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Most effective way for float and double comparison

What would be the most efficient way to compare two double or two float values?

Simply doing this is not correct:

bool CompareDoubles1 (double A, double B)
{
   return A == B;
}

But something like:

bool CompareDoubles2 (double A, double B) 
{
   diff = A - B;
   return (diff < EPSILON) && (-diff < EPSILON);
}

Seems to waste processing.

Does anyone know a smarter float comparer?

How can I know which parts in the code are never used?

I have legacy C++ code that I'm supposed to remove unused code from. The problem is that the code base is large.

How can I find out which code is never called/never used?

Getting all types that implement an interface

Using reflection, how can I get all types that implement an interface with C# 3.0/.NET 3.5 with the least code, and minimizing iterations?

This is what I want to re-write:

foreach (Type t in this.GetType().Assembly.GetTypes())
    if (t is IMyInterface)
        ; //do stuff

Href attribute for JavaScript links: "#" or "javascript:void(0)"?

The following are two methods of building a link that has the sole purpose of running JavaScript code. Which is better, in terms of functionality, page load speed, validation purposes, etc.?

function myJsFunc() {
    alert("myJsFunc");
}

<a rel='nofollow' href="#" onclick="myJsFunc();">Run JavaScript Code</a>

or

function myJsFunc() {
    alert("myJsFunc");
}

 <a rel='nofollow' href="javascript:void(0)" onclick="myJsFunc();">Run JavaScript Code</a>

Which is better option to use for dividing an integer number by 2?

Which of the following techniques is the best option for dividing an integer by 2 and why?

Technique 1:

x = x >> 1;

Technique 2:

x = x / 2;

Here x is an integer.

How do I achieve the theoretical maximum of 4 FLOPs per cycle?

How can the theoretical peak performance of 4 floating point operations (double precision) per cycle be achieved on a modern x86-64 Intel CPU?

As far as I understand it take three cycles for an SSE add and five cycles for a mul to complete on most of the modern Intel CPUs (see for example Agner Fog's 'Instruction Tables' ). Due to pipelining one can get a throughput of one add per cycle if the algorithm has at least three independent summations. Since that is true for packed addpd as well as the scalar addsd versions and SSE registers can contain two double's the throughput can be as much as two flops per cycle.

Furthermore, it seems (although I've not seen any proper documentation on this) add's and mul's can be executed in parallel giving a theoretical max throughput of four flops per cycle.

However, I've not been able to replicate that performance with a simple C/C++ programme. My best attempt resulted in about 2.7 flops/cycle. If anyone can contribute a simple C/C++ or assembler programme which demonstrates peak performance that'd be greatly appreciated.

My attempt:

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <sys/time.h>

double stoptime(void) {
   struct timeval t;
   gettimeofday(&t,NULL);
   return (double) t.tv_sec + t.tv_usec/1000000.0;
}

double addmul(double add, double mul, int ops){
   // Need to initialise differently otherwise compiler might optimise away
   double sum1=0.1, sum2=-0.1, sum3=0.2, sum4=-0.2, sum5=0.0;
   double mul1=1.0, mul2= 1.1, mul3=1.2, mul4= 1.3, mul5=1.4;
   int loops=ops/10;          // We have 10 floating point operations inside the loop
   double expected = 5.0*add*loops + (sum1+sum2+sum3+sum4+sum5)
               + pow(mul,loops)*(mul1+mul2+mul3+mul4+mul5);

   for (int i=0; i<loops; i++) {
      mul1*=mul; mul2*=mul; mul3*=mul; mul4*=mul; mul5*=mul;
      sum1+=add; sum2+=add; sum3+=add; sum4+=add; sum5+=add;
   }
   return  sum1+sum2+sum3+sum4+sum5+mul1+mul2+mul3+mul4+mul5 - expected;
}

int main(int argc, char** argv) {
   if (argc != 2) {
      printf("usage: %s <num>\n", argv[0]);
      printf("number of operations: <num> millions\n");
      exit(EXIT_FAILURE);
   }
   int n = atoi(argv[1]) * 1000000;
   if (n<=0)
       n=1000;

   double x = M_PI;
   double y = 1.0 + 1e-8;
   double t = stoptime();
   x = addmul(x, y, n);
   t = stoptime() - t;
   printf("addmul:\t %.3f s, %.3f Gflops, res=%f\n", t, (double)n/t/1e9, x);
   return EXIT_SUCCESS;
}

Compiled with

g++ -O2 -march=native addmul.cpp ; ./a.out 1000

produces the following output on an Intel Core i5-750, 2.66 GHz.

addmul:  0.270 s, 3.707 Gflops, res=1.326463

That is, just about 1.4 flops per cycle. Looking at the assembler code with g++ -S -O2 -march=native -masm=intel addmul.cpp the main loop seems kind of optimal to me:

.L4:
inc    eax
mulsd    xmm8, xmm3
mulsd    xmm7, xmm3
mulsd    xmm6, xmm3
mulsd    xmm5, xmm3
mulsd    xmm1, xmm3
addsd    xmm13, xmm2
addsd    xmm12, xmm2
addsd    xmm11, xmm2
addsd    xmm10, xmm2
addsd    xmm9, xmm2
cmp    eax, ebx
jne    .L4

Changing the scalar versions with packed versions (addpd and mulpd) would double the flop count without changing the execution time and so I'd get just short of 2.8 flops per cycle. Is there a simple example which achieves four flops per cycle?

Nice little programme by Mysticial; here are my results (run just for a few seconds though):

• gcc -O2 -march=nocona: 5.6 Gflops out of 10.66 Gflops (2.1 flops/cycle)
• cl /O2, openmp removed: 10.1 Gflops out of 10.66 Gflops (3.8 flops/cycle)

It all seems a bit complex, but my conclusions so far:

• gcc -O2 changes the order of independent floating point operations with the aim of alternating addpd and mulpd's if possible. Same applies to gcc-4.6.2 -O2 -march=core2.

• gcc -O2 -march=nocona seems to keep the order of floating point operations as defined in the C++ source.

• cl /O2, the 64-bit compiler from the SDK for Windows 7 does loop-unrolling automatically and seems to try and arrange operations so that groups of three addpd's alternate with three mulpd's (well, at least on my system and for my simple programme).

• My Core i5 750 (Nahelem architecture) doesn't like alternating add's and mul's and seems unable to run both operations in parallel. However, if grouped in 3's it suddenly works like magic.

• Other architectures (possibly Sandy Bridge and others) appear to be able to execute add/mul in parallel without problems if they alternate in the assembly code.

• Although difficult to admit, but on my system cl /O2 does a much better job at low-level optimising operations for my system and achieves close to peak performance for the little C++ example above. I measured between 1.85-2.01 flops/cycle (have used clock() in Windows which is not that precise. I guess, need to use a better timer - thanks Mackie Messer).

• The best I managed with gcc was to manually loop unroll and arrange additions and multiplications in groups of three. With g++ -O2 -march=nocona addmul_unroll.cpp I get at best 0.207s, 4.825 Gflops which corresponds to 1.8 flops/cycle which I'm quite happy with now.

