extern void abort (void);
-foo (int i, int j)
+foo_div (int i, int j)
{
int k;
}
+foo_mult (int i, int j)
+{
+ int k;
+
+ /* [-20, -10] * [2, 10] should give [-200, -20]. */
+ if (i >= -20)
+ if (i <= -10)
+ if (j >= 2)
+ if (j <= 10)
+ {
+ k = i * j;
+ if (k < -200)
+ link_error ();
+ if (k > -20)
+ link_error ();
+
+ return k;
+ }
+
+ /* [-20, -10] * [-10, -2] should give [20, 200]. */
+ if (i >= -20)
+ if (i <= -10)
+ if (j >= -10)
+ if (j <= -2)
+ {
+ k = i * j;
+ if (k < 20)
+ link_error ();
+ if (k > 200)
+ link_error ();
+
+ return k;
+ }
+
+ /* [-20, 10] * [2, 10] should give [-200, 100]. */
+ if (i >= -20)
+ if (i <= 10)
+ if (j >= 2)
+ if (j <= 10)
+ {
+ k = i * j;
+ if (k < -200)
+ link_error ();
+ if (k > 100)
+ link_error ();
+
+ return k;
+ }
+
+ /* [-20, 10] * [-10, -2] should give [-100, 200]. */
+ if (i >= -20)
+ if (i <= 10)
+ if (j >= -10)
+ if (j <= -2)
+ {
+ k = i * j;
+ if (k < -100)
+ link_error ();
+ if (k > 200)
+ link_error ();
+
+ return k;
+ }
+
+ /* [10, 20] * [2, 10] should give [20, 200]. */
+ if (i >= 10)
+ if (i <= 20)
+ if (j >= 2)
+ if (j <= 10)
+ {
+ k = i * j;
+ if (k < 20)
+ link_error ();
+ if (k > 200)
+ link_error ();
+
+ return k;
+ }
+
+ /* [10, 20] * [-10, -2] should give [-200, -20]. */
+ if (i >= 10)
+ if (i <= 20)
+ if (j >= -10)
+ if (j <= -2)
+ {
+ k = i * j;
+ if (k < -200)
+ link_error ();
+ if (k > -20)
+ link_error ();
+
+ return k;
+ }
+
+ abort ();
+}
+
+
main()
{
- if (foo (-10, 5) != -2)
+ if (foo_div (-10, 5) != -2)
+ abort ();
+
+ if (foo_div (-16, 4) != -4)
+ abort ();
+
+ if (foo_div (-15, -5) != 3)
+ abort ();
+
+ if (foo_div (8, 2) != 4)
+ abort ();
+
+ if (foo_div (10, -2) != -5)
+ abort ();
+
+ if (foo_div (20, 5) != 4)
+ abort ();
+
+ if (foo_div (15, -3) != -5)
+ abort ();
+
+ if (foo_mult (-10, 5) != -50)
abort ();
- if (foo (-16, 4) != -4)
+ if (foo_mult (-16, 4) != -64)
abort ();
- if (foo (-15, -5) != 3)
+ if (foo_mult (-15, -5) != 75)
abort ();
- if (foo (8, 2) != 4)
+ if (foo_mult (8, 2) != 16)
abort ();
- if (foo (10, -2) != -5)
+ if (foo_mult (10, -2) != -20)
abort ();
- if (foo (20, 5) != 4)
+ if (foo_mult (20, 5) != 100)
abort ();
- if (foo (15, -3) != -5)
+ if (foo_mult (15, -3) != -45)
abort ();
return 0;
}
+/* Wrapper around int_const_binop. If the operation overflows and we
+ are not using wrapping arithmetic, then adjust the result to be
+ -INF or +INF depending on CODE, VAL1 and VAL2. */
+
+static inline tree
+vrp_int_const_binop (enum tree_code code, tree val1, tree val2)
+{
+ tree res;
+
+ if (flag_wrapv)
+ return int_const_binop (code, val1, val2, 0);
+
+ /* If we are not using wrapping arithmetic, operate symbolically
+ on -INF and +INF. */
+ res = int_const_binop (code, val1, val2, 0);
+
+ /* If the operation overflowed but neither VAL1 nor VAL2 are
+ overflown, return -INF or +INF depending on whether VAL1 CODE
+ VAL2 is a growing function or not. */
+ if (TREE_OVERFLOW (res)
+ && !TREE_OVERFLOW (val1)
+ && !TREE_OVERFLOW (val2))
+ {
+ bool grows = false;
+ int sgn1 = tree_int_cst_sgn (val1);
+ int sgn2 = tree_int_cst_sgn (val2);
+
+ /* Notice that we only need to handle the restricted set of
+ operations handled by extract_range_from_binary_expr. */
+ if (((code == PLUS_EXPR || code == MAX_EXPR) && sgn2 >= 0)
