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Module:Convert/makeunits

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This is an old revision of this page, as edited by Johnuniq (talk | contribs) at 10:55, 26 September 2013 (add alttype to specials for an "alternate unit type" for torque/energy). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

--[==[ makeunits.lua
This script can be run on a stand-alone computer to generate the table
of units that specifies how conversions are performed by Module:Convert.

LATER:
If support additional currencies, need to update table:
    local currency = { ['$'] = true, ['£'] = true }

Procedure:
* Copy the Lua script of [[Module:Convert/makeunits]] to a local file
  (say file makeunits.lua).
* Copy the Lua script of [[Module:Convert/text]] to a local file
  (say file converttext.lua).
* Copy the wikitext of the units specification to a local file
  (say file wikitable.tmp which is the default name for the input).
* Run this script with command-line arguments:
  makeunits.lua converttext.lua wikitable.tmp
* Output is written to a file (default name is makeunits.tmp).
* Copy the output into Module:Convert/data to replace the previous table.

Script method:
* Read lines, ignoring everything before "== Conversions ==".
* Process the following lines:
  * Find next level-3 heading like "=== Length ===".
  * Parse each following line starting with "|"
    (but ignore lines starting with "|-" or "|}".
  * Split such lines into fields (delimiter "||") and trim
    leading/trailing whitespace from each field.
    Remove any "colspan" at front of second field (symbol).
  * Remove thousand separators (commas) from the scale field.
    If the scale is a number, do not change it.
    Otherwise, it should be an expression like "5/9", in
    which case it is replaced by the value of the expression.
  * Remove wiki formatting '[[...]]' from the link field.
  * Remove redundant fields from the unit to reduce size of data file.
  * Create alternative forms of a unit such as an alias or a combination.
* Stop processing when encounter end of file or a line starting
  with a level-2 heading ("==" but not "===").
* Repeat above for each heading listed at prepare_data().
* Output Lua source for the units table.

-- Output has the following form.
local all_units = {
    ["unitcode"] = {                        -- standard format
        name1    = "singular name",         -- omitted if redundant
        name1_us = "singular name sp=us",   -- omitted if redundant
        name2    = "plural name",           -- omitted if redundant
        name2_us = "plural name sp=us",     -- omitted if redundant
        symbol   = "symbol",
        sym_us   = "symbol sp=us",          -- omitted if redundant
        usename  = 1,                       -- omitted if empty
        utype    = "unit type",             -- from level-3 heading
        scale    = 1,                       -- a value, if necessary from evaluating an expression
        subdivs  = { ["ft"] = { 5280, default = "km" }, ["yd"] = { 1760 } }  -- composite input; omitted if empty
        link     = "title of article for wikilink",  -- omitted if empty or redundant
        ...                                 -- other values
    },
    ["unitcode"] = {        -- alternative format to generate an alias
        target   = "unit code",
        ...                                 -- optional values to override those of target
    },
    ["unitcode"] = {        -- alternative format to generate a "per" unit like $/acre or BTU/h
        per      = {u1, u2},                -- numbered table of unitcodes (u1 may be a currency symbol)
        ...                                 -- optional values
    },
    ["unitcode"] = {        -- alternative format to generate an error message
        shouldbe = "message that some other unit code should be used",
    },
    ["unitcode"] = {        -- alternative format for combination outputs (like 'm ft')
        combination = {u1, u2, ...},        -- numbered table of unitcodes
        utype    = "unit type",             -- as for standard format
    },
    ["unitcode"] = {        -- alternative format for output multiples (like 'ftin')
        combination = {u1, u2, ...},        -- numbered table of unitcodes
        multiple = {f1, f2, ...},           -- numbered table of integer factors
        utype    = "unit type",             -- as for standard format
    },
    ...
}
]==]

-- To make updating Module:Convert/data easier, this script inserts a preamble and
-- a postamble so the result is what needs to be uploaded.
local file_preamble = [==[
--[[ Conversion data used by Module:Convert.
Use mw.loadData() to obtain read-only access to this module so that
it is loaded only once per page.

These data tables follow:
    all_units           all properties for a unit, including default output
    default_exceptions  exceptions for default output ('kg' and 'g' have different defaults)
    link_exceptions     exceptions for links ('kg' and 'g' have different links)

These tables are generated by a script which reads the wikitext of a page
that documents the required properties of each unit.
The wiki page is currently:
http://en.wikipedia.org/wiki/User:Johnuniq/Conversion_data
]]
]==]

local file_postamble = [==[

return {
    all_units = all_units,
    default_exceptions = default_exceptions,
    link_exceptions = link_exceptions,
}
]==]

local specials = {
    -- This table is used to add extra fields when defining some units which
    -- require exceptions to normal processing.
    -- Each key is in the local language, while each value is fixed text,
    -- however, this script is NOT edited to localize the keys. Instead,
    -- [[Module:Convert/text]] is edited, and this script replaces sections
    -- of the following with localized definitions, if given.
    -- LATER: It would be better if this was defined in the conversions table.
    utype = {
        -- ["unit type in local language"] = "name_used_in_this_script"
        ["fuel efficiency"] = "type_fuel_efficiency",
        ["length"] = "type_length",
        ["temperature"] = "type_temperature",
        ["volume"] = "type_volume",
    },
    ucode = {
        exception = {
            -- ["unit code in local language"] = "name_used_in_module_convert"
            ["ft"] = "integer_more_precision",
            ["in"] = "subunit_more_precision",
        },
        istemperature = {
            -- Common temperature scales (not keVT or MK).
            -- ["unit code in local language"] = 1
            ["C"] = true,
            ["F"] = true,
            ["K"] = true,
            ["R"] = true,
        },
        usesymbol = {
            -- Use unit symbol not name if abbr not specified.
            -- ["unit code in local language"] = 1
            ["C"] = 1,
            ["F"] = 1,
            ["K"] = 1,
            ["R"] = 1,
            ["C-change"] = 1,
            ["F-change"] = 1,
            ["K-change"] = 1,
        },
        alttype = {
            -- Unit has an alternate type that is valid conversion.
            -- ["unit code in local language"] = "alternate type in local language"
            ["Nm"] = "energy",
            ["ftlb"] = "torque",
            ["ftlb-f"] = "torque",
            ["ftlbf"] = "torque",
            ["inlb"] = "torque",
            ["inlb-f"] = "torque",
            ["inlbf"] = "torque",
            ["inoz-f"] = "torque",
            ["inozf"] = "torque",
        },
    },
}

