Unfortunately I had to use AMD64 instructions here; i think the ISA is pretty shithouse so I haven't bothered to learn it very well so i'm doing some guessing below. I even downloaded the APMs from AMD (i find the intel docs quite poor) to look some stuff up.
For the C code i'm using gcc 4.8.2 with -mtune=native -std=gnu99 and -Ox as indicated in the text.
The actual test calculates 1000x dot products of 2^20 elements each. For java i'm using System.nanoTime() and printing the best result across all runs. For C i couldn't be bothered with the gettimeofday() stuff so i'm just using the time command - over 1000 iterations the difference should be negligable and there are some interesting results regardless.
Simple loop
This is the starting function; obvious what it does.
public float dot(float[] a, float[] b, int len) {
float v = 0;
for (int i=0;i<len;i++)
v += a[i] * b[i];
return v;
}
A C version is identical apart from using pointers rather than arrays
and some extra fluffly conventions.
float dot(const float *a, const float *b, int len) {
float v = 0;
for (int i=0;i<len;i++)
v += a[i] * b[i];
return v;
}
First pass
After some iterations hotspot will recognise this function could benefit from optimisation and this is what jdk8 spits out at the first compilation pass.
This is using gcc syntax so instruction operands are srca,[srcb,],dst rather than the more conventional dst,srca[,srcb].
.1: movslq %esi,%rdi
jae .exception0
vmovss 0x10(%rdx,%rdi,4),%xmm1
movslq %esi,%rdi
jae .exception1
vmovss 0x10(%rcx,%rdi,4),%xmm2
vmulss %xmm2,%xmm1,%xmm1
vaddss %xmm0,%xmm1,%xmm1
inc %esi
mov $0x7ffdffc00ce8,%rdi
mov 0xe0(%rdi),%ebx
add $0x8,%ebx
mov %ebx,0xe0(%rdi)
mov $0x7ffdffc00488,%rdi
and $0xfff8,%ebx
cmp $0x0,%ebx
je .2
.3: test %eax,0x15e4076a(%rip)
mov $0x7ffdffc00ce8,%rdi
incl 0x128(%rdi)
vmovaps %xmm1,%xmm0
cmp %r8d,%esi
mov $0x7ffdffc00ce8,%rdi
mov $0x108,%rbx
jge .4
mov $0x118,%rbx
.4: mov (%rdi,%rbx,1),%rax
lea 0x1(%rax),%rax
mov %rax,(%rdi,%rbx,1)
jl .1
;; clean up and exit
.2: mov %rdi,0x8(%rsp)
movq $0x1d,(%rsp)
callq some_function
jmpq .3
Of these 11 are for the loop itself, the rest seem to be for profiling the loop.
As far as it goes it looks fairly decent - pretty much gcc -O2 level of optimisation with array bounds checking performed at each array read.
Of course the profiling adds a lot of overhead here.
The following is the output for the inner loop of gcc -O2.
10: f3 0f 10 0c 87 movss (%rdi,%rax,4),%xmm1 15: f3 0f 59 0c 86 mulss (%rsi,%rax,4),%xmm1 1a: 48 ff c0 inc %rax 1d: 39 c2 cmp %eax,%edx 1f: f3 0f 58 c1 addss %xmm1,%xmm0 23: 7f eb jg 10
The only real difference apart from having no bounds checking is that it multiplies directly from memory rather than through a register. The latter is how every other mainstream cpu does it so that may have some bearing on it.
I can't easy do comparison timing of the loops (and it isn't very meaningful) but obviously the java will be slower here, and probably on-par with -O0 output from gcc.
