At -O1, GCC lowers (~a & 1) == (~b & 1) into two different GIMPLE
forms depending on whether the boolean values come from a function
return boundary or an inline expression:

  1. Via function return (e.g. inlined is_even), GCC preserves the
     eq/ne form because the function boundary hides the internal
     structure from the gimplifier:
       ((a&1)==0) == ((b&1)==0)   outer node is eq/ne

  2. Via inline expression (directly written), GCC sees the full
     boolean expression tree at once and folds to bit_xor during
     gimplification:
       ((a&1)!=0) ^ ((b&1)==0)   outer node is bit_xor

Add a generalized match.pd rule handling:
  1. ((x & c) == 0) OP ((y & c) == 0)
  2. ((x & c) != 0) OP ((y & c) == 0)
  3. ((x & c) == 0) OP (y & c)

for OP in { ==, !=, ^ } and pow2 masks. The third form is required
because GCC canonicalize: ((x & c) != 0) into (x & c) before this
rule runs.

Fold these directly into the canonical xor-mask form:
  ((x ^ y) & c) == 0
  ((x ^ y) & c) != 0

Bootstrapped and tested on aarch64-linux-gnu.

Changes since v1:
* v3: Collapse both previous simplify rules into one generalized
      matcher covering all combinations of outer {eq, ne, bit_xor}
      and inner {eq, ne} comparisons.
      Add missing mixed-polarity test cases.

* v2: Generalize mask from integer_onep to integer_pow2p.
      Combine both patterns into single one.
      Split test into bool-eq-evenness.c, bool-eq-bitxor.c,
      bool-eq-pow2.c.

        PR tree-optimization/112533
gcc/ChangeLog:
        * match.pd: Canonicalize boolean comparisons of masked pow2
        bits into xor-mask tests.

gcc/testsuite/ChangeLog:
        * gcc.dg/tree-ssa/bool-eq-bitxor.c: New test.
        * gcc.dg/tree-ssa/bool-eq-evenness.c: New test.
        * gcc.dg/tree-ssa/bool-eq-pow2.c: New test.

Signed-off-by: Shivam Gupta <[email protected]>
---
 gcc/match.pd                                  | 38 ++++++++
 .../gcc.dg/tree-ssa/bool-eq-bitxor.c          | 39 ++++++++
 .../gcc.dg/tree-ssa/bool-eq-evenness.c        | 43 +++++++++
 gcc/testsuite/gcc.dg/tree-ssa/bool-eq-pow2.c  | 89 +++++++++++++++++++
 4 files changed, 209 insertions(+)
 create mode 100644 gcc/testsuite/gcc.dg/tree-ssa/bool-eq-bitxor.c
 create mode 100644 gcc/testsuite/gcc.dg/tree-ssa/bool-eq-evenness.c
 create mode 100644 gcc/testsuite/gcc.dg/tree-ssa/bool-eq-pow2.c

diff --git a/gcc/match.pd b/gcc/match.pd
index ff13a07ea94..d41a2b2f329 100644
--- a/gcc/match.pd
+++ b/gcc/match.pd
@@ -1464,6 +1464,44 @@ DEFINE_INT_AND_FLOAT_ROUND_FN (RINT)
   (if (TYPE_UNSIGNED (type))
     (bit_and @0 (bit_not (lshift { build_all_ones_cst (type); } @1)))))
 
