Module:BigNumber

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Revision as of 07:36, 27 December 2022 by 1>A2569875 (負小數底數演算法出爐 https://doi.org/10.48550/arXiv.1701.04506)
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local p={} local getArgs = require('Module:Arguments').getArgs local yesno = require('Module:Yesno') local lib_calc = require('Module:Complex_Number/Calculate') local lib_solve = require("Module:Complex_Number/Solver") local lib_fact = {} --Module:Factorization local lib_bit=require('bit32'); local bit={lS=lib_bit.lshift,rS=lib_bit.rshift,Or=lib_bit.bor,And=lib_bit.band} local utils = require('Module:BigNumber/utils')

--大數運算的Metatable p.bigintMeta = { __add = function (op_1, op_2) --大數加法。如被加數或加數有負值則為大數減法 local op1, op2 = p.bigint(op_1):clone(), p.bigint(op_2):clone() --處理NaN及Inf if op1.isNaN or op2.isNaN then return op1.isNaN and op1:clone() or op2:clone() end if op1.isInf or op2.isInf then if op1.isInf and op2.isInf and (op1.sign ~= op2.sign) then return p.bigint():nan() end local result = p.bigint():inf() result.sign = op1.isInf and op1.sign or op2.sign return result end local result = p.bigint() --位數對齊 if op1.point > op2.point then op2:setpoint(op1.point) elseif op1.point < op2.point then op1:setpoint(op2.point)end result.point = op1.point --計算位數為原始位數+1 (如果進位的話) local length = math.max(op1:length(), op2:length()) + 1 local carry = 0 --進位/借位 for i = 1,length-1 do --該位數相加 local digit = op1.sign * op1:atl(i) + op2.sign * op2:atl(i) + carry --超過底數代表進位 if digit >= op1.base then carry = 1 digit = digit - op1.base --低於0則需借位 elseif digit < 0 then carry = -1 digit = digit + op1.base else carry = 0 end result:setl(i, digit) end --仍有未處理的進位/借位 if carry > 0 then result:setl(length, carry) elseif carry < 0 then --最高位仍有借位代表結果為負 result.sign = -1 carry = 0 --全體取補數 for i = 1,length-1 do local digit = op1.base - result:atl(i) + carry carry = -1 result:setl(i, digit) end end --清除前導零 if not (op1.nodelzero or op2.nodelzero) then result:delzero() end result.isNaN = op1.isNaN or op2.isNaN return result end, __sub = function (op_1, op_2) --大數減法 轉為加法 (減數取相反數) local op1, op2 = p.bigint(op_1):clone(), p.bigint(op_2):clone() op2.sign = op2.sign * -1 --減數取相反數 return op1 + op2 end, __mul = function (op_1, op_2) --大數乘法 使用FFT加速 local op1, op2 = p.bigint(op_1), p.bigint(op_2) --處理NaN及Inf if op1.isNaN or op2.isNaN then return op1.isNaN and op1:clone() or op2:clone() end if op1.isInf or op2.isInf then local result = p.bigint():inf() result.sign = op1.sign * op2.sign return result end local op1_iszero, op2_iszero = op1:equal(0), op2:equal(0) local result = p.bigint() if op1.isInf or op2.isInf then result:inf() result.sing = op1.sing * op2.sing return result end local a_sign, b_sign = op1.sign, op2.sign local a_is_zero, b_is_zero = true, true local res,rea,ina,reb,inb,ret,intt = {0},{0},{0},{0},{0},{0},{0} local len1,len2,lent,lenres,_len; local s1, s2 = tostring(in1), tostring(in2) len1 = op1:length(); len2 = op2:length(); if len1 > len2 then lent = len1 else lent = len2 end; _len=1 while _len < lent do _len = bit.lS(_len,1) end _len = bit.lS(_len,1) --填入FFT序列 for i = 0,_len-1 do if i < len1 then rea[i+1] = op1.data[len1-i] end if i < len2 then reb[i+1] = op2.data[len2-i] end a_is_zero = a_is_zero and (rea[i+1]or 0) < 1e-14 b_is_zero = b_is_zero and (reb[i+1]or 0) < 1e-14 ina[i+1],inb[i+1] = 0,0; end --乘法正負號結果為兩者正負號相乘 local res_sign = a_sign * b_sign --若被乘數或乘數為零則結果為零 if a_is_zero or b_is_zero then local _zero = p.bigint() _zero.sign = res_sign < 0 and -1 or 1 return _zero end --執行FFT p._FFT(rea,ina,_len,false); p._FFT(reb,inb,_len,false); --執行捲積 for i=0,_len-1 do local rec = rea[i+1] * reb[i+1] - ina[i+1] * inb[i+1]; local inc = rea[i+1] * inb[i+1] + ina[i+1] * reb[i+1]; rea[i+1] = rec; ina[i+1] = inc; end --執行逆FFT p._FFT(rea,ina,_len,true);--ifft for i=0,_len-1 do rea[i+1] = rea[i+1] / _len; ina[i+1] = ina[i+1] / _len end

for i=0,_len-1 do res[i+1] = math.floor(rea[i+1] + 0.5)end for i=0,_len-1 do res[i+2] = (res[i+2]or 0) + math.floor((res[i+1]or 0) / op1.base) ; res[i+1] = (res[i+1]or 0) % op1.base end

