Module:Convert

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)

local MINUS = '−'  -- Unicode U+2212 MINUS SIGN (UTF-8: e2 88 92)
local format = string.format
local floor = math.floor
local log10 = math.log10

-- Names when using engineering notation (a prefix of "eN" where N is a number).
-- key = { "name", "linked name, if link wanted" }
-- LATER: Perhaps this should be in convertdata to keep output text in one place.
local eng_scales = {
    ["3"]  = { "thousand" },
    ["6"]  = { "million" },
    ["9"]  = { "billion", "[[1000000000 (number)|billion]]" },
    ["12"] = { "trillion", "[[1000000000000 (number)|trillion]]" },
    ["15"] = { "quadrillion", "[[1000000000000000 (number)|quadrillion]]" },
}

-- Configuration options to keep magic values in one location.
local numdot, numsep, maxsigfig, lang
-- Following specify the conversion data which is defined in another module
-- because it is too large to be conveniently included here.
-- To allow easy comparison between "require" and "loadData", a config option
-- can be set to control which is used.
local SIprefixes, units, default_exceptions, link_exceptions

local function set_config(frame)
    -- Set configuration options from template #invoke or defaults.
    local args = frame.args
    numdot = args.numdot or '.'       -- decimal mark before fractional digits
    numsep = args.numsep or ','       -- thousands separator for numbers (',', '.', '')
    maxsigfig = args.maxsigfig or 14  -- maximum number of significant figures
    lang = args.lang or 'en'          -- language code for messages
    -- Scribunto sets the global variable 'mw'.
    -- A testing program can set the global variable 'is_test_run'.
    local convertdata
    local data_module = is_test_run and "convertdata" or "Module:Convert/data"
    if args.use_require then
        convertdata = require(data_module)
    else
        convertdata = mw.loadData(data_module)
    end
    SIprefixes = convertdata.SIprefixes
    units = convertdata.units
    default_exceptions = convertdata.default_exceptions
    link_exceptions = convertdata.link_exceptions
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

------------------------------------------------------------------------
-- BEGIN: Messages that may be displayed by Module:Convert.
-- LATER: Perhaps move following to another module to simplify this module.
local all_categories = {
    ['en'] = {
        general = '[[Category:Convert error]]',
        unknown = '[[Category:Convert unknown unit]]',
        mismatch = '[[Category:Convert dimension mismatch]]',
    },
}

-- Following puts wanted style around each unit code marked like '...%{ft%}...'.
local unitcode_regex = '%%([{}])'
local unitcode_replace = { ['{'] = '<code style="background:transparent;">', ['}'] = '</code>' }

local all_messages = {
    -- All output messages.
    ['en'] = {
        -- The prefix is inserted before each message.
        cvt_prefix = '[[Module talk:Convert|Conversion error]]:',
        -- Messages; each is a numbered table: { 'error text', 'category key', gsub_regex, gsub_table }.
        cvt_bad_default = { 'Unit "%s" has an invalid default', 'unknown' },
        cvt_bad_num = { 'Value "%s" must be a number', 'general' },
        cvt_bad_num2 = { 'Second value "%s" must be a number', 'general' },
        cvt_bad_prec = { 'Parameter precision "%s" must be an integer', 'general' },
        cvt_bad_sigfig = { 'Parameter sigfig "%s" must be an integer', 'general' },
        cvt_bad_unit = { 'Unit "%s" is invalid here', 'unknown' },
        cvt_big_prec = { 'Precision "%s" is too large', 'general' },
        cvt_bug_convert = { 'Bug: Cannot convert between specified units', 'general' },
        cvt_mismatch = { 'Cannot convert "%s" to "%s"', 'mismatch' },
        cvt_no_default = { 'Unit "%s" has no default output unit', 'unknown' },
        cvt_no_num = { 'Need value', 'general' },
        cvt_no_num2 = { 'Need second value', 'general' },
        cvt_no_unit = { 'Need name of unit', 'unknown' },
        cvt_should_be = { '%s', 'general', unitcode_regex, unitcode_replace },
        cvt_sigfig_pos = { 'sigfig "%s" must be positive', 'general' },
        cvt_unknown = { 'Unit "%s" is not known', 'unknown' },
    },
}

local messages = {}  -- simulating how it would be if in another module

function messages.message(msg, lang)
    -- Return wikitext for an error message, including category if specified
    -- for the message type.
    -- msg = numbered table:
    --    msg[1] = 'cvt_xxx' (string used as a key to get message info)
    --    msg[2] = 'parm1' (string to replace first %s if any in message)
    --    msg[3] = 'parm2' (string to replace second %s if any in message)
    --    msg[4] = 'parm3' (string to replace third %s if any in message)
    -- lang = 'en' (default), or other language code.
    lang = lang or 'en'
    local mlang = all_messages[lang]
    if mlang then
        local t = mlang[msg[1]]
        if t then
            -- t[1] = message text, t[2] = category, t[3] = gsub_regex, t[4] = gsub_replace
            local text = format(t[1] or 'Missing message',
                msg[2] or '?',
                msg[3] or '?',
                msg[4] or '?')
            local cat = all_categories[lang][t[2]] or ''
            local prefix = mlang['cvt_prefix'] or ''
            local regex, replace = t[3], t[4]
            if regex and replace then
                text = text:gsub(regex, replace)
            end
            return '<span style="color:black; background-color:orange;">' ..
                    prefix .. ' ' .. text .. cat .. '</span>'
        end
    end
    return 'Convert internal error: unknown message'
end
-- END: Messages that may be displayed by Module:Convert.
------------------------------------------------------------------------
-- BEGIN: Code required only for built-in units.
-- LATER: Perhaps move following 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 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 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,
    -- or a for a unit that accepts prefixes but where no prefix was used.
    -- In the latter case, and before use, fields symbol, name1, name1_us
    -- must be set from _symbol, _name1, _name1_us respectively.
    __index = function (self, key)
        local value
        if key == 'name1' or key == 'sym_us' then
            value = self.symbol
        elseif key == 'name2' then
            value = self.name1 .. 's'
        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 's'.
                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 .. 's'
            else
                value = self.name2
            end
        elseif key == 'link' then
            value = self.name1
        elseif key == 'engscale' or key == 'per' then
            value = false
        else
            return nil
        end
        rawset(self, key, value)
        return value
    end
}

