Merge pull request #907 from serpilliere/add_simplifications

Expression: add simplifications

1 files changed, 340 insertions, 77 deletions

diff --git a/miasm2/expression/simplifications_common.py b/miasm2/expression/simplifications_common.py
index 6f0eb34a..18529d35 100644
--- a/miasm2/expression/simplifications_common.py
+++ b/miasm2/expression/simplifications_common.py
@@ -382,7 +382,7 @@ def simp_cst_propagation(e_s, expr):
     return ExprOp(op_name, *args)
 
 
-def simp_cond_op_int(e_s, expr):
+def simp_cond_op_int(_, expr):
     "Extract conditions from operations"
 
 
@@ -606,10 +606,11 @@ def simp_compose(e_s, expr):
     return ExprCompose(*args)
 
 
-def simp_cond(e_s, expr):
-    "Common simplifications on ExprCond"
-    # eval exprcond src1/src2 with satifiable/unsatisfiable condition
-    # propagation
+def simp_cond(_, expr):
+    """
+    Common simplifications on ExprCond.
+    Eval exprcond src1/src2 with satifiable/unsatisfiable condition propagation
+    """
     if (not expr.cond.is_int()) and expr.cond.size == 1:
         src1 = expr.src1.replace_expr({expr.cond: ExprInt(1, 1)})
         src2 = expr.src2.replace_expr({expr.cond: ExprInt(0, 1)})
@@ -666,10 +667,11 @@ def simp_cond(e_s, expr):
     return expr
 
 
-def simp_mem(e_s, expr):
-    "Common simplifications on ExprMem"
-
-    # @32[x?a:b] => x?@32[a]:@32[b]
+def simp_mem(_, expr):
+    """
+    Common simplifications on ExprMem:
+    @32[x?a:b] => x?@32[a]:@32[b]
+    """
     if expr.ptr.is_cond():
         cond = expr.ptr
         ret = ExprCond(cond.cond,
@@ -682,6 +684,15 @@ def simp_mem(e_s, expr):
 
 
 def test_cc_eq_args(expr, *sons_op):
+    """
+    Return True if expression's arguments match the list in sons_op, and their
+    sub arguments are identical. Ex:
+    CC_S<=(
+              FLAG_SIGN_SUB(A, B),
+              FLAG_SUB_OF(A, B),
+              FLAG_EQ_CMP(A, B)
+    )
+    """
     if not expr.is_op():
         return False
     if len(expr.args) != len(sons_op):
@@ -694,7 +705,11 @@ def test_cc_eq_args(expr, *sons_op):
     return len(all_args) == 1
 
 
-def simp_cc_conds(expr_simp, expr):
+def simp_cc_conds(_, expr):
+    """
+    High level simplifications. Example:
+    CC_U<(FLAG_SUB_CF(A, B) => A <u B
+    """
     if (expr.is_op("CC_U>=") and
           test_cc_eq_args(
               expr,
@@ -702,8 +717,8 @@ def simp_cc_conds(expr_simp, expr):
           )):
         expr = ExprCond(
             ExprOp(TOK_INF_UNSIGNED, *expr.args[0].args),
-            ExprInt(0, 1),
-            ExprInt(1, 1))
+            ExprInt(0, expr.size),
+            ExprInt(1, expr.size))
 
     elif (expr.is_op("CC_U<") and
           test_cc_eq_args(
@@ -726,8 +741,8 @@ def simp_cc_conds(expr_simp, expr):
           )):
         expr = ExprCond(
             ExprOp(TOK_INF_SIGNED, *expr.args[0].args),
-            ExprInt(0, 1),
-            ExprInt(1, 1)
+            ExprInt(0, expr.size),
+            ExprInt(1, expr.size)
         )
 
     elif (expr.is_op("CC_EQ") and
@@ -746,8 +761,8 @@ def simp_cc_conds(expr_simp, expr):
         arg = expr.args[0].args[0]
         expr = ExprCond(
             ExprOp(TOK_EQUAL,arg, ExprInt(0, arg.size)),
-            ExprInt(0, 1),
-            ExprInt(1, 1)
+            ExprInt(0, expr.size),
+            ExprInt(1, expr.size)
         )
     elif (expr.is_op("CC_NE") and
           test_cc_eq_args(
@@ -756,8 +771,8 @@ def simp_cc_conds(expr_simp, expr):
           )):
         expr = ExprCond(
             ExprOp(TOK_EQUAL, *expr.args[0].args),
-            ExprInt(0, 1),
-            ExprInt(1, 1)
+            ExprInt(0, expr.size),
+            ExprInt(1, expr.size)
         )
 