lenres = len1 + len2 + 2; while (res[lenres+1]or 0) == 0 and lenres > 0 do lenres=lenres-1 end local j = 1 for i=lenres,0,-1 do result.data[j] = (res[i+1]or 0) j = j + 1 end result.sign = res_sign < 0 and -1 or 1 result.point = op1.point + op2.point if result.point > result:length() then result:fractionalzero()end if not (op1.nodelzero or op2.nodelzero) then result:delzero() end return result end, __div = function (op_1, op_2) --大數除法 轉為乘法 (除數取倒數) local op1, op2 = p.bigint(op_1), p.bigint(op_2) --處理NaN及Inf if op1.isNaN or op2.isNaN then return op1.isNaN and op1:clone() or op2:clone() end if op1.isInf or op2.isInf then if op1.isInf and op2.isInf then return p.bigint():nan() end if op1.isInf then return op1:clone() end if op2.isInf then return p.bigint(0) end end --處理零 local op1_iszero, op2_iszero = op1:equal(0), op2:equal(0) if op1_iszero or op2_iszero then --被除數和除數皆為零無意義 if op1_iszero and op2_iszero then return p.bigint():nan() end local result = p.bigint():inf() result.sign = op1.sign * op2.sign --被除數為零結果為零不必計算；除數為零無法計算 return op2_iszero and result or p.bigint(0) end local invop2 = op2:inverse(op_1:length() * 2 + 2) local result = op1 * invop2 --將除法轉換成乘以倒數 result:setpoint(op_1:length() + 1) local pointfix = p.bigint("1") pointfix.point = result.point pointfix:fractionalzero() result = result + pointfix result:setpoint(op_1:length()) if not (op1.nodelzero or op2.nodelzero) then result:delzero() end return result end, __mod = function (op_1, op_2) local op1, op2 = p.bigint(op_1), p.bigint(op_2) --處理NaN及Inf if op1.isNaN or op2.isNaN then return op1.isNaN and op1:clone() or op2:clone() end if op1.isInf or op2.isInf then if op1.isInf or (op1.isInf and op2.isInf) then return p.bigint(0):nan() end return op2:clone() end --處理零 local op1_iszero, op2_iszero = op1:equal(0), op2:equal(0) if op1_iszero or op2_iszero then --被除數和除數皆為零餘數為0 if op1_iszero and op2_iszero then return p.bigint(0) end local result = p.bigint():nan() result.sign = op1.sign * op2.sign --被除數為零結果為零不必計算；除數為零無法計算 return op2_iszero and result or p.bigint(0) end if op1:equal(op2) then return p.bigint(0) end if p.bigintmath.abs(op1) < p.bigintmath.abs(op2) then if op1.sign == op2.sign then return op1 end return op1 + op2 end local divided = op1 / op2 if divided.sign < 0 and divided.point > 0 then divided = divided - 1 end divided:setpoint(0) local result = op1 - divided * op2 if not (op1.nodelzero or op2.nodelzero) then result:delzero() end return result end, __pow = function (op_1, op_2) local op1, op2 = p.bigint(op_1), tonumber(tostring(op_2)) or 1 local this = op1 --處理NaN及Inf if this.isNaN then return this:clone() end if this.isInf then if op2 < 0 then return p.bigint(0) end if op2 == 0 then return p.bigint(1) end return this:clone() end --非整數的指數不支援，目前僅能計算某數的整數次方。使用一般非高精度的math.pow運算 local is_op2_exp = tostring(op2):find("[eE][+-]?%d") if math.abs(utils.myfloor(op2) - op2) > 1e-14 or is_op2_exp then return p.bigint(math.pow(tonumber(tostring(op_1)) or 1, op2)) end if op2 < 0 then --負的次方為倒數自乘 this = this:inverse(this:length() + 1) op2 = -op2 end --零次方 if op2 == 0 then --零的零次方無意義 if op1:equal(0) then return op1:equal():nan() end return p.bigint(1) --任意數的零次方為一 end if op2 == 1 then return this:clone() end --任意數一次方為本身 if op2 == 2 then return this * this end local loge = math.log(op2) local log2 = loge / math.log(2) if utils.isInt(log2) then --次方為2的冪 直接連續自乘，以減少乘法運算的次數 local result = this:clone() for i=1,log2 do result = result * result end return result end local log3 = loge / math.log(3) if utils.isInt(log3) then --次方為3的冪 直接連續的3次自乘，以減少乘法運算的次數 local result = this:clone() for i=1,log3 do result = result * result * result end return result end

local times_data = {} local times_times = {}

local two_time = math.pow(2, math.floor(log2)) --其餘情況轉換成2的冪的組合，以減少乘法運算的次數 local lose_time = op2 - two_time local to_times = this:clone() local zero_flag = 0 repeat --重複分成2的冪的組合 for i=1,log2 do --連續自乘 to_times = to_times * to_times end times_data[#times_data+1] = to_times --紀錄本次自乘次數的結果 times_times[#times_times+1] = two_time log2 = math.log(lose_time) / math.log(2) --計算剩餘數字的2的冪的組合 two_time = math.pow(2, math.floor(log2)) lose_time = lose_time - two_time --計算扣除本次的2的冪的次數後剩下多少次要乘 to_times = this:clone() if lose_time <= 0 then zero_flag = zero_flag + 1 end --剩餘次數為0為迴圈結束條件 until zero_flag > 1

local result = p.bigint(1) for i=1,#times_data do --將所有自乘次數的結果相乘 result = result * times_data[i] end return result end, __tostring = function (this) local this_length = this:length() local result = for i = 1, this_length do if i == this_length - this.point + 1 then result = result .. '.' --到達小數位置放置小數點 end result = result .. string.format(string.format("%%0%dd", this.base_pow), this.data[i]) end if result:find("%.") then else result = result .. '.' --若無小數點，補上小數點，以便清除小數點後方的零 end result = mw.text.trim(result,"0") --移除前導零與小數點後方的零 if result:sub(1,1) == '.' then result = '0' .. result end --將 .XXX 補成 0.XXX result = mw.text.trim(result,".") --移除多餘的小數點 if mw.text.trim(result) == then result = '0' end --若整體為空字串，則結果為零 if this.isInf then result = 'inf' end if this.isNaN then result = 'nan' end if this.sign < 0 then result = '−' .. result end --補上正負號 return result end, __unm = function (this) local result = this:clone() result.sign = result.sign * -1 return result end, __eq = function (op_1, op_2) local op1, op2 = p.bigint(op_1), p.bigint(op_2) return op1:equal(op2) end, __lt = function (op_1, op_2) return op_1:less(op_2) end, __le = function (op_1, op_2) return op_1:lessequal(op_2) end, }

