1	import Base
2	import 0x9ee2e9a299991dcc089fe22c7f3ceb5f/src/containers/bitset.bend as BitWords
3	import 0x9ee2e9a299991dcc089fe22c7f3ceb5f/src/math/pow2.bend as Pow2
4	
5	# Pure indexed bit tree.
6	#
7	# A non-empty BitTree is a perfect binary tree whose leaves are U32 words.
8	# `words` is the logical word count; `capacity` is the power-of-two leaf
9	# capacity, and `height` is log2(capacity). Leaves at indexes >= words are
10	# padding. A word index follows its `height`-bit binary representation from
11	# most-significant bit at the root to least-significant bit at the leaf.
12	#
13	# The empty value is represented by Empty{} with all metadata zero. Bit
14	# indexes outside [0, words * 32) are total: test returns False{} and set is
15	# the identity.
16	
17	# Represent WordTree data used by the packed bit-tree operations.
18	type WordTree is Data:
19	  Empty{}
20	  Leaf{word: U32}
21	  Fork{left: WordTree, right: WordTree}
22	
23	# Represent BitTree data used by the packed bit-tree operations.
24	type BitTree is Data:
25	  BT{root: WordTree, words: Nat, capacity: Nat, height: Nat}
26	
27	# Represent Plan data used by the packed bit-tree operations.
28	type Plan is Data:
29	  Plan{capacity: Nat, height: Nat}
30	
31	# Find the least power of two >= need. `fuel = need` is a conservative
32	# termination bound; each non-final step doubles capacity.
33	def plan_go(fuel: Nat, +need: Nat, +capacity: Nat, +height: Nat, done: Bool) -> Plan:
34	  match fuel:
35	    case 0n:
36	      Plan{capacity, height}
37	    case 1n+f:
38	      match done:
39	        case True{}:
40	          Plan{capacity, height}
41	        case False{}:
42	          +next = Nat.double(capacity)
43	          plan_go(f, need, next, Nat.add(height, 1n), Nat.is_le(need, next))
44	
45	# Handle plan in the packed bit-tree operations.
46	def plan(+need: Nat) -> Plan:
47	  match need:
48	    case 0n:
49	      Plan{0n, 0n}
50	    case 1n+n:
51	      plan_go(need, need, 1n, 0n, Nat.is_le(need, 1n))
52	
53	# Independent subtrees are built in parallel.
54	def zero_tree(+height: Nat) -> WordTree:
55	  match height:
56	    case 0n:
57	      Leaf{0}
58	    case 1n+h:
59	      left right = zero_tree(h) zero_tree(h)
60	      Fork{left, right}
61	
62	# Create from plan for the packed bit-tree operations.
63	def new_from_plan(words: Nat, plan: Plan) -> BitTree:
64	  match plan:
65	    case Plan{capacity, +height}:
66	      BT{zero_tree(height), words, capacity, height}
67	
68	# Handle new in the packed bit-tree operations.
69	def new(+words: Nat) -> BitTree:
70	  match words:
71	    case 0n:
72	      BT{Empty{}, 0n, 0n, 0n}
73	    case 1n+n:
74	      new_from_plan(words, plan(words))
75	
76	# Metadata helpers intended to keep representation laws independent of field
77	# layout.
78	def word_count(tree: BitTree) -> Nat:
79	  match tree:
80	    case BT{root, words, capacity, height}:
81	      words
82	
83	# Handle bit count in the packed bit-tree operations.
84	def bit_count(tree: BitTree) -> Nat:
85	  Nat.mul(word_count(tree), 32n)
86	
87	# Check whether bit holds for the packed bit-tree operations.
88	def valid_bit(tree: BitTree, bit: Nat) -> Bool:
89	  Nat.is_lt(bit, bit_count(tree))
90	
91	# Build the root-to-leaf path by consuming low bits while prepending them.
92	def path_bit(rem: Nat) -> Bool:
93	  match rem:
94	    case 0n:
95	      False{}
96	    case 1n+r:
97	      True{}
98	
99	# Handle index path in the packed bit-tree operations.
100	def index_path(height: Nat, +index: Nat, acc: List<&2, Bool>) -> List<&2, Bool>:
101	  match height:
102	    case 0n:
103	      acc
104	    case 1n+h:
105	      index_path(h, Nat.div(index, 2n), Con{path_bit(Nat.mod(index, 2n)), acc})
106	
107	# Handle tree word in the packed bit-tree operations.
108	def tree_word(path: List<&2, Bool>, tree: WordTree) -> U32:
109	  match path tree:
110	    case Nil{} Empty{}:
111	      0
112	    case Nil{} Leaf{word}:
113	      word
114	    case Nil{} Fork{left, right}:
115	      0
116	    case Con{side, rest} Empty{}:
117	      0
118	    case Con{side, rest} Leaf{word}:
119	      0
120	    case Con{False{}, rest} Fork{left, right}:
121	      tree_word(rest, left)
122	    case Con{True{}, rest} Fork{left, right}:
123	      tree_word(rest, right)
124	
125	# Handle tree set word in the packed bit-tree operations.
126	def tree_set_word(path: List<&2, Bool>, value: U32, tree: WordTree) -> WordTree:
127	  match path tree:
128	    case Nil{} Empty{}:
129	      Empty{}
130	    case Nil{} Leaf{word}:
131	      Leaf{value}
132	    case Nil{} Fork{left, right}:
133	      Fork{left, right}
134	    case Con{side, rest} Empty{}:
135	      Empty{}
136	    case Con{side, rest} Leaf{word}:
137	      Leaf{word}
138	    case Con{False{}, rest} Fork{left, right}:
139	      Fork{tree_set_word(rest, value, left), right}
140	    case Con{True{}, rest} Fork{left, right}:
141	      Fork{left, tree_set_word(rest, value, right)}
142	
143	# Handle word at if in the packed bit-tree operations.
144	def word_at_if(inside: Bool, tree: BitTree, index: Nat) -> U32:
145	  match inside:
146	    case False{}:
147	      0
148	    case True{}:
149	      match tree:
150	        case BT{root, words, capacity, height}:
151	          tree_word(index_path(height, index, Nil{}), root)
152	
153	# Safe logical-word lookup; padding leaves are not externally addressable.
154	def word_at(+tree: BitTree, +index: Nat) -> U32:
155	  word_at_if(Nat.is_lt(index, word_count(tree)), tree, index)
156	
157	# Replace word if for the packed bit-tree operations.
158	def replace_word_if(inside: Bool, tree: BitTree, index: Nat, value: U32) -> BitTree:
159	  match inside:
160	    case False{}:
161	      tree
162	    case True{}:
163	      match tree:
164	        case BT{root, words, capacity, +height}:
165	          BT{tree_set_word(index_path(height, index, Nil{}), value, root), words, capacity, height}
166	
167	# Safe logical-word update. This helper makes metadata preservation and
168	# unaffected-word laws direct to state.
169	def replace_word(+tree: BitTree, +index: Nat, value: U32) -> BitTree:
170	  replace_word_if(Nat.is_lt(index, word_count(tree)), tree, index, value)
171	
172	# Update if for the packed bit-tree operations.
173	def set_if(inside: Bool, +tree: BitTree, +bit: Nat) -> BitTree:
174	  match inside:
175	    case False{}:
176	      tree
177	    case True{}:
178	      +index = Nat.div(bit, 32n)
179	      +old = word_at(tree, index)
180	      replace_word(tree, index, BitWords.word_put(True{}, old, Nat.mod(bit, 32n)))
181	
182	# Set one logical bit. Out-of-range indexes leave the tree unchanged.
183	def set(+tree: BitTree, +bit: Nat) -> BitTree:
184	  set_if(valid_bit(tree, bit), tree, bit)
185	
186	# Handle test if in the packed bit-tree operations.
187	def test_if(inside: Bool, +tree: BitTree, +bit: Nat) -> Bool:
188	  match inside:
189	    case False{}:
190	      False{}
191	    case True{}:
192	      BitWords.word_get(word_at(tree, Nat.div(bit, 32n)), Nat.mod(bit, 32n))
193	
194	# Test one logical bit. Out-of-range indexes, including every index in the
195	# zero-word tree, return False{}.
196	def test(+tree: BitTree, +bit: Nat) -> Bool:
197	  test_if(valid_bit(tree, bit), tree, bit)
198	
199	# Word-wise union for chunked Bloom builds. Both sides always share the exact
200	# shape (same height from the same bit count); mismatched arms are unreachable
201	# by construction and keep the Fork side.
202	def union_bits(ta: WordTree, tb: WordTree) -> WordTree:
203	  match ta tb:
204	    case Empty{} Empty{}:
205	      Empty{}
206	    case Empty{} Leaf{wb}:
207	      Leaf{wb}
208	    case Empty{} Fork{lb, rb}:
209	      Fork{lb, rb}
210	    case Leaf{wa} Empty{}:
211	      Leaf{wa}
212	    case Leaf{wa} Leaf{wb}:
213	      Leaf{U32.or(wa, wb)}
214	    case Leaf{wa} Fork{lb, rb}:
215	      Fork{lb, rb}
216	    case Fork{la, ra} Empty{}:
217	      Fork{la, ra}
218	    case Fork{la, ra} Leaf{wb}:
219	      Fork{la, ra}
220	    case Fork{la, ra} Fork{lb, rb}:
221	      Fork{union_bits(la, lb), union_bits(ra, rb)}
222	
223	# Structural checker for the exact perfect-tree shape described by metadata.
224	def shape_ok(+height: Nat, tree: WordTree) -> Bool:
225	  match height tree:
226	    case 0n Empty{}:
227	      False{}
228	    case 0n Leaf{word}:
229	      True{}
230	    case 0n Fork{left, right}:
231	      False{}
232	    case 1n+h Empty{}:
233	      False{}
234	    case 1n+h Leaf{word}:
235	      False{}
236	    case 1n+h Fork{left, right}:
237	      a b = shape_ok(h, left) shape_ok(h, right)
238	      Bool.and(a, b)
239	
240	# Check whether whether metadata ok holds for the packed bit-tree operations.
241	def empty_metadata_ok(words: Nat, capacity: Nat, height: Nat) -> Bool:
242	  Bool.and(Nat.is_eq(words, 0n), Bool.and(Nat.is_eq(capacity, 0n), Nat.is_eq(height, 0n)))
243	
244	# Handle nonempty metadata ok in the packed bit-tree operations.
245	def nonempty_metadata_ok(root: WordTree, +words: Nat, +capacity: Nat, +height: Nat) -> Bool:
246	  Bool.and(
247	    Nat.is_gt(words, 0n),
248	    Bool.and(
249	      Nat.is_le(words, capacity),
250	      Bool.and(
251	        Nat.is_eq(capacity, Pow2.pow2t(height)),
252	        shape_ok(height, root))))
253	
254	# Checks zero canonicality, logical bounds, power-of-two capacity, height, and
255	# exact tree shape. It does not require padding words to remain zero.
256	def well_formed(tree: BitTree) -> Bool:
257	  match tree:
258	    case BT{Empty{}, words, capacity, height}:
259	      empty_metadata_ok(words, capacity, height)
260	    case BT{root, words, capacity, height}:
261	      nonempty_metadata_ok(root, words, capacity, height)