Module:Convert
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)
-- Conversion data is defined in another module because it is too large
-- to be conveniently included here.
-- A testing program can set the global variable 'is_test_run'.
local convertdata = require(is_test_run and "convertdata" or "Module:Convertdata")
local SIprefixes = convertdata.SIprefixes
local units = convertdata.units
local default_exceptions = convertdata.default_exceptions
local link_exceptions = convertdata.link_exceptions
local MINUS = '−' -- Unicode U+2212 MINUS SIGN (UTF-8: e2 88 92)
local format = string.format
local floor = math.floor
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
-- Configuration options to keep magic values in one location.
local numdot, numsep, maxsigfig, lang
local limit_abuse = 20 -- avoid using very large precision/sigfig
local function set_config(frame)
-- Set configuration options from template #invoke or defaults.
numdot = frame.args.numdot or '.' -- decimal mark before fractional digits
numsep = frame.args.numsep or ',' -- thousands separator for numbers (',', '.', '')
maxsigfig = frame.args.maxsigfig or 14 -- maximum number of significant figures
lang = frame.args.lang or 'en' -- language code for messages
if maxsigfig > limit_abuse then
maxsigfig = limit_abuse
end
end
------------------------------------------------------------------------
-- BEGIN: Messages that may be displayed by Module:Convert.
-- LATER: Perhaps move to Module:Convertmessages to simplify this module.
local all_categories = {
['en'] = {
general = '[[Category:Convert error]]',
unknown = '[[Category:Convert unknown unit]]',
mismatch = '[[Category:Convert dimension mismatch]]',
},
}
local all_messages = {
-- Table of all output messages.
-- Inner value is a numbered table: { 'error text', 'category key' }.
['en'] = {
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_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 = { 'Use "%s" (not "%s") as the unit code', 'general' },
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 t = all_messages[lang]
if t then
t = t[msg[1]]
if t then
-- t[1] = message text, t[2] = category
local text = string.format(t[1] or 'Missing message',
msg[2] or '?',
msg[3] or '?',
msg[4] or '?')
local cat = all_categories[lang][t[2]] or ''
-- LATER: Link should be to 'Template', not 'Module'.
-- Put correct name if have a template established.
text = "[[Module talk:Convert|Conversion error]]: " .. text .. cat
return '<span style="color:black; background-color:orange;">' .. text .. '</span>'
end
end
return 'Convert internal error: unknown message'
end
-- END: Messages that may be displayed by Module:Convert.
------------------------------------------------------------------------
local function shallow_copy(t)
-- Return a shallow copy of t.
-- Do not need the features and overhead of mw.clone() provided by Scribunto.
local result = {}
for k, v in pairs(t) do
result[k] = v
end
return result
end
local usesubstitute = {
-- If unit has an SI prefix, these fields may have "%s" where prefix belongs.
'name1',
'name1_us',
'name2',
'name2_us',
}
local function set_prefixes(unit, prefixname)
-- Insert given prefix name into the fields which require it
-- (and which should contain '%s' to be replaced with the prefix).
-- Pity we have to do all this work when most results are not needed,
-- but it's cleaner to do it here rather than in final processing.
if unit.prefixes then
for _, name in ipairs(usesubstitute) do
local value = unit[name]
unit[name] = value:gsub('%%s', prefixname, 1)
end
end
end
local function lookup(unit, sp, what)
-- Return true, t where t is the unit's converter table,
-- or return false, t where t is an error message table.
-- Parameter 'sp' is 'us' for US spelling of prefixes, or nil.
-- Parameter 'what' determines whether combination units are accepted:
-- 'no_combination' : single unit only
-- 'any_combination' : single unit or combination or multiple
-- 'only_multiple' : single unit or multiple only
-- Parameter 'unit' 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 the 'unit' is a known combination code (and if allowed by what),
-- a table of multiple unit tables is included in the result.
