Module:Convert

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

--[[
Later TODO Too many items to list, but following are some points:
- Some conversions require two outputs: {{convert|55|nmi|km mi}}.
- Some units have two values: {{convert|3.21|m|ftin}}.
- At least one unit has a plural symbol (our output is "(30 acre)"):
    {{convert|12|ha}} --> 12 hectares (30 acres)
]]

local function clonetable(t)
    -- Return a shallow copy of t.
    local result = {}
    for k, v in pairs(t) do
        result[k] = v
    end
    return result
end

local function shouldbe(ucode, shouldbe)
    -- Return an error message for a unit that "should be" something else.
    -- enwiki Template:Convert outputs a much more elaborate message.
    -- LATER: Decide if "shouldbe" is useful, and what to output if it is.
    return 'ERROR: Use "' .. shouldbe .. '" (not "' .. ucode .. '") as the unit code.'
end

--[[-----BEGIN DATA TABLES-----
Three data tables follow:
    SIprefixes      prefixes like 'M' (mega, 10^6)
    units           all properties for a unit, including default output
    defaultunits    default output exceptions ('Mg' and 'g' have different defaults)
SIprefixes and defaultunits are maintained by editing this file.
However, the units table is generated by a script which reads the wikitext
for a wiki page that documents properties of units.
Could consider putting some or all tables in another module.
Check values at http://en.wikipedia.org/wiki/Conversion_of_units
and http://en.wikipedia.org/wiki/Template:Convert/list_of_units
]]

local SIprefixes = {
    ['Y'] = { exponent = 24, name = 'yotta' },
    ['Z'] = { exponent = 21, name = 'zetta' },
    ['E'] = { exponent = 18, name = 'exa'   },
    ['P'] = { exponent = 15, name = 'peta'  },
    ['T'] = { exponent = 12, name = 'tera'  },
    ['G'] = { exponent =  9, name = 'giga'  },
    ['M'] = { exponent =  6, name = 'mega'  },
    ['k'] = { exponent =  3, name = 'kilo'  },
    ['H'] = { exponent =  2, name = 'hecto' },  -- not an SI prefix, but allow for people typing this
    ['h'] = { exponent =  2, name = 'hecto' },
    ['da']= { exponent =  1, name = 'deca'  },
    ['D'] = { exponent =  1, name = 'deca'  },  -- not an SI prefix, but allow for people typing this
    ['d'] = { exponent = -1, name = 'deci'  },
    ['c'] = { exponent = -2, name = 'centi' },
    ['m'] = { exponent = -3, name = 'milli' },
    ['µ'] = { exponent = -6, name = 'micro' },
    ['u'] = { exponent = -6, name = 'micro' },  -- not an SI prefix, but allow for people typing this
    ['n'] = { exponent = -9, name = 'nano'  },
    ['p'] = { exponent =-12, name = 'pico'  },
    ['f'] = { exponent =-15, name = 'femto' },
    ['a'] = { exponent =-18, name = 'atto'  },
    ['z'] = { exponent =-21, name = 'zepto' },
    ['y'] = { exponent =-24, name = 'yocto' },
}

local usesubstitute = {
    -- If unit has an SI prefix, these fields may have "%s" where prefix belongs.
    'name1',
    'name1_us',
    'name2',
    'name2_us',
    'link',
}

local function set_prefixes(unit, prefixname)
    -- Insert given prefix name into the fields which require it
    -- (and which should contain '%s' to be replaced with the prefix).
    -- Pity we have to do all this work when most results are not needed,
    -- but it's cleaner to do it here rather than in final processing.
    if unit.prefixes then
        for _, name in ipairs(usesubstitute) do
            local value = unit[name]
            unit[name] = value:gsub('%%s', prefixname, 1)
        end
    end
end

