builtin prime factor program

src/bin/factor.lua

@@ -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))

src/main.lua

@@ -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