bpf: Fix u32/s32 bounds when ranges cross min/max boundary

Same as in __reg64_deduce_bounds(), refine s32/u32 ranges
in __reg32_deduce_bounds() in the following situations:

- s32 range crosses U32_MAX/0 boundary, positive part of the s32 range
  overlaps with u32 range:

  0                                                   U32_MAX
  |  [xxxxxxxxxxxxxx u32 range xxxxxxxxxxxxxx]              |
  |----------------------------|----------------------------|
  |xxxxx s32 range xxxxxxxxx]                       [xxxxxxx|
  0                     S32_MAX S32_MIN                    -1

- s32 range crosses U32_MAX/0 boundary, negative part of the s32 range
  overlaps with u32 range:

  0                                                   U32_MAX
  |              [xxxxxxxxxxxxxx u32 range xxxxxxxxxxxxxx]  |
  |----------------------------|----------------------------|
  |xxxxxxxxx]                       [xxxxxxxxxxxx s32 range |
  0                     S32_MAX S32_MIN                    -1

- No refinement if ranges overlap in two intervals.

This helps for e.g. consider the following program:

   call %[bpf_get_prandom_u32];
   w0 &= 0xffffffff;
   if w0 < 0x3 goto 1f;    // on fall-through u32 range [3..U32_MAX]
   if w0 s> 0x1 goto 1f;   // on fall-through s32 range [S32_MIN..1]
   if w0 s< 0x0 goto 1f;   // range can be narrowed to  [S32_MIN..-1]
   r10 = 0;
1: ...;

The reg_bounds.c selftest is updated to incorporate identical logic,
refinement based on non-overflowing range halves:

  ((x ∩ [0, smax]) ∩ (y ∩ [0, smax])) ∪
  ((x ∩ [smin,-1]) ∩ (y ∩ [smin,-1]))

Reported-by: Andrea Righi <arighi@nvidia.com>
Reported-by: Emil Tsalapatis <emil@etsalapatis.com>
Closes: https://lore.kernel.org/bpf/aakqucg4vcujVwif@gpd4/T/
Reviewed-by: Emil Tsalapatis <emil@etsalapatis.com>
Acked-by: Shung-Hsi Yu <shung-hsi.yu@suse.com>
Signed-off-by: Eduard Zingerman <eddyz87@gmail.com>
Link: https://lore.kernel.org/r/20260306-bpf-32-bit-range-overflow-v3-1-f7f67e060a6b@gmail.com
Signed-off-by: Alexei Starovoitov <ast@kernel.org>

tools/testing/selftests/bpf/prog_tests/reg_bounds.c

@@ -422,15 +422,69 @@ static bool is_valid_range(enum num_t t, struct range x)
 	}
 }
 
-static struct range range_improve(enum num_t t, struct range old, struct range new)
+static struct range range_intersection(enum num_t t, struct range old, struct range new)
 {
 	return range(t, max_t(t, old.a, new.a), min_t(t, old.b, new.b));
 }
 
+/*
+ * Result is precise when 'x' and 'y' overlap or form a continuous range,
+ * result is an over-approximation if 'x' and 'y' do not overlap.
+ */
+static struct range range_union(enum num_t t, struct range x, struct range y)
+{
+	if (!is_valid_range(t, x))
+		return y;
+	if (!is_valid_range(t, y))
+		return x;
+	return range(t, min_t(t, x.a, y.a), max_t(t, x.b, y.b));
+}
+
+/*
+ * This function attempts to improve x range intersecting it with y.
+ * range_cast(... to_t ...) looses precision for ranges that pass to_t
+ * min/max boundaries. To avoid such precision loses this function
+ * splits both x and y into halves corresponding to non-overflowing
+ * sub-ranges: [0, smin] and [smax, -1].
+ * Final result is computed as follows:
+ *
+ *   ((x ∩ [0, smax]) ∩ (y ∩ [0, smax])) ∪
+ *   ((x ∩ [smin,-1]) ∩ (y ∩ [smin,-1]))
+ *
+ * Precision might still be lost if final union is not a continuous range.
+ */
+static struct range range_refine_in_halves(enum num_t x_t, struct range x,
+					   enum num_t y_t, struct range y)
+{
+	struct range x_pos, x_neg, y_pos, y_neg, r_pos, r_neg;
+	u64 smax, smin, neg_one;
+
+	if (t_is_32(x_t)) {
+		smax = (u64)(u32)S32_MAX;
+		smin = (u64)(u32)S32_MIN;
+		neg_one = (u64)(u32)(s32)(-1);
+	} else {
+		smax = (u64)S64_MAX;
+		smin = (u64)S64_MIN;
+		neg_one = U64_MAX;
+	}
+	x_pos = range_intersection(x_t, x, range(x_t, 0, smax));
+	x_neg = range_intersection(x_t, x, range(x_t, smin, neg_one));
+	y_pos = range_intersection(y_t, y, range(x_t, 0, smax));
+	y_neg = range_intersection(y_t, y, range(y_t, smin, neg_one));
+	r_pos = range_intersection(x_t, x_pos, range_cast(y_t, x_t, y_pos));
+	r_neg = range_intersection(x_t, x_neg, range_cast(y_t, x_t, y_neg));
+	return range_union(x_t, r_pos, r_neg);
+
+}
+
 static struct range range_refine(enum num_t x_t, struct range x, enum num_t y_t, struct range y)
 {
 	struct range y_cast;
 
+	if (t_is_32(x_t) == t_is_32(y_t))
+		x = range_refine_in_halves(x_t, x, y_t, y);
+
 	y_cast = range_cast(y_t, x_t, y);
 
 	/* If we know that
@@ -444,7 +498,7 @@ static struct range range_refine(enum num_t x_t, struct range x, enum num_t y_t,
 	 */
 	if (x_t == S64 && y_t == S32 && y_cast.a <= S32_MAX  && y_cast.b <= S32_MAX &&
 	    (s64)x.a >= S32_MIN && (s64)x.b <= S32_MAX)
-		return range_improve(x_t, x, y_cast);
+		return range_intersection(x_t, x, y_cast);
 
 	/* the case when new range knowledge, *y*, is a 32-bit subregister
 	 * range, while previous range knowledge, *x*, is a full register
@@ -462,7 +516,7 @@ static struct range range_refine(enum num_t x_t, struct range x, enum num_t y_t,
 		x_swap = range(x_t, swap_low32(x.a, y_cast.a), swap_low32(x.b, y_cast.b));
 		if (!is_valid_range(x_t, x_swap))
 			return x;
-		return range_improve(x_t, x, x_swap);
+		return range_intersection(x_t, x, x_swap);
 	}
 
 	if (!t_is_32(x_t) && !t_is_32(y_t) && x_t != y_t) {
@@ -480,7 +534,7 @@ static struct range range_refine(enum num_t x_t, struct range x, enum num_t y_t,
 	}
 
 	/* otherwise, plain range cast and intersection works */
-	return range_improve(x_t, x, y_cast);
+	return range_intersection(x_t, x, y_cast);
 }
 
 /* =======================