-- Functions to access Wikidata for Module:Convert.  
local Collection = {}
Collection.__index = Collection
do
function Collection:add(item)
if item ~= nil then
self.n = self.n + 1
self[self.n] = item
end
end
function Collection:join(sep)
return table.concat(self, sep)
end
function Collection:remove(pos)
if self.n > 0 and (pos == nil or (0 < pos and pos <= self.n)) then
self.n = self.n - 1
return table.remove(self, pos)
end
end
function Collection:sort(comp)
table.sort(self, comp)
end
function Collection.new
return setmetatable({n = 0}, Collection)
end
end  
local function strip_to_nil(text)
-- If text is a non-empty string, return its trimmed content,
-- otherwise return nothing (empty string or not a string).
if type(text) == 'string' then
return text:match('(%S.-)%s*$')
end
end  
local function frequency_unit(value, unit_table)
-- For use when converting m to Hz.
-- Return true, s where s = name of unit's default output unit,
-- or return false, t where t is an error message table.
-- However, for simplicity a valid result is always returned.
local unit
if unit_table._symbol == 'm' then
-- c = speed of light in a vacuum = 299792458 m/s
-- frequency = c / wavelength
local w = value * (unit_table.scale or 1)
local f = 299792458 / w -- if w == 0, f = math.huge which works here
if f >= 1e12 then
unit = 'THz'
elseif f >= 1e9 then
unit = 'GHz'
elseif f >= 1e6 then
unit = 'MHz'
elseif f >= 1e3 then
unit = 'kHz'
else
unit = 'Hz'
end
end
return true, unit or 'Hz'
end  
local function wavelength_unit(value, unit_table)
-- Like frequency_unit but for use when converting Hz to m.
local unit
if unit_table._symbol == 'Hz' then
-- Using 0.9993 rather than 1 avoids rounding which would give results
-- like converting 300 MHz to 100 cm instead of 1 m.
local w = 1 / (value * (unit_table.scale or 1)) -- Hz scale is inverted
if w >= 0.9993e6 then
unit = 'Mm'
elseif w >= 0.9993e3 then
unit = 'km'
elseif w >= 0.9993 then
unit = 'm'
elseif w >= 0.9993e-2 then
unit = 'cm'
elseif w >= 0.9993e-3 then
unit = 'mm'
else
unit = 'um'
end
end
return true, unit or 'm'
end  
local specials = {
frequency = { frequency_unit },
wavelength = { wavelength_unit },
---
-- Following is a removed experiment to show two values as a range
-- using '-' as the separator.
-- frequencyrange = { frequency_unit, '-' },
-- wavelengthrange = { wavelength_unit, '-' },
}  
local function make_unit(units, parms, uid)
-- Return a unit code for convert or nil if unit unknown.
-- If necessary, add a dummy unit to parms so convert will use it
-- for the input without attempting a conversion since nothing
-- useful is available (for example, with unit volt).
local unit = units[uid]
if type(unit) ~= 'table' then
return nil
end
local ucode = unit.ucode
if ucode and not unit.si then
return ucode -- a unit known to convert
end
parms.opt_ignore_error = true
ucode = ucode or unit._ucode -- must be a non-empty string
local ukey, utable
if unit.si then
local base = units[unit.si]
ukey = base.symbol -- must be a non-empty string
local n1 = base.name1
local n2 = base.name2
if not n1 then
n1 = ukey
n2 = n2 or n1 -- do not append 's'
end
utable = {
_symbol = ukey,
_name1 = n1,
_name2 = n2,
link = unit.link or base.link,
utype = n1,
prefixes = 1,
}
else
ukey = ucode
utable = {
symbol = ucode, -- must be a non-empty string
name1 = unit.name1, -- if nil, uses symbol
name2 = unit.name2, -- if nil, uses name1..'s'
link = unit.link, -- if nil, uses name1
utype = unit.name1 or ucode,
}
end
utable.scale = 1
utable.default = ''
utable.defkey = ''
utable.linkey = ''
utable.bad_mcode = ''
parms.unittable = { [ukey] = utable }
return ucode
end  
local function matches_qualifier(statement, qual)
-- Return:
-- false, nil : if statement does not match specification
-- true, nil : if matches, and statement has no qualifier
-- true, sq : if matches, where sq is the statement's qualifier
-- A match means that no qualifier was specified (qual == nil), or that
-- the statement has a qualifier matching the specification.
