def simp_cst_propagation(e_s, expr): """This passe includes: - Constant folding - Common logical identities - Common binary identities """ # merge associatif op args = list(expr.args) op_name = expr.op # simpl integer manip # int OP int => int # TODO: <<< >>> << >> are architecture dependant if op_name in op_propag_cst: while (len(args) >= 2 and args[-1].is_int() and args[-2].is_int()): int2 = args.pop() int1 = args.pop() if op_name == '+': out = int1.arg + int2.arg elif op_name == '*': out = int1.arg * int2.arg elif op_name == '**': out = int1.arg**int2.arg elif op_name == '^': out = int1.arg ^ int2.arg elif op_name == '&': out = int1.arg & int2.arg elif op_name == '|': out = int1.arg | int2.arg elif op_name == '>>': out = int1.arg >> int2.arg elif op_name == '<<': out = int1.arg << int2.arg elif op_name == 'a>>': tmp1 = mod_size2int[int1.arg.size](int1.arg) tmp2 = mod_size2uint[int2.arg.size](int2.arg) out = mod_size2uint[int1.arg.size](tmp1 >> tmp2) elif op_name == '>>>': out = (int1.arg >> (int2.arg % int2.size) | int1.arg << ((int1.size - int2.arg) % int2.size)) elif op_name == '<<<': out = (int1.arg << (int2.arg % int2.size) | int1.arg >> ((int1.size - int2.arg) % int2.size)) elif op_name == '/': out = int1.arg / int2.arg elif op_name == '%': out = int1.arg % int2.arg elif op_name == 'idiv': assert int2.arg.arg tmp1 = mod_size2int[int1.arg.size](int1.arg) tmp2 = mod_size2int[int2.arg.size](int2.arg) out = mod_size2uint[int1.arg.size](tmp1 / tmp2) elif op_name == 'imod': assert int2.arg.arg tmp1 = mod_size2int[int1.arg.size](int1.arg) tmp2 = mod_size2int[int2.arg.size](int2.arg) out = mod_size2uint[int1.arg.size](tmp1 % tmp2) elif op_name == 'umod': assert int2.arg.arg tmp1 = mod_size2uint[int1.arg.size](int1.arg) tmp2 = mod_size2uint[int2.arg.size](int2.arg) out = mod_size2uint[int1.arg.size](tmp1 % tmp2) elif op_name == 'udiv': assert int2.arg.arg tmp1 = mod_size2uint[int1.arg.size](int1.arg) tmp2 = mod_size2uint[int2.arg.size](int2.arg) out = mod_size2uint[int1.arg.size](tmp1 / tmp2) args.append(ExprInt(out, int1.size)) # bsf(int) => int if op_name == "bsf" and args[0].is_int() and args[0].arg != 0: i = 0 while args[0].arg & (1 << i) == 0: i += 1 return ExprInt(i, args[0].size) # bsr(int) => int if op_name == "bsr" and args[0].is_int() and args[0].arg != 0: i = args[0].size - 1 while args[0].arg & (1 << i) == 0: i -= 1 return ExprInt(i, args[0].size) # -(-(A)) => A if (op_name == '-' and len(args) == 1 and args[0].is_op('-') and len(args[0].args) == 1): return args[0].args[0] # -(int) => -int if op_name == '-' and len(args) == 1 and args[0].is_int(): return ExprInt(-int(args[0]), expr.size) # A op 0 =>A if op_name in ['+', '|', "^", "<<", ">>", "<<<", ">>>"] and len(args) > 1: if args[-1].is_int(0): args.pop() # A - 0 =>A if op_name == '-' and len(args) > 1 and args[-1].is_int(0): assert len( args) == 2 # Op '-' with more than 2 args: SantityCheckError return args[0] # A * 1 =>A if op_name == "*" and len(args) > 1 and args[-1].is_int(1): args.pop() # for cannon form # A * -1 => - A if op_name == "*" and len(args) > 1 and args[-1] == args[-1].mask: args.pop() args[-1] = -args[-1] # op A => A if op_name in [ '+', '*', '^', '&', '|', '>>', '<<', 'a>>', '<<<', '>>>', 'idiv', 'imod', 'umod', 'udiv' ] and len(args) == 1: return args[0] # A-B => A + (-B) if op_name == '-' and len(args) > 1: if len(args) > 2: raise ValueError( 'sanity check fail on expr -: should have one or 2 args ' + '%r %s' % (expr, expr)) return ExprOp('+', args[0], -args[1]) # A op 0 => 0 if op_name in ['&', "*"] and args[1].is_int(0): return ExprInt(0, expr.size) # - (A + B +...) => -A + -B + -C if op_name == '-' and len(args) == 1 and args[0].is_op('+'): args = [-a for a in args[0].args] return ExprOp('+', *args) # -(a?int1:int2) => (a?