-- Do not change the data in this table because it is created by running
-- a script on the wikitext from a wiki page (see note above).
local units = {
    lookup = function (self, unit)
        -- Return true, t where t is the unit's converter table (or false, message).
        -- Given 'unit' is a symbol (like 'g'), with an optional SI prefix (as in 'kg').
        -- If, for example, 'kg' is in this table, that entry is used; otherwise prefix is applied.
        local t = self[unit]
        if t ~= nil then
            if t.shouldbe then
                return false, shouldbe(t.shouldbe, unit)
            end
            local result = clonetable(t)
            set_prefixes(result, '')
            result.baseunit = unit
            result.prefix = ''
            return true, result
        end
        for plen = 2, 1, -1 do
            -- Check for longer prefix first ('dam' is decametre).
            local prefix = string.sub(unit, 1, plen)
            local si = SIprefixes[prefix]
            if si then
                local baseunit = unit:sub(plen+1)
                local t = self[baseunit]
                if t and t.prefixes then
                    local result = clonetable(t)
                    set_prefixes(result, si.name)
                    result.symbol = prefix .. result.symbol
                    result.sym_us = prefix .. result.sym_us
                    result.baseunit = baseunit
                    result.prefix = prefix
                    result.scale = t.scale * 10 ^ (si.exponent * t.prefixes)
                    return true, result
                end
            end
        end
        local msg = 'Unit %s is not known.[[Category:Convert unknown unit]]'
        return false, msg:format(unit)
    end,
    ["m2"] = {
	name1    = "square %smetre",
	name1_us = "square %smeter",
	name2    = "square %smetres",
	name2_us = "square %smeters",
	symbol   = "m<sup>2</sup>",
	sym_us   = "m<sup>2</sup>",
	utype    = "area",
	scale    = 1,
	offset   = 0,
	prefixes = 2,
	default  = "sqyd",
	link     = "Square %smetre",
    },
    ["a"] = {
	name1    = "%sare",
	name1_us = "%sare",
	name2    = "%sares",
	name2_us = "%sares",
	symbol   = "a",
	sym_us   = "a",
	utype    = "area",
	scale    = 100,
	offset   = 0,
	prefixes = 1,
	default  = "acre",
	link     = "Hectare#Are",
    },
    ["ha"] = {
	name1    = "hectare",
	name1_us = "hectare",
	name2    = "hectares",
	name2_us = "hectares",
	symbol   = "ha",
	sym_us   = "ha",
	utype    = "area",
	scale    = 10000,
	offset   = 0,
	default  = "acre",
	link     = "Hectare",
    },
    ["sqft"] = {
	name1    = "square foot",
	name1_us = "square foot",
	name2    = "square feet",
	name2_us = "square feet",
	symbol   = "sq ft",
	sym_us   = "sq ft",
	utype    = "area",
	scale    = 0.09290304,
	offset   = 0,
	default  = "m2",
	link     = "Square foot",
    },
    ["ft2"] = {
	name1    = "square foot",
	name1_us = "square foot",
	name2    = "square feet",
	name2_us = "square feet",
	symbol   = "sq ft",
	sym_us   = "sq ft",
	utype    = "area",
	scale    = 0.09290304,
	offset   = 0,
	default  = "m2",
	link     = "Square foot",
    },
    ["sqfoot"] = {
	name1    = "square foot",
	name1_us = "square foot",
	name2    = "square foot",
	name2_us = "square foot",
	symbol   = "sq ft",
	sym_us   = "sq ft",
	utype    = "area",
	scale    = 0.09290304,
	offset   = 0,
	default  = "m2",
	link     = "Square foot",
    },
    ["foot2"] = {
	name1    = "square foot",
	name1_us = "square foot",
	name2    = "square foot",
	name2_us = "square foot",
	symbol   = "sq ft",
	sym_us   = "sq ft",
	utype    = "area",
	scale    = 0.09290304,
	offset   = 0,
	default  = "m2",
	link     = "Square foot",
    },
    ["sqyd"] = {
	name1    = "square yard",
	name1_us = "square yard",
	name2    = "square yards",
