Module:Convert
From Zoophilia Wiki
Documentation for this module may be created at Module:Convert/doc
-- Convert a value from one unit of measurement to another.
-- Example: {{convert|123|lb|kg}} --> 123 pounds (56 kg)
local MINUS = '−' -- Unicode U+2212 MINUS SIGN (UTF-8: e2 88 92)
local format = string.format
local floor = math.floor
local log10 = math.log10
-- Names when using engineering notation (a prefix of "eN" where N is a number).
-- key = { "name", "linked name, if link wanted" }
-- LATER: Perhaps this should be in convertdata to keep output text in one place.
local eng_scales = {
["3"] = { "thousand" },
["6"] = { "million" },
["9"] = { "billion", "[[1000000000 (number)|billion]]" },
["12"] = { "trillion", "[[1000000000000 (number)|trillion]]" },
["15"] = { "quadrillion", "[[1000000000000000 (number)|quadrillion]]" },
}
-- Configuration options to keep magic values in one location.
local numdot, numsep, maxsigfig, lang
-- Following specify the conversion data which is defined in another module
-- because it is too large to be conveniently included here.
-- To allow easy comparison between "require" and "loadData", a config option
-- can be set to control which is used.
local SIprefixes, units, default_exceptions, link_exceptions
local function set_config(frame)
-- Set configuration options from template #invoke or defaults.
local args = frame.args
numdot = args.numdot or '.' -- decimal mark before fractional digits
numsep = args.numsep or ',' -- thousands separator for numbers (',', '.', '')
maxsigfig = args.maxsigfig or 14 -- maximum number of significant figures
lang = args.lang or 'en' -- language code for messages
-- Scribunto sets the global variable 'mw'.
-- A testing program can set the global variable 'is_test_run'.
local convertdata
local data_module = is_test_run and "convertdata" or "Module:Convert/data"
if args.use_require then
convertdata = require(data_module)
else
convertdata = mw.loadData(data_module)
end
SIprefixes = convertdata.SIprefixes
units = convertdata.units
default_exceptions = convertdata.default_exceptions
link_exceptions = convertdata.link_exceptions
end
local function strip(text)
-- If text is a string, return its content with no leading/trailing
-- whitespace. Otherwise return nil (a nil argument gives a nil result).
if type(text) == 'string' then
return text:match("^%s*(.-)%s*$")
end
end
------------------------------------------------------------------------
-- BEGIN: Messages that may be displayed by Module:Convert.
-- LATER: Perhaps move following to another module to simplify this module.
local all_categories = {
['en'] = {
general = '[[Category:Convert error]]',
unknown = '[[Category:Convert unknown unit]]',
mismatch = '[[Category:Convert dimension mismatch]]',
},
}
-- Following puts wanted style around each unit code marked like '...%{ft%}...'.
local unitcode_regex = '%%([{}])'
local unitcode_replace = { ['{'] = '<code style="background:transparent;">', ['}'] = '</code>' }
local all_messages = {
-- All output messages.
['en'] = {
-- The prefix is inserted before each message.
cvt_prefix = '[[Module talk:Convert|Conversion error]]:',
-- Messages; each is a numbered table: { 'error text', 'category key', gsub_regex, gsub_table }.
cvt_bad_default = { 'Unit "%s" has an invalid default', 'unknown' },
cvt_bad_num = { 'Value "%s" must be a number', 'general' },
cvt_bad_num2 = { 'Second value "%s" must be a number', 'general' },
cvt_bad_prec = { 'Parameter precision "%s" must be an integer', 'general' },
cvt_bad_sigfig = { 'Parameter sigfig "%s" must be an integer', 'general' },
cvt_bad_unit = { 'Unit "%s" is invalid here', 'unknown' },
cvt_big_prec = { 'Precision "%s" is too large', 'general' },
cvt_bug_convert = { 'Bug: Cannot convert between specified units', 'general' },
cvt_mismatch = { 'Cannot convert "%s" to "%s"', 'mismatch' },
cvt_no_default = { 'Unit "%s" has no default output unit', 'unknown' },
cvt_no_num = { 'Need value', 'general' },
cvt_no_num2 = { 'Need second value', 'general' },
cvt_no_unit = { 'Need name of unit', 'unknown' },
cvt_should_be = { '%s', 'general', unitcode_regex, unitcode_replace },
cvt_sigfig_pos = { 'sigfig "%s" must be positive', 'general' },
cvt_unknown = { 'Unit "%s" is not known', 'unknown' },
},
}
local messages = {} -- simulating how it would be if in another module
function messages.message(msg, lang)
-- Return wikitext for an error message, including category if specified
-- for the message type.
-- msg = numbered table:
-- msg[1] = 'cvt_xxx' (string used as a key to get message info)
-- msg[2] = 'parm1' (string to replace first %s if any in message)
-- msg[3] = 'parm2' (string to replace second %s if any in message)
-- msg[4] = 'parm3' (string to replace third %s if any in message)
-- lang = 'en' (default), or other language code.
lang = lang or 'en'
local mlang = all_messages[lang]
if mlang then
local t = mlang[msg[1]]
if t then
-- t[1] = message text, t[2] = category, t[3] = gsub_regex, t[4] = gsub_replace
local text = format(t[1] or 'Missing message',
msg[2] or '?',
msg[3] or '?',
msg[4] or '?')
local cat = all_categories[lang][t[2]] or ''
local prefix = mlang['cvt_prefix'] or ''
local regex, replace = t[3], t[4]
if regex and replace then
text = text:gsub(regex, replace)
end
return '<span style="color:black; background-color:orange;">' ..
prefix .. ' ' .. text .. cat .. '</span>'
end
end
return 'Convert internal error: unknown message'
end
-- END: Messages that may be displayed by Module:Convert.
------------------------------------------------------------------------
-- BEGIN: Code required only for built-in units.
-- LATER: Perhaps move following to another module to simplify this module.
local function speed_of_sound(altitude)
-- This is for the Mach built-in unit of speed.
-- Return speed of sound in metres per second at given altitude in feet.
-- If no altitude given, use default (zero altitude = sea level).
-- Table gives speed of sound in miles per hour at various altitudes:
-- altitude = -17,499 to 302,499 feet
-- mach_table[a + 4] = s where
-- a = (altitude / 5000) rounded to nearest integer (-3 to 60)
-- s = speed of sound (mph) at that altitude
-- LATER: Should calculate result from an interpolation between the next
-- lower and higher altitudes in table, rather than rounding to nearest.
-- From: http://www.aerospaceweb.org/question/atmosphere/q0112.shtml
local mach_table = { -- a =
799.5, 787.0, 774.2, 761.207051, -- -3 to 0
748.0, 734.6, 721.0, 707.0, 692.8, 678.3, 663.5, 660.1, 660.1, 660.1, -- 1 to 10
660.1, 660.1, 660.1, 662.0, 664.3, 666.5, 668.9, 671.1, 673.4, 675.6, -- 11 to 20
677.9, 683.7, 689.9, 696.0, 702.1, 708.1, 714.0, 719.9, 725.8, 731.6, -- 21 to 30
737.3, 737.7, 737.7, 736.2, 730.5, 724.6, 718.8, 712.9, 707.0, 701.1, -- 31 to 40
695.0, 688.9, 682.8, 676.6, 670.4, 664.1, 657.8, 652.9, 648.3, 643.7, -- 41 to 50
639.1, 634.4, 629.6, 624.8, 620.0, 615.2, 613.2, 613.2, 613.2, 613.5, -- 51 to 60
}
altitude = altitude or 0
local a = (altitude < 0) and -altitude or altitude
a = floor(a / 5000 + 0.5)
if altitude < 0 then
a = -a
end
if a < -3 then
a = -3
elseif a > 60 then
a = 60
end
return mach_table[a + 4] * 0.44704 -- mph converted to m/s
end
-- END: Code required only for built-in units.
------------------------------------------------------------------------
local function override_from(out_table, in_table, fields)
-- Copy the specified fields from in_table to out_table, but do not
-- copy nil fields (keep any corresponding field in out_table).
for _, field in ipairs(fields) do
if in_table[field] then
out_table[field] = in_table[field]
end
end
end
local function shallow_copy(t)
-- Return a shallow copy of t.
