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Module:number list: Difference between revisions

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Module:number list (view source)

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local export = {}


local m_links = require("Module:links")
--[=[
Terminology:
Number = a bare number; a mathematical entity which has different form types (e.g. cardinal, ordinal)
Form type = a category of the forms that represent a number; examples are cardinal, ordinal, distributive, fractional
Form = a word or expression that represents a number in a given language
Tag = an identifier attached to a form that allows different logical subtypes of forms from the same form type to be
      identified; e.g. 'vuitanta-vuit<tag:Central>' vs. 'huitanta-huit<tag:Valencian>' to identify variants of
  Catalan cardinal number 88 for different dialectal standards; there can be multiple tags per form, e.g.
  'tair ar ddeg<tag:vigesimal><tag:feminine>' for the Welsh number 13 where there are both decimal/vigesimal and
  masculine/feminine variants of this number
Tag list = a list of tags in the order they are specified in the data, e.g. {"vigesimal", "feminine"} for the example
          above
Combined tag = the string representation of a tag list, using ||| to separate individual tags
]=]
local form_types = {
{key = "cardinal", display = "[[wikt:cardinal number|Cardinal]]"},
{key = "ordinal", display = "[[wikt:ordinal number|Ordinal]]"},
{key = "ordinal_abbr", display = "[[wikt:ordinal number|Ordinal]] [[wikt:abbreviation]]"},
{key = "adverbial", display = "[[wikt:adverbial number|Adverbial]]"},
{key = "multiplier", display = "[[wikt:multiplier|Multiplier]]"},
{key = "distributive", display = "[[wikt:distributive number|Distributive]]"},
{key = "collective", display = "[[wikt:collective number|Collective]]"},
{key = "fractional", display = "[[wikt:fractional|Fractional]]"},
{key = "formal", display = "[[wikt:formal|Formal]]"},
}
-- Keys in a `numbers` entry that aren't form types.
local non_form_types = {
numeral = true,
wplink = true,
next = true,
prev = true,
next_outer = true,
prev_outer = true,
upper = true,
lower = true,
}
--[=[
--
-- General set intersection
local function set_intersection(sets)
local intersection = {}
for key, _ in pairs(sets[1]) do
intersection[key] = true
end
for i = 2, #sets do
local this_set = sets[i]
for key, _ in pairs(intersection) do
if not this_set[key] then
-- See https://stackoverflow.com/questions/6167555/how-can-i-safely-iterate-a-lua-table-while-keys-are-being-removed
-- It is safe to modify or remove a key while iterating over the table.
intersection[key] = nil
end
end
end
return intersection
end
]=]
local function set_intersection(set1, set2)
local intersection = {}
for key, _ in pairs(set1) do
intersection[key] = true
end
for key, _ in pairs(intersection) do
if not set2[key] then
-- See https://stackoverflow.com/questions/6167555/how-can-i-safely-iterate-a-lua-table-while-keys-are-being-removed
-- It is safe to modify or remove a key while iterating over the table.
intersection[key] = nil
end
end
return intersection
end
local function list_to_set(list)
local set = {}
for _, item in ipairs(list) do
set[item] = true
end
return set
end
function export.get_data_module_name(langcode, must_exist)
local module_name = "Module:number list/data/" .. langcode
if must_exist and not mw.title.new(module_name).exists then
error(("Data module [[%s]] for language code '%s' does not exist"):format(module_name, langcode))
end
return module_name
end
local function power_of(n)
return "1" .. string.rep("0", n)
end
-- Format a number (either a Lua number or a string) in fixed point without any decimal point or scientific notation.
-- `tostring()` doesn't work because it converts large numbers such as 1000000000000000 to "1e+15".
function export.format_fixed(number)
if type(number) == "string" then
return number
else
return ("%.0f"):format(number)
end
end
-- Parse a form with modifiers such as 'vuitanta-vuit<tag:Central>' or 'سیزده<tr:sizdah>'
-- or 'سیزده<tr:sizdah><tag:Iranian>' into its component parts. Return a form object, i.e. an object with fields
-- `form` for the form, and `alt`, `tr`, `tag`, `q`, `qq` or `link` for the modifiers. The `tag` field is a tag list
-- (see above).
function export.parse_form_and_modifiers(form_with_modifiers)
local retval = {}
local form
form = form_with_modifiers
while true do
local new_form, angle_bracketed = form:match("^(.-)(%b<>)$")
if not new_form then
break
end
local prefix, content = angle_bracketed:match "^<(%w+):(.+)>$"
if not prefix then
break
end
if prefix == "tag" then
if retval.tag then
table.insert(retval.tag, content)
else
retval.tag = {content}
end
elseif prefix == "q" or prefix == "qq" or prefix == "tr" or prefix == "link" or prefix == "alt" then
if retval[prefix] then
error(("Duplicate modifier '%s' in data module form, already saw value '%s': %s"):format(prefix,
retval[prefix], form_with_modifiers))
else
retval[prefix] = content
end
else
error(("Unrecognized modifier '%s' in data module form: %s"):format(prefix, form_with_modifiers))
end
form = new_form
end
retval.form = form
return retval
end
-- Find the `numbers` object for a given number (which should be in string representation).
function export.lookup_data(m_data, numstr)
-- Don't try to convert very large numbers to Lua numbers because they may overflow.
-- Powers of 10 >= 10^22 cannot be represented exactly as a Lua number.
return m_data.numbers[numstr] or #numstr < 22 and m_data.numbers[tonumber(numstr)] or nil
end
-- Return true if a < b, where either may be a Lua number or the string representation of a number.
function export.numbers_less_than(a, b)
a, b = export.format_fixed(a), export.format_fixed(b)
local alen = #a
local blen = #b
if alen < blen then
return true
end
if alen > blen then
return false
end
return a < b
end
-- Return true if a > b, where either may be a Lua number or the string representation of a number.
function export.numbers_greater_than(a, b)
return export.numbers_less_than(b, a)
end
-- Given a number form, convert it to its independent (un-affixed) form. This only makes sense for certain languages
-- where there is a difference between independent and affixed forms of numerals. Currently the only such language
-- is Swahili, where e.g. the cardinal number form for 3 is affixed [[wikt:-tatu]], independent [[wikt:tatu]], and the ordinal
-- number form is [[wikt:-a tatu]], independent [[wikt:tatu]]. We rely on a set of Lua pattern substitutions to convert from
-- affixed to independent form.
