There is a slight difference in the ordering of the bytecode.
2 * (i * i):
iconst_2
iload0
iload0
imul
imul
iadd
vs 2 * i * i:
iconst_2
iload0
imul
iload0
imul
iadd
At first sight this should not make a difference; if anything the second version is more optimal since it uses one slot less.
So we need to dig deeper into the lower level (JIT)1.
Remember that JIT tends to unroll small loops very aggressively. Indeed we observe a 16x unrolling for the 2 * (i * i) case:
030 B2: # B2 B3 <- B1 B2 Loop: B2-B2 inner main of N18 Freq: 1e+006
030 addl R11, RBP # int
033 movl RBP, R13 # spill
036 addl RBP, #14 # int
039 imull RBP, RBP # int
03c movl R9, R13 # spill
03f addl R9, #13 # int
043 imull R9, R9 # int
047 sall RBP, #1
049 sall R9, #1
04c movl R8, R13 # spill
04f addl R8, #15 # int
053 movl R10, R8 # spill
056 movdl XMM1, R8 # spill
05b imull R10, R8 # int
05f movl R8, R13 # spill
062 addl R8, #12 # int
066 imull R8, R8 # int
06a sall R10, #1
06d movl [rsp + #32], R10 # spill
072 sall R8, #1
075 movl RBX, R13 # spill
078 addl RBX, #11 # int
07b imull RBX, RBX # int
07e movl RCX, R13 # spill
081 addl RCX, #10 # int
084 imull RCX, RCX # int
087 sall RBX, #1
089 sall RCX, #1
08b movl RDX, R13 # spill
08e addl RDX, #8 # int
091 imull RDX, RDX # int
094 movl RDI, R13 # spill
097 addl RDI, #7 # int
09a imull RDI, RDI # int
09d sall RDX, #1
09f sall RDI, #1
0a1 movl RAX, R13 # spill
0a4 addl RAX, #6 # int
0a7 imull RAX, RAX # int
0aa movl RSI, R13 # spill
0ad addl RSI, #4 # int
0b0 imull RSI, RSI # int
0b3 sall RAX, #1
0b5 sall RSI, #1
0b7 movl R10, R13 # spill
0ba addl R10, #2 # int
0be imull R10, R10 # int
0c2 movl R14, R13 # spill
0c5 incl R14 # int
0c8 imull R14, R14 # int
0cc sall R10, #1
0cf sall R14, #1
0d2 addl R14, R11 # int
0d5 addl R14, R10 # int
0d8 movl R10, R13 # spill
0db addl R10, #3 # int
0df imull R10, R10 # int
0e3 movl R11, R13 # spill
0e6 addl R11, #5 # int
0ea imull R11, R11 # int
0ee sall R10, #1
0f1 addl R10, R14 # int
0f4 addl R10, RSI # int
0f7 sall R11, #1
0fa addl R11, R10 # int
0fd addl R11, RAX # int
100 addl R11, RDI # int
103 addl R11, RDX # int
106 movl R10, R13 # spill
109 addl R10, #9 # int
10d imull R10, R10 # int
111 sall R10, #1
114 addl R10, R11 # int
117 addl R10, RCX # int
11a addl R10, RBX # int
11d addl R10, R8 # int
120 addl R9, R10 # int
123 addl RBP, R9 # int
126 addl RBP, [RSP + #32 (32-bit)] # int
12a addl R13, #16 # int
12e movl R11, R13 # spill
131 imull R11, R13 # int
135 sall R11, #1
138 cmpl R13, #999999985
13f jl B2 # loop end P=1.000000 C=6554623.000000
We see that there is 1 register that is "spilled" onto the stack.
