Re: [boost] Determining interest: Pure imaginary number library

Subject: Re: [boost] Determining interest: Pure imaginary number library
From: Vicente Botet (vicente.botet_at_[hidden])
Date: 2011-11-17 06:42:05

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&lt;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&lt;double&gt; 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/
> 
> 

Hi, I'm sure that if the performances can be improved, which seems logic,
the Boost community will be interested by your library.

Some comments related to the interface. I will replace

    T& imag();
    const T& imag() const;

by 

    T imag() const;

As there is no reason to provide non-const access to the internal
representation.
 
If these operations are needed by the non-member operators, maybe you can
declare them private and move non-member operators as members, or declare
them friends.

Comparing imaginary and reals seems confusing to me

///Returns true if x equals y
template<typename T>
inline bool operator==(const Imaginary<T>& x, const T& y);
template<typename T>
inline bool operator==(const T& x, const Imaginary<T>& y);

The following divide assign operator is missing:

 Imaginary<T>& operator/=(const Imaginary<T>& rhs)

I would also expect an implicit conversion to complex as an imaginary is
also a complex.

and a kind of imaginary downcast from complex.

template <typename T>
imaginary<T> imaginary_cast(complex<T> const & rhs);

My advice would be to boostify the code, write the documentation including
as much performances tests as you consider could help to consider this
library a should have.

Good luck,
Vicente

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