-- Do not need the features and overhead of the Scribunto mw.clone().
local result = {}
for k, v in pairs(t) do
result[k] = v
end
return result
end
local unit_mt = {
-- Metatable to get missing values for a unit that does not accept SI prefixes,
-- or a for a unit that accepts prefixes but where no prefix was used.
-- In the latter case, and before use, fields symbol, name1, name1_us
-- must be set from _symbol, _name1, _name1_us respectively.
__index = function (self, key)
local value
if key == 'name1' or key == 'sym_us' then
value = self.symbol
elseif key == 'name2' then
value = self.name1 .. 's'
elseif key == 'name1_us' then
value = self.name1
if not rawget(self, 'name2_us') then
-- If name1_us is 'foot', do not make name2_us by appending 's'.
self.name2_us = self.name2
end
elseif key == 'name2_us' then
local raw1_us = rawget(self, 'name1_us')
if raw1_us then
value = raw1_us .. 's'
else
value = self.name2
end
elseif key == 'link' then
value = self.name1
elseif key == 'engscale' or key == 'per' then
value = false
else
return nil
end
rawset(self, key, value)
return value
end
}
local unit_prefixed_mt = {
-- Metatable to get missing values for a unit that accepts SI prefixes,
-- and where a prefix has been used.
-- Before use, fields si_name, si_prefix must be defined.
__index = function (self, key)
local value
if key == 'symbol' then
value = self.si_prefix .. self._symbol
elseif key == 'sym_us' then
value = self.symbol -- always the same as sym_us for prefixed units
elseif key == 'name1' then
local pos = rawget(self, 'prefix_position') or 1
value = self._name1
value = value:sub(1, pos - 1) .. self.si_name .. value:sub(pos)
elseif key == 'name2' then
value = self.name1 .. 's'
elseif key == 'name1_us' then
value = rawget(self, '_name1_us')
if value then
local pos = rawget(self, 'prefix_position') or 1
value = value:sub(1, pos - 1) .. self.si_name .. value:sub(pos)
else
value = self.name1
end
elseif key == 'name2_us' then
if rawget(self, '_name1_us') then
value = self.name1_us .. 's'
else
value = self.name2
end
elseif key == 'link' then
value = self.name1
elseif key == 'engscale' or key == 'per' then
value = false
else
return nil
end
rawset(self, key, value)
return value
end
}
local unit_per_mt = {
-- Metatable to get values for a "per" unit of form "x/y".
-- This is never called to determine a unit name or link because "per" units
-- are handled as a special case.
__index = function (self, key)
local value
if key == 'symbol' then
local per = self.per
local unit1, unit2 = per[1], per[2]
if unit1 then
value = unit1[key] .. '/' .. unit2[key]
else
value = '/' .. unit2[key]
end
elseif key == 'sym_us' then
value = self.symbol
elseif key == 'scale' then
local per = self.per
local unit1, unit2 = per[1], per[2]
value = (unit1 and unit1.scale or 1) / unit2.scale
elseif key == 'engscale' then
value = false
else
return nil
end
rawset(self, key, value)
return value
end
}
local function lookup(unitcode, sp, what)
-- Return true, t where t is a copy of the unit's converter table,
-- or return false, t where t is an error message table.
-- Parameter 'sp' is nil, or is 'us' for US spelling of SI prefixes and
-- the symbol and names of the unit. If 'us', the result includes field
-- sp_us = true (that field may also have been in the unit definition).
-- Parameter 'what' determines whether combination units are accepted:
-- 'no_combination' : single unit only
-- 'any_combination' : single unit or combination or output multiple
-- 'only_multiple' : single unit or output multiple only
-- Parameter unitcode is a symbol (like 'g'), with an optional SI prefix (like 'kg').
-- If, for example, 'kg' is in this table, that entry is used;
-- otherwise the prefix ('k') is applied to the base unit ('g').
-- If unitcode is a known combination code (and if allowed by what),
-- a table of output multiple unit tables is included in the result.
-- For compatibility with the old template, underscores in unitcode are replaced
-- with spaces so {{convert|350|board_feet}} --> 350 board feet (0.83 m³).
if unitcode == nil or unitcode == '' then
return false, { 'cvt_no_unit' }
end
unitcode = unitcode:gsub('_', ' ')
local t = units[unitcode]
if t then
if t.shouldbe then
return false, { 'cvt_should_be', t.shouldbe }
end
local force_sp_us = (sp == 'us')
if t.sp_us then
force_sp_us = true
sp = 'us'
end
local target = t.target -- nil, or unitcode is an alias for this target
if target then
local success, result = lookup(target, sp, what)
if not success then return false, result end
override_from(result, t, { 'customary', 'default', 'link', 'symbol', 'symlink' })
local multiplier = t.multiplier
if multiplier then
result.multiplier = tostring(multiplier)
result.scale = result.scale * multiplier
end
return true, result
end
local per = t.per -- nil/false, or a numbered table for "x/y" units
if per then
local result = { utype = t.utype, per = {} }
override_from(result, t, { 'default', 'invert', 'iscomplex', 'symbol', 'symlink' })
result.symbol_raw = (result.symbol or false) -- to distinguish between a defined exception and a metatable calculation
local cvt = result.per
local prefix
for i, v in ipairs(per) do
if i == 1 and (v == '$' or v == '£') then
prefix = v
else
local success, t = lookup(v, sp, 'no_combination')
if not success then return false, t end
cvt[i] = t
if t.sp_us then -- if the top or bottom unit forces sp=us, set the per unit to use the correct name/symbol id
force_sp_us = true
end
end
end
if prefix then
result.vprefix = prefix
else
result.vprefix = false -- to avoid calling __index
end
result.sp_us = force_sp_us
return true, setmetatable(result, unit_per_mt)
end
local combo = t.combination -- nil or a table of unitcodes
if combo then
local multiple = t.multiple
if what == 'no_combination' or (what == 'only_multiple' and multiple == nil) then
return false, { 'cvt_bad_unit', unitcode }
end
-- Recursively create a combination table containing the
-- converter table of each unitcode.
local result = { utype = t.utype, multiple = multiple, combination = {} }
local cvt = result.combination
for i, v in ipairs(combo) do
local success, t = lookup(v, sp, multiple and 'no_combination' or 'only_multiple')
if not success then return false, t end
cvt[i] = t
end
return true, result
end
local result = shallow_copy(t)
result.sp_us = force_sp_us
if result.prefixes then
result.symbol = result._symbol
result.name1 = result._name1
result.name1_us = result._name1_us
end
return true, setmetatable(result, unit_mt)
end
for plen = 2, 1, -1 do
-- Look for an SI prefix; should never occur with an alias.
-- Check for longer prefix first ('dam' is decametre).
-- Micro (µ) is two bytes in utf-8, so is found with plen = 2.
local prefix = unitcode:sub(1, plen)
local si = SIprefixes[prefix]
if si then
local t = units[unitcode:sub(plen+1)]
if t and t.prefixes then
local result = shallow_copy(t)
if sp == 'us' then
result.sp_us = true
end
if result.sp_us and si.name_us then
result.si_name = si.name_us
else
result.si_name = si.name
end
result.si_prefix = si.prefix or prefix
result.scale = t.scale * 10 ^ (si.exponent * t.prefixes)
return true, setmetatable(result, unit_prefixed_mt)
end
end
end
-- Accept any unit with an engineering notation prefix like "e6cuft"
-- (million cubic feet), but not chained prefixes like "e3e6cuft",
-- and not if the unit is a combination or multiple,
-- and not if the unit has an offset or is a built-in.
local exponent, baseunit = unitcode:match('^e(%d+)(.*)')
if exponent then
local engscale = eng_scales[exponent]
if engscale then
local success, result = lookup(baseunit, sp, 'no_combination')
if not success then return false, result end
if not (result.offset or result.builtin or result.engscale) then
result.defkey = unitcode -- key to lookup default exception
engscale.exponent = exponent
result.engscale = engscale
result.scale = result.scale * 10 ^ tonumber(exponent)
return true, result
end
end
end
return false, { 'cvt_unknown', unitcode }
end
local function ntsh_complement(text)
-- Return text (string of digits) after subtracting each digit from 9.
local result = ''
local first, last = 1, #text
while first <= last do
local lenblock = last + 1 - first
if lenblock > 12 then
lenblock = 12
end
local block = tonumber(text:sub(first, first + lenblock - 1))
local nines = tonumber(string.rep('9', lenblock))
local fmt = '%0' .. tostring(lenblock) .. '.0f'
result = result .. format(fmt, nines - block)
first = first + lenblock
end
return result
end
local function ntsh(n, debug)
-- Return html text to be used for a hidden sort key so that
-- the given number will be sorted in numeric order.
