feat: add Mersenne Twister PRNG

Batteries/Data/Random/MersenneTwister.lean

@@ -72,7 +72,7 @@ structure State (cfg : Config) where
 /-- Mersenne Twister initialization given an optional seed. -/
 @[specialize cfg] protected def Config.init (cfg : MersenneTwister.Config)
     (seed : BitVec cfg.wordSize := cfg.initSeed) : State cfg :=
-  ⟨loop seed #[] (Nat.zero_le _), 0, cfg.zero_lt_stateSize⟩
+  ⟨loop seed (.mkEmpty cfg.stateSize) (Nat.zero_le _), 0, cfg.zero_lt_stateSize⟩
 where
   /-- Inner loop for Mersenne Twister initalization. -/
   loop (w : BitVec cfg.wordSize) (v : Array (BitVec cfg.wordSize)) (h : v.size ≤ cfg.stateSize) :=
@@ -81,24 +81,23 @@ where
       let w := cfg.initMult * (w ^^^ (w >>> cfg.wordSize - 2)) + v.size
       loop w v (by simp only [v, Array.size_push]; omega)
 
+/-- Apply the twisting transformation to the given state. -/
+@[specialize cfg] protected def State.twist (state : State cfg) : State cfg :=
+  let i := state.index
+  let i' : Fin cfg.stateSize :=
+    if h : i.val+1 < cfg.stateSize then ⟨i.val+1, h⟩ else ⟨0, cfg.zero_lt_stateSize⟩
+  let y := state.data[i] &&& cfg.uMask ||| state.data[i'] &&& cfg.lMask
+  let x := state.data[i+cfg.shiftSize] ^^^ bif y[0] then y >>> 1 ^^^ cfg.xorMask else y >>> 1
+  ⟨state.data.set i x, i'⟩
+
 /-- Update the state by a number of generation steps (default 1). -/
-@[specialize cfg] protected def State.update (state : State cfg) (steps := 1) : State cfg :=
-  loop state steps
-where
-  /-- Inner loop for Mersenne Twister update. -/
-  @[inline] loop (s : State cfg) (c : Nat) : State cfg :=
-    if c = 0 then s else
-      let i := s.index
-      let i' : Fin cfg.stateSize :=
-        if h : i.val+1 < cfg.stateSize then ⟨i.val+1, h⟩ else ⟨0, cfg.zero_lt_stateSize⟩
-      let y := s.data[i] &&& cfg.uMask ||| s.data[i'] &&& cfg.lMask
-      let x := s.data[i+cfg.shiftSize] ^^^ bif y[0] then y >>> 1 ^^^ cfg.xorMask else y >>> 1
-      loop ⟨s.data.set i x, i'⟩ (c-1)
+@[inline] protected def State.update (state : State cfg) (steps := 1) : State cfg :=
+  if steps = 0 then state else state.twist.update (steps-1)
 
 /-- Mersenne Twister iteration. -/
 @[specialize cfg] protected def State.next (state : State cfg) : BitVec cfg.wordSize × State cfg :=
   let i := state.index
-  let s := state.update
+  let s := state.twist
   (temper s.data[i], s)
 where
   /-- Tempering step for Mersenne Twister. -/