-int1:-int2) if (op_name == '-' and len(args) == 1 and args[0].is_cond() and args[0].src1.is_int() and args[0].src2.is_int()): int1 = args[0].src1 int2 = args[0].src2 int1 = ExprInt(-int1.arg, int1.size) int2 = ExprInt(-int2.arg, int2.size) return ExprCond(args[0].cond, int1, int2) i = 0 while i < len(args) - 1: j = i + 1 while j < len(args): # A ^ A => 0 if op_name == '^' and args[i] == args[j]: args[i] = ExprInt(0, args[i].size) del args[j] continue # A + (- A) => 0 if op_name == '+' and args[j].is_op("-"): if len(args[j].args) == 1 and args[i] == args[j].args[0]: args[i] = ExprInt(0, args[i].size) del args[j] continue # (- A) + A => 0 if op_name == '+' and args[i].is_op("-"): if len(args[i].args) == 1 and args[j] == args[i].args[0]: args[i] = ExprInt(0, args[i].size) del args[j] continue # A | A => A if op_name == '|' and args[i] == args[j]: del args[j] continue # A & A => A if op_name == '&' and args[i] == args[j]: del args[j] continue j += 1 i += 1 if op_name in ['|', '&', '%', '/', '**'] and len(args) == 1: return args[0] # A <<< A.size => A if (op_name in ['<<<', '>>>'] and args[1].is_int() and args[1].arg == args[0].size): return args[0] # A <<< X <<< Y => A <<< (X+Y) (ou <<< >>>) if (op_name in ['<<<', '>>>'] and args[0].is_op() and args[0].op in ['<<<', '>>>']): op1 = op_name op2 = args[0].op if op1 == op2: op_name = op1 args1 = args[0].args[1] + args[1] else: op_name = op2 args1 = args[0].args[1] - args[1] args0 = args[0].args[0] args = [args0, args1] # A >> X >> Y => A >> (X+Y) if (op_name in ['<<', '>>'] and args[0].is_op(op_name)): args = [args[0].args[0], args[0].args[1] + args[1]] # ((A & A.mask) if op_name == "&" and args[-1] == expr.mask: return ExprOp('&', *args[:-1]) # ((A | A.mask) if op_name == "|" and args[-1] == expr.mask: return args[-1] # ! (!X + int) => X - int # TODO # ((A & mask) >> shift) whith mask < 2**shift => 0 if op_name == ">>" and args[1].is_int() and args[0].is_op("&"): if (args[0].args[1].is_int() and 2**args[1].arg > args[0].args[1].arg): return ExprInt(0, args[0].size) # parity(int) => int if op_name == 'parity' and args[0].is_int(): return ExprInt(parity(int(args[0])), 1) # (-a) * b * (-c) * (-d) => (-a) * b * c * d if op_name == "*" and len(args) > 1: new_args = [] counter = 0 for arg in args: if arg.is_op('-') and len(arg.args) == 1: new_args.append(arg.args[0]) counter += 1 else: new_args.append(arg) if counter % 2: return -ExprOp(op_name, *new_args) args = new_args # A << int with A ExprCompose => move index if (op_name == "<<" and args[0].is_compose() and args[1].is_int() and int(args[1]) != 0): final_size = args[0].size shift = int(args[1]) new_args = [] # shift indexes for index, arg in args[0].iter_args(): new_args.append((arg, index + shift, index + shift + arg.size)) # filter out expression filter_args = [] min_index = final_size for tmp, start, stop in new_args: if start >= final_size: continue if stop > final_size: tmp = tmp[:tmp.size - (stop - final_size)] stop = final_size filter_args.append(tmp) min_index = min(start, min_index) # create entry 0 assert min_index != 0 tmp = ExprInt(0, min_index) args = [tmp] + filter_args return ExprCompose(*args) # A >> int with A ExprCompose => move index if op_name == ">>" and args[0].is_compose() and args[1].is_int(): final_size = args[0].size shift = int(args[1]) new_args = [] # shift indexes for index, arg in args[0].iter_args(): new_args.append((arg, index - shift, index + arg.size - shift)) # filter out expression filter_args = [] max_index = 0 for tmp, start, stop in new_args: if stop <= 0: continue if start < 0: tmp = tmp[-start:] start = 0 filter_args.append(tmp) max_index = max(stop, max_index) # create entry 0 tmp = ExprInt(0, final_size - max_index) args = filter_args + [tmp] return ExprCompose(*args) # Compose(a) OP Compose(b) with a/b same bounds => Compose(a OP b) if op_name in ['|', '&', '^'] and all([arg.is_compose() for arg in args]): bounds = set() for arg in args: bound = tuple([tmp.size for tmp in arg.args]) bounds.add(bound) if len(bounds) == 1: bound = list(bounds)[0] new_args = [[tmp] for tmp in args[0].args] for sub_arg in args[1:]: for i, tmp in enumerate(sub_arg.args): new_args[i].append(tmp) args = [] for i, arg in enumerate(new_args): args.append(ExprOp(op_name, *arg)) return ExprCompose(*args) # <<<c_rez, >>>c_rez if op_name in [">>>c_rez", "<<<c_rez"]: assert len(args) == 3 dest, rounds, carry_flag = args # Skipped if rounds is 0 if rounds.is_int(0): return dest elif all(arg.is_int() for arg in args): # The expression can be resolved tmp = int(dest) carry_flag = int(carry_flag) size = dest.size tmp_count = (int(rounds) & (0x3f if size == 64 else 0x1f)) % (size + 1) if op_name == ">>>c_rez": while tmp_count != 0: tmp_cf = tmp & 1 tmp = (tmp >> 1) + (carry_flag << (size - 1)) carry_flag = tmp_cf tmp_count -= 1 tmp &= int(dest.mask) elif op_name == "<<<c_rez": while tmp_count != 0: tmp_cf = (tmp >> (size - 1)) & 1 tmp = (tmp << 1) + carry_flag carry_flag = tmp_cf tmp_count -= 1 tmp &= int(dest.mask) else: raise RuntimeError("Unknown operation: %s" % op_name) return ExprInt(tmp, size=dest.size) return ExprOp(op_name, *args)
def simp_cst_propagation(e_s, expr): """This passe includes: - Constant folding - Common logical identities - Common binary identities """ # merge associatif op args = list(expr.args) op_name = expr.op # simpl integer manip # int OP int => int # TODO: <<< >>> << >> are architecture dependant if op_name in op_propag_cst: while (len(args) >= 2 and args[-1].is_int() and args[-2].is_int()): int2 = args.pop() int1 = args.pop() if op_name == '+': out = int1.arg + int2.arg elif op_name == '*': out = int1.arg * int2.arg elif op_name == '**': out =int1.arg ** int2.arg elif op_name == '^': out = int1.arg ^ int2.arg elif op_name == '&': out = int1.arg & int2.arg elif op_name == '|': out = int1.arg | int2.arg elif op_name == '>>': if int(int2) > int1.size: out = 0 else: out = int1.arg >> int2.arg elif op_name == '<<': if int(int2) > int1.size: out = 0 else: out = int1.arg << int2.arg elif op_name == 'a>>': tmp1 = mod_size2int[int1.arg.size](int1.arg) tmp2 = mod_size2uint[int2.arg.size](int2.arg) if tmp2 > int1.size: is_signed = int(int1) & (1 << (int1.size - 1)) if is_signed: out = -1 else: out = 0 else: out = mod_size2uint[int1.arg.size](tmp1 >> tmp2) elif op_name == '>>>': shifter = int2.arg % int2.size out = (int1.arg >> shifter) | (int1.arg << (int2.size - shifter)) elif op_name == '<<<': shifter = int2.arg % int2.size out = (int1.arg << shifter) | (int1.arg >> (int2.size - shifter)) elif op_name == '/': out = int1.arg / int2.arg elif op_name == '%': out = int1.arg % int2.arg elif op_name == 'idiv': assert int2.arg.arg tmp1 = mod_size2int[int1.arg.size](int1.arg) tmp2 = mod_size2int[int2.arg.size](int2.arg) out = mod_size2uint[int1.arg.size](tmp1 / tmp2) elif op_name == 'imod': assert int2.arg.arg tmp1 = mod_size2int[int1.arg.size](int1.arg) tmp2 = mod_size2int[int2.arg.size](int2.arg) out = mod_size2uint[int1.arg.size](tmp1 % tmp2) elif op_name == 'umod': assert int2.arg.arg tmp1 = mod_size2uint[int1.arg.size](int1.arg) tmp2 = mod_size2uint[int2.arg.size](int2.arg) out = mod_size2uint[int1.arg.size](tmp1 % tmp2) elif op_name == 'udiv': assert int2.arg.arg tmp1 = mod_size2uint[int1.arg.size](int1.arg) tmp2 = mod_size2uint[int2.arg.size](int2.arg) out = mod_size2uint[int1.arg.size](tmp1 / tmp2) args.append(ExprInt(out, int1.size)) # cnttrailzeros(int) => int if op_name == "cnttrailzeros" and args[0].is_int(): i = 0 while args[0].arg & (1 << i) == 0 and i < args[0].size: i += 1 return ExprInt(i, args[0].size) # cntleadzeros(int) => int if op_name == "cntleadzeros" and args[0].is_int(): if args[0].arg == 0: return ExprInt(args[0].size, args[0].size) i = args[0].size - 1 while args[0].arg & (1 << i) == 0: i -= 1 return ExprInt(expr.size - (i + 1), args[0].size) # -(-(A)) => A if (op_name == '-' and len(args) == 1 and args[0].is_op('-') and len(args[0].args) == 1): return args[0].args[0] # -(int) => -int if op_name == '-' and len(args) == 1 and args[0].is_int(): return ExprInt(-int(args[0]), expr.size) # A op 0 =>A if op_name in ['+', '|', "^", "<<", ">>", "<<<", ">>>"] and len(args) > 1: if args[-1].is_int(0): args.pop() # A - 0 =>A if op_name == '-' and len(args) > 1 and args[-1].is_int(0): assert len(args) == 2 # Op '-' with more than 2 args: SantityCheckError return args[0] # A * 1 =>A if op_name == "*" and len(args) > 1 and args[-1].is_int(1): args.pop() # for cannon form # A * -1 => - A if op_name == "*" and len(args) > 1 and args[-1] == args[-1].mask: args.pop() args[-1] = - args[-1] # op A => A if op_name in ['+', '*', '^', '&', '|', '>>', '<<', 'a>>', '<<<', '>>>', 'idiv', 'imod', 'umod', 'udiv'] and len(args) == 1: return args[0] # A-B => A + (-B) if op_name == '-' and len(args) > 1: if len(args) > 2: raise ValueError( 'sanity check fail on expr -: should have one or 2 args ' + '%r %s' % (expr, expr)) return ExprOp('+', args[0], -args[1]) # A op 0 => 0 if op_name in ['&', "*"] and args[-1].is_int(0): return ExprInt(0, expr.size) # - (A + B +...) => -A + -B + -C if op_name == '-' and len(args) == 1 and args[0].is_op('+'): args = [-a for a in args[0].args] return ExprOp('+', *args) # -(a?int1:int2) => (a?-int1:-int2) if (op_name == '-' and len(args) == 1 and args[0].is_cond() and args[0].src1.is_int() and args[0].src2.is_int()): int1 = args[0].src1 int2 = args[0].src2 int1 = ExprInt(-int1.arg, int1.size) int2 = ExprInt(-int2.arg, int2.size) return ExprCond(args[0].cond, int1, int2) i = 0 while i < len(args) - 1: j = i + 1 while j < len(args): # A ^ A => 0 if op_name == '^' and args[i] == args[j]: args[i] = ExprInt(0, args[i].size) del args[j] continue # A + (- A) => 0 if op_name == '+' and args[j].is_op("-"): if len(args[j].args) == 1 and args[i] == args[j].args[0]: args[i] = ExprInt(0, args[i].size) del args[j] continue # (- A) + A => 0 if op_name == '+' and args[i].is_op("-"): if len(args[i].args) == 1 and args[j] == args[i].args[0]: args[i] = ExprInt(0, args[i].size) del args[j] continue # A | A => A if op_name == '|' and args[i] == args[j]: del args[j] continue # A & A => A if op_name == '&' and args[i] == args[j]: del args[j] continue j += 1 i += 1 if op_name in ['|', '&', '%', '/', '**'] and len(args) == 1: return args[0] # A <<< A.size => A if (op_name in ['<<<', '>>>'] and args[1].is_int() and args[1].arg == args[0].size): return args[0] # (A <<< X) <<< Y => A <<< (X+Y) (or <<< >>>) if X + Y does not overflow if (op_name in ['<<<', '>>>'] and args[0].is_op() and args[0].op in ['<<<', '>>>']): A = args[0].args[0] X = args[0].args[1] Y = args[1] if op_name != args[0].op and e_s(X - Y) == ExprInt(0, X.size): return args[0].args[0] elif X.is_int() and Y.is_int(): new_X = int(X) % expr.size new_Y = int(Y) % expr.size if op_name == args[0].op: rot = (new_X + new_Y) % expr.size op = op_name else: rot = new_Y - new_X op = op_name if rot < 0: rot = - rot op = {">>>": "<<<", "<<<": ">>>"}[op_name] args = [A, ExprInt(rot, expr.size)] op_name = op else: # Do not consider this case, too tricky (overflow on addition / # substraction) pass # A >> X >> Y => A >> (X+Y) if X + Y does not overflow # To be sure, only consider the simplification when X.msb and Y.msb are 0 if (op_name in ['<<', '>>'] and args[0].is_op(op_name)): X = args[0].args[1] Y = args[1] if (e_s(X.msb()) == ExprInt(0, 1) and e_s(Y.msb()) == ExprInt(0, 1)): args = [args[0].args[0], X + Y] # ((var >> int1) << int1) => var & mask # ((var << int1) >> int1) => var & mask if (op_name in ['<<', '>>'] and args[0].is_op() and args[0].op in ['<<', '>>'] and op_name != args[0]): var = args[0].args[0] int1 = args[0].args[1] int2 = args[1] if int1 == int2 and int1.is_int() and int(int1) < expr.size: if op_name == '>>': mask = ExprInt((1 << (expr.size - int(int1))) - 1, expr.size) else: mask = ExprInt( ((1 << int(int1)) - 1) ^ ((1 << expr.size) - 1), expr.size ) ret = var & mask return ret # ((A & A.mask) if op_name == "&" and args[-1] == expr.mask: return ExprOp('&', *args[:-1]) # ((A | A.mask) if op_name == "|" and args[-1] == expr.mask: return args[-1] # ! (!X + int) => X - int # TODO # ((A & mask) >> shift) whith mask < 2**shift => 0 if op_name == ">>" and args[1].is_int() and args[0].is_op("&"): if (args[0].args[1].is_int() and 2 ** args[1].arg > args[0].args[1].arg): return ExprInt(0, args[0].size) # parity(int) => int if op_name == 'parity' and args[0].is_int(): return ExprInt(parity(int(args[0])), 1) # (-a) * b * (-c) * (-d) => (-a) * b * c * d if op_name == "*" and len(args) > 1: new_args = [] counter = 0 for arg in args: if arg.is_op('-') and len(arg.args) == 1: new_args.append(arg.args[0]) counter += 1 else: new_args.append(arg) if counter % 2: return -ExprOp(op_name, *new_args) args = new_args # A << int with A ExprCompose => move index if (op_name == "<<" and args[0].is_compose() and args[1].is_int() and int(args[1]) != 0): final_size = args[0].size shift = int(args[1]) new_args = [] # shift indexes for index, arg in args[0].iter_args(): new_args.append((arg, index+shift, index+shift+arg.size)) # filter out expression filter_args = [] min_index = final_size for tmp, start, stop in new_args: if start >= final_size: continue if stop > final_size: tmp = tmp[:tmp.size - (stop - final_size)] stop = final_size filter_args.append(tmp) min_index = min(start, min_index) # create entry 0 assert min_index != 0 tmp = ExprInt(0, min_index) args = [tmp] + filter_args return ExprCompose(*args) # A >> int with A ExprCompose => move index if op_name == ">>" and args[0].is_compose() and args[1].is_int(): final_size = args[0].size shift = int(args[1]) new_args = [] # shift indexes for index, arg in args[0].iter_args(): new_args.append((arg, index-shift, index+arg.size-shift)) # filter