July 15, 2014
checking assumptions
Very often in computer code integers are divided by powers of two, such as 2, 4, 8, 16, 32, 64, and so on). These divisions are much faster than dividing by other numbers (since computers represent the underlying number in binary). In C/C++, there are two ways this type of division is typically expressed: normal division (x/256), or a shift (x<<8). These two methods produce the same results for non-negative values, and depending on the meaning of the code in question, (x/256) is often more readable, and thus I use it regularly.
If x is signed and is negative, division rounds towards 0, whereas the shift rounds towards negative infinity, but in situations where rounding of negative values is not important, I had generally assumed that modern compilers would generate similarly efficient code (reducing x/256 into a single x86 sar instruction).
It turns out, testing with a two modern compilers (and one slightly out of date compiler), this is not the case.
Here is the C code:
void b(int r);
void f(int v)
{
int i;
for (i=0;i<v/256;i++) b(v > 0 ? v/65536 : 0);
}
void f2(int v)
{
int i;
for (i=0;i<(v>>8);i++) b(v > 0 ? v >> 16 : 0);
}
Ideally, a compiler should generate identical code for each of these functions. In the case of the loop counter, if v is less than 0, how it is rounded makes no difference. In the case of the parameter to b(), the code v >> 16 is only evaluated if v is known to be above 0.
Let's look at the output of some compilers (removing decoration and unrelated code). I've marked some code as bold to signify instructions that could be eliminated (with slight changes to the surrounding instructions):
- Apple LLVM version 5.1 (clang-503.0.40) (based on LLVM 3.4svn)
Xcode 5.1.1 on OSX 10.9.4
Target: x86_64-apple-darwin13.3.0
Command line flags: -O2 -fomit-frame-pointer
f(): # using divides
cmpl $256, %edi
jl LBB0_3 # if v is less than 256, skip loop
# v is known to be 256 or greater.
movl %edi, %ebx
sarl $31, %ebx # ebx=0xffffffff if negative, 0 if non-negative
movl %ebx, %r14d
shrl $24, %r14d # r14d=0xff if negative, 0 if non-negative
addl %edi, %r14d # r14d = (v+255) if v negative, v if v non-negative
sarl $8, %r14d # r14d = v/256
shrl $16, %ebx # this will make ebx 65535 if v negative, 0 if v non-negative
addl %edi, %ebx # ebx = (v+65535) if v negative, v if v non-negative
sarl $16, %ebx # ebx = v/65536
# interestingly, the optimizer used its knowledge of v being greater than 0 to remove the ternary conditional expression completely.
xorl %ebp, %ebp
LBB0_2:
movl %ebx, %edi
callq _b
incl %ebp
cmpl %r14d, %ebp
jl LBB0_2
LBB0_3:
f2(): # using shifts
movl %edi, %ebp
sarl $8, %ebp # ebp = v>>8
testl %ebp, %ebp
jle LBB1_3 # if less than or equal to 0, skip
movl %edi, %eax
sarl $16, %eax # eax = v>>16
xorl %ebx, %ebx
testl %edi, %edi
cmovgl %eax, %ebx # if v is greater than 0, set ebx to eax
# the optimizer could also have removed the xorl/testl/cmovgl sequence as well
LBB1_2:
movl %ebx, %edi
callq _b
decl %ebp
jne LBB1_2
LBB1_3:
In the first function (division), the LLVM optimizer appears to have removed the ternary expression (checking to see if v was greater than 0), likely because it knew that if the loop was running, v was greater than 0. Unfortunately, it didn't apply this knowledge to the integer divisions of v, which would have allowed it to not generate (substantial) rounding code.
In the second function (shifts), LLVM wasn't required to generate rounding code (as C's >> maps to x86 sar directly), but it also didn't use the knowledge that v would be greater than 0.
