problem.py

#
# Copyright 2020, Data61, CSIRO (ABN 41 687 119 230)
#
# SPDX-License-Identifier: BSD-2-Clause
#

from syntax import (Expr, mk_var, Node, true_term, false_term,
  fresh_name, word32T, word8T, mk_eq, mk_word32, builtinTs)
import syntax

from target_objects import functions, pairings, trace, printout
import sys
import logic
from logic import azip

class Abort(Exception):
	pass

last_problem = [None]

class Problem:
	def __init__ (self, pairing, name = None):
		if name == None:
			name = pairing.name
		self.name = 'Problem (%s)' % name
		self.pairing = pairing

		self.nodes = {}
		self.vs = {}
		self.next_node_name = 1
		self.preds = {}
		self.loop_data = {}
		self.node_tags = {}
		self.node_tag_revs = {}
		self.inline_scripts = {}
		self.entries = []
		self.outputs = {}
		self.tarjan_order = []
		self.loop_var_analysis_cache = {}

		self.known_eqs = {}
		self.cached_analysis = {}
		self.hook_tag_hints = {}

		last_problem[0] = self

	def fail_msg (self):
		return 'FAILED %s (size %05d)' % (self.name, len(self.nodes))

	def alloc_node (self, tag, detail, loop_id = None, hint = None):
		name = self.next_node_name
		self.next_node_name = name + 1

		self.node_tags[name] = (tag, detail)
		self.node_tag_revs.setdefault ((tag, detail), [])
		self.node_tag_revs[(tag, detail)].append (name)

		if loop_id != None:
			self.loop_data[name] = ('Mem', loop_id)

		return name

	def fresh_var (self, name, typ):
		name = fresh_name (name, self.vs, typ)
		return mk_var (name, typ)

	def clone_function (self, fun, tag):
		self.nodes = {}
		self.vs = syntax.get_vars (fun)
		for n in fun.reachable_nodes ():
			self.nodes[n] = fun.nodes[n]
			detail = (fun.name, n)
			self.node_tags[n] = (tag, detail)
			self.node_tag_revs.setdefault ((tag, detail), [])
			self.node_tag_revs[(tag, detail)].append (n)
		self.outputs[tag] = fun.outputs
		self.entries = [(fun.entry, tag, fun.name, fun.inputs)]
		self.next_node_name = max (self.nodes.keys () + [2]) + 1
		self.inline_scripts[tag] = []

	def add_function (self, fun, tag, node_renames, loop_id = None):
		if not fun.entry:
			printout ('Aborting %s: underspecified %s' % (
				self.name, fun.name))
			raise Abort ()
		node_renames.setdefault('Ret', 'Ret')
		node_renames.setdefault('Err', 'Err')
		new_node_renames = {}
		vs = syntax.get_vars (fun)
		vs = dict ([(v, fresh_name (v, self.vs, vs[v])) for v in vs])
		ns = fun.reachable_nodes ()
		check_no_symbols ([fun.nodes[n] for n in ns])
		for n in ns:
			assert n not in node_renames
			node_renames[n] = self.alloc_node (tag, (fun.name, n),
				loop_id = loop_id, hint = n)
			new_node_renames[n] = node_renames[n]
		for n in ns:
			self.nodes[node_renames[n]] = syntax.copy_rename (
				fun.nodes[n], (vs, node_renames))

		return (new_node_renames, vs)

	def add_entry_function (self, fun, tag):
		(ns, vs) = self.add_function (fun, tag, {})

		entry = ns[fun.entry]
		args = [(vs[v], typ) for (v, typ) in fun.inputs]
		rets = [(vs[v], typ) for (v, typ) in fun.outputs]
		self.entries.append((entry, tag, fun.name, args))
		self.outputs[tag] = rets

		self.inline_scripts[tag] = []

		return (args, rets, entry)

	def get_entry_details (self, tag):
		[(e, t, fname, args)] = [(e, t, fname, args)
			for (e, t, fname, args) in self.entries if t == tag]
		return (e, fname, args)