     elif (expr.is_op("CC_EQ") and
@@ -781,8 +796,8 @@ def simp_cc_conds(expr_simp, expr):
           )):
         expr = ExprCond(
             ExprOp("&", *expr.args[0].args),
-            ExprInt(0, 1),
-            ExprInt(1, 1)
+            ExprInt(0, expr.size),
+            ExprInt(1, expr.size)
         )
 
     elif (expr.is_op("CC_S>") and
@@ -794,8 +809,8 @@ def simp_cc_conds(expr_simp, expr):
           )):
         expr = ExprCond(
             ExprOp(TOK_INF_EQUAL_SIGNED, *expr.args[0].args),
-            ExprInt(0, 1),
-            ExprInt(1, 1)
+            ExprInt(0, expr.size),
+            ExprInt(1, expr.size)
         )
 
     elif (expr.is_op("CC_S>") and
@@ -806,8 +821,8 @@ def simp_cc_conds(expr_simp, expr):
           expr.args[1].is_int(0)):
         expr = ExprCond(
             ExprOp(TOK_INF_EQUAL_SIGNED, *expr.args[0].args),
-            ExprInt(0, 1),
-            ExprInt(1, 1)
+            ExprInt(0, expr.size),
+            ExprInt(1, expr.size)
         )
 
 
@@ -820,8 +835,8 @@ def simp_cc_conds(expr_simp, expr):
           )):
         expr = ExprCond(
             ExprOp(TOK_INF_SIGNED, *expr.args[0].args),
-            ExprInt(0, 1),
-            ExprInt(1, 1)
+            ExprInt(0, expr.size),
+            ExprInt(1, expr.size)
         )
 
     elif (expr.is_op("CC_S<") and
@@ -865,8 +880,8 @@ def simp_cc_conds(expr_simp, expr):
           )):
         expr = ExprCond(
             ExprOp(TOK_INF_EQUAL_UNSIGNED, *expr.args[0].args),
-            ExprInt(0, 1),
-            ExprInt(1, 1)
+            ExprInt(0, expr.size),
+            ExprInt(1, expr.size)
         )
 
     elif (expr.is_op("CC_S<") and
@@ -882,8 +897,8 @@ def simp_cc_conds(expr_simp, expr):
 
 
 
-def simp_cond_flag(expr_simp, expr):
-    # FLAG_EQ_CMP(X, Y)?A:B => (X == Y)?A:B
+def simp_cond_flag(_, expr):
+    """FLAG_EQ_CMP(X, Y)?A:B => (X == Y)?A:B"""
     cond = expr.cond
     if cond.is_op("FLAG_EQ_CMP"):
         return ExprCond(ExprOp(TOK_EQUAL, *cond.args), expr.src1, expr.src2)
@@ -891,8 +906,10 @@ def simp_cond_flag(expr_simp, expr):
 
 
 def simp_cmp_int(expr_simp, expr):
-    # ({X, 0} == int) => X == int[:]
-    # X + int1 == int2 => X == int2-int1
+    """
+    ({X, 0} == int) => X == int[:]
+    X + int1 == int2 => X == int2-int1
+    """
     if (expr.is_op(TOK_EQUAL) and
           expr.args[1].is_int() and
           expr.args[0].is_compose() and
@@ -931,7 +948,7 @@ def simp_cmp_int(expr_simp, expr):
 
 
 
-def simp_cmp_int_arg(expr_simp, expr):
+def simp_cmp_int_arg(_, expr):
     """
     (0x10 <= R0) ? A:B
     =>
@@ -971,10 +988,8 @@ def simp_cmp_int_arg(expr_simp, expr):
     return ExprCond(ExprOp(op, arg1, arg2), src1, src2)
 
