Module:Convert: Difference between revisions
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>Johnuniq (handle whitespace around parameters) |
>Johnuniq (rewrite rounding code to follow procedures used in old template; refactor) |
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local function get_config(frame) | local function get_config(frame) | ||
-- Return table of configuration options. | -- Return table of configuration options. | ||
local cfg = { | |||
-- Defaults that can be overridden by template. | |||
local cfg = { | numdot = '.', -- decimal mark before fractional digits | ||
numsep = ',', -- thousands separator for numbers (',', '.', or nil) | |||
maxsigfig = 14, -- maximum number of significant figures | |||
} | |||
for k, v in frame:argumentPairs() do | for k, v in frame:argumentPairs() do | ||
cfg[k] = v -- arguments from template's {{#invoke:}} | cfg[k] = v -- arguments from template's {{#invoke:}} | ||
end | end | ||
if cfg.maxsigfig > 20 then | |||
cfg.maxsigfig = 20 -- limit abuse | |||
end | |||
return cfg | return cfg | ||
end | end | ||
Line 92: | Line 93: | ||
end | end | ||
local function | 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 '−' .. text:sub(2) | |||
end | |||
return text | |||
end | |||
local function with_separator(text) | |||
-- Return text with thousand separators inserted. | -- Return text with thousand separators inserted. | ||
-- The given text is ' | -- The given text is like '123' or '12345.6789' or '1.23e45' | ||
-- Separator is inserted only in the integer part (not | -- (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'). | -- Four-digit integer parts have a separator (like '1,234'). | ||
local numsep = config.numsep | local numsep = config.numsep | ||
if | if numsep == '' then | ||
return text | return text | ||
end | end | ||
local | local last = text:match('()[' .. config.numdot .. 'eE]') -- () returns position | ||
if last == nil then | if last == nil then | ||
last = #text | last = #text | ||
Line 119: | Line 127: | ||
last = last - 1 | last = last - 1 | ||
end | 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 | end | ||
local function | -- Input values can use values like 1.23e12, but are never displayed | ||
-- Return result of converting number 'value' to a string, | -- using exponent notation like 1.23×10¹². | ||
-- Very small or very large output values use exponent notation. | |||
-- Use fmtpower:format(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) .. config.numdot .. show:sub(2) | |||
end | |||
return fmtpower:format(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. | -- 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 | if sigfig <= 0 then | ||
sigfig = 1 | sigfig = 1 | ||
Line 142: | Line 176: | ||
end | end | ||
if value == 0 then | if value == 0 then | ||
return | return string.rep('0', sigfig), 1 | ||
end | end | ||
local exp, frac = math.modf(math.log10(value)) | local exp, frac = math.modf(math.log10(value)) | ||
if frac | if frac >= 0 then | ||
frac = frac - 1 | |||
exp = exp + 1 | |||
end | end | ||
local digits = tostring(math.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 | |||
digits = digits:sub(1, exp | |||
end | end | ||
return | assert(#digits == sigfig, 'Bug: rounded number has wrong length') | ||
return digits, exp | |||
end | end | ||
local function | local function format_number(show, exponent) | ||
-- | -- Return wikitext to display the value implied by the arguments: | ||
if | -- exponent is nil; and | ||
-- show is a string of digits (no sign), with an optional dot; | |||
-- or: | |||
-- exponent is a number (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'). | |||
-- The result has numsep inserted where necessary, and uses exponent | |||
-- notation for very small or large values. | |||
-- The result has no more than config.maxsigfig significant digits | |||
-- (same as old template and {{#expr}}). | |||
local numdot = config.numdot | |||
local maxlen = config.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 | end | ||
if exponent ~= nil then | |||
end | 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 with_exponent(show, exponent-1) | |||
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 | end | ||
return | return with_separator(show) | ||
end | end | ||
-- Fraction output format | -- Fraction output format (like old template). | ||
-- frac1: sign, numerator, denominator | -- frac1: sign, numerator, denominator | ||
-- frac2: wholenumber, sign, numerator, denominator | -- frac2: wholenumber, sign, numerator, denominator | ||
