as invalid here (each contains "n").
	if type(num) == 'number' and tostring(num):find('n', 1, true) == nil then
		return true
	end
end

local function hyphenated(name, parts)
	-- Return a hyphenated form of given name (for adjectival usage).
	-- The name may be linked and the target of the link must not be changed.
	-- Hypothetical examples:
	--   [[long ton|ton]]         →  [[long ton|ton]]          (no change)
	--   [[tonne|long ton]]       →  [[tonne|long-ton]]
	--   [[metric ton|long ton]]  →  [[metric ton|long-ton]]
	--   [[long ton]]             →  [[long ton|long-ton]]
	-- Input can also have multiple links in a single name like:
	--   [[United States customary units|U.S.]] [[US gallon|gallon]]
	--   [[mile]]s per [[United States customary units|U.S.]] [[quart]]
	--   [[long ton]]s per [[short ton]]
	-- Assume that links cannot be nested (never like "[[abc[[def]]ghi]]").
	-- 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 (left-to-right, 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 style="white-space: nowrap">'
		local gap = '<span style="margin-left: 0.25em">'
		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 style="margin:0 .15em 0 .25em">×</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 {{frac}} (fraction slash).
		'<span class="frac" role="math">{SIGN}<span class="num">{NUM}</span>&frasl;<span class="den">{DEN}</span></span>',  -- 1/2
		'<span class="frac" role="math">{SIGN}{WHOLE}<span class="sr-only">+</span><span class="num">{NUM}</span>&frasl;<span class="den">{DEN}</span></span>',  -- 1+2/3
		style = 'frac',
	},
	{ -- Like {{sfrac}} (stacked fraction, that is, horizontal bar).
		'<span class="sfrac tion" role="math">{SIGN}<span class="num">{NUM}</span><span class="sr-only">/</span><span class="den">{DEN}</span></span>',  -- 1//2
		'<span class="sfrac" role="math">{SIGN}{WHOLE}<span class="sr-only">+</span><span class="tion"><span class="num">{NUM}</span><span class="sr-only">/</span><span class="den">{DEN}</span></span></span>',  -- 1+2//3
		style = 'sfrac',
	},
}

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),
		DEN = from_en(denstr),
	}
	wikitext = fracfmt[style][wholestr and 2 or 1]:gsub('{(%u+)}', substitute)
	if do_spell then
		if negative then
			if wholestr then
				wholestr = '-' .. wholestr
			else
				numstr = '-' .. numstr
			end
		end
		local s = spell_number(parms, inout, wholestr, numstr, denstr)
		if s then
			return s
		end
	end
	add_style(parms, fracfmt[style].style)
	return wikitext
end

local function format_number(parms, show, exponent, isnegative)
	-- Parameter show is a string or a table containing strings.
	-- Each string is a formatted number in en digits and optional '.' decimal mark.
	-- A table represents a fraction: integer, numerator, denominator;
	-- if a table is given, exponent must be nil.
	-- Return t where t is a table with fields:
	--   show = wikitext formatted to display implied value
	--          (digits in local language)
	--   is_scientific = true if show uses scientific notation
	--   clean = unformatted show (possibly adjusted and with inserted '.')
	--          (en digits)
	--   sign = '' or MINUS
	--   exponent = exponent (possibly adjusted)
	-- The clean and exponent fields can be used to calculate the
	-- rounded absolute value, if needed.
	--
	-- The value implied by the arguments is found from:
	--   exponent is nil; and
	--   show is a string of digits (no sign), with an optional dot;
	--   show = '123.4' is value 123.4, '1234' is value 1234.0;
	-- or:
	--   exponent is an integer indicating where dot should be;
	--   show is a string of digits (no sign and no dot);
	--   there is an implied dot before show;
	--   show does not start with '0';
	--   show = '1234', exponent = 3 is value 0.1234*10^3 = 123.4.
	--
	-- The formatted result:
	-- * Is for an output value and is spelled if wanted and possible.
	-- * Includes a Unicode minus if isnegative and not spelled.
	-- * Uses a custom decimal mark, if wanted.
	-- * Has digits grouped where necessary, if wanted.
	-- * Uses scientific notation if requested, or for very small or large values
	--   (which forces result to not be spelled).
	-- * Has no more than maxsigfig significant digits
	--   (same as old template and {{#expr}}).
	local xhi, xlo  -- these control when scientific notation (exponent) is used
	if parms.opt_scientific then
		xhi, xlo = 4, 2  -- default for output if input uses e-notation
	elseif parms.opt_scientific_always then
		xhi, xlo = 0, 0  -- always use scientific notation (experimental)
	else
		xhi, xlo = 10, 4  -- default
	end
	local sign = isnegative and MINUS or ''
	local maxlen = maxsigfig
	local tfrac
	if type(show) == 'table' then
		tfrac = show
		show = tfrac.wholestr
		assert(exponent == nil, 'Bug: exponent given with fraction')
	end
	if not tfrac and not exponent then
		local integer, dot, decimals = show:match('^(%d*)(%.?)(.*)')
		if integer == '0' or integer == '' then
			local zeros, figs = decimals:match('^(0*)([^0]?.*)')
			if #figs == 0 then
				if #zeros > maxlen then
					show = '0.' .. zeros:sub(1, maxlen)
				end
			elseif #zeros >= xlo then
				show = figs
				exponent = -#zeros
			elseif #figs > maxlen then
				show = '0.' .. zeros .. figs:sub(1, maxlen)
			end
		elseif #integer >= xhi then
			show = integer .. decimals
			exponent = #integer
		else
			maxlen = maxlen + #dot
			if #show > maxlen then
				show = show:sub(1, maxlen)
			end
		end
	end
	if exponent then
		local function zeros(n)
			return string.rep('0', n)
		end
		if #show > maxlen then
			show = show:sub(1, maxlen)
		end
		if exponent > xhi or exponent <= -xlo or (exponent == xhi and show ~= '1' .. zeros(xhi - 1)) then
			-- When xhi, xlo = 10, 4 (the default), scientific notation is used if the
			-- rounded value satisfies: value >= 1e9 or value < 1e-4 (1e9 = 0.1e10),
			-- except if show is '1000000000' (1e9), for example:
			-- {{convert|1000000000|m|m|sigfig=10}} → 1,000,000,000 metres (1,000,000,000 m)
			local significand
			if #show > 1 then
				significand = show:sub(1, 1) .. '.' .. show:sub(2)
			else
				significand = show
			end
			return {
				clean = '.' .. show,
				exponent = exponent,
				sign = sign,
				show = sign .. with_exponent(parms, significand, exponent-1),
				is_scientific = true,
			}
		end
		if exponent >= #show then
			show = show .. zeros(exponent - #show)  -- result has no dot
		elseif exponent <= 0 then
			show = '0.' .. zeros(-exponent) .. show
		else
			show = show:sub(1, exponent) .. '.' .. show:sub(exponent+1)
		end
	end
	local formatted_show
	if tfrac then
		show = tostring(tfrac.value)  -- to set clean in returned table
		formatted_show = format_fraction(parms, 'out', isnegative, tfrac.wholestr, tfrac.numstr, tfrac.denstr, parms.opt_spell_out)
	else
		if isnegative and show:match('^0.?0*$') then
			sign = ''  -- don't show minus if result is negative but rounds to zero
		end
		formatted_show = sign .. with_separator(parms, show)
		if parms.opt_spell_out then
			formatted_show = spell_number(parms, 'out', sign .. show) or formatted_show
		end
	end
	return {
		clean = show,
		sign = sign,
		show = formatted_show,
		is_scientific = false,  -- to avoid calling __index
	}
end

local function extract_fraction(parms, text, negative)
	-- If text represents a fraction, return
	--   value, altvalue, show, denominator
	-- where
	--   value is a number (value of the fraction in argument text)
	--   altvalue is an alternate interpretation of any fraction for the hands
	--        unit where "12.1+3/4" means 12 hands 1.75 inches
	--   show is a string (formatted text for display of an input value,
	--        and is spelled if wanted and possible)
	--   denominator is value of the denominator in the fraction
	-- Otherwise, return nil.
	-- Input uses en digits and '.' decimal mark (input has been translated).
	-- Output uses digits in local language and local decimal mark, if any.
	------------------------------------------------------------------------
	-- Originally this function accepted x+y/z where x, y, z were any valid
	-- numbers, possibly with a sign. For example '1.23e+2+1.2/2.4' = 123.5,
	-- and '2-3/8' = 1.625. However, such usages were found to be errors or
	-- misunderstandings, so since August 2014 the following restrictions apply:
	--   x (if present) is an integer or has a single digit after decimal mark
	--   y and z are unsigned integers
	--   e-notation is not accepted
	-- The overall number can start with '+' or '-' (so '12+3/4' and '+12+3/4'
	-- and '-12-3/4' are valid).
	-- Any leading negative sign is removed by the caller, so only inputs
	-- like the following are accepted here (may have whitespace):
	--   negative = false       false        true (there was a leading '-')
	--   text     = '2/3'       '+2/3'       '2/3'
	--   text     = '1+2/3'     '+1+2/3'     '1-2/3'
	--   text     = '12.3+1/2'  '+12.3+1/2'  '12.3-1/2'
	-- Values like '12.3+1/2' are accepted, but are intended only for use
	-- with the hands unit (not worth adding code to enforce that).
	------------------------------------------------------------------------
	local leading_plus, prefix, numstr, slashes, denstr =
		text:match('^%s*(%+?)%s*(.-)%s*(%d+)%s*(/+)%s*(%d+)%s*$')
	if not leading_plus then
		-- Accept a single U+2044 fraction slash because that may be pasted.
		leading_plus, prefix, numstr, denstr =
			text:match('^%s*(%+?)%s*(.-)%s*(%d+)%s*⁄%s*(%d+)%s*$')
		slashes = '/'
	end
	local numerator = tonumber(numstr)
	local denominator = tonumber(denstr)
	if numerator == nil or denominator == nil or (negative and leading_plus ~= '') then
		return nil
	end
	local whole, wholestr
	if prefix == '' then
		wholestr = ''
		whole = 0
	else
		-- Any prefix must be like '12+' or '12-' (whole number and fraction sign);
		-- '12.3+' and '12.3-' are also accepted (single digit after decimal point)
		-- because '12.3+1/2 hands' is valid (12 hands 3½ inches).
		local num1, num2, frac_sign = prefix:match('^(%d+)(%.?%d?)%s*([+%-])$')
		if num1 == nil then return nil end
		if num2 == '' then  -- num2 must be '' or like '.1' but not '.' or '.12'
			wholestr = num1
		else
			if #num2 ~= 2 then return nil end
			wholestr = num1 .. num2
		end
		if frac_sign ~= (negative and '-' or '+') then return nil end
		whole = tonumber(wholestr)
		if whole == nil then return nil end
	end
	local value = whole + numerator / denominator
	if not valid_number(value) then return nil end
	local altvalue = whole + numerator / (denominator * 10)
	local style = #slashes  -- kludge: 1 or 2 slashes can be used to select style
	if style > 2 then style = 2 end
	local wikitext = format_fraction(parms, 'in', negative, leading_plus .. wholestr, numstr, denstr, parms.opt_spell_in, style)
	return value, altvalue, wikitext, denominator
end