And for the 2 * i * i version:
05a B3: # B2 B4 <- B1 B2 Loop: B3-B2 inner main of N18 Freq: 1e+006
05a addl RBX, R11 # int
05d movl [rsp + #32], RBX # spill
061 movl R11, R8 # spill
064 addl R11, #15 # int
068 movl [rsp + #36], R11 # spill
06d movl R11, R8 # spill
070 addl R11, #14 # int
074 movl R10, R9 # spill
077 addl R10, #16 # int
07b movdl XMM2, R10 # spill
080 movl RCX, R9 # spill
083 addl RCX, #14 # int
086 movdl XMM1, RCX # spill
08a movl R10, R9 # spill
08d addl R10, #12 # int
091 movdl XMM4, R10 # spill
096 movl RCX, R9 # spill
099 addl RCX, #10 # int
09c movdl XMM6, RCX # spill
0a0 movl RBX, R9 # spill
0a3 addl RBX, #8 # int
0a6 movl RCX, R9 # spill
0a9 addl RCX, #6 # int
0ac movl RDX, R9 # spill
0af addl RDX, #4 # int
0b2 addl R9, #2 # int
0b6 movl R10, R14 # spill
0b9 addl R10, #22 # int
0bd movdl XMM3, R10 # spill
0c2 movl RDI, R14 # spill
0c5 addl RDI, #20 # int
0c8 movl RAX, R14 # spill
0cb addl RAX, #32 # int
0ce movl RSI, R14 # spill
0d1 addl RSI, #18 # int
0d4 movl R13, R14 # spill
0d7 addl R13, #24 # int
0db movl R10, R14 # spill
0de addl R10, #26 # int
0e2 movl [rsp + #40], R10 # spill
0e7 movl RBP, R14 # spill
0ea addl RBP, #28 # int
0ed imull RBP, R11 # int
0f1 addl R14, #30 # int
0f5 imull R14, [RSP + #36 (32-bit)] # int
0fb movl R10, R8 # spill
0fe addl R10, #11 # int
102 movdl R11, XMM3 # spill
107 imull R11, R10 # int
10b movl [rsp + #44], R11 # spill
110 movl R10, R8 # spill
113 addl R10, #10 # int
117 imull RDI, R10 # int
11b movl R11, R8 # spill
11e addl R11, #8 # int
122 movdl R10, XMM2 # spill
127 imull R10, R11 # int
12b movl [rsp + #48], R10 # spill
130 movl R10, R8 # spill
133 addl R10, #7 # int
137 movdl R11, XMM1 # spill
13c imull R11, R10 # int
140 movl [rsp + #52], R11 # spill
145 movl R11, R8 # spill
148 addl R11, #6 # int
14c movdl R10, XMM4 # spill
151 imull R10, R11 # int
155 movl [rsp + #56], R10 # spill
15a movl R10, R8 # spill
15d addl R10, #5 # int
161 movdl R11, XMM6 # spill
166 imull R11, R10 # int
16a movl [rsp + #60], R11 # spill
16f movl R11, R8 # spill
172 addl R11, #4 # int
176 imull RBX, R11 # int
17a movl R11, R8 # spill
17d addl R11, #3 # int
181 imull RCX, R11 # int
185 movl R10, R8 # spill
188 addl R10, #2 # int
18c imull RDX, R10 # int
190 movl R11, R8 # spill
193 incl R11 # int
196 imull R9, R11 # int
19a addl R9, [RSP + #32 (32-bit)] # int
19f addl R9, RDX # int
1a2 addl R9, RCX # int
1a5 addl R9, RBX # int
1a8 addl R9, [RSP + #60 (32-bit)] # int
1ad addl R9, [RSP + #56 (32-bit)] # int
1b2 addl R9, [RSP + #52 (32-bit)] # int
1b7 addl R9, [RSP + #48 (32-bit)] # int
1bc movl R10, R8 # spill
1bf addl R10, #9 # int
1c3 imull R10, RSI # int
1c7 addl R10, R9 # int
1ca addl R10, RDI # int
1cd addl R10, [RSP + #44 (32-bit)] # int
1d2 movl R11, R8 # spill
1d5 addl R11, #12 # int
1d9 imull R13, R11 # int
1dd addl R13, R10 # int
1e0 movl R10, R8 # spill
1e3 addl R10, #13 # int
1e7 imull R10, [RSP + #40 (32-bit)] # int
1ed addl R10, R13 # int
1f0 addl RBP, R10 # int
1f3 addl R14, RBP # int
1f6 movl R10, R8 # spill
1f9 addl R10, #16 # int
1fd cmpl R10, #999999985
204 jl B2 # loop end P=1.000000 C=7419903.000000
Here we observe much more "spilling" and more accesses to the stack [RSP + ...], due to more intermediate results that need to be preserved.