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-- In the following, '(3/8)' represents the wikitext required to | -- In the following, '(3/8)' represents the wikitext required to | ||
-- display a fraction with numerator 3 and denominator 8. | -- display a fraction with numerator 3 and denominator 8. | ||
-- In the wikitext, Unicode | -- In the wikitext, Unicode minus is used for a negative value. | ||
-- text value, show value, show | -- text value, show value, show | ||
-- if not negative if negative | -- if not negative if negative | ||
Line 223: | Line 272: | ||
-- 1 - 20/8 -1.5., '1(−20/8)' -3.5 , '−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 | -- Wherever an integer appears above, numbers like 1.25 or 12.5e-3 | ||
-- (which may be negative) are also accepted (like old | -- (which may be negative) are also accepted (like old template). | ||
-- Template interprets '1.23e+2+12/24' as '123(12/24)' = 123.5! | -- Template interprets '1.23e+2+12/24' as '123(12/24)' = 123.5! | ||
local lhs, negfrac, rhs, numstr, numerator, denstr, denominator, wholestr, value | local lhs, negfrac, rhs, numstr, numerator, denstr, denominator, wholestr, whole, value | ||
lhs, denstr = text:match('^%s*([^/]-)%s*/%s*(.-)%s*$') | lhs, denstr = text:match('^%s*([^/]-)%s*/%s*(.-)%s*$') | ||
denominator = tonumber(denstr) | denominator = tonumber(denstr) | ||
Line 246: | Line 295: | ||
else | else | ||
value = whole - numerator / denominator | value = whole - numerator / denominator | ||
numstr = | numstr = change_sign(numstr) | ||
end | end | ||
if tostring(value):find('#', 1, true) then | if tostring(value):find('#', 1, true) then | ||
return nil -- overflow or similar | return nil -- overflow or similar | ||
end | end | ||
numstr = | numstr = use_minus(numstr) | ||
denstr = | denstr = use_minus(denstr) | ||
local wikitext | local wikitext | ||
if wholestr then | if wholestr then | ||
local sign = negative and '−' or '+' | local sign = negative and '−' or '+' | ||
if negative then | if negative then | ||
wholestr = | wholestr = change_sign(wholestr) | ||
end | end | ||
wikitext = frac2:format( | wikitext = frac2:format(use_minus(wholestr), sign, numstr, denstr) | ||
else | else | ||
local sign = negative and '−' or '' | local sign = negative and '−' or '' | ||
Line 285: | Line 334: | ||
-- Value is a valid number. | -- Value is a valid number. | ||
-- Singular is true if value is 1 (singular form of units will be used). | -- Singular is true if value is 1 (singular form of units will be used). | ||
-- Singular is false if value is -1 ( | -- Singular is false if value is -1 (like old template). | ||
-- Clean is cleaned text with any separators and sign removed. | -- Clean is cleaned text with any separators and sign removed. | ||
-- Show is text formatted for output: | -- Show is text formatted for output: | ||
Line 291: | Line 340: | ||
-- * If negative, a Unicode minus is used; otherwise the sign | -- * If negative, a Unicode minus is used; otherwise the sign | ||
-- is '+' (if the input text used '+'), or is ''. | -- 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]) | local text = strip(args[index]) | ||
if text == nil or text == '' then return false, missing[which] end | if text == nil or text == '' then return false, missing[which] end | ||
Line 329: | Line 380: | ||
if show == nil then | if show == nil then | ||
singular = (value == 1) | singular = (value == 1) | ||
show = propersign .. with_separator(clean) | |||
show = propersign .. | |||
end | end | ||
if negative and (value ~= 0) then | if negative and (value ~= 0) then | ||
Line 385: | Line 435: | ||
success, msg = extract_number(args, 1, 1) | success, msg = extract_number(args, 1, 1) | ||
if not success then return success, msg end | if not success then return success, msg end | ||
local in_unit = strip(args[2]) | local in_unit, out_unit, precision | ||
local next = strip(args[2]) | |||
local i = 3 | local i = 3 | ||
local range = range_types[ | local range = range_types[next] | ||
if range | if range == nil then | ||
in_unit = next | |||
else | |||
success, msg = extract_number(args, 3, 2) | success, msg = extract_number(args, 3, 2) | ||
if not success then return success, msg end | if not success then return success, msg end | ||
Line 394: | Line 447: | ||
i = 5 | i = 5 | ||
end | end | ||
next = strip(args[i]) | |||
if tonumber(next) == nil then | |||
out_unit = next | |||
precision = strip(args[i+1]) | |||
