local altvalue = whole + numerator / (denominator * 10)
local style = #slashes -- kludge: 1 or 2 slashes can be used to select style
if style > 2 then style = 2 end
local wikitext = format_fraction(parms, 'in', negative, leading_plus .. wholestr, numstr, denstr, parms.opt_spell_in, style)
return value, altvalue, wikitext, denominator
end  
local function extract_number(parms, text, another, 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.
-- Input can use en digits or digits in local language and can
-- have references at the end. Accepting references is intended
-- for use in infoboxes with a field for a value passed to convert.
-- Parameter another = true if the expected value is not the first.
-- Before processing, the input text is cleaned:
-- * Any thousand separators (valid or not) are removed.
-- * Any sign 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
-- altvalue = a valid number, usually same as value but different
-- if fraction used (for hands unit)
-- singular = true if value is 1 or -1 (to use singular form of units)
-- clean = cleaned text with any separators and sign removed
-- (en digits and '.' decimal mark)
-- show = text formatted for output, possibly with ref strip markers
-- (digits in local language and custom decimal mark)
-- The resulting show:
-- * Is for an input value and is spelled if wanted and possible.
-- * Has a rounded value, if wanted.
-- * Has digits grouped where necessary, if wanted.
-- * If negative, a Unicode minus is used; otherwise the sign is
-- '+' (if the input text used '+'), or is '' (if no sign in input).
text = strip(text or '')
local reference
local pos = text:find('\127', 1, true)
if pos then
local before = text:sub(1, pos - 1)
local remainder = text:sub(pos)
local refs = {}
while #remainder > 0 do
local ref, spaces
ref, spaces, remainder = remainder:match('^(\127[^\127]*UNIQ[^\127]*%-ref[^\127]*\127)(%s*)(.*)')
if ref then
table.insert(refs, ref)
else
refs = {}
break
end
end
if #refs > 0 then
text = strip(before)
reference = table.concat(refs)
end
end
local clean = to_en(text, parms)
if clean == '' then
return false, { another and 'cvt_no_num2' or 'cvt_no_num' }
end
local isnegative, propersign = false, '' -- most common case
local singular, show, denominator
local value = tonumber(clean)
local altvalue
if value then
local sign = clean:sub(1, 1)
if sign == '+' or sign == '-' then
propersign = (sign == '+') and '+' or MINUS
clean = clean:sub(2)
end
if value < 0 then
isnegative = true
value = -value
end
else
local valstr
for _, prefix in ipairs({ '-', MINUS, '&minus;' }) do
-- Including '-' sets isnegative in case input is a fraction like '-2-3/4'.
local plen = #prefix
if clean:sub(1, plen) == prefix then
valstr = clean:sub(plen + 1)
if valstr:match('^%s') then -- "- 1" is invalid but "-1 - 1/2" is ok
return false, { 'cvt_bad_num', text }
end
break
end
end
if valstr then
isnegative = true
propersign = MINUS
clean = valstr
value = tonumber(clean)
end
if value == nil then
if not no_fraction then
value, altvalue, show, denominator = extract_fraction(parms, clean, isnegative)
end
if value == nil then
return false, { 'cvt_bad_num', text }
end
if value <= 1 then
singular = true -- for example, "½ mile" or "one half mile" (singular unit)
end
end
end
if not valid_number(value) then -- for example, "1e310" may overflow
return false, { 'cvt_invalid_num' }
end
if show == nil then
-- clean is a non-empty string with no spaces, and does not represent a fraction,
-- and value = tonumber(clean) is a number >= 0.
-- If the input uses e-notation, show will be displayed using a power of ten, but
-- we use the number as given so it might not be normalized scientific notation.
-- The input value is spelled if specified so any e-notation is ignored;
-- that allows input like 2e6 to be spelled as "two million" which works
-- because the spell module converts '2e6' to '2000000' before spelling.
local function rounded(value, default, exponent)
local precision = parms.opt_ri
if precision then
local fmt = '%.' .. format('%d', precision) .. 'f'
local result = fmt:format(tonumber(value) + 2e-14) -- fudge for some common cases of bad rounding
if not exponent then
singular = (tonumber(result) == 1)
end
return result
end
return default
end
singular = (value == 1)
local scientific
local significand, exponent = clean:match('^([%d.]+)[Ee]([+%-]?%d+)')
if significand then
show = with_exponent(parms, rounded(significand, significand, exponent), exponent)
scientific = true
else
show = with_separator(parms, rounded(value, clean))
end
show = propersign .. show
if parms.opt_spell_in then
show = spell_number(parms, 'in', propersign .. rounded(value, clean)) or show
scientific = false
end
if scientific then
parms.opt_scientific = true
end
end
if isnegative and (value ~= 0) then
value = -value
altvalue = -(altvalue or value)
end
return true, {
value = value,
altvalue = altvalue or value,
singular = singular,
clean = clean,
show = show .. (reference or ''),
denominator = denominator,
}
end  
local function get_number(text)
-- Return v, f where:
-- v = nil (text is not a number)
-- or
-- v = value of text (text is a number)
-- f = true if value is an integer
-- Input can use en digits or digits in local language or separators,
-- but no Unicode minus, and no fraction.
if text then
local number = tonumber(to_en(text))
if number then
local _, fracpart = math.modf(number)
return number, (fracpart == 0)
end
end
end  
local function gcd(a, b)
-- Return the greatest common denominator for the given values,
-- which are known to be positive integers.
if a > b then
a, b = b, a
end
if a <= 0 then
return b
end
local r = b % a
if r <= 0 then
return a
end
if r == 1 then
return 1
end
return gcd(r, a)
end  
local function fraction_table(value, denominator)
-- Return value as a string or a table:
-- * If result is a string, there is no fraction, and the result
-- is value formatted as a string of en digits.
-- * If result is a table, it represents a fraction with named fields:
-- wholestr, numstr, denstr (strings of en digits for integer, numerator, denominator).
-- The result is rounded to the nearest multiple of (1/denominator).
-- If the multiple is zero, no fraction is included.
-- No fraction is included if value is very large as the fraction would
-- be unhelpful, particularly if scientific notation is required.
-- Input value is a non-negative number.
-- Input denominator is a positive integer for the desired fraction.
if value <= 0 then
return '0'
end
if denominator <= 0 or value > 1e8 then
return format('%.2f', value)
end
local integer, decimals = math.modf(value)
local numerator = floor((decimals * denominator) +
0.5 + 2e-14) -- add fudge for some common cases of bad rounding
if numerator >= denominator then
integer = integer + 1
numerator = 0
end
local wholestr = tostring(integer)
if numerator > 0 then
local div = gcd(numerator, denominator)
if div > 1 then
numerator = numerator / div
denominator = denominator / div
end
return {
wholestr = (integer > 0) and wholestr or '',
numstr = tostring(numerator),
denstr = tostring(denominator),
value = value,
}
end
return wholestr
end  
local function preunits(count, preunit1, preunit2)
-- If count is 1:
-- ignore preunit2
-- return p1
-- else:
-- preunit1 is used for preunit2 if the latter is empty
-- return p1, p2
-- where:
-- p1 is text to insert before the input unit
-- p2 is text to insert before the output unit
-- p1 or p2 may be nil to mean "no preunit"
-- Using '+' gives output like "5+ feet" (no space before, but space after).
local function withspace(text, wantboth)
-- Return text with space before and, if wantboth, after.
-- However, no space is added if there is a space or '&nbsp;' or '-'
-- at that position ('-' is for adjectival text).