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Subject: Re: [boost] Review request: extended complex number library
From: Matthieu Schaller (matthieu.schaller_at_[hidden])
Date: 2012-03-11 08:16:37

>> I am not sure people would easily give up the speed of the standard one
>> just to be able to handle numbers that should anyway never enter
>> everyday calculations.
>
> The underflow/overflow problem occurs with finite values.
>

True. But are you willing to give up speed for this ? It is a question
to everyone. I don't know what boost-members think. Some of the
boost::math functions are implemented in a very conservative way which
ensures a correct result in any case.

Looking at the standard (n3242 draft to be exact, the following elements
are, in my opinion, important:

26.4.0.3> If the result of a function is not mathematically defined or not in the range of representable values for its type, the behavior is undefined.

De-normalized numbers are apparently not supported.

26.4.0.4> If z is an lvalue expression of type cv std::complex<T> then:
— the expression reinterpret_cast<cv T(&)[2]>(z) shall be well-formed,
— reinterpret_cast<cv T(&)[2]>(z)[0] shall designate the real part of z, and
— reinterpret_cast<cv T(&)[2]>(z)[1] shall designate the imaginary part of z.
Moreover, if a is an expression of type cv std::complex<T>* and the expression a[i] is well-defined for an integer expression i, then:
— reinterpret_cast<cv T*>(a)[2*i] shall designate the real part of a[i], and
— reinterpret_cast<cv T*>(a)[2*i + 1] shall designate the imaginary part of a[i].

The implementation must thus contain a real and imaginary part.

26.4.8 states that the transcendental functions should behave as the
equivalent C functions. Nothing else is said about the precision of the
functions and operators.

So, if I'm correct, any implementation compliant with the standard
should contain a real en imaginary part but not support for
de-normalized numbers is necessary.
Apparently, the constructors (at least GCC and ICC) have chosen to use
the simplest solution: do nothing about these special cases.

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Matthieu Schaller
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