else | |||
precision = next | |||
end | |||
if in_unit == nil then return false, 'Need input unit' end | if in_unit == nil then return false, 'Need input unit' end | ||
args.in_unit = in_unit | args.in_unit = in_unit | ||
args.out_unit = out_unit | args.out_unit = out_unit | ||
args.range = range | args.range = range | ||
args. | args.precision = args.precision or precision -- allow named parameter | ||
return true, args | return true, args | ||
end | end | ||
local function | local function default_precision(inclean, invalue, outvalue, parms) | ||
-- Return a default value for | -- Return a default value for precision (an integer like 2, 0, -2). | ||
-- | -- Code follows procedures used in old template. | ||
-- | -- LATER: The hand unit of length might need special processing. | ||
local log10 = math.log10 | |||
local prec, minprec, adjust | |||
local utype = parms.out_unit_table.utype | |||
if utype == 'temperature' then | |||
-- Not just multiplication by a factor. | |||
-- TODO Fix following. | |||
adjust = 0 | |||
minprec = 0 -- precision which would give 3 sigfigs in kelvin | |||
else | |||
if outvalue <= 0 then | |||
-- We are never called with a negative outvalue, but it might be zero. | |||
-- This is special-cased to avoid a bad log10() call. | |||
return 0 | |||
if | |||
end | end | ||
local factor | |||
if invalue == 0 then | |||
factor = 1 -- LATER is this correct? | |||
else | |||
factor = math.abs(outvalue / invalue) | |||
end | end | ||
adjust = -log10(factor) + log10(2) | |||
-- Ensure that the output has at least two significant figures. | |||
-- {{Order of magnitude}} adds a fudge, so we do too. | |||
minprec = 1 - math.floor(log10(outvalue) + 1e-14) | |||
end | end | ||
if | -- Find fractional digits, handling cases like inclean = '12.345e6'. | ||
local integer, dot, fraction = inclean:match('^(%d*)([' .. config.numdot .. ']?)(%d*)') | |||
if | if dot == '' then | ||
prec = | prec = -integer:match('0*$'):len() -- '12300' gives -2, but so does '12300e-5' | ||
else | |||
if #fraction == 0 then | |||
prec = 1 -- "123." has same precision as "123.0", like old template | |||
else | |||
prec = #fraction | |||
end | end | ||
end | end | ||
return prec | return math.max(math.floor(prec + adjust), minprec) | ||
end | end | ||
Line 466: | Line 531: | ||
-- This code combines convert/round because some rounding requires | -- This code combines convert/round because some rounding requires | ||
-- knowledge of what we are converting. | -- knowledge of what we are converting. | ||
-- TODO Limit values to avoid abuse (for example, can currently set | -- TODO Limit values to avoid abuse (for example, can currently set | ||
-- | -- precision to very large values like 999). | ||
local show, singular = '', false | local show, exponent, singular = '', nil, false | ||
if invalue == nil or invalue == '' then return true, show, singular end | if invalue == nil or invalue == '' then | ||
return true, show, singular | |||
end | |||
local outvalue = convert(invalue, parms.in_unit_table, parms.out_unit_table) | local outvalue = convert(invalue, parms.in_unit_table, parms.out_unit_table) | ||
local propersign | local propersign | ||
if outvalue < 0 then | if outvalue < 0 then | ||
propersign = '−' -- Unicode | propersign = '−' -- Unicode minus | ||
outvalue = -outvalue | outvalue = -outvalue | ||
else | else | ||
propersign = '' | propersign = '' | ||
end | end | ||
local | local success | ||
local precision = parms.precision | |||
local sigfig = parms.sigfig | local sigfig = parms.sigfig | ||
local disp = parms.disp | local disp = parms.disp | ||
if precision then | |||
if | |||
-- Ignore sigfig, disp. | -- Ignore sigfig, disp. | ||
success, | success, precision = require_integer(precision, 'Need value', 'precision "%s" must be an integer') | ||
if not success then return false, | if not success then return false, precision end | ||
elseif sigfig then | elseif sigfig then | ||
-- Ignore disp. | -- Ignore disp. | ||
Line 500: | Line 561: | ||
return false, msg:format(parms.sigfig) | return false, msg:format(parms.sigfig) | ||
end | end | ||
show = | show, exponent = make_sigfig(outvalue, sigfig) | ||
elseif disp == '5' then | elseif disp == '5' then | ||
outvalue = math.floor((outvalue / 5) + 0.5) * 5 | outvalue = math.floor((outvalue / 5) + 0.5) * 5 | ||
show = string.format('%.0f', outvalue) | show = string.format('%.0f', outvalue) | ||
else | else | ||
precision = default_precision(inclean, invalue, outvalue, parms) | |||
end | end | ||