out expression filter_args = [] max_index = 0 for tmp, start, stop in new_args: if stop <= 0: continue if start < 0: tmp = tmp[-start:] start = 0 filter_args.append(tmp) max_index = max(stop, max_index) # create entry 0 tmp = ExprInt(0, final_size - max_index) args = filter_args + [tmp] return ExprCompose(*args) # Compose(a) OP Compose(b) with a/b same bounds => Compose(a OP b) if op_name in ['|', '&', '^'] and all([arg.is_compose() for arg in args]): bounds = set() for arg in args: bound = tuple([tmp.size for tmp in arg.args]) bounds.add(bound) if len(bounds) == 1: bound = list(bounds)[0] new_args = [[tmp] for tmp in args[0].args] for sub_arg in args[1:]: for i, tmp in enumerate(sub_arg.args): new_args[i].append(tmp) args = [] for i, arg in enumerate(new_args): args.append(ExprOp(op_name, *arg)) return ExprCompose(*args) return ExprOp(op_name, *args)
def simp_cst_propagation(e_s, expr): """This passe includes: - Constant folding - Common logical identities - Common binary identities """ # merge associatif op args = list(expr.args) op_name = expr.op # simpl integer manip # int OP int => int # TODO: <<< >>> << >> are architecture dependant if op_name in op_propag_cst: while (len(args) >= 2 and args[-1].is_int() and args[-2].is_int()): int2 = args.pop() int1 = args.pop() if op_name == '+': out = int1.arg + int2.arg elif op_name == '*': out = int1.arg * int2.arg elif op_name == '**': out =int1.arg ** int2.arg elif op_name == '^': out = int1.arg ^ int2.arg elif op_name == '&': out = int1.arg & int2.arg elif op_name == '|': out = int1.arg | int2.arg elif op_name == '>>': if int(int2) > int1.size: out = 0 else: out = int1.arg >> int2.arg elif op_name == '<<': if int(int2) > int1.size: out = 0 else: out = int1.arg << int2.arg elif op_name == 'a>>': tmp1 = mod_size2int[int1.arg.size](int1.arg) tmp2 = mod_size2uint[int2.arg.size](int2.arg) if tmp2 > int1.size: is_signed = int(int1) & (1 << (int1.size - 1)) if is_signed: out = -1 else: out = 0 else: out = mod_size2uint[int1.arg.size](tmp1 >> tmp2) elif op_name == '>>>': shifter = int2.arg % int2.size out = (int1.arg >> shifter) | (int1.arg << (int2.size - shifter)) elif op_name == '<<<': shifter = int2.arg % int2.size out = (int1.arg << shifter) | (int1.arg >> (int2.size - shifter)) elif op_name == '/': out = int1.arg / int2.arg elif op_name == '%': out = int1.arg % int2.arg elif op_name == 'idiv': assert int2.arg.arg tmp1 = mod_size2int[int1.arg.size](int1.arg) tmp2 = mod_size2int[int2.arg.size](int2.arg) out = mod_size2uint[int1.arg.size](tmp1 / tmp2) elif op_name == 'imod': assert int2.arg.arg tmp1 = mod_size2int[int1.arg.size](int1.arg) tmp2 = mod_size2int[int2.arg.size](int2.arg) out = mod_size2uint[int1.arg.size](tmp1 % tmp2) elif op_name == 'umod': assert int2.arg.arg tmp1 = mod_size2uint[int1.arg.size](int1.arg) tmp2 = mod_size2uint[int2.arg.size](int2.arg) out = mod_size2uint[int1.arg.size](tmp1 % tmp2) elif op_name == 'udiv': assert int2.arg.arg tmp1 = mod_size2uint[int1.arg.size](int1.arg) tmp2 = mod_size2uint[int2.arg.size](int2.arg) out = mod_size2uint[int1.arg.size](tmp1 / tmp2) args.append(ExprInt(out, int1.size)) # cnttrailzeros(int) => int if op_name == "cnttrailzeros" and args[0].is_int(): i = 0 while args[0].arg & (1 << i) == 0 and i < args[0].size: i += 1 return ExprInt(i, args[0].size) # cntleadzeros(int) => int if op_name == "cntleadzeros" and args[0].is_int(): if args[0].arg == 0: return ExprInt(args[0].size, args[0].size) i = args[0].size - 1 