local unit_prefixed_mt = {
    -- Metatable to get missing values for a unit that accepts SI prefixes,
    -- and where a prefix has been used.
    -- Before use, fields si_name, si_prefix must be defined.
    __index = function (self, key)
        local value
        if key == 'symbol' then
            value = self.si_prefix .. self._symbol
        elseif key == 'sym_us' then
            value = self.symbol  -- always the same as sym_us for prefixed units
        elseif key == 'name1' then
            local pos = rawget(self, 'prefix_position') or 1
            value = self._name1
            value = value:sub(1, pos - 1) .. self.si_name .. value:sub(pos)
        elseif key == 'name2' then
            value = self.name1 .. 's'
        elseif key == 'name1_us' then
            value = rawget(self, '_name1_us')
            if value then
                local pos = rawget(self, 'prefix_position') or 1
                value = value:sub(1, pos - 1) .. self.si_name .. value:sub(pos)
            else
                value = self.name1
            end
        elseif key == 'name2_us' then
            if rawget(self, '_name1_us') then
                value = self.name1_us .. 's'
            else
                value = self.name2
            end
        elseif key == 'link' then
            value = self.name1
        elseif key == 'engscale' or key == 'per' then
            value = false
        else
            return nil
        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.
    __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) / unit2.scale
        elseif key == 'engscale' then
            value = false
        else
            return nil
        end
        rawset(self, key, value)
        return value
    end
}

local function lookup(unitcode, sp, what)
    -- 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 'sp' is nil, or is 'us' for US spelling of SI prefixes and
    -- the symbol and names of the unit. If 'us', the result includes field
    -- sp_us = true (that field may also have been in the unit definition).
    -- 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, underscores in unitcode are replaced
    -- with spaces so {{convert|350|board_feet}} --> 350 board feet (0.83 m³).
    if unitcode == nil or unitcode == '' then
        return false, { 'cvt_no_unit' }
    end
    unitcode = unitcode:gsub('_', ' ')
    local t = units[unitcode]
    if t then
        if t.shouldbe then
            return false, { 'cvt_should_be', t.shouldbe }
        end
        local force_sp_us = (sp == 'us')
        if t.sp_us then
            force_sp_us = true
            sp = 'us'
        end
        local target = t.target  -- nil, or unitcode is an alias for this target
        if target then
            local success, result = lookup(target, sp, what)
            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
        local per = t.per  -- nil/false, or a numbered table for "x/y" units
        if per then
            local result = { utype = t.utype, per = {} }
            override_from(result, t, { 'default', 'invert', 'iscomplex', 'symbol', 'symlink' })
            result.symbol_raw = (result.symbol or false)  -- to distinguish between a defined exception and a metatable calculation
            local cvt = result.per
            local prefix
            for i, v in ipairs(per) do
                if i == 1 and (v == '$' or v == '£') then
                    prefix = v
                else
                    local success, t = lookup(v, sp, 'no_combination')
                    if not success then return false, t end
                    cvt[i] = t
                    if t.sp_us then  -- if the top or bottom unit forces sp=us, set the per unit to use the correct name/symbol id
                        force_sp_us = true
                    end
                end
            end
            if prefix then
                result.vprefix = prefix
            else
                result.vprefix = false  -- to avoid calling __index
            end
            result.sp_us = force_sp_us
            return true, setmetatable(result, unit_per_mt)
        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 multiple == nil) 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(v, sp, multiple and 'no_combination' or 'only_multiple')
                if not success then return false, t end
                cvt[i] = t
            end
            return true, result
        end
        local result = shallow_copy(t)
        result.sp_us = force_sp_us
        if result.prefixes then
            result.symbol = result._symbol
            result.name1 = result._name1
            result.name1_us = result._name1_us
        end
        return true, setmetatable(result, unit_mt)
    end
    for plen = 2, 1, -1 do
        -- Look for an SI prefix; should never occur with an alias.
        -- Check for longer prefix first ('dam' is decametre).
        -- Micro (µ) is two bytes in utf-8, so is found with plen = 2.
        local prefix = unitcode:sub(1, plen)
        local si = SIprefixes[prefix]
        if si then
            local t = units[unitcode:sub(plen+1)]
            if t and t.prefixes then
                local result = shallow_copy(t)
                if sp == 'us' then
                    result.sp_us = true
                end
                if result.sp_us and si.name_us then
                    result.si_name = si.name_us
                else
                    result.si_name = si.name
                end
                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 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.
    local exponent, baseunit = unitcode:match('^e(%d+)(.*)')
    if exponent then
        local engscale = eng_scales[exponent]
        if engscale then
            local success, result = lookup(baseunit, sp, 'no_combination')
            if not success then return false, result end
            if not (result.offset or result.builtin or result.engscale) then
                result.defkey = unitcode  -- key to lookup default exception
                engscale.exponent = exponent
                result.engscale = engscale
                result.scale = result.scale * 10 ^ tonumber(exponent)
                return true, result
            end
        end
    end
    return false, { 'cvt_unknown', unitcode }
end

local function ntsh_complement(text)
    -- Return text (string of digits) after subtracting each digit from 9.
    local result = ''
    local first, last = 1, #text
    while first <= last do
        local lenblock = last + 1 - first
        if lenblock > 12 then
            lenblock = 12
        end
        local block = tonumber(text:sub(first, first + lenblock - 1))
        local nines = tonumber(string.rep('9', lenblock))
        local fmt = '%0' .. tostring(lenblock) .. '.0f'
        result = result .. format(fmt, nines - block)
        first = first + lenblock
    end
    return result
end

local function ntsh(n, debug)
    -- Return html text to be used for a hidden sort key so that
    -- the given number will be sorted in numeric order.
    -- If debug == 'yes', output is in a box (not hidden).
    -- This implements Template:Ntsh (number table sorting, hidden).
    local result, i, f, style
    if n >= 0 then
        if n > 1e16 then
            result = '~'
        else
            i, f = math.modf(n)
            f = floor(1e6 * f)
            result = format('&1%016.0f%06d', i, f)
        end
    else
        n = -n
        if n > 1e16 then
            result = '!'
        else
            i, f = math.modf(n)
            f = floor(1e6 * f)
            result = format('%016.0f%06d', i, f)
            result = '&0' .. ntsh_complement(result)
        end
    end
    if debug == 'yes' then
        style = 'border:1px solid'
    else
        style = 'display:none'
    end
    return '<span style="' .. style .. '">' .. result .. '</span>'
end

