/
partitions.py
378 lines (313 loc) · 12.7 KB
/
partitions.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
from typing import List, Any, Generator
from ast import parse
from .base import Formula
from ..op import OpType, CodeOp
from .graph import FormulaGraph, CodeOpNode, ConstantNode, Node, CodeFormula
from .fliparoo import find_fliparoos, AddFliparoo, MulFliparoo
from copy import deepcopy
def reduce_all_adds(formula: Formula, rename=True) -> CodeFormula:
graph = FormulaGraph(formula, rename=rename)
add_fliparoos = find_single_input_add_fliparoos(graph)
for add_fliparoo in add_fliparoos:
reduce_add_fliparoo(add_fliparoo, copy=False)
reduce_all_XplusX(graph)
mul_fliparoos = find_constant_mul_fliparoos(graph)
for mul_fliparoo in mul_fliparoos:
reduce_mul_fliparoo(mul_fliparoo, copy=False)
return graph.to_formula("reduce_add")
def expand_all_muls(formula: Formula, rename=True) -> CodeFormula:
graph = FormulaGraph(formula, rename)
enodes = find_expansion_nodes(graph)
for enode in enodes:
expand_mul(graph, enode, copy=False)
return graph.to_formula("expand_mul")
def expand_all_nopower2_muls(formula: Formula, rename=True) -> CodeFormula:
graph = FormulaGraph(formula, rename)
enodes = find_expansion_nodes(graph, nopower2=True)
for enode in enodes:
expand_mul(graph, enode, copy=False)
return graph.to_formula("expand_np2mul")
def find_single_input_add_fliparoos(graph: FormulaGraph) -> List[AddFliparoo]:
fliparoos = find_fliparoos(graph, AddFliparoo)
single_input_fliparoos = []
for fliparoo in fliparoos:
found = False
for i in range(len(fliparoo), 1, -1):
subfliparoo = fliparoo.slice(0, i)
if len(set(subfliparoo.input_nodes())) == 1:
found = True
break
if found:
s = subfliparoo.slice(0, i)
single_input_fliparoos.append(s)
return single_input_fliparoos
def find_constant_mul_fliparoos(graph: FormulaGraph) -> List[MulFliparoo]:
fliparoos = find_fliparoos(graph, MulFliparoo)
constant_mul_fliparoo = []
for fliparoo in fliparoos:
found = False
for i in range(len(fliparoo), 1, -1):
subfliparoo = fliparoo.slice(0, i)
nonconstant_inputs = list(
filter(
lambda x: not isinstance(x, ConstantNode), subfliparoo.input_nodes()
)
)
if len(nonconstant_inputs) != 1:
continue
inode = nonconstant_inputs[0]
if inode not in fliparoo.first.incoming_nodes:
continue
if not sum(
1
for node in fliparoo.first.incoming_nodes
if isinstance(node, ConstantNode)
):
continue
found = True
break
if found:
s = subfliparoo.slice(0, i)
constant_mul_fliparoo.append(s)
return constant_mul_fliparoo
def find_expansion_nodes(graph: FormulaGraph, nopower2=False) -> List[Node]:
expansion_nodes: List[Node] = []
for node in graph.nodes:
if not isinstance(node, CodeOpNode) or not node.is_mul:
continue
for par in node.incoming_nodes:
if isinstance(par, ConstantNode):
if nopower2 and is_power_of_2(par.value):
continue
expansion_nodes.append(node)
break
return expansion_nodes
def is_power_of_2(n: int) -> bool:
while n > 1:
if n & 1 == 1:
return False
n >>= 1
return True
def reduce_all_XplusX(graph: FormulaGraph):
adds = find_all_XplusX(graph)
for node in adds:
reduce_XplusX(graph, node)
graph.update()
def find_all_XplusX(graph) -> List[CodeOpNode]:
adds = []
for node in graph.nodes:
if not isinstance(node, CodeOpNode) or not node.is_add:
continue
if node.incoming_nodes[0] == node.incoming_nodes[1]:
adds.append(node)
return adds
def reduce_XplusX(graph: FormulaGraph, node: CodeOpNode):
inode = node.incoming_nodes[0]
const_node = ConstantNode(2)
node.incoming_nodes[1] = const_node
const_node.outgoing_nodes = [node]
graph.add_node(const_node)
inode.outgoing_nodes = list(filter(lambda x: x != node, inode.outgoing_nodes))
inode.outgoing_nodes.append(node)