--
-- FIXME: This needs major rethinking in a way that isn't specific to Swahili.
local function maybe_unaffix(m_data, form)
if not m_data.unaffix then
return form
end
for _, entry in ipairs(m_data.unaffix) do
local from, to = unpack(entry)
form = mw.ustring.gsub(form, from, to)
end
return form
end
-- Convert the given number form (taken from the data for `lang`, after parsing the form for modifiers and stripping
-- the modifiers) to an entry name. The form may have links and/or accent/length marks that need to be stripped.
local function form_to_entry_name(form, lang)
return (lang:makeEntryName(m_links.remove_links(form)))
end
-- Return true if the given number form object (taken from the data for `lang`, after parsing the form for modifiers)
-- matches `pagename`. If there is a <link:...> modifier, we check against it. Otherwise, we check against the form
-- itself. In this case, the form may have links and/or accent/length marks that need to be stripped, and we may need
-- to convert the form to its independent (un-affixed) form, if there is a difference between independent and affixed
-- forms (as in Swahili).
local function form_equals_pagename(formobj, pagename, m_data, lang)
if formobj.link == pagename then
return true
end
local entry_name = form_to_entry_name(formobj.form, lang)
return entry_name == pagename or maybe_unaffix(m_data, entry_name) == pagename
end
-- Given the data for a language and a number (which should be in string representation), find the next and previous
-- numbers to display (in string representation).
local function get_next_and_prev_keys(m_data, numstr)
local numdata = export.lookup_data(m_data, numstr)
if not numdata then
return nil, nil
end
local nextnum = numdata.next
local prevnum = numdata.prev
if not nextnum or not prevnum then
-- Find the next/previous numbers by sorting all the keys and locating the number in question among them.
local sorted_list = {}
local index = 1
for key, _ in pairs(m_data.numbers) do
sorted_list[index] = key
index = index + 1
end
table.sort(sorted_list, export.numbers_less_than)
-- We could binary search to save time, but given that we already sort, which is supra-linear, it won't
-- matter to search linearly.
for i, key in ipairs(sorted_list) do
if export.format_fixed(key) == numstr then
nextnum = nextnum or sorted_list[i + 1]
prevnum = prevnum or sorted_list[i - 1]
break
end
end
end
if nextnum then
nextnum = export.format_fixed(nextnum)
end
if prevnum then
prevnum = export.format_fixed(prevnum)
end
return nextnum, prevnum
end
-- Find the "description objects" (a two-element list {NUMBER, TYPE}, where NUMBER is either a Lua number or a string,
-- depending on how it appears in the underlying data) that matches `pagename` and (if given) `matching_type`.
-- Return a list of such objects.
local function lookup_number_by_form(lang, m_data, pagename, matching_type)
local retval = {}
local function check_form(form, num, typ)
local formobj = export.parse_form_and_modifiers(form)
if form_equals_pagename(formobj, pagename, m_data, lang) and (not matching_type or typ == matching_type) then
-- It's possible the same pagename occurs multiply for a given type and number, e.g. with different length
-- or accent marks. The calling code is OK with multiple entries for a given number (which can also occur
-- with different types, e.g. the ordinal and fractional forms for a given number are the same), but will
-- throw an error if different numbers are seen.
table.insert(retval, {num, typ})
end
end
for num, numdata in pairs(m_data.numbers) do
for numtype, forms in pairs(numdata) do
if non_form_types[numtype] then
-- do nothing
elseif type(forms) == "table" then
for _, form in ipairs(forms) do
check_form(form, num, numtype)
end
else
check_form(forms, num, numtype)
end
end
end
return retval
end
local function index_of_number_type(t, type)
for i, subtable in ipairs(t) do
if subtable.key == type then
return i
end
end
end
-- additional_types is an array of tables like form_types,
-- but each table can contain the keys "before" or "after", which specify
-- the numeral type that the form should appear before or after.
-- The transformations are applied in order.
local function add_form_types(additional_types)
local types = require("Module:table").deepcopy(form_types)
for _, type in ipairs(additional_types) do
type = require("Module:table").shallowcopy(type)
local i
if type.before or type.after then
i = index_of_number_type(types, type.before or type.after)
end
-- For now, simply log an error message
-- if the "before" or "after" number type was not found,
-- and insert the number type at the end.
if i then
if type.before then
table.insert(types, i - 1, type)
else
table.insert(types, i + 1, type)
end
else
table.insert(types, type)
if type.before or type.after then
mw.log("Number type "
.. (type.before or type.after)
.. " was not found.")
end
end
type.before, type.after = nil, nil
end
return types
end
-- Return all form types for the language in question, in order.
function export.get_number_types(m_data)
local final_form_types = form_types
if m_data.additional_number_types then
final_form_types = add_form_types(m_data.additional_number_types)
end
return final_form_types
end
-- Convert a number type object (an object with `display` and `key` fields) to its displayed form.
function export.display_number_type(number_type)
if number_type.display then
return number_type.display
else
return (number_type.key:gsub("^.", string.upper):gsub("_", " "))
end
end
-- Group digits with a separator, such as a comma or a period. See [[w:Digit grouping]].
local function add_separator(numstr, separator, group, start)
start = start or group
if start >= #numstr then
return numstr
end
local parts = { numstr:sub(-start) }
for i = start + 1, #numstr, group do
table.insert(parts, 1, numstr:sub(-(i + group - 1), -i))
end
return table.concat(parts, separator)
end
function export.add_thousands_separator(numstr, separator)
if #numstr < 4 then -- < 1000
return numstr
end
return add_separator(numstr, separator or ",", 3)
end
local function add_Indic_separator(numstr, separator)
return add_separator(numstr, separator, 2, 3)
end
-- Convert a number (represented as a string) to non-Arabic form based on the specs in `numeral_config`.