local function hyphenated(name)
    -- Return a hyphenated form of given name (for adjectival usage).
    -- 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)"].
    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, -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

local function change_sign(text)
    -- Change sign of text for correct appearance because it is negated.
    if text:sub(1, 1) == '-' then
        return text:sub(2)
    end
    return '-' .. text
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 with_separator(text)
    -- Return text with thousand separators inserted.
    -- The given text is like '123' or '12345.6789' or '1.23e45'
    -- (e notation can only occur when processing an input value).
    -- The text has no sign (caller inserts that later, if necessary).
    -- Separator is inserted only in the integer part of the significand
    -- (not after numdot, and not after 'e' or 'E').
    -- Four-digit integer parts have a separator (like '1,234').
    if numsep == '' then
        return text
    end
    local last = text:match('()[' .. numdot .. 'eE]')  -- () returns position
    if last == nil then
        last = #text
    else
        last = last - 1  -- index of last character before dot/e/E
    end
    if last >= 4 then
        local groups = {}
        local first = last % 3
        if first > 0 then
            table.insert(groups, text:sub(1, first))
        end
        first = first + 1
        while first < last do
            table.insert(groups, text:sub(first, first+2))
            first = first + 3
        end
        return table.concat(groups, numsep) .. text:sub(last+1)
    end
    return text
end

-- Input values can use values like 1.23e12, but are never displayed
-- using exponent notation like 1.23×10¹².
-- Very small or very large output values use exponent notation.
-- Use format(fmtpower, significand, exponent) where each arg is a string.
local fmtpower = '%s<span style="margin:0 .15em 0 .25em">×</span>10<sup>%s</sup>'

local function with_exponent(show, exponent)
    -- Return wikitext to display the implied value in exponent notation.
    if #show > 1 then
        show = show:sub(1, 1) .. numdot .. show:sub(2)
    end
    return format(fmtpower, show, use_minus(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, frac = math.modf(log10(value))
    if frac >= 0 then
        frac = frac - 1
        exp = exp + 1
    end
    local digits = format('%.0f', 10^(frac + 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

local function format_number(show, exponent, isnegative)
    -- Return t where t is a table with the results; fields:
    --   show = wikitext formatted to display implied value
    --   is_scientific = true if show uses scientific notation
    --   clean = unformatted show (possibly adjusted and with inserted numdot)
    --   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:
    -- * Includes a Unicode minus if isnegative.
    -- * Has numsep inserted where necessary.
    -- * Uses scientific notation for very small or large values.
    -- * Has no more than maxsigfig significant digits
    --   (same as old template and {{#expr}}).
    local sign = isnegative and MINUS or ''
    local maxlen = maxsigfig
    if exponent == nil then
        local integer, dot, fraction = show:match('^(%d*)([' .. numdot .. ']?)(.*)')
        if #integer >= 10 then
            show = integer .. fraction
            exponent = #integer
        elseif integer == '0' or integer == '' then
            local zeros, figs = fraction:match('^(0*)([^0]?.*)')
            if #figs == 0 then
                if #zeros > maxlen then
                    show = '0' .. numdot .. zeros:sub(1, maxlen)
                end
            elseif #zeros >= 4 then
                show = figs
                exponent = -#zeros
            elseif #figs > maxlen then
                show = '0' .. numdot .. zeros .. figs:sub(1, maxlen)
            end
        else
            maxlen = maxlen + #dot
            if #show > maxlen then
                show = show:sub(1, maxlen)
            end
        end
    end
    if exponent then
        if #show > maxlen then
            show = show:sub(1, maxlen)
        end
        if exponent > 10 or exponent <= -4 or (exponent == 10 and show ~= '1000000000') then
            -- Rounded value satisfies: value >= 1e9 or value < 1e-4 (1e9 = 0.1e10).
            return {
                clean = '.' .. show,
                exponent = exponent,
                sign = sign,
                show = sign .. with_exponent(show, exponent-1),
                is_scientific = true }
        end
        if exponent >= #show then
            show = show .. string.rep('0', exponent - #show)  -- result has no dot
        elseif exponent <= 0 then
            show = '0' .. numdot .. string.rep('0', -exponent) .. show
        else
            show = show:sub(1, exponent) .. numdot .. show:sub(exponent+1)
        end
    end
    if isnegative and show:match('^0.?0*$') then
        sign = ''  -- don't show minus if result is negative but rounds to zero
    end
    return {
        clean = show,
        sign = sign,
        show = sign .. with_separator(show) }
end

-- Fraction output format (like old template).
-- frac1: sign, numerator, denominator
-- frac2: wholenumber, sign, numerator, denominator
local frac1 = '<span style="white-space:nowrap">%s<sup>%s</sup>&frasl;<sub>%s</sub></span>'
local frac2 = '<span class="frac nowrap">%s<s style="display:none">%s</s><sup>%s</sup>&frasl;<sub>%s</sub></span>'