Final pass
After it has gained some profiling information the result will be optimised - in this case it recompiles it twice more. The inner loop of the final pass is below:
.1: vmovss 0x10(%rbx,%r14,4),%xmm0
vmulss 0x10(%rcx,%r14,4),%xmm0,%xmm1
vaddss %xmm3,%xmm1,%xmm0
movslq %r14d,%r10
vmovss 0x2c(%rbx,%r10,4),%xmm2
vmulss 0x2c(%rcx,%r10,4),%xmm2,%xmm8
vmovss 0x14(%rbx,%r10,4),%xmm1
vmulss 0x14(%rcx,%r10,4),%xmm1,%xmm2
vmovss 0x18(%rcx,%r10,4),%xmm1
vmulss 0x18(%rbx,%r10,4),%xmm1,%xmm3
vmovss 0x28(%rbx,%r10,4),%xmm1
vmulss 0x28(%rcx,%r10,4),%xmm1,%xmm4
vmovss 0x1c(%rcx,%r10,4),%xmm1
vmulss 0x1c(%rbx,%r10,4),%xmm1,%xmm5
vmovss 0x20(%rbx,%r10,4),%xmm1
vmulss 0x20(%rcx,%r10,4),%xmm1,%xmm6
vmovss 0x24(%rbx,%r10,4),%xmm1
vmulss 0x24(%rcx,%r10,4),%xmm1,%xmm7
vaddss %xmm2,%xmm0,%xmm0
vaddss %xmm0,%xmm3,%xmm1
vaddss %xmm1,%xmm5,%xmm1
vaddss %xmm1,%xmm6,%xmm0
vaddss %xmm0,%xmm7,%xmm1
vaddss %xmm1,%xmm4,%xmm0
vaddss %xmm0,%xmm8,%xmm3
add $0x8,%r14d
cmp %r8d,%r14d
jl .1
cmp %ebp,%r14d
jge .done
xchg %ax,%ax
.2: cmp %edi,%r14d
jae .stuff0
vmovss 0x10(%rcx,%r14,4),%xmm1
cmp %r9d,%r14d
jae .stuff1
vmulss 0x10(%rbx,%r14,4),%xmm1,%xmm1
vaddss %xmm1,%xmm3,%xmm3
inc %r14d
cmp %ebp,%r14d
jl .2
.done:
So this has removed all the array bounds checking from inside the loop (it's elsewhere - too bulky/not important here). It's also unrolled the loop 8x and is using modern 3-operand instructions to stagger most of the operations for better throughput on typical RISC cpus (I have no knowledge of the AMD scheduling rules). And finally it tacks on a simple 1-element loop to finish off anything left over.
Comparing this to the output of gcc -O3 ...
30: f3 0f 10 09 movss (%rcx),%xmm1 34: 41 83 c0 10 add $0x10,%r8d 38: 0f 18 49 50 prefetcht0 0x50(%rcx) 3c: 0f 18 48 50 prefetcht0 0x50(%rax) 40: 48 83 c1 40 add $0x40,%rcx 44: 48 83 c0 40 add $0x40,%rax 48: f3 0f 59 48 c0 mulss -0x40(%rax),%xmm1 4d: f3 0f 58 c1 addss %xmm1,%xmm0 51: f3 0f 10 49 c4 movss -0x3c(%rcx),%xmm1 56: f3 0f 59 48 c4 mulss -0x3c(%rax),%xmm1 5b: f3 0f 58 c1 addss %xmm1,%xmm0 5f: f3 0f 10 49 c8 movss -0x38(%rcx),%xmm1 64: f3 0f 59 48 c8 mulss -0x38(%rax),%xmm1 69: f3 0f 58 c1 addss %xmm1,%xmm0 6d: f3 0f 10 49 cc movss -0x34(%rcx),%xmm1 72: f3 0f 59 48 cc mulss -0x34(%rax),%xmm1 77: f3 0f 58 c1 addss %xmm1,%xmm0 7b: f3 0f 10 49 d0 movss -0x30(%rcx),%xmm1 80: f3 0f 59 48 d0 mulss -0x30(%rax),%xmm1 85: f3 0f 58 c1 addss %xmm1,%xmm0 89: f3 0f 10 49 d4 movss -0x2c(%rcx),%xmm1 8e: f3 0f 59 48 d4 mulss -0x2c(%rax),%xmm1 93: f3 0f 58 c1 addss %xmm1,%xmm0 97: f3 0f 10 49 d8 movss -0x28(%rcx),%xmm1 9c: f3 0f 59 48 d8 mulss -0x28(%rax),%xmm1 a1: f3 0f 58 c1 addss %xmm1,%xmm0 a5: f3 0f 10 49 dc movss -0x24(%rcx),%xmm1 aa: f3 0f 59 48 dc mulss -0x24(%rax),%xmm1 af: f3 0f 58 c1 addss %xmm1,%xmm0 