 
-
-
-def simp_subwc_cf(expr_s, expr):
-    # SUBWC_CF(A, B, SUB_CF(C, D)) => SUB_CF({A, C}, {B, D})
+def simp_subwc_cf(_, expr):
+    """SUBWC_CF(A, B, SUB_CF(C, D)) => SUB_CF({A, C}, {B, D})"""
     if not expr.is_op('FLAG_SUBWC_CF'):
         return expr
     op3 = expr.args[2]
@@ -987,8 +1002,8 @@ def simp_subwc_cf(expr_s, expr):
     return ExprOp("FLAG_SUB_CF", op1, op2)
 
 
-def simp_subwc_of(expr_s, expr):
-    # SUBWC_OF(A, B, SUB_CF(C, D)) => SUB_OF({A, C}, {B, D})
+def simp_subwc_of(_, expr):
+    """SUBWC_OF(A, B, SUB_CF(C, D)) => SUB_OF({A, C}, {B, D})"""
     if not expr.is_op('FLAG_SUBWC_OF'):
         return expr
     op3 = expr.args[2]
@@ -1001,8 +1016,8 @@ def simp_subwc_of(expr_s, expr):
     return ExprOp("FLAG_SUB_OF", op1, op2)
 
 
-def simp_sign_subwc_cf(expr_s, expr):
-    # SIGN_SUBWC(A, B, SUB_CF(C, D)) => SIGN_SUB({A, C}, {B, D})
+def simp_sign_subwc_cf(_, expr):
+    """SIGN_SUBWC(A, B, SUB_CF(C, D)) => SIGN_SUB({A, C}, {B, D})"""
     if not expr.is_op('FLAG_SIGN_SUBWC'):
         return expr
     op3 = expr.args[2]
@@ -1014,8 +1029,8 @@ def simp_sign_subwc_cf(expr_s, expr):
 
     return ExprOp("FLAG_SIGN_SUB", op1, op2)
 
-def simp_double_zeroext(expr_s, expr):
-    # A.zeroExt(X).zeroExt(Y) => A.zeroExt(Y)
+def simp_double_zeroext(_, expr):
+    """A.zeroExt(X).zeroExt(Y) => A.zeroExt(Y)"""
     if not (expr.is_op() and expr.op.startswith("zeroExt")):
         return expr
     arg1 = expr.args[0]
@@ -1024,8 +1039,8 @@ def simp_double_zeroext(expr_s, expr):
     arg2 = arg1.args[0]
     return ExprOp(expr.op, arg2)
 
-def simp_double_signext(expr_s, expr):
-    # A.signExt(X).signExt(Y) => A.signExt(Y)
+def simp_double_signext(_, expr):
+    """A.signExt(X).signExt(Y) => A.signExt(Y)"""
     if not (expr.is_op() and expr.op.startswith("signExt")):
         return expr
     arg1 = expr.args[0]
@@ -1034,8 +1049,8 @@ def simp_double_signext(expr_s, expr):
     arg2 = arg1.args[0]
     return ExprOp(expr.op, arg2)
 
-def simp_zeroext_eq_cst(expr_s, expr):
-    # A.zeroExt(X) == int => A == int[:A.size]
+def simp_zeroext_eq_cst(_, expr):
+    """A.zeroExt(X) == int => A == int[:A.size]"""
     if not expr.is_op(TOK_EQUAL):
         return expr
     arg1, arg2 = expr.args
@@ -1046,12 +1061,31 @@ def simp_zeroext_eq_cst(expr_s, expr):
     src = arg1.args[0]
     if int(arg2) > (1 << src.size):
         # Always false
-        return ExprInt(0, 1)
+        return ExprInt(0, expr.size)
     return ExprOp(TOK_EQUAL, src, ExprInt(int(arg2), src.size))
 
-def simp_ext_eq_ext(expr_s, expr):
-    # A.zeroExt(X) == B.zeroExt(X) => A == B
-    # A.signExt(X) == B.signExt(X) => A == B
+def simp_cond_zeroext(_, expr):
+    """
+    X.zeroExt()?(A:B) => X ? A:B
+    X.signExt()?(A:B) => X ? A:B
+    """
+    if not (
+            expr.cond.is_op() and
+            (
+                expr.cond.op.startswith("zeroExt") or
+                expr.cond.op.startswith("signExt")
+            )
+    ):
+        return expr
+
+    ret = ExprCond(expr.cond.args[0], expr.src1, expr.src2)
+    return ret
+
+def simp_ext_eq_ext(_, expr):
+    """
+    A.zeroExt(X) == B.zeroExt(X) => A == B
+    A.signExt(X) == B.signExt(X) => A == B
+    """
     if not expr.is_op(TOK_EQUAL):
         return expr
     arg1, arg2 = expr.args
@@ -1064,8 +1098,8 @@ def simp_ext_eq_ext(expr_s, expr):
         return expr
     return ExprOp(TOK_EQUAL, arg1.args[0], arg2.args[0])
 
