random: port Alea, one generator per character

pqcli used Python's global Mersenne Twister, seeded once from the clock.
Upstream uses Johannes Baagøe's Alea, with Random(n) = uint32() % n, and
keeps the generator state with each character. The port matches the JS
output bit for bit, including UTF-16 seeding of non-BMP characters.

Each Player now owns an Alea that is pickled with the save, and
Simulation.tick draws from it. Saves without one get a fresh generator.
As upstream does, a new character's game continues from the state the
kept stat roll was made from.

The parity traces are re-recorded, since every random number changes.

pqcli/random.py

@@ -1,9 +1,104 @@
-import random
+import contextlib
+import time
 import typing as T
 
+RngState = T.Tuple[float, float, float, int]
+
+_2_POW_32 = 0x100000000
+_2_POW_MINUS_32 = 2.3283064365386963e-10
+
+
+def _to_uint32(value: float) -> float:
+    # JS `value >>> 0` for the non-negative values Mash produces
+    return float(int(value) % _2_POW_32)
+
+
+def _mash() -> T.Callable[[str], float]:
+    n = float(0xEFC8249D)
+
+    def mash(data: str) -> float:
+        nonlocal n
+        # JS strings are UTF-16, and charCodeAt() returns code units
+        units = data.encode("utf-16-le")
+        for i in range(0, len(units), 2):
+            n += units[i] | (units[i + 1] << 8)
+            h = 0.02519603282416938 * n
+            n = _to_uint32(h)
+            h -= n
+            h *= n
+            n = _to_uint32(h)
+            h -= n
+            n += h * _2_POW_32
+        return _to_uint32(n) * _2_POW_MINUS_32
+
+    return mash
+
+
+class Alea:
+    """Johannes Baagøe's Alea PRNG (MIT), as used by Progress Quest web.
+
+    Ported bit for bit so that games seeded alike play out alike. Saves
+    pickle this class by import path, so it must stay in this module.
+    """
+
+    def __init__(self, *args: str) -> None:
+        if not args:
+            args = (str(int(time.time() * 1000)),)
+        mash = _mash()
+        self._s0 = mash(" ")
+        self._s1 = mash(" ")
+        self._s2 = mash(" ")
+        self._c = 1
+        for arg in args:
+            self._s0 -= mash(arg)
+            if self._s0 < 0:
+                self._s0 += 1
+            self._s1 -= mash(arg)
+            if self._s1 < 0:
+                self._s1 += 1
+            self._s2 -= mash(arg)
+            if self._s2 < 0:
+                self._s2 += 1
+
+    @classmethod
+    def from_state(cls, state: RngState) -> "Alea":
+        rng = cls.__new__(cls)
+        rng._s0, rng._s1, rng._s2, rng._c = state
+        return rng
+
+    def state(self) -> RngState:
+        return (self._s0, self._s1, self._s2, self._c)
+
+    def random(self) -> float:
+        t = 2091639 * self._s0 + self._c * _2_POW_MINUS_32
+        self._s0 = self._s1
+        self._s1 = self._s2
+        self._c = int(t)
+        self._s2 = t - self._c
+        return self._s2
+
+    def uint32(self) -> int:
+        return int(self.random() * _2_POW_32)
+
+
+_current = Alea()
+
 
 def seed(source: str) -> None:
-    random.seed(source.encode())
+    global _current
+    _current = Alea(source)
+
+
+@contextlib.contextmanager
+def using(rng: Alea) -> T.Iterator[None]:
+    """Draw from rng instead of the shared generator inside the block."""
+    global _current
+    previous = _current
+    _current = rng
+    try:
+        yield
+    finally:
+        _current = previous
 
 
 def choice(source: T.Sequence[T.Any]) -> T.Any:
@@ -15,7 +110,7 @@ def choice_low(source: T.Sequence[T.Any]) -> T.Any:
 
 
 def below(num: int) -> int:
-    return random.randint(0, num - 1)
+    return _current.uint32() % num
 
 
 def below_low(num: int) -> int: