I am writing an embedded C code.
Which if condition would be faster/optimized:
if (a == false)
{
Some code
}
OR
if (a != true)
{
Some code
}
If a is of type bool, you won't be able to spot a difference — probably even if you look at the assembly language code. Certainly, it is unlikely to be a measurable difference, especially if Some code is more than a single instruction (or thereabouts). But only measurement or scrutiny of the assembly language can show you the difference.
If a is of type int (or any other non-bool type), the conditions have different meanings and at most one of them is correct. The first is equivalent to a == 0; the second is equivalent to a != 1. Unless a is restricted to the range 0 and 1, the results are different when a is 2, for example.
The idiomatic test would be if (!a) and that works the same for bool and non-bool types. You probably won't be able to spot any difference here, either.
Reading this question, the first thing that came to my mind is "That's ridiculous, the compiler knows better and will optimize it anyway, right?"
Well, turns out I was wrong, here is how MSVC /O2 compiles it:
With if (a == false):
84 C9 | test cl, cl
With if (a != true):
80 F9 01 | cmp cl, 1
Well, that's weird. Mike Nakis explained the difference between cmp and test in this answer. And Peter Cordes commented below:
There can be a perf difference on Intel Core2 or Nehalem, where TEST can macro-fuse with more flavours of JCC than CMP. e.g. Core2 and Nehalem can macro-fuse test eax,eax / js, but not cmp eax,0 / js. Nehalem can macro-fuse cmp eax,0 / jl, though. (Core2 can't, but Core2 can only macro-fuse at all in 32-bit mode).
I believe this is true, test can be faster on some CPUs, but I don't believe its effect is measurable in practical scenarios.
Weirdly enough, for GCC, both -O2 and -O3 prefer cmp over test and will produce the same output for both cases.
Related: Test whether a register is zero with CMP reg, 0 vs OR reg, reg
Same thing. Or just do if (!a) { /* code */ }
When computing fibonacci numbers, a common method is mapping the pair of numbers (a, b) to (b, a + b) multiple times. This can usually be done by defining a third variable c and doing a swap. However, I realised you could do the following, avoiding the use of a third integer variable:
b = a + b; // b2 = a1 + b1
a = b - a; // a2 = b2 - a1 = b1, Ta-da!
I expected this to be faster than using a third variable, since in my mind this new method should only have to consider two memory locations.
So I wrote the following C programs comparing the processes. These mimic the calculation of fibonacci numbers, but rest assured I am aware that they will not calculate the correct values due to size limitations.
(Note: I realise now that it was unnecessary to make n a long int, but I will keep it as it is because that is how I first compiled it)
File: PlusMinus.c
// Using the 'b=a+b;a=b-a;' method.
#include <stdio.h>
int main() {
long int n = 1000000; // Number of iterations.
long int a,b;
a = 0; b = 1;
while (n--) {
b = a + b;
a = b - a;
}
printf("%lu\n", a);
}
File: ThirdVar.c
// Using the third-variable method.
#include <stdio.h>
int main() {
long int n = 1000000; // Number of iterations.
long int a,b,c;
a = 0; b = 1;
while (n--) {
c = a;
a = b;
b = b + c;
}
printf("%lu\n", a);
}
When I run the two with GCC (no optimisations enabled) I notice a consistent difference in speed:
$ time ./PlusMinus
14197223477820724411
real 0m0.014s
user 0m0.009s
sys 0m0.002s
$ time ./ThirdVar
14197223477820724411
real 0m0.012s
user 0m0.008s
sys 0m0.002s
When I run the two with GCC with -O3, the assembly outputs are equal. (I suspect I had confirmation bias when stating that one just outperformed the other in previous edits.)
Inspecting the assembly for each, I see that PlusMinus.s actually has one less instruction than ThirdVar.s, but runs consistently slower.
Question
Why does this time difference occur? Not only at all, but also why is my addition/subtraction method slower contrary to my expectations?
Why does this time difference occur?
There is no time difference when compiled with optimizations (under recent versions of gcc and clang). For instance, gcc 8.1 for x86_64 compiles both to:
Live at Godbolt
.LC0:
.string "%lu\n"
main:
sub rsp, 8
mov eax, 1000000
mov esi, 1
mov edx, 0
jmp .L2
.L3:
mov rsi, rcx
.L2:
lea rcx, [rdx+rsi]
mov rdx, rsi
sub rax, 1
jne .L3
mov edi, OFFSET FLAT:.LC0
mov eax, 0
call printf
mov eax, 0
add rsp, 8
ret
Not only at all, but also why is my addition/subtraction method slower contrary to my expectations?