-def simp_cond_eq_zero(expr_s, expr):
-    # (X == 0)?(A:B) => X?(B:A)
+def simp_cond_eq_zero(_, expr):
+    """(X == 0)?(A:B) => X?(B:A)"""
     cond = expr.cond
     if not cond.is_op(TOK_EQUAL):
         return expr
@@ -1075,13 +1109,122 @@ def simp_cond_eq_zero(expr_s, expr):
     new_expr = ExprCond(arg1, expr.src2, expr.src1)
     return new_expr
 
+def simp_sign_inf_zeroext(expr_s, expr):
+    """
+    /!\ Ensure before: X.zeroExt(X.size) => X
+
+    X.zeroExt() <s 0 => 0
+    X.zeroExt() <=s 0 => X == 0
 
-def simp_cmp_int_int(expr_s, expr):
-    # IntA <s IntB => int
-    # IntA <u IntB => int
-    # IntA <=s IntB => int
-    # IntA <=u IntB => int
-    # IntA == IntB => int
+    X.zeroExt() <s cst => X.zeroExt() <u cst (cst positive)
+    X.zeroExt() <=s cst => X.zeroExt() <=u cst (cst positive)
+
+    X.zeroExt() <s cst => 0 (cst negative)
+    X.zeroExt() <=s cst => 0 (cst negative)
+
+    """
+    if not (expr.is_op(TOK_INF_SIGNED) or expr.is_op(TOK_INF_EQUAL_SIGNED)):
+        return expr
+    arg1, arg2 = expr.args
+    if not arg2.is_int():
+        return expr
+    if not (arg1.is_op() and arg1.op.startswith("zeroExt")):
+        return expr
+    src = arg1.args[0]
+    assert src.size < arg1.size
+
+    # If cst is zero
+    if arg2.is_int(0):
+        if expr.is_op(TOK_INF_SIGNED):
+            # X.zeroExt() <s 0 => 0
+            return ExprInt(0, expr.size)
+        else:
+            # X.zeroExt() <=s 0 => X == 0
+            return ExprOp(TOK_EQUAL, src, ExprInt(0, src.size))
+
+    # cst is not zero
+    cst = int(arg2)
+    if cst & (1 << (arg2.size - 1)):
+        # cst is negative
+        return ExprInt(0, expr.size)
+    # cst is positive
+    if expr.is_op(TOK_INF_SIGNED):
+        # X.zeroExt() <s cst => X.zeroExt() <u cst (cst positive)
+        return ExprOp(TOK_INF_UNSIGNED, src, expr_s(arg2[:src.size]))
+    # X.zeroExt() <=s cst => X.zeroExt() <=u cst (cst positive)
+    return ExprOp(TOK_INF_EQUAL_UNSIGNED, src, expr_s(arg2[:src.size]))
+
+
+def simp_zeroext_and_cst_eq_cst(expr_s, expr):
+    """
+    A.zeroExt(X) & ... & int == int => A & ... & int[:A.size] == int[:A.size]
+    """
+    if not expr.is_op(TOK_EQUAL):
+        return expr
+    arg1, arg2 = expr.args
+    if not arg2.is_int():
+        return expr
+    if not arg1.is_op('&'):
+        return expr
+    is_ok = True
+    sizes = set()
+    for arg in arg1.args:
+        if arg.is_int():
+            continue
+        if (arg.is_op() and
+            arg.op.startswith("zeroExt")):
+            sizes.add(arg.args[0].size)
+            continue
+        is_ok = False
+        break
+    if not is_ok:
+        return expr
+    if len(sizes) != 1:
+        return expr
+    size = list(sizes)[0]
+    if int(arg2) > ((1 << size) - 1):
+        return expr
+    args = [expr_s(arg[:size]) for arg in arg1.args]
+    left = ExprOp('&', *args)
+    right = expr_s(arg2[:size])
+    ret = ExprOp(TOK_EQUAL, left, right)
+    return ret
+
+
+def test_one_bit_set(arg):
+    """
+    Return True if arg has form 1 << X
+    """
+    return arg != 0  and ((arg & (arg - 1)) == 0)
+
+def simp_x_and_cst_eq_cst(_, expr):
+    """
+    (x & ... & onebitmask == onebitmask) ? A:B => (x & ... & onebitmask) ? A:B
+    """
+    cond = expr.cond
+    if not cond.is_op(TOK_EQUAL):
+        return expr
+    arg1, mask2 = cond.args
+    if not mask2.is_int():
+        return expr
+    if not test_one_bit_set(int(mask2)):
+        return expr
+    if not arg1.is_op('&'):
+        return expr
+    mask1 = arg1.args[-1]
+    if mask1 != mask2:
+        return expr
+    cond = ExprOp('&', *arg1.args)
+    return ExprCond(cond, expr.src1, expr.src2)
+
+def simp_cmp_int_int(_, expr):
+    """
+    IntA <s IntB => int
+    IntA <u IntB => int
+    IntA <=s IntB => int
+    IntA <=u IntB => int
+    IntA == IntB => int
+    """
     if expr.op not in [
             TOK_EQUAL,
             TOK_INF_SIGNED, TOK_INF_UNSIGNED,
@@ -1094,8 +1237,7 @@ def simp_cmp_int_int(expr_s, expr):
     if expr.is_op(TOK_EQUAL):
         if int_a == int_b:
             return ExprInt(1, 1)
-        else:
-            return ExprInt(0, 1)
+        return ExprInt(0, expr.size)
 