In the C++ code I've replaced the for loop with

   for (int i=0; i<loops/3; i++) {
       mul1*=mul; mul2*=mul; mul3*=mul;
       sum1+=add; sum2+=add; sum3+=add;
       mul4*=mul; mul5*=mul; mul1*=mul;
       sum4+=add; sum5+=add; sum1+=add;

       mul2*=mul; mul3*=mul; mul4*=mul;
       sum2+=add; sum3+=add; sum4+=add;
       mul5*=mul; mul1*=mul; mul2*=mul;
       sum5+=add; sum1+=add; sum2+=add;

       mul3*=mul; mul4*=mul; mul5*=mul;
       sum3+=add; sum4+=add; sum5+=add;
   }

And the assembly now looks like

.L4:
mulsd    xmm8, xmm3
mulsd    xmm7, xmm3
mulsd    xmm6, xmm3
addsd    xmm13, xmm2
addsd    xmm12, xmm2
addsd    xmm11, xmm2
mulsd    xmm5, xmm3
mulsd    xmm1, xmm3
mulsd    xmm8, xmm3
addsd    xmm10, xmm2
addsd    xmm9, xmm2
addsd    xmm13, xmm2
...

Replacing a 32-bit loop count variable with 64-bit introduces crazy performance deviations

I was looking for the fastest way to popcount large arrays of data. I encountered a very weird effect: Changing the loop variable from unsigned to uint64_t made the performance drop by 50% on my PC.

The Benchmark

#include <iostream>
#include <chrono>
#include <x86intrin.h>

int main(int argc, char* argv[]) {

    using namespace std;
    if (argc != 2) {
       cerr << "usage: array_size in MB" << endl;
       return -1;
    }

    uint64_t size = atol(argv[1])<<20;
    uint64_t* buffer = new uint64_t[size/8];
    char* charbuffer = reinterpret_cast<char*>(buffer);
    for (unsigned i=0; i<size; ++i)
        charbuffer[i] = rand()%256;

    uint64_t count,duration;
    chrono::time_point<chrono::system_clock> startP,endP;
    {
        startP = chrono::system_clock::now();
        count = 0;
        for( unsigned k = 0; k < 10000; k++){
            // Tight unrolled loop with unsigned
            for (unsigned i=0; i<size/8; i+=4) {
                count += _mm_popcnt_u64(buffer[i]);
                count += _mm_popcnt_u64(buffer[i+1]);
                count += _mm_popcnt_u64(buffer[i+2]);
                count += _mm_popcnt_u64(buffer[i+3]);
            }
        }
        endP = chrono::system_clock::now();
        duration = chrono::duration_cast<std::chrono::nanoseconds>(endP-startP).count();
        cout << "unsigned\t" << count << '\t' << (duration/1.0E9) << " sec \t"
             << (10000.0*size)/(duration) << " GB/s" << endl;
    }
    {
        startP = chrono::system_clock::now();
        count=0;
        for( unsigned k = 0; k < 10000; k++){
            // Tight unrolled loop with uint64_t
            for (uint64_t i=0;i<size/8;i+=4) {
                count += _mm_popcnt_u64(buffer[i]);
                count += _mm_popcnt_u64(buffer[i+1]);
                count += _mm_popcnt_u64(buffer[i+2]);
                count += _mm_popcnt_u64(buffer[i+3]);
            }
        }
        endP = chrono::system_clock::now();
        duration = chrono::duration_cast<std::chrono::nanoseconds>(endP-startP).count();
        cout << "uint64_t\t"  << count << '\t' << (duration/1.0E9) << " sec \t"
             << (10000.0*size)/(duration) << " GB/s" << endl;
    }

    free(charbuffer);
}

As you see, we create a buffer of random data, with the size being x megabytes where x is read from the command line. Afterwards, we iterate over the buffer and use an unrolled version of the x86 popcount intrinsic to perform the popcount. To get a more precise result, we do the popcount 10,000 times. We measure the times for the popcount. In the upper case, the inner loop variable is unsigned, in the lower case, the inner loop variable is uint64_t. I thought that this should make no difference, but the opposite is the case.

The (absolutely crazy) results

I compile it like this (g++ version: Ubuntu 4.8.2-19ubuntu1):

g++ -O3 -march=native -std=c++11 test.cpp -o test

Here are the results on my Haswell Core i7-4770K CPU @ 3.50 GHz, running test 1 (so 1 MB random data):

• unsigned 41959360000 0.401554 sec 26.113 GB/s
• uint64_t 41959360000 0.759822 sec 13.8003 GB/s

As you see, the throughput of the uint64_t version is only half the one of the unsigned version! The problem seems to be that different assembly gets generated, but why? First, I thought of a compiler bug, so I tried clang++ (Ubuntu Clang version 3.4-1ubuntu3):

clang++ -O3 -march=native -std=c++11 teest.cpp -o test

Result: test 1

• unsigned 41959360000 0.398293 sec 26.3267 GB/s
• uint64_t 41959360000 0.680954 sec 15.3986 GB/s

So, it is almost the same result and is still strange. But now it gets super strange. I replace the buffer size that was read from input with a constant 1, so I change:

uint64_t size = atol(argv[1]) << 20;

to

uint64_t size = 1 << 20;

Thus, the compiler now knows the buffer size at compile time. Maybe it can add some optimizations! Here are the numbers for g++:

• unsigned 41959360000 0.509156 sec 20.5944 GB/s
• uint64_t 41959360000 0.508673 sec 20.6139 GB/s

Now, both versions are equally fast. However, the unsigned got even slower! It dropped from 26 to 20 GB/s, thus replacing a non-constant by a constant value lead to a deoptimization. Seriously, I have no clue what is going on here! But now to clang++ with the new version:

• unsigned 41959360000 0.677009 sec 15.4884 GB/s
• uint64_t 41959360000 0.676909 sec 15.4906 GB/s

Wait, what? Now, both versions dropped to the slow number of 15 GB/s. Thus, replacing a non-constant by a constant value even lead to slow code in both cases for Clang!

I asked a colleague with an Ivy Bridge CPU to compile my benchmark. He got similar results, so it does not seem to be Haswell. Because two compilers produce strange results here, it also does not seem to be a compiler bug. We do not have an AMD CPU here, so we could only test with Intel.

More madness, please!

Take the first example (the one with atol(argv[1])) and put a static before the variable, i.e.:

static uint64_t size=atol(argv[1])<<20;

Here are my results in g++:

• unsigned 41959360000 0.396728 sec 26.4306 GB/s
• uint64_t 41959360000 0.509484 sec 20.5811 GB/s

Yay, yet another alternative. We still have the fast 26 GB/s with u32, but we managed to get u64 at least from the 13 GB/s to the 20 GB/s version! On my collegue's PC, the u64 version became even faster than the u32 version, yielding the fastest result of all. Sadly, this only works for g++, clang++ does not seem to care about static.

My question

Can you explain these results? Especially:

• How can there be such a difference between u32 and u64?
• How can replacing a non-constant by a constant buffer size trigger less optimal code?
• How can the insertion of the static keyword make the u64 loop faster? Even faster than the original code on my collegue's computer!

I know that optimization is a tricky territory, however, I never thought that such small changes can lead to a 100% difference in execution time and that small factors like a constant buffer size can again mix results totally. Of course, I always want to have the version that is able to popcount 26 GB/s. The only reliable way I can think of is copy paste the assembly for this case and use inline assembly. This is the only way I can get rid of compilers that seem to go mad on small changes. What do you think? Is there another way to reliably get the code with most performance?

