Reworked the number formatting system. Will now attempt to generate the shortest possible representation of the given number.
This commit is contained in:
parent
e5e23422ef
commit
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180
number.lua
180
number.lua
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@ -20,6 +20,17 @@ local function factorial (n)
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return a
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end
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local function inverse_factorial (n)
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-- Returns the inverse factorial of n.
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-- That is some m, where n = m!
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local a, i = 1, 1
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while a < n do
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i = i + 1
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a = a * i
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end
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return (a == n) and i or nil
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end
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local function calculate_fraction (n)
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-- Returns x and y such that x/y = n. If none could be found, returns nil.
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local a, b = 1, n % 1
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@ -35,84 +46,129 @@ local function calculate_fraction (n)
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end
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end
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local MATH_SHORTHAND = {
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-- Only used if options.math_shorthand = true
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['0/0'] = 'nan',
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['1/0'] = '∞',
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['-1/0'] = '-∞',
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['math.pi'] = 'π',
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['math.exp(1)'] = 'e',
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local UNICODE_SUPERSCRIPT = {
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['0'] = '⁰', ['1'] = '¹', ['2'] = '²', ['3'] = '³', ['4'] = '⁴',
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['5'] = '⁵', ['6'] = '⁶', ['7'] = '⁷', ['8'] = '⁸', ['9'] = '⁹',
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['-'] = '⁻', ['+'] = '⁺', ['='] = '⁼', ['('] = '⁽', [')'] = '⁾',
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}
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local function to_superscript (n)
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return tostring(n):gsub('.', function (a) return UNICODE_SUPERSCRIPT[a] end)
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end
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local UNICODE_CHAR_PATTERN = '[\01-\127\192-\255][\128-\191]*'
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local function unicode_len (str)
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local len = 0
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for char in str:gmatch(UNICODE_CHAR_PATTERN) do len = len + 1 end
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return len
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end
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--------------------------------------------------------------------------------
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local SPECIAL_NUMBER = {
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-- x = ∞
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{ est = function (...) return ... end,
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real = function (a) return math.huge end,
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repr = function (a) return '1/0' end,
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short = function (a) return '∞' end,
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},
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-- Factorial
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{ est = function (n) return inverse_factorial(n) end,
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real = function (a) return factorial(a) end,
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repr = function (a) return ('fac(%i)'):format(a) end,
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short = function (a) return a..'!' end,
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},
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-- x = 2^a
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{ est = function (n) return math.log(n)/math.log(2) end,
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real = function (a) return 2^a end,
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repr = function (a) return '2^'..a end,
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short = function (a) return '2'..to_superscript(a) end,
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},
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-- x = 10^a
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{ est = function (n) return math.log(n)/math.log(10) end,
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real = function (a) return 10^a end,
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repr = function (a) return '10^'..a end,
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short = function (a) return '10'..to_superscript(a) end,
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},
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-- x = 1/√a
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{ est = function (n) return 1/(n^2) end,
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real = function (a) return 1/math.sqrt(a) end,
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repr = function (a) return ('1/math.sqrt(%i)'):format(a) end,
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short = function (a) return '1/√'..a end,
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},
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-- x = lg a
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{ est = function (n) return math.exp(n) end,
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real = function (a) return math.log(a) end,
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repr = function (a) return ('math.log(%i)'):format(a) end,
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short = function (a) return ('lg(%i)'):format(a) end,
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},
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-- x = ℯ^a
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{ est = function (n) return math.log(n) end,
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real = function (a) return math.exp(a) end,
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repr = function (a) return ('math.exp(%i)'):format(a) end,
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short = function (a) return a == 1 and 'ℯ' or 'ℯ'..to_superscript(a) end,
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},
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-- x = aπ
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{ est = function (n) return n/math.pi end,
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real = function (a) return a*math.pi end,
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repr = function (a) return a == 1 and 'math.pi' or a..'*math.pi' end,
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short = function (a) return (a == 1 and '' or a)..'π' end,
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},
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-- x = sqrt(a)
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{ est = function (n) return n^2 end,
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real = function (a) return math.sqrt(a) end,
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repr = function (a) return ('math.sqrt(%i)'):format(a) end,
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short = function (a) return '√'..a end,
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},
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-- a = x
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{ est = function (n) return n end,
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real = function (a) return a end,
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repr = function (a) return ('%i'):format(a) end,
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short = function (a) return ('%i'):format(a) end,
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},
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}
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--------------------------------------------------------------------------------
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-- Generate special number table
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-- TODO: Restructure this.