-- For compatibility with the old template, underscores in 'unit' are replaced
-- with spaces so {{convert|350|board_feet}} --> 350 board feet (0.83 m³).
if unit == nil or unit == '' then
return false, { 'cvt_no_unit' }
end
unit = unit:gsub('_', ' ')
local t = units[unit]
if t ~= nil then
if t.shouldbe then
return false, { 'cvt_should_be', t.shouldbe, unit }
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', unit }
end
-- Recursively create a combination table containing the
-- converter table of each unitcode.
local success
local result = { utype = t.utype, multiple = multiple, combination = {} }
local cvt = result.combination
for i, v in ipairs(combo) do
success, cvt[i] = lookup(v, sp, multiple and 'no_combination' or 'only_multiple')
if not success then return false, cvt[i] end
end
return true, result
end
local result = shallow_copy(t)
set_prefixes(result, '')
result.baseunit = unit
result.prefix = ''
return true, result
end
for plen = 2, 1, -1 do
-- Check for longer prefix first ('dam' is decametre).
-- Micro (µ) is two bytes in utf-8, so is found with plen = 2.
local prefix = string.sub(unit, 1, plen)
local si = SIprefixes[prefix]
if si then
local baseunit = unit:sub(plen+1)
local t = units[baseunit]
if t and t.prefixes then
local result = shallow_copy(t)
local name
if sp == 'us' or t.sp_us then
name = si.name_us
else
name = si.name
end
set_prefixes(result, name)
prefix = si.prefix -- what prefix should be
result.symbol = prefix .. result.symbol
result.sym_us = prefix .. result.sym_us
result.baseunit = baseunit
result.prefix = prefix
result.scale = t.scale * 10 ^ (si.exponent * t.prefixes)
return true, result
end
end
end
return false, { 'cvt_unknown', unit }
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 ~= nil 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 ~= nil 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-left:0.2em">×<span style="margin-left:0.1em">10</span></span><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(math.log10(value))
if frac >= 0 then
frac = frac - 1
exp = exp + 1
end
local digits = format('%.0f', floor((10^(frac + sigfig)) + 0.5))
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 = '1234' represents 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 represents 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 ~= nil 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(args, index, which)
-- Return true, info if can extract a number from the text in args[index],
-- 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?
local text = strip(args[index])
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, negative
if sign == MINUS or sign == '-' then
propersign = MINUS
negative = true
elseif sign == '+' then
propersign = '+'
negative = false
elseif sign == '' then
propersign = ''
negative = false
else
return false, { invalid[which], text }
end
local show, singular
local value = tonumber(clean)
if value == nil then
value, show = extract_fraction(clean, negative)
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 negative)
show = propersign .. with_separator(clean)
end
if negative 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 string.match(text, '^-?%d+$') == nil then
return false, { invalid, text }
end
return true, tonumber(text)
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 input, output ranges; for 'x', depends on abbr
['and'] = {' and ', ' and '},
['by'] = {' by ', ' by '},
['to'] = {' to ', ' to '},
['-'] = {'–', '–'},
['to(-)'] = {' to ', '–'},
['to-'] = {' to ', '–'},
['x'] = {{ ['out'] = ' by ' , ['in'] = ' × ', ['off'] = ' by ', ['on'] = ' × ' },
{ ['out'] = ' × ', ['in'] = ' by ' , ['off'] = ' by ', ['on'] = ' × ' }},
['+/-'] = {' ± ', ' ± '},
}
local success, info1, info2
local args = {} -- arguments passed to template
for k, v in pframe:argumentPairs() 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]
if range == nil then
in_unit = next
else
args.range = range
args.is_range_x = (next == '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
in_unit_table.valinfo = { info1, info2 } -- info2 is nil if no range
in_unit_table.inout = 'in' -- this is an input unit
next = strip(args[i])
i = i + 1
if tonumber(next) == nil then
args.out_unit = next
next = strip(args[i])
if tonumber(next) ~= nil then
i = i + 1
precision = next
end
else
precision = next
end
if args.adj == nil and args.sing ~= nil then
args.adj = args.sing -- sing (singular) is apparently 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]) ~= nil then
precision = strip(args[i])
i = i + 1
end
end
local disp = args.disp
if disp == 'x' then
args.joins = { args[i] or '', args[i+1] or '' }
elseif disp == 's' or disp == '/' then
args.disp = 'slash'
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(inclean, invalue, outvalue, in_current, out_current)
-- Return a default value for precision (an integer like 2, 0, -2).
