add RNG reversal script

Lua/RNG index.lua

@@ -0,0 +1,192 @@
+-- Random Number Generator reversal script for Bizhawk
+-- original algorithm by trivial171 (rng, v2, rnginverse functions)
+-- please refer to this video: https://www.youtube.com/watch?v=-9YLCoK5K6o
+-- everything else by notwa
+
+local abs = math.abs
+local floor = math.floor
+local pow = math.pow
+
+-- Lua 5.3 is nice and precise and doesn't coerce everything into doubles.
+local precise = 0xDEADBEEF * 0x12345678 % 0x100000000 == 0x5621CA08
+
+-- constants of the LCG:
+local m = 1664525    -- 0x0019660D
+local b = 1013904223 -- 0x3C6EF35F
+local gcd = 4 -- of m and 2^32
+
+local powers = {}
+for i = 1, 32 do
+    powers[i] = floor(pow(2, i - 1))
+end
+local big32 = floor(pow(2, 32))
+
+local gamedb = {
+    -- pairs of (RNG state address, display list address):
+    -- Ocarina of Time (J) 1.0
+    ["C892BBDA3993E66BD0D56A10ECD30B1EE612210F"] = {0x105440, 0x11F290},
+    -- Ocarina of Time (U) 1.0
+    ["AD69C91157F6705E8AB06C79FE08AAD47BB57BA7"] = {0x105440, 0x11F290},
+    -- Ocarina of Time (J) 1.2
+    ["FA5F5942B27480D60243C2D52C0E93E26B9E6B86"] = {0x105A80, 0x11F958},
+    -- Ocarina of Time (U) 1.2
+    ["41B3BDC48D98C48529219919015A1AF22F5057C2"] = {0x105A80, 0x11F958},
+    -- Majora's Mask (J) 1.0
+    ["5FB2301AACBF85278AF30DCA3E4194AD48599E36"] = {0x098550, 0x1F9E28},
+    -- Majora's Mask (J) 1.1
+    ["41FDB879AB422EC158B4EAFEA69087F255EA8589"] = {0x098490, 0x1FA0D8},
+    -- Majora's Mask (U) 1.0
+    ["D6133ACE5AFAA0882CF214CF88DABA39E266C078"] = {0x097530, 0x1F9CB8},
+    -- Doubutsu no Mori (J) 1.0
+    ["E106DFF7146F72415337C96DEB14F630E1580EFB"] = {0x03C590, 0x145080},
+}
+
+local function mulmod(a, b, q)
+    if precise then return a * b % q end
+
+    -- this needs to be done because old versions of Lua
+    -- store everything as doubles. that means we have 52 bits
+    -- to work with instead of the 64 that Lua 5.3 provides.
+    local limit = 0x10000000000000
+    local halflimit = 0x4000000 -- half in terms of bits
+--  assert(abs(a) < limit)
+--  assert(abs(b) < limit)
+--  assert(abs(q) <= limit)
+
+    local L = halflimit -- shorthand
+    local a_lo = a % L
+    local a_hi = floor(a / L) % L
+    local b_lo = b % L
+    local b_hi = floor(b / L) % L
+    return (a_lo * b_lo + (a_lo * b_hi % L + a_hi * b_lo % L) % L * L) % q
+end
+
+local function powmod(b, e, m)
+    -- blatantly lifted from Wikipedia and tweaked for overflows.
+    if m == 1 then
+        return 0
+    else
+        local r = 1
+        b = b % m
+        while e > 0 do
+            if e % 2 == 1 then
+                r = mulmod(r, b, m)
+            end
+            e = floor(e / 2)
+            b = mulmod(b, b, m)
+        end
+        return r
+    end
+end
+
+local function mul32(a, b)
+    return mulmod(a, b, big32)
+end
+
+local function inv32(x)
+    -- Modular inverse of x, an odd number.
+    -- via https://lemire.me/blog/2017/09/18/computing-the-inverse-of-odd-integers/
+--  assert(x % 2, "inv32(x): x must be odd!")
+    local y = x % big32
+    for i = 1, 4 do
+        y = mul32(y, (2 - mul32(y, x)))
+    end
+    return y
+end
+
+local const = floor((m - 1) / gcd)
+local const_inv = inv32(const)
+
+local function rng(x)
+    -- The xth RNG value returned by the game.
+    -- Computable by geometric series formula:
+    -- RNG(x) = b * (m^x - 1) / (m - 1) % q
+    -- The denominator (m-1) shares a common factor of 4 with q,
+    -- so we compute the numerator mod 4q.
+    -- We divide by (m-1) by first dividing by 4,
+    -- and then multiplying by the modular inverse of the odd number (m-1)/4.
+    local temp = floor((powmod(m, x, gcd * big32) - 1) / gcd)
+    return mul32(mul32(b, temp), const_inv)
+end
+
+local function v2(a)
+    -- The 2-adic valuation of a; that is,
+    -- the largest integer v such that 2^v divides a.
+    if a == 0 then return 100 end -- a large dummy value
+    local n = a
+    local v = 0
+    while n % 2 == 0 do
+        n = floor(n / 2)
+        v = v + 1
+    end
+    return v
+end
+
+local function rnginverse(r)
+    -- Given an RNG value r, compute the unique x in range [0, 2^32)
+    -- such that RNG(x) = r. Note that x is only unique under the assumption
+    -- that the Linear Congruential Generator used has a period of 2^32.
+
+    -- Recover m^x mod 4q from algebra (inverting steps in RNG function above)
+    local q = big32 * gcd
+    local xpow = (mul32(mul32(r, const), inv32(b)) * gcd + 1) % q
+
+    local xguess = 0
+    for _, p in ipairs(powers) do -- Guess binary digits of x one by one
+        -- This technique is based on Mihai's lemma / lifting the exponent
+        local lhs = v2(powmod(m, xguess + p, q) - xpow)
+        local rhs = v2(powmod(m, xguess,     q) - xpow)
+        if lhs > rhs then
+            xguess = xguess + p
+        end
+    end
+    return xguess
+end
+
+if m == 1664525 and b == 1013904223 then
+    -- self-tests:
+    assert(inv32(m - 1) == 4211439296)
+    assert(rng(0) == 0)
+    assert(rng(1) == 1013904223)
+    assert(rng(2) == 1196435762)
+    assert(rng(3) == 3519870697)
+    assert(1 == rnginverse(1013904223))
+    assert(2 == rnginverse(1196435762))
+    assert(3 == rnginverse(3519870697))
+end
+
+-- run the remaining code when executed in Bizhawk, otherwise exit.
+if rawget(_G, "bizstring") == nil then return end
+
+local R4 = mainmemory.read_u32_be
+
+local hash = gameinfo.getromhash()
+local addrs = gamedb[hash]
+if addrs == nil then
+    print("unsupported ROM:")
+    print(hash)
+    return
+end
+
+local ind_prev = nil
+local dlist_prev = 0
+local ind_change = 0
+
+while true do
+    local seed = R4(addrs[1])
+    local dlist = R4(addrs[2])
+    local ind = rnginverse(seed)
+
+    gui.text(8,  8, ("RNG:  0x%08X"):format(seed),       nil, "topright")
+    gui.text(8, 24, ("index:  0x%08X"):format(ind),      nil, "topright")
+    gui.text(8, 40, ("delta: %+11i"):format(ind_change), nil, "topright")
+
+    if dlist ~= dlist_prev and ind_prev ~= nil then
+        ind_change = ind - ind_prev
+    end
+
+    ind_prev = ind
+    dlist_prev = dlist
+
+    emu.frameadvance()
+end