What is the most efficient way to detect even numbers in Java?

If you check the assembly generated by hotspot 7 of these two methods:

public static boolean isEvenBit(int i) {
    return (i & 1) == 0;
}
public static boolean isEvenMod(int i) {
    return i % 2 == 0;
}

you will see that although the mod is optimised and basically does a bitwise and but it has a few extra instructions because the two operations are not strictly equivalent*. Other JVMs might optimise it differently. The assembly is posted below for reference.

I also ran a micro benchmark which confirms our observation: isEventBit is marginally faster (but both run in about 2 nanoseconds so probably won't have much of an inmpact on a typical program as a whole):

Benchmark                     Mode  Samples  Score   Error  Units
c.a.p.SO16969220.isEvenBit    avgt       10  1.869 ± 0.069  ns/op
c.a.p.SO16969220.isEvenMod    avgt       10  2.554 ± 0.142  ns/op

---

isEvenBit

  # {method} 'isEvenBit' '(I)Z' in 'javaapplication4/Test1'
  # parm0:    rdx       = int
  #           [sp+0x20]  (sp of caller)
  0x00000000026c2580: sub    rsp,0x18
  0x00000000026c2587: mov    QWORD PTR [rsp+0x10],rbp  ;*synchronization entry
                                                ; - javaapplication4.Test1::isEvenBit@-1 (line 66)
  0x00000000026c258c: and    edx,0x1
  0x00000000026c258f: mov    eax,edx
  0x00000000026c2591: xor    eax,0x1            ;*ireturn
                                                ; - javaapplication4.Test1::isEvenBit@11 (line 66)
  0x00000000026c2594: add    rsp,0x10
  0x00000000026c2598: pop    rbp
  0x00000000026c2599: test   DWORD PTR [rip+0xfffffffffdb6da61],eax        # 0x0000000000230000
                                                ;   {poll_return}
  0x00000000026c259f: ret    

isEvenMod

  # {method} 'isEvenMod' '(I)Z' in 'javaapplication4/Test1'
  # parm0:    rdx       = int
  #           [sp+0x20]  (sp of caller)
  0x00000000026c2780: sub    rsp,0x18
  0x00000000026c2787: mov    QWORD PTR [rsp+0x10],rbp  ;*synchronization entry
                                                ; - javaapplication4.Test1::isEvenMod@-1 (line 63)
  0x00000000026c278c: mov    r10d,edx
  0x00000000026c278f: and    r10d,0x1           ;*irem
                                                ; - javaapplication4.Test1::isEvenMod@2 (line 63)
  0x00000000026c2793: mov    r11d,r10d
  0x00000000026c2796: neg    r11d
  0x00000000026c2799: test   edx,edx
  0x00000000026c279b: cmovl  r10d,r11d
  0x00000000026c279f: test   r10d,r10d
  0x00000000026c27a2: setne  al
  0x00000000026c27a5: movzx  eax,al
  0x00000000026c27a8: xor    eax,0x1            ;*ireturn
                                                ; - javaapplication4.Test1::isEvenMod@11 (line 63)
  0x00000000026c27ab: add    rsp,0x10
  0x00000000026c27af: pop    rbp
  0x00000000026c27b0: test   DWORD PTR [rip+0xfffffffffdb6d84a],eax        # 0x0000000000230000
                                                ;   {poll_return}
  0x00000000026c27b6: ret    

_{* as pointed out in the comments, % isn't really modulo; it's the remainder. So (i % 2) != (i & 1) if i < 0. The extra instructions in the isEvenMod code sets the sign of the result to the sign of i (and then just compares it to zero, so the effort is wasted).}

Another approach is to run a micro benchmark and analyse the time taken by each variants. Here are the results:

Benchmark    Mean    Units    Time vs. baseline
baseline     10.330  nsec/op     0.000
bitAnd       12.075  nsec/op     1.745
bitShift     12.309  nsec/op     1.979
modulo       12.309  nsec/op     4.529

(the baseline is a method that just returns i == 0)

Conclusion:

• i & 1 -----> takes about 1.75ns
• i << 31 --> takes about 2.00ns
• i % 2 -----> takes about 4.50ns

In other words, i % 2 is 2x slower than i & 1.

Notes: benchmark done with jmh. The baseline is high because I generate random numbers to make sure the method are not optimised away. Tests run on an i7 @ 2.8GHz (i.e. one cycle = 0.35ns) with hotspot 7.