local function extract_number(parms, text, another, no_fraction)
	-- Return true, info if can extract a number from text,
	-- where info is a table with the result,
	-- or return false, t where t is an error message table.
	-- Input can use en digits or digits in local language and can
	-- have references at the end. Accepting references is intended
	-- for use in infoboxes with a field for a value passed to convert.
	-- Parameter another = true if the expected value is not the first.
	-- Before processing, the input text is cleaned:
	-- * Any thousand separators (valid or not) are removed.
	-- * Any sign is replaced with '-' (if negative) or '' (otherwise).
	--   That replaces Unicode minus with '-'.
	-- If successful, the returned info table contains named fields:
	--   value    = a valid number
	--   altvalue = a valid number, usually same as value but different
	--              if fraction used (for hands unit)
	--   singular = true if value is 1 or -1 (to use singular form of units)
	--   clean    = cleaned text with any separators and sign removed
	--              (en digits and '.' decimal mark)
	--   show     = text formatted for output, possibly with ref strip markers
	--              (digits in local language and custom decimal mark)
	-- The resulting show:
	-- * Is for an input value and is spelled if wanted and possible.
	-- * Has a rounded value, if wanted.
	-- * Has digits grouped where necessary, if wanted.
	-- * If negative, a Unicode minus is used; otherwise the sign is
	--   '+' (if the input text used '+'), or is '' (if no sign in input).
	text = strip(text or '')
	local reference
	local pos = text:find('\127', 1, true)
	if pos then
		local before = text:sub(1, pos - 1)
		local remainder = text:sub(pos)
		local refs = {}
		while #remainder > 0 do
			local ref, spaces
			ref, spaces, remainder = remainder:match('^(\127[^\127]*UNIQ[^\127]*%-ref[^\127]*\127)(%s*)(.*)')
			if ref then
				table.insert(refs, ref)
			else
				refs = {}
				break
			end
		end
		if #refs > 0 then
			text = strip(before)
			reference = table.concat(refs)
		end
	end
	local clean = to_en(text, parms)
	if clean == '' then
		return false, { another and 'cvt_no_num2' or 'cvt_no_num' }
	end
	local isnegative, propersign = false, ''  -- most common case
	local singular, show, denominator
	local value = tonumber(clean)
	local altvalue
	if value then
		local sign = clean:sub(1, 1)
		if sign == '+' or sign == '-' then
			propersign = (sign == '+') and '+' or MINUS
			clean = clean:sub(2)
		end
		if value < 0 then
			isnegative = true
			value = -value
		end
	else
		local valstr
		for _, prefix in ipairs({ '-', MINUS, '&minus;' }) do
			-- Including '-' sets isnegative in case input is a fraction like '-2-3/4'.
			local plen = #prefix
			if clean:sub(1, plen) == prefix then
				valstr = clean:sub(plen + 1)
				if valstr:match('^%s') then  -- "- 1" is invalid but "-1 - 1/2" is ok
					return false, { 'cvt_bad_num', text }
				end
				break
			end
		end
		if valstr then
			isnegative = true
			propersign = MINUS
			clean = valstr
			value = tonumber(clean)
		end
		if value == nil then
			if not no_fraction then
				value, altvalue, show, denominator = extract_fraction(parms, clean, isnegative)
			end
			if value == nil then
				return false, { 'cvt_bad_num', text }
			end
			if value <= 1 then
				singular = true  -- for example, "½ mile" or "one half mile" (singular unit)
			end
		end
	end
	if not valid_number(value) then  -- for example, "1e310" may overflow
		return false, { 'cvt_invalid_num' }
	end
	if show == nil then
		-- clean is a non-empty string with no spaces, and does not represent a fraction,
		-- and value = tonumber(clean) is a number >= 0.
		-- If the input uses e-notation, show will be displayed using a power of ten, but
		-- we use the number as given so it might not be normalized scientific notation.
		-- The input value is spelled if specified so any e-notation is ignored;
		-- that allows input like 2e6 to be spelled as "two million" which works
		-- because the spell module converts '2e6' to '2000000' before spelling.
		local function rounded(value, default, exponent)
			local precision = parms.opt_ri
			if precision then
				local fmt = '%.' .. format('%d', precision) .. 'f'
				local result = fmt:format(tonumber(value) + 2e-14)  -- fudge for some common cases of bad rounding
				if not exponent then
					singular = (tonumber(result) == 1)
				end
				return result
			end
			return default
		end
		singular = (value == 1)
		local scientific
		local significand, exponent = clean:match('^([%d.]+)[Ee]([+%-]?%d+)')
		if significand then
			show = with_exponent(parms, rounded(significand, significand, exponent), exponent)
			scientific = true
		else
			show = with_separator(parms, rounded(value, clean))
		end
		show = propersign .. show
		if parms.opt_spell_in then
			show = spell_number(parms, 'in', propersign .. rounded(value, clean)) or show
			scientific = false
		end
		if scientific then
			parms.opt_scientific = true
		end
	end
	if isnegative and (value ~= 0) then
		value = -value
		altvalue = -(altvalue or value)
	end
	return true, {
		value = value,
		altvalue = altvalue or value,
		singular = singular,
		clean = clean,
		show = show .. (reference or ''),
		denominator = denominator,
	}
end

local function get_number(text)
	-- Return v, f where:
	--   v = nil (text is not a number)
	-- or
	--   v = value of text (text is a number)
	--   f = true if value is an integer
	-- Input can use en digits or digits in local language,
	-- but no separators, no Unicode minus, and no fraction.
	if text then
		local number = tonumber(to_en(text))
		if number then
			local _, fracpart = math.modf(number)
			return number, (fracpart == 0)
		end
	end
end

local function gcd(a, b)
	-- Return the greatest common denominator for the given values,
	-- which are known to be positive integers.
	if a > b then
		a, b = b, a
	end
	if a <= 0 then
		return b
	end
	local r = b % a
	if r <= 0 then
		return a
	end
	if r == 1 then
		return 1
	end
	return gcd(r, a)
end

local function fraction_table(value, denominator)
	-- Return value as a string or a table:
	-- * If result is a string, there is no fraction, and the result
	--   is value formatted as a string of en digits.
	-- * If result is a table, it represents a fraction with named fields:
	--   wholestr, numstr, denstr (strings of en digits for integer, numerator, denominator).
	-- The result is rounded to the nearest multiple of (1/denominator).
	-- If the multiple is zero, no fraction is included.
	-- No fraction is included if value is very large as the fraction would
	-- be unhelpful, particularly if scientific notation is required.
	-- Input value is a non-negative number.
	-- Input denominator is a positive integer for the desired fraction.
	if value <= 0 then
		return '0'
	end
	if denominator <= 0 or value > 1e8 then
		return format('%.2f', value)
	end
	local integer, decimals = math.modf(value)
	local numerator = floor((decimals * denominator) +
		0.5 + 2e-14)  -- add fudge for some common cases of bad rounding
	if numerator >= denominator then
		integer = integer + 1
		numerator = 0
	end
	local wholestr = tostring(integer)
	if numerator > 0 then
		local div = gcd(numerator, denominator)
		if div > 1 then
			numerator = numerator / div
			denominator = denominator / div
		end
		return {
			wholestr = (integer > 0) and wholestr or '',
			numstr = tostring(numerator),
			denstr = tostring(denominator),
			value = value,
		}
	end
	return wholestr
end

local function preunits(count, preunit1, preunit2)
	-- If count is 1:
	--     ignore preunit2
	--     return p1
	-- else:
	--     preunit1 is used for preunit2 if the latter is empty
	--     return p1, p2
	-- where:
	--     p1 is text to insert before the input unit
	--     p2 is text to insert before the output unit
	--     p1 or p2 may be nil to mean "no preunit"
	-- Using '+' gives output like "5+ feet" (no space before, but space after).
	local function withspace(text, wantboth)
		-- Return text with space before and, if wantboth, after.
		-- However, no space is added if there is a space or '&nbsp;' or '-'
		-- at that position ('-' is for adjectival text).
		-- There is also no space if text starts with '&'
		-- (e.g. '&deg;' would display a degree symbol with no preceding space).
		local char = text:sub(1, 1)
		if char == '&' then
			return text  -- an html entity can be used to specify the exact display
		end
		if not (char == ' ' or char == '-' or char == '+') then
			text = ' ' .. text
		end
		if wantboth then
			char = text:sub(-1, -1)
			if not (char == ' ' or char == '-' or text:sub(-6, -1) == '&nbsp;') then
				text = text .. ' '
			end
		end
		return text
	end
	local PLUS = '+ '
	preunit1 = preunit1 or ''
	local trim1 = strip(preunit1)
	if count == 1 then
		if trim1 == '' then
			return nil
		end
		if trim1 == '+' then
			return PLUS
		end
		return withspace(preunit1, true)
	end
	preunit1 = withspace(preunit1)
	preunit2 = preunit2 or ''
	local trim2 = strip(preunit2)
	if trim1 == '+' then
		if trim2 == '' or trim2 == '+' then
			return PLUS, PLUS
		end
		preunit1 = PLUS
	end
	if trim2 == '' then
		if trim1 == '' then
			return nil, nil
		end
		preunit2 = preunit1
	elseif trim2 == '+' then
		preunit2 = PLUS
	elseif trim2 == '&#32;' then  -- trick to make preunit2 empty
		preunit2 = nil
	else
		preunit2 = withspace(preunit2)
	end
	return preunit1, preunit2
end

local function range_text(range, want_name, parms, before, after, inout)
	-- Return before .. rtext .. after
	-- where rtext is the text that separates two values in a range.
	local rtext, adj_text, exception
	if type(range) == 'table' then
		-- Table must specify range text for ('off' and 'on') or ('input' and 'output'),
		-- and may specify range text for 'adj=on',
		-- and may specify exception = true.
		rtext = range[want_name and 'off' or 'on'] or
				range[((inout == 'in') == (parms.opt_flip == true)) and 'output' or 'input']
		adj_text = range['adj']
		exception = range['exception']
	else
		rtext = range
	end
	if parms.opt_adjectival then
		if want_name or (exception and parms.abbr_org == 'on') then
			rtext = adj_text or rtext:gsub(' ', '-'):gsub('&nbsp;', '-')
		end
	end
	if rtext == '–' and after:sub(1, #MINUS) == MINUS then
		rtext = '&nbsp;– '
	end
	return before .. rtext .. after
end

local function get_composite(parms, iparm, in_unit_table)
	-- Look for a composite input unit. For example, {{convert|1|yd|2|ft|3|in}}
	-- would result in a call to this function with
	--   iparm = 3 (parms[iparm] = "2", just after the first unit)
	--   in_unit_table = (unit table for "yd"; contains value 1 for number of yards)
	-- Return true, iparm, unit where
	--   iparm = index just after the composite units (7 in above example)
	--   unit = composite unit table holding all input units,
	-- or return true if no composite unit is present in parms,
	-- or return false, t where t is an error message table.
	local default, subinfo
	local composite_units, count = { in_unit_table }, 1
	local fixups = {}
	local total = in_unit_table.valinfo[1].value
	local subunit = in_unit_table
	while subunit.subdivs do  -- subdivs is nil or a table of allowed subdivisions
		local subcode = strip(parms[iparm+1])
		local subdiv = subunit.subdivs[subcode] or subunit.subdivs[(all_units[subcode] or {}).target]
		if not subdiv then
			break
		end
		local success
		success, subunit = lookup(parms, subcode, 'no_combination')
		if not success then return false, subunit end  -- should never occur
		success, subinfo = extract_number(parms, parms[iparm])
		if not success then return false, subinfo end
		iparm = iparm + 2
		subunit.inout = 'in'
		subunit.valinfo = { subinfo }
		-- Recalculate total as a number of subdivisions.
		-- subdiv[1] = number of subdivisions per previous unit (integer > 1).
		total = total * subdiv[1] + subinfo.value
		if not default then  -- set by the first subdiv with a default defined
			default = subdiv.default
		end
		count = count + 1
		composite_units[count] = subunit
		if subdiv.unit or subdiv.name then
			fixups[count] = { unit = subdiv.unit, name = subdiv.name, valinfo = subunit.valinfo }
		end
	end
	if count == 1 then
		return true  -- no error and no composite unit
	end
	for i, fixup in pairs(fixups) do
		local unit = fixup.unit
		local name = fixup.name
		if not unit or (count > 2 and name) then
			composite_units[i].fixed_name = name
		else
			local success, alternate = lookup(parms, unit, 'no_combination')
			if not success then return false, alternate end  -- should never occur
			alternate.inout = 'in'
			alternate.valinfo = fixup.valinfo
			composite_units[i] = alternate
		end
	end
	return true, iparm, {
		utype = in_unit_table.utype,
		scale = subunit.scale,  -- scale of last (least significant) unit
		valinfo = { { value = total, clean = subinfo.clean, denominator = subinfo.denominator } },
		composite = composite_units,
		default = default or in_unit_table.default
	}
end