-- If debug == 'yes', output is in a box (not hidden).
-- This implements Template:Ntsh (number table sorting, hidden).
local result, i, f, style
if n >= 0 then
if n > 1e16 then
result = '~'
else
i, f = math.modf(n)
f = floor(1e6 * f)
result = format('&1%016.0f%06d', i, f)
end
else
n = -n
if n > 1e16 then
result = '!'
else
i, f = math.modf(n)
f = floor(1e6 * f)
result = format('%016.0f%06d', i, f)
result = '&0' .. ntsh_complement(result)
end
end
if debug == 'yes' then
style = 'border:1px solid'
else
style = 'display:none'
end
return '<span style="' .. style .. '">' .. result .. '</span>'
end
local function hyphenated(name)
-- Return a hyphenated form of given name (for adjectival usage).
-- This uses a simple and efficient procedure that works for most cases.
-- Some units (if used) would require more, and can later think about
-- adding a method to handle exceptions.
-- The procedure is to replace each space with a hyphen, but
-- not a space after ')' [for "(pre-1954 US) nautical mile"], and
-- not spaces immediately before '(' or in '(...)' [for cases like
-- "British thermal unit (ISO)" and "Calorie (International Steam Table)"].
local pos
if name:sub(1, 1) == '(' then
pos = name:find(')', 1, true)
if pos then
return name:sub(1, pos+1) .. name:sub(pos+2):gsub(' ', '-')
end
elseif name:sub(-1, -1) == ')' then
pos = name:find('(', 1, true)
if pos then
return name:sub(1, pos-2):gsub(' ', '-') .. name:sub(pos-1)
end
end
return name:gsub(' ', '-')
end
local function change_sign(text)
-- Change sign of text for correct appearance because it is negated.
if text:sub(1, 1) == '-' then
return text:sub(2)
end
return '-' .. text
end
local function use_minus(text)
-- Return text with Unicode minus instead of '-', if present.
if text:sub(1, 1) == '-' then
return MINUS .. text:sub(2)
end
return text
end
local function with_separator(text)
-- Return text with thousand separators inserted.
-- The given text is like '123' or '12345.6789' or '1.23e45'
-- (e notation can only occur when processing an input value).
-- The text has no sign (caller inserts that later, if necessary).
-- Separator is inserted only in the integer part of the significand
-- (not after numdot, and not after 'e' or 'E').
-- Four-digit integer parts have a separator (like '1,234').
if numsep == '' then
return text
end
local last = text:match('()[' .. numdot .. 'eE]') -- () returns position
if last == nil then
last = #text
else
last = last - 1 -- index of last character before dot/e/E
end
if last >= 4 then
local groups = {}
local first = last % 3
if first > 0 then
table.insert(groups, text:sub(1, first))
end
first = first + 1
while first < last do
table.insert(groups, text:sub(first, first+2))
first = first + 3
end
return table.concat(groups, numsep) .. text:sub(last+1)
end
return text
end
-- Input values can use values like 1.23e12, but are never displayed
-- using exponent notation like 1.23×10¹².
-- Very small or very large output values use exponent notation.
-- Use format(fmtpower, significand, exponent) where each arg is a string.
local fmtpower = '%s<span style="margin:0 .15em 0 .25em">×</span>10<sup>%s</sup>'
local function with_exponent(show, exponent)
-- Return wikitext to display the implied value in exponent notation.
if #show > 1 then
show = show:sub(1, 1) .. numdot .. show:sub(2)
end
return format(fmtpower, show, use_minus(tostring(exponent)))
end
local function make_sigfig(value, sigfig)
-- Return show, exponent that are equivalent to the result of
-- converting the number 'value' (where value >= 0) to a string,
-- rounded to 'sigfig' significant figures.
-- The returned items are:
-- show: a string of digits; no sign and no dot;
-- there is an implied dot before show.
-- exponent: a number (an integer) to shift the implied dot.
-- Resulting value = tonumber('.' .. show) * 10^exponent.
-- Examples:
-- make_sigfig(23.456, 3) returns '235', 2 (.235 * 10^2).
-- make_sigfig(0.0023456, 3) returns '235', -2 (.235 * 10^-2).
-- make_sigfig(0, 3) returns '000', 1 (.000 * 10^1).
if sigfig <= 0 then
sigfig = 1
elseif sigfig > maxsigfig then
sigfig = maxsigfig
end
if value == 0 then
return string.rep('0', sigfig), 1
end
local exp, frac = math.modf(log10(value))
if frac >= 0 then
frac = frac - 1
exp = exp + 1
end
local digits = format('%.0f', 10^(frac + sigfig))
if #digits > sigfig then
-- Overflow (for sigfig=3: like 0.9999 rounding to "1000"; need "100").
digits = digits:sub(1, sigfig)
exp = exp + 1
end
assert(#digits == sigfig, 'Bug: rounded number has wrong length')
return digits, exp
end
local function format_number(show, exponent, isnegative)
-- Return t where t is a table with the results; fields:
-- show = wikitext formatted to display implied value
-- is_scientific = true if show uses scientific notation
-- clean = unformatted show (possibly adjusted and with inserted numdot)
-- sign = '' or MINUS
-- exponent = exponent (possibly adjusted)
-- The clean and exponent fields can be used to calculate the
-- rounded absolute value, if needed.
--
-- The value implied by the arguments is found from:
-- exponent is nil; and
-- show is a string of digits (no sign), with an optional dot;
-- show = '123.4' is value 123.4, '1234' is value 1234.0;
-- or:
-- exponent is an integer indicating where dot should be;
-- show is a string of digits (no sign and no dot);
-- there is an implied dot before show;
-- show does not start with '0';
-- show = '1234', exponent = 3 is value 0.1234*10^3 = 123.4.
--
-- The formatted result:
-- * Includes a Unicode minus if isnegative.
-- * Has numsep inserted where necessary.
-- * Uses scientific notation for very small or large values.
-- * Has no more than maxsigfig significant digits
-- (same as old template and {{#expr}}).
local sign = isnegative and MINUS or ''
local maxlen = maxsigfig
if exponent == nil then
local integer, dot, fraction = show:match('^(%d*)([' .. numdot .. ']?)(.*)')
if #integer >= 10 then
show = integer .. fraction
exponent = #integer
elseif integer == '0' or integer == '' then
local zeros, figs = fraction:match('^(0*)([^0]?.*)')
if #figs == 0 then
if #zeros > maxlen then
show = '0' .. numdot .. zeros:sub(1, maxlen)
end
elseif #zeros >= 4 then
show = figs
exponent = -#zeros
elseif #figs > maxlen then
show = '0' .. numdot .. zeros .. figs:sub(1, maxlen)
end
else
maxlen = maxlen + #dot
if #show > maxlen then
show = show:sub(1, maxlen)
end
end
end
if exponent then
if #show > maxlen then
show = show:sub(1, maxlen)
end
if exponent > 10 or exponent <= -4 or (exponent == 10 and show ~= '1000000000') then
-- Rounded value satisfies: value >= 1e9 or value < 1e-4 (1e9 = 0.1e10).
return {
clean = '.' .. show,
exponent = exponent,
sign = sign,
show = sign .. with_exponent(show, exponent-1),
is_scientific = true }
end
if exponent >= #show then
show = show .. string.rep('0', exponent - #show) -- result has no dot
elseif exponent <= 0 then
show = '0' .. numdot .. string.rep('0', -exponent) .. show
else
show = show:sub(1, exponent) .. numdot .. show:sub(exponent+1)
end
end
if isnegative and show:match('^0.?0*$') then
sign = '' -- don't show minus if result is negative but rounds to zero
end
return {
clean = show,
sign = sign,
show = sign .. with_separator(show) }
end
-- Fraction output format (like old template).