-- This is used, for example, to display the Hindu, Eastern Arabic or Roman form of a number along with the standard
-- Arabic form. Most of the code below assumes that the non-Arabic numerals are decimal, and the digits map one-to-one
-- with Arabic numerals. If this is not the case (e.g. for Roman numerals), a special module function is called to do
-- the conversion.
function export.generate_non_arabic_numeral(numeral_config, numstr)
-- `numstr` is a number represented as a string. See comment near top of show_box().
if numeral_config.module and numeral_config.func then
return require("Module:" .. numeral_config.module)[numeral_config.func](numstr)
end
local thousands_separator, Indic_separator, zero_codepoint =
numeral_config.thousands_separator,
numeral_config.Indic_separator,
numeral_config.zero_codepoint
if not zero_codepoint then
return nil
end
if thousands_separator then
numstr = export.add_thousands_separator(numstr, thousands_separator)
elseif Indic_separator then
numstr = add_Indic_separator(numstr, Indic_separator)
end
return numstr:gsub("[0-9]", function (digit)
return mw.ustring.char(zero_codepoint + tonumber(digit))
end)
end
-- Format a number (either a Lua number or a string) for display. Sufficiently small numbers are displayed in fixed
-- point with thousands separators. Larger numbers are displayed in both fixed point and scientific notation using
-- superscripts, and sufficiently large numbers are displayed only in scientific notation.
function export.format_number_for_display(number)
local MAX_NUM_DIGITS_FOR_FIXED_ONLY = 6
local MIN_NUM_DIGITS_FOR_SCIENTIFIC_ONLY = 13
local numstr = export.format_fixed(number)
local fixed = export.add_thousands_separator(numstr)
if #numstr <= MAX_NUM_DIGITS_FOR_FIXED_ONLY then
return fixed
end
local kstr = numstr:match("^([0-9]*[1-9])0*$")
if not kstr then
error("Internal error: Unable to match number '" .. numstr .. "'")
end
local exponent = ("10<sup>%s</sup>"):format(#numstr - 1)
local mantissa
if kstr == "1" then
mantissa = ""
elseif #kstr == 1 then
mantissa = kstr .. " x "
else
mantissa = kstr:gsub("^([0-9])", "%1.") .. " x "
end
local scientific = mantissa .. exponent
if #numstr >= MIN_NUM_DIGITS_FOR_SCIENTIFIC_ONLY then
return scientific
else
return fixed .. " (" .. scientific .. ")"
end
end
-- Map a list of tags to a single string that is equivalent. We need to do this because we can't easily put lists in the
-- keys of tables.
local function tag_list_to_combined_tag(tag_list)
return table.concat(tag_list, "|||")
end
-- Given a list of forms with attached inline modifiers (e.g. 'huitanta-huit<tag:Valencian>' or
-- 'tair ar ddeg<tag:vigesimal><tag:feminine>'), parse the forms into form objects (the return value of
-- parse_form_and_modifiers()) and group by the tag. Three values are returned:
-- `seen_forms`, `forms_by_tag`, `seen_tags` where:
-- (1) `seen_forms` is the list of parsed form objects;
-- (2) `forms_by_tag` is a table grouping the form objects by combined tag, where the key is the tag and the value is
--      a list of the form objects seen with that tag (forms without tag are grouped under the empty-string tag);
-- (3) `seen_tags` is a list of the combined tags encountered, in the order they were encountered;
-- (4) `combined_tags_to_tag_lists` is a map from combined tags to the corresponding tag lists.
function export.group_numeral_forms_by_tag(forms)
local seen_forms = {}
local forms_by_tag = {}
local seen_tags = {}
local combined_tags_to_tag_lists = {}
for _, form in ipairs(forms) do
local formobj = export.parse_form_and_modifiers(form)
table.insert(seen_forms, formobj)
local combined_tag = formobj.tag and tag_list_to_combined_tag(formobj.tag) or ""
if not forms_by_tag[combined_tag] then
table.insert(seen_tags, combined_tag)
forms_by_tag[combined_tag] = {}
combined_tags_to_tag_lists[combined_tag] = formobj.tag or {}
end
table.insert(forms_by_tag[combined_tag], formobj)
end
return seen_forms, forms_by_tag, seen_tags, combined_tags_to_tag_lists
end
-- Given a form object (as returned by parse_form_and_modifiers()), format as appropriate for the current language.
function export.format_formobj(formobj, m_data, lang)
local left_q = formobj.q and require("Module:qualifier").format_qualifier(formobj.q) .. " " or ""
local right_q = formobj.qq and " " .. require("Module:qualifier").format_qualifier(formobj.qq) or ""
return left_q .. m_links.full_link({
lang = lang, term = maybe_unaffix(m_data, formobj.form), alt = formobj.alt or formobj.form, tr = formobj.tr,
}) .. right_q
end
-- Implementation of {{number box}}.
function export.show_box(frame)
local full_link = m_links.full_link
local params = {
[1] = {required = true},
[2] = {},
["pagename"] = {},
["type"] = {},
}
local parent_args = frame:getParent().args
local args = require("Module:parameters").process(parent_args, params, nil, "number list", "show_box")
local langcode = args[1] or "und"
local lang = require("Module:languages").getByCode(langcode, "1")
-- Get the data from the data module. Some modules (e.g. currently [[wikt:Module:number list/data/ka]]) have to be
-- loaded with require() because the exported numbers table has a metatable.
local module_name = export.get_data_module_name(langcode, "must exist")
local m_data = require(module_name)
local pagename = args.pagename or (mw.title.getCurrentTitle().nsText == "Reconstruction" and "*" or "") .. mw.title.getCurrentTitle().subpageText
-- Resolve any risky characters which makeEntryName will escape, so that any matches involving them work correctly.
pagename = (lang:makeEntryName(pagename))
local cur_type = args.type
-- We represent all numbers as strings in this function to deal with the limited precision inherent in Lua numbers.
