slow complex<double>'s with g++

[Greg Buchholz <greg@xxxxxxxxxxxxxxxxxxxx>]

/* 
    While writing a C++ version of the Mandelbrot benchmark over at the
"The Great Computer Language Shootout"...

  http://shootout.alioth.debian.org/gp4/benchmark.php?test=mandelbrot&lang=all

...I've come across the issue that complex<double>'s seem painfully slow
unless compiled with -ffast-math. Of course doing that results in
incorrect answers because of rounding issues.  The speed difference for
the program below is between 5x-8x depending on the version of g++.  It
is also about 5 times slower than the corresponding gcc version at...

http://shootout.alioth.debian.org/gp4/benchmark.php?test=mandelbrot&lang=gcc&id=2

...I'd be interesting in learning the reason for the speed difference.
Does it have something to do with temporaries not being optimized away,
or somesuch?  A limitation of the x87 instruction set?  Is it inherent
in the way the C++ Standard requires complex<double>'s to be calculated?
My bad coding style?

Curious,

Greg Buchholz
*/

// Takes an integer argument "n" on the command line and generates a
// PBM bitmap of the Mandelbrot set on stdout.
// see also: ( http://sleepingsquirrel.org/cpp/mandelbrot.cpp.html )

#include<iostream> 
#include<complex>

int main (int argc, char **argv)
{
  char  bit_num = 0, byte_acc = 0;
  const int iter = 50;
  const double limit_sqr = 2.0 * 2.0;
  
  std::ios_base::sync_with_stdio(false);
  int n = atoi(argv[1]);

  std::cout << "P4\n" << n << " " << n << std::endl;

  for(int y=0; y<n; ++y) 
    for(int x=0; x<n; ++x)
    {
       std::complex<double> Z(0.0,0.0);
       std::complex<double> C(2*(double)x/n - 1.5, 2*(double)y/n - 1.0);
        
       for (int i=0; i<iter and norm(Z) <= limit_sqr; ++i)  Z = Z*Z + C;
        
       byte_acc = (byte_acc << 1) | ((norm(Z) > limit_sqr) ? 0x00:0x01);

       if(++bit_num == 8){ std::cout << byte_acc; bit_num = byte_acc = 0; }
       else if(x == n-1) { byte_acc  <<= (8-n%8);
                           std::cout << byte_acc;
                           bit_num = byte_acc = 0; }
    }
}