if | if precision then | ||
if | if precision >= 0 then | ||
local fmt = '%.' .. string.format('%d', precision) .. 'f' | |||
local fmt = '%.' .. string.format('%d', | |||
show = string.format(fmt, outvalue) | show = string.format(fmt, outvalue) | ||
else | else | ||
precision = -precision -- #digits to zero (in addition to digits after dot) | |||
local shift = 10 ^ precision | |||
local | if shift > outvalue then | ||
if | show = '0' -- like old template, user can zero all digits | ||
show = | |||
else | else | ||
show = | show = tostring(math.floor(outvalue/shift + 0.5)) | ||
exponent = #show + precision | |||
end | end | ||
end | end | ||
Line 544: | Line 587: | ||
singular = true | singular = true | ||
end | end | ||
return true, propersign .. format_number(show, exponent), singular | |||
return true, propersign .. | |||
end | end | ||
Line 573: | Line 615: | ||
end | end | ||
-- TODO: Think about when to use ' ' and when to use ' '. | |||
-- Old template always uses nbsp before a unit symbol, but seems inconsistent | |||
-- before a unit name. Something suggested value 1000 was 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_single = { | local disp_single = { | ||
['or'] = '%s %s or %s %s', | ['or'] = '%s %s or %s %s', |
Revision as of 04:42, 25 October 2012
Documentation for this module may be created at Module:Convert/doc
--[[ Later TODO Too many items to list, but following are some points: - Some conversions require two outputs: {{convert|55|nmi|km mi}}. - Some units have two values: {{convert|3.21|m|ftin}}. - Some units use the plural name, not the symbol, example: {{convert|12|ha}} --should give--> 12 hectares (30 acres) ]] -- 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 units = convertdata.units local defaultunits = convertdata.defaultunits local function strip(text) -- If text is a string, return its content with no leading/trailing -- whitespace. Otherwise return nil. if type(text) == 'string' then return text:match("^%s*(.-)%s*$") end end -- Configuration options to keep magic values in one location. local config = {} local function get_config(frame) -- Return table of configuration options. local cfg = { -- Defaults that can be overridden by template. numdot = '.', -- decimal mark before fractional digits numsep = ',', -- thousands separator for numbers (',', '.', or nil) maxsigfig = 14, -- maximum number of significant figures } for k, v in frame:argumentPairs() do cfg[k] = v -- arguments from template's {{#invoke:}} end if cfg.maxsigfig > 20 then cfg.maxsigfig = 20 -- limit abuse end return cfg 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 .. fmt:format(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 = math.floor(1e6 * f) result = string.format('&1%016.0f%06d', i, f) end else n = -n if n > 1e16 then result = '!' else i, f = math.modf(n) f = math.floor(1e6 * f) result = string.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 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 '−' .. 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'). local numsep = config.numsep if numsep == '' then return text end local last = text:match('()[' .. config.numdot .. 'eE]') -- () returns position if last == nil then last = #text else last = last - 1 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 fmtpower:format(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) .. config.numdot .. show:sub(2) end return fmtpower:format(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 > config.maxsigfig then sigfig = config.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 = tostring(math.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) -- Return wikitext to display the value implied by the arguments: -- exponent is nil; and -- show is a string of digits (no sign), with an optional dot; -- or: -- exponent is a number (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'). -- The result has numsep inserted where necessary, and uses exponent -- notation for very small or large values. -- The result has no more than config.maxsigfig significant digits -- (same as old template and {{#expr}}). local numdot = config.numdot local maxlen = config.