     if expr.op in [TOK_INF_SIGNED, TOK_INF_EQUAL_SIGNED]:
         int_a = int(mod_size2int[int_a.size](int(int_a)))
@@ -1116,9 +1258,11 @@ def simp_cmp_int_int(expr_s, expr):
     return ExprInt(ret, 1)
 
 
-def simp_ext_cst(expr_s, expr):
-    # Int.zeroExt(X) => Int
-    # Int.signExt(X) => Int
+def simp_ext_cst(_, expr):
+    """
+    Int.zeroExt(X) => Int
+    Int.signExt(X) => Int
+    """
     if not (expr.op.startswith("zeroExt") or expr.op.startswith("signExt")):
         return expr
     arg = expr.args[0]
@@ -1132,31 +1276,150 @@ def simp_ext_cst(expr_s, expr):
     return ret
 
 
-def simp_slice_of_ext(expr_s, expr):
-    # zeroExt(X)[0:size(X)] => X
-    if expr.start != 0:
-        return expr
+def simp_slice_of_ext(_, expr):
+    """
+    C.zeroExt(X)[A:B] => 0 if A >= size(C)
+    C.zeroExt(X)[A:B] => C[A:B] if B <= size(C)
+    A.zeroExt(X)[0:Y] => A.zeroExt(Y)
+    """
     if not expr.arg.is_op():
         return expr
     if not expr.arg.op.startswith("zeroExt"):
         return expr
     arg = expr.arg.args[0]
-    if arg.size != expr.size:
+
+    if expr.start >= arg.size:
+        # C.zeroExt(X)[A:B] => 0 if A >= size(C)
+        return ExprInt(0, expr.size)
+    if expr.stop <= arg.size:
+        # C.zeroExt(X)[A:B] => C[A:B] if B <= size(C)
+        return arg[expr.start:expr.stop]
+    if expr.start == 0:
+        # A.zeroExt(X)[0:Y] => A.zeroExt(Y)
+        return arg.zeroExtend(expr.stop)
+    return expr
+
+def simp_slice_of_op_ext(expr_s, expr):
+    """(X.zeroExt() + ... + Int)[0:8] => X + ... + int[:]"""
+    if expr.start != 0:
+        return expr
+    src = expr.arg
+    if not src.is_op("+"):
+        return expr
+    is_ok = True
+    for arg in src.args:
+        if arg.is_int():
+            continue
+        if (arg.is_op() and
+            arg.op.startswith("zeroExt") and
+            arg.args[0].size == expr.stop):
+            continue
+        is_ok = False
+        break
+    if not is_ok:
+        return expr
+    args = [expr_s(arg[:expr.stop]) for arg in src.args]
+    return ExprOp("+", *args)
+
+
+def simp_cond_logic_ext(expr_s, expr):
+    """(X.zeroExt() + ... + Int) ? A:B => X + ... + int[:] ? A:B"""
+    cond = expr.cond
+    if not cond.is_op():
+        return expr
+    if cond.op not in ["&", "^", "|"]:
+        return expr
+    is_ok = True
+    sizes = set()
+    for arg in cond.args:
+        if arg.is_int():
+            continue
+        if (arg.is_op() and
+            arg.op.startswith("zeroExt")):
+            sizes.add(arg.args[0].size)
+            continue
+        is_ok = False
+        break
+    if not is_ok:
+        return expr
+    if len(sizes) != 1:
+        return expr
+    size = list(sizes)[0]
+    args = [expr_s(arg[:size]) for arg in cond.args]