	def get_entry (self, tag):
		(e, fname, args) = self.get_entry_details (tag)
		return e

	def tags (self):
		return self.outputs.keys ()

	def entry_exit_renames (self, tags = None):
		"""computes the rename set of a function's formal parameters
		to the actual input/output variable names at the various entry
		and exit points"""
		mk = lambda xs, ys: dict ([(x[0], y[0]) for (x, y) in
			azip (xs, ys)])
		renames = {}
		if tags == None:
			tags = self.tags ()
		for tag in tags:
			(_, fname, args) = self.get_entry_details (tag)
			fun = functions[fname]
			out = self.outputs[tag]
			renames[tag + '_IN'] = mk (fun.inputs, args)
			renames[tag + '_OUT'] = mk (fun.outputs, out)
		return renames

	def redirect_conts (self, reds):
		for node in self.nodes.itervalues():
			if node.kind == 'Cond':
				node.left = reds.get(node.left, node.left)
				node.right = reds.get(node.right, node.right)
			else:
				node.cont = reds.get(node.cont, node.cont)

	def do_analysis (self):
		self.cached_analysis.clear ()
		self.compute_preds ()
		self.do_loop_analysis ()

	def mk_node_graph (self, node_subset = None):
		if node_subset == None:
			node_subset = self.nodes
		return dict ([(n, [c for c in self.nodes[n].get_conts ()
				if c in node_subset])
			for n in node_subset])

	def do_loop_analysis (self):
		entries = [e for (e, tag, nm, args) in self.entries]
		self.loop_data = {}

		graph = self.mk_node_graph ()
		comps = logic.tarjan (graph, entries)
		self.tarjan_order = []

		for (head, tail) in comps:
			self.tarjan_order.append (head)
			self.tarjan_order.extend (tail)
			if not tail and head not in graph[head]:
				continue
			trace ('Loop (%d, %s)' % (head, tail))

			loop_set = set (tail)
			loop_set.add (head)

			r = self.force_single_loop_return (head, loop_set)
			if r != None:
				tail.append (r)
				loop_set.add (r)
				self.tarjan_order.append (r)
				self.compute_preds ()

			self.loop_data[head] = ('Head', loop_set)
			for t in tail:
				self.loop_data[t] = ('Mem', head)

		# put this in first-to-last order.
		self.tarjan_order.reverse ()

	def check_no_inner_loops (self):
		for loop in self.loop_heads ():
			check_no_inner_loop (self, loop)

	def force_single_loop_return (self, head, loop_set):
		rets = [n for n in self.preds[head] if n in loop_set]
		if (len (rets) == 1 and rets[0] != head and
				self.nodes[rets[0]].is_noop ()):
			return None
		r = self.alloc_node (self.node_tags[head][0],
			'LoopReturn', loop_id = head)
		self.nodes[r] = Node ('Basic', head, [])
		for r2 in rets:
			self.nodes[r2] = syntax.copy_rename (self.nodes[r2],
				({}, {head: r}))
		return r

	def splittable_points (self, n):
		"""splittable points are points which when removed, the loop
		'splits' and ceases to be a loop.

		equivalently, the set of splittable points is the intersection
		of all sub-loops of the loop."""
		head = self.loop_id (n)
		assert head != None
		k = ('Splittables', head)
		if k in self.cached_analysis:
			return self.cached_analysis[k]

		# check if the head point is a split (the inner loop
		# check does exactly that)
		if has_inner_loop (self, head):
			head = logic.get_one_loop_splittable (self,
				self.loop_body (head))
			if head == None:
				return set ()

		splits = self.get_loop_splittables (head)
		self.cached_analysis[k] = splits
		return splits