-- Code follows procedures used in old template.
-- Am putting exceptions to standard calculations here, as they are
-- discovered. Can later decide if something cleaner should be done.
-- LATER: Things like the hand unit of length will need special processing.
local log10 = math.log10
local prec, minprec, adjust
local utype = out_current.utype
local fudge = 1e-14 -- {{Order of magnitude}} adds this, so we do too
-- Find fractional digits, handling cases like inclean = '12.345e6'.
local integer, dot, fraction = inclean:match('^(%d*)([' .. numdot .. ']?)(%d*)')
if utype == 'temperature' then
-- LATER: Give an error message if (invalue < in_current.offset): below absolute zero?
adjust = 0
local kelvin = (invalue - in_current.offset) * in_current.scale
if kelvin <= 0 then -- can get zero, or small but negative value due to precision problems
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 dot == '' then
-- More precision when output ft with integer input value.
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 dot == '' then
prec = -integer:match('0*$'):len() -- '12300' gives -2, but so does '12300e-5'
else
if fraction == '' and utype ~= 'temperature' then
prec = 1 -- "123." has same precision as "123.0", like old template
else
prec = #fraction
end
end
return math.max(floor(prec + adjust), minprec)
end
local function convert(value, in_current, out_current)
local inscale = in_current.scale
local outscale = out_current.scale
if in_current.invert ~= nil then
if in_current.invert * out_current.invert < 0 then
return 1 / (value * inscale * outscale)
end
return value * (inscale / outscale)
elseif in_current.offset ~= nil then
return (value - in_current.offset) * (inscale / outscale) + out_current.offset
else
return value * (inscale / outscale)
end
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 ~= nil then
invalue, inclean = info.value, info.clean
end
if invalue == nil or invalue == '' then
return true, nil
end
local outvalue = convert(invalue, in_current, out_current)
local isnegative
if outvalue < 0 then
isnegative = true
outvalue = -outvalue
end
local success
local precision = parms.precision
local sigfig = parms.sigfig
local disp = parms.disp
if precision then
-- Ignore sigfig, disp.
success, precision = require_integer(precision, 'cvt_bad_prec')
if not success then return false, precision end
elseif sigfig then
-- Ignore disp.
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 disp == '5' then
show = format('%.0f', floor((outvalue / 5) + 0.5) * 5)
else
precision = default_precision(inclean, invalue, outvalue, in_current, out_current)
end
if precision then
if precision >= 0 then
if precision > limit_abuse then
precision = limit_abuse
elseif 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'
show = format(fmt, outvalue)
else
precision = -precision -- #digits to zero (in addition to digits after dot)
if precision > limit_abuse then
precision = limit_abuse
end
local shift = 10 ^ precision
if shift > outvalue then
show = '0' -- like old template, user can zero all digits
else
show = format('%.0f', floor(outvalue/shift + 0.5))
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
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 ~= nil then
value = value * 10^exponent
end
rawset(self, key, value)
return value
end
end })
end
-- TODO Think about when to use ' ' and when to use ' '.
-- For outputs, could use raw_absvalue (not bothering with calculated absvalue).
-- Old template always uses nbsp before a unit symbol, but seems inconsistent
-- before a unit name. Template:Convert/LoffAonSoff says
-- "Numbers less than 1,000 is not wrapped nor are unit symbols"
-- so 1000 is a threshold (use nbsp for smaller values), but no conclusive results.
-- Possibly a concern is wrapping when using {{convert}} in a table
-- (don't want to force a column to be unnecessarily wide by using nbsp).
local disp_joins = {
['or'] = { ' or ' , '' },
['sqbr-sp'] = { ' [' , ']' },
['sqbr-nbsp'] = { ' [' , ']' },
['comma'] = { ', ' , '' },
['slash-sp'] = { ' / ' , '' },
['slash-nbsp'] = { ' / ', '' },
['slash-nosp'] = { '/' , '' },
['b'] = { ' (' , ')' },
}
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 pipe-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.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 make_id(parms, which, unit_table)
-- Return id, f where
-- id = unit symbol or name, possibly modified
-- f = false if id is a symbol, otherwise true (id is a name)
-- for value 1 or 2 (which), and 'in' or 'out' (unit_table.inout).