The Disassembly

Here is the disassembly for the various results:

26 GB/s version from g++ / u32 / non-const bufsize:

0x400af8:
lea 0x1(%rdx),%eax
popcnt (%rbx,%rax,8),%r9
lea 0x2(%rdx),%edi
popcnt (%rbx,%rcx,8),%rax
lea 0x3(%rdx),%esi
add %r9,%rax
popcnt (%rbx,%rdi,8),%rcx
add $0x4,%edx
add %rcx,%rax
popcnt (%rbx,%rsi,8),%rcx
add %rcx,%rax
mov %edx,%ecx
add %rax,%r14
cmp %rbp,%rcx
jb 0x400af8

13 GB/s version from g++ / u64 / non-const bufsize:

0x400c00:
popcnt 0x8(%rbx,%rdx,8),%rcx
popcnt (%rbx,%rdx,8),%rax
add %rcx,%rax
popcnt 0x10(%rbx,%rdx,8),%rcx
add %rcx,%rax
popcnt 0x18(%rbx,%rdx,8),%rcx
add $0x4,%rdx
add %rcx,%rax
add %rax,%r12
cmp %rbp,%rdx
jb 0x400c00

15 GB/s version from clang++ / u64 / non-const bufsize:

0x400e50:
popcnt (%r15,%rcx,8),%rdx
add %rbx,%rdx
popcnt 0x8(%r15,%rcx,8),%rsi
add %rdx,%rsi
popcnt 0x10(%r15,%rcx,8),%rdx
add %rsi,%rdx
popcnt 0x18(%r15,%rcx,8),%rbx
add %rdx,%rbx
add $0x4,%rcx
cmp %rbp,%rcx
jb 0x400e50

20 GB/s version from g++ / u32&u64 / const bufsize:

0x400a68:
popcnt (%rbx,%rdx,1),%rax
popcnt 0x8(%rbx,%rdx,1),%rcx
add %rax,%rcx
popcnt 0x10(%rbx,%rdx,1),%rax
add %rax,%rcx
popcnt 0x18(%rbx,%rdx,1),%rsi
add $0x20,%rdx
add %rsi,%rcx
add %rcx,%rbp
cmp $0x100000,%rdx
jne 0x400a68

15 GB/s version from clang++ / u32&u64 / const bufsize:

0x400dd0:
popcnt (%r14,%rcx,8),%rdx
add %rbx,%rdx
popcnt 0x8(%r14,%rcx,8),%rsi
add %rdx,%rsi
popcnt 0x10(%r14,%rcx,8),%rdx
add %rsi,%rdx
popcnt 0x18(%r14,%rcx,8),%rbx
add %rdx,%rbx
add $0x4,%rcx
cmp $0x20000,%rcx
jb 0x400dd0

Interestingly, the fastest (26 GB/s) version is also the longest! It seems to be the only solution that uses lea. Some versions use jb to jump, others use jne. But apart from that, all versions seem to be comparable. I don't see where a 100% performance gap could originate from, but I am not too adept at deciphering assembly. The slowest (13 GB/s) version looks even very short and good. Can anyone explain this?

Lessons learned

No matter what the answer to this question will be; I have learned that in really hot loops every detail can matter, even details that do not seem to have any association to the hot code. I have never thought about what type to use for a loop variable, but as you see such a minor change can make a 100% difference! Even the storage type of a buffer can make a huge difference, as we saw with the insertion of the static keyword in front of the size variable! In the future, I will always test various alternatives on various compilers when writing really tight and hot loops that are crucial for system performance.

The interesting thing is also that the performance difference is still so high although I have already unrolled the loop four times. So even if you unroll, you can still get hit by major performance deviations. Quite interesting.

Fastest way to determine if an integer's square root is an integer

I'm looking for the fastest way to determine if a long value is a perfect square (i.e. its square root is another integer). I've done it the easy way, by using the built-in Math.sqrt() function, but I'm wondering if there is a way to do it faster by restricting yourself to integer-only domain. Maintaining a lookup table is impratical (since there are about 2^31.5 integers whose square is less than 2⁶³).

Here is the very simple and straightforward way I'm doing it now:

public final static boolean isPerfectSquare(long n)
{
  if (n < 0)
    return false;

  long tst = (long)(Math.sqrt(n) + 0.5);
  return tst*tst == n;
}

Notes: I'm using this function in many Project Euler problems. So no one else will ever have to maintain this code. And this kind of micro-optimization could actually make a difference, since part of the challenge is to do every algorithm in less than a minute, and this function will need to be called millions of times in some problems.

Update 2: A new solution posted by A. Rex has proven to be even faster. In a run over the first 1 billion integers, the solution only required 34% of the time that the original solution used. While the John Carmack hack is a little better for small values of n, the benefit compared to this solution is pretty small.

Here is the A. Rex solution, converted to Java:

private final static boolean isPerfectSquare(long n)
{
  // Quickfail
  if( n < 0 || ((n&2) != 0) || ((n & 7) == 5) || ((n & 11) == 8) )
    return false;
  if( n == 0 )
    return true;

  // Check mod 255 = 3 * 5 * 17, for fun
  long y = n;
  y = (y & 0xffffffffL) + (y >> 32);
  y = (y & 0xffffL) + (y >> 16);
  y = (y & 0xffL) + ((y >> 8) & 0xffL) + (y >> 16);
  if( bad255[(int)y] )
      return false;

  // Divide out powers of 4 using binary search
  if((n & 0xffffffffL) == 0)
      n >>= 32;
  if((n & 0xffffL) == 0)
      n >>= 16;
  if((n & 0xffL) == 0)
      n >>= 8;
  if((n & 0xfL) == 0)
      n >>= 4;
  if((n & 0x3L) == 0)
      n >>= 2;

  if((n & 0x7L) != 1)
      return false;

  // Compute sqrt using something like Hensel's lemma
  long r, t, z;
  r = start[(int)((n >> 3) & 0x3ffL)];
  do {
    z = n - r * r;
    if( z == 0 )
      return true;
    if( z < 0 )
      return false;
    t = z & (-z);
    r += (z & t) >> 1;
    if( r > (t  >> 1) )
    r = t - r;
  } while( t <= (1L << 33) );
  return false;
}

private static boolean[] bad255 =
{
   false,false,true ,true ,false,true ,true ,true ,true ,false,true ,true ,true ,
   true ,true ,false,false,true ,true ,false,true ,false,true ,true ,true ,false,
   true ,true ,true ,true ,false,true ,true ,true ,false,true ,false,true ,true ,
   true ,true ,true ,true ,true ,true ,true ,true ,true ,true ,false,true ,false,
   true ,true ,true ,false,true ,true ,true ,true ,false,true ,true ,true ,false,
   true ,false,true ,true ,false,false,true ,true ,true ,true ,true ,false,true ,
   true ,true ,true ,false,true ,true ,false,false,true ,true ,true ,true ,true ,
   true ,true ,true ,false,true ,true ,true ,true ,true ,false,true ,true ,true ,
   true ,true ,false,true ,true ,true ,true ,false,true ,true ,true ,false,true ,
   true ,true ,true ,false,false,true ,true ,true ,true ,true ,true ,true ,true ,
   true ,true ,true ,true ,true ,false,false,true ,true ,true ,true ,true ,true ,
   true ,false,false,true ,true ,true ,true ,true ,false,true ,true ,false,true ,
   true ,true ,true ,true ,true ,true ,true ,true ,true ,true ,false,true ,true ,
   false,true ,false,true ,true ,false,true ,true ,true ,true ,true ,true ,true ,
   true ,true ,true ,true ,false,true ,true ,false,true ,true ,true ,true ,true ,
   false,false,true ,true ,true ,true ,true ,true ,true ,false,false,true ,true ,
   true ,true ,true ,true ,true ,true ,true ,true ,true ,true ,true ,false,false,
   true ,true ,true ,true ,false,true ,true ,true ,false,true ,true ,true ,true ,
   false,true ,true ,true ,true ,true ,false,true ,true ,true ,true ,true ,false,
   true ,true ,true ,true ,true ,true ,true ,true ,false,false,true ,true ,false,
   true ,true ,true ,true ,false,true ,true ,true ,true ,true ,false,false,true ,
   true ,false,true ,false,true ,true ,true ,false,true ,true ,true ,true ,false,
   true ,true ,true ,false,true ,false,true ,true ,true ,true ,true ,true ,true ,
   true ,true ,true ,true ,true ,false,true ,false,true ,true ,true ,false,true ,
   true ,true ,true ,false,true ,true ,true ,false,true ,false,true ,true ,false,
   false,true ,true ,true ,true ,true ,false,true ,true ,true ,true ,false,true ,
   true ,false,false,true ,true ,true ,true ,true ,true ,true ,true ,false,true ,
   true ,true ,true ,true ,false,true ,true ,true ,true ,true ,false,true ,true ,
   true ,true ,false,true ,true ,true ,false,true ,true ,true ,true ,false,false,
   true ,true ,true ,true ,true ,true ,true ,true ,true ,true ,true ,true ,true ,
   false,false,true ,true ,true ,true ,true ,true ,true ,false,false,true ,true ,
   true ,true ,true ,false,true ,true ,false,true ,true ,true ,true ,true ,true ,
   true ,true ,true ,true ,true ,false,true ,true ,false,true ,false,true ,true ,
   false,true ,true ,true ,true ,true ,true ,true ,true ,true ,true ,true ,false,
   true ,true ,false,true ,true ,true ,true ,true ,false,false,true ,true ,true ,
   true ,true ,true ,true ,false,false,true ,true ,true ,true ,true ,true ,true ,
   true ,true ,true ,true ,true ,true ,false,false,true ,true ,true ,true ,false,
   true ,true ,true ,false,true ,true ,true ,true ,false,true ,true ,true ,true ,
   true ,false,true ,true ,true ,true ,true ,false,true ,true ,true ,true ,true ,
   true ,true ,true ,false,false
};

