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 abs = math.abs
local floor = math.floor
local format = string.format
local log10 = math.log10

-- Configuration options to keep magic values in one location.
local numdot, numsep, maxsigfig
-- The conversion data and message text are defined in separate modules.
-- To allow easy comparison between "require" and "loadData", a config option
-- can be set to control which is used.
local SIprefixes, default_exceptions, link_exceptions, units
local all_categories, all_messages, customary_units, disp_joins, en_option_value
local eng_scales, local_option_name, range_aliases, range_types

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
    -- Scribunto sets the global variable 'mw'.
    -- A testing program can set the global variable 'is_test_run'.
    local convertdata, converttext, data_module, text_module
    if is_test_run then
        data_module = "convertdata"
        text_module = "converttext"
    else
        data_module = "Module:Convert/data"
        text_module = "Module:Convert/text"
    end
    if args.use_require then
        convertdata = require(data_module)
        converttext = require(text_module)
    else
        convertdata = mw.loadData(data_module)
        converttext = mw.loadData(text_module)
    end
    SIprefixes = convertdata.SIprefixes
    default_exceptions = convertdata.default_exceptions
    link_exceptions = convertdata.link_exceptions
    units = convertdata.units
    all_categories = converttext.all_categories
    all_messages = converttext.all_messages
    customary_units = converttext.customary_units
    disp_joins = converttext.disp_joins
    en_option_value = converttext.en_option_value
    eng_scales = converttext.eng_scales
    local_option_name = converttext.local_option_name
    range_aliases = converttext.range_aliases
    range_types = converttext.range_types
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 message(mcode)
    -- 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 first %s if any in message)
    --    mcode[3] = 'parm2' (string to replace second %s if any in message)
    --    mcode[4] = 'parm3' (string to replace third %s if any in message)
    local msg = all_messages[mcode[1]]
    if msg then
        local text = format(msg[1] or 'Missing message',
            mcode[2] or '?',
            mcode[3] or '?',
            mcode[4] or '?')
        local cat = all_categories[msg[2]] or ''
        local prefix = all_messages[msg.warning and 'cvt_prefix_warning' or 'cvt_prefix_error'] or ''
        local suffix = (prefix == '') and '' or '</span>'
        local regex, replace = msg.regex, msg.replace
        if regex and replace then
            text = text:gsub(regex, replace)
        end
        return prefix .. ' ' .. text .. cat .. suffix
    end
    return 'Convert internal error: unknown message'
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 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,
    -- 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, opt_sp_us, 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 opt_sp_us is true for US spelling of SI prefixes and
    -- the symbol and name of the unit. If true, 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 = opt_sp_us
        if t.sp_us then
            force_sp_us = true
            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(target, opt_sp_us, 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, opt_sp_us, '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
                        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, opt_sp_us, 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 opt_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, opt_sp_us, '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
                result.engscale = engscale
                result.scale = result.scale * 10 ^ tonumber(exponent)
                return true, result
            end
        end
    end
    return false, { 'cvt_unknown', unitcode }
end

local function valid_number(num)
    -- Return true if num is a valid number.
    -- Expressed as a string, overflow or other problems are indicated with
    -- text like "1.#INF" or ".#IND" which are regarded as invalid here.
    if type(num) == 'number' and tostring(num):find('#', 1, true) == nil then
        return true
    end
end