local function extract_fraction(text, negative)
    -- If text represents a fraction, return value, show where
    -- value is a number and show is a string.
    -- Otherwise, return nil.
    --
    -- In the following, '(3/8)' represents the wikitext required to
    -- display a fraction with numerator 3 and denominator 8.
    -- In the wikitext, Unicode minus is used for a negative value.
    --   text          value, show            value, show
    --                 if not negative       if negative
    --   3 / 8         0.375, '(3/8)'        -0.375, '−(3/8)'
    --   2 + 3 / 8     2.375, '2(3/8)'       -1.625, '−2(−3/8)'
    --   2 - 3 / 8     1.625, '2(−3/8)'      -2.375, '−2(3/8)'
    --   1 + 20/8      3.5  , '1/(20/8)'     1.5   , '−1/(−20/8)'
    --   1 - 20/8      -1.5., '1(−20/8)'     -3.5  , '−1(20/8)'
    -- Wherever an integer appears above, numbers like 1.25 or 12.5e-3
    -- (which may be negative) are also accepted (like old template).
    -- Template interprets '1.23e+2+12/24' as '123(12/24)' = 123.5!
    local lhs, negfrac, rhs, numstr, numerator, denstr, denominator, wholestr, whole, value
    lhs, denstr = text:match('^%s*([^/]-)%s*/%s*(.-)%s*$')
    denominator = tonumber(denstr)
    if denominator == nil then return nil end
    wholestr, negfrac, rhs = lhs:match('^%s*(.-[^eE])%s*([+-])%s*(.-)%s*$')
    if wholestr == nil or wholestr == '' then
        wholestr = nil
        whole = 0
        numstr = lhs
    else
        whole = tonumber(wholestr)
        if whole == nil then return nil end
        numstr = rhs
    end
    negfrac = (negfrac == '-')
    numerator = tonumber(numstr)
    if numerator == nil then return nil end
    if negative == negfrac or wholestr == nil then
        value = whole + numerator / denominator
    else
        value = whole - numerator / denominator
        numstr = change_sign(numstr)
    end
    if tostring(value):find('#', 1, true) then
        return nil  -- overflow or similar
    end
    numstr = use_minus(numstr)
    denstr = use_minus(denstr)
    local wikitext
    if wholestr then
        local sign = negative and MINUS or '+'
        if negative then
            wholestr = change_sign(wholestr)
        end
        wikitext = format(frac2, use_minus(wholestr), sign, numstr, denstr)
    else
        local sign = negative and MINUS or ''
        wikitext = format(frac1, sign, numstr, denstr)
    end
    return value, wikitext
end

local missing = { 'cvt_no_num', 'cvt_no_num2' }
local invalid = { 'cvt_bad_num', 'cvt_bad_num2' }

local function extract_number(text, which, 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.
    -- Parameter 'which' (1 or 2) selects which input value is being
    -- processed (to select the appropriate error message, if needed).
    -- Before processing, the input text is cleaned:
    -- * Any thousand separators (valid or not) are removed.
    -- * Any sign (and optional following whitespace) 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
    --   singular = true if value is 1 (to use singular form of units)
    --            = false if value is -1 (like old template)
    --   clean    = cleaned text with any separators and sign removed
    --   show     = text formatted for output
    -- For show:
    -- * Thousand separators are inserted.
    -- * If negative, a Unicode minus is used; otherwise the sign
    --   is '+' (if the input text used '+'), or is ''.
    -- TODO Think about fact that the input value might be like 1.23e+123.
    -- Will the exponent break anything?
    text = strip(text)
    if text == nil or text == '' then return false, { missing[which] } end
    local clean, sign
    if numsep == '' then
        clean = text
    else
        clean = text:gsub('[' .. numsep .. ']', '')  -- use '[.]' if numsep is '.'
    end
    -- Remove any sign character (assuming a number starts with '.' or a digit).
    sign, clean = clean:match('^%s*([^ .%d]*)%s*(.*)')
    if sign == nil or clean == nil then
        return false, { missing[which] }  -- should never occur
    end
    local propersign, isnegative
    if sign == MINUS or sign == '-' or sign == '&minus;' then
        propersign = MINUS
        isnegative = true
    elseif sign == '+' then
        propersign = '+'
        isnegative = false
    elseif sign == '' then
        propersign = ''
        isnegative = false
    else
        return false, { invalid[which], text }
    end
    local show, singular
    local value = tonumber(clean)
    if value == nil then
        if not no_fraction then
            value, show = extract_fraction(clean, isnegative)
        end
        if value == nil then
            return false, { invalid[which], text }
        end
        singular = false  -- any fraction (even with value 1) is regarded as plural
    end
    if show == nil then
        singular = (value == 1 and not isnegative)
        show = propersign .. with_separator(clean)
    end
    if isnegative and (value ~= 0) then
        value = -value
    end
    return true, {
        value = value,
        singular = singular,
        clean = clean,
        show = show
    }
end

local function require_integer(text, invalid)
    -- Return true, n where n = integer equivalent to given text,
    -- or return false, t where t is an error message table.
    -- Input should be the text for a simple integer (no separators, no Unicode minus).
    -- Using regex avoids irritations with input like '-0.000001'.
    if text == nil then return false, { 'cvt_no_num' } end
    if text:match('^-?%d+$') == nil then
        return false, { invalid, text }
    end
    return true, tonumber(text)
end