---Begin code from Convert----------------------------------------------
-- Following is adapted from Module:Convert.

local SIprefixes, eng_scales
local plural_suffix = 's'

local function shallow_copy(t)
    -- Return a shallow copy of t.
    -- Do not need the features and overhead of mw.clone() provided by Scribunto.
    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 .. plural_suffix
        elseif key == 'name1_us' then
            value = self.name1
            if not rawget(self, 'name2_us') then
                -- If name1_us is 'foot', do not make name2_us by appending plural_suffix.
                self.name2_us = self.name2
            end
        elseif key == 'name2_us' then
            local raw1_us = rawget(self, 'name1_us')
            if raw1_us then
                value = raw1_us .. plural_suffix
            else
                value = self.name2
            end
        elseif key == 'link' then
            value = self.name1
        else
            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 .. plural_suffix
        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 .. plural_suffix
            else
                value = self.name2
            end
        elseif key == 'link' then
            value = self.name1
        else
            return nil
        end
        rawset(self, key, value)
        return value
    end
}

local function lookup(units, unitcode, sp, what)
    -- Return a copy of the unit if found, or return nil.
    -- In this cut-down code, sp is always nil, and what is ignored.
    local t = units[unitcode]
    if t then
        if t.shouldbe then
            return nil
        end
        local result = shallow_copy(t)
        if result.prefixes then
            result.symbol = result._symbol
            result.name1 = result._name1
            result.name1_us = result._name1_us
        end
        return 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 = string.sub(unitcode, 1, plen)
        local si = SIprefixes[prefix]
        if si then
            local t = units[unitcode:sub(plen+1)]
            if t and t.prefixes then
                local result = shallow_copy(t)
                if (sp == 'us' or t.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
                -- In this script, each scale is a string.
                result.scale = tostring(tonumber(t.scale) * 10 ^ (si.exponent * t.prefixes))
                result.prefixes = nil  -- a prefixed unit does not take more prefixes (in this script, the returned unit may be added to the list of units)
                return setmetatable(result, unit_prefixed_mt)
            end
        end
    end
    local exponent, baseunit = unitcode:match('^e(%d+)(.*)')
    if exponent then
        local engscale = eng_scales[exponent]
        if engscale then
            local result = lookup(units, baseunit, sp, 'no_combination')
            if not result then return nil end
            if result.engscale == nil then
                result.defkey = unitcode  -- key to lookup default exception
                engscale.exponent = exponent
                result.engscale = engscale
                -- Do not set result.scale as this code is called for units where that is not set.
                return result
            end
        end
    end
    return nil
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

---End code from Convert------------------------------------------------

local function strip(text)
    -- Return text with no leading/trailing whitespace.
    return text:match("^%s*(.-)%s*$")
end

local function empty(text)
    -- Return true if text is nil or empty (assuming a string).
    return text == nil or text == ''
end

local function readlines(filename, trim)
    -- Return a table of lines read from a file (line endings removed).
    -- Trim trailing whitespace from each line (if trim = 1), or
    -- trim leading and trailing whitespace (if trim = 2).
    -- Throw an error if a problem occurs.
    local pattern
    if trim == 1 then
        pattern = '^(.-)%s*$'
    elseif trim == 2 then
        pattern = '^%s*(.-)%s*$'
    end
    local f = io.open(filename, 'r')
    if f == nil then
        error('Could not open file ' .. filename, 0)
    end
    local lines = {}
    for line in f:lines() do
        if pattern then
            line = line:match(pattern)
        end
        table.insert(lines, line)
    end
    f:close()
    return lines
end

-- Tables of units: k = unit code, v = unit table.
local units_index = {}  -- all units: normal, alias, per, combination, or multiple
local alias_index = {}  -- all aliases (to detect attempts to define more than once)
local per_index = {}    -- all "per" units (to detect attempts to define more than once)

local function get_unit(ucode)
    -- Look up unit code in our cache of units.
    if empty(ucode) then
        return nil
    end
    return lookup(units_index, ucode)
end

local overrides = {}  -- read from input file for unit codes that should not be checked for a duplicate

local function insert_unique_unit(data, unit, index)
    -- After inserting any required built-in data, insert the unit into the
    -- data table and (if index not nil) add to index,
    -- but not if the unit code is already defined.
    local ucode = unit.unitcode
    local known = get_unit(ucode)
    if known and not overrides[ucode] then
        error('Unit code "' .. ucode .. '" has already been defined', 0)
    end
    for item, t in pairs(specials.ucode) do
        unit[item] = t[ucode]
    end
    if index then
        index[ucode] = unit
    end
    table.insert(data, unit)
end

local function check_condition(condition)
    -- Return true if condition appears to be valid; otherwise return false.
    for _, value in ipairs({ 0, 0.1, 1, 1.1, 10, 100, 1000, 1e4, 1e5 }) do
        local success, result = pcall(evaluate_condition, value, condition)
        if not success then
            return false
        end
    end
    return true
end

local function check_default_expression(default, ucode)
    -- Return a numbered table of names present in param default
    -- (two names if an expression, or one name (param default) otherwise).
    -- Throw an error if a problem occurs.
    -- An expression uses pipe-delimited fields with 'v' representing
    -- the input value for the conversion.
    -- Example (suffix is optional): 'v < 120 ! small ! big ! suffix'
    -- returns { 'smallsuffix', 'bigsuffix' }.
    if default:find('!', 1, true) == nil then
        return { default }
    end
    local t = {}
    for item in (default .. '!'):gmatch('%s*(.-)%s*!') do
        t[#t+1] = item  -- split on '!', removing leading/trailing whitespace
    end
    if not (#t == 3 or #t == 4) then
        error('Default output "' .. default .. '" for unit "' .. ucode .. '" should have 2 or 3 "!"', 0)
    end
    local condition, default1, default2 = t[1], t[2], t[3]
    if #t == 4 then
        default1 = default1 .. t[4]
        default2 = default2 .. t[4]
    end
    if not check_condition(condition) then
        error('Invalid condition in default "' .. default .. '" for unit "' .. ucode .. '"', 0)
    end
    return { default1, default2 }
end