local function translate_parms(parms, kv_pairs)
	-- Update fields in parms by translating each key:value in kv_pairs to terms
	-- used by this module (may involve translating from local language to English).
	-- Also, checks are performed which may display warnings, if enabled.
	-- Return true if successful or return false, t where t is an error message table.
	currency_text = nil  -- local testing can hold module in memory; must clear globals
	local accept_any_text = {
		input = true,
		qid = true,
		qual = true,
		stylein = true,
		styleout = true,
		tracking = true,
	}
	if kv_pairs.adj and kv_pairs.sing then
		-- For enwiki (before translation), warn if attempt to use adj and sing
		-- as the latter is a deprecated alias for the former.
		if kv_pairs.adj ~= kv_pairs.sing and kv_pairs.sing ~= '' then
			add_warning(parms, 1, 'cvt_unknown_option', 'sing=' .. kv_pairs.sing)
		end
		kv_pairs.sing = nil
	end
	kv_pairs.comma = kv_pairs.comma or config.comma  -- for plwiki who want default comma=5
	for loc_name, loc_value in pairs(kv_pairs) do
		local en_name = text_code.en_option_name[loc_name]
		if en_name then
			local en_value
			if en_name == '$' or en_name == 'frac' or en_name == 'sigfig' then
				if loc_value == '' then
					add_warning(parms, 2, 'cvt_empty_option', loc_name)
				elseif en_name == '$' then
					-- Value should be a single character like "€" for the euro currency symbol, but anything is accepted.
					currency_text = (loc_value == 'euro') and '€' or loc_value
				else
					local minimum
					local number, is_integer = get_number(loc_value)
					if en_name == 'frac' then
						minimum = 2
						if number and number < 0 then
							parms.opt_fraction_horizontal = true
							number = -number
						end
					else
						minimum = 1
					end
					if number and is_integer and number >= minimum then
						en_value = number
					else
						add_warning(parms, 1, (en_name == 'frac' and 'cvt_bad_frac' or 'cvt_bad_sigfig'), loc_name .. '=' .. loc_value)
					end
				end
			elseif accept_any_text[en_name] then
				en_value = loc_value ~= '' and loc_value or nil  -- accept non-empty user text with no validation
				if en_name == 'input' then
					-- May have something like {{convert|input=}} (empty input) if source is an infobox
					-- with optional fields. In that case, want to output nothing rather than an error.
					parms.input_text = loc_value  -- keep input because parms.input is nil if loc_value == ''
				end
			else
				en_value = text_code.en_option_value[en_name][loc_value]
				if en_value and en_value:sub(-1) == '?' then
					en_value = en_value:sub(1, -2)
					add_warning(parms, -1, 'cvt_deprecated', loc_name .. '=' .. loc_value)
				end
				if en_value == nil then
					if loc_value == '' then
						add_warning(parms, 2, 'cvt_empty_option', loc_name)
					else
						add_warning(parms, 1, 'cvt_unknown_option', loc_name .. '=' .. loc_value)
					end
				elseif en_value == '' then
					en_value = nil  -- an ignored option like adj=off
				elseif type(en_value) == 'string' and en_value:sub(1, 4) == 'opt_' then
					for _, v in ipairs(split(en_value, ',')) do
						local lhs, rhs = v:match('^(.-)=(.+)$')
						if rhs then
							parms[lhs] = tonumber(rhs) or rhs
						else
							parms[v] = true
						end
					end
					en_value = nil
				end
			end
			parms[en_name] = en_value
		else
			add_warning(parms, 1, 'cvt_unknown_option', loc_name .. '=' .. loc_value)
		end
	end
	local abbr_entered = parms.abbr
	local cfg_abbr = config.abbr
	if cfg_abbr then
		-- Don't warn if invalid because every convert would show that warning.
		if cfg_abbr == 'on always' then
			parms.abbr = 'on'
		elseif cfg_abbr == 'off always' then
			parms.abbr = 'off'
		elseif parms.abbr == nil then
			if cfg_abbr == 'on default' then
				parms.abbr = 'on'
			elseif cfg_abbr == 'off default' then
				parms.abbr = 'off'
			end
		end
	end
	if parms.abbr then
		if parms.abbr == 'unit' then
			parms.abbr = 'on'
			parms.number_word = true
		end
		parms.abbr_org = parms.abbr  -- original abbr, before any flip
	elseif parms.opt_hand_hh then
		parms.abbr_org = 'on'
		parms.abbr = 'on'
	else
		parms.abbr = 'out'  -- default is to abbreviate output only (use symbol, not name)
	end
	if parms.opt_order_out then
		-- Disable options that do not work in a useful way with order=out.
		parms.opt_flip = nil  -- override adj=flip
		parms.opt_spell_in = nil
		parms.opt_spell_out = nil
		parms.opt_spell_upper = nil
	end
	if parms.opt_spell_out and not abbr_entered then
		parms.abbr = 'off'  -- should show unit name when spelling the output value
	end
	if parms.opt_flip then
		local function swap_in_out(option)
			local value = parms[option]
			if value == 'in' then
				parms[option] = 'out'
			elseif value == 'out' then
				parms[option] = 'in'
			end
		end
		swap_in_out('abbr')
		swap_in_out('lk')
		if parms.opt_spell_in and not parms.opt_spell_out then
			-- For simplicity, and because it does not appear to be needed,
			-- user cannot set an option to spell the output only.
			parms.opt_spell_in = nil
			parms.opt_spell_out = true
		end
	end
	if parms.opt_spell_upper then
		parms.spell_upper = parms.opt_flip and 'out' or 'in'
	end
	if parms.opt_table or parms.opt_tablecen then
		if abbr_entered == nil and parms.lk == nil then
			parms.opt_values = true
		end
		parms.table_align = parms.opt_table and 'right' or 'center'
	end
	if parms.table_align or parms.opt_sortable_on then
		parms.need_table_or_sort = true
	end
	local disp_joins = text_code.disp_joins
	local default_joins = disp_joins['b']
	parms.join_between = default_joins[3] or '; '
	local disp = parms.disp
	if disp == nil then  -- special case for the most common setting
		parms.joins = default_joins
	elseif disp == 'x' then
		-- Later, parms.joins is set from the input parameters.
	else
		-- Old template does this.
		local abbr = parms.abbr
		if disp == 'slash' then
			if abbr_entered == nil then
				disp = 'slash-nbsp'
			elseif abbr == 'in' or abbr == 'out' then
				disp = 'slash-sp'
			else
				disp = 'slash-nosp'
			end
		elseif disp == 'sqbr' then
			if abbr == 'on' then
				disp = 'sqbr-nbsp'
			else
				disp = 'sqbr-sp'
			end
		end
		parms.joins = disp_joins[disp] or default_joins
		parms.join_between = parms.joins[3] or parms.join_between
		parms.wantname = parms.joins.wantname
	end
	if (en_default and not parms.opt_lang_local and (parms[1] or ''):find('%d')) or parms.opt_lang_en then
		from_en_table = nil
	end
	if en_default and from_en_table then
		-- For hiwiki: localized symbol/name is defined with the US symbol/name field,
		-- and is used if output uses localized numbers.
		parms.opt_sp_us = true
	end
	return true
end

local function get_values(parms)
	-- If successful, update parms and return true, v, i where
	--   v = table of input values
	--   i = index to next entry in parms after those processed here
	-- or return false, t where t is an error message table.
	local valinfo = collection()  -- numbered table of input values
	local range = collection()  -- numbered table of range items (having, for example, 2 range items requires 3 input values)
	local had_nocomma  -- true if removed "nocomma" kludge from second parameter (like "tonocomma")
	local parm2 = strip(parms[2])
	if parm2 and parm2:sub(-7, -1) == 'nocomma' then
		parms[2] = strip(parm2:sub(1, -8))
		parms.opt_nocomma = true
		had_nocomma = true
	end
	local function extractor(i)
		-- If the parameter is not a value, try unpacking it as a range ("1-23" for "1 to 23").
		-- However, "-1-2/3" is a negative fraction (-1⅔), so it must be extracted first.
		-- Do not unpack a parameter if it is like "3-1/2" which is sometimes incorrectly
		-- used instead of "3+1/2" (and which should not be interpreted as "3 to ½").
		-- Unpacked items are inserted into the parms table.
		-- The tail recursion allows combinations like "1x2 to 3x4".
		local valstr = strip(parms[i])  -- trim so any '-' as a negative sign will be at start
		local success, result = extract_number(parms, valstr, i > 1)
		if not success and valstr and i < 20 then  -- check i to limit abuse
			local lhs, sep, rhs = valstr:match('^(%S+)%s+(%S+)%s+(%S.*)')
			if lhs and not (sep == '-' and rhs:match('/')) then
				if sep:find('%d') then
					return success, result  -- to reject {{convert|1 234 567|m}} with a decent message (en only)
				end
				parms[i] = rhs
				table.insert(parms, i, sep)
				table.insert(parms, i, lhs)
				return extractor(i)
			end
			if not valstr:match('%-.*/') then
				for _, sep in ipairs(text_code.ranges.words) do
					local start, stop = valstr:find(sep, 2, true)  -- start at 2 to skip any negative sign for range '-'
					if start then
						parms[i] = valstr:sub(stop + 1)
						table.insert(parms, i, sep)
						table.insert(parms, i, valstr:sub(1, start - 1))
						return extractor(i)
					end
				end
			end
		end
		return success, result
	end
	local i = 1
	local is_change
	while true do
		local success, info = extractor(i)  -- need to set parms.opt_nocomma before calling this
		if not success then return false, info end
		i = i + 1
		if is_change then
			info.is_change = true  -- value is after "±" and so is a change (significant for range like {{convert|5|±|5|°C}})
			is_change = nil
		end
		valinfo:add(info)
		local range_item = get_range(strip(parms[i]))
		if not range_item then
			break
		end
		i = i + 1
		range:add(range_item)
		if type(range_item) == 'table' then
			-- For range "x", if append unit to some values, append it to all.
			parms.in_range_x = parms.in_range_x or range_item.in_range_x
			parms.out_range_x = parms.out_range_x or range_item.out_range_x
			parms.abbr_range_x = parms.abbr_range_x or range_item.abbr_range_x
			is_change = range_item.is_range_change
		end
	end
	if range.n > 0 then
		if range.n > 30 then  -- limit abuse, although 4 is a more likely upper limit
			return false, { 'cvt_invalid_num' }  -- misleading message but it will do
		end
		parms.range = range
	elseif had_nocomma then
		return false, { 'cvt_unknown', parm2 }
	end
	return true, valinfo, i
end

local function simple_get_values(parms)
	-- If input is like "{{convert|valid_value|valid_unit|...}}",
	-- return true, i, in_unit, in_unit_table
	-- i = index in parms of what follows valid_unit, if anything.
	-- The valid_value is not negative and does not use a fraction, and
	-- no options requiring further processing of the input are used.
	-- Otherwise, return nothing or return false, parm1 for caller to interpret.
	-- Testing shows this function is successful for 96% of converts in articles,
	-- and that on average it speeds up converts by 8%.
	local clean = to_en(strip(parms[1] or ''), parms)
	if parms.opt_ri or parms.opt_spell_in or #clean > 10 or not clean:match('^[0-9.]+$') then
		return false, clean
	end
	local value = tonumber(clean)
	if not value then return end
	local info = {
		value = value,
		altvalue = value,
		singular = (value == 1),
		clean = clean,
		show = with_separator(parms, clean),
	}
	local in_unit = strip(parms[2])
	local success, in_unit_table = lookup(parms, in_unit, 'no_combination')
	if not success then return end
	in_unit_table.valinfo = { info }
	return true, 3, in_unit, in_unit_table
end

