def mk_bin_inst_spec(fname):
if not fname.startswith("instruction'"):
return
if functions[fname].entry:
return
(_, ident) = fname.split("'", 1)
(ident, addr) = split_inst_name_addr(ident)
(regs, ident) = split_inst_name_regs(ident)
ident = instruction_name_aliases.get(ident, ident)
base_ident = ident.split("_")[0]
if base_ident not in instruction_fun_specs:
return
(impl_fname, regspecs) = instruction_fun_specs[base_ident]
add_impl_fun(impl_fname, regspecs)
assert len(regspecs) == len(regs), (fname, regs, regspecs)
inp_regs = [reg for (reg, d) in zip(regs, regspecs) if d == 'I']
out_regs = [reg for (reg, d) in zip(regs, regspecs) if d == 'O']
call = syntax.Node(
'Call', 'Ret',
('l_' + impl_fname,
[syntax.mk_var(reg, syntax.word32T)
for reg in inp_regs] + [syntax.mk_token(ident)] +
[syntax.mk_var(nm, typ)
for (nm, typ) in bin_globs], [(reg, syntax.word32T)
for reg in out_regs] + bin_globs))
assert not functions[fname].nodes
functions[fname].nodes[1] = call
functions[fname].entry = 1
def node_const_rets(node):
if "instruction'" in node.fname:
return inst_const_rets(node)
if node.fname in pre_pairings:
if pre_pairings[node.fname]['ASM'] != node.fname:
return None
cc = get_asm_calling_convention_at_node(node)
input_set = set(
[v for arg in node.args for v in syntax.get_expr_var_set(arg)])
callee_saved_set = set(cc['callee_saved'])
return [
mk_var(nm, typ) for (nm, typ) in node.rets
if mk_var(nm, typ) in callee_saved_set if (nm, typ) in input_set
]
elif preserves_sp(node.fname):
if node.fname not in get_functions_with_tag('ASM'):
return None
f_outs = functions[node.fname].outputs
return [
mk_var(nm, typ)
for ((nm, typ), (nm2, _)) in azip(node.rets, f_outs)
if nm2 == 'r13'
]
else:
return None
def mk_bin_inst_spec (fname):
if not fname.startswith ("instruction'"):
return
if functions[fname].entry:
return
(_, ident) = fname.split ("'", 1)
(ident, addr) = split_inst_name_addr (ident)
(regs, ident) = split_inst_name_regs (ident)
ident = instruction_name_aliases.get (ident, ident)
base_ident = ident.split ("_")[0]
if base_ident not in instruction_fun_specs:
return
(impl_fname, regspecs) = instruction_fun_specs[base_ident]
add_impl_fun (impl_fname, regspecs)
assert len (regspecs) == len (regs), (fname, regs, regspecs)
inp_regs = [reg for (reg, d) in zip (regs, regspecs) if d == 'I']
out_regs = [reg for (reg, d) in zip (regs, regspecs) if d == 'O']
call = syntax.Node ('Call', 'Ret', (impl_fname,
[syntax.mk_var (reg, syntax.word32T) for reg in inp_regs]
+ [syntax.mk_token (ident)]
+ [syntax.mk_var (nm, typ) for (nm, typ) in bin_globs],
[(reg, syntax.word32T) for reg in out_regs] + bin_globs))
assert not functions[fname].nodes
functions[fname].nodes[1] = call
functions[fname].entry = 1
def get_stack_sp(p, tag):
"""get stack and stack-pointer variables"""
entry = p.get_entry(tag)
renames = p.entry_exit_renames(tags=[tag])
r = renames[tag + '_IN']
sp = syntax.rename_expr(mk_var('r13', syntax.word32T), r)
stack = syntax.rename_expr(mk_var('stack', syntax.builtinTs['Mem']), r)
return (stack, sp)
def get_stack_sp (p, tag):
"""get stack and stack-pointer variables"""
entry = p.get_entry (tag)
renames = p.entry_exit_renames (tags = [tag])
r = renames[tag + '_IN']
sp = syntax.rename_expr (mk_var ('r13', syntax.word32T), r)
stack = syntax.rename_expr (mk_var ('stack',
syntax.builtinTs['Mem']), r)
return (stack, sp)
def node_const_rets (node): if "instruction'" in node.fname: return inst_const_rets (node) if node.fname not in pre_pairings: return None if pre_pairings[node.fname]['ASM'] != node.fname: return None cc = get_asm_calling_convention_at_node (node) input_set = set ([v for arg in node.args for v in syntax.get_expr_var_set (arg)]) callee_saved_set = set (cc['callee_saved']) return [mk_var (nm, typ) for (nm, typ) in node.rets if mk_var (nm, typ) in callee_saved_set if (nm, typ) in input_set]
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 stack_virtualise_expr(expr, sp_offs):
if expr.is_op('MemAcc') and is_stack(expr.vals[0]):
[m, p] = expr.vals