local function ntsh(num, 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, style
    if not valid_number(num) then
        if num < 0 then
            result = '1000000000000000000'
        else
            result = '9000000000000000000'
        end
    elseif num == 0 then
        result = '5000000000000000000'
    else
        local mag = floor(log10(abs(num)) + 1e-14)
        local prefix
        if num > 0 then
            prefix = 7000 + mag
        else
            prefix = 2999 - mag
            num = num + 10^(mag+1)
        end
        result = format('%d', prefix) .. format('%015.0f', floor(num * 10^(14-mag)))
    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 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
    if parms.opt_adjectival then
        if inout == (parms.opt_flip and 'out' or 'in') then
            mid = parms.mid
        end
        if want_name then
            return '-' .. hyphenated(id) .. (mid or ''), true
        end
    end
    return sep .. id .. (mid or '')
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(parms, text)
    -- Return text with thousand separators inserted, if wanted.
    -- 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 parms.opt_nocomma or 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(parms, 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, if wanted.
    -- * 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(parms, 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 not valid_number(value) 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(parms, 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:
    -- * Value is rounded, if wanted.
    -- * Thousand separators are inserted, 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).
    -- 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 not valid_number(value) then  -- for example, "1e310" overflows
        return false, { 'cvt_invalid_num' }
    end
    if show == nil then
        singular = (value == 1 and not isnegative)
        local precision = parms.input_precision
        if precision and 0 <= precision and precision <= 8 then
            value = value + 2e-14  -- fudge for some common cases of bad rounding
            local fmt = '%.' .. format('%d', precision) .. 'f'
            show = fmt:format(value)
        else
            show = clean
        end
        show = propersign .. with_separator(parms, show)
    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,
    -- limited size). Using regex avoids irritations with input like '-0.000001'.
    if text == nil then return false, { 'cvt_no_num' } end
    if #text > 9 or text:match('^-?%d+$') == nil then
        return false, { invalid, text }
    end
    return true, tonumber(text)
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"
    --     p1 or p2 may be nil to mean "no preunit"
    -- Using '+ ' gives output like "5+ feet" (no preceding space).
    local function withspace(text, i)
        -- Insert space at beginning if i == 1, or at end if i == -1.
        -- However, no space is inserted if there is a space or '&nbsp;'
        -- or '-' at that position ('-' is for adjectival text).
        local current = text:sub(i, i)
        if current == ' ' or current == '-' then
            return text
        end
        if i == 1 then
            current = text:sub(1, 6)
        else
            current = text:sub(-6, -1)
        end
        if current == '&nbsp;' then
            return text
        end
        if i == 1 then
            return ' ' .. text
        end
        return text .. ' '
    end
    preunit1 = preunit1 or ''
    local trim1 = strip(preunit1)
    if count == 1 then
        if trim1 == '' then
            return nil
        end
	return withspace(withspace(preunit1, 1), -1)
    end
    preunit2 = preunit2 or ''
    local trim2 = strip(preunit2)
    if trim1 == '' and trim2 == '' then
	return nil, nil
    end
    if trim1 ~= '+' then
	preunit1 = withspace(preunit1, 1)
    end
    if trim2 == '&#32;' then  -- trick to make preunit2 empty
	preunit2 = nil
    elseif trim2 == '' then
	preunit2 = preunit1
    elseif trim2 ~= '+' then
	preunit2 = withspace(preunit2, 1)
    end
    return preunit1, preunit2
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 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 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 add_warning(parms, mcode, text)
    -- If enabled, add a warning that will be displayed after the convert result.
    -- Currently, only the first warning is displayed.
    if parms.test == 'warnings' then  -- LATER replace this by enabling via a config option
        if parms.warnings == nil then
            parms.warnings = message({ mcode, text })
        end
    end
end

local function translate_parms(parms)
    -- Update fields in parms by translating parameters to those used at enwiki.
    for en_name, loc_name in pairs(local_option_name) do
        if en_name ~= 'sing' then  -- 'sing' is an old equivalent of 'adj'; cannot have both
            local loc_value = parms[loc_name]
            if loc_value == nil and en_name == 'adj' then
                loc_name = local_option_name['sing']
                loc_value = parms[loc_name]
            end
            if loc_value then
                local en_value = en_option_value[en_name][loc_value]
                if en_value == nil then
                    if loc_value == '' then
                        add_warning(parms, 'cvt_empty_option', loc_name)
                    else
                        add_warning(parms, 'cvt_unknown_option', loc_name .. '=' .. loc_value)
                    end
                elseif en_value == '' then
                    en_value = nil
                elseif en_value:sub(1, 4) == 'opt_' then
                    parms[en_value] = true
                    en_value = nil
                end
                parms[en_name] = en_value
            end
        end
    end
    if parms.adj then
        if parms.adj:sub(1, 2) == 'ri' then
            -- It is known that adj is 'ri1' or 'ri2' or 'ri3', so precision is valid.
            parms.input_precision = tonumber(parms.adj:sub(-1))
            parms.adj = nil
        end
    end
    if parms.disp then
        if parms.disp == 'special_flip5' then
            parms.opt_round5 = true
            parms.opt_flip = true
            parms.disp = nil
        end
    end
    if parms.abbr then
        parms.abbr_org = parms.abbr  -- original abbr that was set, before any flip
    else
        parms.abbr = 'out'  -- default is to abbreviate output only (use symbol, not name)
    end
    if parms.opt_flip then
        if parms.abbr == 'in' then
            parms.abbr = 'out'
        elseif parms.abbr == 'out' then
            parms.abbr = 'in'
        end
        if parms.lk == 'in' then
            parms.lk = 'out'
        elseif parms.lk == 'out' then
            parms.lk = 'in'
        end
    end
    if parms.opt_table or parms.opt_tablecen then
        if parms.abbr_org == nil and parms.lk == nil then
            parms.opt_values = true
        end
        local align = format('align="%s"', parms.opt_table and 'right' or 'center')
        parms.table_joins = { align .. '|', '\n|' .. align .. '|' }
    end
end