local function wikidata_call(parms, operation, ...)
	-- Return true, s where s is the result of a Wikidata operation,
	-- or return false, t where t is an error message table.
	local function worker(...)
		wikidata_code = wikidata_code or require(wikidata_module)
		wikidata_data = wikidata_data or mw.loadData(wikidata_data_module)
		return wikidata_code[operation](wikidata_data, ...)
	end
	local success, status, result = pcall(worker, ...)
	if success then
		return status, result
	end
	if parms.opt_sortable_debug then
		-- Use debug=yes to crash if an error while accessing Wikidata.
		error('Error accessing Wikidata: ' .. status, 0)
	end
	return false, { 'cvt_wd_fail' }
end

local function get_parms(parms, args)
	-- If successful, update parms and return true, unit where
	--   parms is a table of all arguments passed to the template
	--        converted to named arguments, and
	--   unit is the input unit table;
	-- or return false, t where t is an error message table.
	-- For special processing (not a convert), can also return
	-- true, wikitext where wikitext is the final result.
	-- The returned input unit table may be for a fake unit using the specified
	-- unit code as the symbol and name, and with bad_mcode = message code table.
	-- MediaWiki removes leading and trailing whitespace from the values of
	-- named arguments. However, the values of numbered arguments include any
	-- whitespace entered in the template, and whitespace is used by some
	-- parameters (example: the numbered parameters associated with "disp=x").
	local kv_pairs = {}  -- table of input key:value pairs where key is a name; needed because cannot iterate parms and add new fields to it
	for k, v in pairs(args) do
		if type(k) == 'number' or k == 'test' then  -- parameter "test" is reserved for testing and is not translated
			parms[k] = v
		else
			kv_pairs[k] = v
		end
	end
	if parms.test == 'wikidata' then
		local ulookup = function (ucode)
			-- Use empty table for parms so it does not accumulate results when used repeatedly.
			return lookup({}, ucode, 'no_combination')
		end
		return wikidata_call(parms, '_listunits', ulookup)
	end
	local success, msg = translate_parms(parms, kv_pairs)
	if not success then return false, msg end
	if parms.input then
		success, msg = wikidata_call(parms, '_adjustparameters', parms, 1)
		if not success then return false, msg end
	end
	local success, i, in_unit, in_unit_table = simple_get_values(parms)
	if not success then
		if type(i) == 'string' and i:match('^NNN+$') then
			-- Some infoboxes have examples like {{convert|NNN|m}} (3 or more "N").
			-- Output an empty string for these.
			return false, { 'cvt_no_output' }
		end
		local valinfo
		success, valinfo, i = get_values(parms)
		if not success then return false, valinfo end
		in_unit = strip(parms[i])
		i = i + 1
		success, in_unit_table = lookup(parms, in_unit, 'no_combination')
		if not success then
			in_unit = in_unit or ''
			if parms.opt_ignore_error then  -- display given unit code with no error (for use with {{val}})
				in_unit_table = ''  -- suppress error message and prevent processing of output unit
			end
			in_unit_table = setmetatable({
				symbol = in_unit, name2 = in_unit, utype = in_unit,
				scale = 1, default = '', defkey = '', linkey = '',
				bad_mcode = in_unit_table }, unit_mt)
		end
		in_unit_table.valinfo = valinfo
	end
	if parms.test == 'msg' then
		-- Am testing the messages produced when no output unit is specified, and
		-- the input unit has a missing or invalid default.
		-- Set two units for testing that.
		-- LATER: Remove this code.
		if in_unit == 'chain' then
			in_unit_table.default = nil  -- no default
		elseif in_unit == 'rd' then
			in_unit_table.default  = "ft!X!m"  -- an invalid expression
		end
	end
	in_unit_table.inout = 'in'  -- this is an input unit
	if not parms.range then
		local success, inext, composite_unit = get_composite(parms, i, in_unit_table)
		if not success then return false, inext end
		if composite_unit then
			in_unit_table = composite_unit
			i = inext
		end
	end
	if in_unit_table.builtin == 'mach' then
		-- As with old template, a number following Mach as the input unit is the altitude,
		-- and there is no way to specify an altitude for the output unit.
		-- Could put more code in this function to get any output unit and check for
		-- an altitude following that unit.
		local success, info = extract_number(parms, parms[i], false, true)
		if success then
			i = i + 1
			in_unit_table.altitude = info.value
		end
	end
	local word = strip(parms[i])
	i = i + 1
	local precision, is_bad_precision
	local function set_precision(text)
		local number, is_integer = get_number(text)
		if number then
			if is_integer then
				precision = number
			else
				precision = text
				is_bad_precision = true
			end
			return true  -- text was used for precision, good or bad
		end
	end
	if word and not set_precision(word) then
		parms.out_unit = parms.out_unit or word
		if set_precision(strip(parms[i])) then
			i = i + 1
		end
	end
	if parms.opt_adj_mid then
		word = parms[i]
		i = i + 1
		if word then  -- mid-text words
			if word:sub(1, 1) == '-' then
				parms.mid = word
			else
				parms.mid = ' ' .. word
			end
		end
	end
	if parms.opt_one_preunit then
		parms[parms.opt_flip and 'preunit2' or 'preunit1'] = preunits(1, parms[i])
		i = i + 1
	end
	if parms.disp == 'x' then
		-- Following is reasonably compatible with the old template.
		local first = parms[i] or ''
		local second = parms[i+1] or ''
		i = i + 2
		if strip(first) == '' then  -- user can enter '&#32;' rather than ' ' to avoid the default
			first = ' [&nbsp;' .. first
			second = '&nbsp;]' .. second
		end
		parms.joins = { first, second }
	elseif parms.opt_two_preunits then
		local p1, p2 = preunits(2, parms[i], parms[i+1])
		i = i + 2
		if parms.preunit1 then
			-- To simplify documentation, allow unlikely use of adj=pre with disp=preunit
			-- (however, an output unit must be specified with adj=pre and with disp=preunit).
			parms.preunit1 = parms.preunit1 .. p1
			parms.preunit2 = p2
		else
			parms.preunit1, parms.preunit2 = p1, p2
		end
	end
	if precision == nil then
		if set_precision(strip(parms[i])) then
			i = i + 1
		end
	end
	if is_bad_precision then
		add_warning(parms, 1, 'cvt_bad_prec', precision)
	else
		parms.precision = precision
	end
	for j = i, i + 3 do
		local parm = parms[j]  -- warn if find a non-empty extraneous parameter
		if parm and parm:match('%S') then
			add_warning(parms, 1, 'cvt_unknown_option', parm)
			break
		end
	end
	return true, in_unit_table
end

local function record_default_precision(parms, out_current, precision)
	-- If necessary, adjust parameters and return a possibly adjusted precision.
	-- When converting a range of values where a default precision is required,
	-- that default is calculated for each value because the result sometimes
	-- depends on the precise input and output values. This function may cause
	-- the entire convert process to be repeated in order to ensure that the
	-- same default precision is used for each individual convert.
	-- If that were not done, a range like 1000 to 1000.4 may give poor results
	-- because the first output could be heavily rounded, while the second is not.
	-- For range 1000.4 to 1000, this function can give the second convert the
	-- same default precision that was used for the first.
	if not parms.opt_round_each then
		local maxdef = out_current.max_default_precision
		if maxdef then
			if maxdef < precision then
				parms.do_convert_again = true
				out_current.max_default_precision = precision
			else
				precision = out_current.max_default_precision
			end
		else
			out_current.max_default_precision = precision
		end
	end
	return precision
end

local function default_precision(parms, invalue, inclean, denominator, outvalue, in_current, out_current, extra)
	-- Return a default value for precision (an integer like 2, 0, -2).
	-- If denominator is not nil, it is the value of the denominator in inclean.
	-- Code follows procedures used in old template.
	local fudge = 1e-14  -- {{Order of magnitude}} adds this, so we do too
	local prec, minprec, adjust
	local subunit_ignore_trailing_zero
	local subunit_more_precision  -- kludge for "in" used in input like "|2|ft|6|in"
	local composite = in_current.composite
	if composite then
		subunit_ignore_trailing_zero = true  -- input "|2|st|10|lb" has precision 0, not -1
		if composite[#composite].exception == 'subunit_more_precision' then
			subunit_more_precision = true  -- do not use standard precision with input like "|2|ft|6|in"
		end
	end
	if denominator and denominator > 0 then
		prec = math.max(log10(denominator), 1)
	else
		-- Count digits after decimal mark, handling cases like '12.345e6'.
		local exponent
		local integer, dot, decimals, expstr = inclean:match('^(%d*)(%.?)(%d*)(.*)')
		local e = expstr:sub(1, 1)
		if e == 'e' or e == 'E' then
			exponent = tonumber(expstr:sub(2))
		end
		if dot == '' then
			prec = subunit_ignore_trailing_zero and 0 or -integer:match('0*$'):len()
		else
			prec = #decimals
		end
		if exponent then
			-- So '1230' and '1.23e3' both give prec = -1, and '0.00123' and '1.23e-3' give 5.
			prec = prec - exponent
		end
	end
	if in_current.istemperature and out_current.istemperature then
		-- Converting between common temperatures (°C, °F, °R, K); not keVT.
		-- Kelvin value can be almost zero, or small but negative due to precision problems.
		-- Also, an input value like -300 C (below absolute zero) gives negative kelvins.
		-- Calculate minimum precision from absolute value.
		adjust = 0
		local kelvin = abs((invalue - in_current.offset) * in_current.scale)
		if kelvin < 1e-8 then  -- assume nonzero due to input or calculation precision problem
			minprec = 2
		else
			minprec = 2 - floor(log10(kelvin) + fudge)  -- 3 sigfigs in kelvin
		end
	else
		if invalue == 0 or outvalue <= 0 then
			-- We are never called with a negative outvalue, but it might be zero.
			-- This is special-cased to avoid calculation exceptions.
			return record_default_precision(parms, out_current, 0)
		end
		if out_current.exception == 'integer_more_precision' and floor(invalue) == invalue then
			-- With certain output units that sometimes give poor results
			-- with default rounding, use more precision when the input
			-- value is equal to an integer. An example of a poor result
			-- is when input 50 gives a smaller output than input 49.5.
			-- Experiment shows this helps, but it does not eliminate all
			-- surprises because it is not clear whether "50" should be
			-- interpreted as "from 45 to 55" or "from 49.5 to 50.5".
			adjust = -log10(in_current.scale)
		elseif subunit_more_precision then
			-- Conversion like "{{convert|6|ft|1|in|cm}}" (where subunit is "in")
			-- has a non-standard adjust value, to give more output precision.
			adjust = log10(out_current.scale) + 2
		else
			adjust = log10(abs(invalue / outvalue))
		end
		adjust = adjust + log10(2)
		-- Ensure that the output has at least two significant figures.
		minprec = 1 - floor(log10(outvalue) + fudge)
	end
	if extra then
		adjust = extra.adjust or adjust
		minprec = extra.minprec or minprec
	end
	return record_default_precision(parms, out_current, math.max(floor(prec + adjust), minprec))
end