local function check_default(default, ucode, utype, unit_table)
    -- Check the given name (or expression) of a default output.
    -- Throw an error if a problem occurs.
    for _, default in ipairs(check_default_expression(default, ucode)) do
        local default_table = get_unit(default)
        if default_table == nil then
            error('Default output "' .. default .. '" for unit "' .. ucode .. '" is not defined', 0)
        end
        if not (utype == unit_table.utype and utype == default_table.utype) then
            error('Default output "' .. default .. '" for unit "' .. ucode .. '" has wrong type', 0)
        end
    end
end

local function check_all_defaults(units, maxerrors)
    -- Check each default in units and warn if needed.
    -- This is done after all input data has been processed.
    -- Throw an error if a problem occurs.
    local errors = {}
    local missing = {}  -- unitcodes with missing defaults
    for _, unit in ipairs(units) do
        if unit.shouldbe == nil and unit.combination == nil then
            -- This is a standard unit or an alias/per (not shouldbe, combo).
            -- An alias may have a default defined, but it is optional.
            local default = unit.default
            local ucode = unit.unitcode
            if empty(default) then
                if unit.target == nil then  -- unit should have a default
                    table.insert(missing, ucode)
                end
            else
                local ok, msg = pcall(check_default, default, ucode, unit.utype, unit)
                if not ok then
                    table.insert(errors, msg)
                    if #errors >= maxerrors then
                        break
                    end
                end
            end
        end
    end
    if #errors > 0 then
        error(table.concat(errors, '\n'), 0)
    end
    if #missing > 0 then
        print('Warning: Units with the following unit codes have no default output.')
        local limit = maxerrors
        for _, v in ipairs(missing) do
            limit = limit - 1
            if limit < 0 then
                print('  (and more not shown)')
                break
            end
            print('  ' .. v)
        end
    end
end

local function check_all_pers(units, maxerrors)
    -- Check each component of each "per" unit and warn if needed.
    -- In addition, add any required extra fields for some types of units.
    -- This is done after all input data has been processed.
    -- Throw an error if a problem occurs.
    local currency = { ['$'] = true, ['£'] = true }
    local errors = {}
    local function errmsg(text)
        table.insert(errors, text)
    end
    for _, unit in ipairs(units) do
        local per = unit.per
        if per then
            local ucode = unit.unitcode
            if #per ~= 2 then
                errmsg('Unit "' .. ucode .. '" does not have exactly 2 fields in the "per"')
            else
                local types = {}
                for i, v in ipairs(per) do
                    if empty(v) then
                        errmsg('Unit "' .. ucode .. '" has an empty field in the "per"')
                    end
                    if not currency[v] then
                        local t = get_unit(v)
                        if t then
                            types[i] = t.utype
                        else
                            errmsg('Unit "' .. ucode .. '" has undefined unit code "' .. v .. '" in the "per"')
                        end
                    end
                end
                if specials.utype[unit.utype] == 'type_fuel_efficiency' then
                    local expected = { type_volume = 1, type_length = 2 }
                    local top_type = expected[specials.utype[types[1]]]
                    local bot_type = expected[specials.utype[types[2]]]
                    if top_type and bot_type and top_type ~= bot_type then
                        unit.iscomplex = true
                        if top_type == 1 then
                            unit.invert = 1
                        else
                            unit.invert = -1
                        end
                    else
                        errmsg('Unit "' .. ucode .. '" has invalid unit types for fuel efficiency')
                    end
                end
            end
        end
        if #errors >= maxerrors then
            break
        end
    end
    if #errors > 0 then
        error(table.concat(errors, '\n'), 0)
    end
end

local function update_units(units, composites)
    -- Update some unit definitions with extra data defined in other sections.
    -- This is done after all input data has been processed.
    for _, unit in ipairs(units) do
        local comp = composites[unit.unitcode]
        if comp then
            unit.subdivs = '{ ' .. table.concat(comp.subdivs, ', ') .. ' }'
        end
    end
end

local function make_override(data)
    -- Return a function which, when called, stores a unit code is not to be
    -- checked for a duplicate. The table is stored in data (also a table).
    return function (utype, fields)
        local ucode = fields[1]
        if ucode == nil then
            error('Missing unit code for an override', 0)
        end
        if data[ucode] then
            error('Override "' .. ucode .. '" is already defined', 0)
        end
        data[ucode] = true
    end
end

local function make_default(data)
    -- Return a function which, when called, stores a table that defines a
    -- default output unit. The table is stored in data (also a table).
    local defaults_index = {}  -- to detect attempts to define a default twice
    return function (utype, fields)
        -- Store a table defining a unit.
        -- This is for a unit such as 'kg' that has a default output unit
        -- different from what is defined for the base unit ('g').
        -- Throw an error if a problem occurs.
        local ucode = fields[1]
        local default = fields[2]
        if empty(ucode) then
            error('Defaults section: no unit code specified', 0)
        end
        if empty(default) then
            error('Defaults section: unit "' .. ucode .. '" has no default specified', 0)
        end
        if #fields ~= 2 then
            error('Defaults section: unit "' .. ucode .. '" should have two fields only', 0)
        end
        local unit_table = get_unit(ucode)
        if unit_table == nil then
            error('Defaults section: unit "' .. ucode .. '" is not defined', 0)
        end
        local symbol = unit_table.defkey or unit_table.symbol
        if empty(symbol) then
            error('Defaults section: unit "' .. ucode .. '" must have a symbol', 0)
        end
        check_default(default, ucode, utype, unit_table)
        if defaults_index[ucode] then
            error('Defaults section: unit "' .. ucode .. '" has already been specified', 0)
        end
        defaults_index[ucode] = default
        table.insert(data, { symbol = symbol, default = default })
    end
end

local function clean_link(link, name)
    -- Return link, customary where:
    --   link = given link after removing any '[[...]]' wiki formatting
    --          and removing any leading '+' or '*' or '@';
    --   customary = 1 if leading '+', or 2 if '*' or 3 if '@', or nil
    --   (for extra "US" or "U.S." or "Imperial" customary units link).
    -- Result has leading/trailing whitespace removed, and is nil if empty
    -- or if link matches the name, if a name is specified.
    -- If the resulting link is nil, no link field is stored, and
    -- if a link is required, it will be set from the unit's name.
    if empty(link) then
        return nil
    end
    local prefixes = { ['+'] = 1, ['*'] = 2, ['@'] = 3 }
    local customary = prefixes[link:sub(1, 1)]
    if customary then
        link = strip(link:sub(2))
    end
    if link:sub(1, 2) == '[[' then
        link = link:sub(3)
    end
    if link:sub(-2) == ']]' then
        link = link:sub(1, -3)
    end
    link = strip(link)
    if link == '' then
        link = nil
    elseif name then
        local l = link:sub(1, 1):lower() .. link:sub(2)
        local n = name:sub(1, 1):lower() .. name:sub(2)
        if l == n then
            link = nil  -- link == name, ignoring case of first letter
        end
    end
    return link, customary
end