	name2_us = "square yards",
	symbol   = "sq yd",
	sym_us   = "sq yd",
	utype    = "area",
	scale    = 0.83612736,
	offset   = 0,
	default  = "m2",
	link     = "Square yard",
    },
    ["sqin"] = {
	name1    = "square inch",
	name1_us = "square inch",
	name2    = "square inches",
	name2_us = "square inches",
	symbol   = "sq in",
	sym_us   = "sq in",
	utype    = "area",
	scale    = 0.00064516,
	offset   = 0,
	default  = "cm2",
	link     = "Square inch",
    },
    ["acre"] = {
	name1    = "acre",
	name1_us = "acre",
	name2    = "acres",
	name2_us = "acres",
	symbol   = "acre",
	sym_us   = "acre",
	utype    = "area",
	scale    = 4046.8564224,
	offset   = 0,
	default  = "ha",
	link     = "Acre",
    },
    ["m"] = {
	name1    = "%smetre",
	name1_us = "%smeter",
	name2    = "%smetres",
	name2_us = "%smeters",
	symbol   = "m",
	sym_us   = "m",
	utype    = "length",
	scale    = 1,
	offset   = 0,
	prefixes = 1,
	default  = "ft",
	link     = "%smetre",
    },
    ["mi"] = {
	name1    = "mile",
	name1_us = "mile",
	name2    = "miles",
	name2_us = "miles",
	symbol   = "mi",
	sym_us   = "mi",
	utype    = "length",
	scale    = 1609.344,
	offset   = 0,
	default  = "km",
	link     = "Mile",
    },
    ["ft"] = {
	name1    = "foot",
	name1_us = "foot",
	name2    = "feet",
	name2_us = "feet",
	symbol   = "ft",
	sym_us   = "ft",
	utype    = "length",
	scale    = 0.3048,
	offset   = 0,
	default  = "m",
	link     = "Foot (unit)",
    },
    ["foot"] = {
	name1    = "foot",
	name1_us = "foot",
	name2    = "foot",
	name2_us = "foot",
	symbol   = "ft",
	sym_us   = "ft",
	utype    = "length",
	scale    = 0.3048,
	offset   = 0,
	default  = "m",
	link     = "Foot (unit)",
    },
    ["feet"] = {
	shouldbe = "ft",
    },
    ["yd"] = {
	name1    = "yard",
	name1_us = "yard",
	name2    = "yards",
	name2_us = "yards",
	symbol   = "yd",
	sym_us   = "yd",
	utype    = "length",
	scale    = 0.3048 * 3,
	offset   = 0,
	default  = "m",
	link     = "Yard",
    },
    ["in"] = {
	name1    = "inch",
	name1_us = "inch",
	name2    = "inches",
	name2_us = "inches",
	symbol   = "in",
	sym_us   = "in",
	utype    = "length",
	scale    = 0.0254,
	offset   = 0,
	default  = "cm",
	link     = "Inch",
    },
    ["g"] = {
	name1    = "%sgram",
	name1_us = "%sgram",
	name2    = "%sgrams",
	name2_us = "%sgrams",
	symbol   = "g",
	sym_us   = "g",
	utype    = "mass",
	scale    = 0.001,
	offset   = 0,
	prefixes = 1,
	default  = "oz",
	link     = "%sgram",
    },
    ["lb"] = {
	name1    = "pound",
	name1_us = "pound",
	name2    = "pounds",
	name2_us = "pounds",
	symbol   = "lb",
	sym_us   = "lb",
	utype    = "mass",
	scale    = 0.45359237,
	offset   = 0,
	default  = "kg",
	link     = "Pound (mass)",
    },
    ["oz"] = {
	name1    = "ounce",
	name1_us = "ounce",
	name2    = "ounces",
	name2_us = "ounces",
	symbol   = "oz",
	sym_us   = "oz",
	utype    = "mass",
	scale    = 0.45359237/16,
	offset   = 0,
	default  = "g",
	link     = "Ounce",
    },
    ["ozt"] = {
	name1    = "troy ounce",
	name1_us = "troy ounce",
	name2    = "troy ounces",
	name2_us = "troy ounces",
	symbol   = "ozt",
	sym_us   = "ozt",
	utype    = "mass",
	scale    = 0.0311034768,
	offset   = 0,
	default  = "g",
	link     = "Troy ounce",
    },
    ["K"] = {
	name1    = "kelvin",
	name1_us = "kelvin",
	name2    = "kelvins",
	name2_us = "kelvins",
	symbol   = "K",
	sym_us   = "K",
	utype    = "temperature",
	scale    = 1,
	offset   = 0,
	default  = "C",
	link     = "Kelvin",
    },
    ["C"] = {
	name1    = "degree Celsius",
	name1_us = "degree Celsius",
	name2    = "degrees Celsius",
	name2_us = "degrees Celsius",
	symbol   = "°C",
	sym_us   = "°C",
	utype    = "temperature",
	scale    = 1,
	offset   = -273.15,
	default  = "F",
	link     = "Celsius",
    },
    ["°C"] = {
	name1    = "degree Celsius",