local function convert(parms, invalue, info, in_current, out_current)
	-- Convert given input value from one unit to another.
	-- Return output_value (a number) if a simple convert, or
	-- return f, t where
	--   f = true, t = table of information with results, or
	--   f = false, t = error message table.
	local inscale = in_current.scale
	local outscale = out_current.scale
	if not in_current.iscomplex and not out_current.iscomplex then
		return invalue * (inscale / outscale)  -- minimize overhead for most common case
	end
	if in_current.invert or out_current.invert then
		-- Inverted units, such as inverse length, inverse time, or
		-- fuel efficiency. Built-in units do not have invert set.
		if (in_current.invert or 1) * (out_current.invert or 1) < 0 then
			return 1 / (invalue * inscale * outscale)
		end
		return invalue * (inscale / outscale)
	elseif in_current.offset then
		-- Temperature (there are no built-ins for this type of unit).
		if info.is_change then
			return invalue * (inscale / outscale)
		end
		return (invalue - in_current.offset) * (inscale / outscale) + out_current.offset
	else
		-- Built-in unit.
		local in_builtin = in_current.builtin
		local out_builtin = out_current.builtin
		if in_builtin and out_builtin then
			if in_builtin == out_builtin then
				return invalue
			end
			-- There are no cases (yet) where need to convert from one
			-- built-in unit to another, so this should never occur.
			return false, { 'cvt_bug_convert' }
		end
		if in_builtin == 'mach' or out_builtin == 'mach' then
			local adjust
			if in_builtin == 'mach' then
				inscale = speed_of_sound(in_current.altitude)
				adjust = outscale / 0.1
			else
				outscale = speed_of_sound(out_current.altitude)
				adjust = 0.1 / inscale
			end
			return true, {
				outvalue = invalue * (inscale / outscale),
				adjust = log10(adjust) + log10(2),
			}
		elseif in_builtin == 'hand' then
			-- 1 hand = 4 inches; 1.2 hands = 6 inches.
			-- Decimals of a hand are only defined for the first digit, and
			-- the first fractional digit should be a number of inches (1, 2 or 3).
			-- However, this code interprets the entire fractional part as the number
			-- of inches / 10 (so 1.75 inches would be 0.175 hands).
			-- A value like 12.3 hands is exactly 12*4 + 3 inches; base default precision on that.
			local integer, fracpart = math.modf(invalue)
			local inch_value = 4 * integer + 10 * fracpart  -- equivalent number of inches
			local factor = inscale / outscale
			if factor == 4 then
				-- Am converting to inches: show exact result, and use "inches" not "in" by default.
				if parms.abbr_org == nil then
					out_current.usename = true
				end
				local show = format('%g', abs(inch_value))  -- show and clean are unsigned
				if not show:find('e', 1, true) then
					return true, {
						invalue = inch_value,
						outvalue = inch_value,
						clean = show,
						show = show,
					}
				end
			end
			local outvalue = (integer + 2.5 * fracpart) * factor
			local fracstr = info.clean:match('%.(.*)') or ''
			local fmt
			if fracstr == '' then
				fmt = '%.0f'
			else
				fmt = '%.' .. format('%d', #fracstr - 1) .. 'f'
			end
			return true, {
				invalue = inch_value,
				clean = format(fmt, inch_value),
				outvalue = outvalue,
				minprec = 0,
			}
		end
	end
	return false, { 'cvt_bug_convert' }  -- should never occur
end

local function user_style(parms, i)
	-- Return text for a user-specified style for a table cell, or '' if none,
	-- given i = 1 (input style) or 2 (output style).
	local style = parms[(i == 1) and 'stylein' or 'styleout']
	if style then
		style = style:gsub('"', '')
		if style ~= '' then
			if style:sub(-1) ~= ';' then
				style = style .. ';'
			end
			return style
		end
	end
	return ''
end

local function make_table_or_sort(parms, invalue, info, in_current, scaled_top)
	-- Set options to handle output for a table or a sort key, or both.
	-- The text sort key is based on the value resulting from converting
	-- the input to a fake base unit with scale = 1, and other properties
	-- required for a conversion derived from the input unit.
	-- For other modules, return the sort key in a hidden span element, and
	-- the scaled value used to generate the sort key.
	-- If scaled_top is set, it is the scaled value of the numerator of a per unit
	-- to be combined with this unit (the denominator) to make the sort key.
	-- Scaling only works with units that convert with a factor (not temperature).
	local sortkey, scaled_value
	if parms.opt_sortable_on then
		local base = {  -- a fake unit with enough fields for a valid convert
			scale = 1,
			invert = in_current.invert and 1,
			iscomplex = in_current.iscomplex,
			offset = in_current.offset and 0,
		}
		local outvalue, extra = convert(parms, invalue, info, in_current, base)
		if extra then
			outvalue = extra.outvalue
		end
		if in_current.istemperature then
			-- Have converted to kelvin; assume numbers close to zero have a
			-- rounding error and should be zero.
			if abs(outvalue) < 1e-12 then
				outvalue = 0
			end
		end
		if scaled_top and outvalue ~= 0 then
			outvalue = scaled_top / outvalue
		end
		scaled_value = outvalue
		if not valid_number(outvalue) then
			if outvalue < 0 then
				sortkey = '1000000000000000000'
			else
				sortkey = '9000000000000000000'
			end
		elseif outvalue == 0 then
			sortkey = '5000000000000000000'
		else
			local mag = floor(log10(abs(outvalue)) + 1e-14)
			local prefix
			if outvalue > 0 then
				prefix = 7000 + mag
			else
				prefix = 2999 - mag
				outvalue = outvalue + 10^(mag+1)
			end
			sortkey = format('%d', prefix) .. format('%015.0f', floor(outvalue * 10^(14-mag)))
		end
	end
	local sortspan
	if sortkey and not parms.table_align then
		sortspan = parms.opt_sortable_debug and
			'<span data-sort-value="' .. sortkey .. '♠"><span style="border:1px solid">' .. sortkey .. '♠</span></span>' or
			'<span data-sort-value="' .. sortkey .. '♠"></span>'
		parms.join_before = sortspan
	end
	if parms.table_align then
		local sort
		if sortkey then
			sort = ' data-sort-value="' .. sortkey .. '"'
			if parms.opt_sortable_debug then
				parms.join_before = '<span style="border:1px solid">' .. sortkey .. '</span>'
			end
		else
			sort = ''
		end
		local style = 'style="text-align:' .. parms.table_align .. ';'
		local joins = {}
		for i = 1, 2 do
			joins[i] = (i == 1 and '' or '\n|') .. style .. user_style(parms, i) .. '"' .. sort .. '|'
		end
		parms.table_joins = joins
	end
	return sortspan, scaled_value
end

local cvt_to_hand

local function cvtround(parms, info, in_current, out_current)
	-- Return true, t where t is a table with the conversion results; fields:
	--   show = rounded, formatted string with the result of converting value in info,
	--      using the rounding specified in parms.
	--   singular = true if result (after rounding and ignoring any negative sign)
	--      is "1", or like "1.00", or is a fraction with value < 1;
	--   (and more fields shown below, and a calculated 'absvalue' field).
	-- or return false, t where t is an error message table.
	-- Input info.clean uses en digits (it has been translated, if necessary).
	-- Output show uses en or non-en digits as appropriate, or can be spelled.
	if out_current.builtin == 'hand' then
		return cvt_to_hand(parms, info, in_current, out_current)
	end
	local invalue = in_current.builtin == 'hand' and info.altvalue or info.value
	local outvalue, extra = convert(parms, invalue, info, in_current, out_current)
	if parms.need_table_or_sort then
		parms.need_table_or_sort = nil  -- process using first input value only
		make_table_or_sort(parms, invalue, info, in_current)
	end
	if extra then
		if not outvalue then return false, extra end
		invalue = extra.invalue or invalue
		outvalue = extra.outvalue
	end
	if not valid_number(outvalue) then
		return false, { 'cvt_invalid_num' }
	end
	local isnegative
	if outvalue < 0 then
		isnegative = true
		outvalue = -outvalue
	end
	local precision, show, exponent
	local denominator = out_current.frac
	if denominator then
		show = fraction_table(outvalue, denominator)
	else
		precision = parms.precision
		if not precision then
			if parms.sigfig then
				show, exponent = make_sigfig(outvalue, parms.sigfig)
			elseif parms.opt_round then
				local n = parms.opt_round
				if n == 0.5 then
					local integer, fracpart = math.modf(floor(2 * outvalue + 0.5) / 2)
					if fracpart == 0 then
						show = format('%.0f', integer)
					else
						show = format('%.1f', integer + fracpart)
					end
				else
					show = format('%.0f', floor((outvalue / n) + 0.5) * n)
				end
			else
				local inclean = info.clean
				if extra then
					inclean = extra.clean or inclean
					show = extra.show
				end
				if not show then
					precision = default_precision(parms, invalue, inclean, info.denominator, outvalue, in_current, out_current, extra)
				end
			end
		end
	end
	if precision then
		if precision >= 0 then
			local fudge
			if precision <= 8 then
				-- Add a fudge to handle common cases of bad rounding due to inability
				-- to precisely represent some values. This makes the following work:
				-- {{convert|-100.1|C|K}} and {{convert|5555000|um|m|2}}.
				-- Old template uses #expr round, which invokes PHP round().
				-- LATER: Investigate how PHP round() works.
				fudge = 2e-14
			else
				fudge = 0
			end
			local fmt = '%.' .. format('%d', precision) .. 'f'
			local success
			success, show = pcall(format, fmt, outvalue + fudge)
			if not success then
				return false, { 'cvt_big_prec', tostring(precision) }
			end
		else
			precision = -precision  -- #digits to zero (in addition to any digits after dot)
			local shift = 10 ^ precision
			show = format('%.0f', outvalue/shift)
			if show ~= '0' then
				exponent = #show + precision
			end
		end
	end
	local t = format_number(parms, show, exponent, isnegative)
	if type(show) == 'string' then
		-- Set singular using match because on some systems 0.99999999999999999 is 1.0.
		if exponent then
			t.singular = (exponent == 1 and show:match('^10*$'))
		else
			t.singular = (show == '1' or show:match('^1%.0*$'))
		end
	else
		t.fraction_table = show
		t.singular = (outvalue <= 1)  -- cannot have 'fraction == 1', but if it were possible it would be singular
	end
	t.raw_absvalue = outvalue  -- absolute value before rounding
	return true, setmetatable(t, {
		__index = function (self, key)
			if key == 'absvalue' then
				-- Calculate absolute value after rounding, if needed.
				local clean, exponent = rawget(self, 'clean'), rawget(self, 'exponent')
				local value = tonumber(clean)  -- absolute value (any negative sign has been ignored)
				if exponent then
					value = value * 10^exponent
				end
				rawset(self, key, value)
				return value
			end
		end })
end

function cvt_to_hand(parms, info, in_current, out_current)
	-- Convert input to hands, inches.
	-- Return true, t where t is a table with the conversion results;
	-- or return false, t where t is an error message table.
	if parms.abbr_org == nil then
		out_current.usename = true  -- default is to show name not symbol
	end
	local precision = parms.precision
	local frac = out_current.frac
	if not frac and precision and precision > 1 then
		frac = (precision == 2) and 2 or 4
	end
	local out_next = out_current.out_next
	if out_next then
		-- Use magic knowledge to determine whether the next unit is inches without requiring i18n.
		-- The following ensures that when the output combination "hand in" is used, the inches
		-- value is rounded to match the hands value. Also, displaying say "61½" instead of 61.5
		-- is better as 61.5 implies the value is not 61.4.
		if out_next.exception == 'subunit_more_precision' then
			out_next.frac = frac
		end
	end
	-- Convert to inches; calculate hands from that.
	local dummy_unit_table = { scale = out_current.scale / 4, frac = frac }
	local success, outinfo = cvtround(parms, info, in_current, dummy_unit_table)
	if not success then return false, outinfo end
	local tfrac = outinfo.fraction_table
	local inches = outinfo.raw_absvalue
	if tfrac then
		inches = floor(inches)  -- integer part only; fraction added later
	else
		inches = floor(inches + 0.5)  -- a hands measurement never shows decimals of an inch
	end
	local hands, inches = divide(inches, 4)
	outinfo.absvalue = hands + inches/4  -- supposed to be the absolute rounded value, but this is close enough
	local inchstr = tostring(inches)  -- '0', '1', '2' or '3'
	if precision and precision <= 0 then  -- using negative or 0 for precision rounds to nearest hand
		hands = floor(outinfo.raw_absvalue/4 + 0.5)
		inchstr = ''
	elseif tfrac then
		-- Always show an integer before fraction (like "15.0½") because "15½" means 15-and-a-half hands.
		inchstr = numdot .. format_fraction(parms, 'out', false, inchstr, tfrac.numstr, tfrac.denstr)
	else
		inchstr = numdot .. from_en(inchstr)
	end
	outinfo.show = outinfo.sign .. with_separator(parms, format('%.0f', hands)) .. inchstr
	return true, outinfo
end