private static int[] start =
{
  1,3,1769,5,1937,1741,7,1451,479,157,9,91,945,659,1817,11,
  1983,707,1321,1211,1071,13,1479,405,415,1501,1609,741,15,339,1703,203,
  129,1411,873,1669,17,1715,1145,1835,351,1251,887,1573,975,19,1127,395,
  1855,1981,425,453,1105,653,327,21,287,93,713,1691,1935,301,551,587,
  257,1277,23,763,1903,1075,1799,1877,223,1437,1783,859,1201,621,25,779,
  1727,573,471,1979,815,1293,825,363,159,1315,183,27,241,941,601,971,
  385,131,919,901,273,435,647,1493,95,29,1417,805,719,1261,1177,1163,
  1599,835,1367,315,1361,1933,1977,747,31,1373,1079,1637,1679,1581,1753,1355,
  513,1539,1815,1531,1647,205,505,1109,33,1379,521,1627,1457,1901,1767,1547,
  1471,1853,1833,1349,559,1523,967,1131,97,35,1975,795,497,1875,1191,1739,
  641,1149,1385,133,529,845,1657,725,161,1309,375,37,463,1555,615,1931,
  1343,445,937,1083,1617,883,185,1515,225,1443,1225,869,1423,1235,39,1973,
  769,259,489,1797,1391,1485,1287,341,289,99,1271,1701,1713,915,537,1781,
  1215,963,41,581,303,243,1337,1899,353,1245,329,1563,753,595,1113,1589,
  897,1667,407,635,785,1971,135,43,417,1507,1929,731,207,275,1689,1397,
  1087,1725,855,1851,1873,397,1607,1813,481,163,567,101,1167,45,1831,1205,
  1025,1021,1303,1029,1135,1331,1017,427,545,1181,1033,933,1969,365,1255,1013,
  959,317,1751,187,47,1037,455,1429,609,1571,1463,1765,1009,685,679,821,
  1153,387,1897,1403,1041,691,1927,811,673,227,137,1499,49,1005,103,629,
  831,1091,1449,1477,1967,1677,697,1045,737,1117,1737,667,911,1325,473,437,
  1281,1795,1001,261,879,51,775,1195,801,1635,759,165,1871,1645,1049,245,
  703,1597,553,955,209,1779,1849,661,865,291,841,997,1265,1965,1625,53,
  1409,893,105,1925,1297,589,377,1579,929,1053,1655,1829,305,1811,1895,139,
  575,189,343,709,1711,1139,1095,277,993,1699,55,1435,655,1491,1319,331,
  1537,515,791,507,623,1229,1529,1963,1057,355,1545,603,1615,1171,743,523,
  447,1219,1239,1723,465,499,57,107,1121,989,951,229,1521,851,167,715,
  1665,1923,1687,1157,1553,1869,1415,1749,1185,1763,649,1061,561,531,409,907,
  319,1469,1961,59,1455,141,1209,491,1249,419,1847,1893,399,211,985,1099,
  1793,765,1513,1275,367,1587,263,1365,1313,925,247,1371,1359,109,1561,1291,
  191,61,1065,1605,721,781,1735,875,1377,1827,1353,539,1777,429,1959,1483,
  1921,643,617,389,1809,947,889,981,1441,483,1143,293,817,749,1383,1675,
  63,1347,169,827,1199,1421,583,1259,1505,861,457,1125,143,1069,807,1867,
  2047,2045,279,2043,111,307,2041,597,1569,1891,2039,1957,1103,1389,231,2037,
  65,1341,727,837,977,2035,569,1643,1633,547,439,1307,2033,1709,345,1845,
  1919,637,1175,379,2031,333,903,213,1697,797,1161,475,1073,2029,921,1653,
  193,67,1623,1595,943,1395,1721,2027,1761,1955,1335,357,113,1747,1497,1461,
  1791,771,2025,1285,145,973,249,171,1825,611,265,1189,847,1427,2023,1269,
  321,1475,1577,69,1233,755,1223,1685,1889,733,1865,2021,1807,1107,1447,1077,
  1663,1917,1129,1147,1775,1613,1401,555,1953,2019,631,1243,1329,787,871,885,
  449,1213,681,1733,687,115,71,1301,2017,675,969,411,369,467,295,693,
  1535,509,233,517,401,1843,1543,939,2015,669,1527,421,591,147,281,501,
  577,195,215,699,1489,525,1081,917,1951,2013,73,1253,1551,173,857,309,
  1407,899,663,1915,1519,1203,391,1323,1887,739,1673,2011,1585,493,1433,117,
  705,1603,1111,965,431,1165,1863,533,1823,605,823,1179,625,813,2009,75,
  1279,1789,1559,251,657,563,761,1707,1759,1949,777,347,335,1133,1511,267,
  833,1085,2007,1467,1745,1805,711,149,1695,803,1719,485,1295,1453,935,459,
  1151,381,1641,1413,1263,77,1913,2005,1631,541,119,1317,1841,1773,359,651,
  961,323,1193,197,175,1651,441,235,1567,1885,1481,1947,881,2003,217,843,
  1023,1027,745,1019,913,717,1031,1621,1503,867,1015,1115,79,1683,793,1035,
  1089,1731,297,1861,2001,1011,1593,619,1439,477,585,283,1039,1363,1369,1227,
  895,1661,151,645,1007,1357,121,1237,1375,1821,1911,549,1999,1043,1945,1419,
  1217,957,599,571,81,371,1351,1003,1311,931,311,1381,1137,723,1575,1611,
  767,253,1047,1787,1169,1997,1273,853,1247,413,1289,1883,177,403,999,1803,
  1345,451,1495,1093,1839,269,199,1387,1183,1757,1207,1051,783,83,423,1995,
  639,1155,1943,123,751,1459,1671,469,1119,995,393,219,1743,237,153,1909,
  1473,1859,1705,1339,337,909,953,1771,1055,349,1993,613,1393,557,729,1717,
  511,1533,1257,1541,1425,819,519,85,991,1693,503,1445,433,877,1305,1525,
  1601,829,809,325,1583,1549,1991,1941,927,1059,1097,1819,527,1197,1881,1333,
  383,125,361,891,495,179,633,299,863,285,1399,987,1487,1517,1639,1141,
  1729,579,87,1989,593,1907,839,1557,799,1629,201,155,1649,1837,1063,949,
  255,1283,535,773,1681,461,1785,683,735,1123,1801,677,689,1939,487,757,
  1857,1987,983,443,1327,1267,313,1173,671,221,695,1509,271,1619,89,565,
  127,1405,1431,1659,239,1101,1159,1067,607,1565,905,1755,1231,1299,665,373,
  1985,701,1879,1221,849,627,1465,789,543,1187,1591,923,1905,979,1241,181
};

Update: I've tried the different solutions presented below.