-- These large numbers do occur, such as 100 trillion ([[wikt:རབ་བཀྲམ་ཆེན་པོ]]), 1 sextillion, etc. Lua represents all
-- numbers as 64-bit floats, meaning that some numbers above 2^53 cannot be represented exactly. The first power of
-- 10 that cannot be represented exactly is 10^22 (ten sextillion in short scale, ten thousand trillion in long
-- scale), but the first power of ten whose neighboring numbers cannot be represented exactly is 10^16 (ten
-- quadrillion or ten thousand billion). Ideally we would use a big integer library of some kind, but unfortunately
-- Wiktionary does not seem to have any such library installed. MediaWiki docs make mention of bcmath, but
-- mw.bcmath.new() throws an error.
--
-- In module data, we allow numbers to be indexed as Lua numbers or as strings. See lookup_data() above.
local cur_num = args[2] or langcode == "und" and mw.title.getCurrentTitle().nsText == "Template" and "2" or nil
-- If a current number wasn't specified, find it by looking through the data for the current language and matching
-- forms against the pagename.
if not cur_num then
local nums_and_types = lookup_number_by_form(lang, m_data, pagename, cur_type)
if #nums_and_types == 0 then
error("The current page name '" .. pagename .. "' does not match the spelling of any known number in [[" ..
module_name .. "]]. Check the data module or the spelling of the page.")
end
for _, num_and_type in ipairs(nums_and_types) do
local num, typ = unpack(num_and_type)
num = export.format_fixed(num)
if cur_num and num ~= cur_num then
local errparts = {}
for _, num_and_type in ipairs(nums_and_types) do
local num, typ = unpack(num_and_type)
table.insert(errparts, ("%s (%s)"):format(num, typ))
end
error("The current page name '" .. pagename .. "' matches the spelling of multiple numbers in [[" ..
module_name .. "]]: " .. table.concat(errparts, ",") .. ". Please specify the number explicitly.")
else
cur_num = num
end
end
end
cur_num = cur_num:gsub(",", "") -- remove thousands separators
if not cur_num:find("^%d+$") then
error("Extraneous characters in parameter 2: should be decimal number (integer): '" .. cur_num .. "'")
end
-- Wrapper around `export.lookup_data` that may throw an error if the number can't be found (specifically if
-- param_for_error is given).
local function lookup_data(numstr, param_for_error)
local retval = export.lookup_data(m_data, numstr)
if not retval and param_for_error then
error(('The %s number "%s" specified in the "numbers" table entry for "%s" cannot be found in '
.. "[[%s]]; please fix the module."):format(param_for_error, numstr, cur_num, module_name))
end
return retval
end
local cur_data = lookup_data(cur_num)
if not cur_data then
error('The number "' .. cur_num .. '" is not found in the "numbers" table in [[' .. module_name .. "]].")
end
local formatted_forms = {}
if cur_type and not cur_data[cur_type] then
error("The numeral type " .. cur_type .. " for " .. cur_num .. " is not found in [[" .. module_name .. "]].")
end
-- See above for the definition of "combined tag" and "tag list". The combined tag is just the concatenation of the
-- tag list with ||| between the tags.
local cur_tag_list, cur_combined_tag
local form_types = export.get_number_types(m_data)
-- LONG COMMENT EXPLAINING TAG HANDLING:
--
-- For each form type (see `form_types` at top of file), group the entries for that form type by tag and figure out
-- what the current form type and tag is, i.e. the form type and tag for the form matching the pagename. Tags are
-- e.g. as in 'vuitanta-vuit<tag:Central>' or 'huitanta-huit<tag:Valencian>' for Catalan and allow different
-- logical sets of numbers for the same form type to be identified. There can potentially be multiple tags per
-- form, e.g. 'tair ar ddeg<tag:vigesimal><tag:feminine>' for the Welsh number 13 where there are both decimal/
-- vigesimal and masculine/feminine variants of this number.
--
-- We need to do two passes over all form types. In the first pass, for each form type we parse all the forms,
-- group them by tag, and store the results in a per-form-type table. In the second pass, we then format all forms
-- for all form types. The reason for doing two passes is because we need to know the current tag in order to
-- display a form type correctly (because we display the forms for the current tag before the forms for any other
-- tags), but we won't know the current tag until we have done a pass over all form types and forms of those form
-- types in order to determine which one matches the pagename.
--
-- We use the current tag in two ways:
-- 1. When displaying all the forms for a given number, we group both by form type and tag, and display the forms
--    for a given form type/tag combination on a single line. For a given form type, we display the forms for each
--    tag in the order the tags were specified in the data, except that the forms for the current tag are placed
--    before all others (so e.g. for Catalan, if the current tag is "Valencian", we list the Valencian form(s)
--    first even if the Central form(s) are listed first in the data file).
-- 2. When displaying links to adjacent numbers in display_adjacent_number_links(), if there aren't form(s) for the
--    current type, we don't display any links; but if there are mutiple tagged forms for the current type, we only
--    display links for the forms for the current tag if there are any such forms, otherwise we display links for
--    all forms of all tags.
--
-- In the presence of multiple tags, things get a bit more complicated:
-- 1. When displaying links to adjacent numbers, say the current tag is vigesimal+feminine, we want to prefer an
--    adjacent-number form that's both vigesimal and feminine, but otherwise we prefer one that's vigesimal or
--    feminine over one that's neither. Say the current tag is just vigesimal; we of course prefer an
--    adjacent-number form that's just vigesimal, but otherwise we prefer a tag that's vigesimal + either masculine
--    or feminine to a tag that's not vigesimal. So it seems we want the form(s) that have the maximum intersection
--    of tags, and if there are two different tag lists with the same number of intersecting tags (e.g. the current
--    tag is vigesimal+feminine and we have a choice of decimal+feminine or just vigesimal), we should prefer the
--    form that has fewer non-matching tags, hence we prefer the just-vigesimal form.