local function make_link(data)
    -- Return a function which, when called, stores a table that defines a
    -- link exception. The table is stored in data (also a table).
    local links_index = {}  -- to detect attempts to define a link twice
    return function (utype, fields)
        -- Store a table defining a unit.
        -- This is for a unit such as 'kg' that has a linked article
        -- different from what is defined for the base unit ('g').
        -- Throw an error if a problem occurs.
        local ucode = fields[1]
        local link = clean_link(fields[2])
        if empty(ucode) then
            error('Missing unit code for a link', 0)
        end
        if empty(link) then
            error('No link defined for unit "' .. ucode .. '"', 0)
        end
        if #fields ~= 2 then
            error('Row for unit "' .. ucode .. '" link should have two fields only', 0)
        end
        local unit_table = get_unit(ucode)
        if unit_table == nil then
            error('Unit code "' .. ucode .. '" for a link is not defined', 0)
        end
        local symbol = unit_table.symbol
        if empty(symbol) then
            error('Unit code "' .. ucode .. '" for a link must have a symbol', 0)
        end
        if links_index[ucode] then
            error('Link exception "' .. ucode .. '" is already defined', 0)
        end
        links_index[ucode] = link
        table.insert(data, { symbol = symbol, link = link })
    end
end

local function clean_scale(scale)
    -- Return cleaned scale as a string, after evaluating any expression.
    -- It would be better to retain scale expressions like "5/9" so that
    -- the expression is evaluated on the server and maintains the full
    -- resolution of the server. However, there are many such expressions
    -- in the table of all units, and it seems pointless to require the
    -- server to evaluate all of them just to do one convert.
    if empty(scale) then
        error('Missing scale', 0)
    end
    assert(type(scale) == 'string', 'Bug: scale has an unexpected type')
    scale = string.gsub(scale, ',', '')  -- remove comma separators
    if tonumber(scale) then  -- not an expression
        return scale
    end
    -- Do some simple sanity checks to avoid executing rubbish.
    if #scale > 50 then
        error('Scale is too long: "' .. scale .. '"', 0)
    end
    if string.len(scale:gsub('[ %d%-*/+()^eE.]+', '')) > 0 then
        error('Scale expression contains invalid characters: "' .. scale .. '"', 0)
    end
    local status, value = pcall(loadstring('return (' .. scale .. ')'))
    if not (status and type(value) == 'number') then
        error('Scale expression is invalid: "' .. scale .. '"', 0)
    end
    local result = string.format('%.30g', value)
    if result:find('#', 1, true) then
        -- Overflow or similar (scale = '1/0' gives result = '1.#INF').
        error('Scale expression gives an invalid value: "' .. scale .. '"', 0)
    end
    -- Omit redundant zeros from results like '1.2e-005'.
    -- Do not bother looking for results like '1.2e+005' as none occur in practice.
    local lhs, zeros, rhs = result:match('^(.-e%-)(0+)(.*)')
    if zeros then
        result = lhs .. rhs
    end
    return result
end

local function add_alias_optional_fields(unit, start, fields, target)
    -- Inspect fields[i] for i = start, start+1 ..., and extract any
    -- definitions appropriate for an alias or "per", and add them to unit.
    -- For an alias, target is a valid unit; for a "per", target is nil.
    -- Throw error if encounter an invalid entry.
    for i = start, #fields do
        local field = fields[i]
        if not empty(field) then
            local lhs, rhs = field:match('^%s*(.-)%s*=%s*(.-)%s*$')
            local good
            if not empty(rhs) then
                for _, item in ipairs({ 'sp', 'default', 'link', 'multiplier', 'symbol', 'symlink' }) do
                    if lhs == item then
                        if item == 'sp' then
                            if rhs == 'us' then
                                unit.sp_us = true
                                good = true
                            end
                        elseif item == 'link' then
                            local tlink
                            if target then
                                tlink = target[item]
                            end
                            local link, customary = clean_link(rhs, tlink)
                            if link then
                                unit[item] = link
                            end
                            if customary then
                                unit.customary = customary
                            end
                            good = true
                        elseif item == 'symlink' then
                            local pos1 = rhs:find('[[', 1, true)
                            local pos2 = rhs:find(']]', 1, true)
                            if not (pos1 and pos2 and (pos1 < pos2)) then
                                error('Alias "' .. unit.unitcode .. '" must include a wikilink ("[[...]]") in the symlink text', 0)
                            end
                            unit.symlink = rhs
                            good = true
                        elseif item == 'multiplier' then
                            if not tonumber(rhs) then
                                error('Alias "' .. unit.unitcode .. '" has multiplier "' .. rhs .. '" which is not a number', 0)
                            end
                            unit[item] = rhs
                            good = true
                        else
                            if target and rhs == target[item] then
                                error('Should omit "' .. item .. '" for alias "' .. unit.unitcode .. '" because it is the same as its target', 0)
                            end
                            unit[item] = rhs
                            good = true
                        end
                        break
                    end
                end
            end
            if not good then
                error('Alias has invalid text in field "' .. field .. '"', 0)
            end
        end
    end
end

local function make_alias(fields, ucode, utype, symbol)
    -- Return a new alias unit, or return nil if symbol is not already
    -- defined as the unit code of the target unit.
    -- Throw an error if invalid.
    local target = get_unit(symbol)
    if not target then
        return nil
    end
    local unit = { unitcode = ucode, utype = utype, target = symbol }
    add_alias_optional_fields(unit, 3, fields, target)
    if alias_index[ucode] then
        error('Alias "' .. ucode .. '" already defined', 0)
    else
        alias_index[ucode] = unit
    end
    if target.utype ~= utype then
        error('Target of alias "' .. ucode .. '" has wrong type', 0)
    end
    return unit
end