-- frac1: sign, numerator, denominator
-- frac2: wholenumber, sign, numerator, denominator
local frac1 = '<span style="white-space:nowrap">%s<sup>%s</sup>⁄<sub>%s</sub></span>'
local frac2 = '<span class="frac nowrap">%s<s style="display:none">%s</s><sup>%s</sup>⁄<sub>%s</sub></span>'
local function extract_fraction(text, negative)
-- If text represents a fraction, return value, show where
-- value is a number and show is a string.
-- Otherwise, return nil.
--
-- In the following, '(3/8)' represents the wikitext required to
-- display a fraction with numerator 3 and denominator 8.
-- In the wikitext, Unicode minus is used for a negative value.
-- text value, show value, show
-- if not negative if negative
-- 3 / 8 0.375, '(3/8)' -0.375, '−(3/8)'
-- 2 + 3 / 8 2.375, '2(3/8)' -1.625, '−2(−3/8)'
-- 2 - 3 / 8 1.625, '2(−3/8)' -2.375, '−2(3/8)'
-- 1 + 20/8 3.5 , '1/(20/8)' 1.5 , '−1/(−20/8)'
-- 1 - 20/8 -1.5., '1(−20/8)' -3.5 , '−1(20/8)'
-- Wherever an integer appears above, numbers like 1.25 or 12.5e-3
-- (which may be negative) are also accepted (like old template).
-- Template interprets '1.23e+2+12/24' as '123(12/24)' = 123.5!
local lhs, negfrac, rhs, numstr, numerator, denstr, denominator, wholestr, whole, value
lhs, denstr = text:match('^%s*([^/]-)%s*/%s*(.-)%s*$')
denominator = tonumber(denstr)
if denominator == nil then return nil end
wholestr, negfrac, rhs = lhs:match('^%s*(.-[^eE])%s*([+-])%s*(.-)%s*$')
if wholestr == nil or wholestr == '' then
wholestr = nil
whole = 0
numstr = lhs
else
whole = tonumber(wholestr)
if whole == nil then return nil end
numstr = rhs
end
negfrac = (negfrac == '-')
numerator = tonumber(numstr)
if numerator == nil then return nil end
if negative == negfrac or wholestr == nil then
value = whole + numerator / denominator
else
value = whole - numerator / denominator
numstr = change_sign(numstr)
end
if tostring(value):find('#', 1, true) then
return nil -- overflow or similar
end
numstr = use_minus(numstr)
denstr = use_minus(denstr)
local wikitext
if wholestr then
local sign = negative and MINUS or '+'
if negative then
wholestr = change_sign(wholestr)
end
wikitext = format(frac2, use_minus(wholestr), sign, numstr, denstr)
else
local sign = negative and MINUS or ''
wikitext = format(frac1, sign, numstr, denstr)
end
return value, wikitext
end
local missing = { 'cvt_no_num', 'cvt_no_num2' }
local invalid = { 'cvt_bad_num', 'cvt_bad_num2' }
local function extract_number(text, which, no_fraction)
-- Return true, info if can extract a number from text,
-- where info is a table with the result,
-- or return false, t where t is an error message table.
-- Parameter 'which' (1 or 2) selects which input value is being
-- processed (to select the appropriate error message, if needed).
-- Before processing, the input text is cleaned:
-- * Any thousand separators (valid or not) are removed.
-- * Any sign (and optional following whitespace) is replaced with
-- '-' (if negative) or '' (otherwise).
-- That replaces Unicode minus with '-'.
-- If successful, the returned info table contains named fields:
-- value = a valid number
-- singular = true if value is 1 (to use singular form of units)
-- = false if value is -1 (like old template)
-- clean = cleaned text with any separators and sign removed
-- show = text formatted for output
-- For show:
-- * Thousand separators are inserted.
-- * If negative, a Unicode minus is used; otherwise the sign
-- is '+' (if the input text used '+'), or is ''.
-- TODO Think about fact that the input value might be like 1.23e+123.
-- Will the exponent break anything?
text = strip(text)
if text == nil or text == '' then return false, { missing[which] } end
local clean, sign
if numsep == '' then
clean = text
else
clean = text:gsub('[' .. numsep .. ']', '') -- use '[.]' if numsep is '.'
end
-- Remove any sign character (assuming a number starts with '.' or a digit).
sign, clean = clean:match('^%s*([^ .%d]*)%s*(.*)')
if sign == nil or clean == nil then
return false, { missing[which] } -- should never occur
end
local propersign, isnegative
if sign == MINUS or sign == '-' or sign == '−' then
propersign = MINUS
isnegative = true
elseif sign == '+' then
propersign = '+'
isnegative = false
elseif sign == '' then
propersign = ''
isnegative = false
else
return false, { invalid[which], text }
end
local show, singular
local value = tonumber(clean)
if value == nil then
if not no_fraction then
value, show = extract_fraction(clean, isnegative)
end
if value == nil then
return false, { invalid[which], text }
end
singular = false -- any fraction (even with value 1) is regarded as plural
end
if show == nil then
singular = (value == 1 and not isnegative)
show = propersign .. with_separator(clean)
end
if isnegative and (value ~= 0) then
value = -value
end
return true, {
value = value,
singular = singular,
clean = clean,
show = show
}
end
local function require_integer(text, invalid)
-- Return true, n where n = integer equivalent to given text,
-- or return false, t where t is an error message table.
-- Input should be the text for a simple integer (no separators, no Unicode minus).
-- Using regex avoids irritations with input like '-0.000001'.
if text == nil then return false, { 'cvt_no_num' } end
if text:match('^-?%d+$') == nil then
return false, { invalid, text }
end
return true, tonumber(text)
end
local function range_text(range, want_name, parms, before, after)
-- Return before .. rtext .. after
-- where rtext is the text that separates two values in a range.
local adj = parms.adj
local rtext, adj_text, exception
if type(range) == 'table' then
-- Table must specify range text for abbr=off and for abbr=on,
-- and may specify range text for 'adj=on',
-- and may specify exception = true.
rtext = range[want_name and 'off' or 'on']
adj_text = range['adj']
exception = range['exception']
else
rtext = range
end
if adj == 'on' then
if want_name or (exception and parms.abbr_org == 'on') then
rtext = adj_text or rtext:gsub(' ', '-'):gsub(' ', '-')
end
end
if rtext == '–' and after:sub(1, #MINUS) == MINUS then
rtext = ' – '
end
return before .. rtext .. after
end
local function get_parms(pframe)
-- If successful, return true, args, unit where
-- args is a table of all arguments passed to the template
-- converted to named arguments, and
-- unit is the input unit table;
-- or return false, t where t is an error message table.
-- Some of the named args that are added here could be provided by the
-- user of the template.
-- MediaWiki removes leading and trailing whitespace from the values of
-- named arguments. However, the values of numbered arguments include any
-- whitespace entered in the template, and whitespace is used by some
-- parameters (example: the numbered parameters associated with "disp=x").
local range_types = { -- text to separate values in a range
['by'] = ' by ',
['-'] = '–',
['and'] = { ['off'] = ' and ', ['on'] = ' and ', exception = true },
['or'] = { ['off'] = ' or ' , ['on'] = ' or ' , exception = true },
['to'] = { ['off'] = ' to ' , ['on'] = ' to ' , exception = true },
['xx'] = ' × ',
['to(-)'] = { ['off'] = ' to ', ['on'] = '–' },
['+/-'] = { ['off'] = ' ± ', ['on'] = ' ± ', ['adj'] = ' ± ' },
['x'] = { ['off'] = ' by ', ['on'] = ' × ', is_range_x = true },
}
local range_aliases = {
['and(-)'] = 'and',
['&'] = 'and',
['–'] = '-',
['–'] = '-',
['to-'] = 'to(-)',
['×'] = 'x',
['±'] = '+/-',
}
local success, info1, info2
local args = {} -- arguments passed to template
for k, v in pairs(pframe.args) do
args[k] = v
end
success, info1 = extract_number(args[1], 1)
if not success then return false, info1 end
local in_unit, precision
local next = strip(args[2])
local i = 3
local range = range_types[next] or range_types[range_aliases[next]]
if range == nil then
in_unit = next
else
args.range = range
args.is_range_x = range.is_range_x
success, info2 = extract_number(args[3], 2)
if not success then return false, info2 end
in_unit = strip(args[4])
i = 5
end
local success, in_unit_table = lookup(in_unit, args.sp, 'no_combination')
if not success then return false, in_unit_table end
if args.test == 'msg' then
-- Am testing the messages produced when no output unit is specified, and
-- the input unit has a missing or invalid default.