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local LONG_ASS_CONSTANT = '___________________________________________________'
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local SPECIAL_NUMBER = {}
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do
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SPECIAL_NUMBER[ 1/0] = '1/0'
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SPECIAL_NUMBER[math.pi] = 'math.pi'
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SPECIAL_NUMBER[math.exp(1)] = 'math.exp(1)'
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for i = -10, -6 do
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SPECIAL_NUMBER[math.pow(10, i)] = '10^'..i
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end
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for i = -15, -7 do
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SPECIAL_NUMBER[math.pow( 2, i)] = '2^'..i
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local function format_number (n, shorthand)
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if n ~= n then return shorthand and 'NaN' or '0/0'
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elseif n < 0 then return '-' .. format_number(-n, shorthand)
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end
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for i = 5, 308 do
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SPECIAL_NUMBER[math.pow(10, i)] = '10^'..i
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-- Finding the shortest
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local shortest, length = LONG_ASS_CONSTANT, unicode_len(LONG_ASS_CONSTANT)
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local function alternative_repr (repr)
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local repr_len = unicode_len(repr)
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if repr_len < length then shortest, length = repr, repr_len end
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end
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for i = 17, 1023 do
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SPECIAL_NUMBER[math.pow( 2, i) ] = '2^'..i
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--SPECIAL_NUMBER[math.pow( 2, i) - 1] = '2^'..i..'-1'
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--SPECIAL_NUMBER[math.pow( 2, i) + 1] = '2^'..i..'+1'
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-- Maybe it's a "special" number?
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for _, special_number_tests in pairs(SPECIAL_NUMBER) do
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local a = special_number_tests.est(n)
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if a then
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local a_near = math.floor(a + 0.5)
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if n == special_number_tests.real(a_near) then
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alternative_repr( special_number_tests[shorthand and 'short' or 'repr'](a_near) )
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end
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for i = 9, 170 do
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SPECIAL_NUMBER[factorial(i)] = i..'!'
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end
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for i = 1, 100 do
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local sqrt = math.sqrt(i)
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if not is_integer(sqrt) then
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SPECIAL_NUMBER[1/sqrt] = '1/math.sqrt('..i..')'
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SPECIAL_NUMBER[sqrt] = 'math.sqrt('..i..')'
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end
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end
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for i = 1, 100 do
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local log = math.log(i)
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if not is_integer(log) then
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SPECIAL_NUMBER[log] = 'math.log('..i..')'
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end
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end
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end
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--------------------------------------------------------------------------------
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local function format_number (n)
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-- Returns a string of n formatted as to allow easy back into a lua interpreter.
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if n ~= n then return '0/0'
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elseif n < 0 then return '-' .. format_number(-n)
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elseif SPECIAL_NUMBER[n] then return SPECIAL_NUMBER[n]
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end
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-- Maybe it's an integer?
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if is_integer(n) then return tostring(n) end
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-- Maybe it's a fraction?
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-- Maybe it's a fractional number?
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do
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local numerator, denumberator = calculate_fraction(n)
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if numerator then
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return format_number(numerator)..'/'..format_number(denumberator)
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if numerator and denumberator ~= 1 then
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alternative_repr( format_number(numerator)..'/'..format_number(denumberator) )
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end
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return ( tostring(n):gsub('e%+?', '*10^') ) -- Parantheses to return first result.
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end
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-- Maybe it's a decimal number?
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alternative_repr( tostring(n):gsub('([^e]+)e%+?(%-?)0+', function(a, b) return (a == '1' and '' or a..'*')..'10^'..b end))
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-- Well, this is not a pretty number!
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return shortest
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end
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return function (value, options, depth, l)
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l[#l+1] = format_number(value)
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if options.math_shorthand then
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l[#l] = MATH_SHORTHAND[ l[#l] ]
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end
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l[#l+1] = format_number(value, options.math_shorthand)
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end
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179
test/test_number.lua
Normal file
179
test/test_number.lua
Normal file
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@ -0,0 +1,179 @@
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local SUITE = require('TestSuite').new('number')
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SUITE:setEnviroment{
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format = require('pretty')
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}
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local function format_test (t)
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SUITE:addTest(t.expect, function ()
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assert_equal(t.expect, format(t.input, t.options))
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end)
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end
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local function number_test (t)
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SUITE:addTest(t.expect, function ()
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assert_equal(t.expect, format(t.input, {}))
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end)
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SUITE:addTest(t.shorthand or (t.expect .. ' shorthand'), function ()
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assert_equal(t.shorthand or t.expect, format(t.input, { math_shorthand = true }))
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end)
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end
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--------------------------------------------------------------------------------
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-- Integers
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number_test {
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input = 0,
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expect = '0',
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}
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number_test {
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input = -0,
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expect = '0',
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}
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number_test {
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input = 2000,
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expect = '2000',
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}
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number_test {
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input = -2000,
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expect = '-2000',
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}
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--------------------------------------------------------------------------------
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-- Exponents
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number_test {
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input = 10^5,
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expect = '10^5',
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shorthand = '10⁵',
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}
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number_test {
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input = 10^-6,
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expect = '10^-6',
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shorthand = '10⁻⁶',
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}
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number_test {
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input = 2^17,
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expect = '2^17',
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shorthand = '2¹⁷',
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}
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number_test {
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input = 2^-7,
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expect = '2^-7',
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shorthand = '2⁻⁷',
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}
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--------------------------------------------------------------------------------
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-- Decimal numbers
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number_test {
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input = 0.1,
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expect = '0.1',
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}
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number_test {
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input = 0.65,
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expect = '0.65',
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}
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--------------------------------------------------------------------------------
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-- Fractions
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number_test {
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input = 1/3,
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expect = '1/3',
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}