while args[0].arg & (1 << i) == 0: i -= 1 return ExprInt(expr.size - (i + 1), args[0].size) # -(-(A)) => A if (op_name == '-' and len(args) == 1 and args[0].is_op('-') and len(args[0].args) == 1): return args[0].args[0] # -(int) => -int if op_name == '-' and len(args) == 1 and args[0].is_int(): return ExprInt(-int(args[0]), expr.size) # A op 0 =>A if op_name in ['+', '|', "^", "<<", ">>", "<<<", ">>>"] and len(args) > 1: if args[-1].is_int(0): args.pop() # A - 0 =>A if op_name == '-' and len(args) > 1 and args[-1].is_int(0): assert len(args) == 2 # Op '-' with more than 2 args: SantityCheckError return args[0] # A * 1 =>A if op_name == "*" and len(args) > 1 and args[-1].is_int(1): args.pop() # for cannon form # A * -1 => - A if op_name == "*" and len(args) > 1 and args[-1] == args[-1].mask: args.pop() args[-1] = - args[-1] # op A => A if op_name in ['+', '*', '^', '&', '|', '>>', '<<', 'a>>', '<<<', '>>>', 'idiv', 'imod', 'umod', 'udiv'] and len(args) == 1: return args[0] # A-B => A + (-B) if op_name == '-' and len(args) > 1: if len(args) > 2: raise ValueError( 'sanity check fail on expr -: should have one or 2 args ' + '%r %s' % (expr, expr)) return ExprOp('+', args[0], -args[1]) # A op 0 => 0 if op_name in ['&', "*"] and args[-1].is_int(0): return ExprInt(0, expr.size) # - (A + B +...) => -A + -B + -C if op_name == '-' and len(args) == 1 and args[0].is_op('+'): args = [-a for a in args[0].args] return ExprOp('+', *args) # -(a?int1:int2) => (a?-int1:-int2) if (op_name == '-' and len(args) == 1 and args[0].is_cond() and args[0].src1.is_int() and args[0].src2.is_int()): int1 = args[0].src1 int2 = args[0].src2 int1 = ExprInt(-int1.arg, int1.size) int2 = ExprInt(-int2.arg, int2.size) return ExprCond(args[0].cond, int1, int2) i = 0 while i < len(args) - 1: j = i + 1 while j < len(args): # A ^ A => 0 if op_name == '^' and args[i] == args[j]: args[i] = ExprInt(0, args[i].size) del args[j] continue # A + (- A) => 0 if op_name == '+' and args[j].is_op("-"): if len(args[j].args) == 1 and args[i] == args[j].args[0]: args[i] = ExprInt(0, args[i].size) del args[j] continue # (- A) + A => 0 if op_name == '+' and args[i].is_op("-"): if len(args[i].args) == 1 and args[j] == args[i].args[0]: args[i] = ExprInt(0, args[i].size) del args[j] continue # A | A => A if op_name == '|' and args[i] == args[j]: del args[j] continue # A & A => A if op_name == '&' and args[i] == args[j]: del args[j] continue j += 1 i += 1 if op_name in ['|', '&', '%', '/', '**'] and len(args) == 1: return args[0] # A <<< A.size => A if (op_name in ['<<<', '>>>'] and args[1].is_int() and args[1].arg == args[0].size): return args[0] # (A <<< X) <<< Y => A <<< (X+Y) (or <<< >>>) if X + Y does not overflow if (op_name in ['<<<', '>>>'] and args[0].is_op() and args[0].op in ['<<<', '>>>']): A = args[0].args[0] X = args[0].args[1] Y = args[1] if op_name != args[0].op and e_s(X - Y) == ExprInt(0, X.size): return args[0].args[0] elif X.is_int() and Y.is_int(): new_X = int(X) % expr.size new_Y = int(Y) % expr.size if op_name == args[0].op: rot = (new_X + new_Y) % expr.size op = op_name else: rot = new_Y - new_X op = op_name if rot < 0: rot = - rot op = {">>>": "<<<", "<<<": ">>>"}[op_name] args = [A, ExprInt(rot, expr.size)] op_name = op else: # Do not consider this case, too tricky (overflow on addition / # substraction) pass # A >> X >> Y => A >> (X+Y) if X + Y does not overflow # To be sure, only consider the simplification when X.msb and Y.msb are 0 if (op_name in ['<<', '>>'] and