if expr.typ == syntax.word8T:
ps = [(syntax.mk_minus(p, syntax.mk_word32(n)), n)
for n in [0, 1, 2, 3]]
elif expr.typ == syntax.word32T:
ps = [(p, 0)]
else:
assert expr.typ == syntax.word32T, expr
ptrs = [(p, 'MemAcc') for (p, _) in ps]
if sp_offs == None:
return (ptrs, None)
# FIXME: very 32-bit specific
ps = [(p, n) for (p, n) in ps if p in sp_offs
if sp_offs[p][1] % 4 == 0]
if not ps:
return (ptrs, expr)
[(p, n)] = ps
if p not in sp_offs:
raise StackOffsMissing()
(k, offs) = sp_offs[p]
v = mk_var(('Fake', k, offs), syntax.word32T)
if n != 0:
v = syntax.mk_shiftr(v, n * 8)
v = syntax.mk_cast(v, expr.typ)
return (ptrs, v)
elif expr.kind == 'Op':
vs = [stack_virtualise_expr(v, sp_offs) for v in expr.vals]
return ([p for (ptrs, _) in vs for p in ptrs],
syntax.adjust_op_vals(expr, [v for (_, v) in vs]))
else:
return ([], expr)
def get_induct_eq_hyp(p, split, restrs, n):
details = (split, (0, 1), [])
(tag, _) = p.node_tags[split]
visit = split_visit_one_visit(tag, details, restrs, vc_offs(0))
from syntax import mk_var, word32T, mk_word32
return eq_hyp((mk_var("%n", word32T), visit), (mk_word32(n), visit), (split, 0))
def split_hyps_at_visit (tags, split, restrs, visit):
(l_details, r_details, eqs, _, _) = split
(l_split, (l_seq_start, l_step), l_eqs) = l_details
(r_split, (r_seq_start, r_step), r_eqs) = r_details
(l_visit, r_visit) = split_visit_visits (tags, split, restrs, visit)
(l_start, r_start) = split_visit_visits (tags, split, restrs, vc_num (0))
(l_tag, r_tag) = tags
def mksub (v):
return lambda exp: logic.var_subst (exp, {('%i', word32T) : v},
must_subst = False)
def inst (exp):
return logic.inst_eq_at_visit (exp, visit)
zsub = mksub (mk_word32 (0))
if visit.kind == 'Number':
lsub = mksub (mk_word32 (visit.n))
else:
lsub = mksub (mk_plus (mk_var ('%n', word32T),
mk_word32 (visit.n)))
hyps = [(Hyp ('PCImp', l_visit, r_visit), 'pc imp'),
(Hyp ('PCImp', l_visit, l_start), '%s pc imp' % l_tag),
(Hyp ('PCImp', r_visit, r_start), '%s pc imp' % r_tag)]
hyps += [(eq_hyp ((zsub (l_exp), l_start), (lsub (l_exp), l_visit),
(l_split, r_split)), '%s const' % l_tag)
for l_exp in l_eqs if inst (l_exp)]
hyps += [(eq_hyp ((zsub (r_exp), r_start), (lsub (r_exp), r_visit),
(l_split, r_split)), '%s const' % r_tag)
for r_exp in r_eqs if inst (r_exp)]
hyps += [(eq_hyp ((lsub (l_exp), l_visit), (lsub (r_exp), r_visit),
(l_split, r_split)), 'eq')
for (l_exp, r_exp) in eqs
if inst (l_exp) and inst (r_exp)]
return hyps
def mk_seq_eqs (p, split, step, with_rodata):
# eqs take the form of a number of constant expressions
eqs = []
# the variable 'loop' will be converted to the point in
# the sequence - note this should be multiplied by the step size
loop = mk_var ('%i', word32T)
if step == 1:
minus_loop_step = mk_uminus (loop)
else:
minus_loop_step = mk_times (loop, mk_word32 (- step))
for (var, data) in get_loop_var_analysis_at (p, split):
if data == 'LoopVariable':
if with_rodata and var.typ == builtinTs['Mem']:
eqs.append (logic.mk_rodata (var))
elif data == 'LoopConst':
if var.typ not in syntax.phantom_types:
eqs.append (var)
elif data == 'LoopLeaf':
continue
elif data[0] == 'LoopLinearSeries':
(_, form, _) = data
eqs.append (form (var, minus_loop_step))
else:
assert not 'var_deps type understood'
return eqs
def stack_virtualise_expr (expr, sp_offs):
if expr.is_op ('MemAcc') and is_stack (expr.vals[0]):
[m, p] = expr.vals
if expr.typ == syntax.word8T:
ps = [(syntax.mk_minus (p, syntax.mk_word32 (n)), n)
for n in [0, 1, 2, 3]]
elif expr.typ == syntax.word32T:
ps = [(p, 0)]
else:
assert expr.typ == syntax.word32T, expr
ptrs = [(p, 'MemAcc') for (p, _) in ps]
if sp_offs == None:
return (ptrs, None)
# FIXME: very 32-bit specific
ps = [(p, n) for (p, n) in ps if p in sp_offs
if sp_offs[p][1] % 4 == 0]
if not ps:
return (ptrs, expr)
[(p, n)] = ps
(k, offs) = sp_offs[p]
v = mk_var (('Fake', k, offs), syntax.word32T)
if n != 0:
v = syntax.mk_shiftr (v, n * 8)
v = syntax.mk_cast (v, expr.typ)
return (ptrs, v)
elif expr.kind == 'Op':