+    cond = ExprOp(cond.op, *args)
+    return ExprCond(cond, expr.src1, expr.src2)
+
+
+def simp_cond_sign_bit(_, expr):
+    """(a & .. & 0x80000000) ? A:B => (a & ...) <s 0 ? A:B"""
+    cond = expr.cond
+    if not cond.is_op('&'):
+        return expr
+    last = cond.args[-1]
+    if not last.is_int(1 << (last.size - 1)):
+        return expr
+    zero = ExprInt(0, expr.cond.size)
+    if len(cond.args) == 2:
+        args = [cond.args[0], zero]
+    else:
+        args = [ExprOp('&', *list(cond.args[:-1])), zero]
+    cond = ExprOp(TOK_INF_SIGNED, *args)
+    return ExprCond(cond, expr.src1, expr.src2)
+
+
+def simp_test_signext_inf(expr_s, expr):
+    """A.signExt() <s int => A <s int[:]"""
+    if not (expr.is_op(TOK_INF_SIGNED) or expr.is_op(TOK_INF_EQUAL_SIGNED)):
+        return expr
+    arg, cst = expr.args
+    if not (arg.is_op() and arg.op.startswith("signExt")):
         return expr
-    return arg
+    if not cst.is_int():
+        return expr
+    base = arg.args[0]
+    tmp = int(mod_size2int[cst.size](int(cst)))
+    if -(1 << (base.size - 1)) <= tmp < (1 << (base.size - 1)):
+        # Can trunc integer
+        return ExprOp(expr.op, base, expr_s(cst[:base.size]))
+    if (tmp >= (1 << (base.size - 1)) or
+        tmp < -(1 << (base.size - 1)) ):
+        return ExprInt(1, 1)
+    return expr
 
-def simp_add_multiple(expr_s, expr):
-    # X + X => 2 * X
-    # X + X * int1 => X * (1 + int1)
-    # X * int1 + (- X) => X * (int1 - 1)
-    # X + (X << int1) => X * (1 + 2 ** int1)
-    # Correct even if addition overflow/underflow
+
+def simp_test_zeroext_inf(expr_s, expr):
+    """A.zeroExt() <u int => A <u int[:]"""
+    if not (expr.is_op(TOK_INF_UNSIGNED) or expr.is_op(TOK_INF_EQUAL_UNSIGNED)):
+        return expr
+    arg, cst = expr.args
+    if not (arg.is_op() and arg.op.startswith("zeroExt")):
+        return expr
+    if not cst.is_int():
+        return expr
+    base = arg.args[0]
+    tmp = int(mod_size2uint[cst.size](int(cst)))
+    if 0 <= tmp < (1 << base.size):
+        # Can trunc integer
+        return ExprOp(expr.op, base, expr_s(cst[:base.size]))
+    if tmp >= (1 << base.size):
+        return ExprInt(1, 1)
+    return expr
+
+
+def simp_add_multiple(_, expr):
+    """
+    X + X => 2 * X
+    X + X * int1 => X * (1 + int1)
+    X * int1 + (- X) => X * (int1 - 1)
+    X + (X << int1) => X * (1 + 2 ** int1)
+    Correct even if addition overflow/underflow
+    """
     if not expr.is_op('+'):
         return expr
 
     # Extract each argument and its counter
     operands = {}
-    for i, arg in enumerate(expr.args):
+    for arg in expr.args:
         if arg.is_op('*') and arg.args[1].is_int():
             base_expr, factor = arg.args
             operands[base_expr] = operands.get(base_expr, 0) + int(factor)