local function range_text(range, want_name, parms, before, after)
    -- Return before .. rtext .. after
    -- where rtext is the text that separates two values in a range.
    local adj = parms.adj
    local rtext, adj_text, exception
    if type(range) == 'table' then
        -- Table must specify range text for abbr=off and for abbr=on,
        -- and may specify range text for 'adj=on',
        -- and may specify exception = true.
        rtext = range[want_name and 'off' or 'on']
        adj_text = range['adj']
        exception = range['exception']
    else
        rtext = range
    end
    if adj == 'on' 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_parms(pframe)
    -- If successful, return true, args, unit where
    --   args 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.
    -- Some of the named args that are added here could be provided by the
    -- user of the template.
    -- 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 range_types = {  -- text to separate values in a range
        ['by']     = ' by ',
        ['-']      = '–',
        ['and']    = { ['off'] = ' and ', ['on'] = ' and ', exception = true },
        ['or']     = { ['off'] = ' or ' , ['on'] = ' or ' , exception = true },
        ['to']     = { ['off'] = ' to ' , ['on'] = ' to ' , exception = true },
        ['xx']     = '&nbsp;×&nbsp;',
        ['to(-)']  = { ['off'] = '&nbsp;to ', ['on'] = '–' },
        ['+/-']    = { ['off'] = '&nbsp;±&nbsp;', ['on'] = '&nbsp;±&nbsp;', ['adj'] = '&nbsp;±&nbsp;' },
        ['x']      = { ['off'] = ' by ', ['on'] = ' ×&nbsp;', is_range_x = true },
    }
    local range_aliases = {
        ['and(-)']  = 'and',
        ['&']       = 'and',
        ['–']       = '-',
        ['&ndash;'] = '-',
        ['to-']     = 'to(-)',
        ['×']       = 'x',
        ['±']       = '+/-',
    }
    local success, info1, info2
    local args = {}  -- arguments passed to template
    for k, v in pairs(pframe.args) do
        args[k] = v
    end
    success, info1 = extract_number(args[1], 1)
    if not success then return false, info1 end
    local in_unit, precision
    local next = strip(args[2])
    local i = 3
    local range = range_types[next] or range_types[range_aliases[next]]
    if range == nil then
        in_unit = next
    else
        args.range = range
        args.is_range_x = range.is_range_x
        success, info2 = extract_number(args[3], 2)
        if not success then return false, info2 end
        in_unit = strip(args[4])
        i = 5
    end
    local success, in_unit_table = lookup(in_unit, args.sp, 'no_combination')
    if not success then return false, in_unit_table end
    if args.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.valinfo = { info1, info2 }  -- info2 is nil if no range
    in_unit_table.inout = 'in'  -- this is an input unit
    if not range then
        local subdivs = in_unit_table.subdivs  -- nil or a table of allowed subdivisions
        if subdivs then
            -- Look for a composite input unit like "|2|ft|6|in".
            local subcode = strip(args[i + 1])
            local subdiv = subdivs[subcode]
            if subdiv then
                -- subcode = unit code of a valid subdivision of main unit,
                -- but it can be replaced by the optional subdiv[3].
                local success, subunit, subinfo
                success, subunit = lookup(subdiv[3] or subcode, args.sp, 'no_combination')
                if not success then return false, subunit end  -- should never occur
                success, subinfo = extract_number(args[i], 1)
                if not success then return false, subinfo end
                i = i + 2
                subunit.inout = 'in'
                subunit.valinfo = { subinfo }
                -- Calculate total value as a number of subdivisions.
                -- subdiv[1] = number of subdivisions per main unit (integer > 1).
                local total = info1.value * subdiv[1] + subinfo.value
                in_unit_table = {
                        utype = in_unit_table.utype,
                        scale = subunit.scale,
                        default = subdiv[2] or in_unit_table.default,
                        valinfo = { { value = total, clean = subinfo.clean } },
                        composite = { in_unit_table, subunit },
                    }
            end
        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(args[i], 1, true)
        if success then
            i = i + 1
            in_unit_table.altitude = info.value
        end
    end
    next = strip(args[i])
    i = i + 1
    if tonumber(next) then
        precision = next
    else
        args.out_unit = next
        next = strip(args[i])
        if tonumber(next) then
            i = i + 1
            precision = next
        end
    end
    if args.adj == nil and args.sing ~= nil then
        args.adj = args.sing  -- sing (singular) is an old equivalent of adj
    end
    if args.adj == 'mid' then
        args.adj = 'on'
        next = args[i]
        i = i + 1
        if next == nil then
            args.mid = ''
        else  -- mid-text words
            if next:sub(1, 1) == '-' then
                args.mid = next
            else
                args.mid = ' ' .. next
            end
        end
    elseif args.adj == 'on' then
        args.mid = ''
    end
    if precision == nil then
        if tonumber(args[i]) then
            precision = strip(args[i])
            i = i + 1
        end
    end
    -- Change disp to standard name so subsequent processing can ignore aliases.
    local disp = args.disp
    if disp == '5' then
        args.disp5 = true
    elseif disp == 'flip5' then
        args.disp5 = true
        args.disp = 'flip'
    elseif disp == 'number' then
        args.disp = 'output number only'
    elseif disp == 'out' or disp == '2' then
        args.disp = 'output only'
    elseif disp == 'u2' then
        args.disp = 'unit2'
    elseif disp == 's' or disp == '/' then
        args.disp = 'slash'
    end
    disp = args.disp
    if disp == 'x' then
        args.joins = { args[i] or '', args[i+1] or '' }
    end
    args.precision = args.precision or precision  -- allow named parameter
    local abbr = args.abbr
    if abbr == nil then
        -- Default is to abbreviate output (use symbol), or input if flipped.
        args.abbr = (disp == 'flip') and 'in' or 'out'
    else
        args.abbr_org = abbr  -- original abbr (as entered by user)
        if disp == 'flip' then  -- 'in' = LHS, 'out' = RHS
            if abbr == 'in' then
                abbr = 'out'
            elseif abbr == 'out' then
                abbr = 'in'
            end
        end
        args.abbr = abbr
    end
    return true, args, in_unit_table
end

local function default_precision(invalue, inclean, outvalue, in_current, out_current, extra)
    -- Return a default value for precision (an integer like 2, 0, -2).
    -- 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 utype = out_current.utype
    -- Count digits after decimal mark, handling cases like '12.345e6'.
    local exponent
    local integer, dot, fraction, expstr = inclean:match('^(%d*)([' .. numdot .. ']?)(%d*)(.*)')
    local e = expstr:sub(1, 1)
    if e == 'e' or e == 'E' then
        exponent = tonumber(expstr:sub(2))
    end
    if dot == '' then
        prec = -integer:match('0*$'):len()
    else
        prec = #fraction
    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
    local exception = (utype == 'temperature' and not
            (in_current.exception == 'temperature' or out_current.exception == 'temperature'))
    if exception then
        -- 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 = math.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 0
        end
        if out_current.symbol == 'ft' and floor(invalue) == invalue then
            -- More precision when output ft with input value equal to an integer.
            adjust = -log10(in_current.scale)
        else
            adjust = log10(math.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 math.max(floor(prec + adjust), minprec)
end

local function convert(invalue, inclean, 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 then
        -- Fuel efficiency (there are no built-ins for this type of unit).
        if in_current.invert * out_current.invert < 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).
        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.
            -- Fractions 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 fraction 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, fraction = math.modf(invalue)
            local outvalue = (integer + 2.5 * fraction) * (inscale / outscale)
            local inch_value = 4 * integer + 10 * fraction  -- equivalent number of inches
            local fraction = inclean:match('[' .. numdot .. '](.*)') or ''
            local fmt
            if fraction == '' then
                fmt = '%.0f'
            else
                fmt = '%.' .. format('%d', #fraction - 1) .. 'f'
            end
            return true, {
                invalue = inch_value,
                inclean = format(fmt, inch_value),
                outvalue = outvalue,
                minprec = 0,
            }
        end
    end
    return false, { 'cvt_bug_convert' }  -- should never occur
end