	name1_us = "degree Celsius",
	name2    = "degrees Celsius",
	name2_us = "degrees Celsius",
	symbol   = "°C",
	sym_us   = "°C",
	utype    = "temperature",
	scale    = 1,
	offset   = -273.15,
	default  = "F",
	link     = "Celsius",
    },
    ["F"] = {
	name1    = "degree Fahrenheit",
	name1_us = "degree Fahrenheit",
	name2    = "degrees Fahrenheit",
	name2_us = "degrees Fahrenheit",
	symbol   = "°F",
	sym_us   = "°F",
	utype    = "temperature",
	scale    = 5/9,
	offset   = 32-273.15*(9/5),
	default  = "C",
	link     = "Fahrenheit",
    },
    ["°F"] = {
	name1    = "degree Fahrenheit",
	name1_us = "degree Fahrenheit",
	name2    = "degrees Fahrenheit",
	name2_us = "degrees Fahrenheit",
	symbol   = "°F",
	sym_us   = "°F",
	utype    = "temperature",
	scale    = 5/9,
	offset   = 32-273.15*(9/5),
	default  = "C",
	link     = "Fahrenheit",
    },
    ["m3"] = {
	name1    = "cubic %smetre",
	name1_us = "cubic %smeter",
	name2    = "cubic %smetres",
	name2_us = "cubic %smeters",
	symbol   = "m<sup>3</sup>",
	sym_us   = "m<sup>3</sup>",
	utype    = "volume",
	scale    = 1,
	offset   = 0,
	prefixes = 3,
	default  = "cuyd",
	link     = "Cubic %smetre",
    },
    ["l"] = {
	name1    = "%slitre",
	name1_us = "%sliter",
	name2    = "%slitres",
	name2_us = "%sliters",
	symbol   = "l",
	sym_us   = "l",
	utype    = "volume",
	scale    = 0.001,
	offset   = 0,
	prefixes = 1,
	default  = "imppt",
	link     = "Litre",
    },
    ["L"] = {
	name1    = "%slitre",
	name1_us = "%sliter",
	name2    = "%slitres",
	name2_us = "%sliters",
	symbol   = "L",
	sym_us   = "L",
	utype    = "volume",
	scale    = 0.001,
	offset   = 0,
	prefixes = 1,
	default  = "imppt",
	link     = "Litre",
    },
    ["cuyd"] = {
	name1    = "cubic yard",
	name1_us = "cubic yard",
	name2    = "cubic yards",
	name2_us = "cubic yards",
	symbol   = "cu yd",
	sym_us   = "cu yd",
	utype    = "volume",
	scale    = 0.764554857984,
	offset   = 0,
	default  = "m3",
	link     = "Cubic yard",
    },
    ["USgal"] = {
	name1    = "US gallon",
	name1_us = "U.S. gallon",
	name2    = "US gallons",
	name2_us = "U.S. gallons",
	symbol   = "US gal",
	sym_us   = "U.S. gal",
	utype    = "volume",
	scale    = 0.003785411784,
	offset   = 0,
	default  = "L",
	link     = "US gallon",
    },
    ["USoz"] = {
	name1    = "US fluid ounce",
	name1_us = "U.S. fluid ounce",
	name2    = "US fluid ounces",
	name2_us = "U.S. fluid ounces",
	symbol   = "US fl oz",
	sym_us   = "U.S. fl oz",
	utype    = "volume",
	scale    = 0.003785411784/128,
	offset   = 0,
	default  = "cL",
	link     = "US fluid ounce",
    },
    ["USpt"] = {
	name1    = "U.S. pint",
	name1_us = "U.S. pint",
	name2    = "U.S. pints",
	name2_us = "U.S. pints",
	symbol   = "US pt",
	sym_us   = "US pt",
	utype    = "volume",
	scale    = 0.003785411784/8,
	offset   = 0,
	default  = "dL",
    },
    ["impgal"] = {
	name1    = "imperial gallon",
	name1_us = "imperial gallon",
	name2    = "imperial gallons",
	name2_us = "imperial gallons",
	symbol   = "imp gal",
	sym_us   = "imp gal",
	utype    = "volume",
	scale    = 0.00454609,
	offset   = 0,
	default  = "L",
	link     = "Imperial gallon",
    },
    ["impoz"] = {
	name1    = "imperial fluid ounce",
	name1_us = "imperial fluid ounce",
	name2    = "imperial fluid ounces",
	name2_us = "imperial fluid ounces",
	symbol   = "imp fl oz",
	sym_us   = "imp fl oz",
	utype    = "volume",
	scale    = 0.00454609/160,
	offset   = 0,
	default  = "cL",
	link     = "Imperial fluid ounce",
    },
    ["imppt"] = {
	name1    = "imperial pint",
	name1_us = "imperial pint",
	name2    = "imperial pints",
	name2_us = "imperial pints",
	symbol   = "imp pt",
	sym_us   = "imp pt",
	utype    = "volume",
	scale    = 0.00454609/8,
	offset   = 0,
	default  = "dL",
	link     = "Imperial pint",
    },
}