Adding and subtracting could be slower than just moving. However, in most architectures (e.g. a x86 CPU), it is basically the same (1 cycle plus the memory latency); so this does not explain it.
The real problem is, most likely, the dependencies between the data. See:
b = a + b;
a = b - a;
To compute the second line, you have to have finished computing the value of the first. If the compiler uses the expressions as they are (which is the case under -O0), that is what the CPU will see.
In your second example, however:
c = a;
a = b;
b = b + c;
You can compute both the new a and b at the same time, since they do not depend on each other. And, in a modern processor, those operations can actually be computed in parallel. Or, putting it another way, you are not "stopping" the processor by making it wait on a previous result. This is called Instruction-level parallelism.
This is for C, if the language matters. If it goes down to assembly language, it sets things to negative using two's complements. And with the variable, you're storing the value "0" inside the variable int. Which I'm not entirely sure what happens.
I got: 1.90s user 0.01s system 99% cpu 1.928 total for the beneath code and I'm guessing most of the runtime was in adding up the counter variables.
int i;
int n;
i = 0;
while (i < 999999999)
{
n = 0;
i++;
n++;
}
I got: 4.56s user 0.02s system 99% cpu 4.613 total for the beneath code.
int i;
int n;
i = 0;
n = 5;
while (i < 999999999)
{
n *= -1;
i++;
n++;
}
return (0);
I don't particularly understand much about assembly, but it doesn't seem intuitive that using the two's complement operation takes more time than setting one thing to another. What's the underlying implementation that makes one faster than the other, and what's happening beneath the surface? Or is my test simply a bad one that doesn't accurately portray how quick it'll actually be in practice.
If it seems pointless, the reason for it is because I can easily implement a "checklist" by simply multiplying an integer on a map by -1, meaning it's already been checked(But I need to keep the value, so when I do the check, I can just -1 whatever I'm comparing it to). But I was wondering if that's too slow, I could make a separate boolean 2D array to check if the value was checked or not, or change my data structure into an array of structures so it could hold an int 1/0. I'm wondering what the best implementation will be-- doing the -1 operation itself a billion times will already total up to around 5 seconds not counting the rest of my program. But making a separate 1 billion square int array or creating a billion square struct doesn't seem to be the best way either.
Assigning zero is very cheap.
But your microbenchmark tells you very little about what you should do for your large array. Memory bandwidth / cache-miss / cache footprint considerations will dominate there, and your microbench doesn't test that at all.
Using one bit of your integer values to represent checked / not-checked seems reasonable compared to having a separate bitmap. (Having a separate array of 0/1 32-bit integers would be totally silly, but a bitmap is worth considering, especially if you want to search quickly for the next unchecked or the next checked entry. It's not clear what you're doing with this, so I'll mostly just stick to explaining the observed performance in your microbenchmark.)
And BTW, questions like this are a perfect example of why SO comments like "why don't you benchmark it yourself" are misguided: because you have to understand what you're testing in quite a lot of detail to write a useful microbenchmark.
You obviously compiled this in debug mode, e.g. gcc with the default -O0, which spills everything to memory after every C statement (so your program still works even if you modify variables with a debugger). Otherwise the loops would optimize away, because you didn't use volatile or an asm statement to limit optimization, and your loops are trivial to optimize.
Benchmarking with -O0 does not reflect reality (of compiling normally), and is a total waste of time (unless you're actually worried about the performance of debug builds of something like a game).
That said, your results are easy to explain: Since -O0 compiles each C statement separately and predictably.
n = 0; is write-only, and breaks the dependency on the old value.
n *= -1; compiles the same as n = -n; with gcc (even with -O0). It has to read the old value from memory before writing the new value.
The store/reload between a write and a read of a C variable across statements costs about 5 cycles of store-forwarding latency on Intel Haswell for example (see http://agner.org/optimize and other links on the x86 tag wiki). (You didn't say what CPU microarchitecture you tested on, but I'm assuming some kind of x86 because that's usually "the default"). But dependency analysis still works the same way in this case.
So the n*=-1 version has a loop-carried dependency chain involving n, with an n++ and a negate.
The n=0 version breaks that dependency every iteration by doing a store without reading the old value. The loop only bottlenecks on the 6-cycle loop-carried dependency of the i++ loop counter. The latency of the n=0; n++ chain doesn't matter, because each loop iteration starts a fresh chain, so multiple can be in flight at once. (Store forwarding provides a sort of memory renaming, like register renaming but for a memory location).
This is all unrealistic nonsense: With optimization enabled, the cost of a unary - totally depends on the surrounding code. You can't just add up the costs of separate operations to get a total, that's not how pipelined out-of-order CPUs work, and compiler optimization itself also makes that model bogus.
