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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 ' ' 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 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).
        -- 1/2    : sign, numerator, denominator
        -- 1+2/3  : signed_wholenumber, numerator, denominator
        '<span class="frac nowrap">%s<sup>%s</sup>&frasl;<sub>%s</sub></span>',
        '<span class="frac nowrap">%s<span class="visualhide">&nbsp;</span><sup>%s</sup>&frasl;<sub>%s</sub></span>',
    },
    { -- Like {{sfrac}} (fraction horizontal bar).
        -- 1//2   : sign, numerator, denominator (sign should probably be before the fraction, but then it can wrap, and html is already too long)
        -- 1+2//3 : signed_wholenumber, numerator, denominator
        '<span class="sfrac nowrap" style="display:inline-block; vertical-align:-0.5em; font-size:85%%; text-align:center;"><span style="display:block; line-height:1em; padding:0 0.1em;">%s%s</span><span class="visualhide">/</span><span style="display:block; line-height:1em; padding:0 0.1em; border-top:1px solid;">%s</span></span>',
        '<span class="sfrac nowrap">%s<span class="visualhide">&nbsp;</span><span style="display:inline-block; vertical-align:-0.5em; font-size:85%%; text-align:center;"><span style="display:block; line-height:1em; padding:0 0.1em;">%s</span><span class="visualhide">/</span><span style="display:block; line-height:1em; padding:0 0.1em; border-top:1px solid;">%s</span></span></span>',
    },
}
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
    if wholestr then
        local decorated = with_separator(parms, wholestr)
        if negative then
            decorated = MINUS .. decorated
        end
        local fmt = fracfmt[style][2]
        wikitext = format(fmt, decorated, from_en(numstr), from_en(denstr))
    else
        local sign = negative and MINUS or ''
        wikitext = format(fracfmt[style][1], sign, from_en(numstr), from_en(denstr))
    end
    if do_spell then
        if negative then
            if wholestr then
                wholestr = '-' .. wholestr
            else
                numstr = '-' .. numstr
            end
        end
        wikitext = spell_number(parms, inout, wholestr, numstr, denstr) or wikitext
    end
    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, 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 }
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