-- 2. By the same logic, when displaying all the forms for a given number, we should order by the size of the
--    intersection of the tag list in question with the current tag list, then inversely by the size of the tag list
--    (so we prefer tag lists with fewer non-matching tags), then by the order of the tag lists in the data file.
local forms_by_tag_per_form_type = {}
local seen_tags_per_form_type = {}
local combined_tags_to_tag_lists_per_form_type = {}
for _, form_type in ipairs(form_types) do
local numeral = cur_data[form_type.key]
if numeral then
local numerals
if type(numeral) == "string" then
numerals = {numeral}
elseif type(numeral) == "table" then
numerals = numeral
end
local seen_forms, forms_by_tag, seen_tags, combined_tags_to_tag_lists = export.group_numeral_forms_by_tag(numerals)
forms_by_tag_per_form_type[form_type] = forms_by_tag
seen_tags_per_form_type[form_type] = seen_tags
combined_tags_to_tag_lists_per_form_type[form_type] = combined_tags_to_tag_lists
for _, formobj in ipairs(seen_forms) do
if not cur_tag_list and form_equals_pagename(formobj, pagename, m_data, lang) then
cur_tag_list = formobj.tag or {}
cur_combined_tag = tag_list_to_combined_tag(cur_tag_list)
cur_type = cur_type or form_type.key
end
end
end
end
-- Error if we couldn't locate the pagename among the forms for the current number. This only happens if the
-- number if given explicitly in 2=.
if not cur_type and mw.title.getCurrentTitle().nsText ~= "Template" then
error("The current page name '" .. pagename .. "' does not match any of the numbers listed in [[" ..
module_name .. "]] for " .. cur_num .. ". Check the data module or the spelling of the page.")
end
-- Now, format all the forms for all form types for the current number.
local function sort_combined_tags(combined_tags, seen_tags, combined_tags_to_tag_lists)
-- cur_tag_list should normally never be nil, but can be so in template space
local cur_tag_set = list_to_set(cur_tag_list or {})
local tags_to_order = {}
for i, tag in ipairs(seen_tags) do
tags_to_order[tag] = i
end
local function compare_tags(tag1, tag2)
-- See long comment above.
-- First compare by number of tags in common with the current tag list.
local tag_list1 = combined_tags_to_tag_lists[tag1]
local tag_list2 = combined_tags_to_tag_lists[tag2]
local common1 = set_intersection(cur_tag_set, list_to_set(tag_list1))
local common2 = set_intersection(cur_tag_set, list_to_set(tag_list2))
if #common1 ~= #common2 then
return #common1 < #common2
end
-- Then compare inversely by number of tags not in common with the current tag list (which is equivalent to
-- comparing by total number of tags, since tags should be distinct).
if #tag_list1 ~= #tag_list2 then
return #tag_list1 > #tag_list2
end
-- Finally, compare by the original ordering in the number data, but if a tag is the same as the current
-- tag, put it first, and if somehow we encounter a tag that's not in the original ordering, put it last.
local index1 = tag1 == cur_combined_tag and 0 or tags_to_order[tag1] or #seen_tags + 1
local index2 = tag2 == cur_combined_tag and 0 or tags_to_order[tag2] or #seen_tags + 1
return index1 < index2
end
table.sort(combined_tags, compare_tags)
end
for _, form_type in ipairs(form_types) do
local forms_by_tag = forms_by_tag_per_form_type[form_type]
local seen_tags = seen_tags_per_form_type[form_type]
local combined_tags_to_tag_lists = combined_tags_to_tag_lists_per_form_type[form_type]
if forms_by_tag then
local function insert_forms_by_tag(tag)
local formatted_tag_forms = {}
local pagename_among_forms = false
for _, formobj in ipairs(forms_by_tag[tag]) do
table.insert(formatted_tag_forms, export.format_formobj(formobj, m_data, lang))
if form_equals_pagename(formobj, pagename, m_data, lang) then
pagename_among_forms = true
end
end
if tag ~= "" then
local tag_list = combined_tags_to_tag_lists[tag]
tag = table.concat(tag_list, " / ")
end
local displayed_number_type = export.display_number_type(form_type) .. (tag == "" and "" or (" (%s)"):format(tag))
if pagename_among_forms then
displayed_number_type = "'''" .. displayed_number_type .. "'''"
end
table.insert(formatted_forms, " &nbsp;&nbsp;&nbsp; ''" .. displayed_number_type .. "'': " ..
table.concat(formatted_tag_forms, ", "))
end
sort_combined_tags(seen_tags, seen_tags, combined_tags_to_tag_lists)
for _, tag in ipairs(seen_tags) do
insert_forms_by_tag(tag)
end
end
end
-- Current number in header
local cur_display = export.format_number_for_display(cur_num)
local numeral
if m_data.numeral_config then
numeral = export.generate_non_arabic_numeral(m_data.numeral_config, cur_num)
if langcode == "qay" then numeral = numeral:gsub("A","¹"):gsub("B","²") end
elseif cur_data["numeral"] then
numeral = export.format_fixed(cur_data["numeral"])
end
if numeral then
cur_display = full_link({lang = lang, alt = numeral, tr = "-"}) .. "<br/><span style=\"font-size: smaller;\">" .. cur_display .. "</span>"
end
--------------------- Determine next/prev, next/prev outer, and upper/lower numbers. ----------------------
-- We have three series of numbers to determine:
--
-- 1. The next/previous numbers, which are always those in the sorted series of available numbers unless overridden
--    by `next`/`prev` specs in an individual number.
-- 2. The next/previous outer numbers, which are displayed to the outside of the next/previous numbers. These can
--    be overridden for an individual number using `next_outer`/`prev_outer`. Otherwise, we try according to an
--    algorithm described below in the code for computing the outer numbers.
-- 3. The upper/lower numbers, which are displayed above or below the central number box. These can be overridden
--    for an individual number using `upper`/`lower`. These are always 10x greater or less than the number in
--    question, number not considering a number if it's the same as the next/previous number.
local next_num, prev_num = get_next_and_prev_keys(m_data, cur_num)
local next_data = next_num and lookup_data(next_num, "next")
local prev_data = prev_num and lookup_data(prev_num, "previous")
--------- Decompose number into mantissa (k) and exponent (m). ----------
local k, m
if cur_num == "0" then
k = 0
m = 1
else
local kstr, mstr = cur_num:match("^([0-9]*[1-9])(0*)$")
if not kstr then
error("Internal error: Unable to match number '" .. cur_num .. "'")
elseif #kstr > 15 then
-- This is because some numbers with 16 or more digits can't be represented exactly.