About the code itself
I compiled your pieces of code into x86_64 assembly outputs using GCC 7.2 without any optimization. I also shortened each piece of code without changing the assembly output. Here are the results.
Code 1:
// C
int main() {
int n;
for (int i = 0; i < 999999999; i++) {
n = 0;
n++;
}
}
// assembly
main:
push rbp
mov rbp, rsp
mov DWORD PTR [rbp-4], 0
jmp .L2
.L3:
mov DWORD PTR [rbp-8], 0
add DWORD PTR [rbp-8], 1
add DWORD PTR [rbp-4], 1
.L2:
cmp DWORD PTR [rbp-4], 999999998
jle .L3
mov eax, 0
pop rbp
ret
Code 2:
// C
int main() {
int n = 5;
for (int i = 0; i < 999999999; i++) {
n *= -1;
n++;
}
}
// assembly
main:
push rbp
mov rbp, rsp
mov DWORD PTR [rbp-4], 5
mov DWORD PTR [rbp-8], 0
jmp .L2
.L3:
neg DWORD PTR [rbp-4]
add DWORD PTR [rbp-4], 1
add DWORD PTR [rbp-8], 1
.L2:
cmp DWORD PTR [rbp-8], 999999998
jle .L3
mov eax, 0
pop rbp
ret
The C instructions inside the loop are, in the assembly, located between the two labels (.L3: and .L2:). In both cases, that's three instructions, among which only the first one is different. In the first code, it is a mov, corresponding to n = 0;. In the second code however, it is a neg, corresponding to n *= -1;.
According to this manual, these two instructions have different execution speed depending on the CPU. One can be faster than the other on one chip while being slower on another.
Thanks to aschepler in the comments for the input.
This means, all the other instructions being identical, that you cannot tell which code will be faster in general. Therefore, trying to compare their performance is pointless.
About your intent
Your reason for asking about the performance of these short pieces of code is faulty. What you want is to implement a checklist structure, and you have two conflicting ideas on how to build it. One uses a special value, -1, to add special meaning onto variables in a map. The other uses additional data, either an external boolean array or a boolean for each variable, to add the same meaning without changing the purpose of the existing variables.
The choice you have to make should be a design decision rather than be motivated by unclear performance issues. Personally, whenever I am facing this kind of choice between a special value or additional data with precise meaning, I tend to prefer the latter option. That's mainly because I don't like dealing with special values, but it's only my opinion.
My advice would be to go for the solution you can maintain better, namely the one you are most comfortable with and won't harm future code, and ask about performance when it matters, or rather if it even matters.
I'm trying to compute the bit parity of a large number of uint64's. By bit parity I mean a function that accepts a uint64 and outputs 0 if the number of set bits is even, and 1 otherwise.
Currently I'm using the following function (by #Troyseph, found here):
uint parity64(uint64 n){
n ^= n >> 1;
n ^= n >> 2;
n = (n & 0x1111111111111111) * 0x1111111111111111;
return (n >> 60) & 1;
}
The same SO page has the following assembly routine (by #papadp):
.code
; bool CheckParity(size_t Result)
CheckParity PROC
mov rax, 0
add rcx, 0
jnp jmp_over
mov rax, 1
jmp_over:
ret
CheckParity ENDP
END
which takes advantage of the machine's parity flag. But I cannot get it to work with my C program (I know next to no assembly).
Question. How can I include the above (or similar) code as inline assembly in my C source file, so that the parity64() function runs that instead?
(I'm using GCC with 64-bit Ubuntu 14 on an Intel Xeon Haswell)
In case it's of any help, the parity64() function is called inside the following routine:
uint bindot(uint64* a, uint64* b, uint64 entries){
uint parity = 0;
for(uint i=0; i<entries; ++i)
parity ^= parity64(a[i] & b[i]); // Running sum!
return parity;
}
(This is supposed to be the "dot product" of two vectors over the field Z/2Z, aka. GF(2).)
This may sound a bit harsh, but I believe it needs to be said. Please don't take it personally; I don't mean it as an insult, especially since you already admitted that you "know next to no assembly." But if you think code like this:
CheckParity PROC
mov rax, 0
add rcx, 0
jnp jmp_over
mov rax, 1
jmp_over:
ret
CheckParity ENDP
will beat what a C compiler generates, then you really have no business using inline assembly. In just those 5 lines of code, I see 2 instructions that are glaringly sub-optimal. It could be optimized by just rewriting it slightly:
xor eax, eax
test ecx, ecx ; logically, should use RCX, but see below for behavior of PF
jnp jmp_over
mov eax, 1 ; or possibly even "inc eax"; would need to verify
jmp_over:
ret
Or, if you have random input values that are likely to foil the branch predictor (i.e., there is no predictable pattern to the parity of the input values), then it would be faster yet to remove the branch, writing it as:
xor eax, eax
test ecx, ecx
setp al
ret
Or perhaps the equivalent (which will be faster on certain processors, but not necessarily all):
xor eax, eax
test ecx, ecx
mov ecx, 1
cmovp eax, ecx
ret
And these are just the improvements I could see off the top of my head, given my existing knowledge of the x86 ISA and previous benchmarks that I have conducted. But lest anyone be fooled, this is undoubtedly not the fastest code, because (borrowing from Michael Abrash), "there ain't no such thing as the fastest code"—someone can virtually always make it faster yet.
