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
[docs]
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")
[docs]
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")
[docs]
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")
[docs]
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
[docs]
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
[docs]
def is_power_of_2(n: int) -> bool:
while n > 1:
if n & 1 == 1:
return False
n >>= 1
return True
[docs]
def reduce_all_XplusX(graph: FormulaGraph):
adds = find_all_XplusX(graph)
for node in adds:
reduce_XplusX(graph, node)
graph.update()
[docs]
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
[docs]
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))
[docs]
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
[docs]
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
[docs]
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
[docs]
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
[docs]
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
[docs]
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
[docs]
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)