local function get_parms(pframe)
    -- If successful, return true, parms, 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.
    -- 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 success, info1, info2
    local parms = {}  -- arguments passed to template
    for k, v in pairs(pframe.args) do
        parms[k] = v
    end
    translate_parms(parms)
    local range
    local next = strip(parms[2])
    local i = 3
    if next then
        range = range_types[next] or range_types[range_aliases[next]]
        if range == nil and next:sub(-7, -1) == 'nocomma' then
            local base = strip(next:sub(1, -8))
            range = range_types[base] or range_types[range_aliases[base]]
            if range then
                parms.opt_nocomma = true
            end
        end
    end
    success, info1 = extract_number(parms, parms[1], 1)  -- need to set parms.opt_nocomma before calling this
    if not success then return false, info1 end
    local in_unit
    if range == nil then
        in_unit = next
    else
        parms.range = range
        parms.is_range_x = range.is_range_x
        success, info2 = extract_number(parms, parms[3], 2)
        if not success then return false, info2 end
        in_unit = strip(parms[4])
        i = 5
    end
    local success, in_unit_table = lookup(in_unit, parms.opt_sp_us, 'no_combination')
    if not success then return false, in_unit_table 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.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(parms[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, parms.opt_sp_us, 'no_combination')
                if not success then return false, subunit end  -- should never occur
                success, subinfo = extract_number(parms, parms[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(parms, parms[i], 1, true)
        if success then
            i = i + 1
            in_unit_table.altitude = info.value
        end
    end
    next = strip(parms[i])
    i = i + 1
    local precision
    if tonumber(next) then
        precision = next
    else
        parms.out_unit = next
        next = strip(parms[i])
        if tonumber(next) then
            i = i + 1
            precision = next
        end
    end
    if parms.opt_adj_mid then
        parms.opt_adjectival = true
        next = parms[i]
        i = i + 1
        if next then  -- mid-text words
            if next:sub(1, 1) == '-' then
                parms.mid = next
            else
                parms.mid = ' ' .. next
            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 tonumber(parms[i]) then
            precision = strip(parms[i])
            i = i + 1
        end
    end
    parms.precision = parms.precision or precision  -- allow named parameter
    return true, parms, 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 = 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.exception == 'moreprecision' 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)
        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 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(parms, 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
    if not valid_number(outvalue) then
        return false, { 'cvt_invalid_num' }
    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
    if precision then
        success, precision = require_integer(precision, 'cvt_bad_prec')
        if not success then return false, precision end
    elseif sigfig then
        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 parms.opt_round5 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(parms, 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 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 make_link(link, id)
    -- Return wikilink "[[link|id]]", possibly abbreviated as in examples:
    --   [[Mile|mile]]  --> [[mile]]
    --   [[Mile|miles]] --> [[mile]]s
    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 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.
    -- If linked, set unit_table.linked = true so will not link same unit again
    -- (like in {{convert|3|x|4|in|mm|lk=on}}).
    -- key_id is one of: 'symbol', 'sym_us', 'name1', 'name1_us', 'name2', 'name2_us'.
    if want_link then
        if unit_table.linked then
            want_link = false
        else
            unit_table.linked = true
        end
    end
    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 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
            id = customary .. make_link(link, id)
        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).
    if parms.opt_values then
        unit_table.sep = ''
        return ''
    end
    local inout = unit_table.inout
    local valinfo = unit_table.valinfo
    local abbr_org = parms.abbr_org
    local adjectival = parms.opt_adjectival
    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.
            local flipped = parms.opt_flip
            if inout == 'in' then
                if not adjectival and (abbr_org == 'out' or flipped) then
                    local value = valinfo[which].value
                    singular = (0 < value and value < 1.0001)
                end
            else
                if (abbr_org == 'on') or
                (not flipped and (abbr_org == nil or abbr_org == 'out')) or
                (flipped and abbr_org == 'in') then
                    singular = (valinfo[which].absvalue < 1.0001 and
                                not valinfo[which].is_scientific)
                end
            end
        end
    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
            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 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 = valinfo[which].value
            else
                value = valinfo[which].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 or parms.is_range_x then
            -- engscale: so "|1|e3kg" gives "1 thousand kilograms" (plural)
            -- is_range_x: so "|0.5|x|0.9|mi" gives "0.5 by 0.9 miles" (plural)
            singular = false
        end
        key = (adjectival or singular) and 'name1' or 'name2'
        if unit_table.sp_us then
            key = key .. '_us'
        end
    else
        unit_table.sep = '&nbsp;'
        key = unit_table.sp_us and 'sym_us' or 'symbol'
    end
    return linked_id(unit_table, key, lk == 'on' or lk == inout), want_name
end