function p.bigint(input_data, base) local _base_pow = 6 local _base = 10 ^ _base_pow if type(input_data) == type({}) and (input_data or {})['type'] == 'bigint' then return input_data end local _bigint = { --大數資料結構 data = {0}, --大數的各個位數 sign = 1, --大數的正負號 point = 0, --小數位數數量 base = _base, --運算的底數 (必須是10的次方) base_pow = _base_pow, --該底數是10的多少次方，用於處理輸出 ['type'] = 'bigint', --標記type為bigint numberType = 'bigint' } function _bigint:length() --取得大數的位數 return #(self.data) end function _bigint:atl(dig) --取得從右起算的第n位數 local idx = self:length() - dig + 1 if idx <= 0 then for i = 1,1-idx do table.insert(self.data, 1, 0) end end return self.data[self:length() - dig + 1] or 0 end function _bigint:setl(dig, value) --設定從右起算的第n位數 local idx = self:length() - dig + 1 if idx <= 0 then for i = 1,1-idx do table.insert(self.data, 1, 0) end end self.data[self:length() - dig + 1] = value return self end function _bigint:nan() --標記為NaN self.isNaN = true return self end function _bigint:inf() --標記為Inf self.isInf = true return self end function _bigint:setpoint(point) --設定小數位數 local point_diff = point - self.point if point_diff > 0 then for i=1,point_diff do self.data[self:length() + 1] = 0 end elseif point_diff < 0 then for i=1,-point_diff do table.remove( self.data, self:length()) end end self.point = point return self end function _bigint:fractionalzero() --依據小數位數補齊零至個位數 if self.point >= self:length() then local lost_digs = self.point - self:length() for i=1,lost_digs+1 do table.insert(self.data, 1, 0) end end end function _bigint:delzero() --移除前導零 for i=1,self:length()-self.point do if math.abs(self.data[1]) > 1e-14 then break else table.remove( self.data, 1) end end local self_point = self.point for i=1,self_point do if math.abs(self:atl(1)) > 1e-14 then break else table.remove( self.data, self:length()) self.point = self.point - 1 end end return self end function _bigint:equal(op) --大數相等判斷 local other = p.bigint(op):clone() if self.isNaN or other.isNaN then return false end if self.isInf or other.isInf then return (self.isInf and other.isInf) and (self.sing == other.sing) or (self.isInf == other.isInf) end if self.sign ~= other.sign then if utils.is_zero(self.data) and utils.is_zero(other.data) then return true end return false end local myself = self:clone() myself:delzero() other:delzero() local max_point = math.max(myself.point, other.point) myself:setpoint(max_point + 1) other:setpoint(max_point + 1) local max_digs = math.max(myself:length(), other:length()) for i = 1, max_digs do if myself:atl(i) ~= other:atl(i) then return false end end return true end function _bigint:clone() --複製一份大數物件 local result = p.bigint() for i=1,self:length() do result.data[i] = self.data[i]end for k,v in pairs(self) do if k~="data" and type(v) ~= type({}) and type(v) ~= type(function()end) then result[k] = v end end return result end function _bigint:intlength() --取得整數部分的位數 local length = self:length() - self.point if length == 1 and math.abs(self.data[length]) < 1e-14 then return 0 end return length end function _bigint:divsmall(other) --大數除一般的數 (長除法) local num = (type(other) == type(0)) and other or (tonumber(tostring(other)) or 1) local result = self:clone() result.data = utils.modulo_div(result.data, result.base, num) return result end function _bigint:divdigits(op_2, digit) --大數除法指定計算位數 local op1, op2 = self, p.bigint(op_2) local invop2 = op2:inverse(digit * 2 + 2) local result = op1 * invop2 result:setpoint(digit + 1) local pointfix = p.bigint("1") pointfix.point = result.point pointfix:fractionalzero() result = result + pointfix result:setpoint(digit) if not (op1.nodelzero or op2.nodelzero) then result:delzero() end result.isNaN = op1.isNaN or op2.isNaN return result end function _bigint:inverse(_digs) --大數倒數 (牛頓法) if self.isNaN then return p.bigint():nan() end if self.isInf then return p.bigint(0) end local digs = (_digs or (self:length() * 2)) + 1 if self:equal(p.bigint("0")) then error("嘗試除以零",2) end --計算牛頓法迭代起始值 local init = p.bigint("1") local intlength = self:intlength() for i=1,digs - intlength + 1 do init.data[init:length() + 1] = 0 end local myself = self:clone() local to_div = self:clone() to_div.sign = 1 myself:delzero() local first_non_zero, pre_point = myself.data[1], 0 --若要計算的數絕對值小於1需要補齊位數 for i = 2, myself:length() do if math.abs(first_non_zero) > 1e-14 then break end pre_point = pre_point + 1 first_non_zero = myself.data[i] end --以1除以最高位數作為起始值，使用長除法 init.data = utils.modulo_div(init.data, myself.base, first_non_zero) init.nodelzero = true for i=1,intlength - pre_point - 1 do table.insert(init.data, 1, 0) end for i=1,pre_point do init.data[#init.data + 1] = 0 end init.point = digs --設定牛頓法起始值 local x0 = (2 - init * to_div) * init x0:fractionalzero() x0.nodelzero = true x0:setpoint(digs)

local x1 = x0 x0 = init

local i = 0 --迭代，當各個位數值不再改變則結束計算 while not x0:equal(x1) do --x1 = (2 - x0 * num) * x0 local new_x1 = (2 - x0 * to_div) * x0 new_x1:fractionalzero() new_x1.nodelzero = true new_x1:setpoint(digs) x1 = x0 x0 = new_x1 --避免無窮迴圈，設定最高迭代次數 if i > 20 then break end i = i + 1 end x0.sign = self.sign return x0 end function _bigint:less(other) local op1, op2 = p.bigint(self), p.bigint(other) if op1.isNaN or op2.isNaN then return false end if op1.isInf or op2.isInf then if op1.isInf and op2.isInf then return op1.sign < op2.sign end if op1.isInf then return op1.sign < 0 end return op2.sign > 0 end if op1.point > op2.point then op2:setpoint(op1.point) elseif op1.point < op2.point then op1:setpoint(op2.point)end local total_len = math.max(op1:length(), op2:length()) for i=1,total_len do local j = total_len - i + 1 local a, b = op1:atl(j) * op1.sign, op2:atl(j) * op2.sign if a ~= b then return a < b end end return false end function _bigint:lessequal(other) local op1, op2 = p.bigint(self), p.bigint(other) if op1.isNaN or op2.isNaN then return false end if op1.isInf or op2.isInf then if op1.isInf and op2.isInf then return op1.sign <= op2.sign end if op1.isInf then return op1.sign < 0 end return op2.sign > 0 end if op1.point > op2.point then op2:setpoint(op1.point) elseif op1.point < op2.point then op1:setpoint(op2.point)end local total_len = math.max(op1:length(), op2:length()) for i=1,total_len do local j = total_len - i + 1 local a, b = op1:atl(j) * op1.sign, op2:atl(j) * op2.sign if a ~= b then return a < b end end return true end setmetatable(_bigint, p.bigintMeta) if input_data == nil then return _bigint end local in_str = tostring(input_data) in_str = mw.text.trim(in_str) --取得第一個字元判斷正負號 local first_sign = mw.ustring.sub(in_str,1,1) if first_sign == '-' or first_sign == '−' then _bigint.sign = -1 end local src_base = tonumber(base) or 10 if src_base < 24 then if utils.isInf(in_str) then return _bigint:inf() end if utils.isNaN(in_str) then return _bigint:nan() end end --特殊底數的進制先轉成十進制 if ((base ~= nil) and not tonumber(base)) or (src_base < 0) or (not (utils.isInt(src_base))) or (mw.ustring.match(in_str,"^[+-−]?0[xX]")) then first_sign = mw.ustring.sub(in_str,1,1) --先前已記錄正負號，故先移除正負號 if first_sign == '+' or first_sign == '-' or first_sign == '−' then in_str = mw.ustring.sub(in_str,2,-1)end in_str = p.convertBase(in_str .. ((math.abs(src_base) > 36) and ';' or ), 10, base) --轉成十進制 first_sign = mw.ustring.sub(in_str,1,1) --若轉換完畢仍有正負號，更新正負號 if first_sign == '-' or first_sign == '−' then _bigint.sign = _bigint.sign * -1 end src_base = 10 --已經轉成十進制 if in_str:find('i') then _bigint:nan() end end --從字串讀取位數 local int_digits, fractional_digits = lib_calc._getNumString(in_str .. ((math.abs(src_base) > 36) and ';' or ), src_base>14) if math.abs(src_base) <= 1 then src_base = 10 end --轉換為大數運算的目標進位制 _bigint.data = utils._convertBase(int_digits, src_base, _base, false) fractional_digits = utils._convertBase(fractional_digits, src_base, _base, true) --將位數存入大數物件 for i=1,#fractional_digits do _bigint.data[_bigint:length() + 1] = fractional_digits[i] end _bigint.point = #fractional_digits return _bigint end