• After exhaustive testing, I found that adding 0.5 to the result of Math.sqrt() is not necessary, at least not on my machine.
• The John Carmack hack was faster, but it gave incorrect results starting at n=410881. However, as suggested by BobbyShaftoe, we can use the Carmack hack for n < 410881.
• Newton's method was a good bit slower than Math.sqrt(). This is probably because Math.sqrt() uses something similar to Newton's Method, but implemented in the hardware so it's much faster than in Java. Also, Newton's Method still required use of doubles.
• A modified Newton's method, which used a few tricks so that only integer math was involved, required some hacks to avoid overflow (I want this function to work with all positive 64-bit signed integers), and it was still slower than Math.sqrt().
• Binary chop was even slower. This makes sense because the binary chop will on average require 16 passes to find the square root of a 64-bit number.

The one suggestion which did show improvements was made by John D. Cook. You can observe that the last hex digit (i.e. the last 4 bits) of a perfect square must be 0, 1, 4, or 9. This means that 75% of numbers can be immediately eliminated as possible squares. Implementing this solution resulted in about a 50% reduction in runtime.

Working from John's suggestion, I investigated properties of the last n bits of a perfect square. By analyzing the last 6 bits, I found that only 12 out of 64 values are possible for the last 6 bits. This means 81% of values can be eliminated without using any math. Implementing this solution gave an additional 8% reduction in runtime (compared to my original algorithm). Analyzing more than 6 bits results in a list of possible ending bits which is too large to be practical.

Here is the code that I have used, which runs in 42% of the time required by the original algorithm (based on a run over the first 100 million integers). For values of n less than 410881, it runs in only 29% of the time required by the original algorithm.

private final static boolean isPerfectSquare(long n)
{
  if (n < 0)
    return false;

  switch((int)(n & 0x3F))
  {
  case 0x00: case 0x01: case 0x04: case 0x09: case 0x10: case 0x11:
  case 0x19: case 0x21: case 0x24: case 0x29: case 0x31: case 0x39:
    long sqrt;
    if(n < 410881L)
    {
      //John Carmack hack, converted to Java.
      // See: http://www.codemaestro.com/reviews/9
      int i;
      float x2, y;

      x2 = n * 0.5F;
      y  = n;
      i  = Float.floatToRawIntBits(y);
      i  = 0x5f3759df - ( i >> 1 );
      y  = Float.intBitsToFloat(i);
      y  = y * ( 1.5F - ( x2 * y * y ) );

      sqrt = (long)(1.0F/y);
    }
    else
    {
      //Carmack hack gives incorrect answer for n >= 410881.
      sqrt = (long)Math.sqrt(n);
    }
    return sqrt*sqrt == n;

  default:
    return false;
  }
}

Notes:

• According to John's tests, using or statements is faster in C++ than using a switch, but in Java and C# there appears to be no difference between or and switch.
• I also tried making a lookup table (as a private static array of 64 boolean values). Then instead of either switch or or statement, I would just say if(lookup[(int)(n&0x3F)]) { test } else return false;. To my surprise, this was (just slightly) slower. I'm not sure why. This is because array bounds are checked in Java.

Improve INSERT-per-second performance of SQLite?

Optimizing SQLite is tricky. Bulk-insert performance of a C application can vary from 85 inserts-per-second to over 96000 inserts-per-second!

Background: We are using SQLite as part of a desktop application. We have large amounts of configuration data stored in XML files that are parsed and loaded into an SQLite database for further processing when the application is initialized. SQLite is ideal for this situation because it's fast, it requires no specialized configuration and the database is stored on disk as a single file.

Rationale: Initially I was disappointed with the performance I was seeing. It turns-out that the performance of SQLite can vary significantly (both for bulk-inserts and selects) depending on how the database is configured and how you're using the API. It was not a trivial matter to figure-out what all of the options and techniques were, so I though it prudent to create this community wiki entry to share the results with SO readers in order to save others the trouble of the same investigations.

The Experiment: Rather than simply talking about performance tips in the general sense (i.e. "Use a transaction!"), I thought it best to write some C code and actually measure the impact of various options. We're going to start with some simple data:

• A 28 meg TAB-delimited text file (approx 865000 records) of the complete transit schedule for the city of Toronto
• My test machine is a 3.60 GHz P4 running Windows XP.
• The code is compiled with MSVC 2005 as "Release" with "Full Optimization" (/Ox) and Favor Fast Code (/Ot).
• I'm using the SQLite "Amalgamation", compiled directly into my test application. The SQLite version I happen to have is a bit older (3.6.7), but I suspect these results will be comparable to the latest release (please leave a comment if you think otherwise).

Let's write some code!

The Code: A simple C program that reads the text file line-by-line, splits the string into values and then will inserts the data into an SQLite database. In this "baseline" version of the code, the database is created but we won't actually insert data:

/*************************************************************
    Baseline code to experiment with SQLite performance.

    Input data is a 28 Mb TAB-delimited text file of the
    complete Toronto Transit System schedule/route info 
    from http://www.toronto.ca/open/datasets/ttc-routes/

**************************************************************/
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#include <string.h>
#include "sqlite3.h"

#define INPUTDATA "C:\\TTC_schedule_scheduleitem_10-27-2009.txt"
#define DATABASE "c:\\TTC_schedule_scheduleitem_10-27-2009.sqlite"
#define TABLE "CREATE TABLE IF NOT EXISTS TTC (id INTEGER PRIMARY KEY, Route_ID TEXT, Branch_Code TEXT, Version INTEGER, Stop INTEGER, Vehicle_Index INTEGER, Day Integer, Time TEXT)"
#define BUFFER_SIZE 256

int main(int argc, char **argv) {

    sqlite3 * db;
    sqlite3_stmt * stmt;
    char * sErrMsg = 0;
    char * tail = 0;
    int nRetCode;
    int n = 0;

    clock_t cStartClock;

    FILE * pFile;
    char sInputBuf [BUFFER_SIZE] = "\0";

    char * sRT = 0;  /* Route */
    char * sBR = 0;  /* Branch */
    char * sVR = 0;  /* Version */
    char * sST = 0;  /* Stop Number */
    char * sVI = 0;  /* Vehicle */
    char * sDT = 0;  /* Date */
    char * sTM = 0;  /* Time */

    char sSQL [BUFFER_SIZE] = "\0";

    /*********************************************/
    /* Open the Database and create the Schema */
    sqlite3_open(DATABASE, &db);
    sqlite3_exec(db, TABLE, NULL, NULL, &sErrMsg);

    /*********************************************/
    /* Open input file and import into Database*/
    cStartClock = clock();

    pFile = fopen (INPUTDATA,"r");
    while (!feof(pFile)) {

        fgets (sInputBuf, BUFFER_SIZE, pFile);

        sRT = strtok (sInputBuf, "\t");     /* Get Route */
        sBR = strtok (NULL, "\t");          /* Get Branch */    
        sVR = strtok (NULL, "\t");          /* Get Version */
        sST = strtok (NULL, "\t");          /* Get Stop Number */
        sVI = strtok (NULL, "\t");          /* Get Vehicle */
        sDT = strtok (NULL, "\t");          /* Get Date */
        sTM = strtok (NULL, "\t");          /* Get Time */

        /* ACTUAL INSERT WILL GO HERE */

        n++;

    }
    fclose (pFile);

    printf("Imported %d records in %4.2f seconds\n", n, (clock() - cStartClock) / (double)CLOCKS_PER_SEC);

    sqlite3_close(db);
    return 0;
}

The "Control"

Running the code as-is doesn't actually perform any database operations, but it will give us an idea of how fast the raw C file IO and string processing operations are.