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 with_exponent(show, exponent-1) 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 return 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 '−' or '+' if negative then wholestr = change_sign(wholestr) end wikitext = frac2:format(use_minus(wholestr), sign, numstr, denstr) else local sign = negative and '−' or '' wikitext = frac1:format(sign, numstr, denstr) end return value, wikitext end local missing = { 'Need value', 'Need second value' } local invalid = { 'Value "%s" must be a number', 'Second value "%s" must be a number' } local function extract_number(args, index, which) -- Return true if successfully extract a number from the text in args[index]. -- Otherwise, return false, message. -- Parameter 'which' (1 or 2) selects which input value is being processed. -- 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, following elements in table args are updated -- (first row applies if which == 1, second otherwise): -- args.in_value1, args.in_singular1, args.in_clean1, args.in_show1 -- args.in_value2, args.in_singular2, args.in_clean2, args.in_show2 -- Value is a valid number. -- Singular is true if value is 1 (singular form of units will be used). -- Singular is false if value is -1 (like old template). -- Clean is cleaned text with any separators and sign removed. -- Show is text formatted for output: -- * 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 local numsep = config.numsep 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 == '−' or sign == '-' then propersign = '−' -- Unicode U+2212 MINUS SIGN (UTF-8: e2 88 92) negative = true elseif sign == '+' then propersign = '+' negative = false elseif sign == '' then propersign = '' negative = false else return false, (invalid[which]):format(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]):format(text) end singular = false -- any fraction (even with value 1) is regarded as plural end if show == nil then singular = (value == 1) show = propersign .. with_separator(clean) end if negative and (value ~= 0) then value = -value end if which == 1 then args.in_value1 = value args.in_singular1 = singular args.in_clean1 = clean args.in_show1 = show else args.in_value2 = value args.in_singular2 = singular args.in_clean2 = clean args.in_show2 = show end return true end local function require_integer(text, missing, invalid) -- Return true, n where n = integer equivalent to given text (or false, message). -- 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, missing end if string.match(text, '^-?%d+$') == nil then return false, invalid:format(text) end return true, tonumber(text) end local function get_parms(pframe) -- Return true, t where t is a table with all arguments passed to the -- template converted to named arguments, or return false, message. -- Except for range, which is nil or a table, 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 ['and'] = {' and ', ' and '}, ['by'] = {' by ', ' by '}, ['to'] = {' to ', ' to '}, ['-'] = {'–', '–'}, ['to(-)'] = {' to ', '–'}, ['x'] = {' by ', ' × '}, ['+/-'] = {' ± ', ' ± '}, } local success, msg local args = {} -- arguments passed to template for k, v in pframe:argumentPairs() do args[k] = v end success, msg = extract_number(args, 1, 1) if not success then return success, msg end local in_unit, out_unit, precision local next = strip(args[2]) local i = 3 local range = range_types[next] if range == nil then in_unit = next else success, msg = extract_number(args, 3, 2) if not success then return success, msg end in_unit = strip(args[4]) i = 5 end next = strip(args[i]) if tonumber(next) == nil then out_unit = next precision = strip(args[i+1]) else precision = next end if in_unit == nil then return false, 'Need input unit' end args.in_unit = in_unit args.out_unit = out_unit args.range = range args.precision = args.precision or precision -- allow named parameter return true, args end local function default_precision(inclean, invalue, outvalue, parms) -- Return a default value for precision (an integer like 2, 0, -2). -- Code follows procedures used in old template. -- LATER: The hand unit of length might need special processing. local log10 = math.log10 local prec, minprec, adjust local utype = parms.out_unit_table.utype if utype == 'temperature' then -- Not just multiplication by a factor. -- TODO Fix following. adjust = 0 minprec = 0 -- precision which would give 3 sigfigs in kelvin else if outvalue <= 0 then -- We are never called with a negative outvalue, but it might be zero. -- This is special-cased to avoid a bad log10() call. return 0 end local factor if invalue == 0 then factor = 1 -- LATER is this correct? else factor = math.abs(outvalue / invalue) end adjust = -log10(factor) + log10(2) -- Ensure that the output has at least two significant figures. -- {{Order of magnitude}} adds a fudge, so we do too. minprec = 1 - math.floor(log10(outvalue) + 1e-14) end -- Find fractional digits, handling cases like inclean = '12.345e6'. local integer, dot, fraction = inclean:match('^(%d*)([' .. config.numdot .. ']?)