p.bigintmath = { abs=function(op) local num = p.bigint(op):clone() num.sign = 1 return num end, floor=function(op) local num = p.bigint(op):clone() if num.sign < 0 then num.sign = 1 num = p.bigintmath.ceil(num) num.sign = -1 return num end num:setpoint(0) return num end, ceil=function(op) local num = p.bigint(op):clone() if num.sign < 0 then num.sign = 1 num = p.bigintmath.floor(num) num.sign = -1 return num end num:delzero() if num.point > 0 then num:setpoint(0) num = num + 1 end return num end, div=function(op1,op2) return op1 / op2 end, re=function(z)return p.bigint(z) end, nonRealPart=function(z) return p.bigint(0) end, inverse=function(op) local num = p.bigint(op):clone() return num:inverse(16) end, digits=function(op) local num = p.bigint(op) if num.isInf or num.isNaN then return num:clone() end return p.bigint(num:intlength()) end, sqrt=function(op) --計算平方根，牛頓法 local num = p.bigint(op) if num.isInf or num.isNaN then return num:clone() end if num:less(0) then error('不支援計算負值的平方根',2) end local i = 0

--先用一般的math.sqrt計算 local init_sqrt = math.sqrt(tonumber(tostring(op))) local x0 = p.bigint(-1) local x1 = p.bigint(init_sqrt) local check_sqrt = tostring(init_sqrt) if check_sqrt:find("[Ee]") then else local strlen = check_sqrt:gsub("%.",):len() --若結果位於有效數字內，則直接回傳運算結果 if strlen < 13 then return x1 end end --若計算的數字大小超過math.sqrt能計算的範圍及精度，則開始調用牛頓法 local i = 0 local digits = x1:length()+num:length() --計算至各個位數不變時則停止 while not x0:equal(x1) and not x0:equal(x1 - 1) do x0 = x1 --牛頓法迭代 -- x1 = (num / x0 + x0) / 2 x1 = (num:divdigits(x0,digits+3) + x0):divsmall(2) if x0.point > 0 or x1.point > 0 then x0:setpoint(digits+2) x1:setpoint(digits+2) end x0:delzero() x1:delzero() --避免無窮迴圈，設定最高迭代次數 if i > 20 then break end i = i + 1 end if x0.point > 0 then x0:setpoint(digits)end return x0 end, modf = function (op_1) local op1 = p.bigint(op_1):clone() local sign = op1.sign local int_part = p.bigint(op_1):clone() op1.sign = 1 int_part.sign = 1 int_part:setpoint(0) local frac_part = op1 - int_part int_part.sign = sign frac_part.sign = sign return int_part, frac_part end, fmod = function (op_1, op_2) local op1, op2 = p.bigint(op_1), p.bigint(op_2) --處理NaN及Inf if op1.isNaN or op2.isNaN then return op1.isNaN and op1:clone() or op2:clone() end if op1.isInf or op2.isInf then if op1.isInf or (op1.isInf and op2.isInf) then return p.bigint(0):nan() end return op2:clone() end --處理零 local op1_iszero, op2_iszero = op1:equal(0), op2:equal(0) if op1_iszero or op2_iszero then --被除數和除數皆為零餘數為0 if op1_iszero and op2_iszero then return p.bigint(0) end local result = p.bigint():nan() result.sign = op1.sign * op2.sign --被除數為零結果為零不必計算；除數為零無法計算 return op2_iszero and result or p.bigint(0) end if op1:equal(op2) then return p.bigint(0) end if p.bigintmath.abs(op1) < p.bigintmath.abs(op2) then return op1 end local divided = op1 / op2 divided:setpoint(0) local result = op1 - divided * op2 if not (op1.nodelzero or op2.nodelzero) then result:delzero() end result.isNaN = op1.isNaN or op2.isNaN return result end, frexp=function(op) local num = tostring(op) local bignum = p.bigint(op) local result = p.bigint() --處理NaN及Inf if utils.isNaN(num) then return p.bigint(op), p.bigint(0)end if utils.isInf(num) then return p.bigint(op), p.bigint(0)end --計算目標數是2的多少次方 local log2 = math.log(math.abs(tonumber(num) or 1)) / math.log(2) --為了避免精度丟失，當是2的負數次方時，乘到正數次方 if log2 < 0 then log2 = utils.myceil(log2) bignum = bignum * (p.bigint(2)^math.abs(log2)) num = tostring(bignum) else log2 = 0 end --轉換為二進制 local result_str = p.convertBase(num, 2, 10, 0, 192) --使用比double高3倍的精度以便處理無窮小數 (64 * 3 = 192) local sign_text = mw.ustring.sub(result_str,1,1) local sign = 1 --讀取正負號 if sign_text == '+' or sign_text == '-' or sign_text == '−' then result_str = mw.ustring.sub(result_str,2,-1) sign = (sign_text == '-' or sign_text == '−') and -1 or 1 end --frexp當x為零，則回傳兩個零 if result_str=='0' then result.sign = sign return result, p.bigint(0) end --當數值為0.XXX時 if result_str:sub(1,2) == '0.' then if result_str:match("0%.[1-9]")then return p.bigint(num), p.bigint(0 + log2) else --當數值為0.00...00XXX result_str = result_str:sub(3,-1) --去除 "0." local find_num = result_str:find("[1-9]") --找到第一個有效數字 if not find_num then --找不到意味著數字為0 result.sign = sign return result, p.bigint(0) end result_str = '0.'..result_str:sub(find_num,-1) --處理成0.XXX result_str = p.convertBase(result_str, 10, 2, 0, result.base_pow * 9) --轉回十進制 result = p.bigint(result_str) --超出的精度處理 local pointfix = p.bigint("1") --準備一個極小的數值相加，讓諸如 0.999999....的可以進位 pointfix.point = result.point pointfix:fractionalzero() result.sign = 1 result = result + pointfix result:setpoint(8) result:delzero() result.sign = sign return result, p.bigint(log2 - find_num + 1) end else --當數值為 XX.XXX 時 local find_point = (result_str..'.'):find("%.") local turn_str = result_str:gsub("%.",) turn_str = '0.'..turn_str result = p.bigint(turn_str,2) result.sign = sign return result, p.bigint(find_point-1) end end, max=function(...) local nums = {...} local max_val = -p.bigint():inf() for i=1,#nums do local value = p.bigint(nums[i]) if not utils.isNaN(value) then if max_val < value then max_val = value end end end return max_val end, min=function(...) local nums = {...