local function decorate_value(parms, unit_table, which)
    -- 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 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.opt_adjectival 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).
    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, 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)
    local sep = first_unit.sep  -- 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
            id1 = id1 .. ' ' .. make_id(parms, 1, second_unit)
        end
        if want_name and parms.opt_adjectival then
            return preunit .. hyphenated(id1)
        end
        return  preunit .. id1
    end
    local abbr = parms.abbr
    local disp = parms.disp
    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 parms.opt_extra and not composite then
        local join1 = parms.joins[1]
        if join1 == ' (' or join1 == ' [' then
            parms.joins = { join1 .. first_unit[first_unit.sp_us and 'sym_us' or 'symbol'] .. ', ', parms.joins[2] }
        end
    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 preunit .. result
    end
    if composite then
        -- Simplify: assume there is no range, and no decoration.
        local mid = ''
        local sep1 = '&nbsp;'
        local sep2 = ' '
        if parms.opt_adjectival then
            if not parms.opt_flip then
                mid = parms.mid or ''
            end
            if want_name then
                sep1 = '-'
                sep2 = '-'
            end
        end
        return first_unit.valinfo[1].show .. sep1 .. id1 .. sep2 ..
               second_unit.valinfo[1].show .. sep1 .. (make_id(parms, 1, second_unit)) .. mid
    end
    local result, mos
    local range = parms.range
    if range then
        mos = (abbr == 'mos')
        if not (mos or (parms.is_range_x and not want_name)) then
            first_unit.linked = false  -- so the second and only id will be linked, if wanted
        end
    end
    local id = (range == nil) and id1 or make_id(parms, 2, first_unit)
    local extra, was_hyphenated = hyphenated_maybe(parms, want_name, sep, id, 'in')
    if mos and was_hyphenated then
        mos = false  -- suppress repeat of unit in a range
        if first_unit.linked then
            first_unit.linked = false
            id = make_id(parms, 2, first_unit)
            extra = hyphenated_maybe(parms, want_name, sep, id, 'in')
        end
    end
    local valinfo = first_unit.valinfo
    if range then
        local sep1 = first_unit.sep
        if mos then
            decorate_value(parms, in_current, 1)
            decorate_value(parms, in_current, 2)
            result = valinfo[1].show .. sep1 .. 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 .. sep1 .. id1
        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)
    else
        decorate_value(parms, first_unit, 1)
        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 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' 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 preunit .. result
    end
    local result
    local range = parms.range
    if range then
        if not (parms.is_range_x and not want_name) then
            out_current.linked = false  -- so the second and only id will be linked, if wanted
        end
    end
    local id = (range == nil) and id1 or make_id(parms, 2, out_current)
    local extra = hyphenated_maybe(parms, want_name, sep, id, 'out')
    local valinfo = out_current.valinfo
    if range then
        local sep1 = out_current.sep
        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 .. sep1 .. id1
        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)
    else
        decorate_value(parms, out_current, 1)
        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.
    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 mid = ''
    local sep1 = '&nbsp;'
    local sep2 = ' '
    if parms.opt_adjectival then
        if parms.opt_flip then
            mid = parms.mid or ''
        end
        if want_name then
            sep1 = '-'
            sep2 = '-'
        end
    end
    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 = make_link(link, id)
                end
            end
            local strval = (thisvalue == 0) and '0' or with_separator(parms, format(fmt, thisvalue))
            table.insert(results, strval .. sep1 .. 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, sep2)
    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 .. mid
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.opt_sp_us, '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 in_block = process_input(parms, in_unit_table)
    local out_block = parms.opt_input_unit_only and '' or table.concat(outputs, '; ')
    if parms.opt_flip then
        in_block, out_block = out_block, in_block
    end
    if parms.opt_sortable then
        in_block = ntsh(invalue1, parms.debug) .. in_block
    end
    local wikitext
    if parms.table_joins then
        wikitext = parms.table_joins[1] .. in_block .. parms.table_joins[2] .. out_block
    else
        wikitext = in_block .. parms.joins[1] .. out_block .. parms.joins[2]
    end
    if parms.warnings then
        wikitext = wikitext .. parms.warnings
    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 message(result)
end

return { convert = main_convert }