-- If a match occurs, the caller needs the statement's qualifier (if any)
-- so statements that duplicate the qualifier are not used, after the first.
-- Then, if convert is showing all values for a property such as the diameter
-- of a telescope's mirror (diameters of primary and secondary mirrors), it
-- will not show alternative values that could in principle be present for the
-- same item (telescope) and property (diameter) and qualifier (primary/secondary).
local target = (statement.qualifiers or {}).P518 -- P518 is "applies to part"
if type(target) == 'table' then
for _, q in ipairs(target) do
if type(q) == 'table' then
local value = (q.datavalue or {}).value
if value then
if qual == nil or qual == value.id then
return true, value.id
end
end
end
end
end
if qual == nil then
return true, nil -- only occurs if statement has no qualifier
end
return false, nil -- statement's qualifier is not relevant because statement will be skipped
end  
local function get_statements(parms, pid)
-- Get specified item and return a list of tables with each statement for property pid.
-- Each table is of form {statqual=sq, stmt=statement} where sq = statement qualifier (nil if ).
-- Statements are in Wikidata's order except that those with preferred rank
-- are first, then normal rank. Any other rank is ignored.
local stored = {} -- qualifiers of statements that are first for the qualifier, and will be returned
local qid = strip_to_nil(parms.qid) -- nil for current page's item, or an item id (expensive)
local qual = strip_to_nil(parms.qual) -- nil or id of wanted P518 (applies to part) item in qualifiers
local result = Collection.new
local entity = mw.wikibase.getEntity(qid)
if type(entity) == 'table' then
local statements = (entity.claims or {})[pid]
if type(statements) == 'table' then
for _, rank in ipairs({ 'preferred', 'normal' }) do
for _, statement in ipairs(statements) do
if type(statement) == 'table' and rank == statement.rank then
local is_match, statqual = matches_qualifier(statement, qual)
if is_match then
result:add({ statqual = statqual, stmt = statement })
end
end
end
end
end
end
return result
end  
local function input_from_property(tdata, parms, pid)
-- Given that pid is a Wikidata property identifier like 'P123',
-- return a collection of {amount, ucode} pairs (two strings)
-- for each matching item/property, or return nothing.
---
-- There appear to be few restrictions on how Wikidata is organized so it is
-- very likely that any decision a module makes about how to handle data
-- will be wrong for some cases at some time. This meets current requirements.
-- For each qualifier (or if no qualifier), if there are any preferred
-- statements, use them and ignore any normal statements.
-- For each qualifier, for the preferred statements if any, or for
-- the normal statements (but not both):
-- * Accept each statement if it has no qualifier (this will not occur
-- if qual=x is specified because other code already ensures that in that
-- case, only statements with a qualifier matching x are considered).
-- * Ignore any statements after the first if it has a qualifier.
-- The rationale is that for the diameter at South Pole Telescope, want
-- convert to show the diameters for both the primary and secondary mirrors
-- if the convert does not specify which diameter is wanted.
-- However, if convert is given the wanted qualifier, only one value
-- (_the_ diameter) is wanted. For simplicity/consistency, that is also done
-- even if no qual=x is specified. Unclear what should happen.
-- For the wavelength at Nançay Radio Telescope, want to show all three
-- values, and the values have no qualifiers.
---
local result = Collection.new
local done = {}
local skip_normal
for _, t in ipairs(get_statements(parms, pid)) do
local statement = t.stmt
if statement.mainsnak and statement.mainsnak.datatype == 'quantity' then
local value = (statement.mainsnak.datavalue or {}).value
if value then
local amount = value.amount
if amount then