There are enough problems with using inline assembly when you're an expert assembly-language programmer and a wizard when it comes to the intricacies of the x86 ISA. Optimizers are pretty darn good nowadays, which means it's hard enough for a true guru to produce better code (though certainly not impossible). It also takes trustworthy benchmarks that will verify your assumptions and confirm that your optimized inline assembly is actually faster. Never commit yourself to using inline assembly to outsmart the compiler's optimizer without running a good benchmark. I see no evidence in your question that you've done anything like this. I'm speculating here, but it looks like you saw that the code was written in assembly and assumed that meant it would be faster. That is rarely the case. C compilers ultimately emit assembly language code, too, and it is often more optimal than what us humans are capable of producing, given a finite amount of time and resources, much less limited expertise.
In this particular case, there is a notion that inline assembly will be faster than the C compiler's output, since the C compiler won't be able to intelligently use the x86 architecture's built-in parity flag (PF) to its benefit. And you might be right, but it's a pretty shaky assumption, far from universalizable. As I've said, optimizing compilers are pretty smart nowadays, and they do optimize to a particular architecture (assuming you specify the right options), so it would not at all surprise me that an optimizer would emit code that used PF. You'd have to look at the disassembly to see for sure.
As an example of what I mean, consider the highly specialized BSWAP instruction that x86 provides. You might naïvely think that inline assembly would be required to take advantage of it, but it isn't. The following C code compiles to a BSWAP instruction on almost all major compilers:
uint32 SwapBytes(uint32 x)
{
return ((x << 24) & 0xff000000 ) |
((x << 8) & 0x00ff0000 ) |
((x >> 8) & 0x0000ff00 ) |
((x >> 24) & 0x000000ff );
}
The performance will be equivalent, if not better, because the optimizer has more knowledge about what the code does. In fact, a major benefit this form has over inline assembly is that the compiler can perform constant folding with this code (i.e., when called with a compile-time constant). Plus, the code is more readable (at least, to a C programmer), much less error-prone, and considerably easier to maintain than if you'd used inline assembly. Oh, and did I mention it's reasonably portable if you ever wanted to target an architecture other than x86?
I know I'm making a big deal of this, and I want you to understand that I say this as someone who enjoys the challenge of writing highly-tuned assembly code that beats the compiler's optimizer in performance. But every time I do it, it's just that: a challenge, which comes with sacrifices. It isn't a panacea, and you need to remember to check your assumptions, including:
Is this code actually a bottleneck in my application, such that optimizing it would even make any perceptible difference?
Is the optimizer actually emitting sub-optimal machine language instructions for the code that I have written?
Am I wrong in what I naïvely think is sub-optimal? Maybe the optimizer knows more than I do about the target architecture, and what looks like slow or sub-optimal code is actually faster. (Remember that less code is not necessarily faster.)
Have I tested it in a meaningful, real-world benchmark, and proven that the compiler-generated code is slow and that my inline assembly is actually faster?
Is there absolutely no way that I can tweak the C code to persuade the optimizer to emit better machine code that is close, equal to, or even superior to the performance of my inline assembly?
In an attempt to answer some of these questions, I set up a little benchmark. (Using MSVC, because that's what I have handy; if you're targeting GCC, it's best to use that compiler, but we can still get a general idea. I use and recommend Google's benchmarking library.) And I immediately ran into problems. See, I first run my benchmarks in "debugging" mode, with assertions compiled in that verify that my "tweaked"/"optimized" code is actually producing the same results for all test cases as the original code (that is presumably known to be working/correct). In this case, an assertion immediately fired. It turns out that the CheckParity routine written in assembly language does not return identical results to the parity64 routine written in C! Uh-oh. Well, that's another bullet we need to add to the above list:
Have I ensured that my "optimized" code is returning the correct results?
This one is especially critical, because it's easy to make something faster if you also make it wrong. :-) I jest, but not entirely, because I've done this many times in the pursuit of faster code.