+ || (code == MULT_EXPR && sgn1 == sgn2)
+ || (code == MINUS_EXPR && sgn2 < 0))
+ grows = true;
+
+ if (grows)
+ return TYPE_MAX_VALUE (TREE_TYPE (res));
+ else
+ return TYPE_MIN_VALUE (TREE_TYPE (res));
+ }
+
+ return res;
+}
+
+
/* Extract range information from a binary expression EXPR based on
the ranges of each of its operands and the expression code. */
max = fold_binary (code, TREE_TYPE (expr), vr0.max, vr1.max);
}
else if (code == PLUS_EXPR
- || code == MULT_EXPR
|| code == MIN_EXPR
|| code == MAX_EXPR)
{
/* For operations that make the resulting range directly
proportional to the original ranges, apply the operation to
the same end of each range. */
- min = int_const_binop (code, vr0.min, vr1.min, 0);
- max = int_const_binop (code, vr0.max, vr1.max, 0);
+ min = vrp_int_const_binop (code, vr0.min, vr1.min);
+ max = vrp_int_const_binop (code, vr0.max, vr1.max);
}
- else if (code == TRUNC_DIV_EXPR
+ else if (code == MULT_EXPR
+ || code == TRUNC_DIV_EXPR
|| code == FLOOR_DIV_EXPR
|| code == CEIL_DIV_EXPR
|| code == EXACT_DIV_EXPR
|| code == ROUND_DIV_EXPR)
{
- tree zero;
+ tree val[4];
+ size_t i;
+
+ /* Multiplications and divisions are a bit tricky to handle,
+ depending on the mix of signs we have in the two ranges, we
+ need to operate on different values to get the minimum and
+ maximum values for the new range. One approach is to figure
+ out all the variations of range combinations and do the
+ operations.
- /* Divisions are a bit tricky to handle, depending on the mix of
- signs we have in the two range, we will need to divide
- different values to get the minimum and maximum values for
- the new range. If VR1 includes zero, the result is VARYING. */
- if (range_includes_zero_p (&vr1))
+ However, this involves several calls to compare_values and it
+ is pretty convoluted. It's simpler to do the 4 operations
+ (MIN0 OP MIN1, MIN0 OP MAX1, MAX0 OP MIN1 and MAX0 OP MAX0 OP
+ MAX1) and then figure the smallest and largest values to form
+ the new range. */
+
+ /* Divisions by zero result in a VARYING value. */
+ if (code != MULT_EXPR && range_includes_zero_p (&vr1))
{
set_value_range_to_varying (vr);
return;
}
- /* We have three main variations to handle for VR0: all negative
- values, all positive values and a mix of negative and
- positive. For each of these, we need to consider if VR1 is
- all negative or all positive. In total, there are 6
- combinations to handle. */
- zero = build_int_cst (TREE_TYPE (expr), 0);
- if (compare_values (vr0.max, zero) == -1)
- {
- /* VR0 is all negative. */
- if (compare_values (vr1.min, zero) == 1)
- {
- /* If VR1 is all positive, the new range is obtained
- with [VR0.MIN / VR1.MIN, VR0.MAX / VR1.MAX]. */
- min = int_const_binop (code, vr0.min, vr1.min, 0);
- max = int_const_binop (code, vr0.max, vr1.max, 0);
- }
- else
- {
- /* If VR1 is all negative, the new range is obtained
- with [VR0.MAX / VR1.MIN, VR0.MIN / VR1.MAX]. */
- gcc_assert (compare_values (vr1.max, zero) == -1);
- min = int_const_binop (code, vr0.max, vr1.min, 0);
- max = int_const_binop (code, vr0.min, vr1.max, 0);
- }
- }
- else if (range_includes_zero_p (&vr0))
- {
- /* VR0 is a mix of negative and positive values. */
- if (compare_values (vr1.min, zero) == 1)
- {
- /* If VR1 is all positive, the new range is obtained