-- Set two units for testing that.
-- LATER: Remove this code.
if in_unit == 'chain' then
in_unit_table.default = nil -- no default
elseif in_unit == 'rd' then
in_unit_table.default = "ft!X!m" -- an invalid expression
end
end
in_unit_table.valinfo = { info1, info2 } -- info2 is nil if no range
in_unit_table.inout = 'in' -- this is an input unit
if not range then
local subdivs = in_unit_table.subdivs -- nil or a table of allowed subdivisions
if subdivs then
-- Look for a composite input unit like "|2|ft|6|in".
local subcode = strip(args[i + 1])
local subdiv = subdivs[subcode]
if subdiv then
-- subcode = unit code of a valid subdivision of main unit,
-- but it can be replaced by the optional subdiv[3].
local success, subunit, subinfo
success, subunit = lookup(subdiv[3] or subcode, args.sp, 'no_combination')
if not success then return false, subunit end -- should never occur
success, subinfo = extract_number(args[i], 1)
if not success then return false, subinfo end
i = i + 2
subunit.inout = 'in'
subunit.valinfo = { subinfo }
-- Calculate total value as a number of subdivisions.
-- subdiv[1] = number of subdivisions per main unit (integer > 1).
local total = info1.value * subdiv[1] + subinfo.value
in_unit_table = {
utype = in_unit_table.utype,
scale = subunit.scale,
default = subdiv[2] or in_unit_table.default,
valinfo = { { value = total, clean = subinfo.clean } },
composite = { in_unit_table, subunit },
}
end
end
end
if in_unit_table.builtin == 'mach' then
-- As with old template, a number following Mach as the input unit is the altitude,
-- and there is no way to specify an altitude for the output unit.
-- Could put more code in this function to get any output unit and check for
-- an altitude following that unit.
local success, info = extract_number(args[i], 1, true)
if success then
i = i + 1
in_unit_table.altitude = info.value
end
end
next = strip(args[i])
i = i + 1
if tonumber(next) then
precision = next
else
args.out_unit = next
next = strip(args[i])
if tonumber(next) then
i = i + 1
precision = next
end
end
if args.adj == nil and args.sing ~= nil then
args.adj = args.sing -- sing (singular) is an old equivalent of adj
end
if args.adj == 'mid' then
args.adj = 'on'
next = args[i]
i = i + 1
if next == nil then
args.mid = ''
else -- mid-text words
if next:sub(1, 1) == '-' then
args.mid = next
else
args.mid = ' ' .. next
end
end
elseif args.adj == 'on' then
args.mid = ''
end
if precision == nil then
if tonumber(args[i]) then
precision = strip(args[i])
i = i + 1
end
end
-- Change disp to standard name so subsequent processing can ignore aliases.
local disp = args.disp
if disp == '5' then
args.disp5 = true
elseif disp == 'flip5' then
args.disp5 = true
args.disp = 'flip'
elseif disp == 'number' then
args.disp = 'output number only'
elseif disp == 'out' or disp == '2' then
args.disp = 'output only'
elseif disp == 'u2' then
args.disp = 'unit2'
elseif disp == 's' or disp == '/' then
args.disp = 'slash'
end
disp = args.disp
if disp == 'x' then
args.joins = { args[i] or '', args[i+1] or '' }
end
args.precision = args.precision or precision -- allow named parameter
local abbr = args.abbr
if abbr == nil then
-- Default is to abbreviate output (use symbol), or input if flipped.
args.abbr = (disp == 'flip') and 'in' or 'out'
else
args.abbr_org = abbr -- original abbr (as entered by user)
if disp == 'flip' then -- 'in' = LHS, 'out' = RHS
if abbr == 'in' then
abbr = 'out'
elseif abbr == 'out' then
abbr = 'in'
end
end
args.abbr = abbr
end
return true, args, in_unit_table
end
local function default_precision(invalue, inclean, outvalue, in_current, out_current, extra)
-- Return a default value for precision (an integer like 2, 0, -2).
-- Code follows procedures used in old template.
local fudge = 1e-14 -- {{Order of magnitude}} adds this, so we do too
local prec, minprec, adjust
local utype = out_current.utype
-- Count digits after decimal mark, handling cases like '12.345e6'.
local exponent
local integer, dot, fraction, expstr = inclean:match('^(%d*)([' .. numdot .. ']?)(%d*)(.*)')
local e = expstr:sub(1, 1)
if e == 'e' or e == 'E' then
exponent = tonumber(expstr:sub(2))
end
if dot == '' then
prec = -integer:match('0*$'):len()
else
prec = #fraction
end
if exponent then
-- So '1230' and '1.23e3' both give prec = -1, and '0.00123' and '1.23e-3' give 5.
prec = prec - exponent
end
local exception = (utype == 'temperature' and not
(in_current.exception == 'temperature' or out_current.exception == 'temperature'))
if exception then
-- Kelvin value can be almost zero, or small but negative due to precision problems.
-- Also, an input value like -300 C (below absolute zero) gives negative kelvins.
-- Calculate minimum precision from absolute value.
adjust = 0
local kelvin = math.abs((invalue - in_current.offset) * in_current.scale)
if kelvin < 1e-8 then -- assume nonzero due to input or calculation precision problem
minprec = 2
else
minprec = 2 - floor(log10(kelvin) + fudge) -- 3 sigfigs in kelvin
end
else
if invalue == 0 or outvalue <= 0 then
-- We are never called with a negative outvalue, but it might be zero.
-- This is special-cased to avoid calculation exceptions.
return 0
end
if out_current.symbol == 'ft' and floor(invalue) == invalue then
-- More precision when output ft with input value equal to an integer.
adjust = -log10(in_current.scale)
else
adjust = log10(math.abs(invalue / outvalue))
end
adjust = adjust + log10(2)
-- Ensure that the output has at least two significant figures.
minprec = 1 - floor(log10(outvalue) + fudge)
end
if extra then
adjust = extra.adjust or adjust
minprec = extra.minprec or minprec
end
return math.max(floor(prec + adjust), minprec)
end
local function convert(invalue, inclean, in_current, out_current)
-- Convert given input value from one unit to another.
-- Return output_value (a number) if a simple convert, or
-- return f, t where
-- f = true, t = table of information with results, or
-- f = false, t = error message table.
local inscale = in_current.scale
local outscale = out_current.scale
if not in_current.iscomplex and not out_current.iscomplex then
return invalue * (inscale / outscale) -- minimize overhead for most common case
end
if in_current.invert then
-- Fuel efficiency (there are no built-ins for this type of unit).
if in_current.invert * out_current.invert < 0 then
return 1 / (invalue * inscale * outscale)
end
return invalue * (inscale / outscale)
elseif in_current.offset then
-- Temperature (there are no built-ins for this type of unit).
return (invalue - in_current.offset) * (inscale / outscale) + out_current.offset
else
-- Built-in unit.
local in_builtin = in_current.builtin
local out_builtin = out_current.builtin
if in_builtin and out_builtin then
if in_builtin == out_builtin then
return invalue
end
-- There are no cases (yet) where need to convert from one
-- built-in unit to another, so this should never occur.
return false, { 'cvt_bug_convert' }
end
if in_builtin == 'mach' or out_builtin == 'mach' then
local adjust
if in_builtin == 'mach' then
inscale = speed_of_sound(in_current.altitude)
adjust = outscale / 0.1
else
outscale = speed_of_sound(out_current.altitude)
adjust = 0.1 / inscale
end
return true, {
outvalue = invalue * (inscale / outscale),
adjust = log10(adjust) + log10(2),
}
elseif in_builtin == 'hand' then
-- 1 hand = 4 inches; 1.2 hands = 6 inches.
-- Fractions of a hand are only defined for the first digit, and
-- the first fractional digit should be a number of inches (1, 2 or 3).
-- However, this code interprets the entire fraction as the number
-- of inches / 10 (so 1.75 inches would be 0.175 hands).