local function evaluate_condition(value, condition)
	-- Return true or false from applying a conditional expression to value,
	-- or throw an error if invalid.
	-- A very limited set of expressions is supported:
	--    v < 9
	--    v * 9 < 9
	-- where
	--    'v' is replaced with value
	--    9 is any number (as defined by Lua tonumber)
	--      only en digits are accepted
	--    '<' can also be '<=' or '>' or '>='
	-- In addition, the following form is supported:
	--    LHS and RHS
	-- where
	--    LHS, RHS = any of above expressions.
	local function compare(value, text)
		local arithop, factor, compop, limit = text:match('^%s*v%s*([*]?)(.-)([<>]=?)(.*)$')
		if arithop == nil then
			error('Invalid default expression', 0)
		elseif arithop == '*' then
			factor = tonumber(factor)
			if factor == nil then
				error('Invalid default expression', 0)
			end
			value = value * factor
		end
		limit = tonumber(limit)
		if limit == nil then
			error('Invalid default expression', 0)
		end
		if compop == '<' then
			return value < limit
		elseif compop == '<=' then
			return value <= limit
		elseif compop == '>' then
			return value > limit
		elseif compop == '>=' then
			return value >= limit
		end
		error('Invalid default expression', 0)  -- should not occur
	end
	local lhs, rhs = condition:match('^(.-%W)and(%W.*)')
	if lhs == nil then
		return compare(value, condition)
	end
	return compare(value, lhs) and compare(value, rhs)
end

local function get_default(value, unit_table)
	-- Return true, s where s = name of unit's default output unit,
	-- or return false, t where t is an error message table.
	-- Some units have a default that depends on the input value
	-- (the first value if a range of values is used).
	-- If '!' is in the default, the first bang-delimited field is an
	-- expression that uses 'v' to represent the input value.
	-- Example: 'v < 120 ! small ! big ! suffix' (suffix is optional)
	-- evaluates 'v < 120' as a boolean with result
	-- 'smallsuffix' if (value < 120), or 'bigsuffix' otherwise.
	-- Input must use en digits and '.' decimal mark.
	local default = data_code.default_exceptions[unit_table.defkey or unit_table.symbol] or unit_table.default
	if not default then
		local per = unit_table.per
		if per then
			local function a_default(v, u)
				local success, ucode = get_default(v, u)
				if not success then
					return '?'  -- an unlikely error has occurred; will cause lookup of default to fail
				end
				-- Attempt to use only the first unit if a combination or output multiple.
				-- This is not bulletproof but should work for most cases.
				-- Where it does not work, the convert will need to specify the wanted output unit.
				local t = all_units[ucode]
				if t then
					local combo = t.combination
					if combo then
						-- For a multiple like ftin, the "first" unit (ft) is last in the combination.
						local i = t.multiple and table_len(combo) or 1
						ucode = combo[i]
					end
				else
					-- Try for an automatically generated combination.
					local item = ucode:match('^(.-)%+') or ucode:match('^(%S+)%s')
					if all_units[item] then
						return item
					end
				end
				return ucode
			end
			local unit1, unit2 = per[1], per[2]
			local def1 = (unit1 and a_default(value, unit1) or unit_table.vprefix or '')
			local def2 = a_default(1, unit2)  -- 1 because per unit of denominator
			return true, def1 .. '/' .. def2
		end
		return false, { 'cvt_no_default', unit_table.symbol }
	end
	if default:find('!', 1, true) == nil then
		return true, default
	end
	local t = split(default, '!')
	if #t == 3 or #t == 4 then
		local success, result = pcall(evaluate_condition, value, t[1])
		if success then
			default = result and t[2] or t[3]
			if #t == 4 then
				default = default .. t[4]
			end
			return true, default
		end
	end
	return false, { 'cvt_bad_default', unit_table.symbol }
end

local linked_pages  -- to record linked pages so will not link to the same page more than once

local function unlink(unit_table)
	-- Forget that the given unit has previously been linked (if it has).
	-- That is needed when processing a range of inputs or outputs when an id
	-- for the first range value may have been evaluated, but only an id for
	-- the last value is displayed, and that id may need to be linked.
	linked_pages[unit_table.unitcode or unit_table] = nil
end

local function make_link(link, id, unit_table)
	-- Return wikilink "[[link|id]]", possibly abbreviated as in examples:
	--   [[Mile|mile]]  --> [[mile]]
	--   [[Mile|miles]] --> [[mile]]s
	-- However, just id is returned if:
	-- * no link given (so caller does not need to check if a link was defined); or
	-- * link has previously been used during the current convert (to avoid overlinking).
	local link_key
	if unit_table then
		link_key = unit_table.unitcode or unit_table
	else
		link_key = link
	end
	if not link or link == '' or linked_pages[link_key] then
		return id
	end
	linked_pages[link_key] = true
	-- Following only works for language en, but it should be safe on other wikis,
	-- and overhead of doing it generally does not seem worthwhile.
	local l = link:sub(1, 1):lower() .. link:sub(2)
	if link == id or l == id then
		return '[[' .. id .. ']]'
	elseif link .. 's' == id or l .. 's' == id then
		return '[[' .. id:sub(1, -2) .. ']]s'
	else
		return '[[' .. link .. '|' .. id .. ']]'
	end
end

local function variable_name(clean, unit_table)
	-- For slwiki, a unit name depends on the value.
	-- Parameter clean is the unsigned rounded value in en digits, as a string.
	-- Value             Source    Example for "m"
	-- integer 1:        name1     meter  (also is the name of the unit)
	-- integer 2:        var{1}    metra
	-- integer 3 and 4:  var{2}    metri
	-- integer else:     var{3}    metrov (0 and 5 or more)
	-- real/fraction:    var{4}    metra
	-- var{i} means the i'th field in unit_table.varname if it exists and has
	-- an i'th field, otherwise name2.
	-- Fields are separated with "!" and are not empty.
	-- A field for a unit using an SI prefix has the prefix name inserted,
	-- replacing '#' if found, or before the field otherwise.
	local vname
	if clean == '1' then
		vname = unit_table.name1
	elseif unit_table.varname then
		local i
		if clean == '2' then
			i = 1
		elseif clean == '3' or clean == '4' then
			i = 2
		elseif clean:find('.', 1, true) then
			i = 4
		else
			i = 3
		end
		if i > 1 and varname == 'pl' then
			i = i - 1
		end
		vname = split(unit_table.varname, '!')[i]
	end
	if vname then
		local si_name = rawget(unit_table, 'si_name') or ''
		local pos = vname:find('#', 1, true)
		if pos then
			vname = vname:sub(1, pos - 1) .. si_name .. vname:sub(pos + 1)
		else
			vname = si_name .. vname
		end
		return vname
	end
	return unit_table.name2
end

local function linked_id(parms, unit_table, key_id, want_link, clean)
	-- Return final unit id (symbol or name), optionally with a wikilink,
	-- and update unit_table.sep if required.
	-- key_id is one of: 'symbol', 'sym_us', 'name1', 'name1_us', 'name2', 'name2_us'.
	local abbr_on = (key_id == 'symbol' or key_id == 'sym_us')
	if abbr_on and want_link then
		local symlink = rawget(unit_table, 'symlink')
		if symlink then
			return symlink  -- for exceptions that have the linked symbol built-in
		end
	end
	local multiplier = rawget(unit_table, 'multiplier')
	local per = unit_table.per
	if per then
		local paren1, paren2 = '', ''  -- possible parentheses around bottom unit
		local unit1 = per[1]  -- top unit_table, or nil
		local unit2 = per[2]  -- bottom unit_table
		if abbr_on then
			if not unit1 then
				unit_table.sep = ''  -- no separator in "$2/acre"
			end
			if not want_link then
				local symbol = unit_table.symbol_raw
				if symbol then
					return symbol  -- for exceptions that have the symbol built-in
				end
			end
			if (unit2.symbol):find('⋅', 1, true) then
				paren1, paren2 = '(', ')'
			end
		end
		local key_id2  -- unit2 is always singular
		if key_id == 'name2' then
			key_id2 = 'name1'
		elseif key_id == 'name2_us' then
			key_id2 = 'name1_us'
		else
			key_id2 = key_id
		end
		local result
		if abbr_on then
			result = '/'
		elseif omitsep then
			result = per_word
		elseif unit1 then
			result = ' ' .. per_word .. ' '
		else
			result = per_word .. ' '
		end
		if want_link and unit_table.link then
			if abbr_on or not varname then
				result = (unit1 and linked_id(parms, unit1, key_id, false, clean) or '') .. result .. linked_id(parms, unit2, key_id2, false, '1')
			else
				result = (unit1 and variable_name(clean, unit1) or '') .. result .. variable_name('1', unit2)
			end
			if omit_separator(result) then
				unit_table.sep = ''
			end
			return make_link(unit_table.link, result, unit_table)
		end
		if unit1 then
			result = linked_id(parms, unit1, key_id, want_link, clean) .. result
			if unit1.sep then
				unit_table.sep = unit1.sep
			end
		elseif omitsep then
			unit_table.sep = ''
		end
		return result .. paren1 .. linked_id(parms, unit2, key_id2, want_link, '1') .. paren2
	end
	if multiplier then
		-- A multiplier (like "100" in "100km") forces the unit to be plural.
		multiplier = from_en(multiplier)
		if not omitsep then
			multiplier = multiplier .. (abbr_on and '&nbsp;' or ' ')
		end
		if not abbr_on then
			if key_id == 'name1' then
				key_id = 'name2'
			elseif key_id == 'name1_us' then
				key_id = 'name2_us'
			end
		end
	else
		multiplier = ''
	end
	local id = unit_table.fixed_name or ((varname and not abbr_on) and variable_name(clean, unit_table) or unit_table[key_id])
	if omit_separator(id) then
		unit_table.sep = ''
	end
	if want_link then
		local link = data_code.link_exceptions[unit_table.linkey or unit_table.symbol] or unit_table.link
		if link then
			local before = ''
			local i = unit_table.customary
			if i == 1 and parms.opt_sp_us then
				i = 2  -- show "U.S." not "US"
			end
			if i == 3 and abbr_on then
				i = 4  -- abbreviate "imperial" to "imp"
			end
			local customary = text_code.customary_units[i]
			if customary then
				-- LATER: This works for language en only, but it's esoteric so ignore for now.
				local pertext
				if id:sub(1, 1) == '/' then
					-- Want unit "/USgal" to display as "/U.S. gal", not "U.S. /gal".
					pertext = '/'
					id = id:sub(2)
				elseif id:sub(1, 4) == 'per ' then
					-- Similarly want "per U.S. gallon", not "U.S. per gallon" (but in practice this is unlikely to be used).
					pertext = 'per '
					id = id:sub(5)
				else
					pertext = ''
				end
				-- Omit any "US"/"U.S."/"imp"/"imperial" from start of id since that will be inserted.
				local removes = (i < 3) and { 'US&nbsp;', 'US ', 'U.S.&nbsp;', 'U.S. ' } or { 'imp&nbsp;', 'imp ', 'imperial ' }
				for _, prefix in ipairs(removes) do
					local plen = #prefix
					if id:sub(1, plen) == prefix then
						id = id:sub(plen + 1)
						break
					end
				end
				before = pertext .. make_link(customary.link, customary[1]) .. ' '
			end
			id = before .. make_link(link, id, unit_table)
		end
	end
	return multiplier .. id
end