} local min_val = p.bigint():inf() for i=1,#nums do local value = p.bigint(nums[i]) if not utils.isNaN(value) then if value < min_val then min_val = value end end end return min_val end, random=function(op_1, op_2) if (not op_1) and (not op_2) then local random_number = '0.' for i=1,36 do random_number=string.format("%s%d", random_number, math.random(0,9))end return p.bigint(random_number) end --計算op1到op2之間的亂數 local op1, op2 = p.bigint(op_1), p.bigint(op_2) if not op_2 then --若只輸入op1，則計算1到op1之間的亂數 op2 = op1 op1 = p.bigint(1) end if op2 < op1 then --若op1較大，則計算op2到op1之間的亂數 local tmp = op1 op1 = op2 op2 = tmp end op1:setpoint(0)--取整 op2:setpoint(0) if op1:equal(op2) then return op1:clone() end --若op1==op2則直接回傳 local all_digit = op2 - op1 local random_number = local all_digit_number = tonumber(tostring(all_digit)) if all_digit_number < 2147483647 then --若落在math.random可計算的範圍內則直接計算 random_number = p.bigint(math.random(0, all_digit_number)) else all_digit:delzero() local all_digit_length = all_digit:length() for i=1,all_digit_length do random_number=string.format(string.format("%%s%%0%dd", all_digit.base_pow), random_number, math.random(0,all_digit.base))end random_number = p.bigint(random_number) random_number = random_number % (all_digit + 1) end return random_number + op1 end, coterminal_angle=function(op) if not p.bigintmath.isinit then p.bigintmath.init() end local num = p.bigint(op) local twopi = p.bigintmath.pi * 2 return num - p.bigintmath.floor(num / twopi) * twopi end, deg=function(op) if not p.bigintmath.isinit then p.bigintmath.init() end local num = p.bigint(op) return num * 180 / p.bigintmath.pi end, rad=function(op) if not p.bigintmath.isinit then p.bigintmath.init() end local num = p.bigint(op) return num * p.bigintmath["°"] end, sin=function(op_1) local op1 = tonumber(tostring(p.bigintmath.coterminal_angle(p.bigint(op_1)))) or 0 return p.bigint(math.sin(op1)) end, cos=function(op_1) if not p.bigintmath.isinit then p.bigintmath.init() end local op1 = tonumber(tostring(p.bigintmath.coterminal_angle(p.bigint(op_1)))) or p.bigintmath.pi return p.bigint(math.cos(op1)) end, tan=function(op_1) local op1 = tonumber(tostring(p.bigintmath.coterminal_angle(p.bigint(op_1)))) or 0 return p.bigint(math.tan(op1)) end, cot=function(op_1) local op1 = tonumber(tostring(p.bigintmath.coterminal_angle(p.bigint(op_1)))) or 0 return p.bigint(1/math.tan(op1)) end, asin=function(op_1) local op1 = tonumber(tostring(op_1)) or 0 return p.bigint(math.asin(op1)) end, acos=function(op_1) local op1 = tonumber(tostring(op_1)) or 1 return p.bigint(math.acos(op1)) end, atan=function(op_1) local op1 = tonumber(tostring(op_1)) or 1 return p.bigint(math.atan(op1)) end, atan2=function(op_1, op_2) local op1, op2 = tonumber(tostring(op_1)) or 1, tonumber(tostring(op_2)) or 1 return p.bigint(math.atan2(op1, op2)) end, acot=function(op_1) local op1 = tonumber(tostring(op_1)) or 1 return p.bigint(math.atan(1/op1)) end, sinh=function(op_1) local op1 = tonumber(tostring(op_1)) or 0 return p.bigint(math.sinh(op1)) end, cosh=function(op_1) local op1 = tonumber(tostring(op_1)) or 1 return p.bigint(math.cosh(op1)) end, tanh=function(op_1) local op1 = tonumber(tostring(op_1)) or 1 return p.bigint(math.tanh(op1)) end, coth=function(op_1) local op1 = tonumber(tostring(op_1)) or 1 return p.bigint(math.cosh(op1) / math.sinh(op1)) end, asinh=function(op_1) local op1 = tonumber(tostring(op_1)) or 0 return p.bigint(math.log( op1 + math.sqrt( op1 * op1 + 1 ) )) end, acosh=function(op_1) local op1 = tonumber(tostring(op_1)) or 1 return p.bigint(math.log( op1 + math.sqrt( op1 * op1 - 1 ) )) end, atanh=function(op_1) local op1 = tonumber(tostring(op_1)) or 1 return p.bigint(0.5 * math.log((1+op1)/(1-op1))) end, acoth=function(op_1) local op1 = tonumber(tostring(op_1)) or 1 return p.bigint(0.5 * math.log((op1+1)/(op1-1))) end, dot=function (op_1, op_2) local op1, op2 = p.bigint(op_1), p.bigint(op_2) return op1 * op2 end, sgn=function(op) local num = p.bigint(op) return p.bigint(num.sign) end, exp=function(op) if not p.bigintmath.isinit then p.bigintmath.init() end local result = p.bigintmath.e ^ tonumber(tostring(op)) result:setpoint(p.bigintmath.e.point) return result end, ldexp=function(op1, op2) return p.bigint(op1) * (p.bigint(2) ^ tonumber(tostring(op2))) end, pow=function(op_1, op_2) local op1, op2 = p.bigint(op_1), tonumber(tostring(op_2)) or 1 return op1 ^ op2 end, elog=function(op_1) local invlog10e = p.bigint("2.30258509299404568401799145468436420760110148862877297603332790096757260967735248023599720508960")--1/log10(e) local result = p.bigintmath.log10(op_1) * invlog10e--1/log10(e) result:setpoint(invlog10e.point) return result end, ["log10"]=function(op) local num_str = tostring(op) --處理NaN及Inf if utils.isNaN(num_str) then return p.bigint():nan() end if utils.isInf(num_str) then return p.bigint(op) end local result_str = num_str local sign_text = result_str:sub(1,1) local sign = 1 if sign_text == '+' or sign_text == '-' or sign_text == '−' then result_str = mw.ustring.sub(result_str,2,-1) sign = (sign_text == '-' or sign_text == '−') and -1 or 1 end if sign < 0 then return -p.bigint():nan() end local result_str_len = result_str:len() local digits = 0 if result_str:match("^[0.]+$") then --零 return -p.bigint():inf() --log(0) = -inf end --當數值為0.XXX時 if result_str:sub(1,2) == '0.' then result_str = result_str:sub(3,-1) --去除 "0." local find_num = result_str:find("[1-9]") --找到第一個有效數字 if not find_num then --找不到意味著數字為0 return -p.bigint():inf() end --處理成X.XXX result_str = result_str:sub(find_num,find_num)..((find_num >= result_str_len)andor('.'..result_str:sub(find_num+1,-1))) digits = -find_num else --當數值為 XX.XXX 時 local find_point = (result_str..'.'):find("%.") local turn_str = result_str:gsub("%.",) --處理成X.XXX result_str = (turn_str:len()==1) and turn_str or (turn_str:sub(1,1)..'.'..turn_str:sub(2,-1)) digits = find_point-2 end --計算X.XXX的常用對數 local log_value = p.bigint(math.log10(tonumber(result_str))) --將結果與位數相加 log_value = log_value + digits return log_value end, log=function(_z,_basez) local z = tonumber(tostring(_z)) or 1 local basez = tonumber(tostring(_basez)) if basez~=nil then return math.log(basez) / math.log(z) end return p.bigint(math.log(z)) end,