Thus the answer to the question is simple: 2 * (i * i) is faster than 2 * i * i because the JIT generates more optimal assembly code for the first case.
But of course it is obvious that neither the first nor the second version is any good; the loop could really benefit from vectorization, since any x86-64 CPU has at least SSE2 support.
So it's an issue of the optimizer; as is often the case, it unrolls too aggressively and shoots itself in the foot, all the while missing out on various other opportunities.
In fact, modern x86-64 CPUs break down the instructions further into micro-ops (µops) and with features like register renaming, µop caches and loop buffers, loop optimization takes a lot more finesse than a simple unrolling for optimal performance. According to Agner Fog's optimization guide:
The gain in performance due to the µop cache can be quite
considerable if the average instruction length is more than 4 bytes.
The following methods of optimizing the use of the µop cache may
be considered:
- Make sure that critical loops are small enough to fit into the µop cache.
- Align the most critical loop entries and function entries by 32.
- Avoid unnecessary loop unrolling.
- Avoid instructions that have extra load time
. . .
Regarding those load times - even the fastest L1D hit costs 4 cycles, an extra register and µop, so yes, even a few accesses to memory will hurt performance in tight loops.
But back to the vectorization opportunity - to see how fast it can be, we can compile a similar C application with GCC, which outright vectorizes it (AVX2 is shown, SSE2 is similar)2:
vmovdqa ymm0, YMMWORD PTR .LC0[rip]
vmovdqa ymm3, YMMWORD PTR .LC1[rip]
xor eax, eax
vpxor xmm2, xmm2, xmm2
.L2:
vpmulld ymm1, ymm0, ymm0
inc eax
vpaddd ymm0, ymm0, ymm3
vpslld ymm1, ymm1, 1
vpaddd ymm2, ymm2, ymm1
cmp eax, 125000000 ; 8 calculations per iteration
jne .L2
vmovdqa xmm0, xmm2
vextracti128 xmm2, ymm2, 1
vpaddd xmm2, xmm0, xmm2
vpsrldq xmm0, xmm2, 8
vpaddd xmm0, xmm2, xmm0
vpsrldq xmm1, xmm0, 4
vpaddd xmm0, xmm0, xmm1
vmovd eax, xmm0
vzeroupper
With run times:
- SSE: 0.24 s, or 2 times faster.
- AVX: 0.15 s, or 3 times faster.
- AVX2: 0.08 s, or 5 times faster.
1 To get JIT generated assembly output, get a debug JVM and run with -XX:+PrintOptoAssembly
2 The C version is compiled with the -fwrapv flag, which enables GCC to treat signed integer overflow as a two's-complement wrap-around.
ByteCodes: https://cs.nyu.edu/courses/fall00/V22.0201-001/jvm2.html
ByteCodes Viewer: https://github.com/Konloch/bytecode-viewer
On my JDK (Win10 64 1.8.0_65-b17) I can reproduce and explain:
public static void main(String[] args) {
int repeat = 10;
long A = 0;
long B = 0;
for (int i = 0; i < repeat; i++) {
A += test();
B += testB();
}
System.out.println(A / repeat + " ms");
System.out.println(B / repeat + " ms");
}
private static long test() {
int n = 0;
for (int i = 0; i < 1000; i++) {
n += multi(i);
}
long startTime = System.currentTimeMillis();
for (int i = 0; i < 1000000000; i++) {
n += multi(i);
}
long ms = (System.currentTimeMillis() - startTime);
System.out.println(ms + " ms A " + n);
return ms;
}
private static long testB() {
int n = 0;
for (int i = 0; i < 1000; i++) {
n += multiB(i);
}
long startTime = System.currentTimeMillis();
for (int i = 0; i < 1000000000; i++) {
n += multiB(i);
}
long ms = (System.currentTimeMillis() - startTime);
System.out.println(ms + " ms B " + n);
return ms;
}
private static int multiB(int i) {
return 2 * (i * i);
}
private static int multi(int i) {
return 2 * i * i;
}
Output:
...