error("Can't handle number with more than 15 digits before the trailing zeros: '" .. cur_num .. "'")
end
k = tonumber(kstr)
m = #mstr
end
-- Find the next greater power of 10 for cur_num, up to 10^6. `try` should look up the data for a power of 10
-- and return it if it's available and the number passes any checks, otherwise nil.
local function make_greater_power_of_ten(power)
return cur_num .. string.rep("0", power)
end
-- Find the next lesser power of 10 for cur_num, up to 10^6. `try` should look up the data for a power of 10
-- and return it if it's available and the number passes any checks, otherwise nil.
local function make_lesser_power_of_ten(power)
local desired_zeros = m - power
if desired_zeros < 0 then
return nil
end
return k .. string.rep("0", desired_zeros)
end
local next_outer_data, prev_outer_data
local next_outer_num, prev_outer_num = cur_data.next_outer, cur_data.prev_outer
-- When trying to find then next/previous outer numbers, first, if the base-10 mantissa is not 1 or 0, we add 1 to
-- or subtract 1 from the mantissa, keeping the same number of zeros. Hence, for 300, we try 400 for the next outer,
-- 200 for the previous outer. For 900, we try 1000 for the next outer and 800 for the previous outer. If the
-- mantissa is 1, the next outer is computed the same but for the previous outer we use 9 followed by one fewer
-- zero. Hence, for 100 we try 200 for the next outer but 90 for the previous outer. If the mantissa is 0 (i.e. the
-- entire number is 0), we try 10 for the next outer, and have no previous outer.
--
-- Next, if the number is an even power of 10, we try 10x, 1000x greater, 100x greater and 1,000,000x greater, in
-- that sequence. Essentially, first we try the next power of 10; then we try the next short-scale number (billion,
-- trillion, etc. where large numbers follow a 10^3 sequence); then we try the next long-scale number (where large
-- numbers follow a 10^6 sequence); then we try the next Indic-scale number (where large numbers follow a 10^2
-- sequence: lakh, crore, arab, ...). We don't just try powers of 10 in order because then if e.g. we have entries
-- for one million, ten million, one hundred million and one billion, and the current number is one million, the
-- next number will be ten million and the next outer number one hundred million, when it would be cleaner to have
-- one billion as the outer number (and in many cases, there is no Wiktionary entry for one hundred million).
--
-- For the previous outer number, we do an analogous algorithm but make sure we don't try numbers less than 1.
local power_of_10_sequence = { 1, 3, 2, 6 }
--------- Determine next outer number. ----------
if next_outer_num then
next_outer_data = lookup_data(next_outer_num, "next outer")
else
local function try(num)
local data = (not next_num or export.numbers_greater_than(num, next_num)) and lookup_data(num) or nil
if data then
next_outer_num = num
next_outer_data = data
end
return data
end
if not try((k + 1) .. string.rep("0", m)) and k == 1 then
-- Try looking up a greater power of ten instead.
for _, power_of_10 in ipairs(power_of_10_sequence) do
if try(make_greater_power_of_ten(power_of_10)) then
break
end
end
end
end
--------- Determine previous outer number. ----------
if prev_outer_num then
prev_outer_data = lookup_data(prev_outer_num, "previous outer")
else
local function try(num)
local data = (not prev_num or export.numbers_less_than(num, prev_num)) and lookup_data(num) or nil
if data then
prev_outer_num = num
prev_outer_data = data
end
return data
end
if k == 0 or m == 0 then
-- less than 10; no previous outer num
else
local num_to_try
if k == 1 then
num_to_try = "9" .. string.rep("0", m - 1)
else
num_to_try = (k - 1) .. string.rep("0", m)
end
if not try(num_to_try) and k == 1 then
-- Try looking up a smaller power of ten instead.
for _, power_of_10 in ipairs(power_of_10_sequence) do
local num_to_try = make_lesser_power_of_ten(power_of_10)
if num_to_try and try(num_to_try) then
break
end
end
end
end
end
local upper_data, lower_data
local upper_num, lower_num = cur_data.upper, cur_data.lower
--------- Determine upper number. ----------
if upper_num then
upper_data = lookup_data(upper_num, "upper")
else
-- Try looking up the next power of ten.
upper_num = make_greater_power_of_ten(1)
if upper_num == next_num or cur_num == "0" then
upper_num = nil
else
upper_data = lookup_data(upper_num)
end
end
--------- Determine lower number. ----------
if lower_num then
lower_data = lookup_data(lower_num, "lower")
elseif k == 0 or m == 0 then
-- less than 10; no lower num
else
-- Try looking up the previous power or 10.
lower_num = make_lesser_power_of_ten(1)
if lower_num == prev_num then
lower_num = nil
else
lower_data = lookup_data(lower_num)
end
end
-- For a number `num` (an "adjacent" number to the current number, i.e. either next, previous, next/previous outer,
-- or upper/lower) with corresponding entry data `num_data`, display link(s) to the form(s) for this number that
-- are associated with the current type and tag. If there is a single form to be linked to, the form is linked
-- using the number itself as the display text; otherwise, the multiple forms are linked with superscripted [a],
-- [b], etc. and the number it displayed adjacent to the links. In either case, beside the number there may be an
-- arrow. If `arrow` == "rarrow", the format is like this:
-- if multiple entries:
-- <numeral> → <sup>[a], [b], ...</sup>
-- else
-- <numeral> →
-- If `arrow` == "larrow", the format is like this:
-- if multiple entries:
-- <sup>[a], [b], ...</sup> ← <numeral>
-- else
-- ← <numeral>
-- Otherwise, the format is like this:
-- if multiple entries:
-- <numeral><sup>[a], [b], ...</sup>
-- else
-- <numeral>
--
-- Returns nil if `num_data` is nil or there is no entry in `num_data` for the current number type.