factorial=function(op) local num = math.floor(tonumber(tostring(op)) or 1) if num < 0 then return p.bigint():inf() end local result = p.bigint(1) for i=1,num do result = result * i end return result end, bigint=function() return 1 end, init = function(base) p.bigintmath.base = tonumber(base) or 10 p.bigintmath.e = p.bigint("2.71828182845904523536028747135266249775724709369995957496696762772407663035354759457138217852517") p.bigintmath.pi = p.bigint("3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534212") p.bigintmath["π"] = p.bigintmath.pi p.bigintmath["°"] = p.bigint(p.bigintmath.pi/180) p.bigintmath.nan = p.bigint():nan() p.bigintmath.inf = p.bigint():inf() p.bigintmath.huge = p.bigintmath.inf p.bigintmath.zero = p.bigint(0) p.bigintmath.one = p.bigint(1) p.bigintmath[-1] = p.bigint(-1) p.bigintmath[0],p.bigintmath[1] = p.bigint(0),p.bigint(1) p.bigintmath.elements = {p.bigint(1)} p.bigintmath.numberType = lib_solve._numberType p.bigintmath.isinit = true p.bigintmath.constructor = function(x) if type(x) == type({}) and (x or {})['type'] == 'bigint' then return x end if tonumber(tostring(x), p.bigintmath.base) then return p.bigint(x) end return nil end return p.bigintmath end }

function p._FFT(reA, inA, num, flag) --提供大數乘法使用 local lgn = math.floor(math.log(num) / math.log(2)) for i=0,num-1 do local j = bit.rev(i,lgn) if j > i then utils._swap(reA, i+1, reA, j+1); utils._swap(inA, i+1, inA, j+1) end end for s=1,lgn do local m = bit.lS(1,s) local reWm, inWm = math.cos(2*math.pi/m), math.sin(2*math.pi/m) if flag==true then inWm = -inWm end local k = 0 while k < num do local reW, inW = 1.0, 0.0 for j=0,math.floor(m/2)-1 do local tag = k + j + math.floor(m / 2); 

               local reT = reW * (reA[tag+1]or 0) - inW * (inA[tag+1]or 0);
               local inT = reW * (inA[tag+1]or 0) + inW * (reA[tag+1]or 0);
               local reU, inU = (reA[k+j+1]or 0), (inA[k+j+1]or 0);
               reA[k+j+1] = reU + reT; inA[k+j+1] = inU + inT;
               reA[tag+1] = reU - reT; inA[tag+1] = inU - inT;
               local reWt = reW * reWm - inW * inWm;
               local inWt = reW * inWm + inW * reWm;
               reW = reWt; inW = inWt;

end k=k+m end end end

function bit.rev(x,_len) local ans = 0 for i=1,_len do ans=bit.lS(ans,1);ans=bit.Or(ans,bit.And(x,1));x=bit.rS(x,1) end return ans end

