NEON's BCAX has been in service for SHA3 intrinsic implementation (https://github.com/openjdk/jdk/blob/a13af650437de508d64f0b12285a6ffc9901f85f/src/hotspot/cpu/aarch64/stubGenerator_aarch64.cpp#L3934 ). As well it can be generated by code generator if we matched such patterns.

Test case:

  public static void testBCAXI() {
         for (int i = 0; i < i128specs.loopBound(ARR_LEN); i += i128specs.length()) {
             IntVector v1 = IntVector.fromArray(i128specs, iarr, i);
             IntVector v2 = IntVector.fromArray(i128specs, iarr, i);
             IntVector v3 = IntVector.fromArray(i128specs, iarr, i);

             v3.lanewise(VectorOperators.NOT).lanewise(VectorOperators.AND, v2).
                                                       lanewise(VectorOperators.XOR, v1).intoArray(ir, i);
         }
   }

 Generated code:
  0x0000fffe18c8ede8: ldr q16, [x11, #16]
  0x0000fffe18c8edec: bic v17.16b, v16.16b, v16.16b
  0x0000fffe18c8edf0: eor v16.16b, v17.16b, v16.16b
  0x0000fffe18c8edf4: add x10, x17, x10
  0x0000fffe18c8edf8: str q16, [x10, #16]

BIC and EOR can be optimized to BCAX.