405 ms A 785527736
327 ms B 785527736
404 ms A 785527736
329 ms B 785527736
404 ms A 785527736
328 ms B 785527736
404 ms A 785527736
328 ms B 785527736
410 ms
333 ms
So why?
The Byte code is this:
private static multiB(int arg0) { // 2 * (i * i)
<localVar:index=0 , name=i , desc=I, sig=null, start=L1, end=L2>
L1 {
iconst_2
iload0
iload0
imul
imul
ireturn
}
L2 {
}
}
private static multi(int arg0) { // 2 * i * i
<localVar:index=0 , name=i , desc=I, sig=null, start=L1, end=L2>
L1 {
iconst_2
iload0
imul
iload0
imul
ireturn
}
L2 {
}
}
The difference being:
With brackets (2 * (i * i)):
- push const stack
- push local on stack
- push local on stack
- multiply top of stack
- multiply top of stack
Without brackets (2 * i * i):
- push const stack
- push local on stack
- multiply top of stack
- push local on stack
- multiply top of stack
Loading all on stack and then working back down is faster than switching between putting on stack and operating on it.
I tried a JMH using the default archetype: I also added optimized version based Runemoro' explanation .
@State(Scope.Benchmark)
@Warmup(iterations = 2)
@Fork(1)
@Measurement(iterations = 10)
@OutputTimeUnit(TimeUnit.NANOSECONDS)
//@BenchmarkMode({ Mode.All })
@BenchmarkMode(Mode.AverageTime)
public class MyBenchmark {
@Param({ "100", "1000", "1000000000" })
private int size;
@Benchmark
public int two_square_i() {
int n = 0;
for (int i = 0; i < size; i++) {
n += 2 * (i * i);
}
return n;
}
@Benchmark
public int square_i_two() {
int n = 0;
for (int i = 0; i < size; i++) {
n += i * i;
}
return 2*n;
}
@Benchmark
public int two_i_() {
int n = 0;
for (int i = 0; i < size; i++) {
n += 2 * i * i;
}
return n;
}
}
The result are here:
Benchmark (size) Mode Samples Score Score error Units
o.s.MyBenchmark.square_i_two 100 avgt 10 58,062 1,410 ns/op
o.s.MyBenchmark.square_i_two 1000 avgt 10 547,393 12,851 ns/op
o.s.MyBenchmark.square_i_two 1000000000 avgt 10 540343681,267 16795210,324 ns/op
o.s.MyBenchmark.two_i_ 100 avgt 10 87,491 2,004 ns/op
o.s.MyBenchmark.two_i_ 1000 avgt 10 1015,388 30,313 ns/op
o.s.MyBenchmark.two_i_ 1000000000 avgt 10 967100076,600 24929570,556 ns/op
o.s.MyBenchmark.two_square_i 100 avgt 10 70,715 2,107 ns/op
o.s.MyBenchmark.two_square_i 1000 avgt 10 686,977 24,613 ns/op
o.s.MyBenchmark.two_square_i 1000000000 avgt 10 652736811,450 27015580,488 ns/op
On my PC (Core i7 860, doing nothing much apart reading on my smartphone):
n += i*i then n*2 is first2 * (i * i) is second.
The JVM is clearly not optimizing the same way than a human does (based on Runemoro answer).
Now then, reading bytecode: javap -c -v ./target/classes/org/sample/MyBenchmark.class
- Differences between 2*(i*i) (left) and 2*i*i (right) here: https://www.diffchecker.com/cvSFppWI
- Differences between 2*(i*i) and the optimized version here: https://www.diffchecker.com/I1XFu5dP
I am not expert on bytecode but we iload_2 before we imul: that's probably where you get the difference: I can suppose that the JVM optimize reading i twice (i is already here, there is no need to load it again) whilst in the 2*i*i it can't.