- with [VR0.MIN / VR1.MIN, VR0.MAX / VR1.MIN]. */
- min = int_const_binop (code, vr0.min, vr1.min, 0);
- max = int_const_binop (code, vr0.max, vr1.min, 0);
- }
- else
- {
- /* If VR1 is all negative, the new range is obtained
- with [VR0.MAX / VR1.MAX, VR0.MIN / VR1.MAX]. */
- gcc_assert (compare_values (vr1.max, zero) == -1);
- min = int_const_binop (code, vr0.max, vr1.max, 0);
- max = int_const_binop (code, vr0.min, vr1.max, 0);
- }
- }
- else
+ /* Compute the 4 cross operations. */
+ val[0] = vrp_int_const_binop (code, vr0.min, vr1.min);
+
+ val[1] = (vr1.max != vr1.min)
+ ? vrp_int_const_binop (code, vr0.min, vr1.max)
+ : NULL_TREE;
+
+ val[2] = (vr0.max != vr0.min)
+ ? vrp_int_const_binop (code, vr0.max, vr1.min)
+ : NULL_TREE;
+
+ val[3] = (vr0.min != vr1.min && vr0.max != vr1.max)
+ ? vrp_int_const_binop (code, vr0.max, vr1.max)
+ : NULL_TREE;
+
+ /* Set MIN to the minimum of VAL[i] and MAX to the maximum
+ of VAL[i]. */
+ min = val[0];
+ max = val[0];
+ for (i = 1; i < 4; i++)
{
- /* VR0 is all positive. */
- gcc_assert (compare_values (vr0.min, zero) == 1);
- if (compare_values (vr1.min, zero) == 1)
- {
- /* If VR1 is all positive, the new range is obtained
- with [VR0.MIN / VR1.MAX, VR0.MAX / VR1.MIN]. */
- min = int_const_binop (code, vr0.min, vr1.max, 0);
- max = int_const_binop (code, vr0.max, vr1.min, 0);
- }
- else
+ if (TREE_OVERFLOW (min) || TREE_OVERFLOW (max))
+ break;
+
+ if (val[i])
{
- /* If VR1 is all negative, the new range is obtained
- with [VR0.MAX / VR1.MAX, VR0.MIN / VR1.MIN]. */
- gcc_assert (compare_values (vr1.max, zero) == -1);
- min = int_const_binop (code, vr0.max, vr1.max, 0);
- max = int_const_binop (code, vr0.min, vr1.min, 0);
+ if (TREE_OVERFLOW (val[i]))
+ {
+ /* If we found an overflowed value, set MIN and MAX
+ to it so that we set the resulting range to
+ VARYING. */
+ min = max = val[i];
+ break;
+ }
+
+ if (compare_values (val[i], min) == -1)
+ min = val[i];
+
+ if (compare_values (val[i], max) == 1)
+ max = val[i];
}
}
}
{
/* For MINUS_EXPR, apply the operation to the opposite ends of
each range. */
- min = int_const_binop (code, vr0.min, vr1.max, 0);
- max = int_const_binop (code, vr0.max, vr1.min, 0);
+ min = vrp_int_const_binop (code, vr0.min, vr1.max);
+ max = vrp_int_const_binop (code, vr0.max, vr1.min);
}
else
gcc_unreachable ();
- /* If MAX overflowed, then the result depends on whether we are
- using wrapping arithmetic or not. */
- if (TREE_OVERFLOW (max))
+ /* If either MIN or MAX overflowed, then set the resulting range to
+ VARYING. */
+ if (TREE_OVERFLOW (min) || TREE_OVERFLOW (max))
{
- /* If we are using wrapping arithmetic, set the result to
- VARYING. */
- if (flag_wrapv)
- {
- set_value_range_to_varying (vr);
- return;
- }
-
- /* Otherwise, set MAX to +INF. */
- max = TYPE_MAX_VALUE (TREE_TYPE (expr));
- }
-
- /* If MIN overflowed, then the result depends on whether we are
- using wrapping arithmetic or not. */
- if (TREE_OVERFLOW (min))
- {
- /* If we are using wrapping arithmetic, set the result to
- VARYING. */
- if (flag_wrapv)
- {
- set_value_range_to_varying (vr);
- return;
- }
-
- /* Otherwise, set MIN to -INF. */
- min = TYPE_MIN_VALUE (TREE_TYPE (expr));
+ set_value_range_to_varying (vr);
+ return;
}
cmp = compare_values (min, max);