	def get_loop_splittables (self, head):
		loop_set = self.loop_body (head)
		splittable = dict ([(n, False) for n in loop_set])
		arc = [head]
		n = head
		while True:
			ns = [n2 for n2 in self.nodes[n].get_conts ()
				if n2 in loop_set]
			ns2 = [x for x in ns if x == head or x not in arc]
			#n = ns[0]
			n = ns2[0]
			arc.append (n)
			splittable[n] = True
			if n == head:
				break
		last_descs = {}
		for i in range (len (arc)):
			last_descs[arc[i]] = i
		def last_desc (n):
			if n in last_descs:
				return last_descs[n]
			n2s = [n2 for n2 in self.nodes[n].get_conts()
				if n2 in loop_set]
			last_descs[n] = None
			for n2 in n2s:
			  x = last_desc(n2)
			  if last_descs[n] == None or x >= last_descs[n]:
			    last_descs[n] = x
			return last_descs[n]
		for i in range (len (arc)):
			max_arc = max ([last_desc (n)
				for n in self.nodes[arc[i]].get_conts ()
				if n in loop_set])
			for j in range (i + 1, max_arc):
				splittable[arc[j]] = False
		return set ([n for n in splittable if splittable[n]])

	def loop_heads (self):
		return [n for n in self.loop_data
			if self.loop_data[n][0] == 'Head']

	def loop_id (self, n):
		if n not in self.loop_data:
			return None
		elif self.loop_data[n][0] == 'Head':
			return n
		else:
			assert self.loop_data[n][0] == 'Mem'
			return self.loop_data[n][1]

	def loop_body (self, n):
		head = self.loop_id (n)
		return self.loop_data[head][1]

	def compute_preds (self):
		self.preds = logic.compute_preds (self.nodes)

	def var_dep_outputs (self, n):
		return self.outputs[self.node_tags[n][0]]

	def compute_var_dependencies (self):
		if 'var_dependencies' in self.cached_analysis:
			return self.cached_analysis['var_dependencies']
		var_deps = logic.compute_var_deps (self.nodes,
			self.var_dep_outputs, self.preds)
		var_deps2 = dict ([(n, dict ([(v, None)
				for v in var_deps.get (n, [])]))
			for n in self.nodes])
		self.cached_analysis['var_dependencies'] = var_deps2
		return var_deps2

	def get_loop_var_analysis (self, var_deps, n):
		head = self.loop_id (n)
		assert head, n
		assert n in self.splittable_points (n)
		loop_sort = tuple (sorted (self.loop_body (head)))
		node_data = [(self.nodes[n2], sorted (self.preds[n]),
				sorted (var_deps[n2].keys ()))
			for n2 in loop_sort]
		k = (n, loop_sort)
		data = (node_data, n)
		if k in self.loop_var_analysis_cache:
			for (data2, va) in self.loop_var_analysis_cache[k]:
				if data2 == data:
					return va
		va = logic.compute_loop_var_analysis (self, var_deps, n)
		group = self.loop_var_analysis_cache.setdefault (k, [])
		group.append ((data, va))
		del group[:-10]
		return va

	def save_graph (self, fname):
		cols = mk_graph_cols (self.node_tags)
		save_graph (self.nodes, fname, cols = cols,
			node_tags = self.node_tags)

	def save_graph_summ (self, fname):
		node_ids = {}
		def is_triv (n):
			if n not in self.nodes:
				return False
			if len (self.preds[n]) != 1:
				return False
			node = self.nodes[n]
			if node.kind == 'Basic':
				return (True, node.cont)
			elif node.kind == 'Cond' and node.right == 'Err':
				return (True, node.left)
			else:
				return False
		for n in self.nodes:
			if n in node_ids:
				continue
			ns = []
			while is_triv (n):
				ns.append (n)
				n = is_triv (n)[1]
			for n2 in ns:
				node_ids[n2] = n
		nodes = {}
		for n in self.nodes:
			if is_triv (n):
				continue
			nodes[n] = syntax.copy_rename (self.nodes[n],
				({}, node_ids))
		cols = mk_graph_cols (self.node_tags)
		save_graph (nodes, fname, cols = cols,
			node_tags = self.node_tags)