-- A value like 12.3 hands is exactly 12*4 + 3 inches; base default precision on that.
local integer, fraction = math.modf(invalue)
local outvalue = (integer + 2.5 * fraction) * (inscale / outscale)
local inch_value = 4 * integer + 10 * fraction -- equivalent number of inches
local fraction = inclean:match('[' .. numdot .. '](.*)') or ''
local fmt
if fraction == '' then
fmt = '%.0f'
else
fmt = '%.' .. format('%d', #fraction - 1) .. 'f'
end
return true, {
invalue = inch_value,
inclean = format(fmt, inch_value),
outvalue = outvalue,
minprec = 0,
}
end
end
return false, { 'cvt_bug_convert' } -- should never occur
end
local function cvtround(parms, info, in_current, out_current)
-- Return true, t where t is a table with the conversion results; fields:
-- show = rounded, formatted string from converting value in info,
-- using the rounding specified in parms.
-- singular = true if result is positive, and (after rounding)
-- is "1", or like "1.00";
-- (and more fields shown below, and a calculated 'absvalue' field).
-- or return true, nil if no value specified;
-- or return false, t where t is an error message table.
-- This code combines convert/round because some rounding requires
-- knowledge of what we are converting.
local invalue, inclean, show, exponent, singular
if info then
invalue, inclean = info.value, info.clean
end
if invalue == nil or invalue == '' then
return true, nil
end
if out_current.builtin == 'hand' then
-- Convert to hands, then convert the fractional part to inches.
local dummy_unit_table = { scale = out_current.scale }
local success, outinfo = cvtround(parms, info, in_current, dummy_unit_table)
if not success then return false, outinfo end
local fmt
local fraction = (outinfo.show):match('[' .. numdot .. '](.*)') or ''
if fraction == '' then
if not outinfo.use_default_precision then
return true, outinfo
end
fmt = '%.0f'
else
fmt = '%.' .. format('%d', #fraction - 1) .. 'f'
end
local hands, inches = math.modf(tonumber(outinfo.raw_absvalue))
inches = format(fmt, inches * 4)
if inches:sub(1, 1) == '4' then
hands = hands + 1
inches = '0' .. inches:sub(2)
if tonumber(inches) == 0 then
inches = '0'
end
end
if inches:sub(2, 2) == numdot then
inches = inches:sub(1, 1) .. inches:sub(3)
end
return true, {
sign = outinfo.sign,
singular = outinfo.singular,
show = outinfo.sign .. with_separator(format('%d', hands)) .. '.' .. inches
}
end
local outvalue, extra = convert(invalue, inclean, in_current, out_current)
if extra then
if not outvalue then return false, extra end
invalue = extra.invalue or invalue
inclean = extra.inclean or inclean
outvalue = extra.outvalue
end
local isnegative
if outvalue < 0 then
isnegative = true
outvalue = -outvalue
end
local success, use_default_precision
local precision = parms.precision
local sigfig = parms.sigfig
local disp5 = parms.disp5
if precision then
-- Ignore sigfig, disp5.
success, precision = require_integer(precision, 'cvt_bad_prec')
if not success then return false, precision end
elseif sigfig then
-- Ignore disp5.
success, sigfig = require_integer(sigfig, 'cvt_bad_sigfig')
if not success then return false, sigfig end
if sigfig <= 0 then
return false, { 'cvt_sigfig_pos', parms.sigfig }
end
show, exponent = make_sigfig(outvalue, sigfig)
elseif disp5 then
show = format('%.0f', floor((outvalue / 5) + 0.5) * 5)
else
use_default_precision = true
precision = default_precision(invalue, inclean, outvalue, in_current, out_current, extra)
end
if precision then
if precision >= 0 then
if precision <= 8 then
-- Add a fudge to handle common cases of bad rounding due to inability
-- to precisely represent some values. This makes the following work:
-- {{convert|-100.1|C|K}} and {{convert|5555000|um|m|2}}.
-- Old template uses #expr round, which invokes PHP round().
-- LATER: Investigate how PHP round() works.
outvalue = outvalue + 2e-14
end
local fmt = '%.' .. format('%d', precision) .. 'f'
local success
success, show = pcall(format, fmt, outvalue)
if not success then
return false, { 'cvt_big_prec', tostring(precision) }
end
else
precision = -precision -- #digits to zero (in addition to digits after dot)
local shift = 10 ^ precision
show = format('%.0f', outvalue/shift)
if show ~= '0' then
exponent = #show + precision
end
end
end
-- TODO Does following work when exponent ~= nil?
-- What if show = '1000' and exponent = 1 (value = .1000*10^1 = 1)?
-- What if show = '1000' and exponent = 2 (value = .1000*10^2 = 10)?
if (show == '1' or show:match('^1%.0*$') ~= nil) and not isnegative then
-- Use match because on some systems 0.99999999999999999 is 1.0.
singular = true
end
local t = format_number(show, exponent, isnegative)
t.singular = singular
t.raw_absvalue = outvalue -- absolute value before rounding
t.use_default_precision = use_default_precision
return true, setmetatable(t, {
__index = function (self, key)
if key == 'absvalue' then
-- Calculate absolute value after rounding, if needed.
local clean, exponent = rawget(self, 'clean'), rawget(self, 'exponent')
local value = tonumber(clean) -- absolute value (any negative sign has been ignored)
if exponent then
value = value * 10^exponent
end
rawset(self, key, value)
return value
end
end })
end
local disp_joins = {
['or'] = { ' or ' , '' },
['sqbr-sp'] = { ' [' , ']' },
['sqbr-nbsp'] = { ' [' , ']' },
['comma'] = { ', ' , '' },
['slash-sp'] = { ' / ' , '' },
['slash-nbsp'] = { ' / ', '' },
['slash-nosp'] = { '/' , '' },
['b'] = { ' (' , ')' },
['br'] = { '<br/>' , '' },
}
local function evaluate_condition(value, condition)
-- Return true or false from applying a conditional expression to value,
-- or throw an error if invalid.
-- A very limited set of expressions is supported:
-- v < 9
-- v * 9 < 9
-- where
-- 'v' is replaced with value
-- 9 is any number (as defined by Lua tonumber)
-- '<' can also be '<=' or '>' or '>='
-- In addition, the following form is supported:
-- LHS and RHS
-- where
-- LHS, RHS = any of above expressions.
local function compare(value, text)
local arithop, factor, compop, limit = text:match('^%s*v%s*([*]?)(.-)([<>]=?)(.*)$')
if arithop == nil then
error('Invalid default expression', 0)
elseif arithop == '*' then
factor = tonumber(factor)
if factor == nil then
error('Invalid default expression', 0)
end
value = value * factor
end
limit = tonumber(limit)
if limit == nil then
error('Invalid default expression', 0)
end
if compop == '<' then
return value < limit
elseif compop == '<=' then
return value <= limit
elseif compop == '>' then
return value > limit
elseif compop == '>=' then
return value >= limit
end
error('Invalid default expression', 0) -- should not occur
end
local lhs, rhs = condition:match('^(.-%W)and(%W.*)')
if lhs == nil then
return compare(value, condition)
end
return compare(value, lhs) and compare(value, rhs)
end
local function get_default(value, unit_table)
-- Return true, s where s = name of unit's default output unit,
-- or return false, t where t is an error message table.
-- Some units have a default that depends on the input value
-- (the first value if a range of values is used).
-- If '!' is in the default, the first bang-delimited field is an
-- expression that uses 'v' to represent the input value.
-- Example: 'v < 120 ! small ! big ! suffix' (suffix is optional)
-- evaluates 'v < 120' as a boolean with result
-- 'smallsuffix' if (value < 120), or 'bigsuffix' otherwise.
local default = default_exceptions[unit_table.defkey or unit_table.symbol] or unit_table.default
if default == nil then
return false, { 'cvt_no_default', unit_table.symbol }
end
if default:find('!', 1, true) == nil then
return true, default
end
local t = {}
default = default .. '!' -- to get last item
for item in default:gmatch('%s*(.-)%s*!') do
table.insert(t, item) -- split on '!', removing leading/trailing whitespace
end
if #t == 3 or #t == 4 then
local success, result = pcall(evaluate_condition, value, t[1])
if success then
default = result and t[2] or t[3]
if #t == 4 then
default = default .. t[4]
end
return true, default
end
end
return false, { 'cvt_bad_default', unit_table.symbol }
end
local function linked_id(unit_table, key_id, want_link)
-- Return final unit id (symbol or name), optionally with a wikilink,
-- and update unit_table.sep if required.