+/* PR112533: Canonicalize boolean comparisons of masked pow2 bits into
+   xor-mask tests.
+   ((x & c) == 0) == ((y & c) == 0) -> (((x ^ y) & c) == 0)
+   ((x & c) == 0) != ((y & c) == 0) -> (((x ^ y) & c) != 0)
+   and equivalent xor forms.  */
+(for ocmp (eq ne bit_xor)
+ (for icmp0 (eq eq ne ne)
+      icmp1 (eq ne eq ne)
+  (simplify
+   (ocmp
+    (icmp0 (bit_and @0 integer_pow2p@1) integer_zerop@3)
+    (icmp1 (bit_and @2 @1) @3))
+   (if (types_match (@0, @2))
+    (with {
+      bool innersame
+        = (icmp0 == EQ_EXPR) == (icmp1 == EQ_EXPR);
+    }
+     (if (innersame == (ocmp == EQ_EXPR))
+      (eq (bit_and (bit_xor @0 @2) @1) @3)
+      (ne (bit_and (bit_xor @0 @2) @1) @3)))))
+
+  /* Canonicalized: ((x & c) == 0) OP (y & c)
+     because ((y & c) != 0) may fold into (y & c).  */
+  (simplify
+   (ocmp
+    (convert?@4
+     (icmp0 (bit_and @0 integer_pow2p@1) integer_zerop@3))
+    (convert?@5
+     (bit_and @2 @1)))
+   (if (types_match (@0, @2))
+    (with {
+      bool innersame
+        = (icmp0 == EQ_EXPR) == false;
+    }
+     (if (innersame == (ocmp == EQ_EXPR))
+      (eq (bit_and (bit_xor @0 @2) @1) @3)
+      (ne (bit_and (bit_xor @0 @2) @1) @3)))))))
+
 (for bitop (bit_and bit_ior)
      cmp (eq ne)
  /* PR35691: Transform
diff --git a/gcc/testsuite/gcc.dg/tree-ssa/bool-eq-bitxor.c 
b/gcc/testsuite/gcc.dg/tree-ssa/bool-eq-bitxor.c
new file mode 100644
index 00000000000..05cee9696cf
--- /dev/null
+++ b/gcc/testsuite/gcc.dg/tree-ssa/bool-eq-bitxor.c
@@ -0,0 +1,39 @@
+/* { dg-do compile } */
+/* { dg-options "-O1 -fdump-tree-optimized" } */
+
+typedef unsigned int u32;
+
+_Bool
+xor_ne_eq (u32 a, u32 b)
+{
+  u32 t1 = a & 1;
+  u32 t2 = b & 1;
+  return (t1 != 0) ^ (t2 == 0);
+}
+
+_Bool
+xor_eq_eq (u32 a, u32 b)
+{
+  u32 t1 = a & 1;
+  u32 t2 = b & 1;
+  return (t1 == 0) ^ (t2 == 0);
+}
+
+_Bool
+xor_eq_ne (u32 a, u32 b)
+{
+  u32 t1 = a & 1;
+  u32 t2 = b & 1;
+  return (t1 == 0) ^ (t2 != 0);
+}
+
+_Bool
+xor_ne_ne (u32 a, u32 b)
+{
+  u32 t1 = a & 1;
+  u32 t2 = b & 1;
+  return (t1 != 0) ^ (t2 != 0);
+}
+
+/* Verify all functions canonicalize to xor-mask tests.  */
+/* { dg-final { scan-tree-dump-times "& 1" 4 "optimized" } } */
diff --git a/gcc/testsuite/gcc.dg/tree-ssa/bool-eq-evenness.c 
b/gcc/testsuite/gcc.dg/tree-ssa/bool-eq-evenness.c
new file mode 100644
index 00000000000..75df70dc6a4
--- /dev/null
+++ b/gcc/testsuite/gcc.dg/tree-ssa/bool-eq-evenness.c
@@ -0,0 +1,43 @@
+/* { dg-do compile } */
+/* { dg-options "-O1 -fdump-tree-optimized" } */
+
+/* Verify the GIMPLE-level fix for PR112533. */