I believe Michael Petch has already pointed out the reason for the discrepancy: in the x86 implementation, the parity flag (PF) only concerns itself with the bits in the low byte, not the entire value. If that's all you need, then great. But even then, we can go back to the C code and further optimize it to do less work, which will make it faster—perhaps faster than the assembly code, eliminating the one advantage that inline assembly ever had.
For now, let's assume that you need the parity of the full value, since that's the original implementation you had that was working, and you're just trying to make it faster without changing its behavior. Thus, we need to fix the assembly code's logic before we can even proceed with meaningfully benchmarking it. Fortunately, since I am writing this answer late, Ajay Brahmakshatriya (with collaboration from others) has already done that work, saving me the extra effort.
…except, not quite. When I first drafted this answer, my benchmark revealed that draft 9 of his "tweaked" code still did not produce the same result as the original C function, so it's unsuitable according to our test cases. You say in a comment that his code "works" for you, which means either (A) the original C code was doing extra work, making it needlessly slow, meaning that you can probably tweak it to beat the inline assembly at its own game, or worse, (B) you have insufficient test cases and the new "optimized" code is actually a bug lying in wait. Since that time, Ped7g suggested a couple of fixes, which both fixed the bug causing the incorrect result to be returned, and further improved the code. The amount of input required here, and the number of drafts that he has gone through, should serve as testament to the difficulty of writing correct inline assembly to beat the compiler. But we're not even done yet! His inline assembly remains incorrectly written. SETcc instructions require an 8-bit register as their operand, but his code doesn't use a register specifier to request that, meaning that the code either won't compile (because Clang is smart enough to detect this error) or will compile on GCC but won't execute properly because that instruction has an invalid operand.
Have I convinced you about the importance of testing yet? I'll take it on faith, and move on to the benchmarking part. The benchmark results use the final draft of Ajay's code, with Ped7g's improvements, and my additional tweaks. I also compare some of the other solutions from that question you linked, modified for 64-bit integers, plus a couple of my own invention. Here are my benchmark results (mobile Haswell i7-4850HQ):
Benchmark Time CPU Iterations
-------------------------------------------------------------------
Naive 36 ns 36 ns 19478261
OriginalCCode 4 ns 4 ns 194782609
Ajay_Brahmakshatriya_Tweaked 4 ns 4 ns 194782609
Shreyas_Shivalkar 37 ns 37 ns 17920000
TypeIA 5 ns 5 ns 154482759
TypeIA_Tweaked 4 ns 4 ns 160000000
has_even_parity 227 ns 229 ns 3200000
has_even_parity_Tweaked 36 ns 36 ns 19478261
GCC_builtin_parityll 4 ns 4 ns 186666667
PopCount 3 ns 3 ns 248888889
PopCount_Downlevel 5 ns 5 ns 100000000
Now, keep in mind that these are for randomly-generated 64-bit input values, which disrupts branch prediction. If your input values are biased in a predictable way, either towards parity or non-parity, then the branch predictor will work for you, rather than against you, and certain approaches may be faster. This underscores the importance of benchmarking against data that simulates real-world use cases. (That said, when I write general library functions, I tend to optimize for random inputs, balancing size and speed.)
Notice how the original C function compares to the others. I'm going to make the claim that optimizing it any further is probably a big fat waste of time. So hopefully you learned something more general from this answer, rather than just scrolled down to copy-paste the code snippets. :-)
The Naive function is a completely unoptimized sanity check to determine the parity, taken from here. I used it to validate even your original C code, and also to provide a baseline for the benchmarks. Since it loops through each bit, one-by-one, it is relatively slow, as expected:
unsigned int Naive(uint64 n)
{
bool parity = false;
while (n)
{
parity = !parity;
n &= (n - 1);
}
return parity;
}
OriginalCCode is exactly what it sounds like—it's the original C code that you had, as shown in the question. Notice how it posts up at exactly the same time as the tweaked/corrected version of Ajay Brahmakshatriya's inline assembly code! Now, since I ran this benchmark in MSVC, which doesn't support inline assembly for 64-bit builds, I had to use an external assembly module containing the function, and call it from there, which introduced some additional overhead. With GCC's inline assembly, the compiler probably would have been able to inline the code, thus eliding a function call. So on GCC, you might see the inline-assembly version be up to a nanosecond faster (or maybe not). Is that worth it? You be the judge. For reference, this is the code I tested for Ajay_Brahmakshatriya_Tweaked:
Ajay_Brahmakshatriya_Tweaked PROC
mov rax, rcx ; Windows 64-bit calling convention passes parameter in ECX (System V uses EDI)
shr rax, 32
xor rcx, rax
mov rax, rcx
shr rax, 16
xor rcx, rax
mov rax, rcx
shr rax, 8
xor eax, ecx ; Ped7g's TEST is redundant; XOR already sets PF
setnp al
movzx eax, al
ret
Ajay_Brahmakshatriya_Tweaked ENDP
The function named Shreyas_Shivalkar is from his answer here, which is just a variation on the loop-through-each-bit theme, and is, in keeping with expectations, slow:
Shreyas_Shivalkar PROC
; unsigned int parity = 0;
; while (x != 0)
; {
; parity ^= x;
; x >>= 1;
; }
; return (parity & 0x1);
xor eax, eax
test rcx, rcx
je SHORT Finished
Process:
xor eax, ecx
shr rcx, 1
jne SHORT Process
Finished:
and eax, 1
ret
Shreyas_Shivalkar ENDP
TypeIA and TypeIA_Tweaked are the code from this answer, modified to support 64-bit values, and my tweaked version. They parallelize the operation, resulting in a significant speed improvement over the loop-through-each-bit strategy. The "tweaked" version is based on an optimization originally suggested by Mathew Hendry to Sean Eron Anderson's Bit Twiddling Hacks, and does net us a tiny speed-up over the original.