-- key_id is one of: 'symbol', 'sym_us', 'name1', 'name1_us', 'name2', 'name2_us'.
local abbr_on = (key_id == 'symbol' or key_id == 'sym_us')
if abbr_on and want_link then
local symlink = rawget(unit_table, 'symlink')
if symlink then
return symlink -- for exceptions that have the linked symbol built-in
end
end
local multiplier = rawget(unit_table, 'multiplier')
local per = unit_table.per
if per then
local unit1 = per[1] -- top unit_table, or nil
local unit2 = per[2] -- bottom unit_table
if abbr_on then
if not unit1 then
unit_table.sep = '' -- no separator in "$2/acre"
end
if not want_link then
local symbol = unit_table.symbol_raw
if symbol then
return symbol -- for exceptions that have the symbol built-in
end
end
end
local key_id2 -- unit2 is always singular
if key_id == 'name2' then
key_id2 = 'name1'
elseif key_id == 'name2_us' then
key_id2 = 'name1_us'
else
key_id2 = key_id
end
local result
if abbr_on then
result = '/'
elseif unit1 then
result = ' per '
else
result = 'per '
end
if unit1 then
result = linked_id(unit1, key_id, want_link) .. result
end
return result .. linked_id(unit2, key_id2, want_link)
end
if multiplier then
-- A multiplier (like "100" in "100km") forces the unit to be plural.
if abbr_on then
multiplier = multiplier .. ' '
else
multiplier = multiplier .. ' '
if key_id == 'name1' then
key_id = 'name2'
elseif key_id == 'name1_us' then
key_id = 'name2_us'
end
end
else
multiplier = ''
end
local id = unit_table[key_id]
if want_link then
local link = link_exceptions[unit_table.symbol] or unit_table.link
if link then
local customary_units = {
'[[United States customary units|US]] ',
'[[United States customary units|U.S.]] ',
'[[Imperial unit|imperial]] ',
'[[Imperial unit|imp]] ',
}
local i = unit_table.customary
if i == 1 and unit_table.sp_us then
i = 2 -- show "U.S." not "US"
end
if i == 3 and abbr_on then
i = 4 -- abbreviate "imperial" to "imp"
end
local customary = customary_units[i]
if customary then
-- Omit any "US"/"U.S."/"imp"/"imperial" from start of id since that will be inserted.
local removes = (i < 3) and { 'US ', 'US ', 'U.S. ', 'U.S. ' } or { 'imp ', 'imp ', 'imperial ' }
for _, prefix in ipairs(removes) do
local plen = #prefix
if id:sub(1, plen) == prefix then
id = id:sub(plen + 1)
break
end
end
else
customary = ''
end
-- Change, for example: [[Mile|mile]] --> [[mile]], and [[Mile|miles]] --> [[mile]]s.
local l = link:sub(1, 1):lower() .. link:sub(2)
if link == id or l == id then
id = customary .. '[[' .. id .. ']]'
elseif link .. 's' == id or l .. 's' == id then
id = customary .. '[[' .. id:sub(1, -2) .. ']]s'
else
id = customary .. '[[' .. link .. '|' .. id .. ']]'
end
end
end
return multiplier .. id
end
local function make_id(parms, which, unit_table)
-- Return id, f where
-- id = unit name or symbol, possibly modified
-- f = true if id is a name, or false if id is a symbol
-- using 1st or 2nd values (which), and for 'in' or 'out' (unit_table.inout).
-- Result is '' if no symbol/name is to be used.
-- In addition, set unit_table.sep = ' ' or ' ' or ''
-- (the separator that caller will normally insert before the id).
local abbr = parms.abbr
if abbr == 'values' then
unit_table.sep = ''
return ''
end
local inout = unit_table.inout
local valinfo = unit_table.valinfo
local abbr_org = parms.abbr_org
local adj = parms.adj
local disp = parms.disp
local lk = parms.lk
local usename = unit_table.usename
local singular = valinfo[which].singular
if usename then
-- Old template does something like this.
if lk == 'on' or lk == inout then
-- A linked unit uses the standard singular.
else
-- Set non-standard singular.
if inout == 'in' then
if adj ~= 'on' and (abbr_org == 'out' or disp == 'flip') then
local value = valinfo[which].value
singular = (0 < value and value < 1.0001)
end
else
if (abbr_org == 'on') or
(disp == nil and (abbr_org == nil or abbr_org == 'out')) or
(disp == 'flip' and abbr_org == 'in') then
singular = (valinfo[which].absvalue < 1.0001 and
not valinfo[which].is_scientific)
end
end
end
end
if unit_table.engscale then
singular = false -- so 1 e3kg gives 1 thousand kilograms (plural)
end
local key_name = (adj == 'on' or (singular and not parms.is_range_x)) and 'name1' or 'name2'
local key_symbol = 'symbol'
if unit_table.sp_us then
key_name = key_name .. '_us'
key_symbol = 'sym_us'
end
local want_name
if usename then
want_name = true
else
if abbr_org == nil then
if disp == 'br' or disp == 'or' or disp == 'slash' then
want_name = true
end
if unit_table.utype == 'temperature' or unit_table.utype == 'temperature change' then
if not (unit_table.exception == 'temperature') then
want_name = false
end
end
end
if want_name == nil then
if abbr == 'on' or abbr == inout or (abbr == 'mos' and inout == 'out') then
want_name = false
else
want_name = true
end
end
end
unit_table.sep = want_name and ' ' or ' '
return linked_id(unit_table, want_name and key_name or key_symbol, lk == 'on' or lk == inout), want_name
end
local function decorate_value(parms, unit_table, which)
-- If needed, update unit_table.valinfo so values will be shown with
-- extra information.
-- For consistency with the old template (but different from fmtpower),
-- the style to display powers of 10 includes "display:none" to allow some
-- browsers to copy, for example, "10³" as "10^3", rather than as "103".
local engscale = unit_table.engscale
if engscale then
local inout = unit_table.inout
local info = unit_table.valinfo[which]
local abbr = parms.abbr
if abbr == 'on' or abbr == inout then
info.show = info.show ..
'<span style="margin-left:0.2em">×<span style="margin-left:0.1em">10</span></span><s style="display:none">^</s><sup>'
.. engscale.exponent .. '</sup>'
else
local number_id
local lk = parms.lk
if lk == 'on' or lk == inout then
number_id = engscale[2] or engscale[1]
else
number_id = engscale[1]
end
info.show = info.show .. (parms.adj == 'on' and '-' or ' ') .. number_id
end
end
local prefix = unit_table.vprefix
if prefix then
local info = unit_table.valinfo[which]
info.show = prefix .. info.show
end
end
local function process_input(parms, in_current)
-- Processing required once per conversion.
-- Return block of text to represent input (value/unit).
local disp = parms.disp
if disp == 'output only' or
disp == 'output number only' or
disp == 'unit2' then
parms.joins = { '', '' }
return ''
end
local first_unit, second_unit
local composite = in_current.composite -- nil or table of units
if composite then
first_unit = composite[1]
second_unit = composite[2]
else
first_unit = in_current
end
local id1, want_name = make_id(parms, 1, first_unit)
if disp == 'unit' then
parms.joins = { '', '' }
if composite then
id1 = id1 .. ' ' .. make_id(parms, 1, second_unit)
end
if want_name and parms.adj == 'on' then
return hyphenated(id1)
end
return id1
end
local abbr = parms.abbr
if disp == nil then -- special case for the most common setting
parms.joins = disp_joins['b']
elseif disp ~= 'x' then
-- Old template does this.
if disp == 'slash' then
if parms.abbr_org == nil then
disp = 'slash-nbsp'
elseif abbr == 'in' or abbr == 'out' then
disp = 'slash-sp'
else
disp = 'slash-nosp'
end
elseif disp == 'sqbr' then
if abbr == 'on' then
disp = 'sqbr-nbsp'
else
disp = 'sqbr-sp'
end
end
parms.joins = disp_joins[disp] or disp_joins['b']
end
if in_current.builtin == 'mach' then
local prefix = id1 .. ' '
local range = parms.range
local valinfo = first_unit.valinfo
local result = prefix .. valinfo[1].show
if range then
result = range_text(range, want_name, parms, result, prefix .. valinfo[2].show)
end
return result
end
if composite then
-- Simplify: assume that adj is off, and there is no range, and no decoration.