opstr = f"{node.result} = {inode.result}{OpType.Mult.op_str}{const_node.value}"
node.op = CodeOp(parse(opstr))
def reduce_mul_fliparoo(fliparoo: MulFliparoo, copy=True):
if copy:
fliparoo = fliparoo.deepcopy()
first, last = fliparoo.first, fliparoo.last
inode = next(
filter(lambda x: not isinstance(x, ConstantNode), first.incoming_nodes)
)
const_nodes: List[ConstantNode] = [
node for node in fliparoo.input_nodes() if isinstance(node, ConstantNode)
]
sum_const_node = ConstantNode(sum(v.value for v in const_nodes))
fliparoo.graph.add_node(sum_const_node)
inode.outgoing_nodes = [n if n != first else last for n in inode.outgoing_nodes]
last.incoming_nodes = [inode, sum_const_node]
sum_const_node.outgoing_nodes = [last]
opstr = f"{last.result} = {inode.result}{OpType.Mult.op_str}{sum_const_node.value}"
last.op = CodeOp(parse(opstr))
for node in fliparoo:
if node == last:
continue
fliparoo.graph.remove_node(node)
for node in const_nodes:
if not node.outgoing_nodes:
fliparoo.graph.remove_node(node)
fliparoo.graph.update()
return fliparoo.graph
def reduce_add_fliparoo(fliparoo: AddFliparoo, copy=True):
if copy:
fliparoo = fliparoo.deepcopy()
first, last = fliparoo.first, fliparoo.last
par = first.incoming_nodes[0]
const_node = ConstantNode(len(fliparoo) + 1)
fliparoo.graph.add_node(const_node)
mul_node = CodeOpNode.from_str(
last.result, const_node.result, OpType.Mult, par.result
)
fliparoo.graph.add_node(mul_node)
mul_node.incoming_nodes = [const_node, par]
par.outgoing_nodes.append(mul_node)
const_node.outgoing_nodes.append(mul_node)
mul_node.output_node = last.output_node
last.reconnect_outgoing_nodes(mul_node)
for node in fliparoo:
fliparoo.graph.remove_node(node)
fliparoo.graph.update()
return fliparoo.graph
def expand_mul(graph: FormulaGraph, node: Node, copy=True) -> FormulaGraph:
if copy:
i = graph.node_index(node)
graph = deepcopy(graph)
node = graph.nodes[i]
const_par = next(filter(lambda x: isinstance(x, ConstantNode), node.incoming_nodes))
par = next(filter(lambda x: not isinstance(x, ConstantNode), node.incoming_nodes))
initial_node = CodeOpNode.from_str(node.result, par.result, OpType.Add, par.result)
graph.add_node(initial_node)
initial_node.incoming_nodes = [par, par]
par.outgoing_nodes.extend([initial_node, initial_node])
prev_node = initial_node
for _ in range(const_par.value - 2):
anode = CodeOpNode.from_str(
node.result, prev_node.result, OpType.Add, par.result
)
anode.incoming_nodes = [prev_node, par]
par.outgoing_nodes.append(anode)
graph.add_node(anode)
prev_node.outgoing_nodes = [anode]
prev_node = anode
prev_node.output_node = node.output_node
node.reconnect_outgoing_nodes(prev_node)
graph.remove_node(node)
graph.remove_node(const_par)
graph.update()
return graph
class Partition:
value: int
parts: List["Partition"]
def __init__(self, n: int):
self.value = n
self.parts = []
@property
def is_final(self):
return not self.parts
def __repr__(self):
if self.is_final:
return f"({self.value})"
l, r = self.parts
return f"({l.__repr__()},{r.__repr__()})"
def __add__(self, other):
a = Partition(self.value + other.value)
a.parts = [self, other]
return a
def __eq__(self, other):
if self.value != other.value:
return False
if self.is_final or other.is_final:
return self.is_final == other.is_final
l, r = self.parts
lo, ro = other.parts
return (l == lo and r == ro) or (l == ro and r == lo)
# unhashable at the moment
__hash__ = None # type: ignore
def compute_partitions(n: int) -> List[Partition]:
partitions = [Partition(n)]
for d in range(1, n // 2 + 1):
n_d = n - d
for partition_dp in compute_partitions(d):
for partition_n_dp in compute_partitions(n_d):
partitions.append(partition_dp + partition_n_dp)