local function make_per(fields, ucode, utype, symbol)
    -- Return a new "per" unit, or return nil if symbol is not of form "x/y".
    -- Throw an error if invalid.
    -- The top, bottom unit codes are checked later, after all units are defined.
    local top, bottom = symbol:match('^(.-)/(.*)$')
    if not top then
        return nil
    end
    local unit = { unitcode = ucode, utype = utype, per = { strip(top), strip(bottom) } }
    add_alias_optional_fields(unit, 3, fields)
    if per_index[ucode] then
        error('Per unit "' .. ucode .. '" already defined', 0)
    else
        per_index[ucode] = unit
    end
    return unit
end

local function make_unit(data)
    -- Return a function which, when called, stores a table that defines a
    -- single unit. The table is stored in data (also a table).
    local fieldnames = {
        -- Fields in the Conversions section are assumed to be in the following order.
        'unitcode',
        'symbol',
        'sym_us',
        'scale',
        'extra',
        'name1',
        'name2',
        'name1_us',
        'name2_us',
        'prefixes',
        'default',
        'link',
    }
    return function (utype, fields)
        -- Store a table defining a unit.
        -- Throw an error if a problem occurs.
        local ucode, symbol = fields[1], fields[2]
        if empty(utype) then
            error('Missing unit type', 0)
        end
        if empty(ucode) then
            error('Missing unit code', 0)
        end
        if empty(symbol) then
            error('Missing symbol', 0)
        end
        local prefix = symbol:sub(1, 1)
        if prefix == '~' or prefix == '=' or prefix == '!' then
            if symbol:sub(1, 2) == '==' then
                prefix = symbol:sub(1, 2)
            end
            symbol = strip(symbol:sub(#prefix + 1))  -- omit prefix and any following whitespace
            fields[2] = symbol
        else
            prefix = nil  -- not a valid prefix
        end
        if prefix == '=' or prefix == '==' then
            -- ucode is an alias (a fake unit code used in a convert template), or
            -- defines a "per" unit like "$/acre" or "BTU/h".
            -- For an alias, symbol is the unit code of the actual unit.
            -- For a "per", symbol is of form "x/y" where x and y are unit codes,
            -- or x is a recognized currency symbol and y is a unit code.
            -- Checking that x and y are valid is deferred until all units have
            -- been defined so, for example, "BTU/h" can be defined before "h".
            local unit
            if prefix == '=' then
                unit = make_alias(fields, ucode, utype, symbol)
            else
                unit = make_per(fields, ucode, utype, symbol)
            end
            if not unit then
                -- Do not define an alias in terms of another alias.
                error('Primary unit must be defined before alias =' .. symbol, 0)
            end
            insert_unique_unit(data, unit, units_index)
            return
        elseif prefix == '!' then
            -- ucode may be incorrectly entered as a unit code.
            -- symbol is a message saying what unit code should be used.
            local unit = { unitcode = ucode, shouldbe = symbol }
            insert_unique_unit(data, unit, nil)
            return
        end
        -- Make the unit.
        local unit = { utype = utype }
        for i, name in ipairs(fieldnames) do
            if not empty(fields[i]) then
                unit[name] = fields[i]
            end
        end
        -- Remove redundancy from unit.
        if unit.sym_us == symbol then
            unit.sym_us = nil
        end
        local prefixes = unit.prefixes
        if empty(prefixes) then
            prefixes = nil
        end
        local name1, name2 = unit.name1, unit.name2
        if name1 then
            if name1 == symbol and not prefixes then
                -- A unit which takes an SI prefix must not have a nil name because,
                -- for example, the name for "kW" = "kilo" .. "watt" (name for "W").
                -- The "not prefixes" test is needed for bn.wikipedia where the
                -- watt unit has the same name and symbol.
                unit.name1 = nil
            end
        else
            name1 = symbol
        end
        if name2 then
            if plural_suffix ~= '' and name2 == name1 .. plural_suffix then
                unit.name2 = nil
            end
        end
        local name1_us, name2_us = unit.name1_us, unit.name2_us
        if name1_us then
            if name1_us == name1 then
                unit.name1_us = nil
            end
        else
            name1_us = name1
        end
        if name2_us then
            if plural_suffix ~= '' and name2_us == name1_us .. plural_suffix then
                unit.name2_us = nil
            end
        end
        -- Other changes to unit.
        unit.scale = clean_scale(unit.scale)
        local extra = unit.extra
        if not empty(extra) then
            -- Set appropriate fields for a unit that needs more than a simple
            -- multiplication by a ratio of unit scales to convert values.
            unit.iscomplex = true
            if extra == 'volume/length' then
                unit.invert = 1
            elseif extra == 'length/volume' then
                unit.invert = -1
            elseif specials.utype[utype] == 'type_temperature' then
                unit.offset = extra
            else
                unit.builtin = extra
            end
        end
        if prefix == '~' then
            -- Magic code for units like "acre" where the symbol is not really a
            -- symbol, and output should use the singular or plural name instead.
            unit.usename = 1
        end
        local name_for_link
        if prefixes then
            -- If set name_for_link = name1 for a prefixed unit like g, then the
            -- link is "kilogram" for kg, and "yottagram" for Yg, and so on for all
            -- prefixes. That might be good for some units, but not all.
            if prefixes == 'SI' then
                unit.prefixes = 1
            elseif prefixes == 'SI2' then
                unit.prefixes = 2
            elseif prefixes == 'SI3' then
                unit.prefixes = 3
            else
                error('Unknown prefix: "' .. prefixes .. '"', 0)
            end
        else
            name_for_link = name1
        end
        unit.link, unit.customary = clean_link(unit.link, name_for_link)
        if prefixes then
            local name1, name1_us = unit.name1, unit.name1_us  -- after redundancy removed
            if name1 == nil then
                error('Unit with Prefix set must include Name', 0)
            end
            if unit.name2 or unit.name2_us then
                error('Unit with Prefix set must have plural name that is Name + "s"', 0)
            end
            if unit.sym_us then
                error('Unit with Prefix set must have same Symbol and US symbol', 0)
            end
            local pos = name1:find('%s', 1, true)
            local pos_us
            if name1_us then
                pos_us = name1_us:find('%s', 1, true)
            else
                pos_us = pos
            end
            if pos ~= pos_us then
                -- The only cases with "%s" are "square %smetre" and "cubic %smetre" (or "meter" for US),
                -- so do not bother having a procedure to handle different positions of "%s".
                error('Unit with Prefix set and "%s" in Name and US name, must have the "%s" at the same position', 0)
            end
            if pos then
                if pos == 1 then
                    -- Omit leading "%s"; convert will assume position = 1 since not stored.
                    unit.name1 = name1:sub(3)
                    if name1_us then
                        unit.name1_us = name1_us:sub(3)
                    end
                else
                    -- Omit "%s" and store its position.
                    unit.name1 = name1:sub(1, pos - 1) .. name1:sub(pos + 2)
                    if name1_us then
                        unit.name1_us = name1_us:sub(1, pos - 1) .. name1_us:sub(pos + 2)
                    end
                    unit.prefix_position = pos
                end
            end
            for _, name in ipairs({ 'symbol', 'name1', 'name1_us' }) do
                unit['_' .. name] = unit[name]
                unit[name] = nil  -- force call to __index metamethod so any SI prefix can be handled
            end
        end
        for name, v in pairs(unit) do
            -- Reject if a string field includes "%s" (should never occur after above).
            if type(v) == 'string' and v:find('%s', 1, true) then
                error('Field "' .. name .. '" must not contain "%s"', 0)
            end
        end
        insert_unique_unit(data, unit, units_index)
    end
end