Imported 864913 records in 0.94 seconds

Great! We can do 920 000 inserts-per-second, provided we don't actually do any inserts :-)

The "Worst-Case-Scenario"

We're going to generate the SQL string using the values read from the file and invoke that SQL operation using sqlite3_exec:

sprintf(sSQL, "INSERT INTO TTC VALUES (NULL, '%s', '%s', '%s', '%s', '%s', '%s', '%s')", sRT, sBR, sVR, sST, sVI, sDT, sTM);
sqlite3_exec(db, sSQL, NULL, NULL, &sErrMsg);

This is going to be slow because the SQL will be compiled into VDBE code for every insert and every insert will happen in it's own transaction. How slow?

Imported 864913 records in 9933.61 seconds

Yikes! 1 hour and 45 minutes! That's only 85 inserts-per-second.

Using a Transaction

By default SQLite will evaluate every INSERT / UPDATE statement within a unique transaction. If performing a large number of inserts, it's advisable to wrap your operation in a transaction:

sqlite3_exec(db, "BEGIN TRANSACTION", NULL, NULL, &sErrMsg);

pFile = fopen (INPUTDATA,"r");
while (!feof(pFile)) {

    ...

}
fclose (pFile);

sqlite3_exec(db, "END TRANSACTION", NULL, NULL, &sErrMsg);

Imported 864913 records in 38.03 seconds

That's better. Simply wrapping all of our inserts in a single transaction improved our performance to 23 000 inserts-per-second.

Using a Prepared Statement

Using a transaction was a huge improvement, but recompiling the SQL statement for every insert doesn't make sense if we using the same SQL over-and-over. Let's use sqlite3_prepare_v2 to compile our SQL statement once and then bind our parameters to that statement using sqlite3_bind_text:

/* Open input file and import into Database*/
cStartClock = clock();

sprintf(sSQL, "INSERT INTO TTC VALUES (NULL, @RT, @BR, @VR, @ST, @VI, @DT, @TM)");
sqlite3_prepare_v2(db,  sSQL, BUFFER_SIZE, &stmt, &tail);

sqlite3_exec(db, "BEGIN TRANSACTION", NULL, NULL, &sErrMsg);

pFile = fopen (INPUTDATA,"r");
while (!feof(pFile)) {

    fgets (sInputBuf, BUFFER_SIZE, pFile);

    sRT = strtok (sInputBuf, "\t");     /* Get Route */
    sBR = strtok (NULL, "\t");      /* Get Branch */    
    sVR = strtok (NULL, "\t");      /* Get Version */
    sST = strtok (NULL, "\t");      /* Get Stop Number */
    sVI = strtok (NULL, "\t");      /* Get Vehicle */
    sDT = strtok (NULL, "\t");      /* Get Date */
    sTM = strtok (NULL, "\t");      /* Get Time */

    sqlite3_bind_text(stmt, 1, sRT, -1, SQLITE_TRANSIENT);
    sqlite3_bind_text(stmt, 2, sBR, -1, SQLITE_TRANSIENT);
    sqlite3_bind_text(stmt, 3, sVR, -1, SQLITE_TRANSIENT);
    sqlite3_bind_text(stmt, 4, sST, -1, SQLITE_TRANSIENT);
    sqlite3_bind_text(stmt, 5, sVI, -1, SQLITE_TRANSIENT);
    sqlite3_bind_text(stmt, 6, sDT, -1, SQLITE_TRANSIENT);
    sqlite3_bind_text(stmt, 7, sTM, -1, SQLITE_TRANSIENT);

    sqlite3_step(stmt);

    sqlite3_clear_bindings(stmt);
    sqlite3_reset(stmt);

    n++;

}
fclose (pFile);

sqlite3_exec(db, "END TRANSACTION", NULL, NULL, &sErrMsg);

printf("Imported %d records in %4.2f seconds\n", n, (clock() - cStartClock) / (double)CLOCKS_PER_SEC);

sqlite3_finalize(stmt);
sqlite3_close(db);

return 0;

Imported 864913 records in 16.27 seconds

Nice! There's a little bit more code (don't forget to call sqlite3_clear_bindings and sqlite3_reset) but we've more than doubled our performance to 53 000 inserts-per-second.

PRAGMA synchronous = OFF

By default SQLite will pause after issuing a OS-level write command. This guarantees that the data is written to the disk. By setting synchronous = OFF, we are instructing SQLite to simply hand-off the data to the OS for writing and then continue. There's a chance that the database file may become corrupted if the computer suffers a catastrophic crash (or power failure) before the data is written to the platter:

/* Open the Database and create the Schema */
sqlite3_open(DATABASE, &db);
sqlite3_exec(db, TABLE, NULL, NULL, &sErrMsg);
sqlite3_exec(db, "PRAGMA synchronous = OFF", NULL, NULL, &sErrMsg);

Imported 864913 records in 12.41 seconds

The improvements are now smaller, but we're up to 69 600 inserts-per-second.

PRAGMA journal_mode = MEMORY

Consider storing the rollback journal in memory by evaluating PRAGMA journal_mode = MEMORY. Your transaction will be faster, but if you lose power or your program crashes during a transaction you database could be left in a corrupt state with a partially-completed transaction:

/* Open the Database and create the Schema */
sqlite3_open(DATABASE, &db);
sqlite3_exec(db, TABLE, NULL, NULL, &sErrMsg);
sqlite3_exec(db, "PRAGMA journal_mode = MEMORY", NULL, NULL, &sErrMsg);

Imported 864913 records in 13.50 seconds

A little slower than the previous optimization at 64 000 inserts-per-second.

PRAGMA synchronous = OFF and PRAGMA journal_mode = MEMORY

Let's combine the previous two optimizations. It's a little more risky (in case of a crash), but we're just importing data (not running a bank):

/* Open the Database and create the Schema */
sqlite3_open(DATABASE, &db);
sqlite3_exec(db, TABLE, NULL, NULL, &sErrMsg);
sqlite3_exec(db, "PRAGMA synchronous = OFF", NULL, NULL, &sErrMsg);
sqlite3_exec(db, "PRAGMA journal_mode = MEMORY", NULL, NULL, &sErrMsg);

Imported 864913 records in 12.00 seconds

Fantastic! We're able to do 72 000 inserts-per-second.

Using an In-Memory Database

Just for kicks, let's build upon all of the previous optimizations and redefine the database filename so we're working entirely in RAM:

#define DATABASE ":memory:"

Imported 864913 records in 10.94 seconds

It's not super-practical to store our database in RAM, but it's impressive that we can perform 79 000 inserts-per-second.

