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builtin prime factor program

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This commit is contained in:
osmarks 2021-02-05 12:58:04 +00:00
parent 49eaf55b95
commit b23652ad92
2 changed files with 146 additions and 2 deletions
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140
src/bin/factor.lua Normal file
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@ -0,0 +1,140 @@
local function gen_vers()
return ("%d.%d.%d"):format(math.random(0, 4), math.random(0, 20), math.random(0, 8))
end
local vers = potatOS.registry.get "potatOS.factor_version"
if not vers then
vers = gen_vers()
potatOS.registry.set("potatOS.factor_version", vers)
end
print(fs.getName(shell.getRunningProgram()) - "%.lua$", "v" .. vers)
local x
repeat
write "Provide an integer to factorize: "
x = tonumber(read())
if not x or math.floor(x) ~= x then print("That is NOT an integer.") end
until x
if x > (2^40) then print("WARNING: Number is quite big. Due to Lua floating point limitations, draconic entities MAY be present. If this runs for several seconds, it's probably frozen due to this.") end
local floor, abs, random, log, pow = math.floor, math.abs, math.random, math.log, math.pow
local function gcd(x, y)
local r = x % y
if r == 0 then return y end
return gcd(y, r)
end
local function eps_compare(x, y)
return abs(x - y) < 1e-14
end
local function modexp(a, b, n)
if b == 0 then return 1 % n end
if b == 1 then return a % n end
local bdiv2 = b / 2
local fbdiv2 = floor(bdiv2)
if eps_compare(bdiv2, fbdiv2) then
-- b is even, so it is possible to just modexp with HALF the exponent and square it (mod n)
local x = modexp(a, fbdiv2, n)
return (x * x) % n
else
-- not even, so subtract 1 (this is even), modexp that, and multiply by a again (mod n)
return (modexp(a, b - 1, n) * a) % n
end
end
local bases = {2, 3, 5, 7, 11, 13, 17, 19}
local primes = {}
for _, k in pairs(bases) do primes[k] = true end
local function is_probably_prime(n)
if primes[n] then return true end
if n > 2 and n % 2 == 0 then return false end
-- express n as 2^r * d + 1
-- by dividing n - 1 by 2 until this is no longer possible
local d = n - 1
local r = 0
while true do
local ddiv = d / 2
if ddiv == floor(ddiv) then
r = r + 1
d = ddiv
else
break
end
end
sleep()
for _, a in pairs(bases) do
local x = modexp(a, d, n)
if x == 1 or x == n - 1 then
-- continue looping
else
local c = true
for i = 2, r do
x = (x * x) % n
if x == n - 1 then c = false break end
end
if c then
return false
end
end
end
primes[n] = true
return true
end
local function is_power(n)
local i = 2
while true do
local x = pow(n, 1/i)
if x == floor(x) then
return i, x
elseif x < 2 then return end
i = i + 1
end
end
local function insertmany(xs, ys)
for _, y in pairs(ys) do table.insert(xs, y) end
end
-- pollard's rho algorithm
-- it iterates again if it doesn't find a factor in one iteration, which causes infinite loops for actual primes
-- so a Miller-Rabin primality test is used to detect these (plus optimization for small primes); this will work for any number Lua can represent accurately, apparently
-- this also checks if something is an integer power of something else
-- You may argue that this is "stupid" and "pointless" and that "trial division would be faster anyway, the numbers are quite small" in which case bee you.
local function factor(n, c)
if is_probably_prime(n) then return {n} end
local p, q = is_power(n)
if p then
local qf = factor(q)
local o = {}
for i = 1, p do
insertmany(o, qf)
end
return o
end
local c = (c or 0) + random(1, 1000)
local function g(x) return ((x * x) + c) % n end
local x, y, d = 2, 2, 1
local count = 0
while d == 1 do
x = g(x)
y = g(g(y))
d = gcd(abs(x - y), n)
count = count + 1
if count % 1e6 == 0 then sleep() end
end
if d == n then return factor(n, c) end
local facs = {}
insertmany(facs, factor(d))
insertmany(facs, factor(n / d))
return facs
end
local facs = factor(x)
if (potatOS.is_uninstalling and potatOS.is_uninstalling()) and x > 1e5 then
for k, v in pairs(facs) do facs[k] = facs[k] + random(-1000, 1000) end
end
print("Factors:", unpack(facs))

8
src/main.lua
View File

@ -1081,6 +1081,7 @@ local function run_with_sandbox()
end
end
local is_uninstalling = false
-- PotatOS API functionality
local potatOS = {
ecc = require "ecc",
@ -1148,12 +1149,14 @@ local function run_with_sandbox()
full_build = full_build,
-- Just pass on the hidden-ness option to the PotatoBIOS code.
hidden = registry.get "potatOS.hidden" or settings.get "potatOS.hidden",
is_uninstalling = function() return is_uninstalling end,
-- Allow uninstallation of potatOS with the simple challenge of factoring a 14-digit or so (UPDATE: ~10) semiprime.
-- Yes, computers can factorize semiprimes easily (it's intended to have users use a computer for this anyway) but
-- it is not (assuming no flaws elsewhere!) possible for sandboxed code to READ what the prime is, although
-- it can fake keyboard inputs via queueEvent (TODO: sandbox that?)
begin_uninstall_process = function()
if settings.get "potatOS.pjals_mode" then error "Protocol Omega Initialized. Access Denied." end
is_uninstalling = true
math.randomseed(secureish_randomseed)
secureish_randomseed = math.random(0xFFFFFFF)
print "Please wait. Generating semiprime number..."
@ -1163,11 +1166,11 @@ local function run_with_sandbox()
print("Please find the prime factors of the following number (or enter 'quit') to exit:", num)
write "Factor 1: "
local r1 = read()
if r1 == "quit" then return end
if r1 == "quit" then is_uninstalling = false return end
local f1 = tonumber(r1)
write "Factor 2: "
local r2 = read()
if r2 == "quit" then return end
if r2 == "quit" then is_uninstalling = false return end
local f2 = tonumber(r2)
if (f1 == p1 and f2 == p2) or (f1 == p2 and f2 == p1) then
term.clear()
@ -1180,6 +1183,7 @@ local function run_with_sandbox()
})
print("Factors", f1, f2, "invalid.", p1, p2, "expected. This incident has been reported.")
end
is_uninstalling = false
end,
--[[
Fix bug PS#5A1549BE