local function make_id(parms, which, unit_table)
	-- Return id, f where
	--   id = unit name or symbol, possibly modified
	--   f = true if id is a name, or false if id is a symbol
	-- using the value for index 'which', and for 'in' or 'out' (unit_table.inout).
	-- Result is '' if no symbol/name is to be used.
	-- In addition, set unit_table.sep = ' ' or '&nbsp;' or ''
	-- (the separator that caller will normally insert before the id).
	if parms.opt_values then
		unit_table.sep = ''
		return ''
	end
	local inout = unit_table.inout
	local info = unit_table.valinfo[which]
	local abbr_org = parms.abbr_org
	local adjectival = parms.opt_adjectival
	local lk = parms.lk
	local want_link = (lk == 'on' or lk == inout)
	local usename = unit_table.usename
	local singular = info.singular
	local want_name
	if usename then
		want_name = true
	else
		if abbr_org == nil then
			if parms.wantname then
				want_name = true
			end
			if unit_table.usesymbol then
				want_name = false
			end
		end
		if want_name == nil then
			local abbr = parms.abbr
			if abbr == 'on' or abbr == inout or (abbr == 'mos' and inout == 'out') then
				want_name = false
			else
				want_name = true
			end
		end
	end
	local key
	if want_name then
		if lk == nil and unit_table.builtin == 'hand' then
			want_link = true
		end
		if parms.opt_use_nbsp then
			unit_table.sep = '&nbsp;'
		else
			unit_table.sep = ' '
		end
		if parms.opt_singular then
			local value
			if inout == 'in' then
				value = info.value
			else
				value = info.absvalue
			end
			if value then  -- some unusual units do not always set value field
				value = abs(value)
				singular = (0 < value and value < 1.0001)
			end
		end
		if unit_table.engscale then
			-- engscale: so "|1|e3kg" gives "1 thousand kilograms" (plural)
			singular = false
		end
		key = (adjectival or singular) and 'name1' or 'name2'
		if parms.opt_sp_us then
			key = key .. '_us'
		end
	else
		if unit_table.builtin == 'hand' then
			if parms.opt_hand_hh then
				unit_table.symbol = 'hh'  -- LATER: might want i18n applied to this
			end
		end
		unit_table.sep = '&nbsp;'
		key = parms.opt_sp_us and 'sym_us' or 'symbol'
	end
	return linked_id(parms, unit_table, key, want_link, info.clean), want_name
end

local function decorate_value(parms, unit_table, which, number_word)
	-- If needed, update unit_table so values will be shown with extra information.
	-- For consistency with the old template (but different from fmtpower),
	-- the style to display powers of 10 includes "display:none" to allow some
	-- browsers to copy, for example, "10³" as "10^3", rather than as "103".
	local info
	local engscale = unit_table.engscale
	local prefix = unit_table.vprefix
	if engscale or prefix then
		info = unit_table.valinfo[which]
		if info.decorated then
			return  -- do not redecorate if repeating convert
		end
		info.decorated = true
		if engscale then
			local inout = unit_table.inout
			local abbr = parms.abbr
			if (abbr == 'on' or abbr == inout) and not parms.number_word then
				info.show = info.show ..
					'<span style="margin-left:0.2em">×<span style="margin-left:0.1em">' ..
					from_en('10') ..
					'</span></span><s style="display:none">^</s><sup>' ..
					from_en(tostring(engscale.exponent)) .. '</sup>'
			elseif number_word then
				local number_id
				local lk = parms.lk
				if lk == 'on' or lk == inout then
					number_id = make_link(engscale.link, engscale[1])
				else
					number_id = engscale[1]
				end
				-- WP:NUMERAL recommends "&nbsp;" in values like "12 million".
				info.show = info.show .. (parms.opt_adjectival and '-' or '&nbsp;') .. number_id
			end
		end
		if prefix then
			info.show = prefix .. info.show
		end
	end
end

local function process_input(parms, in_current)
	-- Processing required once per conversion.
	-- Return block of text to represent input (value/unit).
	if parms.opt_output_only or parms.opt_output_number_only or parms.opt_output_unit_only then
		parms.joins = { '', '' }
		return ''
	end
	local first_unit
	local composite = in_current.composite  -- nil or table of units
	if composite then
		first_unit = composite[1]
	else
		first_unit = in_current
	end
	local id1, want_name = make_id(parms, 1, first_unit)
	local sep = first_unit.sep  -- separator between value and unit, set by make_id
	local preunit = parms.preunit1
	if preunit then
		sep = ''  -- any separator is included in preunit
	else
		preunit = ''
	end
	if parms.opt_input_unit_only then
		parms.joins = { '', '' }
		if composite then
			local parts = { id1 }
			for i, unit in ipairs(composite) do
				if i > 1 then
					table.insert(parts, (make_id(parms, 1, unit)))
				end
			end
			id1 = table.concat(parts, ' ')
		end
		if want_name and parms.opt_adjectival then
			return preunit .. hyphenated(id1)
		end
		return  preunit .. id1
	end
	if parms.opt_also_symbol and not composite and not parms.opt_flip then
		local join1 = parms.joins[1]
		if join1 == ' (' or join1 == ' [' then
			parms.joins = { ' [' .. first_unit[parms.opt_sp_us and 'sym_us' or 'symbol'] .. ']' .. join1 , parms.joins[2] }
		end
	end
	if in_current.builtin == 'mach' and first_unit.sep ~= '' then  -- '' means omitsep with non-enwiki name
		local prefix = id1 .. '&nbsp;'
		local range = parms.range
		local valinfo = first_unit.valinfo
		local result = prefix .. valinfo[1].show
		if range then
			-- For simplicity and because more not needed, handle one range item only.
			local prefix2 = make_id(parms, 2, first_unit) .. '&nbsp;'
			result = range_text(range[1], want_name, parms, result, prefix2 .. valinfo[2].show, 'in')
		end
		return preunit .. result
	end
	if composite then
		-- Simplify: assume there is no range, and no decoration.
		local mid = (not parms.opt_flip) and parms.mid or ''
		local sep1 = '&nbsp;'
		local sep2 = ' '
		if parms.opt_adjectival and want_name then
			sep1 = '-'
			sep2 = '-'
		end
		if omitsep and sep == '' then
			-- Testing the id of the most significant unit should be sufficient.
			sep1 = ''
			sep2 = ''
		end
		local parts = { first_unit.valinfo[1].show .. sep1 .. id1 }
		for i, unit in ipairs(composite) do
			if i > 1 then
				table.insert(parts, unit.valinfo[1].show .. sep1 .. (make_id(parms, 1, unit)))
			end
		end
		return table.concat(parts, sep2) .. mid
	end
	local add_unit = (parms.abbr == 'mos') or
		parms[parms.opt_flip and 'out_range_x' or 'in_range_x'] or
		(not want_name and parms.abbr_range_x)
	local range = parms.range
	if range and not add_unit then
		unlink(first_unit)
	end
	local id = range and make_id(parms, range.n + 1, first_unit) or id1
	local extra, was_hyphenated = hyphenated_maybe(parms, want_name, sep, id, 'in')
	if was_hyphenated then
		add_unit = false
	end
	local result
	local valinfo = first_unit.valinfo
	if range then
		for i = 0, range.n do
			local number_word
			if i == range.n then
				add_unit = false
				number_word = true
			end
			decorate_value(parms, first_unit, i+1, number_word)
			local show = valinfo[i+1].show
			if add_unit then
				show = show .. first_unit.sep .. (i == 0 and id1 or make_id(parms, i+1, first_unit))
			end
			if i == 0 then
				result = show
			else
				result = range_text(range[i], want_name, parms, result, show, 'in')
			end
		end
	else
		decorate_value(parms, first_unit, 1, true)
		result = valinfo[1].show
	end
	return result .. preunit .. extra
end

local function process_one_output(parms, out_current)
	-- Processing required for each output unit.
	-- Return block of text to represent output (value/unit).
	local inout = out_current.inout  -- normally 'out' but can be 'in' for order=out
	local id1, want_name = make_id(parms, 1, out_current)
	local sep = out_current.sep  -- set by make_id
	local preunit = parms.preunit2
	if preunit then
		sep = ''  -- any separator is included in preunit
	else
		preunit = ''
	end
	if parms.opt_output_unit_only then
		if want_name and parms.opt_adjectival then
			return preunit .. hyphenated(id1)
		end
		return preunit .. id1
	end
	if out_current.builtin == 'mach' and out_current.sep ~= '' then  -- '' means omitsep with non-enwiki name
		local prefix = id1 .. '&nbsp;'
		local range = parms.range
		local valinfo = out_current.valinfo
		local result = prefix .. valinfo[1].show
		if range then
			-- For simplicity and because more not needed, handle one range item only.
			result = range_text(range[1], want_name, parms, result, prefix .. valinfo[2].show, inout)
		end
		return preunit .. result
	end
	local add_unit = (parms[parms.opt_flip and 'in_range_x' or 'out_range_x'] or
		(not want_name and parms.abbr_range_x)) and
		not parms.opt_output_number_only
	local range = parms.range
	if range and not add_unit then
		unlink(out_current)
	end
	local id = range and make_id(parms, range.n + 1, out_current) or id1
	local extra, was_hyphenated = hyphenated_maybe(parms, want_name, sep, id, inout)
	if was_hyphenated then
		add_unit = false
	end
	local result
	local valinfo = out_current.valinfo
	if range then
		for i = 0, range.n do
			local number_word
			if i == range.n then
				add_unit = false
				number_word = true
			end
			decorate_value(parms, out_current, i+1, number_word)
			local show = valinfo[i+1].show
			if add_unit then
				show = show .. out_current.sep .. (i == 0 and id1 or make_id(parms, i+1, out_current))
			end
			if i == 0 then
				result = show
			else
				result = range_text(range[i], want_name, parms, result, show, inout)
			end
		end
	else
		decorate_value(parms, out_current, 1, true)
		result = valinfo[1].show
	end
	if parms.opt_output_number_only then
		return result
	end
	return result .. preunit .. extra
end

local function make_output_single(parms, in_unit_table, out_unit_table)
	-- Return true, item where item = wikitext of the conversion result
	-- for a single output (which is not a combination or a multiple);
	-- or return false, t where t is an error message table.
	if parms.opt_order_out and in_unit_table.unitcode == out_unit_table.unitcode then
		out_unit_table.valinfo = in_unit_table.valinfo
	else
		out_unit_table.valinfo = collection()
		for _, v in ipairs(in_unit_table.valinfo) do
			local success, info = cvtround(parms, v, in_unit_table, out_unit_table)
			if not success then return false, info end
			out_unit_table.valinfo:add(info)
		end
	end
	return true, process_one_output(parms, out_unit_table)
end