local defaultunits = {
    lookup = function (self, unit_table)
        -- Return true, s where s = name of unit's default output unit (or false, message).
        local baseunit = unit_table.baseunit
        local prefix = unit_table.prefix
        local unit = prefix .. baseunit
        local default = self[unit]
        if default ~= nil then return true, default end
        local t = units[baseunit]
        if t ~= nil then
            local default = t.default
            if default ~= nil then return true, default end
        end
        local msg = 'Unit %s has no default target conversion.[[Category:Convert unknown unit]]'
        return false, msg:format(unit)
    end,
    -- Prefixed units with a default different from that of the base unit.
    ['kg']  = 'lb',
    ['Mg']  = 'lb',
    ['Gg']  = 'lb',
    ['pm']  = 'in',
    ['nm']  = 'in',
    ['um']  = 'in',
    ['mm']  = 'in',
    ['cm']  = 'in',
    ['dm']  = 'in',
    ['dam'] = 'yd',
    ['Hm']  = 'yd',
    ['km']  = 'mi',
    ['Mm']  = 'mi',
    ['mL']  = 'impoz',
    ['cL']  = 'impoz',
    ['dL']  = 'impoz',
    ['daL'] = 'impgal',
    ['HL']  = 'impgal',
}

-------END DATA TABLES-----

-- Configuration options to keep magic values in one location.
local config = {}

local function get_config(frame)
    -- Return table of configuration options.
    -- Unclear if this is currently needed, but it may help if adapting
    -- code for a different wiki.
    local cfg = {}
    -- Following settings are defaults that can be overridden by template.
    cfg.numdot = '.'        -- decimal mark before fractional digits
    cfg.numsep = ','        -- thousands separator for numbers (',', '.', or nil)
    for k, v in frame:argumentPairs() do
        cfg[k] = v          -- arguments from template's {{#invoke:}}
    end
    -- Following settings are mandatory (to limit abuse).
    cfg.maxsigfig = 20      -- maximum number of significant figures
    return cfg
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 .. fmt:format(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 = math.floor(1e6 * f)
            result = string.format('&1%016.0f%06d', i, f)
        end
    else
        n = -n
        if n > 1e16 then
            result = '!'
        else
            i, f = math.modf(n)
            f = math.floor(1e6 * f)
            result = string.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 withseparator(text)
    -- Return text with thousand separators inserted.
    -- The given text is '0' or is a positive number like '12345.6789'.
    -- Separator is inserted only in the integer part (not in fraction).
    -- Four-digit integer parts have a separator (like '1,234').
    local numsep = config.numsep
    if #numsep == 0 then
        return text
    end
    local function insert(text, last)
        local result = ''
        while last >= 1 do
            if last >= 4 then
                result = numsep .. text:sub(last-2, last) .. result
                last = last - 3
            else
                return text:sub(1, last) .. result
            end
        end
        return result
    end
    local last = text:find(config.numdot, 1, true)
    if last == nil then
        last = #text
    else
        last = last - 1
    end
    return insert(text, last) .. text:sub(last+1)
end

local function formatnumber(value, sigfig)
    -- Return result of converting number 'value' to a string,
    -- rounded to 'sigfig' significant figures.
    local format = string.format
    local rep = string.rep
    local sign = ''
    local numdot = config.numdot
    local function zeropad(text, dot)
        local count = sigfig - #text
        if count <= 0 then
            return text
        end
        return text .. dot .. rep('0', count)
    end
    if sigfig <= 0 then
        sigfig = 1
    elseif sigfig > config.maxsigfig then
        sigfig = config.maxsigfig
    end
    if value == 0 then
        return zeropad('0', numdot)
    end
    if value < 0 then
        sign = '-'  -- need proper Unicode minus
        value = -value
    end
    local digits
    local exp, frac = math.modf(math.log10(value))
    if frac == 0 then
        -- Value 1 gives frac = 0, and 0.1 gives frac = -0 (negative zero).
        -- Both results give true in 'if frac == 0'.
        digits = zeropad('1', '')
        exp = exp + 1  -- adjust so dot is before digits
    else
        local prec = sigfig
        if value > 1 then
            prec = prec - 1  -- will be one sig fig before dot
        end
        digits = format(format('%%.%df', prec), 10^frac)
        if value < 1 then
            -- Is MediaWiki run in a locale where following might be '0,'?
            assert(digits:sub(1, 2) == '0.', 'Bug: rounded number not 0.xxx')
            digits = digits:sub(3)
        else
            if prec == 0 then
                assert(digits:find(numdot, 1, true) == nil, 'Bug: unexpected dot')
            else
                assert(digits:sub(2, 2) == numdot, 'Bug: rounded number not x.xxx')
                digits = digits:sub(1, 1) .. digits:sub(3)
            end
            exp = exp + 1  -- adjust so dot is before digits
        end
    end
    if exp >= #digits then
        digits = digits .. rep('0', exp - #digits)  -- result has no dot
    elseif exp <= 0 then
        digits = '0' .. numdot .. rep('0', -exp) .. digits
    else
        digits = digits:sub(1, exp) .. numdot .. digits:sub(exp+1)
    end
    return sign .. digits
end

local missing = { 'Need value', 'Need second value' }
local invalid = { 'Value "%s" must be a number', 'Second value "%s" must be a number' }