local function make_combination(data)
    -- Return a function which, when called, stores a table that defines a
    -- single combination unit. The table is stored in data (also a table).
    return function (utype, fields)
        -- Store a table defining a unit.
        -- This is for a combination unit that specifies more than one output.
        -- The target units must be defined first.
        -- Throw an error if a problem occurs.
        local unit = { utype = utype, combination = {} }
        for i, v in ipairs(fields) do
            if i == 1 then  -- unitcode
                if v == '' then
                    error('Missing unit code for a combination', 0)
                end
                unit.unitcode = v
            elseif v == '' then
                -- Ignore empty fields.
            else
                local target = get_unit(v)
                if target == nil then
                    error('Unit "' .. v .. '" in combination "' .. unit.unitcode .. '" not defined', 0)
                end
                if target.utype ~= utype then
                    error('Unit "' .. v .. '" in combination "' .. unit.unitcode .. '" has wrong type', 0)
                end
                table.insert(unit.combination, v)
            end
        end
        if #unit.combination < 2 then
            local msg
            if #unit.combination == 0 then
                msg = 'No units specified for combination "' .. unit.unitcode .. '"'
            else
                msg = 'Only one unit specified for combination "' .. unit.unitcode .. '"'
            end
            error(msg, 0)
        end
        insert_unique_unit(data, unit, units_index)
    end
end

local function reversed(t)
    -- Return a numbered table in reverse order.
    local reversed, count = {}, #t
    for i = 1, count do
        reversed[i] = t[count + 1 - i]
    end
    return reversed
end

local function make_inputmultiple(data)
    -- Return a function which, when called, stores a table that defines a
    -- single composite (multiple input) unit. The table is stored in data (also a table).
    return function (utype, fields)
        -- Set or update an entry in the data table to record that a unit
        -- accepts subdivisions to make a composite input unit like '|2|ft|6|in'.
        -- The target units must be defined first.
        -- Throw an error if a problem occurs.
        local unitcode  -- dummy code required for simplicity, but which is not used in output
        local alternate_code  -- an alternative unit code can be specified to replace convert input
        local fixed_name  -- a fixed name can be specified to replace the unit's normal symbol/name
        local default_code
        local ucodes, scales = {}, {}
        for i, v in ipairs(fields) do
            -- 1=composite, 2=ucode1, 3=ucode2, 4=default, 5=alternate, 6=name
            if i == 1 then
                if v == '' then
                    error('Missing unit code for a composite', 0)
                end
                unitcode = v
            elseif 2 <= i and i <= 5 then
                if not (i == 5 and v == '') then
                    local target = get_unit(v)
                    if target == nil then
                        error('Unit "' .. v .. '" in composite "' .. unitcode .. '" not defined', 0)
                    end
                    if target.utype ~= utype then
                        error('Unit "' .. v .. '" in composite "' .. unitcode .. '" has wrong type', 0)
                    end
                    if i < 4 then
                        table.insert(ucodes, v)
                        table.insert(scales, target.scale)
                    elseif i == 4 then
                        default_code = v
                    else
                        if scales[#scales] ~= target.scale then
                            error('Alternate unit "' .. v .. '" in composite "' .. unitcode .. '" has wrong scale', 0)
                        end
                        alternate_code = v
                    end
                end
            elseif i == 6 then
                if v ~= '' then
                    fixed_name = v
                end
            else
                error('Composite "' .. unitcode .. '" has too many fields', 0)
            end
        end
        if #ucodes ~= 2 then
            error('Composite "' .. unitcode .. '" must specify exactly two unit codes', 0)
        end
        if default_code == nil then
            error('Composite "' .. unitcode .. '" must specify a default unit code', 0)
        end
        -- Component units must be specified from most-significant to least-significant,
        -- and each ratio of a pair of scales must be very close to an integer.
        -- Currently, there will be exactly two scales and one ratio.
        local ratios, count = {}, #scales
        for i = 1, count do
            local scale = tonumber(scales[i])
            if scale == nil or scale <= 0 then
                error('Composite "' .. unitcode .. '" has a component with an invalid scale, "' .. scales[i] .. '"', 0)
            end
            scales[i] = scale
        end
        for i = 1, count - 1 do
            local ratio = scales[i] / scales[i + 1]
            local rounded = math.floor(ratio + 0.5)
            if rounded < 2 then
                error('Composite "' .. unitcode .. '" has components in wrong order or with invalid scales', 0)
            end
            if math.abs(ratio - rounded)/ratio > 1e-6 then
                error('Composite "' .. unitcode .. '" has components where scale ratios are not integers', 0)
            end
            ratios[i] = rounded
        end
        local text = { tostring(ratios[1]) }
        local function add_text(key, value)
            table.insert(text, string.format('%s = %q', key, value))
        end
        if default_code then
            add_text('default', default_code)
        end
        if alternate_code then
            add_text('unit', alternate_code)
        end
        if fixed_name then
            add_text('name', fixed_name)
        end
        local subdiv = string.format('["%s"] = { %s }', ucodes[2], table.concat(text, ', '))
        local main_code = ucodes[1]
        local item = data[main_code]
        if item then
            table.insert(item.subdivs, subdiv)
        else
            data[main_code] = { subdivs = { subdiv } }
        end
    end
end