b3: f3 0f 10 49 e0 movss -0x20(%rcx),%xmm1 b8: f3 0f 59 48 e0 mulss -0x20(%rax),%xmm1 bd: f3 0f 58 c1 addss %xmm1,%xmm0 c1: f3 0f 10 49 e4 movss -0x1c(%rcx),%xmm1 c6: f3 0f 59 48 e4 mulss -0x1c(%rax),%xmm1 cb: f3 0f 58 c1 addss %xmm1,%xmm0 cf: f3 0f 10 49 e8 movss -0x18(%rcx),%xmm1 d4: f3 0f 59 48 e8 mulss -0x18(%rax),%xmm1 d9: f3 0f 58 c1 addss %xmm1,%xmm0 dd: f3 0f 10 49 ec movss -0x14(%rcx),%xmm1 e2: f3 0f 59 48 ec mulss -0x14(%rax),%xmm1 e7: f3 0f 58 c1 addss %xmm1,%xmm0 eb: f3 0f 10 49 f0 movss -0x10(%rcx),%xmm1 f0: f3 0f 59 48 f0 mulss -0x10(%rax),%xmm1 f5: f3 0f 58 c1 addss %xmm1,%xmm0 f9: f3 0f 10 49 f4 movss -0xc(%rcx),%xmm1 fe: f3 0f 59 48 f4 mulss -0xc(%rax),%xmm1 103: f3 0f 58 c1 addss %xmm1,%xmm0 107: f3 0f 10 49 f8 movss -0x8(%rcx),%xmm1 10c: f3 0f 59 48 f8 mulss -0x8(%rax),%xmm1 111: f3 0f 58 c1 addss %xmm1,%xmm0 115: f3 0f 10 49 fc movss -0x4(%rcx),%xmm1 11a: f3 0f 59 48 fc mulss -0x4(%rax),%xmm1 11f: 45 39 c8 cmp %r9d,%r8d 122: f3 0f 58 c1 addss %xmm1,%xmm0 126: 0f 85 04 ff ff ff jne 30 12c: 49 63 c0 movslq %r8d,%rax 12f: 48 c1 e0 02 shl $0x2,%rax 133: 48 01 c7 add %rax,%rdi 136: 48 01 c6 add %rax,%rsi 139: 31 c0 xor %eax,%eax 13b: 0f 1f 44 00 00 nopl 0x0(%rax,%rax,1) 140: f3 0f 10 0c 87 movss (%rdi,%rax,4),%xmm1 145: f3 0f 59 0c 86 mulss (%rsi,%rax,4),%xmm1 14a: 48 ff c0 inc %rax 14d: 41 8d 0c 00 lea (%r8,%rax,1),%ecx 151: 39 ca cmp %ecx,%edx 153: f3 0f 58 c1 addss %xmm1,%xmm0 157: 7f e7 jg 140
The main differences here are that it unrolls the loop 16x here. It only uses the 2-operand instructions - it uses fewer registers. It has also transformed the array indexing into pre-increment pointer arithmetic (in batches).
Well this definitely isn't a RISC cpu as that scheduling looks pants as everything keeps writing to the same registers. But x86 being so dominant has allowed a lot of money to be spent optimising the chip to run shitty code faster to make up for the compiler.
Benchmarks
Here are some timing results. All values are in ms for equivalent of 1 loop (or seconds for 1000 loops).
what time
gcc -O0 4.86
-O2 1.44
-O3 1.44
java 1.60
time java 1.7
The last is using the 'time' command on the whole java loop. i.e. this includes the jvm startup, profiling, and compilation. This isn't too shabby.
Either way these times are pretty good vs effort - maybe one or the other is more tuned to the cpu I have vs intel stuff but it's really neither here nor there.
Unrolled loop
Actually what prompted the idea for this article was some results I had from unrolling loops 4x in Java. I subsequently found that unrolling 2x did just as good a job in this case so i'll do that here just for simplicity. The assembly is almost identical anyway as it just gets unrolled an additional 2x rather than 4x by the compiler.