	def serialise (self):
		ss = ['Problem']
		for (n, tag, fname, inputs) in self.entries:
			xs = ['Entry', '%d' % n, tag, fname,
				'%d' % len (inputs)]
			for (nm, typ) in inputs:
				xs.append (nm)
				typ.serialise (xs)
			xs.append ('%d' % len (self.outputs[tag]))
			for (nm, typ) in self.outputs[tag]:
				xs.append (nm)
				typ.serialise (xs)
			ss.append (' '.join (xs))
		for n in self.nodes:
			xs = ['%d' % n]
			self.nodes[n].serialise (xs)
			ss.append (' '.join (xs))
		ss.append ('EndProblem')
		return ss

	def save_serialise (self, fname):
		ss = self.serialise ()
		f = open (fname, 'w')
		for s in ss:
			f.write (s + '\n')
		f.close ()

	def pad_merge_points (self):
		self.compute_preds ()

		arcs = [(pred, n) for n in self.preds
			if len (self.preds[n]) > 1
			if n in self.nodes
			for pred in self.preds[n]
			if (self.nodes[pred].kind != 'Basic'
				or self.nodes[pred].upds != [])]

		for (pred, n) in arcs:
			(tag, _) = self.node_tags[pred]
			name = self.alloc_node (tag, 'MergePadding')
			self.nodes[name] = Node ('Basic', n, [])
			self.nodes[pred] = syntax.copy_rename (self.nodes[pred],
				({}, {n: name}))

	def function_call_addrs (self):
		return [(n, self.nodes[n].fname)
			for n in self.nodes if self.nodes[n].kind == 'Call']

	def function_calls (self):
		return set ([fn for (n, fn) in self.function_call_addrs ()])

	def get_extensions (self):
		if 'extensions' in self.cached_analysis:
			return self.cached_analysis['extensions']
		extensions = set ()
		for node in self.nodes.itervalues ():
			extensions.update (syntax.get_extensions (node))
		self.cached_analysis['extensions'] = extensions
		return extensions

	def replay_inline_script (self, tag, script):
		for (detail, idx, fname) in script:
			n = self.node_tag_revs[(tag, detail)][idx]
			assert self.nodes[n].kind == 'Call', self.nodes[n]
			assert self.nodes[n].fname == fname, self.nodes[n]
			inline_at_point (self, n, do_analysis = False)
		if script:
			self.do_analysis ()

	def is_reachable_from (self, source, target):
		'''discover if graph addr "target" is reachable
			from starting node "source"'''
		k = ('is_reachable_from', source)
		if k in self.cached_analysis:
			reachable = self.cached_analysis[k]
			if target in reachable:
				return reachable[target]

		reachable = {}
		visit = [source]
		while visit:
			n = visit.pop ()
			if n not in self.nodes:
				continue
			for n2 in self.nodes[n].get_conts ():
				if n2 not in reachable:
					reachable[n2] = True
					visit.append (n2)
		for n in list (self.nodes) + ['Ret', 'Err']:
			if n not in reachable:
				reachable[n] = False
		self.cached_analysis[k] = reachable
		return reachable[target]

	def is_reachable_without (self, cutpoint, target):
		'''discover if graph addr "target" is reachable
			without visiting node "cutpoint"
			(an oddity: cutpoint itself is considered reachable)'''
		k = ('is_reachable_without', cutpoint)
		if k in self.cached_analysis:
			reachable = self.cached_analysis[k]
			if target in reachable:
				return reachable[target]

		reachable = dict ([(self.get_entry (t), True)
			for t in self.tags ()])
		for n in self.tarjan_order + ['Ret', 'Err']:
			if n in reachable:
				continue
			reachable[n] = bool ([pred for pred in self.preds[n]
				if pred != cutpoint
				if reachable.get (pred) == True])
		self.cached_analysis[k] = reachable
		return reachable[target]