+
+typedef unsigned int u32;
+
+static _Bool
+is_even (u32 a)
+{
+  return a % 2 == 0;
+}
+
+_Bool
+same_evenness (u32 a, u32 b)
+{
+  return is_even (a) == is_even (b);
+}
+
+_Bool
+diff_evenness (u32 a, u32 b)
+{
+  return is_even (a) != is_even (b);
+}
+
+_Bool
+same_evenness_cmp_zero (u32 a, u32 b)
+{
+  u32 t1 = a & 1;
+  u32 t2 = b & 1;
+  return (t1 == 0) == (t2 == 0);
+}
+
+_Bool
+diff_evenness_cmp_zero (u32 a, u32 b)
+{
+  u32 t1 = a & 1;
+  u32 t2 = b & 1;
+  return (t1 == 0) != (t2 == 0);
+}
+
+/* Verify all functions canonicalize to xor forms.  */
+/* { dg-final { scan-tree-dump-times "\\^" 4 "optimized" } } */
diff --git a/gcc/testsuite/gcc.dg/tree-ssa/bool-eq-pow2.c 
b/gcc/testsuite/gcc.dg/tree-ssa/bool-eq-pow2.c
new file mode 100644
index 00000000000..109c5f03610
--- /dev/null
+++ b/gcc/testsuite/gcc.dg/tree-ssa/bool-eq-pow2.c
@@ -0,0 +1,89 @@
+/* { dg-do compile } */
+/* { dg-options "-O1 -fdump-tree-optimized" } */
+
+typedef unsigned int u32;
+
+_Bool
+eq_eq_outer_eq_mask2 (u32 a, u32 b)
+{
+  u32 t1 = a & 2;
+  u32 t2 = b & 2;
+  return (t1 == 0) == (t2 == 0);
+}
+
+_Bool
+eq_eq_outer_eq_mask4 (u32 a, u32 b)
+{
+  u32 t1 = a & 4;
+  u32 t2 = b & 4;
+  return (t1 == 0) == (t2 == 0);
+}
+
+_Bool
+eq_eq_outer_ne (u32 a, u32 b)
+{
+  u32 t1 = a & 1;
+  u32 t2 = b & 1;
+  return (t1 == 0) != (t2 == 0);
+}
+
+_Bool
+ne_eq_outer_eq (u32 a, u32 b)
+{
+  u32 t1 = a & 1;
+  u32 t2 = b & 1;
+  return (t1 != 0) == (t2 == 0);
+}
+
+_Bool
+ne_eq_outer_ne (u32 a, u32 b)
+{
+  u32 t1 = a & 1;
+  u32 t2 = b & 1;
+  return (t1 != 0) != (t2 == 0);
+}
+
+_Bool
+eq_ne_outer_eq (u32 a, u32 b)
+{
+  u32 t1 = a & 1;
+  u32 t2 = b & 1;
+  return (t1 == 0) == (t2 != 0);
+}
+
+_Bool
+eq_ne_outer_ne (u32 a, u32 b)
+{
+  u32 t1 = a & 1;
+  u32 t2 = b & 1;
+  return (t1 == 0) != (t2 != 0);
+}
+
+_Bool
+ne_ne_outer_eq (u32 a, u32 b)
+{
+  u32 t1 = a & 1;
+  u32 t2 = b & 1;
+  return (t1 != 0) == (t2 != 0);
+}
+
+_Bool
+ne_ne_outer_ne (u32 a, u32 b)
+{
+  u32 t1 = a & 1;
+  u32 t2 = b & 1;
+  return (t1 != 0) != (t2 != 0);
+}
+
+/* Non-power-of-2: should not be simplified.  */
+_Bool
+eq_eq_outer_eq_nonpow2 (u32 a, u32 b)
+{
+  u32 t1 = a & 3;
+  u32 t2 = b & 3;
+  return (t1 == 0) == (t2 == 0);
+}
+
+/* Verify power-of-2 masks are simplified, non-power-of-2 masks are not.  */
+/* { dg-final { scan-tree-dump-times "a_\[0-9\]+\\(D\\) \\^ b_\[0-9\]+\\(D\\)" 
9 "optimized" } } */
+/* { dg-final { scan-tree-dump-times "& 3" 2 "optimized" } } */
-- 
2.34.1

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