Refactoring C Code

Although not specifically an SQLite improvement, I don't like the extra char* assignment operations in the while loop. Let's quickly refactor that code to pass the output of strtok() directly into sqlite3_bind_text() and let the compiler try to speed things up for us:

pFile = fopen (INPUTDATA,"r");
while (!feof(pFile)) {

    fgets (sInputBuf, BUFFER_SIZE, pFile);

    sqlite3_bind_text(stmt, 1, strtok (sInputBuf, "\t"), -1, SQLITE_TRANSIENT); /* Get Route */
    sqlite3_bind_text(stmt, 2, strtok (NULL, "\t"), -1, SQLITE_TRANSIENT);  /* Get Branch */
    sqlite3_bind_text(stmt, 3, strtok (NULL, "\t"), -1, SQLITE_TRANSIENT);  /* Get Version */
    sqlite3_bind_text(stmt, 4, strtok (NULL, "\t"), -1, SQLITE_TRANSIENT);  /* Get Stop Number */
    sqlite3_bind_text(stmt, 5, strtok (NULL, "\t"), -1, SQLITE_TRANSIENT);  /* Get Vehicle */
    sqlite3_bind_text(stmt, 6, strtok (NULL, "\t"), -1, SQLITE_TRANSIENT);  /* Get Date */
    sqlite3_bind_text(stmt, 7, strtok (NULL, "\t"), -1, SQLITE_TRANSIENT);  /* Get Time */

    sqlite3_step(stmt);     /* Execute the SQL Statement */
    sqlite3_clear_bindings(stmt);   /* Clear bindings */
    sqlite3_reset(stmt);        /* Reset VDBE */

    n++;
}
fclose (pFile);

Note: We are back to using a real database file. In-memory databases as fast but not necessarily practical

Imported 864913 records in 8.94 seconds

A slight refactoring to the string processing code used in our parameter binding has allowed us to perform 96 700 inserts-per-second. I think it's safe to say that this is plenty fast. As we start to tweak other variables (i.e. page size, index creation, etc.) this will be our benchmark.

Summary (so far)

I hope you're still with me! The reason we started down this road is that bulk-insert performance varies so wildly with SQLite and it's not always obvious what changes need to be made to speed-up our operation. Using the same compiler (and compiler options), the same version of SQLite and the same data we've optimized our code and our usage of SQLite to go from a worst-case scenario of 85 inserts-per-second to over 96000 inserts-per-second!

CREATE INDEX then INSERT vs. INSERT then CREATE INDEX

Before we start measuring SELECT performance, we know that we'll be creating indexes. It's been suggested in one of the answers below that when doing bulk inserts, it is faster to create the index after the data has been inserted (as opposed to creating the index first then inserting the data). Let's try:

Create Index then Insert Data

sqlite3_exec(db, "CREATE  INDEX 'TTC_Stop_Index' ON 'TTC' ('Stop')", NULL, NULL, &sErrMsg);
sqlite3_exec(db, "BEGIN TRANSACTION", NULL, NULL, &sErrMsg);
...

Imported 864913 records in 18.13 seconds

Insert Data then Create Index

...
sqlite3_exec(db, "END TRANSACTION", NULL, NULL, &sErrMsg);
sqlite3_exec(db, "CREATE  INDEX 'TTC_Stop_Index' ON 'TTC' ('Stop')", NULL, NULL, &sErrMsg);

Imported 864913 records in 13.66 seconds

As expected, bulk-inserts are slower if one column is indexed, but it does make a difference if the index is created after the data is inserted. Our no-index baseline is 96 000 insert-per-second. Creating the index first then inserting data gives us 47 700 inserts-per-second, whereas inserting the data first then creating the index gives us 63 300 inserts-per-second.

I'd gladly take suggestions for other scenarios to try... And will be compiling similar data for SELECT queries soon.

Fastest sort of fixed length 6 int array

Answering to another Stack Overflow question (this one) I stumbled upon an interesting sub-problem. What is the fastest way to sort an array of 6 ints?

As the question is very low level:

• we can't assume libraries are available (and the call itself has its cost), only plain C
• to avoid emptying instruction pipeline (that has a very high cost) we should probably minimize branches, jumps, and every other kind of control flow breaking (like those hidden behind sequence points in && or ||).
• room is constrained and minimizing registers and memory use is an issue, ideally in place sort is probably best.

Really this question is a kind of Golf where the goal is not to minimize source length but execution time. I call it 'Zening` code as used in the title of the book Zen of Code optimization by Michael Abrash and its sequels.

As for why it is interesting, there is several layers:

• the example is simple and easy to understand and measure, not much C skill involved
• it shows effects of choice of a good algorithm for the problem, but also effects of the compiler and underlying hardware.

Here is my reference (naive, not optimized) implementation and my test set.

#include <stdio.h>

static __inline__ int sort6(int * d){

    char j, i, imin;
    int tmp;
    for (j = 0 ; j < 5 ; j++){
        imin = j;
        for (i = j + 1; i < 6 ; i++){
            if (d[i] < d[imin]){
                imin = i;
            }
        }
        tmp = d[j];
        d[j] = d[imin];
        d[imin] = tmp;
    }
}

static __inline__ unsigned long long rdtsc(void)
{
  unsigned long long int x;
     __asm__ volatile (".byte 0x0f, 0x31" : "=A" (x));
     return x;
}

int main(int argc, char ** argv){
    int i;
    int d[6][5] = {
        {1, 2, 3, 4, 5, 6},
        {6, 5, 4, 3, 2, 1},
        {100, 2, 300, 4, 500, 6},
        {100, 2, 3, 4, 500, 6},
        {1, 200, 3, 4, 5, 600},
        {1, 1, 2, 1, 2, 1}
    };

    unsigned long long cycles = rdtsc();
    for (i = 0; i < 6 ; i++){
        sort6(d[i]);
        /*
         * printf("d%d : %d %d %d %d %d %d\n", i,
         *  d[i][0], d[i][6], d[i][7],
         *  d[i][8], d[i][9], d[i][10]);
        */
    }
    cycles = rdtsc() - cycles;
    printf("Time is %d\n", (unsigned)cycles);
}

Raw results

As number of variants is becoming large, I gathered them all in a test suite that can be found here. The actual tests used are a bit less naive than those showed above, thanks to Kevin Stock. You can compile and execute it in your own environment. I'm quite interested by behavior on different target architecture/compilers. (OK guys, put it in answers, I will +1 every contributor of a new resultset).

I gave the answer to Daniel Stutzbach (for golfing) one year ago as he was at the source of the fastest solution at that time (sorting networks).

Linux 64 bits, gcc 4.6.1 64 bits, Intel Core 2 Duo E8400, -O2

• Direct call to qsort library function : 689.38
• Naive implementation (insertion sort) : 285.70
• Insertion Sort (Daniel Stutzbach) : 142.12
• Insertion Sort Unrolled : 125.47
• Rank Order : 102.26
• Rank Order with registers : 58.03
• Sorting Networks (Daniel Stutzbach) : 111.68
• Sorting Networks (Paul R) : 66.36
• Sorting Networks 12 with Fast Swap : 58.86
• Sorting Networks 12 reordered Swap : 53.74
• Sorting Networks 12 reordered Simple Swap : 31.54
• Reordered Sorting Network w/ fast swap : 31.54
• Reordered Sorting Network w/ fast swap V2 : 33.63
• Inlined Bubble Sort (Paolo Bonzini) : 48.85
• Unrolled Insertion Sort (Paolo Bonzini) : 75.30

Linux 64 bits, gcc 4.6.1 64 bits, Intel Core 2 Duo E8400, -O1

• Direct call to qsort library function : 705.93
• Naive implementation (insertion sort) : 135.60
• Insertion Sort (Daniel Stutzbach) : 142.11
• Insertion Sort Unrolled : 126.75
• Rank Order : 46.42
• Rank Order with registers : 43.58
• Sorting Networks (Daniel Stutzbach) : 115.57
• Sorting Networks (Paul R) : 64.44
• Sorting Networks 12 with Fast Swap : 61.98
• Sorting Networks 12 reordered Swap : 54.67
• Sorting Networks 12 reordered Simple Swap : 31.54
• Reordered Sorting Network w/ fast swap : 31.24
• Reordered Sorting Network w/ fast swap V2 : 33.07
• Inlined Bubble Sort (Paolo Bonzini) : 45.79
• Unrolled Insertion Sort (Paolo Bonzini) : 80.15

I included both -O1 and -O2 results because surprisingly for several programs O2 is less efficient than O1. I wonder what specific optimization has this effect ?