(%d*)') if dot == '' then prec = -integer:match('0*$'):len() -- '12300' gives -2, but so does '12300e-5' else if #fraction == 0 then prec = 1 -- "123." has same precision as "123.0", like old template else prec = #fraction end end return math.max(math.floor(prec + adjust), minprec) end local function convert(value, in_unit, out_unit) local inscale = in_unit.scale local outscale = out_unit.scale if in_unit.invert ~= nil then if in_unit.invert * out_unit.invert < 0 then return 1 / (value * inscale * outscale) end return value * (inscale / outscale) elseif in_unit.offset ~= nil then return (value - in_unit.offset) * (inscale / outscale) + out_unit.offset else return value * (inscale / outscale) end end local function cvtround(invalue, inclean, parms) -- Return true, show, singular -- where -- show = '' if invalue is nil or ''. Otherwise: -- show = rounded, formatted string from converting invalue, -- using the rounding specified in parms. -- singular = true if result is positive, and (after rounding) -- is "1", or like "1.00". -- or return false, message if problem. -- This code combines convert/round because some rounding requires -- knowledge of what we are converting. -- TODO Limit values to avoid abuse (for example, can currently set -- precision to very large values like 999). local show, exponent, singular = '', nil, false if invalue == nil or invalue == '' then return true, show, singular end local outvalue = convert(invalue, parms.in_unit_table, parms.out_unit_table) local propersign if outvalue < 0 then propersign = '−' -- Unicode minus outvalue = -outvalue else propersign = '' 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, 'Need value', 'precision "%s" must be an integer') if not success then return false, precision end elseif sigfig then -- Ignore disp. success, sigfig = require_integer(sigfig, 'Need value', 'sigfig "%s" must be an integer') if not success then return false, sigfig end if sigfig <= 0 then local msg = 'sigfig "%s" must be positive' return false, msg:format(parms.sigfig) end show, exponent = make_sigfig(outvalue, sigfig) elseif disp == '5' then outvalue = math.floor((outvalue / 5) + 0.5) * 5 show = string.format('%.0f', outvalue) else precision = default_precision(inclean, invalue, outvalue, parms) end if precision then if precision >= 0 then local fmt = '%.' .. string.format('%d', precision) .. 'f' show = string.format(fmt, outvalue) else precision = -precision -- #digits to zero (in addition to digits after dot) local shift = 10 ^ precision if shift > outvalue then show = '0' -- like old template, user can zero all digits else show = tostring(math.floor(outvalue/shift + 0.5)) exponent = #show + precision end end end if (show == '1' or show:match('^1%.0*$') ~= nil) and propersign == '' then -- Use match because on some systems 0.99999999999999999 is 1.0. singular = true end return true, propersign .. format_number(show, exponent), singular end local function linked(in_id, out_id, parms) -- Return in_id, out_id after modifying none, one, or both by replacing -- the text with a wikilink, if requested in template. local function substitute(link) -- TODO Work out how to insert a reasonable prefix in %s. return link:gsub('%%s', 'xxx', 1) end local lk = parms.lk if lk == 'in' or lk == 'on' then local link = parms.in_unit_table.link if link ~= nil then link = substitute(link) in_id = '[[' .. link .. '|' .. in_id .. ']]' end end if lk == 'out' or lk == 'on' then local link = parms.out_unit_table.link if link ~= nil then link = substitute(link) out_id = '[[' .. link .. '|' .. out_id .. ']]' end end return in_id, out_id end -- TODO: Think about when to use ' ' and when to use ' '. -- Old template always uses nbsp before a unit symbol, but seems inconsistent -- before a unit name. Something suggested value 1000 was 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_single = { ['or'] = '%s %s or %s %s', ['sqbr'] = '%s %s [%s %s]', ['comma'] = '%s %s, %s %s', ['slash'] = '%s %s / %s %s', ['s'] = '%s %s / %s %s', ['b'] = '%s %s (%s %s)', } local disp_double = { ['or'] = '%s%s%s %s or %s%s%s %s', ['sqbr'] = '%s%s%s %s [%s%s%s %s]', ['comma'] = '%s%s%s %s, %s%s%s %s', ['slash'] = '%s%s%s %s / %s%s%s %s', ['s'] = '%s%s%s %s / %s%s%s %s', ['b'] = '%s%s%s %s (%s%s%s %s)', } local function