--
-- For the handling of tags in this function, see the "LONG COMMENT EXPLAINING TAG HANDLING" above.
local function display_adjacent_number_links(num, num_data, arrow)
if not num_data then
return nil
end
local num_type_data = num_data[cur_type]
if not num_type_data then
return nil
end
local forms = num_type_data
if type(forms) ~= "table" then
forms = {forms}
end
local seen_forms, forms_by_tag = export.group_numeral_forms_by_tag(forms)
local forms_to_display
if cur_tag and forms_by_tag[cur_tag] then
forms_to_display = forms_by_tag[cur_tag]
else
forms_to_display = seen_forms
end
for i, form_to_display in ipairs(forms_to_display) do
forms_to_display[i] = form_to_display.link or maybe_unaffix(m_data,
form_to_entry_name(form_to_display.form, lang))
end
local seen_pagenames = {}
local pagenames_to_display = {}
for _, form in ipairs(forms_to_display) do
if not seen_pagenames[form] then
table.insert(pagenames_to_display, form)
seen_pagenames[form] = true
end
end
num = export.format_number_for_display(num)
local num_arrow =
arrow == "rarrow" and num .. "&nbsp;&nbsp;→&nbsp;" or
arrow == "larrow" and "&nbsp;←&nbsp;&nbsp;" .. num or
num
if #pagenames_to_display > 1 then
local a = ("a"):byte()
local links = {}
for i, term in ipairs(pagenames_to_display) do
links[i] = m_links.language_link{lang = lang, term = term, alt = "[" .. string.char(a + i - 1) .. "]"}
end
links = "<sup>" .. table.concat(links, ", ") .. "</sup>"
return arrow == "larrow" and links .. num_arrow or num_arrow .. links
else
return m_links.language_link {
lang = lang,
term = pagenames_to_display[1],
alt = num_arrow,
}
end
end
-- Display links to previous/next numbers
local prev_display = display_adjacent_number_links(prev_num, prev_data, "larrow") or ""
local next_display = display_adjacent_number_links(next_num, next_data, "rarrow") or ""
-- Display links to previous/next outer numbers
local prev_outer_display = display_adjacent_number_links(prev_outer_num, prev_outer_data, "larrow")
local next_outer_display = display_adjacent_number_links(next_outer_num, next_outer_data, "rarrow")
-- Display links to upper/lower numbers
local upper_display = display_adjacent_number_links(upper_num, upper_data)
local lower_display = display_adjacent_number_links(lower_num, lower_data)
local canonical_name = lang:getCanonicalName()
local title = canonical_name .. " numbers"
local function format_cell(contents, font_size, background, colspan, bold)
font_size = font_size and (" font-size:%s;"):format(font_size) or ""
background = background and (" background:%s;"):format(background) or ""
colspan = colspan and ('colspan="%s" '):format(colspan) or ""
bold = bold and "!" or "|"
return ('%s %sstyle="min-width: 6em;%s%s | %s\n'):format(bold, colspan, font_size, background, contents)
end
local has_outer_display = not not (prev_outer_display or next_outer_display)
local function format_upper_lower_display_row(display)
local blank_cell
if has_outer_display then
blank_cell = '| colspan="2" |\n'
else
blank_cell = "|\n"
end
local parts = {'|- style="text-align: center; background:#dddddd;"\n'}
table.insert(parts, blank_cell)
table.insert(parts, format_cell(display, "smaller"))
table.insert(parts, blank_cell)
return table.concat(parts)
end
upper_display = upper_display and format_upper_lower_display_row(upper_display) or ""
lower_display = lower_display and format_upper_lower_display_row(lower_display) or ""
local function format_display_cell(display)
return format_cell(display, "smaller", "#dddddd")
end
prev_display = format_display_cell(prev_display)
next_display = format_display_cell(next_display)
prev_outer_display = has_outer_display and format_display_cell(prev_outer_display or "") or ""
next_outer_display = has_outer_display and format_display_cell(next_outer_display or "") or ""
cur_display = format_cell(cur_display, "larger", nil, nil, "bold")
local forms_display = ('| colspan="%s" style="text-align: center;" | %s\n'):format(
has_outer_display and 5 or 3, table.concat(formatted_forms, "<br/>"))
local footer_display
if cur_data.wplink then
local footer =
"[[w:" .. lang:getCode() .. ":Main Page|" .. lang:getCanonicalName() .. " Wikipedia]] article on " ..
m_links.full_link({lang = lang, term = "w:" .. lang:getCode() .. ":" .. cur_data.wplink,
alt = export.format_number_for_display(cur_num)})
footer_display = '|- style="text-align: center;"\n' .. format_cell(footer, nil, "#dddddd", has_outer_display and 5 or 3)
else
footer_display = ""
end
local edit_link = ' <sup>(<span class="plainlinks">[' ..
tostring(mw.uri.fullUrl(module_name, { action = "edit" })) ..
" edit]</span>)</sup>"
return [=[{| class="floatright" cellpadding="5" cellspacing="0" style="background: #ffffff; border: 1px #aaa solid; border-collapse: collapse; margin-top: .5em;" rules="all"
|+ ''']=] .. title .. edit_link .. "'''\n" ..
upper_display .. '|- style="text-align: center;"\n' ..
prev_outer_display .. prev_display .. cur_display .. next_display .. next_outer_display .. "|-\n" ..
lower_display .. "|-\n" ..
forms_display .. footer_display .. "|}"
end
-- Assumes string or nil (or false), the types that can be found in an args table.
local function if_not_empty(val)
if val and mw.text.trim(val) == "" then
return nil
else
return val
end
end
function export.show_box_manual(frame)
local m_links = require("Module:links")
local num_type = frame.args["type"]
local args = {}
--cloning parent's args while also assigning nil to empty strings
for pname, param in pairs(frame:getParent().args) do
args[pname] = if_not_empty(param)
end
local lang = args[1] or (mw.title.getCurrentTitle().nsText == "Template" and "und") or error("Language code has not been specified. Please pass parameter 1 to the template.")