local function extract_number(args, index, which)
    -- Return true if successfully extract a number from the text in args[index].
    -- Otherwise, return false, message.
    -- Parameter 'which' (1 or 2) selects which input value is being processed.
    -- 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, following elements in table args are updated
    -- (first row applies if which == 1, second otherwise):
    --    args.in_value1,  args.in_singular1,  args.in_clean1,  args.in_show1
    --    args.in_value2,  args.in_singular2,  args.in_clean2,  args.in_show2
    -- Value is a valid number.
    -- Singular is true if value is 1 (singular form of units will be used).
    -- Singular is false if value is -1 (that's how old Template:Convert worked).
    -- Clean is cleaned text with any separators and sign removed.
    -- Show is text formatted for output:
    -- * Thousand separators are inserted.
    -- * If negative, a Unicode minus is used; otherwise the sign
    --   is '+' (if the input text used '+'), or is ''.
    local text = args[index]
    if text == nil or text == '' then return false, missing[which] end
    local clean, sign
    local numsep = config.numsep
    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, negative
    if sign == '−' or sign == '-' then
        propersign = '−'  -- Unicode U+2212 MINUS SIGN (UTF-8: e2 88 92)
        negative = true
    elseif sign == '+' then
        propersign = '+'
        negative = false
    elseif sign == '' then
        propersign = ''
        negative = false
    else
        return false, (invalid[which]):format(text)
    end
    local value = tonumber(clean)
    if value == nil then return false, (invalid[which]):format(text) end
    local singular = (value == 1)
    if negative and (value ~= 0) then
        value = -value
    end
    -- TODO Someone has to change text to use exponents for very large/small.
    local show = propersign .. withseparator(clean)
    if which == 1 then
        args.in_value1 = value
        args.in_singular1 = singular
        args.in_clean1 = clean
        args.in_show1 = show
    else
        args.in_value2 = value
        args.in_singular2 = singular
        args.in_clean2 = clean
        args.in_show2 = show
    end
    return true
end

local function require_integer(text, missing, invalid)
    -- Return true, n where n = integer equivalent to given text (or false, message).
    -- 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, missing end
    if string.match(text, '^-?%d+$') == nil then
        return false, invalid:format(text)
    end
    return true, tonumber(text)
end

local function get_parms(pframe)
    -- Return true, t where t is a table with all arguments passed to the
    -- template converted to named arguments.
    -- Except for range, which is nil or a table, the named args that are
    -- added here could be provided by the user of the template.
    local range_types = {  -- text to separate input, output ranges
        ['and']   = {' and ', '&nbsp;and '},
        ['by']    = {' by ', '&nbsp;by '},
        ['to']    = {' to ', '&nbsp;to '},
        ['-']     = {'–', '–'},
        ['to(-)'] = {'&nbsp;to ', '–'},
        ['x']     = {' by ', '&nbsp;×&nbsp;'},
        ['+/-']   = {'&nbsp;±&nbsp;', '&nbsp;±&nbsp;'},
    }
    local success, msg
    local args = {}  -- arguments passed to template
    for k, v in pframe:argumentPairs() do
        args[k] = v
    end
    success, msg = extract_number(args, 1, 1)
    if not success then return success, msg end
    local in_unit = args[2]
    local i = 3
    local range = range_types[in_unit]
    if range ~= nil then
        success, msg = extract_number(args, 3, 2)
        if not success then return success, msg end
        in_unit = args[4]
        i = 5
    end
    local out_unit = args[i]
    local round_to = args[i+1]
    if in_unit == nil then return false, 'Need input unit' end
    args.in_unit = in_unit
    args.out_unit = out_unit
    args.range = range
    args.round_to = args.round_to or round_to  -- allow named parameter
    return true, args
end

local function default_roundto(inclean, factor)
    -- Return a default value for round_to (an integer like 2, 0, -2).
    -- prec = (precision implied in inclean)
    --      = (#digits after dot, or negative of #zeroes before dot)
    -- If conversion is multiplication by a factor, and
    -- if factor >= 0.02, compensate prec by adding N where:
    --     N    factor is in range
    --     1     .02  :   .2   =    .1/5 :   .1*2
    --     0     .2   :   2    =    1/5  :   1*2
    --    -1     2    :  20    =   10/5  :  10*2
    --    -2    20    : 200    =  100/5  : 100*2  etc.
    -- TODO Exception required for temperature.
    local prec = 0
    local dot = inclean:find('.', 1, true)
    -- TODO SHOULD DO THIS?  local dot = inclean:find(config.numdot, 1, true)
    if dot ~= nil then
        prec = inclean:sub(dot+1):len()
        if prec == 0 then
            inclean = inclean:sub(1, -2)
        end
    end
    if prec == 0 then
        prec = inclean:match('0*$'):len()
        if prec ~= 0 then
            prec = -prec
        end
    end
    if factor ~= nil then
        factor = math.abs(factor)
        if factor >= 0.02 then
            prec = prec - math.floor(math.log10(factor*5))
        end
    end
    return prec
end

local function scaled(value, in_unit, out_unit)
    -- Return scaled value for a simple convert.
    local result = (value - in_unit.offset) * (in_unit.scale / out_unit.scale) + out_unit.offset
    if result == 0 then return 0 end  -- safety: result is 0 even for -0 (negative zero)
    return result
end