process(parms) -- Return true, s where s = final wikitext result (or false, message). -- TODO Clean up: avoid repeatedly accessing the same field in parms, -- and avoid the clumsy calculation of items that are not needed. local success, t success, t = units:lookup(parms.in_unit, parms.sp) if success then parms.in_unit_table = t else return success, t end if parms.out_unit == nil then -- need to catch empty string also? success, t = defaultunits:lookup(parms.in_unit_table) if success then parms.out_unit = t else return success, t end end success, t = units:lookup(parms.out_unit, parms.sp, true) if success then parms.out_unit_table = t else return success, t end local in_utype = parms.in_unit_table.utype if in_utype ~= parms.out_unit_table.utype then local msg = 'Cannot convert %s to %s.[[Category:Convert dimension mismatch]]' return false, msg:format(in_utype, parms.out_unit_table.utype) end if parms.out_unit_table.combination then local msg = 'Combinations not implemented, %s' return false, msg:format(parms.out_unit) end local outshow1, outshow2, outsingular1, outsingular2 success, outshow1, outsingular1 = cvtround(parms.in_value1, parms.in_clean1, parms) if not success then return success, outshow1 end success, outshow2, outsingular2 = cvtround(parms.in_value2, parms.in_clean2, parms) if not success then return success, outshow2 end local range = parms.range local disp = parms.disp local wikitext local inshow1, inshow2 = parms.in_show1, parms.in_show2 local inkey, outkey = 'name2', 'name2' local insymkey, outsymkey = 'symbol', 'symbol' if parms.in_singular1 then -- TODO how process second input value? inkey = 'name1' end if outsingular1 then outkey = 'name1' end if parms.sp == 'us' or parms.in_unit_table.sp_us then inkey = inkey .. '_us' insymkey = 'sym_us' end if parms.sp == 'us' or parms.out_unit_table.sp_us then outkey = outkey .. '_us' outsymkey = 'sym_us' end if parms.in_unit_table.usename then insymkey = inkey end if parms.out_unit_table.usename then outsymkey = outkey end local in_name = parms.in_unit_table[inkey] -- will not need to calculate all of these local in_symbol = parms.in_unit_table[insymkey] local out_name = parms.out_unit_table[outkey] local out_symbol = parms.out_unit_table[outsymkey] local abbr = parms.abbr local in_id, out_id = in_symbol, out_symbol local istemperature = (in_utype == 'temperature') if abbr == 'on' then -- all symbols -- Both symbols. elseif abbr == 'off' then -- all names in_id = in_name out_id = out_name elseif abbr == 'in' then -- input symbols -- Both symbols. elseif abbr == 'out' then -- output symbols [is this just the default?] if not istemperature then in_id = in_name end elseif abbr == 'values' then -- show only values -- TODO Probably more needed (no preceding space for a start). in_id = '' out_id = '' elseif abbr == 'mos' then -- for ranges, abbreviate with input unit repeated -- LATER else -- default if not istemperature then in_id = in_name end end in_id, out_id = linked(in_id, out_id, parms) if range == nil then if disp == 'output only' then wikitext = '%s %s' wikitext = wikitext:format(outshow1, out_id) elseif disp == 'output number only' or disp == 'number' then wikitext = outshow1 elseif disp == 'unit' then wikitext = in_id elseif disp == 'unit2' then wikitext = out_id elseif disp == 'flip' then wikitext = disp_single['b'] wikitext = wikitext:format(outshow1, out_id, inshow1, in_id) else wikitext = disp_single[disp] or disp_single['b'] wikitext = wikitext:format(inshow1, in_id, outshow1, out_id) end else -- TODO Need in_id, out_id (and more) here. wikitext = disp_double[disp] or disp_double['b'] wikitext = wikitext:format(inshow1, range[1], inshow2, in_id, outshow1, range[2], outshow2, out_id) end if parms.sortable == 'on' then wikitext = ntsh(parms.in_value1, parms.debug) .. wikitext end return true, wikitext end local p = {} -- A testing program can set the global variable 'is_test_run'. -- The following sets global variable 'mw' to simulate what Scribunto will do. local bodge = require(is_test_run and "mw" or "Module:mw") -- fix up mw.text.tag function p.convert(frame) config = get_config(frame) local pframe = frame:getParent() local success, parms, text success, parms = get_parms(pframe) if success then success, text = process(parms) else text = parms end if not success then local params = {style="color:black; background-color:orange;"} text = mw.text.tag({name="span", contents="[[Module talk:Convert|Conversion error]]: " .. text, params=params}) end return text end return p