--能提供給模板調用的進制轉換函數 function p.convertBase(_num, _to, _from, _digs, _precision, _sub) local num, from, to, digs, subarg, precision = tostring(_num) or "0", _from or 10, _to or 10, _digs or 0, _sub or 0, _precision or -1 local from_str, to_str = tostring(_from or ), tostring(_to or ) local default, prefix, suffix = , , local no_from = not _from local is_template = false --從模板讀取參數 if type(_num) == type({}) then local frame = _num local success, args = false, frame is_template = true if type((((type(_num) == type(0)) and {} or _num) or {}).args) == type({}) then success, args = pcall(getArgs, frame, { parentFirst=true }) --frame.args if not success then args = frame.args or frame end end local arg1 = mw.ustring.gsub(mw.text.trim(args[1] or args['1'] or ), "[-−]+", "-") local arg2 = mw.text.trim(args[2] or args['2'] or args.number or args.Number or args.num or args.Num or args.n or args.N or ) local arg3 = mw.text.trim(args[3] or args['3'] or args.width or args.Width or ) local argTo = mw.ustring.gsub(mw.text.trim(args.to or args.To or args.base or args.Base or ), "[-−]+", "-") local argFrom = mw.ustring.gsub(mw.text.trim(args.from or args.From or ), "[-−]+", "-") local argSub = mw.text.trim(args['sub'] or args.Sub or ) local argDefault = args.default or args.Default or local argPrecision = mw.text.trim(args.precision or args.Precision or ) local argPrefix = args.prefix or args.Prefix or local argSuffix = args.suffix or args.Suffix or if arg1 ~= then success, to = pcall(utils.checkSpecialBase, arg1) to = to or arg1 to_str = tostring(arg1) elseif argTo ~= then success, to = pcall(utils.checkSpecialBase, argTo) to = to or argTo to_str = tostring(argTo) end num = tostring(arg2) if arg3 ~= then digs = tonumber(arg3) or 0 end if argFrom ~= then success, from = pcall(utils.checkSpecialBase, argFrom) no_from = not from from = from or argFrom from_str = tostring(argFrom) else no_from = true end if argSub ~= then subarg = tonumber(argSub) or 0 end if argDefault ~= then default = argDefault end if argPrefix ~= then prefix = argPrefix end if argSuffix ~= then suffix = argSuffix end if argPrecision ~= then precision = tonumber(argPrecision) or -1 end if yesno(args.error or args.Error or ) then is_template = false end end

---------------- 例外處理 ---------------- --無限大判斷 (若放任無限大進去計算會無窮迴圈而超時) if utils.isInf(from) then if mw.ustring.find(num, "[,:]") then --判斷是否為多個位數的字串 check_digits = lib_calc._getNumString(num..';') for i=1,#check_digits do if check_digits[1] == 0 then table.remove(check_digits, 1) end end if #check_digits > 1 then --不只一個位數的無限大進制無法轉換 if not is_template then error(string.format("底數不能為 '%s'", from_str),2) end return utils.print_base_string('∞', --硬要說的話其值就是無限大 "", {tonumber("inf")}, {},({mw.ustring.find(num, "[-−]")})[1] and -1 or 1, from, to, subarg, prefix, suffix) end end --只有一個位數的無限大進制就原數輸出 local find_point = mw.ustring.find(num, "%.") local targen_decimal = find_point and mw.ustring.sub(num, 1, find_point-1) or num return p.convertBase({to,targen_decimal,digs,from=10,sub=subarg,default=default,precision=precision,prefix=prefix,error=not is_template}) end if mw.ustring.match(num,"^%s*[+-−]?%s*∞%s*$")then--本身是無限大就不用算了，因為無法計算 return utils.print_base_string(num, "", {tonumber("inf")}, {},({mw.ustring.find(num, "[-−]")})[1] and -1 or 1, from, to, subarg, prefix, suffix) end

--NaN判斷 (若放任NaN進去計算會無窮迴圈而超時) if utils.isNaN(from) then --並非有效的底數，無法轉換 if not is_template then error(string.format("底數不能為 '%s'", from_str),2) end return default end if utils.isNaN(to) then --並非有效的底數，無法轉換 if not is_template then error(string.format("底數不能為 '%s'", to_str),2) end return default end

--大過整數運算範圍的底數無法計算 (誤差導致運算結果不準確) if math.abs(utils.tonumber(from)or 0) > 9007199254740991 and not utils.isInf(from) then if not is_template then error(string.format("底數 '%s' 過大", from_str),2) end return default end if math.abs(utils.tonumber(to)or 0) > 9007199254740991 and not utils.isInf(to) then if not is_template then error(string.format("底數 '%s' 過大", to_str),2) end return default end

--判斷是否為特殊進制 local special_base_data_from, from_error = utils.getSpecialBase(from) local special_base_data_to, to_error = utils.getSpecialBase(to)

if from_error then if not is_template then error(from_error,2) end return default end if to_error then if not is_template then error(to_error,2) end return default end

if (not utils.tonumber(from) and not special_base_data_from) or (not utils.tonumber(to) and not special_base_data_to) then --複數進位制 local success, int_string, frac_string = pcall(utils.complexBaseConvert, num, to, from, digs, precision) if success and int_string then return utils.print_base_string(int_string, frac_string, {}, {}, 1, from, to, subarg, prefix, suffix) elseif not success then local error_result = mw.ustring.match(tostring(int_string or ), '轉換失敗：(.-)。') if error_result then if not is_template then error(error_result, 2) end return default end end end --並非能夠運算的底數 if not utils.tonumber(from) and not special_base_data_from then if not is_template then error(string.format("'%s' 不是有效的底數", from_str),2) end return default end if not utils.tonumber(to) and not special_base_data_to then if not is_template then error(string.format("'%s' 不是有效的底數", to_str),2) end return default end ---------------- 例外處理結束，開始轉換進制 ---------------- local to_num = utils.tonumber(to) or 10 local from_num = utils.tonumber(from) or 10 if math.abs(to_num) < 1 then --base can not less then 1 if not is_template then error("底數的絕對值不能小於1",2) end return default end local sign = 1 num = mw.text.trim(num) if _num == nil or num == then return default end local first_sign = mw.ustring.sub(num,1,1) --讀取正負號 if first_sign == '+' or first_sign == '-' or first_sign == '−' then num = mw.ustring.sub(num,2,-1) if first_sign == '-' or first_sign == '−' then sign = -1 end end --當輸入開頭為'0x'時視為16進制 if no_from or from == 16 then local chex_hex = mw.ustring.sub(num,1,2) if chex_hex == '0x' or chex_hex == '0X' then from = 16 num = mw.ustring.sub(num,3,-1) end end --Fibonacci code word是反向排列的 if (special_base_data_from or {}).name=="fibcode" then local find_point = mw.ustring.find(num, "%.") if find_point then num = mw.ustring.sub(num, 1, find_point-1)end local fibcode2fibbase = for i=1,#num-1 do fibcode2fibbase = mw.ustring.sub(num, i, i) .. fibcode2fibbase end num = fibcode2fibbase..'0' end