def deserialise (name, lines):
	assert lines[0] == 'Problem', lines[0]
	assert lines[-1] == 'EndProblem', lines[-1]
	i = 1
	# not easy to reconstruct pairing
	p = Problem (pairing = None, name = name)
	while lines[i].startswith ('Entry'):
		bits = lines[i].split ()
		en = int (bits[1])
		tag = bits[2]
		fname = bits[3]
		(n, inputs) = syntax.parse_list (syntax.parse_lval, bits, 4)
		(n, outputs) = syntax.parse_list (syntax.parse_lval, bits, n)
		assert n == len (bits), (n, bits)
		p.entries.append ((en, tag, fname, inputs))
		p.outputs[tag] = outputs
		i += 1
	for i in range (i, len (lines) - 1):
		bits = lines[i].split ()
		n = int (bits[0])
		node = syntax.parse_node (bits, 1)
		p.nodes[n] = node
	return p

# trivia

def check_no_symbols (nodes):
	import pseudo_compile
	symbs = pseudo_compile.nodes_symbols (nodes)
	if not symbs:
		return
	printout ('Aborting %s: undefined symbols %s' % (self.name, symbs))
	raise Abort ()

# printing of problem graphs

def sanitise_str (s):
	return s.replace ('"', '_').replace ("'", "_").replace (' ', '')

def graph_name (nodes, node_tags, n, prev=None):
	if type (n) == str:
		return 't_%s_%d' % (n, prev)
	if n not in nodes:
		return 'unknown_%d' % n
	if n not in node_tags:
		ident = '%d' % n
	else:
		(tag, details) = node_tags[n]
		if len (details) > 1 and logic.is_int (details[1]):
			ident = '%d_%s_%s_0x%x' % (n, tag,
				details[0], details[1])
		elif type (details) != str:
			details = '_'.join (map (str, details))
			ident = '%d_%s_%s' % (n, tag, details)
		else:
			ident = '%d_%s_%s' % (n, tag, details)
	ident = sanitise_str (ident)
	node = nodes[n]
	if node.kind == 'Call':
		return 'fcall_%s' % ident
	if node.kind == 'Cond':
		return ident
	if node.kind == 'Basic':
		return 'ass_%s' % ident
	assert not 'node kind understood'

def graph_node_tooltip (nodes, n):
	if n == 'Err':
		return 'Error point'
	if n == 'Ret':
		return 'Return point'
	node = nodes[n]
	if node.kind == 'Call':
		return "%s: call to '%s'" % (n, sanitise_str (node.fname))
	if node.kind == 'Cond':
		return '%s: conditional node' % n
	if node.kind == 'Basic':
		var_names = [sanitise_str (x[0][0]) for x in node.upds]
		return '%s: assignment to [%s]' % (n, ', '.join (var_names))
	assert not 'node kind understood'

def graph_edges (nodes, n):
	node = nodes[n]
	if node.is_noop ():
		return [(node.get_conts () [0], 'N')]
	elif node.kind == 'Cond':
		return [(node.left, 'T'), (node.right, 'F')]
	else:
		return [(node.cont, 'C')]

def get_graph_font (n, col):
	font = 'fontname = "Arial", fontsize = 20, penwidth=3'
	if col:
		font = font + ', color=%s, fontcolor=%s' % (col, col)
	return font

def get_graph_loops (nodes):
	graph = dict ([(n, [c for c in nodes[n].get_conts ()
		if type (c) != str]) for n in nodes])
	graph['ENTRY'] = list (nodes)
	comps = logic.tarjan (graph, ['ENTRY'])
	comp_ids = {}
	for (head, tail) in comps:
		comp_ids[head] = head
		for n in tail:
			comp_ids[n] = head
	loops = set ([(n, n2) for n in graph for n2 in graph[n]
		if comp_ids[n] == comp_ids[n2]])
	return loops

def make_graph (nodes, cols, node_tags = {}, entries = []):
	graph = []
	graph.append ('digraph foo {')

	loops = get_graph_loops (nodes)