local function cvtround(invalue, inclean, parms)
    -- Return true, show, singular
    -- where
    --   show = '' if invalue == nil or '', otherwise
    --   show = rounded, formatted string from converting invalue,
    --      using the rounding specified in parms.
    --   singular = true if result is positive, and (after rounding)
    --      is "1", or like "1.00".
    -- or return false, message if problem.
    -- This code combines convert/round because some rounding requires
    -- knowledge of what we are converting.
    -- TODO Lots of checking required. Will need tweaks for special cases
    -- handled by old Template:Convert.
    -- TODO Limit values to avoid abuse (for example, can currently set
    -- round_to to very large values like 999).
    local show, singular = '', false
    if invalue == nil or invalue == '' then return true, show, singular end
    local outvalue = scaled(invalue, parms.in_unit_table, parms.out_unit_table)
    local propersign
    if outvalue < 0 then
        propersign = '−'  -- Unicode U+2212 MINUS SIGN
        outvalue = -outvalue
    else
        if outvalue == 0 then
            outvalue = 0  -- ensure no silly -0 issues
        end
        propersign = ''
    end
    local round_to = parms.round_to
    local sigfig = parms.sigfig
    local disp = parms.disp
    local auto = false
    local success
    if round_to then
        -- Ignore sigfig, disp.
        success, round_to = require_integer(round_to, 'Need value', 'round_to "%s" must be an integer')
        if not success then return false, round_to end
    elseif sigfig then
        -- Ignore disp.
        success, sigfig = require_integer(sigfig, 'Need value', 'sigfig "%s" must be an integer')
        if not success then return false, sigfig end
        if sigfig <= 0 then
            local msg = 'sigfig "%s" must be positive'
            return false, msg:format(parms.sigfig)
        end
        show = formatnumber(outvalue, sigfig)
    elseif disp == '5' then
        outvalue = math.floor((outvalue / 5) + 0.5) * 5
        show = string.format('%.0f', outvalue)
    else
        auto = true  -- using default rounding
        -- TODO If conversion is not multiplication by a number, need factor = nil.
        local factor
        if invalue == 0 then
            factor = 1  -- LATER is this correct?
        else
            factor = outvalue / invalue
        end
        round_to = default_roundto(inclean, factor)
    end
    if round_to then
        if round_to >= 0 then
            if auto then
                -- TODO No less than two significant figures.
            end
            local fmt = '%.' .. string.format('%d', round_to) .. 'f'
            show = string.format(fmt, outvalue)
        else
            -- This always keeps two sig figs. Should that be done if not auto?
            round_to = -round_to  -- #digits that want to zero
            local maxzeroes = 0  -- maximum #digits that should be zeroed
            if outvalue > 100 then
                maxzeroes = math.modf(math.log10(outvalue)) - 1
            end
            if round_to > maxzeroes then
                round_to = maxzeroes
            end
            if round_to > 0 then
                local scaled = string.format('%.0f', outvalue/(10^round_to))
                show = scaled .. string.rep('0', round_to)
            else
                show = formatnumber(outvalue, 2)  -- can't zero digits; keep 2 sig figs
            end
        end
    end
    if (show == '1' or show:match('^1%.0*$') ~= nil) and propersign == '' then
        -- Use match because on some systems 0.99999999999999999 is 1.0.
        singular = true
    end
    -- TODO Someone has to change text to use exponents for very large/small.
    return true, propersign .. withseparator(show), singular
end

local function linked(in_id, out_id, parms)
    -- Return in_id, out_id after modifying none, one, or both by replacing
    -- the text with a wikilink, if requested in template.
    local function substitute(link)
        -- TODO Work out how to insert a reasonable prefix in %s.
        return link:gsub('%%s', 'xxx', 1)
    end
    local lk = parms.lk
    if lk == 'in' or lk == 'on' then
        local link = parms.in_unit_table.link
        if link ~= nil then
            link = substitute(link)
            in_id = '[[' .. link .. '|' .. in_id .. ']]'
        end
    end
    if lk == 'out' or lk == 'on' then
        local link = parms.out_unit_table.link
        if link ~= nil then
            link = substitute(link)
            out_id = '[[' .. link .. '|' .. out_id .. ']]'
        end
    end
    return in_id, out_id
end

local disp_single = {
    ['or']    = '%s&nbsp;%s or %s&nbsp;%s',
    ['sqbr']  = '%s&nbsp;%s [%s&nbsp;%s]',
    ['comma'] = '%s&nbsp;%s, %s&nbsp;%s',
    ['slash'] = '%s&nbsp;%s / %s&nbsp;%s',
    ['s']     = '%s&nbsp;%s / %s&nbsp;%s',
    ['b']     = '%s&nbsp;%s (%s&nbsp;%s)',
}

local disp_double = {
    ['or']    = '%s%s%s&nbsp;%s or %s%s%s&nbsp;%s',
    ['sqbr']  = '%s%s%s&nbsp;%s [%s%s%s&nbsp;%s]',
    ['comma'] = '%s%s%s&nbsp;%s, %s%s%s&nbsp;%s',
    ['slash'] = '%s%s%s&nbsp;%s / %s%s%s&nbsp;%s',
    ['s']     = '%s%s%s&nbsp;%s / %s%s%s&nbsp;%s',
    ['b']     = '%s%s%s&nbsp;%s (%s%s%s&nbsp;%s)',
}