unsigned int TypeIA(uint64 n)
{
n ^= n >> 32;
n ^= n >> 16;
n ^= n >> 8;
n ^= n >> 4;
n ^= n >> 2;
n ^= n >> 1;
return !((~n) & 1);
}
unsigned int TypeIA_Tweaked(uint64 n)
{
n ^= n >> 32;
n ^= n >> 16;
n ^= n >> 8;
n ^= n >> 4;
n &= 0xf;
return ((0x6996 >> n) & 1);
}
has_even_parity is based on the accepted answer to that question, modified to support 64-bit values. I knew this would be slow, since it's yet another loop-through-each-bit strategy, but obviously someone thought it was a good approach. It's interesting to see just how slow it actually is, even compared to what I termed the "naïve" approach, which does essentially the same thing, but faster, with less-complicated code.
unsigned int has_even_parity(uint64 n)
{
uint64 count = 0;
uint64 b = 1;
for (uint64 i = 0; i < 64; ++i)
{
if (n & (b << i)) { ++count; }
}
return (count % 2);
}
has_even_parity_Tweaked is an alternate version of the above that saves a branch by taking advantage of the fact that Boolean values are implicitly convertible into 0 and 1. It is substantially faster than the original, clocking in at a time comparable to the "naïve" approach:
unsigned int has_even_parity_Tweaked(uint64 n)
{
uint64 count = 0;
uint64 b = 1;
for (uint64 i = 0; i < 64; ++i)
{
count += static_cast<int>(static_cast<bool>(n & (b << i)));
}
return (count % 2);
}
Now we get into the good stuff. The function GCC_builtin_parityll consists of the assembly code that GCC would emit if you used its __builtin_parityll intrinsic. Several others have suggested that you use this intrinsic, and I must echo their endorsement. Its performance is on par with the best we've seen so far, and it has a couple of additional advantages: (1) it keeps the code simple and readable (simpler than the C version); (2) it is portable to different architectures, and can be expected to remain fast there, too; (3) as GCC improves its implementation, your code may get faster with a simple recompile. You get all the benefits of inline assembly, without any of the drawbacks.
GCC_builtin_parityll PROC ; GCC's __builtin_parityll
mov edx, ecx
shr rcx, 32
xor edx, ecx
mov eax, edx
shr edx, 16
xor eax, edx
xor al, ah
setnp al
movzx eax, al
ret
GCC_builtin_parityll ENDP
PopCount is an optimized implementation of my own invention. To come up with this, I went back and considered what we were actually trying to do. The definition of "parity" is an even number of set bits. Therefore, it can be calculated simply by counting the number of set bits and testing to see if that count is even or odd. That's two logical operations. As luck would have it, on recent generations of x86 processors (Intel Nehalem or AMD Barcelona, and newer), there is an instruction that counts the number of set bits—POPCNT (population count, or Hamming weight)—which allows us to write assembly code that does this in two operations.
(Okay, actually three instructions, because there is a bug in the implementation of POPCNT on certain microarchitectures that creates a false dependency on its destination register, and to ensure we get maximum throughput from the code, we need to break this dependency by pre-clearing the destination register. Fortunately, this a very cheap operation, one that can generally be handled for "free" by register renaming.)