vs = [stack_virtualise_expr (v, sp_offs) for v in expr.vals]
return ([p for (ptrs, _) in vs for p in ptrs],
syntax.Expr ('Op', expr.typ, name = expr.name,
vals = [v for (_, v) in vs]))
else:
return ([], expr)
def split_hyps_at_visit(tags, split, restrs, visit):
(l_details, r_details, eqs, _, _) = split
(l_split, (l_seq_start, l_step), l_eqs) = l_details
(r_split, (r_seq_start, r_step), r_eqs) = r_details
(l_visit, r_visit) = split_visit_visits(tags, split, restrs, visit)
(l_start, r_start) = split_visit_visits(tags, split, restrs, vc_num(0))
(l_tag, r_tag) = tags
def mksub(v):
return lambda exp: logic.var_subst(exp, {('%i', word32T): v},
must_subst=False)
def inst(exp):
return logic.inst_eq_at_visit(exp, visit)
zsub = mksub(mk_word32(0))
if visit.kind == 'Number':
lsub = mksub(mk_word32(visit.n))
else:
lsub = mksub(mk_plus(mk_var('%n', word32T), mk_word32(visit.n)))
hyps = [(Hyp('PCImp', l_visit, r_visit), 'pc imp'),
(Hyp('PCImp', l_visit, l_start), '%s pc imp' % l_tag),
(Hyp('PCImp', r_visit, r_start), '%s pc imp' % r_tag)]
hyps += [(eq_hyp((zsub(l_exp), l_start), (lsub(l_exp), l_visit),
(l_split, r_split)), '%s const' % l_tag)
for l_exp in l_eqs if inst(l_exp)]
hyps += [(eq_hyp((zsub(r_exp), r_start), (lsub(r_exp), r_visit),
(l_split, r_split)), '%s const' % r_tag)
for r_exp in r_eqs if inst(r_exp)]
hyps += [(eq_hyp((lsub(l_exp), l_visit), (lsub(r_exp), r_visit),
(l_split, r_split)), 'eq') for (l_exp, r_exp) in eqs
if inst(l_exp) and inst(r_exp)]
return hyps
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 adjust_ret_ptr (ptr):
"""this is a bit of a hack.
the return slots are named based on r0_input, which will be unchanged,
which is handy, but we really want to be talking about r0, which will
produce meaningful offsets against the pointers actually used in the
program."""
return logic.var_subst (ptr, {('r0_input', syntax.word32T):
syntax.mk_var ('r0', syntax.word32T)}, must_subst = False)
def adjusted_var_dep_outputs_for_tag(p, tag):
(ent, fname, _) = p.get_entry_details(tag)
fun = functions[fname]
cc = get_asm_calling_convention(fname)
callee_saved_set = set(cc['callee_saved'])
ret_set = set([(nm, typ) for ret in cc['rets']
for (nm, typ) in syntax.get_expr_var_set(ret)])
rets = [(nm2, typ)
for ((nm, typ), (nm2, _)) in azip(fun.outputs, p.outputs[tag])
if (nm, typ) in ret_set or mk_var(nm, typ) in callee_saved_set]
return rets
def adjusted_var_dep_outputs_for_tag (p, tag): (ent, fname, _) = p.get_entry_details (tag) fun = functions[fname] cc = get_asm_calling_convention (fname) callee_saved_set = set (cc['callee_saved']) ret_set = set ([(nm, typ) for ret in cc['rets'] for (nm, typ) in syntax.get_expr_var_set (ret)]) rets = [(nm2, typ) for ((nm, typ), (nm2, _)) in azip (fun.outputs, p.outputs[tag]) if (nm, typ) in ret_set or mk_var (nm, typ) in callee_saved_set] return rets
def compute_loop_var_analysis (nodes, var_deps, n, loop, preds): upd_vs = set ([v for n2 in loop if not nodes[n2].is_noop () for v in nodes[n2].get_lvals ()]) const_vs = set ([v for n2 in loop for v in var_deps[n2] if v not in upd_vs]) vca = compute_var_cycle_analysis (nodes, n, loop, preds, const_vs, set (var_deps[n])) vca = [(syntax.mk_var (nm, typ), data) for ((nm, typ), data) in vca.items ()] return vca
def get_asm_calling_convention_inner(num_c_args, num_c_rets, const_mem):
key = ('Inner', num_c_args, num_c_rets, const_mem)
if key in asm_cc_cache:
return asm_cc_cache[key]
from logic import mk_var_list, mk_stack_sequence
from syntax import mk_var, word32T, builtinTs
arg_regs = mk_var_list(['r0', 'r1', 'r2', 'r3'], word32T)
r0 = arg_regs[0]
sp = mk_var('r13', word32T)
st = mk_var('stack', builtinTs['Mem'])
r0_input = mk_var('ret_addr_input', word32T)
mem = mk_var('mem', builtinTs['Mem'])
dom = mk_var('dom', builtinTs['Dom'])
dom_stack = mk_var('dom_stack', builtinTs['Dom'])
global_args = [mem, dom, st, dom_stack, sp, mk_var('ret', word32T)]
sregs = mk_stack_sequence(sp, 4, st, word32T, num_c_args + 1)
arg_seq = [r for r in arg_regs] + [s for (s, _) in sregs]
if num_c_rets > 1:
# the 'return-too-much' issue.
# instead r0 is a save-returns-here pointer
arg_seq.pop(0)
rets = mk_stack_sequence(r0_input, 4, st, word32T, num_c_rets)
rets = [r for (r, _) in rets]
else:
rets = [r0]
callee_saved_vars = (
[mk_var(v, word32T)
for v in 'r4 r5 r6 r7 r8 r9 r10 r11 r13'.split()] + [dom, dom_stack])
if const_mem:
callee_saved_vars += [mem]
else:
rets += [mem]
rets += [st]
cc = {
'args': arg_seq[:num_c_args] + global_args,
'rets': rets,
'callee_saved': callee_saved_vars
}
asm_cc_cache[key] = cc
return cc
def add_impl_fun(impl_fname, regspecs):
l_fname = 'l_' + impl_fname
r_fname = 'r_' + impl_fname
if l_fname in functions:
return
assert r_fname not in functions
ident_v = ("inst_ident", syntax.builtinTs['Token'])
inps = [s for s in regspecs if s == 'I']
inps = ['reg_val%d' % (i + 1) for (i, s) in enumerate(inps)]
rets = [s for s in regspecs if s == 'O']
rets = ['ret_val%d' % (i + 1) for (i, s) in enumerate(rets)]
l_fun = mk_fun(l_fname, inps, [ident_v], rets, [], bin_globs)
r_fun = mk_fun(r_fname, inps, [ident_v], rets, [], bin_globs)
inp_eqs = [((mk_var(nm, typ), 'ASM_IN'), (mk_var(nm, typ), 'C_IN'))
for (nm, typ) in l_fun.inputs]
inp_eqs += [((logic.mk_rodata(mk_var(nm, typ)), 'ASM_IN'),
(syntax.true_term, 'C_IN')) for (nm, typ) in bin_globs]
out_eqs = [((mk_var(nm, typ), 'ASM_OUT'), (mk_var(nm, typ), 'C_OUT'))
for (nm, typ) in l_fun.outputs]
out_eqs += [((logic.mk_rodata(mk_var(nm, typ)), 'ASM_OUT'),
(syntax.true_term, 'C_OUT')) for (nm, typ) in bin_globs]
pair = logic.Pairing(['ASM', 'C'], {
'ASM': l_fname,
'C': r_fname
}, (inp_eqs, out_eqs))
assert l_fname not in pairings
assert r_fname not in pairings
functions[l_fname] = l_fun
functions[r_fname] = r_fun
pairings[l_fname] = [pair]
pairings[r_fname] = [pair]
def adjust_ret_ptr(ptr):
"""this is a bit of a hack.
the return slots are named based on r0_input, which will be unchanged,
which is handy, but we really want to be talking about r0, which will
produce meaningful offsets against the pointers actually used in the
program."""
return logic.var_subst(ptr, {
('ret_addr_input', syntax.word32T):
syntax.mk_var('r0', syntax.word32T)
},
must_subst=False)
def pseudo_node_lvals_rvals(node):
assert node.kind == 'Call'
cc = get_asm_calling_convention_at_node(node)
if not cc:
return None
arg_vars = set(
[var for arg in cc['args'] for var in syntax.get_expr_var_set(arg)])
callee_saved_set = set(cc['callee_saved'])
rets = [(nm, typ) for (nm, typ) in node.rets
if mk_var(nm, typ) not in callee_saved_set]
return (rets, arg_vars)
def pseudo_node_lvals_rvals (node): assert node.kind == 'Call' cc = get_asm_calling_convention_at_node (node) if not cc: return None arg_vars = set ([var for arg in cc['args'] for var in syntax.get_expr_var_set (arg)]) callee_saved_set = set (cc['callee_saved']) rets = [(nm, typ) for (nm, typ) in node.rets if mk_var (nm, typ) not in callee_saved_set] return (rets, arg_vars)
def get_asm_calling_convention_inner (num_c_args, num_c_rets, const_mem):
key = ('Inner', num_c_args, num_c_rets, const_mem)
if key in asm_cc_cache:
return asm_cc_cache[key]
from logic import mk_var_list, mk_stack_sequence
from syntax import mk_var, word32T, builtinTs
arg_regs = mk_var_list (['r0', 'r1', 'r2', 'r3'], word32T)
r0 = arg_regs[0]
sp = mk_var ('r13', word32T)
st = mk_var ('stack', builtinTs['Mem'])
r0_input = mk_var ('r0_input', word32T)
mem = mk_var ('mem', builtinTs['Mem'])
dom = mk_var ('dom', builtinTs['Dom'])
dom_stack = mk_var ('dom_stack', builtinTs['Dom'])
global_args = [mem, dom, st, dom_stack, sp, mk_var ('ret', word32T)]
sregs = mk_stack_sequence (sp, 4, st, word32T, num_c_args + 1)
arg_seq = [r for r in arg_regs] + [s for (s, _) in sregs]
if num_c_rets > 1:
# the 'return-too-much' issue.
# instead r0 is a save-returns-here pointer
arg_seq.pop (0)
rets = mk_stack_sequence (r0_input, 4, st, word32T, num_c_rets)
rets = [r for (r, _) in rets]
else:
rets = [r0]
callee_saved_vars = ([mk_var (v, word32T)
for v in 'r4 r5 r6 r7 r8 r9 r10 r11 r13'.split ()]
+ [dom, dom_stack])
if const_mem:
callee_saved_vars += [mem]
else:
rets += [mem]
rets += [st]
cc = {'args': arg_seq[: num_c_args] + global_args,
'rets': rets, 'callee_saved': callee_saved_vars}
asm_cc_cache[key] = cc
return cc
def inst_const_rets (node):
assert "instruction'" in node.fname
bits = set ([s.lower () for s in node.fname.split ('_')])
fun = functions[node.fname]
def is_const (nm, typ):
if typ in [builtinTs['Mem'], builtinTs['Dom']]:
return True
if typ != word32T:
return False
return not (nm in bits or [al for al in reg_aliases.get (nm, [])
if al in bits])
is_consts = [is_const (nm, typ) for (nm, typ) in fun.outputs]
input_set = set ([v for arg in node.args
for v in syntax.get_expr_var_set (arg)])
return [mk_var (nm, typ)
for ((nm, typ), const) in azip (node.rets, is_consts)
if const and (nm, typ) in input_set]
def candidate_additional_eqs(p, split):
eq_vals = set()
def visitor(expr):
if expr.is_op('Equals') and expr.vals[0].typ.kind == 'Word':
[x, y] = expr.vals
eq_vals.update([(x, y), (y, x)])
for n in p.loop_body(split):
p.nodes[n].visit(lambda x: (), visitor)
for (x, y) in list(eq_vals):
if is_zero(x) and y.is_op('Plus'):
[x, y] = y.vals
eq_vals.add((x, syntax.mk_uminus(y)))
eq_vals.add((y, syntax.mk_uminus(x)))
elif is_zero(x) and y.is_op('Minus'):
[x, y] = y.vals
eq_vals.add((x, y))
eq_vals.add((y, x))
loop = syntax.mk_var('%i', syntax.word32T)
minus_loop_step = syntax.mk_uminus(loop)
vas = search.get_loop_var_analysis_at(p, split)
ls_vas = dict([(var, [data]) for (var, data) in vas
if data[0] == 'LoopLinearSeries'])
cmp_series = [(x, y, rew, offs) for (x, y) in eq_vals
for (_, rew, offs) in ls_vas.get(x, [])]
odd_eqs = []
for (x, y, rew, offs) in cmp_series:
x_init_cmp1 = syntax.mk_less_eq(x, rew(x, minus_loop_step))
x_init_cmp2 = syntax.mk_less_eq(rew(x, minus_loop_step), x)
fin_cmp1 = syntax.mk_less(x, y)
fin_cmp2 = syntax.mk_less(y, x)
odd_eqs.append(syntax.mk_eq(x_init_cmp1, fin_cmp1))
odd_eqs.append(syntax.mk_eq(x_init_cmp2, fin_cmp1))
odd_eqs.append(syntax.mk_eq(x_init_cmp1, fin_cmp2))
odd_eqs.append(syntax.mk_eq(x_init_cmp2, fin_cmp2))
ass_eqs = []
var_deps = p.compute_var_dependencies()
for hook in target_objects.hooks('extra_wcet_assertions'):
for assn in hook(var_deps[split]):
ass_eqs.append(assn)
return odd_eqs + ass_eqs
def mk_function_link_hyps (p, call_vis, tag, adjust_eq_seq = None): (entry, _, args) = p.get_entry_details (tag) ((call_site, restrs), call_tag) = call_vis assert p.nodes[call_site].kind == 'Call' entry_vis = ((entry, ()), p.node_tags[entry][0]) args = [syntax.mk_var (nm, typ) for (nm, typ) in args] pc = pc_true_hyp (call_vis) eq_seq = logic.azip (p.nodes[call_site].args, args) if adjust_eq_seq: eq_seq = adjust_eq_seq (eq_seq) hyps = [pc] + [eq_hyp ((x, call_vis), (y, entry_vis)) for (x, y) in eq_seq if x.typ.kind == 'Word' or x.typ == syntax.builtinTs['Mem'] or x.typ.kind == 'WordArray'] return hyps
def get_extra_sp_defs (rep, tag):
"""all functions will keep the stack pointer equal, whether they have
pairing partners or not. add these extra defs/equalities for the
purposes of stack depth analysis."""