local function make_outputmultiple(data)
    -- Return a function which, when called, stores a table that defines a
    -- single multiple output unit. The table is stored in data (also a table).
    return function (utype, fields)
        -- Store a table defining a unit.
        -- This is for a multiple unit like 'ydftin' (result in yards, feet, inches).
        -- The target units must be defined first.
        -- Throw an error if a problem occurs.
        local unit = { utype = utype }
        local ucodes, scales = {}, {}
        for i, v in ipairs(fields) do
            if i == 1 then  -- unitcode
                if v == '' then
                    error('Missing unit code for a multiple', 0)
                end
                unit.unitcode = v
            elseif v == '' then
                -- Ignore empty fields.
            else
                local target = get_unit(v)
                if target == nil then
                    error('Unit "' .. v .. '" in multiple "' .. unit.unitcode .. '" not defined', 0)
                end
                if target.utype ~= utype then
                    error('Unit "' .. v .. '" in multiple "' .. unit.unitcode .. '" has wrong type', 0)
                end
                table.insert(ucodes, v)
                table.insert(scales, target.scale)
            end
        end
        if #ucodes < 2 then
            local msg
            if #ucodes == 0 then
                msg = 'No units specified for multiple "' .. unit.unitcode .. '"'
            else
                msg = 'Only one unit specified for multiple "' .. unit.unitcode .. '"'
            end
            error(msg, 0)
        end
        -- Component units must be specified from most-significant to least-significant
        -- (so scale values will be in descending order),
        -- and each ratio of a pair of scales must be very close to an integer.
        -- The componenets and ratios are stored in reverse order (least significant first).
        -- This script stores a unit scale as a string (might be an expression like "5/9"),
        -- but scales in a multiple are handled as numbers (should never be expressions).
        local ratios, count = {}, #scales
        for i = 1, count do
            local scale = tonumber(scales[i])
            if scale == nil or scale <= 0 then
                error('Multiple "' .. unit.unitcode .. '" has a component with an invalid scale, "' .. scales[i] .. '"', 0)
            end
            scales[i] = scale
        end
        for i = 1, count - 1 do
            local ratio = scales[i] / scales[i + 1]
            local rounded = math.floor(ratio + 0.5)
            if rounded < 2 then
                error('Multiple "' .. unit.unitcode .. '" has components in wrong order or with invalid scales', 0)
            end
            if math.abs(ratio - rounded)/ratio > 1e-6 then
                error('Multiple "' .. unit.unitcode .. '" has components where scale ratios are not integers', 0)
            end
            ratios[i] = rounded
        end
        unit.combination = reversed(ucodes)
        unit.multiple = reversed(ratios)
        insert_unique_unit(data, unit, units_index)
    end
end

local out_unit_prefix = [[

---------------------------------------------------------------------------
-- Do not change the data in this table because it is created by running --
-- a script that reads the wikitext from a wiki page (see note above).   --
---------------------------------------------------------------------------
local all_units = {
]]

local out_unit_suffix = [[
}
]]

local out_default_prefix = [[

---------------------------------------------------------------------------
-- Do not change the data in this table because it is created by running --
-- a script that reads the wikitext from a wiki page (see note above).   --
---------------------------------------------------------------------------
local default_exceptions = {
    -- Prefixed units with a default different from that of the base unit.
    -- Each key item is a prefixed symbol (unitcode for engineering notation).
]]

local out_default_suffix = [[
}
]]

local out_default_item = [[
    ["{symbol}"] = "{default}",
]]

local out_link_prefix = [[

---------------------------------------------------------------------------
-- Do not change the data in this table because it is created by running --
-- a script that reads the wikitext from a wiki page (see note above).   --
---------------------------------------------------------------------------
local link_exceptions = {
    -- Prefixed units with a linked article different from that of the base unit.
    -- Each key item is a prefixed symbol (not unitcode).
]]

local out_link_suffix = [[
}
]]

local out_link_item = [[
    ["{symbol}"] = "{link}",
]]

local combination_specification = {     -- pure combination like 'm ft', or a multiple like 'ftin'
    'combination',
    'multiple',
    'utype',
}

local alias_specification = {
    'target',
    'symbol',
    'sp_us',
    'default',
    'link',
    'symlink',
    'customary',
    'multiplier',
}

local per_specification = {
    'per',
    'symbol',
    'sp_us',
    'utype',
    'invert',
    'iscomplex',
    'default',
    'link',
    'symlink',
    'customary',
}

local shouldbe_specification = {
    'shouldbe',
}

local unit_specification = {
    '_name1',
    '_name1_us',
    '_symbol',
    'prefix_position',
    'name1',
    'name1_us',
    'name2',
    'name2_us',
    'symbol',
    'sym_us',
    'usename',
    'usesymbol',
    'utype',
    'alttype',
    'builtin',
    'scale',
    'offset',
    'invert',
    'iscomplex',
    'istemperature',
    'exception',
    'prefixes',
    'default',
    'subdivs',
    'link',
    'customary',
    'sp_us',
}

local no_quotes = {
    combination = true,
    customary = true,
    multiple = true,
    multiplier = true,
    offset = true,
    per = true,
    prefix_position = true,
    scale = true,
    subdivs = true,
}

local function unit_lines(unit, spec)
    -- Return string of lines of Lua source that defines a unit.
    local first_item = '    ["' .. unit.unitcode .. '"] = {'
    local last_item  = '    },'
    local t = { first_item }
    for _, k in ipairs(spec) do
        local v = unit[k]
        if v then
            local want_quotes = (type(v) == 'string' and not no_quotes[k])
            if type(v) == 'boolean' then
                v = tostring(v)
            elseif type(v) == 'number' or k == 'scale' then
                -- Replace results like '1e-006' with '1e-6'.
                v = string.gsub(tostring(v), '(e[+-])0+([1-9].*)', '%1%2', 1)
            elseif type(v) ~= 'string' then
                error('Fatal error: unknown data type for ' .. unit.unitcode)
            end
            local fmt = string.format('\t%%s%s = %%%s,',
                    (#k < 8) and '\t' or '',
                    want_quotes and 'q' or 's')
            t[#t+1] = fmt:format(k, v)
        end
    end
    t[#t+1] = last_item
    t[#t+1] = ''  -- so last_item gets '\n'
    return table.concat(t, '\n')
end