local function process(parms)
    -- Return true, s where s = final wikitext result (or false, message).
    local success, t
    success, t = units:lookup(parms.in_unit)
    if success then parms.in_unit_table = t else return success, t end
    if parms.out_unit == nil then           -- need to catch empty string also?
        success, t = defaultunits:lookup(parms.in_unit_table)
        if success then parms.out_unit = t else return success, t end
    end
    success, t = units:lookup(parms.out_unit)
    if success then parms.out_unit_table = t else return success, t end
    local in_utype = parms.in_unit_table.utype
    if in_utype ~= parms.out_unit_table.utype then
        local msg = 'Cannot convert %s to %s.[[Category:Convert dimension mismatch]]'
        return false, msg:format(in_utype, parms.out_unit_table.utype)
    end
    local outshow1, outshow2, outsingular1, outsingular2
    success, outshow1, outsingular1 = cvtround(parms.in_value1, parms.in_clean1, parms)
    if not success then return success, outshow1 end
    success, outshow2, outsingular2 = cvtround(parms.in_value2, parms.in_clean2, parms)
    if not success then return success, outshow2 end
    local range = parms.range
    local disp = parms.disp
    local wikitext
    -----------------------------------------------------------------------------
    -- TODO Clean up following.
    local inshow1, inshow2 = parms.in_show1, parms.in_show2
    local inkey, outkey = 'name2', 'name2'
    local insymkey, outsymkey = 'symbol', 'symbol'
    if parms.in_singular1 then     -- TODO how process second input value?
        inkey = 'name1'
    end
    if outsingular1 then
        outkey = 'name1'
    end
    if parms.sp == 'us' or parms.in_unit_table.sp_us then
        inkey = inkey .. '_us'
        insymkey = 'sym_us'
    end
    if parms.sp == 'us' or parms.out_unit_table.sp_us then
        outkey = outkey .. '_us'
        outsymkey = 'sym_us'
    end
    local in_name = parms.in_unit_table[inkey]       -- will not need to calculate all of these
    local in_symbol = parms.in_unit_table[insymkey]
    local out_name = parms.out_unit_table[outkey]
    local out_symbol = parms.out_unit_table[outsymkey]
    local abbr = parms.abbr
    local in_id, out_id = in_symbol, out_symbol
    local istemperature = (in_utype == 'temperature')
    if abbr == 'on' then            -- all symbols
        -- Both symbols.
    elseif abbr == 'off' then       -- all names
        in_id = in_name
        out_id = out_name
    elseif abbr == 'in' then        -- input symbols
        -- Both symbols.
    elseif abbr == 'out' then       -- output symbols [is this just the default?]
        if not istemperature then
            in_id = in_name
        end
    elseif abbr == 'values' then    -- show only values
        -- TODO Probably more needed (no preceding space for a start).
        in_id = ''
        out_id = ''
    elseif abbr == 'mos' then       -- for ranges, abbreviate with input unit repeated
        -- LATER
    else                            -- default
        if not istemperature then
            in_id = in_name
        end
    end
    in_id, out_id = linked(in_id, out_id, parms)
    if range == nil then
        if disp == 'output only' then
            wikitext = '%s %s'
            wikitext = wikitext:format(outshow1, out_id)
        elseif disp == 'output number only' or disp == 'number' then
            wikitext = outshow1
        elseif disp == 'unit' then
            wikitext = in_id
        elseif disp == 'unit2' then
            wikitext = out_id
        elseif disp == 'flip' then
            wikitext = disp_single['b']
            wikitext = wikitext:format(outshow1, out_id, inshow1, in_id)
        else
            wikitext = disp_single[disp] or disp_single['b']
            wikitext = wikitext:format(inshow1, in_id, outshow1, out_id)
        end
    else
        -- TODO Need in_id, out_id (and more) here.
        wikitext = disp_double[disp] or disp_double['b']
        wikitext = wikitext:format(inshow1, range[1], inshow2, in_id, outshow1, range[2], outshow2, out_id)
    end
    if parms.sortable == 'on' then
        wikitext = ntsh(parms.in_value1, parms.debug) .. wikitext
    end
    -----------------------------------------------------------------------------
    return true, wikitext
end

local p = {}

function p.convert(frame)
    config = get_config(frame)
    local pframe = frame:getParent()
    local success, parms, text
    success, parms = get_parms(pframe)
    if success then
        success, text = process(parms)
    end
    if not success then
        if not is_test_run then
            -- A testing program can set the above global variable so this script
            -- will not attempt to load mw, which is only needed on the wiki.
            local bodge = require "Module:mw" -- This fixes up mw.text.tag for us.
            local params = {style="color:black; background-color:orange;"}
            text = mw.text.tag({name="span", contents="[[Module talk:Convert|Conversion error]]: " .. text, params=params})
        end
    end
    return text
end

return p