# remove duplicates
result = []
for p in partitions:
if p not in result:
result.append(p)
return result
def generate_partitioned_formulas(formula: Formula, rename=True):
graph = FormulaGraph(formula, rename)
enodes = find_expansion_nodes(graph)
for i, enode in enumerate(enodes):
for j, part_graph in enumerate(generate_all_node_partitions(graph, enode)):
yield part_graph.to_formula(f"partition[{i},{j}]")
def generate_all_node_partitions(
original_graph: FormulaGraph, node: Node
) -> Generator[FormulaGraph, Any, None]:
const_par = next(filter(lambda x: isinstance(x, ConstantNode), node.incoming_nodes))
const_par_value = const_par.value
par = next(filter(lambda x: not isinstance(x, ConstantNode), node.incoming_nodes))
i, ic, ip = (
original_graph.node_index(node),
original_graph.node_index(const_par),
original_graph.node_index(par),
)
for partition in compute_partitions(const_par_value):
if partition.is_final:
continue
# copy
graph = deepcopy(original_graph)
node, const_par, par = graph.nodes[i], graph.nodes[ic], graph.nodes[ip]
graph.remove_node(const_par)
lresult, rresult = f"{node.result}L", f"{node.result}R"
empty_left_node = CodeOpNode.from_str(lresult, "PART", OpType.Add, "PART")
empty_right_node = CodeOpNode.from_str(rresult, "PART", OpType.Add, "PART")
addition_node = CodeOpNode.from_str(node.result, lresult, OpType.Add, rresult)
graph.add_node(empty_left_node)
graph.add_node(empty_right_node)
graph.add_node(addition_node)
addition_node.outgoing_nodes = node.outgoing_nodes
addition_node.output_node = node.output_node
addition_node.incoming_nodes = [empty_left_node, empty_right_node]
empty_left_node.outgoing_nodes = [addition_node]
empty_right_node.outgoing_nodes = [addition_node]
left, right = partition.parts
partition_node(graph, empty_left_node, left, par)
partition_node(graph, empty_right_node, right, par)
graph.remove_node(node)
graph.update()
yield graph
def partition_node(
graph: FormulaGraph, node: CodeOpNode, partition: Partition, source_node: Node
):
if partition.is_final and partition.value == 1:
# source node will take the role of node
# note: node has precisely one output node, since it was created during partitions
assert len(node.outgoing_nodes) == 1
child = node.outgoing_nodes[0]
source_node.outgoing_nodes.append(child)
left, right = child.incoming_nodes[0].result, child.incoming_nodes[1].result
if child.incoming_nodes[0] == node:
left = source_node.result
child.incoming_nodes[0] = source_node
else:
right = source_node.result
child.incoming_nodes[1] = source_node
opstr = f"{child.result} = {left}{child.optype.op_str}{right}"
child.op = CodeOp(parse(opstr))
graph.remove_node(node)
return
if partition.is_final:
source_node.outgoing_nodes.append(node)
const_node = ConstantNode(partition.value)
graph.add_node(const_node)
opstr = (
f"{node.result} = {source_node.result}{OpType.Mult.op_str}{partition.value}"
)
node.op = CodeOp(parse(opstr))
node.incoming_nodes = [source_node, const_node]
const_node.outgoing_nodes = [node]
return
lresult, rresult = f"{node.result}L", f"{node.result}R"
empty_left_node = CodeOpNode.from_str(lresult, "PART", OpType.Add, "PART")
empty_right_node = CodeOpNode.from_str(rresult, "PART", OpType.Add, "PART")
opstr = f"{node.result} = {lresult}{OpType.Add.op_str}{rresult}"
node.op = CodeOp(parse(opstr))
graph.add_node(empty_left_node)
graph.add_node(empty_right_node)
node.incoming_nodes = [empty_left_node, empty_right_node]
empty_left_node.outgoing_nodes = [node]
empty_right_node.outgoing_nodes = [node]
left, right = partition.parts
partition_node(graph, empty_left_node, left, source_node)
partition_node(graph, empty_right_node, right, source_node)