local function numbered_table_as_string(data, unit)
    local t = {}
    for _, v in ipairs(data) do
        if type(v) == 'string' then
            table.insert(t, '"' .. v .. '"')
        elseif type(v) == 'number' then
            table.insert(t, tostring(v))
        else
            error('Fatal error: unknown data type for ' .. unit.unitcode)
        end
    end
    return '{ ' .. table.concat(t, ', ') .. ' }'
end

local function write_results(outfile, units, defaults, links)
    io.output(outfile)
    io.write(file_preamble)
    io.write(out_unit_prefix)
    for _, unit in ipairs(units) do
        local spec
        if unit.target then
            spec = alias_specification
        elseif unit.per then
            spec = per_specification
            unit.per = numbered_table_as_string(unit.per, unit)
        elseif unit.shouldbe then
            spec = shouldbe_specification
        elseif unit.combination then
            spec = combination_specification
            unit.combination = numbered_table_as_string(unit.combination, unit)
            if unit.multiple then
                unit.multiple = numbered_table_as_string(unit.multiple, unit)
            end
        else
            spec = unit_specification
        end
        io.write(unit_lines(unit, spec))
    end
    io.write(out_unit_suffix)
    io.write(out_default_prefix)
    for _, unit in ipairs(defaults) do
        io.write((out_default_item:gsub('{([%w_]+)}', unit)))
    end
    io.write(out_default_suffix)
    io.write(out_link_prefix)
    for _, unit in ipairs(links) do
        io.write((out_link_item:gsub('{([%w_]+)}', unit)))
    end
    io.write(out_link_suffix)
    io.write(file_postamble)
    io.close()
end

local function extract_heading(line)
    -- Return n, s where n = heading level number (nil if none), and
    -- s = heading text (with leading/trailing whitespace removed).
    local pattern = '^(==+)%s*(.-)%s*(==+)%s*$'
    local before, heading, after = line:match(pattern)
    if heading and #heading > 0 then
        -- Don't bother checking if before == after.
        return #before, heading
    end
end

local function fields(line)
    -- Return a numbered table of fields split from line.
    -- Items are delimited by "||".
    -- Each item has leading/trailing whitespace removed, and any encoded pipe
    -- characters are decoded.
    -- The second field (for symbol when processing units) is adjusted to
    -- remove any "colspan" at the front of lines like:
    -- "| unitcode || colspan="11" | !Text to display for an error message".
    local t = {}
    line = line .. "||"  -- to get last field
    for item in line:gmatch("%s*(.-)%s*||") do
        table.insert(t, (item:gsub('&#124;', '|')))
    end
    local cleaned = t[2]:match('^%s*colspan%s*=.-|%s*(.*)$')
    if cleaned then
        t[2] = cleaned
    end
    return t
end

local function prepare_section(maker, lines, section, maxerrors)
    -- Process the first level-two section with the given section name
    -- in the given table of lines of wikitext.
    -- If successful, maker inserts each item into a table.
    -- Otherwise, an error is thrown.
    local skip = true
    local errors = {}
    local utype  -- unit type (from level-three heading)
    local nbsp = '\160'  -- nonbreaking space is utf-8 encoded as hex c2 a0
    for linenumber, line in ipairs(lines) do
        if skip then
            -- Skip down to and including the starting heading.
            local level, heading = extract_heading(line)
            if level == 2 and heading == section then
                skip = false
            end
        else
            -- Accummulate unit definitions.
            local c1 = line:sub(1, 1)
            local c2 = line:sub(2, 2)
            if c1 == '|' and not (c2 == '-' or c2 == '}') then
                if empty(utype) then
                    error('No level 3 heading before: ' .. line, 0)
                end
                if line:find(nbsp, 1, true) then
                    -- For example, "acre ft" does not work if it contains nbsp.
                    print('Warning: line ' .. linenumber .. ' contains a nonbreaking space')
                end
                local ok, msg = pcall(maker, utype, fields(line:sub(2)))
                if not ok then
                    table.insert(errors, msg .. ' (line ' .. linenumber .. ')')
                    if #errors >= maxerrors then
                        break
                    end
                end
            else
                local level, heading = extract_heading(line)
                if level == 3 then
                    utype = heading:lower()
                elseif level == 2 then
                    break
                end
            end
        end
    end
    if #errors > 0 then
        error(table.concat(errors, '\n'), 0)
    end
end

local function prepare_data(filename, maxerrors)
    -- Read the file with the given name, and process the wikitext
    -- in the sections with wanted level-two headings.
    -- Return units, defaults, links (three tables).
    -- Throw an error if a problem occurs.
    if filename == nil then
        error('Need name of file with unit definitions', 0)
    end
    print('Reading wikitext from file ' .. filename)
    local composites, defaults, links, units = {}, {}, {}, {}
    local sections = {
        -- LATER: Section names must be in English to match following text.
        { 'Overrides'       , make_override      , overrides  },
        { 'Conversions'     , make_unit          , units      },
        { 'Output multiples', make_outputmultiple, units      },
        { 'Combinations'    , make_combination   , units      },
        { 'Input multiples' , make_inputmultiple , composites },  -- after all units defined so default will be defined
        { 'Defaults'        , make_default       , defaults   },
        { 'Links'           , make_link          , links      },
    }
    local lines = readlines(filename, 2)
    for _, section in ipairs(sections) do
        local heading = section[1]
        local maker = section[2](section[3])
        prepare_section(maker, lines, heading, maxerrors)
    end
    check_all_defaults(units, maxerrors)
    check_all_pers(units, maxerrors)
    update_units(units, composites)
    return units, defaults, links
end

local function main(text_module, infile, outfile)
    if not text_module then
        print('Must specify text_module in first argument.')
        print('Error, output not created.')
        os.exit(1)
    end
    local text_code = require(text_module)
    SIprefixes = text_code.SIprefixes
    eng_scales = text_code.eng_scales
    local translation = text_code.translation_table
    if translation then
        if translation.plural_suffix then
            plural_suffix = translation.plural_suffix
        end
        local ts = translation.specials
        if ts then
            if ts.utype then
                specials.utype = ts.utype
            end
            if ts.ucode then
                specials.ucode = ts.ucode
            end
        end
    end
    local ok, units, defaults, links = pcall(prepare_data, infile, 20)
    if ok then
        write_results(outfile, units, defaults, links)
        print('Results written to file ' .. outfile)
    else
        print('Error, output not created.')
        print(units)
        os.exit(1)
    end
end

main(arg[1], arg[2] or 'wikitable.tmp', arg[3] or 'makeunits.tmp')