159 lines
6.1 KiB
Lua
159 lines
6.1 KiB
Lua
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local utf8 = require "utf8"
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-- Constants
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local MAXIMUM_INT = 2^53 -- The maximum double for where all integers can be represented exactly.
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local MAXIMUM_ZERO = 10^-7 -- Used when attempting to determine fraction. Anything below is counted as 0.
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--------------------------------------------------------------------------------
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-- Util
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local function is_integer (n)
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-- Predicate. Neither +inf, -inf nor nan are integer.
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return n == math.floor(n) and n ~= 1/0 and n ~= -1/0
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end
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local function factorial (n)
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-- Returns the factorial of n.
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-- That is n! = n * (n-1) * (n-2) * ... * 1
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local a = 1
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for i = 2, n do a = a * i end
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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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while MAXIMUM_ZERO < b and a <= MAXIMUM_INT do
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local r = math.pow(b, -1)
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a, b = a * r, r % 1
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-- Invariant: n * a / a = n
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end
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-- Check the values make sense.
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local numerator, denumberator = math.floor(n * a), math.floor(a)
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if numerator / denumberator == n then
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return numerator, denumberator
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end
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end
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--------------------------------------------------------------------------------
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local format_num
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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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-- x = a/b
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{ est = calculate_fraction,
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real = function (a, b) return b ~= 1 and (a/b) end,
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repr = function (a, b) return format_num(a)..'/'..format_num(b) end,
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short = function (a, b) return format_num(a)..'/'..format_num(b) 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'..utf8.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'..utf8.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/√'..utf8.overline(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'..utf8.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 '√'..utf8.overline(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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function format_num (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_num(-n, shorthand)
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end
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-- Finding the shortest
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local shortest, length = nil, math.huge
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local function alternative_repr (repr)
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local repr_len = utf8.width(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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-- 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[1] then
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for i = 1, #a do a[i] = math.floor(a[i] + 0.5) end
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if n == special_number_tests.real(unpack(a)) then
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alternative_repr( special_number_tests[shorthand and 'short' or 'repr'](unpack(a)) )
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end
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end
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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_num(value, options.math_shorthand)
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end
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