119 lines
3.2 KiB
Lua
119 lines
3.2 KiB
Lua
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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 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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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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}
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--------------------------------------------------------------------------------
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-- Generate special number table
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-- TODO: Restructure this.
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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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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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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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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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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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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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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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end
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