Interesting observation using Java 11 and switching off loop unrolling with the following VM option:
-XX:LoopUnrollLimit=0
The loop with the 2 * (i * i) expression results in a more compact native code1:
L0001: add eax,r11d
inc r8d
mov r11d,r8d
imul r11d,r8d
shl r11d,1h
cmp r8d,r10d
jl L0001
in comparison with the 2 * i * i version:
L0001: add eax,r11d
mov r11d,r8d
shl r11d,1h
add r11d,2h
inc r8d
imul r11d,r8d
cmp r8d,r10d
jl L0001
Java version:
java version "11" 2018-09-25
Java(TM) SE Runtime Environment 18.9 (build 11+28)
Java HotSpot(TM) 64-Bit Server VM 18.9 (build 11+28, mixed mode)
Benchmark results:
Benchmark (size) Mode Cnt Score Error Units
LoopTest.fast 1000000000 avgt 5 694,868 ± 36,470 ms/op
LoopTest.slow 1000000000 avgt 5 769,840 ± 135,006 ms/op
Benchmark source code:
@BenchmarkMode(Mode.AverageTime)
@OutputTimeUnit(TimeUnit.MILLISECONDS)
@Warmup(iterations = 5, time = 5, timeUnit = TimeUnit.SECONDS)
@Measurement(iterations = 5, time = 5, timeUnit = TimeUnit.SECONDS)
@State(Scope.Thread)
@Fork(1)
public class LoopTest {
@Param("1000000000") private int size;
public static void main(String[] args) throws RunnerException {
Options opt =
new OptionsBuilder().include(LoopTest.class.getSimpleName())
.jvmArgs("-XX:LoopUnrollLimit=0")
.build();
new Runner(opt).run();
}
@Benchmark
public int slow() {
int n = 0;
for (int i = 0; i < size; i++) {
n += 2 * i * i;
}
return n;
}
@Benchmark
public int fast() {
int n = 0;
for (int i = 0; i < size; i++) {
n += 2 * (i * i);
}
return n;
}
}
1 - VM options used: -XX:+UnlockDiagnosticVMOptions -XX:+PrintAssembly -XX:LoopUnrollLimit=0
The two methods of adding do generate slightly different byte code:
17: iconst_2
18: iload 4
20: iload 4
22: imul
23: imul
24: iadd
For 2 * (i * i) vs:
17: iconst_2
18: iload 4
20: imul
21: iload 4
23: imul
24: iadd
For 2 * i * i.
And when using a JMH benchmark like this:
@Warmup(iterations = 5, batchSize = 1)
@Measurement(iterations = 5, batchSize = 1)
@Fork(1)
@BenchmarkMode(Mode.AverageTime)
@OutputTimeUnit(TimeUnit.MILLISECONDS)
@State(Scope.Benchmark)
public class MyBenchmark {
@Benchmark
public int noBrackets() {
int n = 0;
for (int i = 0; i < 1000000000; i++) {
n += 2 * i * i;
}
return n;
}
@Benchmark
public int brackets() {
int n = 0;
for (int i = 0; i < 1000000000; i++) {
n += 2 * (i * i);
}
return n;
}
}
The difference is clear:
# JMH version: 1.21
# VM version: JDK 11, Java HotSpot(TM) 64-Bit Server VM, 11+28
# VM options: <none>
Benchmark (n) Mode Cnt Score Error Units
MyBenchmark.brackets 1000000000 avgt 5 380.889 ± 58.011 ms/op
MyBenchmark.noBrackets 1000000000 avgt 5 512.464 ± 11.098 ms/op
What you observe is correct, and not just an anomaly of your benchmarking style (i.e. no warmup, see How do I write a correct micro-benchmark in Java?)
Running again with Graal:
# JMH version: 1.21
# VM version: JDK 11, Java HotSpot(TM) 64-Bit Server VM, 11+28
# VM options: -XX:+UnlockExperimentalVMOptions -XX:+EnableJVMCI -XX:+UseJVMCICompiler
Benchmark (n) Mode Cnt Score Error Units
MyBenchmark.brackets 1000000000 avgt 5 335.100 ± 23.085 ms/op
MyBenchmark.noBrackets 1000000000 avgt 5 331.163 ± 50.670 ms/op
You see that the results are much closer, which makes sense, since Graal is an overall better performing, more modern, compiler.
So this is really just up to how well the JIT compiler is able to optimize a particular piece of code, and doesn't necessarily have a logical reason to it.
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