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