# FIXME how to parametrise this?
sp = mk_var ('r13', syntax.word32T)
defs = {}
items = [(n_vc, x) for (n_vc, x) in rep.funcs.iteritems ()
if logic.is_int (n_vc[0])]
for ((n, vc), (inputs, outputs, _)) in items:
if rep.p.node_tags[n][0] == tag:
inp_sp = solver.smt_expr (sp, inputs, rep.solv)
inp_sp = solver.parse_s_expression (inp_sp)
out_sp = solver.smt_expr (sp, outputs, rep.solv)
out_sp = solver.parse_s_expression (out_sp)
if inp_sp != out_sp:
defs[out_sp] = inp_sp
return defs
def candidate_additional_eqs(p, split):
eq_vals = set()
def visitor(expr):
if expr.is_op("Equals") and expr.vals[0].typ.kind == "Word":
[x, y] = expr.vals
eq_vals.update([(x, y), (y, x)])
for n in p.loop_body(split):
p.nodes[n].visit(lambda x: (), visitor)
for (x, y) in list(eq_vals):
if is_zero(x) and y.is_op("Plus"):
[x, y] = y.vals
eq_vals.add((x, syntax.mk_uminus(y)))
eq_vals.add((y, syntax.mk_uminus(x)))
elif is_zero(x) and y.is_op("Minus"):
[x, y] = y.vals
eq_vals.add((x, y))
eq_vals.add((y, x))
loop = syntax.mk_var("%i", syntax.word32T)
minus_loop_step = syntax.mk_uminus(loop)
vas = search.get_loop_var_analysis_at(p, split)
ls_vas = dict([(var, [data]) for (var, data) in vas if data[0] == "LoopLinearSeries"])
cmp_series = [(x, y, rew, offs) for (x, y) in eq_vals for (_, rew, offs) in ls_vas.get(x, [])]
odd_eqs = []
for (x, y, rew, offs) in cmp_series:
x_init_cmp1 = syntax.mk_less_eq(x, rew(x, minus_loop_step))
x_init_cmp2 = syntax.mk_less_eq(rew(x, minus_loop_step), x)
fin_cmp1 = syntax.mk_less(x, y)
fin_cmp2 = syntax.mk_less(y, x)
odd_eqs.append(syntax.mk_eq(x_init_cmp1, fin_cmp1))
odd_eqs.append(syntax.mk_eq(x_init_cmp2, fin_cmp1))
odd_eqs.append(syntax.mk_eq(x_init_cmp1, fin_cmp2))
odd_eqs.append(syntax.mk_eq(x_init_cmp2, fin_cmp2))
ass_eqs = []
var_deps = p.compute_var_dependencies()
for hook in target_objects.hooks("extra_wcet_assertions"):
for assn in hook(var_deps[split]):
ass_eqs.append(assn)
return odd_eqs + ass_eqs
def get_asm_calling_convention_at_node (node):
cc = get_asm_calling_convention (node.fname)
if not cc:
return None
fun = functions[node.fname]
arg_input_map = dict (azip (fun.inputs, node.args))
ret_output_map = dict (azip (fun.outputs,
[mk_var (nm, typ) for (nm, typ) in node.rets]))
args = [logic.var_subst (arg, arg_input_map) for arg in cc['args']]
rets = [logic.var_subst (ret, ret_output_map) for ret in cc['rets']]
# these are useful because they happen to map ret r0_input back to
# the previous value r0, rather than the useless value r0_input_ignore.
rets_inp = [logic.var_subst (ret, arg_input_map) for ret in cc['rets']]
saved = [logic.var_subst (v, ret_output_map)
for v in cc['callee_saved']]
return {'args': args, 'rets': rets,
'rets_inp': rets_inp, 'callee_saved': saved}
def inst_const_rets(node):
assert "instruction'" in node.fname
bits = set([s.lower() for s in node.fname.split('_')])
fun = functions[node.fname]
def is_const(nm, typ):
if typ in [builtinTs['Mem'], builtinTs['Dom']]:
return True
if typ != word32T:
return False
return not (nm in bits
or [al for al in reg_aliases.get(nm, []) if al in bits])
is_consts = [is_const(nm, typ) for (nm, typ) in fun.outputs]
input_set = set(
[v for arg in node.args for v in syntax.get_expr_var_set(arg)])
return [
mk_var(nm, typ) for ((nm, typ), const) in azip(node.rets, is_consts)
if const and (nm, typ) in input_set
]
def stack_virtualise_expr (expr, sp_offs):
if expr.is_op ('MemAcc') and is_stack (expr.vals[0]):
[m, p] = expr.vals
assert expr.typ == syntax.word32T
ptrs = [(p, 'MemAcc')]
if sp_offs == None:
return (ptrs, None)
else:
if p not in sp_offs:
return (ptrs, expr)
(k, offs) = sp_offs[p]
return (ptrs, mk_var (('Fake', k, offs),
syntax.word32T))
elif expr.kind == 'Op':
vs = [stack_virtualise_expr (v, sp_offs) for v in expr.vals]
return ([p for (ptrs, _) in vs for p in ptrs],
syntax.Expr ('Op', expr.typ, name = expr.name,
vals = [v for (_, v) in vs]))
else:
return ([], expr)
def loop_eq_hyps_at_visit(tag, split, eqs, restrs, visit_num, use_if_at=False):
details = (split, (0, 1), eqs)
visit = split_visit_one_visit(tag, details, restrs, visit_num)
start = split_visit_one_visit(tag, details, restrs, vc_num(0))
def mksub(v):
return lambda exp: logic.var_subst(exp, {('%i', word32T): v},
must_subst=False)
zsub = mksub(mk_word32(0))
if visit_num.kind == 'Number':
isub = mksub(mk_word32(visit_num.n))
else:
isub = mksub(mk_plus(mk_var('%n', word32T), mk_word32(visit_num.n)))
hyps = [(Hyp('PCImp', visit, start), '%s pc imp' % tag)]
hyps += [(eq_hyp((zsub(exp), start), (isub(exp), visit), (split, 0),
use_if_at=use_if_at), '%s const' % tag) for exp in eqs
if logic.inst_eq_at_visit(exp, visit_num)]
return hyps
def linear_eq_hyps_at_visit (tag, split, eqs, restrs, visit_num):
details = (split, (0, 1), eqs)
visit = split_visit_one_visit (tag, details, restrs, visit_num)
start = split_visit_one_visit (tag, details, restrs, vc_num (0))
from syntax import mk_word32, mk_plus, mk_var, word32T
def mksub (v):
return lambda exp: logic.var_subst (exp, {('%i', word32T) : v},
must_subst = False)
zsub = mksub (mk_word32 (0))
if visit_num.kind == 'Number':
isub = mksub (mk_word32 (visit_num.n))
else:
isub = mksub (mk_plus (mk_var ('%n', word32T),
mk_word32 (visit_num.n)))
hyps = [(Hyp ('PCImp', visit, start), '%s pc imp' % tag)]
hyps += [(eq_hyp ((zsub (exp), start), (isub (exp), visit),
(split, 0)), '%s const' % tag)
for exp in eqs if logic.inst_eq_at_visit (exp, visit_num)]
return hyps
def get_asm_calling_convention_at_node(node):
cc = get_asm_calling_convention(node.fname)
if not cc:
return None
fun = functions[node.fname]
arg_input_map = dict(azip(fun.inputs, node.args))
ret_output_map = dict(
azip(fun.outputs, [mk_var(nm, typ) for (nm, typ) in node.rets]))
args = [logic.var_subst(arg, arg_input_map) for arg in cc['args']]
rets = [logic.var_subst(ret, ret_output_map) for ret in cc['rets']]