	for n in nodes:
		n_nm = graph_name (nodes, node_tags, n)
		f = get_graph_font (n, cols.get (n))
		graph.append ('%s [%s\n label="%s"\n tooltip="%s"];' % (n,
			f, n_nm, graph_node_tooltip (nodes, n)))
		for (c, l) in graph_edges (nodes, n):
			if c in ['Ret', 'Err']:
				c_nm = '%s_%s' % (c, n)
				if c == 'Ret':
					f2 = f + ', shape=doubleoctagon'
				else:
					f2 = f + ', shape=Mdiamond'
				graph.append ('%s [label="%s", %s];'
					% (c_nm, c, f2))
			else:
				c_nm = c
			ft = f
			if (n, c) in loops:
				ft = f + ', penwidth=6'
			graph.append ('%s -> %s [label=%s, %s];' % (
				n, c_nm, l, ft))

	for (i, (n, tag, inps)) in enumerate (entries):
		f = get_graph_font (n, cols.get (n))
		nm1 = tag + ' ENTRY_POINT'
		nm2 = 'entry_point_%d' % i
		graph.extend (['%s -> %s [%s];' % (nm2, n, f),
			'%s [label = "%s", shape=none, %s];' % (nm2, nm1, f)])

	graph.append ('}')
	return graph

def print_graph (nodes, cols = {}, entries = []):
	for line in make_graph (nodes, cols, entries):
		print line

def save_graph (nodes, fname, cols = {}, entries = [], node_tags = {}):
	f = open (fname, 'w')
	for line in make_graph (nodes, cols = cols, node_tags = node_tags,
			entries = entries):
		f.write (line + '\n')
	f.close ()

def mk_graph_cols (node_tags):
	known_cols = {'C': "forestgreen", 'ASM_adj': "darkblue",
		'ASM': "darkorange"}
	cols = {}
	for n in node_tags:
		if node_tags[n][0] in known_cols:
			cols[n] = known_cols[node_tags[n][0]]
	return cols

def make_graph_with_eqs (p, invis = False):
	if invis:
		invis_s = ', style=invis'
	else:
		invis_s = ''
	cols = mk_graph_cols (p.node_tags)
	graph = make_graph (p.nodes, cols = cols)
	graph.pop ()
	for k in p.known_eqs:
		if k == 'Hyps':
			continue
		(n_vc_x, tag_x) = k
		nm1 = graph_name (p.nodes, p.node_tags, n_vc_x[0])
		for (x, n_vc_y, tag_y, y, hyps) in p.known_eqs[k]:
			nm2 = graph_name (p.nodes, p.node_tags, n_vc_y[0])
			graph.extend ([('%s -> %s [ dir = back, color = blue, '
				'penwidth = 3, weight = 0 %s ]')
					% (nm2, nm1, invis_s)])
	graph.append ('}')
	return graph

def save_graph_with_eqs (p, fname = 'diagram.dot', invis = False):
	graph = make_graph_with_eqs (p, invis = invis)
	f = open (fname, 'w')
	for s in graph:
		f.write (s + '\n')
	f.close ()

def get_problem_vars (p):
	inout = set.union (* ([set(xs) for xs in p.outputs.itervalues ()]
		+ [set (args) for (_, _, _, args) in p.entries]))

	vs = dict(inout)
	for node in p.nodes.itervalues():
		syntax.get_node_vars(node, vs)
	return vs

def is_trivial_fun (fun):
	for node in fun.nodes.itervalues ():
		if node.is_noop ():
			continue
		if node.kind == 'Call':
			return False
		elif node.kind == 'Basic':
			for (lv, v) in node.upds:
				if v.kind not in ['Var', 'Num']:
					return False
		elif node.kind == 'Cond':
			if node.cond.kind != 'Var' and node.cond not in [
					true_term, false_term]:
				return False
	return True

last_alt_nodes = [0]

def avail_val (vs, typ):
	for (nm, typ2) in vs:
		if typ2 == typ:
			return mk_var (nm, typ2)
	return logic.default_val (typ)

def inline_at_point (p, n, do_analysis = True):
	node = p.nodes[n]
	if node.kind != 'Call':
		return

	f_nm = node.fname
	fun = functions[f_nm]
	(tag, detail) = p.node_tags[n]
	idx = p.node_tag_revs[(tag, detail)].index (n)
	p.inline_scripts[tag].append ((detail, idx, f_nm))

	trace ('Inlining %s into %s' % (f_nm, p.name))
	if n in p.loop_data:
		trace ('  inlining into loop %d!' % p.loop_id (n))

	ex = p.alloc_node (tag, (f_nm, 'RetToCaller'))