return first_unit.valinfo[1].show .. ' ' .. id1 .. ' ' ..
second_unit.valinfo[1].show .. ' ' .. (make_id(parms, 1, second_unit))
end
local result
local extra = ''
local sep = first_unit.sep
local mos = (abbr == 'mos')
local range = parms.range
local id = (range == nil) and id1 or make_id(parms, 2, first_unit)
if id ~= '' then
if want_name and parms.adj == 'on' then
mos = false -- if hyphenated, suppress repeat of unit in a range
extra = '-' .. hyphenated(id) .. parms.mid
else
extra = sep .. id
end
end
local valinfo = first_unit.valinfo
if range == nil then
decorate_value(parms, first_unit, 1)
result = valinfo[1].show
else
if mos then
decorate_value(parms, in_current, 1)
decorate_value(parms, in_current, 2)
result = valinfo[1].show .. sep .. id1
elseif parms.is_range_x and not want_name then
if abbr == 'in' or abbr == 'on' then
decorate_value(parms, in_current, 1)
end
decorate_value(parms, in_current, 2)
result = valinfo[1].show .. sep .. id
else
if abbr == 'in' or abbr == 'on' then
decorate_value(parms, in_current, 1)
end
decorate_value(parms, in_current, 2)
result = valinfo[1].show
end
result = range_text(range, want_name, parms, result, valinfo[2].show)
end
return result .. extra
end
local function process_one_output(parms, out_current)
-- Processing required for each output unit.
-- Return block of text to represent output (value/unit).
local id1, want_name = make_id(parms, 1, out_current)
local disp = parms.disp
if disp == 'unit2' then
if want_name and parms.adj == 'on' then
return hyphenated(id1)
end
return id1
end
if out_current.builtin == 'mach' then
local prefix = id1 .. ' '
local range = parms.range
local valinfo = out_current.valinfo
local result = prefix .. valinfo[1].show
if range then
result = range_text(range, want_name, parms, result, prefix .. valinfo[2].show)
end
return result
end
local result
local extra, id, sep = '', '', ''
local range = parms.range
if disp ~= 'output number only' then
id = (range == nil) and id1 or make_id(parms, 2, out_current)
if id ~= '' then
sep = out_current.sep
if want_name and parms.adj == 'on' then
extra = '-' .. hyphenated(id)
else
extra = sep .. id
end
end
end
local valinfo = out_current.valinfo
if range == nil then
decorate_value(parms, out_current, 1)
result = valinfo[1].show
else
local abbr = parms.abbr
if parms.is_range_x and not want_name then
if abbr == 'out' or abbr == 'on' then
decorate_value(parms, out_current, 1)
end
decorate_value(parms, out_current, 2)
result = valinfo[1].show .. sep .. id
else
if abbr == 'out' or abbr == 'on' then
decorate_value(parms, out_current, 1)
end
decorate_value(parms, out_current, 2)
result = valinfo[1].show
end
result = range_text(range, want_name, parms, result, valinfo[2].show)
end
return result .. extra
end
local function make_output_single(parms, in_unit_table, out_unit_table)
-- Return true, item where item = wikitext of the conversion result
-- for a single output (which is not a combination or a multiple);
-- or return false, t where t is an error message table.
local success, info1, info2
local valinfo = in_unit_table.valinfo
success, info1 = cvtround(parms, valinfo[1], in_unit_table, out_unit_table)
if not success then return false, info1 end
success, info2 = cvtround(parms, valinfo[2], in_unit_table, out_unit_table)
if not success then return false, info2 end
out_unit_table.valinfo = { info1, info2 }
return true, process_one_output(parms, out_unit_table)
end
local function make_output_multiple(parms, in_unit_table, out_unit_table)
-- Return true, item where item = wikitext of the conversion result
-- for an output which is a multiple (like 'ftin');
-- or return false, t where t is an error message table.
local multiple = out_unit_table.multiple -- table of scaling factors (will not be nil)
local combos = out_unit_table.combination -- table of unit tables (will not be nil)
local abbr = parms.abbr
local abbr_org = parms.abbr_org
local disp = parms.disp
local want_name = (abbr_org == nil and (disp == 'or' or disp == 'slash')) or
not (abbr == 'on' or abbr == 'out' or abbr == 'mos')
local want_link = (parms.lk == 'on' or parms.lk == 'out')
local function make_result(info)
local outvalue, sign, fmt
local results = {}
for i = 1, #combos do
local thisvalue
local out_current = combos[i]
out_current.inout = 'out'
local scale = multiple[i]
if i == 1 then -- least significant unit ('in' from 'ftin')
local success, outinfo = cvtround(parms, info, in_unit_table, out_current)
if not success then return false, outinfo end
sign = outinfo.sign
local fraction = (outinfo.show):match('[' .. numdot .. '](.*)') or ''
fmt = '%.' .. #fraction .. 'f' -- to reproduce precision
if fraction == '' then
outvalue = floor(outinfo.raw_absvalue + 0.5) -- keep all integer digits of least significant unit
else
outvalue = outinfo.absvalue
end
end
if scale then
outvalue, thisvalue = floor(outvalue / scale), outvalue % scale
else
thisvalue = outvalue
end
local id
if want_name then
id = out_current[(thisvalue == 1) and 'name1' or 'name2']
else
id = out_current['symbol']
end
if want_link then
local link = out_current.link
if link then
id = '[[' .. link .. '|' .. id .. ']]'
end
end
local strval = (thisvalue == 0) and '0' or with_separator(format(fmt, thisvalue))
table.insert(results, strval .. ' ' .. id)
if outvalue == 0 then
break
end
fmt = '%.0f' -- only least significant unit can have a fraction
end
local reversed, count = {}, #results
for i = 1, count do
reversed[i] = results[count + 1 - i]
end
return true, sign .. table.concat(reversed, ' ')
end
local valinfo = in_unit_table.valinfo
local success, result = make_result(valinfo[1])
if not success then return false, result end
local range = parms.range
if range then
local success, result2 = make_result(valinfo[2])
if not success then return false, result2 end
result = range_text(range, want_name, parms, result, result2)
end
return true, result
end
local function process(parms, in_unit_table)
-- Return true, s where s = final wikitext result,
-- or return false, t where t is an error message table.
local success, out_unit_table
local invalue1 = in_unit_table.valinfo[1].value
local out_unit = parms.out_unit
if out_unit == nil or out_unit == '' then
success, out_unit = get_default(invalue1, in_unit_table)
if not success then return false, out_unit end
end
success, out_unit_table = lookup(out_unit, parms.sp, 'any_combination')
if not success then return false, out_unit_table end
if in_unit_table.utype ~= out_unit_table.utype then
return false, { 'cvt_mismatch', in_unit_table.utype, out_unit_table.utype }
end
local outputs = {}
local combos -- nil (for 'ft' or 'ftin'), or table of unit tables (for 'm ft')
if out_unit_table.multiple == nil then -- nil ('ft' or 'm ft'), or table of factors ('ftin')
combos = out_unit_table.combination
end
local imax = combos and #combos or 1 -- 1 (single unit) or number of unit tables
for i = 1, imax do
local success, item
local out_current = combos and combos[i] or out_unit_table
out_current.inout = 'out'
if out_current.multiple == nil then
success, item = make_output_single(parms, in_unit_table, out_current)
else
success, item = make_output_multiple(parms, in_unit_table, out_current)
end
if not success then return false, item end
table.insert(outputs, item)
end
local disp = parms.disp
local in_block = process_input(parms, in_unit_table)
local out_block = (disp == 'unit') and '' or table.concat(outputs, '; ')
if disp == 'flip' then
in_block, out_block = out_block, in_block
end
local wikitext = in_block .. parms.joins[1] .. out_block .. parms.joins[2]
if parms.sortable == 'on' then
wikitext = ntsh(invalue1, parms.debug) .. wikitext
end
return true, wikitext
end
local function main_convert(frame)
set_config(frame)
local result
local success, parms, in_unit_table = get_parms(frame:getParent())
if success then
success, result = process(parms, in_unit_table)
else
result = parms
end
if success then
return result
end
return messages.message(result, lang)
end
return { convert = main_convert }