PopCount PROC
xor eax, eax ; break false dependency
popcnt rax, rcx
and eax, 1
ret
PopCount ENDP
In fact, as it turns out, GCC knows to emit exactly this code for the __builtin_parityll intrinsic when you target a microarchitecture that supports POPCNT (otherwise, it uses the fallback implementation shown below). As you can see from the benchmarks, this is the fastest code yet. It isn't a major difference, so it's unlikely to matter unless you're doing this repeatedly within a tight loop, but it is a measurable difference and presumably you wouldn't be optimizing this so heavily unless your profiler indicated that this was a hot-spot.
But the POPCNT instruction does have the drawback of not being available on older processors, so I also measured a "fallback" version of the code that does a population count with a sequence of universally-supported instructions. That is the PopCount_Downlevel function, taken from my private library, originally adapted from this answer and other sources.
PopCount_Downlevel PROC
mov rax, rcx
shr rax, 1
mov rdx, 5555555555555555h
and rax, rdx
sub rcx, rax
mov rax, 3333333333333333h
mov rdx, rcx
and rcx, rax
shr rdx, 2
and rdx, rax
add rdx, rcx
mov rcx, 0FF0F0F0F0F0F0F0Fh
mov rax, rdx
shr rax, 4
add rax, rdx
mov rdx, 0FF01010101010101h
and rax, rcx
imul rax, rdx
shr rax, 56
and eax, 1
ret
PopCount_Downlevel ENDP
As you can see from the benchmarks, all of the bit-twiddling instructions that are required here exact a cost in performance. It is slower than POPCNT, but supported on all systems and still reasonably quick. If you needed a bit count anyway, this would be the best solution, especially since it can be written in pure C without the need to resort to inline assembly, potentially yielding even more speed:
unsigned int PopCount_Downlevel(uint64 n)
{
uint64 temp = n - ((n >> 1) & 0x5555555555555555ULL);
temp = (temp & 0x3333333333333333ULL) + ((temp >> 2) & 0x3333333333333333ULL);
temp = (temp + (temp >> 4)) & 0x0F0F0F0F0F0F0F0FULL;
temp = (temp * 0x0101010101010101ULL) >> 56;
return (temp & 1);
}
But run your own benchmarks to see if you wouldn't be better off with one of the other implementations, like OriginalCCode, which simplifies the operation and thus requires fewer total instructions. Fun fact: Intel's compiler (ICC) always uses a population count-based algorithm to implement __builtin_parityll; it emits a POPCNT instruction if the target architecture supports it, or otherwise, it simulates it using essentially the same code as I've shown here.
Or, better yet, just forget the whole complicated mess and let your compiler deal with it. That's what built-ins are for, and there's one for precisely this purpose.
Because C sucks when handling bit operations, I suggest using gcc built in functions, in this case __builtin_parityl(). See:
https://gcc.gnu.org/onlinedocs/gcc/Other-Builtins.html
You will have to use extended inline assembly (which is a gcc extension) to get the similar effect.
Your parity64 function can be changed as follows -
uint parity64_unsafe_and_broken(uint64 n){
uint result = 0;
__asm__("addq $0, %0" : : "r"(n) :);
// editor's note: compiler-generated instructions here can destroy EFLAGS
// Don't depending on FLAGS / regs surviving between asm statements
// also, jumping out of an asm statement safely requires asm goto
__asm__("jnp 1f");
__asm__("movl $1, %0" : "=r"(result) : : );
__asm__("1:");
return result;
}
But as commented by #MichaelPetch the parity flag is computed only on the lower 8 bits. So this will work for your if your n is less than 255. For bigger numbers you will have to use the code you mentioned in your question.
To get it working for 64 bits you can collapse the parity of the 32 bit integer into single byte by doing
n = (n >> 32) ^ n;
n = (n >> 16) ^ n;
n = (n >> 8) ^ n;
This code will have to be just at the start of the function before the assembly.
You will have to check how it affects the performance.
The most optimized I could get it is
uint parity64(uint64 n){
unsigned char result = 0;
n = (n >> 32) ^ n;
n = (n >> 16) ^ n;
n = (n >> 8) ^ n;
__asm__("test %1, %1 \n\t"
"setp %0"
: "+r"(result)
: "r"(n)
:
);
return result;
}
How can I include the above (or similar) code as inline assembly in my C source file, so that the parity64() function runs that instead?
This is an XY problem... You think you need to inline that assembly to gain from its benefits, so you asked about how to inline it... but you don't need to inline it.
You shouldn't include assembly into your C source code, because in this case you don't need to, and the better alternative (in terms of portability and maintainability) is to keep the two pieces of source code separate, compile them separately and use the linker to link them.
In parity64.c you should have your portable version (with a wrapper named bool CheckParity(size_t result)), which you can default to in non-x86/64 situations.