local function make_output_multiple(parms, in_unit_table, out_unit_table)
	-- Return true, item where item = wikitext of the conversion result
	-- for an output which is a multiple (like 'ftin');
	-- or return false, t where t is an error message table.
	local inout = out_unit_table.inout  -- normally 'out' but can be 'in' for order=out
	local multiple = out_unit_table.multiple  -- table of scaling factors (will not be nil)
	local combos = out_unit_table.combination  -- table of unit tables (will not be nil)
	local abbr = parms.abbr
	local abbr_org = parms.abbr_org
	local disp = parms.disp
	local want_name = (abbr_org == nil and (disp == 'or' or disp == 'slash')) or
						not (abbr == 'on' or abbr == inout or abbr == 'mos')
	local want_link = (parms.lk == 'on' or parms.lk == inout)
	local mid = parms.opt_flip and parms.mid or ''
	local sep1 = '&nbsp;'
	local sep2 = ' '
	if parms.opt_adjectival and want_name then
		sep1 = '-'
		sep2 = '-'
	end
	local do_spell = parms.opt_spell_out
	parms.opt_spell_out = nil  -- so the call to cvtround does not spell the value
	local function make_result(info, isfirst)
		local fmt, outvalue, sign
		local results = {}
		for i = 1, #combos do
			local tfrac, thisvalue, strforce
			local out_current = combos[i]
			out_current.inout = inout
			local scale = multiple[i]
			if i == 1 then  -- least significant unit ('in' from 'ftin')
				local decimals
				out_current.frac = out_unit_table.frac
				local success, outinfo = cvtround(parms, info, in_unit_table, out_current)
				if not success then return false, outinfo end
				if isfirst then
					out_unit_table.valinfo = { outinfo }  -- in case output value of first least significant unit is needed
				end
				sign = outinfo.sign
				tfrac = outinfo.fraction_table
				if outinfo.is_scientific then
					strforce = outinfo.show
					decimals = ''
				elseif tfrac then
					decimals = ''
				else
					local show = outinfo.show  -- number as a string in local language
					local p1, p2 = show:find(numdot, 1, true)
					decimals = p1 and show:sub(p2 + 1) or ''  -- text after numdot, if any
				end
				fmt = '%.' .. ulen(decimals) .. 'f'  -- to reproduce precision
				if decimals == '' then
					if tfrac then
						outvalue = floor(outinfo.raw_absvalue)  -- integer part only; fraction added later
					else
						outvalue = floor(outinfo.raw_absvalue + 0.5)  -- keep all integer digits of least significant unit
					end
				else
					outvalue = outinfo.absvalue
				end
			end
			if scale then
				outvalue, thisvalue = divide(outvalue, scale)
			else
				thisvalue = outvalue
			end
			local id
			if want_name then
				if varname then
					local clean
					if strforce or tfrac then
						clean = '.1'  -- dummy value to force name for floating point
					else
						clean = format(fmt, thisvalue)
					end
					id = variable_name(clean, out_current)
				else
					local key = 'name2'
					if parms.opt_adjectival then
						key = 'name1'
					elseif tfrac then
						if thisvalue == 0 then
							key = 'name1'
						end
					elseif parms.opt_singular then
						if 0 < thisvalue and thisvalue < 1.0001 then
							key = 'name1'
						end
					else
						if thisvalue == 1 then
							key = 'name1'
						end
					end
					id = out_current[key]
				end
			else
				id = out_current['symbol']
			end
			if i == 1 and omit_separator(id) then
				-- Testing the id of the least significant unit should be sufficient.
				sep1 = ''
				sep2 = ''
			end
			if want_link then
				local link = out_current.link
				if link then
					id = make_link(link, id, out_current)
				end
			end
			local strval
			local spell_inout = (i == #combos or outvalue == 0) and inout or ''  -- trick so the last value processed (first displayed) has uppercase, if requested
			if strforce and outvalue == 0 then
				sign = ''  -- any sign is in strforce
				strval = strforce  -- show small values in scientific notation; will only use least significant unit
			elseif tfrac then
				local wholestr = (thisvalue > 0) and tostring(thisvalue) or nil
				strval = format_fraction(parms, spell_inout, false, wholestr, tfrac.numstr, tfrac.denstr, do_spell)
			else
				strval = (thisvalue == 0) and from_en('0') or with_separator(parms, format(fmt, thisvalue))
				if do_spell then
					strval = spell_number(parms, spell_inout, strval) or strval
				end
			end
			table.insert(results, strval .. sep1 .. id)
			if outvalue == 0 then
				break
			end
			fmt = '%.0f'  -- only least significant unit can have a non-integral value
		end
		local reversed, count = {}, #results
		for i = 1, count do
			reversed[i] = results[count + 1 - i]
		end
		return true, sign .. table.concat(reversed, sep2)
	end
	local valinfo = in_unit_table.valinfo
	local success, result = make_result(valinfo[1], true)
	if not success then return false, result end
	local range = parms.range
	if range then
		for i = 1, range.n do
			local success, result2 = make_result(valinfo[i+1])
			if not success then return false, result2 end
			result = range_text(range[i], want_name, parms, result, result2, inout)
		end
	end
	return true, result .. mid
end

local function process(parms, in_unit_table, out_unit_table)
	-- Return true, s, outunit where s = final wikitext result,
	-- or return false, t where t is an error message table.
	linked_pages = {}
	local success, bad_output
	local bad_input_mcode = in_unit_table.bad_mcode  -- nil if input unit is a valid convert unit
	local out_unit = parms.out_unit
	if out_unit == nil or out_unit == '' or type(out_unit) == 'function' then
		if bad_input_mcode or parms.opt_input_unit_only then
			bad_output = ''
		else
			local getdef = type(out_unit) == 'function' and out_unit or get_default
			success, out_unit = getdef(in_unit_table.valinfo[1].value, in_unit_table)
			parms.out_unit = out_unit
			if not success then
				bad_output = out_unit
			end
		end
	end
	if not bad_output and not out_unit_table then
		success, out_unit_table = lookup(parms, out_unit, 'any_combination')
		if success then
			local mismatch = check_mismatch(in_unit_table, out_unit_table)
			if mismatch then
				bad_output = mismatch
			end
		else
			bad_output = out_unit_table
		end
	end
	local lhs, rhs
	local flipped = parms.opt_flip and not bad_input_mcode
	if bad_output then
		rhs = (bad_output == '') and '' or message(parms, bad_output)
	elseif parms.opt_input_unit_only then
		rhs = ''
	else
		local combos  -- nil (for 'ft' or 'ftin'), or table of unit tables (for 'm ft')
		if not out_unit_table.multiple then  -- nil/false ('ft' or 'm ft'), or table of factors ('ftin')
			combos = out_unit_table.combination
		end
		local frac = parms.frac  -- nil or denominator of fraction for output values
		if frac then
			-- Apply fraction to the unit (if only one), or to non-SI units (if a combination),
			-- except that if a precision is also specified, the fraction only applies to
			-- the hand unit; that allows the following result:
			-- {{convert|156|cm|in hand|1|frac=2}} → 156 centimetres (61.4 in; 15.1½ hands)
			-- However, the following is handled elsewhere as a special case:
			-- {{convert|156|cm|hand in|1|frac=2}} → 156 centimetres (15.1½ hands; 61½ in)
			if combos then
				local precision = parms.precision
				for _, unit in ipairs(combos) do
					if unit.builtin == 'hand' or (not precision and not unit.prefixes) then
						unit.frac = frac
					end
				end
			else
				out_unit_table.frac = frac
			end
		end
		local outputs = {}
		local imax = combos and #combos or 1  -- 1 (single unit) or number of unit tables
		if imax == 1 then
			parms.opt_order_out = nil  -- only useful with an output combination
		end
		if not flipped and not parms.opt_order_out then
			-- Process left side first so any duplicate links (from lk=on) are suppressed
			-- on right. Example: {{convert|28|e9pc|e9ly|abbr=off|lk=on}}
			lhs = process_input(parms, in_unit_table)
		end
		for i = 1, imax do
			local success, item
			local out_current = combos and combos[i] or out_unit_table
			out_current.inout = 'out'
			if i == 1 then
				if imax > 1 and out_current.builtin == 'hand' then
					out_current.out_next = combos[2]  -- built-in hand can influence next unit in a combination
				end
				if parms.opt_order_out then
					out_current.inout = 'in'
				end
			end
			if out_current.multiple then
				success, item = make_output_multiple(parms, in_unit_table, out_current)
			else
				success, item = make_output_single(parms, in_unit_table, out_current)
			end
			if not success then return false, item end
			outputs[i] = item
		end
		if parms.opt_order_out then
			lhs = outputs[1]
			table.remove(outputs, 1)
		end
		local sep = parms.table_joins and parms.table_joins[2] or parms.join_between
		rhs = table.concat(outputs, sep)
	end
	if flipped or not lhs then
		local input = process_input(parms, in_unit_table)
		if flipped then
			lhs = rhs
			rhs = input
		else
			lhs = input
		end
	end
	if parms.join_before then
		lhs = parms.join_before .. lhs
	end
	local wikitext
	if bad_input_mcode then
		if bad_input_mcode == '' then
			wikitext = lhs
		else
			wikitext = lhs .. message(parms, bad_input_mcode)
		end
	elseif parms.table_joins then
		wikitext = parms.table_joins[1] .. lhs .. parms.table_joins[2] .. rhs
	else
		wikitext = lhs .. parms.joins[1] .. rhs .. parms.joins[2]
	end
	if parms.warnings and not bad_input_mcode then
		wikitext = wikitext .. parms.warnings
	end
	return true, get_styles(parms) .. wikitext, out_unit_table
end

local function main_convert(frame)
	-- Do convert, and if needed, do it again with higher default precision.
	local parms = { frame = frame }  -- will hold template arguments, after translation
	set_config(frame.args)
	local success, result = get_parms(parms, frame:getParent().args)
	if success then
		if type(result) ~= 'table' then
			return tostring(result)
		end
		local in_unit_table = result
		local out_unit_table
		for _ = 1, 2 do  -- use counter so cannot get stuck repeating convert
			success, result, out_unit_table = process(parms, in_unit_table, out_unit_table)
			if success and parms.do_convert_again then
				parms.do_convert_again = false
			else
				break
			end
		end
	end
	-- If input=x gives a problem, the result should be just the user input
	-- (if x is a property like P123 it has been replaced with '').
	-- An unknown input unit would display the input and an error message
	-- with success == true at this point.
	-- Also, can have success == false with a message that outputs an empty string.
	if parms.input_text then
		if success and not parms.have_problem then
			return result
		end
		local cat
		if parms.tracking then
			-- Add a tracking category using the given text as the category sort key.
			-- There is currently only one type of tracking, but in principle multiple
			-- items could be tracked, using different sort keys for convenience.
			cat = wanted_category('tracking', parms.tracking)
		end
		return parms.input_text .. (cat or '')
	end
	return success and result or message(parms, result)
end

local function _unit(unitcode, options)
	-- Helper function for Module:Val to look up a unit.
	-- Parameter unitcode must be a string to identify the wanted unit.
	-- Parameter options must be nil or a table with optional fields:
	--   value = number (for sort key; default value is 1)
	--   scaled_top = nil for a normal unit, or a number for a unit which is
	--                the denominator of a per unit (for sort key)
	--   si = { 'symbol', 'link' }
	--                (a table with two strings) to make an SI unit
	--                that will be used for the look up
	--   link = true if result should be [[linked]]
	--   sort = 'on' or 'debug' if result should include a sort key in a
	--                span element ('debug' makes the key visible)
	--   name = true for the name of the unit instead of the symbol
	--   us = true for the US spelling of the unit, if any
	-- Return nil if unitcode is not a non-empty string.
	-- Otherwise return a table with fields:
	--   text = requested symbol or name of unit, optionally linked
	--   scaled_value = input value adjusted by unit scale; used for sort key
	--   sortspan = span element with sort key like that provided by {{ntsh}},
	--     calculated from the result of converting value
	--     to a base unit with scale 1.
	--   unknown = true if the unitcode was not known
	unitcode = strip(unitcode)
	if unitcode == nil or unitcode == '' then
		return nil
	end
	set_config({})
	linked_pages = {}
	options = options or {}
	local parms = {
		abbr = options.name and 'off' or 'on',
		lk = options.link and 'on' or nil,
		opt_sp_us = options.us and true or nil,
		opt_ignore_error = true,  -- do not add pages using this function to 'what links here' for Module:Convert/extra
		opt_sortable_on = options.sort == 'on' or options.sort == 'debug',
		opt_sortable_debug = options.sort == 'debug',
	}
	if options.si then
		-- Make a dummy table of units (just one unit) for lookup to use.
		-- This makes lookup recognize any SI prefix in the unitcode.
		local symbol = options.si[1] or '?'
		parms.unittable = { [symbol] = {
			_name1 = symbol,
			_name2 = symbol,
			_symbol = symbol,
			utype = symbol,
			scale = symbol == 'g' and 0.001 or 1,
			prefixes = 1,
			default = symbol,
			link = options.si[2],
		}}
	end
	local success, unit_table = lookup(parms, unitcode, 'no_combination')
	if not success then
		unit_table = setmetatable({
			symbol = unitcode, name2 = unitcode, utype = unitcode,
			scale = 1, default = '', defkey = '', linkey = '' }, unit_mt)
	end
	local value = tonumber(options.value) or 1
	local clean = tostring(abs(value))
	local info = {
		value = value,
		altvalue = value,
		singular = (clean == '1'),
		clean = clean,
		show = clean,
	}
	unit_table.inout = 'in'
	unit_table.valinfo = { info }
	local sortspan, scaled_value
	if options.sort then
		sortspan, scaled_value = make_table_or_sort(parms, value, info, unit_table, options.scaled_top)
	end
	return {
		text = make_id(parms, 1, unit_table),
		sortspan = sortspan,
		scaled_value = scaled_value,
		unknown = not success and true or nil,
	}
end

return { convert = main_convert, _unit = _unit }
Retrieved from "https://wiki.randomisland.ca/index.php?title=Module:Convert&oldid=190"