# these are useful because they happen to map ret r0_input back to
# the previous value r0, rather than the useless value r0_input_ignore.
rets_inp = [logic.var_subst(ret, arg_input_map) for ret in cc['rets']]
saved = [logic.var_subst(v, ret_output_map) for v in cc['callee_saved']]
return {
'args': args,
'rets': rets,
'rets_inp': rets_inp,
'callee_saved': saved
}
def get_extra_sp_defs(rep, tag):
"""add extra defs/equalities about stack pointer for the
purposes of stack depth analysis."""
# FIXME how to parametrise this?
sp = mk_var('r13', syntax.word32T)
defs = {}
fcalls = [
n_vc for n_vc in rep.funcs if logic.is_int(n_vc[0])
if rep.p.node_tags[n_vc[0]][0] == tag
if preserves_sp(rep.p.nodes[n_vc[0]].fname)
]
for (n, vc) in fcalls:
(inputs, outputs, _) = rep.funcs[(n, vc)]
if (sp.name, sp.typ) not in outputs:
continue
inp_sp = solver.smt_expr(sp, inputs, rep.solv)
inp_sp = solver.parse_s_expression(inp_sp)
out_sp = solver.smt_expr(sp, outputs, rep.solv)
out_sp = solver.parse_s_expression(out_sp)
if inp_sp != out_sp:
defs[out_sp] = inp_sp
return defs
def add_impl_fun (impl_fname, regspecs):
if impl_fname in functions:
return
ident_v = ("inst_ident", syntax.builtinTs['Token'])
inps = [s for s in regspecs if s == 'I']
inps = ['reg_val%d' % (i + 1) for (i, s) in enumerate (inps)]
rets = [s for s in regspecs if s == 'O']
rets = ['ret_val%d' % (i + 1) for (i, s) in enumerate (rets)]
fun = mk_fun (impl_fname, inps, [ident_v], rets, [], bin_globs)
inp_eqs = [((mk_var (nm, typ), 'ASM_IN'), (mk_var (nm, typ), 'C_IN'))
for (nm, typ) in fun.inputs]
inp_eqs += [((logic.mk_rodata (mk_var (nm, typ)), 'ASM_IN'),
(syntax.true_term, 'C_IN')) for (nm, typ) in bin_globs]
out_eqs = [((mk_var (nm, typ), 'ASM_OUT'), (mk_var (nm, typ), 'C_OUT'))
for (nm, typ) in fun.outputs]
out_eqs += [((logic.mk_rodata (mk_var (nm, typ)), 'ASM_OUT'),
(syntax.true_term, 'C_OUT')) for (nm, typ) in bin_globs]
pair = logic.Pairing (['ASM', 'C'],
{'C': impl_fname, 'ASM': impl_fname},
(inp_eqs, out_eqs))
assert impl_fname not in pairings
functions[impl_fname] = fun
pairings[impl_fname] = [pair]
def add_recursion_ident(f, group, idents, extra_unfolds):
from syntax import mk_eq, mk_implies, mk_var
p = problem.Problem(None, name='Recursion Test')
chain = []
tag = 'fun0'
p.add_entry_function(functions[f], tag)
p.do_analysis()
assns = []
recursion_last_assns[0] = assns
while True:
res = find_unknown_recursion(p, group, idents, tag, assns,
extra_unfolds)
if res == None:
break
if p.nodes[res].fname not in group:
problem.inline_at_point(p, res)
continue
fname = p.nodes[res].fname
chain.append(fname)
tag = 'fun%d' % len(chain)
(args, _, entry) = p.add_entry_function(functions[fname], tag)
p.do_analysis()
assns += function_link_assns(p, res, tag)
if chain == []:
return None
recursion_trace.append(' created fun chain %s' % chain)
word_args = [(i, mk_var(s, typ)) for (i, (s, typ)) in enumerate(args)
if typ.kind == 'Word']
rep = rep_graph.mk_graph_slice(p, fast=True)
(_, env) = rep.get_node_pc_env((entry, ()))
m = {}
res = rep.test_hyp_whyps(syntax.false_term, assns, model=m)
assert m
if find_unknown_recursion(p, group, idents, tag, [], []) == None:
idents.setdefault(fname, [])
idents[fname].append(syntax.true_term)
recursion_trace.append(' found final ident for %s' % fname)
return syntax.true_term
assert word_args
recursion_trace.append(' scanning for ident for %s' % fname)
for (i, arg) in word_args:
(nm, typ) = functions[fname].inputs[i]
arg_smt = solver.to_smt_expr(arg, env, rep.solv)
val = search.eval_model_expr(m, rep.solv, arg_smt)
if not rep.test_hyp_whyps(mk_eq(arg_smt, val), assns):
recursion_trace.append(' discarded %s = 0x%x, not stable' %
(nm, val.val))
continue
entry_vis = ((entry, ()), tag)
ass = rep_graph.eq_hyp((arg, entry_vis), (val, entry_vis))
res = find_unknown_recursion(p, group, idents, tag, assns + [ass], [])