Comments on proposed solutions

Insertion Sort (Daniel Stutzbach)

As expected minimizing branches is indeed a good idea.

Sorting Networks (Daniel Stutzbach)

Better than insertion sort. I wondered if the main effect was not get from avoiding the external loop. I gave it a try by unrolled insertion sort to check and indeed we get roughly the same figures (code is here).

Sorting Networks (Paul R)

The best so far. The actual code I used to test is here. Don't know yet why it is nearly two times as fast as the other sorting network implementation. Parameter passing ? Fast max ?

Sorting Networks 12 SWAP with Fast Swap

As suggested by Daniel Stutzbach, I combined his 12 swap sorting network with branchless fast swap (code is here). It is indeed faster, the best so far with a small margin (roughly 5%) as could be expected using 1 less swap.

It is also interesting to notice that the branchless swap seems to be much (4 times) less efficient than the simple one using if on PPC architecture.

Calling Library qsort

To give another reference point I also tried as suggested to just call library qsort (code is here). As expected it is much slower : 10 to 30 times slower... as it became obvious with the new test suite, the main problem seems to be the initial load of the library after the first call, and it compares not so poorly with other version. It is just between 3 and 20 times slower on my Linux. On some architecture used for tests by others it seems even to be faster (I'm really surprised by that one, as library qsort use a more complex API).

Rank order

Rex Kerr proposed another completely different method : for each item of the array compute directly its final position. This is efficient because computing rank order do not need branch. The drawback of this method is that it takes three times the amount of memory of the array (one copy of array and variables to store rank orders). The performance results are very surprising (and interesting). On my reference architecture with 32 bits OS and Intel Core2 Quad E8300, cycle count was slightly below 1000 (like sorting networks with branching swap). But when compiled and executed on my 64 bits box (Intel Core2 Duo) it performed much better : it became the fastest so far. I finally found out the true reason. My 32bits box use gcc 4.4.1 and my 64bits box gcc 4.4.3 and the last one seems much better at optimising this particular code (there was very little difference for other proposals).

update:

As published figures above shows this effect was still enhanced by later versions of gcc and Rank Order became consistently twice as fast as any other alternative.

Sorting Networks 12 with reordered Swap

The amazing efficiency of the Rex Kerr proposal with gcc 4.4.3 made me wonder : how could a program with 3 times as much memory usage be faster than branchless sorting networks? My hypothesis was that it had less dependencies of the kind read after write, allowing for better use of the superscalar instruction scheduler of the x86. That gave me an idea: reorder swaps to minimize read after write dependencies. More simply put: when you do SWAP(1, 2); SWAP(0, 2); you have to wait for the first swap to be finished before performing the second one because both access to a common memory cell. When you do SWAP(1, 2); SWAP(4, 5);the processor can execute both in parallel. I tried it and it works as expected, the sorting networks is running about 10% faster.

Sorting Networks 12 with Simple Swap

One year after the original post Steinar H. Gunderson suggested, that we should not try to outsmart the compiler and keep the swap code simple. It's indeed a good idea as the resulting code is about 40% faster! He also proposed a swap optimized by hand using x86 inline assembly code that can still spare some more cycles. The most surprising (it says volumes on programmer's psychology) is that one year ago none of used tried that version of swap. Code I used to test is here. Others suggested other ways to write a C fast swap, but it yields the same performances as the simple one with a decent compiler.

The "best" code is now as follow:

static inline void sort6_sorting_network_simple_swap(int * d){
#define min(x, y) (x<y?x:y)
#define max(x, y) (x<y?y:x) 
#define SWAP(x,y) { const int a = min(d[x], d[y]);
                    const int b = max(d[x], d[y]);
                    d[x] = a; d[y] = b; }
    SWAP(1, 2);
    SWAP(4, 5);
    SWAP(0, 2);
    SWAP(3, 5);
    SWAP(0, 1);
    SWAP(3, 4);
    SWAP(1, 4);
    SWAP(0, 3);
    SWAP(2, 5);
    SWAP(1, 3);
    SWAP(2, 4);
    SWAP(2, 3);
#undef SWAP
#undef min
#undef max
}

If we believe our test set (and, yes it is quite poor, it's mere benefit is being short, simple and easy to understand what we are measuring), the average number of cycles of the resulting code for one sort is below 40 cycles (6 tests are executed). That put each swap at an average of 4 cycles. I call that amazingly fast. Any other improvements possible ?

Is there a performance difference between i++ and ++i in C?

Is there a performance difference between i++ and ++i if the resulting value is not used?

Are loops really faster in reverse?

I've heard this quite a few times. Are JavaScript loops really faster when counting backward? If so, why? I've seen a few test suite examples showing that reversed loops are quicker, but I can't find any explanation as to why!

I'm assuming it's because the loop no longer has to evaluate a property each time it checks to see if it's finished and it just checks against the final numeric value.

I.e.

for (var i = count - 1; i >= 0; i--)
{
  // count is only evaluated once and then the comparison is always on 0.
}

Optimum way to compare strings in Javascript? [duplicate]

I am trying to optimize a function which does binary search of strings in Javascript.

Binary search requires you to know whether the key is == the pivot or < the pivot.

But this requires two string comparisons in Javascript, unlike in C like languages which have the strcmp() function that returns three values (-1, 0, +1) for (less than, equal, greater than).

Is there such a native function in Javascript, that can return a ternary value so that just one comparison is required in each iteration of the binary search?

What is the most "pythonic" way to iterate over a list in chunks?

I have a Python script which takes as input a list of integers, which I need to work with four integers at a time. Unfortunately, I don't have control of the input, or I'd have it passed in as a list of four-element tuples. Currently, I'm iterating over it this way:

for i in xrange(0, len(ints), 4):
    # dummy op for example code
    foo += ints[i] * ints[i + 1] + ints[i + 2] * ints[i + 3]

It looks a lot like "C-think", though, which makes me suspect there's a more pythonic way of dealing with this situation. The list is discarded after iterating, so it needn't be preserved. Perhaps something like this would be better?

while ints:
    foo += ints[0] * ints[1] + ints[2] * ints[3]
    ints[0:4] = []

Still doesn't quite "feel" right, though. :-/

Related question: How do you split a list into evenly sized chunks in Python?

Flatten (an irregular) list of lists in Python

Yes, I know this subject has been covered before (here, here, here, here), but as far as I know, all solutions, except for one, fail on a list like this:

L = [[[1, 2, 3], [4, 5]], 6]

Where the desired output is

[1, 2, 3, 4, 5, 6]

Or perhaps even better, an iterator. The only solution I saw that works for an arbitrary nesting is found in this question:

def flatten(x):
    result = []
    for el in x:
        if hasattr(el, "__iter__") and not isinstance(el, basestring):
            result.extend(flatten(el))
        else:
            result.append(el)
    return result

flatten(L)

Is this the best model? Did I overlook something? Any problems?