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number_test {
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input = 9/17,
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expect = '9/17',
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}
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--------------------------------------------------------------------------------
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-- Squareroots, logarithms, and other fine functions
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number_test {
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input = math.sqrt(8),
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expect = 'math.sqrt(8)',
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shorthand = '√8',
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}
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number_test {
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input = 1/math.sqrt(8),
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expect = '1/math.sqrt(8)',
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shorthand = '1/√8',
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}
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number_test {
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input = math.log(8),
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expect = 'math.log(8)',
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shorthand = 'lg(8)',
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}
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number_test {
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input = 6227020800,
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expect = 'fac(13)',
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shorthand = '13!',
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}
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--------------------------------------------------------------------------------
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-- Constants, and multiples of constants
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number_test {
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input = math.pi,
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expect = 'math.pi',
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shorthand = 'π',
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}
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number_test {
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input = 7*math.pi,
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expect = '7*math.pi',
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shorthand = '7π',
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}
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number_test {
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input = math.exp(1),
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expect = 'math.exp(1)',
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shorthand = 'ℯ',
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}
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number_test {
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input = math.exp(10),
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expect = 'math.exp(10)',
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shorthand = 'ℯ¹⁰',
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}
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number_test {
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input = 1/0,
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expect = '1/0',
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shorthand = '∞'
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}
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number_test {
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input = -1/0,
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expect = '-1/0',
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shorthand = '-∞'
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}
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number_test {
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input = 0/0,
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expect = '0/0',
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shorthand = 'NaN',
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}
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--------------------------------------------------------------------------------
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format_test {
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input = { 1/2, 1/3, 1/4, 1/5 },
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expect = '{ 1/2, 1/3, 1/4, 1/5 }',
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}
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--------------------------------------------------------------------------------
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return SUITE
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@ -106,135 +106,6 @@ format_test {
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expect = '\'ø\'',
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}
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--------------------------------------------------------------------------------
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-- Numbers
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format_test {
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input = 0,
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expect = '0',
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}
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format_test {
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input = 2000,
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expect = '2000',
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}
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format_test {
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input = -2000,
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expect = '-2000',
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}
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--------------------------------------------------------------------------------
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-- Numbers, Other formats
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format_test {
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input = 10^5,
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expect = '10^5',
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}
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format_test {
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input = 10^-6,
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expect = '10^-6',
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}
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format_test {
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input = 2^17,
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expect = '2^17',
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}
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format_test {
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input = 2^-7,
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expect = '2^-7',
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}
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format_test {
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input = 1/3,
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expect = '1/3',
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}
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format_test {
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input = 9/17,
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expect = '9/17',
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}
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format_test {
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input = math.sqrt(2),
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expect = 'math.sqrt(2)',
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}
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format_test {
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input = 1/math.sqrt(2),
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expect = '1/math.sqrt(2)',
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}
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format_test {
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input = math.log(2),
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expect = 'math.log(2)',
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}
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--------------------------------------------------------------------------------
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-- Numbers, Constants
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format_test {
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input = math.pi,
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expect = 'math.pi',
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}
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format_test {
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input = math.exp(1),
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expect = 'math.exp(1)',
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}
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format_test {
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input = 1/0, -- Same as math.huge
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expect = '1/0',
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}
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format_test {
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input = -1/0, -- Same as -math.huge
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expect = '-1/0',
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}
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format_test {
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input = 0/0, -- Same as nan
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expect = '0/0',
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}
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format_test {
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input = 1/0, -- Same as math.huge
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options = { math_shorthand = true },
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expect = '∞',
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}
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format_test {
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input = -1/0, -- Same as -math.huge
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options = { math_shorthand = true },
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expect = '-∞',
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}
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format_test {
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input = 0/0, -- Same as nan
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options = { math_shorthand = true },
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expect = 'nan',
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}
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format_test {
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input = math.pi,
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options = { math_shorthand = true },
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expect = 'π',
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}
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format_test {
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input = math.exp(1),
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options = { math_shorthand = true },
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expect = 'e',
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}
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format_test {
|
||||
input = { 1/2, 1/3, 1/4, 1/5 },
|
||||
expect = '{ 1/2, 1/3, 1/4, 1/5 }',
|
||||
}
|
||||
|
||||
--------------------------------------------------------------------------------
|
||||
-- Primitive types
|
||||
|
||||
|
|
|
|||
|
|
@ -3,4 +3,5 @@ package.path = package.path .. ';./test/?.lua;./src/?.lua'
|
|||
|
||||
local TEST_SUITE = require("TestSuite").new('pretty')
|
||||
TEST_SUITE:addModules('test/test_*')
|
||||
TEST_SUITE:setOptions(...)
|
||||
TEST_SUITE:runTests()
|
||||
|
|
|
|||
Loading…
Reference in New Issue
Block a user