public float dot(float[] a, float[] b, int len) {
float v0 = 0, v1=0;
int i = 0;
for (int e = len & ~1;i<e;i+=2) {
v0 += a[i] * b[i];
v1 += a[i+1] * b[i+1];
}
for (;i<len;i++)
v0 += a[i] * b[i];
return v0+v1;
}
Final pass
And here's just the inner loop of the final pass:
.1: vmovss 0x10(%rcx,%r8,4),%xmm0
vmulss 0x10(%rdx,%r8,4),%xmm0,%xmm1
vaddss %xmm3,%xmm1,%xmm0
movslq %r8d,%r11
vmovss 0x2c(%rcx,%r11,4),%xmm2
vmulss 0x2c(%rdx,%r11,4),%xmm2,%xmm9
vmovss 0x24(%rcx,%r11,4),%xmm1
vmulss 0x24(%rdx,%r11,4),%xmm1,%xmm8
vmovss 0x1c(%rcx,%r11,4),%xmm2
vmulss 0x1c(%rdx,%r11,4),%xmm2,%xmm1
vmovss 0x18(%rcx,%r11,4),%xmm3
vmulss 0x18(%rdx,%r11,4),%xmm3,%xmm2
vmovss 0x14(%rcx,%r11,4),%xmm4
vmulss 0x14(%rdx,%r11,4),%xmm4,%xmm3
vmovss 0x20(%rcx,%r11,4),%xmm5
vmulss 0x20(%rdx,%r11,4),%xmm5,%xmm4
vmovss 0x28(%rcx,%r11,4),%xmm6
vmulss 0x28(%rdx,%r11,4),%xmm6,%xmm5
vaddss %xmm3,%xmm0,%xmm3
vaddss %xmm2,%xmm3,%xmm0
vaddss %xmm1,%xmm0,%xmm1
vaddss %xmm1,%xmm4,%xmm0
vaddss %xmm8,%xmm0,%xmm1
vaddss %xmm1,%xmm5,%xmm0
vaddss %xmm0,%xmm9,%xmm3
add $0x8,%r8d
cmp %r10d,%r8d
jl .1
So now it's unrolled the loop an addition 4x times so that it looks the same at first glance. But now the moves have been spread across many registers rather than mostly going through xmm1. It runs quite a bit faster.
This is getting too long so i wont include it but the same simple modification applied to the C version also makes a difference - quite a big one. The generated code is almost identical apart from every second xmm0 being replaced with xmm1 - i.e. interleaved as written.
Benchmarks
And here's some benchmarks of this 'version'.
what time
gcc -O0 2.76
-O2 0.833
-O3 0.735
java 1.00
time java 1.2
Conclusions
Well hotspot is pretty good, but could be a little bit better. And it seems mostly just to fall down on some seemingly simple areas like instruction scheduling (simple compared to the rest of the work it's done).
Although I don't have enough knowledge of the architecture here to state that the original scheduling isn't very optimal the benchmark results probably speak loud enough in that absence. It is clearly not optimal as the same machine code which interleaves the output register runs 2x faster in the C case. I don't really feel like translating this to assembly so i can see if some simple re-arrangement would make a difference.
But what is odd that neither compiler is doing this on it's own, one could argue (quite convincingly) that due to floating point peculiarities (addition is only weakly associative) both loops are not actually calculating the same result. In the case of hotspot however this argument is weak because the optimised version is already spreading the addition accross multiple registers.
Lambdas & de-optimisation
This is getting long and the next part could probably go into another article but i've spent enough of my weekend on this so i'll get it out of the way now with a quick summary.
For simplcity I created the following simple 3-parameter map/reduce operation.
public interface FloatTrinaryFunction {
public float applyAsFloat(float a, float b, float c);
}
public float reduce(float[] a, float[] b, int len, FloatTrinaryFunction func) {
float v = 0;
for (int i=0;i<len;i++)
v = func.applyAsFloat(v, a[i], b[i]);
return v;
}
And invoke it thus:
reduce(a, b, a.length, (float v, float x, float y)->v + x*y);
Opt and de-opt
In short, if you use up to two lambdas it results in equivalent code to the direct dot product equation - nice. But once you go to three or more it de-optimises the loop and reverts to a function call. It also spends more time in the compiler.
The following is what the deoptimised loop looks like:
.1: mov (%rsp),%rdx
mov %rdx,(%rsp)
cmp %r10d,%ebp
jae .exception0
mov 0x8(%rsp),%r10
vmovss 0x10(%rdx,%rbp,4),%xmm1
cmp %r10d,%ebp
jae .exception1
mov 0x8(%rsp),%r10
vmovss 0x10(%r10,%rbp,4),%xmm2
mov 0x18(%rsp),%rsi
xchg %ax,%ax
mov $0xffffffffffffffff,%rax
callq applyAsFloat
inc %ebp
cmp 0x10(%rsp),%ebp
jl .1
So it retains the array bounds checks inside the loop (bummer) and invokes the interface as a function call (expected), but it removes any profiling instrumentation that was present in the first pass (expected also) and generates the smallest code.
This hits around the 4.5ms mark.
Conclusions 2
It's important to note that this is just a run-time decision made by the current version of hotspot - this could be changed or could be tweaked in the future. And as I showed in some previous posts it can be worked-around even with the current hotspot using some bytecode foo.
Given the prevalence of lambdas in java8 i suspect it is something that will gain some tuning attention in future revisions. It's not something one would change lightly so it will probably be based on profiling data and usage.