if res:
fname2 = p.nodes[res].fname
recursion_trace.append(
' discarded %s, allows recursion to %s' % (nm, fname2))
continue
eq = syntax.mk_eq(mk_var(nm, typ), val)
idents.setdefault(fname, [])
idents[fname].append(eq)
recursion_trace.append(' found ident for %s: %s' % (fname, eq))
return eq
assert not "identifying assertion found"
def pretty_lambda (t):
v = syntax.mk_var ('#seq-visits', word32T)
t = logic.var_subst (t, {('%i', word32T) : v}, must_subst = False)
return syntax.pretty_expr (t, print_type = True)
def fresh_var(self, name, typ):
name = fresh_name(name, self.vs, typ)
return mk_var(name, typ)
def avail_val(vs, typ):
for (nm, typ2) in vs:
if typ2 == typ:
return mk_var(nm, typ2)
return logic.default_val(typ)
def mk_var_list (vs, typ): return [syntax.mk_var (v, typ) for v in vs]
def avail_val (vs, typ): for (nm, typ2) in vs: if typ2 == typ: return mk_var (nm, typ2) return logic.default_val (typ)
def const_ret_hook(node, nm, typ):
consts = node_const_rets(node)
return consts and mk_var(nm, typ) in consts
def fresh_var (self, name, typ): name = fresh_name (name, self.vs, typ) return mk_var (name, typ)
def mk_loop_counter_eq_hyp(p, split, restrs, n):
details = (split, (0, 1), [])
(tag, _) = p.node_tags[split]
visit = split_visit_one_visit(tag, details, restrs, vc_offs(0))
return eq_hyp((mk_var('%n', word32T), visit), (mk_word32(n), visit),
(split, 0))
def pretty_lambda(t):
v = syntax.mk_var('#seq-visits', word32T)
t = logic.var_subst(t, {('%i', word32T): v}, must_subst=False)
return syntax.pretty_expr(t, print_type=True)
def const_ret_hook (node, nm, typ): consts = node_const_rets (node) return consts and mk_var (nm, typ) in consts
def add_recursion_ident (f, group, idents, extra_unfolds):
from syntax import mk_eq, mk_implies, mk_var
p = problem.Problem (None, name = 'Recursion Test')
chain = []
tag = 'fun0'
p.add_entry_function (functions[f], tag)
p.do_analysis ()
assns = []
recursion_last_assns[0] = assns
while True:
res = find_unknown_recursion (p, group, idents, tag, assns,
extra_unfolds)
if res == None:
break
if p.nodes[res].fname not in group:
problem.inline_at_point (p, res)
continue
fname = p.nodes[res].fname
chain.append (fname)
tag = 'fun%d' % len (chain)
(args, _, entry) = p.add_entry_function (functions[fname], tag)
p.do_analysis ()
assns += function_link_assns (p, res, tag)
if chain == []:
return None
recursion_trace.append (' created fun chain %s' % chain)
word_args = [(i, mk_var (s, typ))
for (i, (s, typ)) in enumerate (args)
if typ.kind == 'Word']
rep = rep_graph.mk_graph_slice (p, fast = True)
(_, env) = rep.get_node_pc_env ((entry, ()))
m = {}
res = rep.test_hyp_whyps (syntax.false_term, assns, model = m)
assert m
if find_unknown_recursion (p, group, idents, tag, [], []) == None:
idents.setdefault (fname, [])
idents[fname].append (syntax.true_term)
recursion_trace.append (' found final ident for %s' % fname)
return syntax.true_term
assert word_args
recursion_trace.append (' scanning for ident for %s' % fname)
for (i, arg) in word_args:
(nm, typ) = functions[fname].inputs[i]
arg_smt = solver.to_smt_expr (arg, env, rep.solv)
val = search.eval_model_expr (m, rep.solv, arg_smt)
if not rep.test_hyp_whyps (mk_eq (arg_smt, val), assns):
recursion_trace.append (' discarded %s = 0x%x, not stable' % (nm, val.val))
continue
entry_vis = ((entry, ()), tag)
ass = rep_graph.eq_hyp ((arg, entry_vis), (val, entry_vis))
res = find_unknown_recursion (p, group, idents, tag,
assns + [ass], [])
if res:
fname2 = p.nodes[res].fname
recursion_trace.append (' discarded %s, allows recursion to %s' % (nm, fname2))
continue
eq = syntax.mk_eq (mk_var (nm, typ), val)
idents.setdefault (fname, [])
idents[fname].append (eq)
recursion_trace.append (' found ident for %s: %s' % (fname, eq))
return eq
assert not "identifying assertion found"