- Microsoft (R) C/C++ Optimizing Compiler Version 18.00.30501 for x64
Visual Studio Express 2013 for Windows Desktop on Windows 7
Command line flags: /O2 (/Os produced different results, but nothing related to rounding)
f(): # using divides
mov eax, ecx
mov ebx, ecx
cdq # set edx to 0xffffffff if v negative, 0 otherwise
movzx edx, dl # set edx to 0xff if v negative, 0 otherwise
add eax, edx # eax = v+255 if v negative, v otherwise
sar eax, 8 # eax = v/256
test eax, eax
jle SHORT $LN1@f # skip loop if v/256 is less than or equal to 0
mov QWORD PTR [rsp+48], rdi
mov edi, eax # edi is loop counter
$LL3@f:
test ebx, ebx
jle SHORT $LN6@f # if v is less than or equal to 0, jump to set eax to 0
mov eax, ebx
cdq # set edx to 0xffffffff if v negative, 0 otherwise
movzx edx, dx # set edx to 0xffff if v negative, 0 otherwise
add eax, edx # eax = v+65535 if v negative, v otherwise
sar eax, 16 # eax = v/65536
jmp SHORT $LN7@f
$LN6@f:
xor eax, eax
$LN7@f:
mov ecx, eax
call b
dec rdi
jne SHORT $LL3@f
mov rdi, QWORD PTR [rsp+48]
$LN1@f:
f2(): # using shifts
mov eax, ecx
mov ebx, ecx
sar eax, 8 # eax = v>>8
test eax, eax
jle SHORT $LN1@f2 # skip loop if v>>8 is less than or equal to 0
mov QWORD PTR [rsp+48], rdi
mov edi, eax
$LL3@f2:
test ebx, ebx
jle SHORT $LN6@f2 # if v is less than or equal to 0, jump to set ecx to 0
mov ecx, ebx
sar ecx, 16 # ecx = v>>16
jmp SHORT $LN7@f2
$LN6@f2:
xor ecx, ecx
$LN7@f2:
call b
dec rdi
jne SHORT $LL3@f2
mov rdi, QWORD PTR [rsp+48]
$LN1@f2:
VS 2013 generates different rounding code for the division, using cdq/movzx (or cdq/and if shifting by something other than 8 or 16 bits).
Also worth noting is that VS 2013 doesn't even bother moving the invariant ternary operator and (v/65536) or (v>>16) out of the loop. Ideally, it could move that calculation out of the loop, or remove the ternary operator completely. Ouch. I have to say, VS 2013 does seem to produce pretty good code overall, but I guess most of ours is heavily in floating point these days.
- gcc 4.4.5
Linux x86_64
Command line flags: -O2 -fomit-frame-pointer
f(): # using divides
testl %edi, %edi
movl %edi, %ebp # ebp = edi = v
leal 255(%rbp), %r12d # r12d = v+255
cmovns %edi, %r12d # set r12d to v, if v is non-negative (otherwise r12d was v+255)
sarl $8, %r12d # r12d = v/256
testl %r12d, %r12d
jle .L14 # if r12d is less than or equal to 0, skip
movl %edi, %r14d
xorl %ebx, %ebx # ebx is loop counter
xorl %r13d, %r13d
sarl $16, %r14d # r14d = v>>16
.L13:
testl %ebp, %ebp
movl %r13d, %edi
cmovg %r14d, %edi # if v is greater than 0, use v>>16 instead of 0
addl $1, %ebx
call b
cmpl %r12d, %ebx
jl .L13
.L14:
f2(): # using shifts
movl %edi, %r12d
sarl $8, %r12d
testl %r12d, %r12d
movl %edi, %ebp
jle .L6 # skip loop if (v>>8) is less than or equal to 0
movl %edi, %r14d
xorl %ebx, %ebx # ebx is loop counter
xorl %r13d, %r13d
sarl $16, %r14d # r14d = (v>>16)
.L5:
testl %ebp, %ebp
movl %r13d, %edi
cmovg %r14d, %edi # if v is greater than 0, use v>>16 instead of 0
addl $1, %ebx
call b
cmpl %r12d, %ebx
jl .L5
.L6:
gcc 4.4 does an interesting job, using lea to generate v+255, and then cmovns to replace it with v if v is non-negative. It doesn't bother generating rounding code for v/65536, but it does still generate rounding code for v/256, even though any non-positive result for v/256 is treated the same way throughout. Also, gcc doesn't eliminate the non-varying ternary expression, nor put the constant v/65536 or v>>16 outside of the loop.
Conclusions?
I'm not sure what to say here -- modern compilers can generate a lot of really good code, especially looking at floating point and SSE, but this makes me feel as though some of the basics have been neglected. If I were a better programmer I'd go dig into LLVM and GCC and submit patches.
I should have also tested ICC, but I've spent enough time on this, and the only ICC version we use is old enough that I would just regret not using the latest.
For comparison, here is what I would like to see LLVM generate for f():
f(): # using divides
cmpl $256, %edi
jl LBB0_3 # if v is less than 256, skip loop
movl %edi, %ebx
movl %edi, %ebp
shrl $8, %ebx # ebx = v/256, since v is non-negative
shrl $16, %ebp # ebp = v/65536, since v is non-negative
LBB0_2:
movl %ebp, %edi
callq _b
decl %ebx
jnz LBB0_2
LBB0_3:
Performance-wise, I'm sure they wouldn't differ in any meaningful way, but the decrease in size would be nice.
Finally: write for the compiler you have, not the compiler you wish you had. When performance is important, use shifts instead of divides, or use unsigned types (which really should generate the same code for (x/256) vs (x>>8)). Move as much logic out of the loop as you can -- yes, the compiler might be able to do it for you, but why depend on that? But most important of all: test your assumptions.
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