local sc = args["sc"];
local headlink = args["headlink"]
local wplink = args["wplink"]
local alt = args["alt"]
local tr = args["tr"]
local prev_symbol = if_not_empty(args[2])
local cur_symbol = if_not_empty(args[3]);
local next_symbol = if_not_empty(args[4])
local prev_term = if_not_empty(args[5])
local next_term = if_not_empty(args[6])
local cardinal_term = args["card"]; local cardinal_alt = args["cardalt"]; local cardinal_tr = args["cardtr"]
local ordinal_term = args["ord"]; local ordinal_alt = args["ordalt"]; local ordinal_tr = args["ordtr"]
local adverbial_term = args["adv"]; local adverbial_alt = args["advalt"]; local adverbial_tr = args["advtr"]
local multiplier_term = args["mult"]; local multiplier_alt = args["multalt"]; local multiplier_tr = args["multtr"]
local distributive_term = args["dis"]; local distributive_alt = args["disalt"]; local distributive_tr = args["distr"]
local collective_term = args["coll"]; local collective_alt = args["collalt"]; local collective_tr = args["colltr"]
local fractional_term = args["frac"]; local fractional_alt = args["fracalt"]; local fractional_tr = args["fractr"]
local optional1_title = args["opt"]
local optional1_term = args["optx"]; local optional1_alt = args["optxalt"]; local optional1_tr = args["optxtr"]
local optional2_title = args["opt2"]
local optional2_term = args["opt2x"]; local optional2_alt = args["opt2xalt"]; local optional2_tr = args["opt2xtr"]
lang = require("Module:languages").getByCode(lang) or error("The language code \"" .. lang .. "\" is not valid.")
sc = (sc and (require("Module:scripts").getByCode(sc) or error("The script code \"" .. sc .. "\" is not valid.")) or nil)
local subpage = mw.title.getCurrentTitle().subpageText
local is_reconstructed = lang:hasType("reconstructed") or mw.title.getCurrentTitle().nsText == "Reconstruction"
alt = alt or (is_reconstructed and "*" or "") .. subpage
if num_type == "cardinal" then
cardinal_term = (is_reconstructed and "*" or "") .. subpage
cardinal_alt = alt
cardinal_tr = tr
elseif num_type == "ordinal" then
ordinal_term = (is_reconstructed and "*" or "") .. subpage
ordinal_alt = alt
ordinal_tr = tr
end
local header = lang:getCanonicalName() .. " " .. num_type .. " numbers"
if headlink then
header = "[[" .. headlink .. "|" .. header .. "]]"
end
local previous = ""
if prev_term or prev_symbol then
previous = m_links.full_link({lang = lang, sc = sc, term = prev_term, alt = "&nbsp;&lt;&nbsp;&nbsp;" .. prev_symbol, tr = "-"})
end
local current = m_links.full_link({lang = lang, sc = sc, alt = cur_symbol, tr = "-"})
local next = ""
if next_term or next_symbol then
next = m_links.full_link({lang = lang, sc = sc, term = next_term, alt = next_symbol .. "&nbsp;&nbsp;&gt;&nbsp;", tr = "-"})
end
local forms = {}
if cardinal_term then
table.insert(forms, " &nbsp;&nbsp;&nbsp; ''[[wikt:cardinal number|Cardinal]]'' : " .. m_links.full_link({lang = lang, sc = sc, term = cardinal_term, alt = cardinal_alt, tr = cardinal_tr}))
end
if ordinal_term then
table.insert(forms, " &nbsp;&nbsp;&nbsp; ''[[wikt:ordinal number|Ordinal]]'' : " .. m_links.full_link({lang = lang, sc = sc, term = ordinal_term, alt = ordinal_alt, tr = ordinal_tr}))
end
if adverbial_term then
table.insert(forms, " &nbsp;&nbsp;&nbsp; ''[[wikt:adverbial number|Adverbial]]'' : " .. m_links.full_link({lang = lang, sc = sc, term = adverbial_term, alt = adverbial_alt, tr = adverbial_tr}))
end
if multiplier_term then
table.insert(forms, " &nbsp;&nbsp;&nbsp; ''[[wikt:multiplier|Multiplier]]'' : " .. m_links.full_link({lang = lang, sc = sc, term = multiplier_term, alt = multiplier_alt, tr = multiplier_tr}))
end
if distributive_term then
table.insert(forms, " &nbsp;&nbsp;&nbsp; ''[[wikt:distributive number|Distributive]]'' : " .. m_links.full_link({lang = lang, sc = sc, term = distributive_term, alt = distributive_alt, tr = distributive_tr}))
end
if collective_term then
table.insert(forms, " &nbsp;&nbsp;&nbsp; ''[[wikt:collective number|Collective]]'' : " .. m_links.full_link({lang = lang, sc = sc, term = collective_term, alt = collective_alt, tr = collective_tr}))
end
if fractional_term then
table.insert(forms, " &nbsp;&nbsp;&nbsp; ''[[wikt:fractional|Fractional]]'' : " .. m_links.full_link({lang = lang, sc = sc, term = fractional_term, alt = fractional_alt, tr = fractional_tr}))
end
if optional1_title then
table.insert(forms, " &nbsp;&nbsp;&nbsp; ''" .. optional1_title .. "'' : " .. m_links.full_link({lang = lang, sc = sc, term = optional1_term, alt = optional1_alt, tr = optional1_tr}))
end
if optional2_title then
table.insert(forms, " &nbsp;&nbsp;&nbsp; ''" .. optional2_title .. "'' : " .. m_links.full_link({lang = lang, sc = sc, term = optional2_term, alt = optional2_alt, tr = optional2_tr}))
end
local footer = ""
if wplink then
footer =
"[[w:" .. lang:getCode() .. ":Main Page|" .. lang:getCanonicalName() .. " Wikipedia]] article on " ..
m_links.full_link({lang = lang, sc = sc, term = "w:" .. lang:getCode() .. ":" .. wplink, alt = alt, tr = tr})
end
return [=[{| class="floatright" cellpadding="5" cellspacing="0" style="background: #ffffff; border: 1px #aaa solid; border-collapse: collapse; margin-top: .5em;" rules="all"
|+ ''']=] .. header .. [=['''
|-
| style="width: 64px; background:#dddddd; text-align: center; font-size:smaller;" | ]=] .. previous .. [=[
! style="width: 98px; text-align: center; font-size:larger;" | ]=] .. current .. [=[
| style="width: 64px; text-align: center; background:#dddddd; font-size:smaller;" | ]=] .. next .. [=[
|-
| colspan="3" style="text-align: center;" | ]=] .. table.concat(forms, "<br/>") .. [=[
|-
| colspan="3" style="text-align: center; background: #dddddd;" | ]=] .. footer .. [=[
|}]=]
end
return export
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