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 from converting value in info,
    --      using the rounding specified in parms.
    --   singular = true if result is positive, and (after rounding)
    --      is "1", or like "1.00";
    --   (and more fields shown below, and a calculated 'absvalue' field).
    -- or return true, nil if no value specified;
    -- or return false, t where t is an error message table.
    -- This code combines convert/round because some rounding requires
    -- knowledge of what we are converting.
    local invalue, inclean, show, exponent, singular
    if info then
        invalue, inclean = info.value, info.clean
    end
    if invalue == nil or invalue == '' then
        return true, nil
    end
    if out_current.builtin == 'hand' then
        -- Convert to hands, then convert the fractional part to inches.
        local dummy_unit_table = { scale = out_current.scale }
        local success, outinfo = cvtround(parms, info, in_current, dummy_unit_table)
        if not success then return false, outinfo end
        local fmt
        local fraction = (outinfo.show):match('[' .. numdot .. '](.*)') or ''
        if fraction == '' then
            if not outinfo.use_default_precision then
                return true, outinfo
            end
            fmt = '%.0f'
        else
            fmt = '%.' .. format('%d', #fraction - 1) .. 'f'
        end
        local hands, inches = math.modf(tonumber(outinfo.raw_absvalue))
        inches = format(fmt, inches * 4)
        if inches:sub(1, 1) == '4' then
            hands = hands + 1
            inches = '0' .. inches:sub(2)
            if tonumber(inches) == 0 then
                inches = '0'
            end
        end
        if inches:sub(2, 2) == numdot then
            inches = inches:sub(1, 1) .. inches:sub(3)
        end
        return true, {
            sign = outinfo.sign,
            singular = outinfo.singular,
            show = outinfo.sign .. with_separator(format('%d', hands)) .. '.' .. inches
        }
    end
    local outvalue, extra = convert(invalue, inclean, in_current, out_current)
    if extra then
        if not outvalue then return false, extra end
        invalue = extra.invalue or invalue
        inclean = extra.inclean or inclean
        outvalue = extra.outvalue
    end
    local isnegative
    if outvalue < 0 then
        isnegative = true
        outvalue = -outvalue
    end
    local success, use_default_precision
    local precision = parms.precision
    local sigfig = parms.sigfig
    local disp5 = parms.disp5
    if precision then
        -- Ignore sigfig, disp5.
        success, precision = require_integer(precision, 'cvt_bad_prec')
        if not success then return false, precision end
    elseif sigfig then
        -- Ignore disp5.
        success, sigfig = require_integer(sigfig, 'cvt_bad_sigfig')
        if not success then return false, sigfig end
        if sigfig <= 0 then
            return false, { 'cvt_sigfig_pos', parms.sigfig }
        end
        show, exponent = make_sigfig(outvalue, sigfig)
    elseif disp5 then
        show = format('%.0f', floor((outvalue / 5) + 0.5) * 5)
    else
        use_default_precision = true
        precision = default_precision(invalue, inclean, outvalue, in_current, out_current, extra)
    end
    if precision then
        if precision >= 0 then
            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.
                outvalue = outvalue + 2e-14
            end
            local fmt = '%.' .. format('%d', precision) .. 'f'
            local success
            success, show = pcall(format, fmt, outvalue)
            if not success then
                return false, { 'cvt_big_prec', tostring(precision) }
            end
        else
            precision = -precision  -- #digits to zero (in addition to digits after dot)
            local shift = 10 ^ precision
            show = format('%.0f', outvalue/shift)
            if show ~= '0' then
                exponent = #show + precision
            end
        end
    end
    -- TODO Does following work when exponent ~= nil?
    --      What if show = '1000' and exponent = 1 (value = .1000*10^1 = 1)?
    --      What if show = '1000' and exponent = 2 (value = .1000*10^2 = 10)?
    if (show == '1' or show:match('^1%.0*$') ~= nil) and not isnegative then
        -- Use match because on some systems 0.99999999999999999 is 1.0.
        singular = true
    end
    local t = format_number(show, exponent, isnegative)
    t.singular = singular
    t.raw_absvalue = outvalue  -- absolute value before rounding
    t.use_default_precision = use_default_precision
    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

local disp_joins = {
    ['or']         = { ' or '    , ''  },
    ['sqbr-sp']    = { ' ['      , ']' },
    ['sqbr-nbsp']  = { '&nbsp;[' , ']' },
    ['comma']      = { ', '      , ''  },
    ['slash-sp']   = { ' / '     , ''  },
    ['slash-nbsp'] = { '&nbsp;/ ', ''  },
    ['slash-nosp'] = { '/'       , ''  },
    ['b']          = { ' ('      , ')' },
    ['br']         = { '<br/>'   , ''  },
}