You can compile this to an object file like so: gcc -c parity64.c -o parity64.o
... and then link the object code generated from assembly, with the C code: gcc bindot.c parity64.o -o bindot
In parity64_x86.s you might have the following assembly code from your question:
.code
; bool CheckParity(size_t Result)
CheckParity PROC
mov rax, 0
add rcx, 0
jnp jmp_over
mov rax, 1
jmp_over:
ret
CheckParity ENDP
END
You can compile this to an alternative parity64.o object file object code using gcc with this command: gcc -c parity64_x86.s -o parity64.o
... and then link the object code generated like so: gcc bindot.c parity64.o -o bindot
Similarly, if you wanted to use __builtin_parityl instead (as suggested by hdantes answer, you could (and should) once again keep that code separate (in the same place you keep other gcc/x86 optimisations) from your portable code. In parity64_x86.c you might have:
bool CheckParity(size_t result) {
return __builtin_parityl(result);
}
To compile this, your command would be: gcc -c parity64_x86.c -o parity64.o
... and then link the object code generated like so: gcc bindot.c parity64.o -o bindot
On a side-note, if you'd like to inspect the assembly gcc would produce from this: gcc -S parity64_x86.c
Comments in your assembly indicate that the equivalent function prototype in C would be bool CheckParity(size_t Result), so with that in mind, here's what bindot.c might look like:
extern bool CheckParity(size_t Result);
uint64_t bindot(uint64_t *a, uint64_t *b, size_t entries){
uint64_t parity = 0;
for(size_t i = 0; i < entries; ++i)
parity ^= a[i] & b[i]; // Running sum!
return CheckParity(parity);
}
You can build this and link it to any of the above parity64.o versions like so: gcc bindot.c parity64.o -o bindot...
I highly recommend reading the manual for your compiler, when you have the time...
Naturally, I've assumed the < and <= operators run at the same speed (per Jonathon Reinhart's logic, here). Recently, I decided to test that assumption, and I was a little surprised by my results.
I know, for most modern hardware, this question is purely academic, so had to write test programs that looped about 1 billion times (to get any minuscule difference to add up to more acceptable levels). The programs were as basic as possible (to cut out all possible sources of interference).
lt.c:
int main() {
for (int i = 0; i < 1000000001; i++);
return 0;
}
le.c:
int main() {
for (int i = 0; i <= 1000000000; i++);
return 0;
}
They were compiled and run on a Linux VirtualBox 3.19.0-18-generic #18-Ubuntu x86_64 installation, using GCC with the -std=c11 flag set.
The average time for lt.c's binary was:
real 0m2.404s
user 0m2.389s
sys 0m0.000s
The average time for le.c was:
real 0m2.397s
user 0m2.384s
sys 0m0.000s
The difference is small, but I couldn't get it to go away or reverse no matter how many times I ran the binaries.
I made the comparison value in the for-loop of lt.c one larger than le.c (so they'd both loop the same number of times). Was this somehow a mistake?
According the answer in Is < faster than <=?, < compiles to jge and <= compiles to jg. That was dealing with if statements rather than a for-loop, but could this still be the reason? Could the execution of jge take slightly longer than jg? (I think this would be ironic since that would mean moving from C to ASM inverts which one is the more complicated instruction, with lt in C translating to gte in ASM and lte to gt.)
Or, is this just so hardware specific that different x86 lines or individual chips may consistently show the reverse trend, the same trend, or no difference?
There were a few requests in the comments to my question to include the assembly being generated for me by GCC. After getting to compiler to pop out the assembly versions of each file, I checked it.
Result:
It turns out the default optimization setting turned both for-loops into the same assembly. Both files were identical in assembly-form, actually. (diff confirmed this.)
Possible reason for the previously observed time difference:
It seems the order in which I ran the binaries was the cause for the run time difference.
On a given runthrough, the programs generally were executed quicker with each successive execution, before plateauing after about 3 executions.
I alternated back and forth between time ./lt and time ./le, so the one run first would have a bias towards extra time in its average.
I usually ran lt first.
I did several separate runthroughs (increasing the averaged bias).
Code excerpt:
movl $0, -4(%rbp)
jmp .L2
.L3:
addl $1, -4($rbp)
.L2
cmpl $1000000000, -4(%rbp)
jle .L3
mol $0, %eax
pop %rbp
... * covers face * ...carry on....
Let's speak in assembly. (depends on the architecture of course)
When comparing you'll use cmp or test instruction and then
- when you use < the equal instruction would be jl which checks if SF and OF are not the same (some special flags called sign and overflow)
- when you use <= the equal instruction is jle which checks not only SF != OF but also ZF == 1 (zero flag)
and so one, more here
but honestly it's not even the whole cycle so...I think the difference is unmeasurable under normal circumstances