local ori_int_digits, ori_fractional_digits = lib_calc._getNumString(num, math.abs(from_num) > 14) --負進制、非整數進制等無法經由長除法整數進制轉整數進制的Case先轉為十進制再做處理 if from_num < -1 or math.abs(utils.myfloor(from_num) - from_num) > 1e-14 or (special_base_data_from or{}).needtoDecimal then if (special_base_data_from or{}).name == 'ContinuedFraction' then local dec_string = tostring(utils.fromContinuedFraction(ori_int_digits, ori_fractional_digits)) ori_int_digits, ori_fractional_digits = lib_calc._getNumString(dec_string, math.abs(from_num) > 14) else local dec_number = utils.toDecimal(ori_int_digits, ori_fractional_digits, from) * sign if dec_number < 0 then sign = -1 dec_number = -dec_number else sign = 1 end ori_int_digits, ori_fractional_digits = lib_calc._getNumString(tostring(dec_number), math.abs(from_num) > 14) end from = 10 end local ori_sign = sign if to_num < 0 then local check = math.abs(to_num) --負底數進制在轉換過程中要連正負號一同考量 if sign < 0 then sign = 1 for i=1,#ori_int_digits do ori_int_digits[i] = -ori_int_digits[i]end for i=1,#ori_fractional_digits do ori_fractional_digits[i] = -ori_fractional_digits[i]end end end local int_digits, fractional_digits = ori_int_digits, ori_fractional_digits if math.abs(utils.myfloor(to_num) - to_num) > 1e-14 or math.abs(from_num + 1) < 1e-14 then --非整數進制的處理 if to_num > 0 then int_digits, fractional_digits, sign = utils.non_integer_base(int_digits, fractional_digits, from, to, sign) else int_digits, fractional_digits, sign = utils.real_negabase(int_digits, fractional_digits, from, to, sign) end for i = #fractional_digits, 1, -1 do if fractional_digits[i] ~= 0 then break else table.remove(fractional_digits, i) end end elseif math.abs(math.abs(to_num) - 1) < 1e-14 then --一進制，自然數中最簡單的進制，輸出跟數字相同數量的1即可 local number = utils.myfloor(utils.toDecimal(ori_int_digits, {}, from)) if math.abs(number) <= 9007199254740991 then --Lua整數運算上限 local base1 = (math.abs(number) > 0) and ((to_num < 0) and ((number < 0) and string.rep('10', math.abs(number)) or ('1' .. ((math.abs(number - 1) < 1e-14) and or string.rep('01', number - 1) )) ) or string.rep('1', math.abs(number))) or '0' if base1:len() < digs then --補齊位數 local lose_digs = digs - base1:len() base1 = string.rep('0', lose_digs) .. base1 end return utils.print_base_string(base1, "", ori_int_digits, {},(to_num < 0) and 1 or sign, from, to, subarg, prefix, suffix) end if not is_template then error(string.format("無法將 '%s' 轉換為底數 '%s' 的進制", num, to_str),2) end return default else --其餘情況即一般情況，使用整數進制轉整數進制的長除法演算法 int_digits = ((special_base_data_to or{}).convertBase or utils._convertBase)(int_digits, from, to, false) fractional_digits = ((special_base_data_to or{}).convertBase or utils._convertBase)(fractional_digits, from, to, true, tonumber(precision<0 and or precision)) if to_num < 0 then int_digits, fractional_digits = utils.negabaseCarry(int_digits, fractional_digits, to_num, ori_sign)end end ---------------- 進制轉換完成，準備輸出數字 ---------------- local int_result, fractional_result = ,

if #int_digits < digs then --補齊整數位數 local lose_digs = digs - #int_digits for i=1,lose_digs do table.insert(int_digits, 1, 0) end end if #fractional_digits < precision then --補齊小數位數 local lose_digs = precision - #fractional_digits for i=1,lose_digs do fractional_digits[#fractional_digits+1] = 0 end end

int_result = utils.printAllDigit(int_digits, to, -1, subarg, false) fractional_result = utils.printAllDigit(fractional_digits, to, precision, subarg, true)

local result = utils.print_base_string(int_result, fractional_result, ori_int_digits, ori_fractional_digits, sign, from, to, subarg, prefix, suffix) return result end

function utils.fromContinuedFraction(int_digits, fractional_digits) local result = p.bigint(0) local calclen = math.floor(#fractional_digits / 6) + 1 for i=#fractional_digits,1,-1 do result = (result + fractional_digits[i]):inverse(calclen + 2) end result:setpoint(calclen) local result = ..(int_digits[1] or 0)..'.'..tostring(result):gsub("^%d+%.","") return result end

function utils.ContinuedFraction(digits, original_base, _destination_base, fractional_flag, total_digit) local result_digits, zero_digits = {}, {} local decimal_string = if not fractional_flag then result_digits = utils._convertBase(digits, original_base, 10, false) for i=1,#result_digits do if math.abs(tonumber(result_digits[1]) or 1) < 1e-14 then table.remove(result_digits, 1) end end decimal_string = table.concat(result_digits, "") if decimal_string == then decimal_string = 0 end return {decimal_string} end result_digits = utils._convertBase(digits, original_base, 10, true) decimal_string = '0.'..table.concat(result_digits, "") zero_digits, result_digits = p.ContinuedFraction(decimal_string, math.ceil(total_digit or (decimal_string:len() * 0.8))) return result_digits end

--以大數運算計算連分數 function p.ContinuedFraction(input_str, _length) local num = input_str local length = tonumber(_length) or 10 local is_template = false local suffix = _suffix or if type(input_str) == type({"table"}) then num = (input_str.args or {})[1] or input_str[1] or length = tonumber((input_str.args or {})[2] or input_str[2] or ) or 4 if input_str.args then is_template = true end elseif type(input_str) ~= type("string") then num = tostring(input_str) end

local input_num = p.bigint(num) local sign = input_num.sign input_num.sign = 1 local calclen = (input_num:length() < 4) and (input_num:length() * 2) or (input_num:length() + 2) local int_part = input_num:clone():setpoint(0) local int_digits, fractional_digits = {tonumber(tostring(int_part))}, {} local it = input_num - int_part local i = 1 while not it:equal(0) do it = it:inverse(calclen) int_part = it:clone():setpoint(0) fractional_digits[#fractional_digits + 1] = tonumber(tostring(int_part)) it = it - int_part if i >= length then break end i = i + 1 end if is_template then return table.concat(int_digits,',') .. ';' .. table.concat(fractional_digits,',') end return int_digits, fractional_digits end

return p

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