Prime multiplication

--require "PNumber"
--require "factoredNumber"

local CLASS = require "middleclass.middleclass"

fNumber256 = CLASS("fNumber256")

function fNumber256:initialize(n)
  --self.decimal = n
  self.primeTable = getPrimeFactorsTable(n) -- 128 = {[2]=7} ...
  --self.factored = {factorize(n)}
end

function fNumber256:getDecimal()
  local result = 1
  for k,v in pairs(self.primeTable) do
    result = result*k^v
  end
  return result
end

function fNumber256:mult(b)
  for k,v in pairs(b.primeTable) do
    self.primeTable[k] = (self.primeTable[k] or 0) + (b.primeTable[k] or 0)
  end
end

function fNumber256:div(b)
  for k,v in pairs(b.primeTable) do
    self.primeTable[k] = (self.primeTable[k] or 0) - (b.primeTable[k] or 0)
  end
end

local floor, infinite = math.floor, math.huge
factorsTable = {}

primes = setmetatable({2,3--[[just hard-code the even special case and following number]]}, {__index = function(self, index)
  if type(index) == 'number' then
    for i=#self,index-1 do local dummy = self[i] end -- Precalculate previous primes to avoid building up a stack
    for candidate = self[index-1] + 2--[[All primes >2 are odd]], infinite do
      local half = floor(candidate/2)
      for i=1,index-1 do
        local div = self[i]
        if div > half then rawset(self, index, candidate); return candidate end -- A number can't possibly be divisible by something greater than its half
        if candidate % div == 0 then break end -- Candidate is divisible by a prime, this not prime itself
      end
    end
  end
end})

prime256table =
{[0] = 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251}

inversePrime256table =
{[2]=0,[3]=1,[5]=2,[7]=3,[11]=4,[13]=5,[17]=6,[19]=7,[23]=8,[29]=9,[31]=10,[37]=11,[41]=12,[43]=13,[47]=14,[53]=15,[59]=16,[61]=17,[67]=18,[71]=19,[73]=20,[79]=21,[83]=22,[89]=23,[97]=24,[101]=25,[103]=26,[107]=27,[109]=28,[113]=29,[127]=30,[131]=31,[137]=32,[139]=33,[149]=34,[151]=35,[157]=36,[163]=37,[167]=38,[173]=39,[179]=40,[181]=41,[191]=42,[193]=43,[197]=44,[199]=45,[211]=46,[223]=47,[227]=48,[229]=49,[233]=50,[239]=51,[241]=52,[251]=53}

function factorize(subject)
  if subject == 1 then
    return -- Can be ommitted for implicit return ;)
  elseif subject > 0 then
    for i=1, infinite do
      local candidate = primes[i]
        if subject % candidate == 0 then
          return candidate, factorize(subject/candidate)
        end
    end
  else
    return nil, "Can't be bothered to look up if negative numbers have a prime factorization"
  end
end

---Checks to see if a number is prime or not
function isPrimeExp(n)
    --primesExp={}
    if n<=0 then return false end
    if n<=2 then return true end
    if (n%2==0) then return false end
    for i=3,n/2,2 do
        if (n%i==0) then return false end
    end
    return true
end

function generateFactorsTable(n)
  for i = 2, n do
    factorsTable[i]={factorize(i)}
  end
end

function multFactoredNumber(a,b)
  for i=1,#b do
    a[#a+1] = b[i]
  end
  return a
end

function getPrimeFactorsTable(n)
  local t = {factorize(n)}
  local result = {}
  for k,v in ipairs(t) do
    result[v] = (result[v] or 0)+1
  end
  return result
end

function divideFactoredNumber(a,b)
  for i=1,#b do
    a[#a+1] = b[i]
  end
  return a
end

generateFactorsTable(256)

if arg[#arg] == "-debug" then require("mobdebug").start() end

n1 = 255
n2 = 123

p1 = fNumber256:new(255) -- 3x5x17
p2 = fNumber256:new(123) -- 3x41

---- test prime multiplication -----
before = os.time()

for i = 1, 100000000 do
  p1:mult(p2)

end

for i = 1, 100000000 do
  p1:div(p2)
end

after = os.time()
print("answer: "..p1:getDecimal())
print("prime multiplication takes ".. after - before.. " sec")
--------------------------------------

---- test regular multiplication ----- DOESNT WORK!!!!!!
--[[before = os.time()

for i = 1, 100000000 do
  n1 = n1 * n2

end

for i = 1, 100000000 do
  n1 = n1 / n2
end

after = os.time()
print("answer: "..n1)
print("regular multiplication takes ".. after - before.. " sec")
--------------------------------------]]