args[0].is_op(op_name)): X = args[0].args[1] Y = args[1] if (e_s(X.msb()) == ExprInt(0, 1) and e_s(Y.msb()) == ExprInt(0, 1)): args = [args[0].args[0], X + Y] # ((var >> int1) << int1) => var & mask # ((var << int1) >> int1) => var & mask if (op_name in ['<<', '>>'] and args[0].is_op() and args[0].op in ['<<', '>>'] and op_name != args[0]): var = args[0].args[0] int1 = args[0].args[1] int2 = args[1] if int1 == int2 and int1.is_int() and int(int1) < expr.size: if op_name == '>>': mask = ExprInt((1 << (expr.size - int(int1))) - 1, expr.size) else: mask = ExprInt( ((1 << int(int1)) - 1) ^ ((1 << expr.size) - 1), expr.size ) ret = var & mask return ret # ((A & A.mask) if op_name == "&" and args[-1] == expr.mask: return ExprOp('&', *args[:-1]) # ((A | A.mask) if op_name == "|" and args[-1] == expr.mask: return args[-1] # ! (!X + int) => X - int # TODO # ((A & mask) >> shift) whith mask < 2**shift => 0 if op_name == ">>" and args[1].is_int() and args[0].is_op("&"): if (args[0].args[1].is_int() and 2 ** args[1].arg > args[0].args[1].arg): return ExprInt(0, args[0].size) # parity(int) => int if op_name == 'parity' and args[0].is_int(): return ExprInt(parity(int(args[0])), 1) # (-a) * b * (-c) * (-d) => (-a) * b * c * d if op_name == "*" and len(args) > 1: new_args = [] counter = 0 for arg in args: if arg.is_op('-') and len(arg.args) == 1: new_args.append(arg.args[0]) counter += 1 else: new_args.append(arg) if counter % 2: return -ExprOp(op_name, *new_args) args = new_args # -(a * b * int) => a * b * (-int) if op_name == "-" and args[0].is_op('*') and args[0].args[-1].is_int(): args = args[0].args return ExprOp('*', *(list(args[:-1]) + [ExprInt(-int(args[-1]), expr.size)])) # A << int with A ExprCompose => move index if (op_name == "<<" and args[0].is_compose() and args[1].is_int() and int(args[1]) != 0): final_size = args[0].size shift = int(args[1]) new_args = [] # shift indexes for index, arg in args[0].iter_args(): new_args.append((arg, index+shift, index+shift+arg.size)) # filter out expression filter_args = [] min_index = final_size for tmp, start, stop in new_args: if start >= final_size: continue if stop > final_size: tmp = tmp[:tmp.size - (stop - final_size)] filter_args.append(tmp) min_index = min(start, min_index) # create entry 0 assert min_index != 0 tmp = ExprInt(0, min_index) args = [tmp] + filter_args return ExprCompose(*args) # A >> int with A ExprCompose => move index if op_name == ">>" and args[0].is_compose() and args[1].is_int(): final_size = args[0].size shift = int(args[1]) new_args = [] # shift indexes for index, arg in args[0].iter_args(): new_args.append((arg, index-shift, index+arg.size-shift)) # filter out expression filter_args = [] max_index = 0 for tmp, start, stop in new_args: if stop <= 0: continue if start < 0: tmp = tmp[-start:] filter_args.append(tmp) max_index = max(stop, max_index) # create entry 0 tmp = ExprInt(0, final_size - max_index) args = filter_args + [tmp] return ExprCompose(*args) # Compose(a) OP Compose(b) with a/b same bounds => Compose(a OP b) if op_name in ['|', '&', '^'] and all([arg.is_compose() for arg in args]): bounds = set() for arg in args: bound = tuple([tmp.size for tmp in arg.args]) bounds.add(bound) if len(bounds) == 1: new_args = [[tmp] for tmp in args[0].args] for sub_arg in args[1:]: for i, tmp in enumerate(sub_arg.args): new_args[i].append(tmp) args = [] for i, arg in enumerate(new_args): args.append(ExprOp(op_name, *arg)) return ExprCompose(*args) return ExprOp(op_name, *args)