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)
    --    '<' 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.
    local default = default_exceptions[unit_table.defkey or unit_table.symbol] or unit_table.default
    if default == nil then
        return false, { 'cvt_no_default', unit_table.symbol }
    end
    if default:find('!', 1, true) == nil then
        return true, default
    end
    local t = {}
    default = default .. '!'  -- to get last item
    for item in default:gmatch('%s*(.-)%s*!') do
        table.insert(t, item)  -- split on '!', removing leading/trailing whitespace
    end
    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 function linked_id(unit_table, key_id, want_link)
    -- 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 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
        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 unit1 then
            result = ' per '
        else
            result = 'per '
        end
        if unit1 then
            result = linked_id(unit1, key_id, want_link) .. result
        end
        return result .. linked_id(unit2, key_id2, want_link)
    end
    if multiplier then
        -- A multiplier (like "100" in "100km") forces the unit to be plural.
        if abbr_on then
            multiplier = multiplier .. '&nbsp;'
        else
            multiplier = multiplier .. ' '
            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[key_id]
    if want_link then
        local link = link_exceptions[unit_table.symbol] or unit_table.link
        if link then
            local customary_units = {
                '[[United States customary units|US]] ',
                '[[United States customary units|U.S.]] ',
                '[[Imperial unit|imperial]] ',
                '[[Imperial unit|imp]] ',
            }
            local i = unit_table.customary
            if i == 1 and unit_table.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 = customary_units[i]
            if customary then
                -- 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
            else
                customary = ''
            end
            -- Change, for example: [[Mile|mile]] --> [[mile]], and [[Mile|miles]] --> [[mile]]s.
            local l = link:sub(1, 1):lower() .. link:sub(2)
            if link == id or l == id then
                id = customary .. '[[' .. id .. ']]'
            elseif link .. 's' == id or l .. 's' == id then
                id = customary .. '[[' .. id:sub(1, -2) .. ']]s'
            else
                id = customary .. '[[' .. link .. '|' .. id .. ']]'
            end
        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 1st or 2nd values (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).
    local abbr = parms.abbr
    if abbr == 'values' then
        unit_table.sep = ''
        return ''
    end
    local inout = unit_table.inout
    local valinfo = unit_table.valinfo
    local abbr_org = parms.abbr_org
    local adj = parms.adj
    local disp = parms.disp
    local lk = parms.lk
    local usename = unit_table.usename
    local singular = valinfo[which].singular
    if usename then
        -- Old template does something like this.
        if lk == 'on' or lk == inout then
            -- A linked unit uses the standard singular.
        else
            -- Set non-standard singular.
            if inout == 'in' then
                if adj ~= 'on' and (abbr_org == 'out' or disp == 'flip') then
                    local value = valinfo[which].value
                    singular = (0 < value and value < 1.0001)
                end
            else
                if (abbr_org == 'on') or
                (disp == nil and (abbr_org == nil or abbr_org == 'out')) or
                (disp == 'flip' and abbr_org == 'in') then
                    singular = (valinfo[which].absvalue < 1.0001 and
                                not valinfo[which].is_scientific)
                end
            end
        end
    end
    if unit_table.engscale then
        singular = false  -- so 1 e3kg gives 1 thousand kilograms (plural)
    end
    local key_name = (adj == 'on' or (singular and not parms.is_range_x)) and 'name1' or 'name2'
    local key_symbol = 'symbol'
    if unit_table.sp_us then
        key_name = key_name .. '_us'
        key_symbol = 'sym_us'
    end
    local want_name
    if usename then
        want_name = true
    else
        if abbr_org == nil then
            if disp == 'br' or disp == 'or' or disp == 'slash' then
                want_name = true
            end
            if unit_table.utype == 'temperature' or unit_table.utype == 'temperature change' then
                if not (unit_table.exception == 'temperature') then
                    want_name = false
                end
            end
        end
        if want_name == nil then
            if abbr == 'on' or abbr == inout or (abbr == 'mos' and inout == 'out') then
                want_name = false
            else
                want_name = true
            end
        end
    end
    unit_table.sep = want_name and ' ' or '&nbsp;'
    return linked_id(unit_table, want_name and key_name or key_symbol, lk == 'on' or lk == inout), want_name
end

local function decorate_value(parms, unit_table, which)
    -- If needed, update unit_table.valinfo 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 engscale = unit_table.engscale
    if engscale then
        local inout = unit_table.inout
        local info = unit_table.valinfo[which]
        local abbr = parms.abbr
        if abbr == 'on' or abbr == inout then
            info.show = info.show ..
                '<span style="margin-left:0.2em">×<span style="margin-left:0.1em">10</span></span><s style="display:none">^</s><sup>'
                .. engscale.exponent .. '</sup>'
        else
            local number_id
            local lk = parms.lk
            if lk == 'on' or lk == inout then
                number_id = engscale[2] or engscale[1]
            else
                number_id = engscale[1]
            end
            info.show = info.show .. (parms.adj == 'on' and '-' or ' ') .. number_id
        end
    end
    local prefix = unit_table.vprefix
    if prefix then
        local info = unit_table.valinfo[which]
        info.show = prefix .. info.show
    end
end

