Interesting stuff but I found some minor problems with the code 1). in Imaginary.hpp on lines 293,300 * /// Returns the value of x divided by y template<typename T> inline Imaginary<T> operator/(const T& x, const Imaginary<T>& y) { Imaginary<T> r = y; r /= x; return r; } *as you can see there is an error in this we should be calculating x/y but instead y/x is calculated it should be Imaginary<T>(-x/y.imag()) i.e. x/(0 + y.imag()**/I/*) == x*(-*/i/*)/y.imag() 2). some of the comments are wrong in the cases of operator!=() on lines 383 & 390 & 397 & 404 & 411 it says ///Returns true if x equals y of course it should say true if x does not equal y no doubt you forgot to change them after cut/copy & paste thats how I make those sort of errors those are the only errors I found, simply beautiful code and very handy they should add it to the STL love your work Francis Grizzly Smit On 16/11/11 10:40, Matthieu Schaller wrote:
Dear all,
I have recently been playing a lot on numerical analysis problems containing complex numbers and functions. I have been using the SL std::complex<> library and could observe that some of the algorithms weren't optimized in cases where complex numbers have to be multiplied by pure imaginary numbers (i.e. x*sqrt(-1)). I have implemented a class to represent these numbers and overloaded all relevant operators in a more optimized fashion thanks to the knowledge that the real part of these complex numbers is 0. I could observe an important speed-up in some calculations. As an example, this piece of code (1D Schroedinger equation using finite differences):
for(size_t i(0); i<nbPoints; ++i) { Psi_new[i] = Psi_old[i] + ii * hbar * deltaT / (12.*m*deltaX*deltaX) * (-Psi_cur[i-2] + 16.*Psi_cur[i-1] - 30.*Psi_cur[i] + 16.*Psi_cur[i+1] - Psi_cur[i+2]) - 2. * ii * V(x[i]) / hbar * deltaT * Psi_cur[i];
}
is more than 2 times faster (g++ 4.6.1 core i7 2820QM) when the imaginary unit (constant) variable ii is defined to be
Imaginary<double> ii(1.);
than when it is defined as
std::complex<double> ii(0.,1.);
Some other expressions also benefit from this improvement and can run faster. Expressions including square roots or exponentials of pure imaginary numbers are improved a lot.
The range of application of such a class is quite narrow but it may be helpful to speed-up some simple numerical problems. The source code as well as a working example is available here: http://code.google.com/p/cpp-imaginary-numbers/
Thanks,
Matthieu
_______________________________________________ Unsubscribe& other changes: http://lists.boost.org/mailman/listinfo.cgi/boost