	(ns, vs) = p.add_function (fun, tag, {'Ret': ex})
	en = ns[fun.entry]

	inp_lvs = [(vs[v], typ) for (v, typ) in fun.inputs]
	p.nodes[n] = Node ('Basic', en, azip (inp_lvs, node.args))

	out_vs = [mk_var (vs[v], typ) for (v, typ) in fun.outputs]
	p.nodes[ex] = Node ('Basic', node.cont, azip (node.rets, out_vs))

	p.cached_analysis.clear ()

	if do_analysis:
		p.do_analysis ()

	trace ('Problem size now %d' % len(p.nodes))
	sys.stdin.flush ()

	return ns.values ()

def loop_body_inner_loops (p, head, loop_body):
	loop_set_all = set (loop_body)
	loop_set = loop_set_all - set ([head])
	graph = dict([(n, [c for c in p.nodes[n].get_conts ()
			if c in loop_set])
		for n in loop_set_all])

	comps = logic.tarjan (graph, [head])
	assert sum ([1 + len (t) for (_, t) in comps]) == len (loop_set_all)
	return [comp for comp in comps if comp[1]]

def loop_inner_loops (p, head):
	k = ('inner_loop_set', head)
	if k in p.cached_analysis:
		return p.cached_analysis[k]
	res = loop_body_inner_loops (p, head, p.loop_body (head))
	p.cached_analysis[k] = res
	return res

def loop_heads_including_inner (p):
	heads = p.loop_heads ()
	check = [(head, p.loop_body (head)) for head in heads]
	while check:
		(head, body) = check.pop ()
		comps = loop_body_inner_loops (p, head, body)
		heads.extend ([head for (head, _) in comps])
		check.extend ([(head, [head] + list (body))
			for (head, body) in comps])
	return heads

def check_no_inner_loop (p, head):
	subs = loop_inner_loops (p, head)
	if subs:
		printout ('Aborting %s, complex loop' % p.name)
		trace ('  sub-loops %s of loop at %s' % (subs, head))
		for (h, _) in subs:
			trace ('    head %d tagged %s' % (h, p.node_tags[h]))
		raise Abort ()

def has_inner_loop (p, head):
	return bool (loop_inner_loops (p, head))

def fun_has_inner_loop (f):
	p = f.as_problem (Problem)
	p.do_analysis ()
	return bool ([head for head in p.loop_heads ()
		if has_inner_loop (p, head)])

def loop_var_analysis (p, head, tail):
	# getting the set of variables that go round the loop
	nodes = set (tail)
	nodes.add (head)
	used_vs = set ([])
	created_vs_at = {}
	visit = []

	def process_node (n, created):
		if p.nodes[n].is_noop ():
			lvals = set ([])
		else:
			vs = syntax.get_node_rvals (p.nodes[n])
			for rv in vs.iteritems ():
				if rv not in created:
					used_vs.add (rv)
			lvals = set (p.nodes[n].get_lvals ())

		created = set.union (created, lvals)
		created_vs_at[n] = created

		visit.extend (p.nodes[n].get_conts ())

	process_node (head, set ([]))

	while visit:
		n = visit.pop ()
		if (n not in nodes) or (n in created_vs_at):
			continue
		if not all ([pr in created_vs_at for pr in p.preds[n]]):
			continue

		pre_created = [created_vs_at[pr] for pr in p.preds[n]]
		process_node (n, set.union (* pre_created))

	final_pre_created = [created_vs_at[pr] for pr in p.preds[head]
		if pr in nodes]
	created = set.union (* final_pre_created)

	loop_vs = set.intersection (created, used_vs)
	trace ('Loop vars at head: %s' % loop_vs)

	return loop_vs