-- Result is '' if no symbol/name is to be used.
local abbr = parms.abbr
if abbr == 'values' then
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 singular = valinfo[which].singular or (inout == 'in' and adj == 'on')
if unit_table.usename then
-- Old template does something like this.
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
local key_name = (singular and not parms.is_range_x) and 'name1' or 'name2'
local key_symbol = 'symbol'
if parms.sp == 'us' or unit_table.sp_us then
key_name = key_name .. '_us'
key_symbol = 'sym_us'
end
local want_name
if unit_table.usename then
want_name = true
else
if abbr_org == nil then
if disp == 'or' or disp == 'slash' then
want_name = true
end
if unit_table.utype == 'temperature' then
want_name = false
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
local id = unit_table[want_name and key_name or key_symbol]
local lk = parms.lk
if lk == 'on' or lk == inout then
local link = link_exceptions[unit_table.symbol] or unit_table.link
if link ~= nil then
id = '[[' .. link .. '|' .. id .. ']]'
end
end
return id, want_name
end
local function process_input(parms, in_current)
-- Processing required once per conversion.
-- Return block of text to represent input (value/unit).
local id1, want_name = make_id(parms, 1, in_current)
local extra = ''
local result
local adj = parms.adj
local disp = parms.disp
if disp == 'output only' or
disp == 'output number only' or disp == 'number' or
disp == 'u2' or disp == 'unit2' then
result = ''
parms.joins = { '', '' }
elseif disp == 'unit' then
if adj == 'on' then
result = hyphenated(id1)
else
result = id1
end
parms.joins = { '', '' }
else
local abbr = parms.abbr
local mos = (abbr == 'mos')
local range = parms.range
local id = (range == nil) and id1 or make_id(parms, 2, in_current)
if id ~= '' then
if adj == 'on' then
mos = false -- if hyphenated, suppress repeat of unit in a range
extra = '-' .. hyphenated(id) .. parms.mid
else
extra = ' ' .. id
end
end
local valinfo = in_current.valinfo
if range == nil then
result = valinfo[1].show
else
local rtext = range[1]
if type(rtext) == 'table' then
rtext = rtext[abbr] or rtext['off']
end
if mos then
result = valinfo[1].show .. ' ' .. id1 .. rtext .. valinfo[2].show
elseif parms.is_range_x and not want_name then
result = valinfo[1].show .. ' ' .. id .. rtext .. valinfo[2].show
else
result = valinfo[1].show .. rtext .. valinfo[2].show
end
end
if disp == nil then -- special case 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
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 extra = ''
local result
local disp = parms.disp
if disp == 'u2' or disp == 'unit2' then -- 'unit2' is not in old template
if parms.adj == 'on' then
result = hyphenated(id1)
else
result = id1
end
else
local range = parms.range
if not (disp == 'output number only' or disp == 'number') then
local id = (range == nil) and id1 or make_id(parms, 2, out_current)
if id ~= '' then
extra = ' ' .. id
end
end
local valinfo = out_current.valinfo
if range == nil then
result = valinfo[1].show
else
local rtext = range[2]
if type(rtext) == 'table' then
rtext = rtext[parms.abbr] or rtext['on']
end
if parms.is_range_x and not want_name then
result = valinfo[1].show .. extra .. rtext .. valinfo[2].show
else
result = valinfo[1].show .. rtext .. valinfo[2].show
end
end
end
return result .. extra
end
local function make_output_single(parms, info, 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
success, info1 = cvtround(parms, info[1], in_unit_table, out_unit_table)
if not success then return false, info1 end
success, info2 = cvtround(parms, info[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, info, 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 ~= nil 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 sign .. table.concat(reversed, ' ')
end
local result = make_result(info[1])
local range = parms.range
if range ~= nil then
local rtext = range[2]
if type(rtext) == 'table' then
rtext = rtext[abbr] or rtext['on']
end
result = result .. rtext .. make_result(info[2])
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 info = in_unit_table.valinfo
local invalue1 = info[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, info, in_unit_table, out_current)
else
success, item = make_output_multiple(parms, info, 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 p = {}
function p.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 p