local function process_input(parms, in_current)
    -- Processing required once per conversion.
    -- Return block of text to represent input (value/unit).
    local disp = parms.disp
    if disp == 'output only' or
       disp == 'output number only' or
       disp == 'unit2' then
        parms.joins = { '', '' }
        return ''
    end
    local first_unit, second_unit
    local composite = in_current.composite  -- nil or table of units
    if composite then
        first_unit = composite[1]
        second_unit = composite[2]
    else
        first_unit = in_current
    end
    local id1, want_name = make_id(parms, 1, first_unit)
    if disp == 'unit' then
        parms.joins = { '', '' }
        if composite then
            id1 = id1 .. ' ' .. make_id(parms, 1, second_unit)
        end
        if want_name and parms.adj == 'on' then
            return hyphenated(id1)
        end
        return id1
    end
    local abbr = parms.abbr
    if disp == nil then  -- special case for the most common setting
        parms.joins = disp_joins['b']
    elseif disp ~= 'x' then
        -- Old template does this.
        if disp == 'slash' then
            if parms.abbr_org == 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 disp_joins['b']
    end
    if in_current.builtin == 'mach' then
        local prefix = id1 .. '&nbsp;'
        local range = parms.range
        local valinfo = first_unit.valinfo
        local result = prefix .. valinfo[1].show
        if range then
            result = range_text(range, want_name, parms, result, prefix .. valinfo[2].show)
        end
        return result
    end
    if composite then
        -- Simplify: assume that adj is off, and there is no range, and no decoration.
        return first_unit.valinfo[1].show .. '&nbsp;' .. id1 .. ' ' ..
               second_unit.valinfo[1].show .. '&nbsp;' .. (make_id(parms, 1, second_unit))
    end
    local result
    local extra = ''
    local sep = first_unit.sep
    local mos = (abbr == 'mos')
    local range = parms.range
    local id = (range == nil) and id1 or make_id(parms, 2, first_unit)
    if id ~= '' then
        if want_name and parms.adj == 'on' then
            mos = false  -- if hyphenated, suppress repeat of unit in a range
            extra = '-' .. hyphenated(id) .. parms.mid
        else
            extra = sep .. id
        end
    end
    local valinfo = first_unit.valinfo
    if range == nil then
        decorate_value(parms, first_unit, 1)
        result = valinfo[1].show
    else
        if mos then
            decorate_value(parms, in_current, 1)
            decorate_value(parms, in_current, 2)
            result = valinfo[1].show .. sep .. id1
        elseif parms.is_range_x and not want_name then
            if abbr == 'in' or abbr == 'on' then
                decorate_value(parms, in_current, 1)
            end
            decorate_value(parms, in_current, 2)
            result = valinfo[1].show .. sep .. id
        else
            if abbr == 'in' or abbr == 'on' then
                decorate_value(parms, in_current, 1)
            end
            decorate_value(parms, in_current, 2)
            result = valinfo[1].show
        end
        result = range_text(range, want_name, parms, result, valinfo[2].show)
    end
    return result .. 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 id1, want_name = make_id(parms, 1, out_current)
    local disp = parms.disp
    if disp == 'unit2' then
        if want_name and parms.adj == 'on' then
            return hyphenated(id1)
        end
        return id1
    end
    if out_current.builtin == 'mach' then
        local prefix = id1 .. '&nbsp;'
        local range = parms.range
        local valinfo = out_current.valinfo
        local result = prefix .. valinfo[1].show
        if range then
            result = range_text(range, want_name, parms, result, prefix .. valinfo[2].show)
        end
        return result
    end
    local result
    local extra, id, sep = '', '', ''
    local range = parms.range
    if disp ~= 'output number only' then
        id = (range == nil) and id1 or make_id(parms, 2, out_current)
        if id ~= '' then
            sep = out_current.sep
            if want_name and parms.adj == 'on' then
                extra = '-' .. hyphenated(id)
            else
                extra = sep .. id
            end
        end
    end
    local valinfo = out_current.valinfo
    if range == nil then
        decorate_value(parms, out_current, 1)
        result = valinfo[1].show
    else
        local abbr = parms.abbr
        if parms.is_range_x and not want_name then
            if abbr == 'out' or abbr == 'on' then
                decorate_value(parms, out_current, 1)
            end
            decorate_value(parms, out_current, 2)
            result = valinfo[1].show .. sep .. id
        else
            if abbr == 'out' or abbr == 'on' then
                decorate_value(parms, out_current, 1)
            end
            decorate_value(parms, out_current, 2)
            result = valinfo[1].show
        end
        result = range_text(range, want_name, parms, result, valinfo[2].show)
    end
    return result .. 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.
    local success, info1, info2
    local valinfo = in_unit_table.valinfo
    success, info1 = cvtround(parms, valinfo[1], in_unit_table, out_unit_table)
    if not success then return false, info1 end
    success, info2 = cvtround(parms, valinfo[2], in_unit_table, out_unit_table)
    if not success then return false, info2 end
    out_unit_table.valinfo = { info1, info2 }
    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 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 == 'out' or abbr == 'mos')
    local want_link = (parms.lk == 'on' or parms.lk == 'out')
    local function make_result(info)
        local outvalue, sign, fmt
        local results = {}
        for i = 1, #combos do
            local thisvalue
            local out_current = combos[i]
            out_current.inout = 'out'
            local scale = multiple[i]
            if i == 1 then  -- least significant unit ('in' from 'ftin')
                local success, outinfo = cvtround(parms, info, in_unit_table, out_current)
                if not success then return false, outinfo end
                sign = outinfo.sign
                local fraction = (outinfo.show):match('[' .. numdot .. '](.*)') or ''
                fmt = '%.' .. #fraction .. 'f'  -- to reproduce precision
                if fraction == '' then
                    outvalue = floor(outinfo.raw_absvalue + 0.5)  -- keep all integer digits of least significant unit
                else
                    outvalue = outinfo.absvalue
                end
            end
            if scale then
                outvalue, thisvalue = floor(outvalue / scale), outvalue % scale
            else
                thisvalue = outvalue
            end
            local id
            if want_name then
                id = out_current[(thisvalue == 1) and 'name1' or 'name2']
            else
                id = out_current['symbol']
            end
            if want_link then
                local link = out_current.link
                if link then
                    id = '[[' .. link .. '|' .. id .. ']]'
                end
            end
            local strval = (thisvalue == 0) and '0' or with_separator(format(fmt, thisvalue))
            table.insert(results, strval .. '&nbsp;' .. id)
            if outvalue == 0 then
                break
            end
            fmt = '%.0f'  -- only least significant unit can have a fraction
        end
        local reversed, count = {}, #results
        for i = 1, count do
            reversed[i] = results[count + 1 - i]
        end
        return true, sign .. table.concat(reversed, ' ')
    end
    local valinfo = in_unit_table.valinfo
    local success, result = make_result(valinfo[1])
    if not success then return false, result end
    local range = parms.range
    if range then
        local success, result2 = make_result(valinfo[2])
        if not success then return false, result2 end
        result = range_text(range, want_name, parms, result, result2)
    end
    return true, result
end

local function process(parms, in_unit_table)
    -- Return true, s where s = final wikitext result,
    -- or return false, t where t is an error message table.
    local success, out_unit_table
    local invalue1 = in_unit_table.valinfo[1].value
    local out_unit = parms.out_unit
    if out_unit == nil or out_unit == '' then
        success, out_unit = get_default(invalue1, in_unit_table)
        if not success then return false, out_unit end
    end
    success, out_unit_table = lookup(out_unit, parms.sp, 'any_combination')
    if not success then return false, out_unit_table end
    if in_unit_table.utype ~= out_unit_table.utype then
        return false, { 'cvt_mismatch', in_unit_table.utype, out_unit_table.utype }
    end
    local outputs = {}
    local combos  -- nil (for 'ft' or 'ftin'), or table of unit tables (for 'm ft')
    if out_unit_table.multiple == nil then  -- nil ('ft' or 'm ft'), or table of factors ('ftin')
        combos = out_unit_table.combination
    end
    local imax = combos and #combos or 1  -- 1 (single unit) or number of unit tables
    for i = 1, imax do
        local success, item
        local out_current = combos and combos[i] or out_unit_table
        out_current.inout = 'out'
        if out_current.multiple == nil then
            success, item = make_output_single(parms, in_unit_table, out_current)
        else
            success, item = make_output_multiple(parms, in_unit_table, out_current)
        end
        if not success then return false, item end
        table.insert(outputs, item)
    end
    local disp = parms.disp
    local in_block = process_input(parms, in_unit_table)
    local out_block = (disp == 'unit') and '' or table.concat(outputs, '; ')
    if disp == 'flip' then
        in_block, out_block = out_block, in_block
    end
    local wikitext = in_block .. parms.joins[1] .. out_block .. parms.joins[2]
    if parms.sortable == 'on' then
        wikitext = ntsh(invalue1, parms.debug) .. wikitext
    end
    return true, wikitext
end

local function main_convert(frame)
    set_config(frame)
    local result
    local success, parms, in_unit_table = get_parms(frame:getParent())
    if success then
        success, result = process(parms, in_unit_table)
    else
        result = parms
    end
    if success then
        return result
    end
    return messages.message(result, lang)
end

return { convert = main_convert }