Re: wrong result in complex pow

From: John Maddock (jz.maddock_at_[hidden])
Date: 2021-02-05 17:00:00

On 04/02/2021 20:23, Gero Peterhoff via Boost wrote:
> Hello Chris,
> Unfortunately, a few things have come up with me so that I (probably) won't be able to really help in the near future.
> Some other functions (e.g. log, exp) also give incorrect results for some combinations of nan, inf and 0.

The place to check for this is C99 Annex G - but note that this is 
non-normative so there will be implementations of std::complex which do 
not do anything in particular in these cases... platforms too with no 
infinity or NaN.

> But I saw that gcc libquadmath (https://gcc.gnu.org/onlinedocs/libquadmath/Math-Library-Routines.html#Math-Library-Routines) offers some complex functions that work correctly. These could be used. But I don't know if clang, intel and/or other compilers can do that too.
> example
> inline complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE> log(const complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>& x)
> {
> 	__complex128
> 		res = __complex128{x.real(), x.imag()};
> 	res = clogq(res);
> 	return complex<BOOST_CSTDFLOAT_EXTENDED_COMPLEX_FLOAT_TYPE>{crealq(res), cimagq(res)};
> }
>
> I also noticed a few basic things, maybe you can say why that is:
> - Why are there explicit complex classes for FP types, why is this not implemented completely via template? The advantage is that built-ins can be used, on the other hand, a separate class must be written for each FP type - with the problems we are currently having.
This is all a question for the C++ committee, my speculation would be 
that they wished to restrict the scope of std::complex to 
float/double/long double.
> - Why are there missing template conversion ctors for the complex<FP-Type>? That will not do:
> std::complex<int> ci{4711, 23};
> std::complex<double> cd=ci;
> or
> std::complex<double> cd = std::complex<double>{ci};
> but a ctor must be called explicitly
> std::complex<double> cd=std::complex<double>{double(ci.real()), double(ci.imag())}; // prevent warnings
> It's really annoying.
> - Why are many std-math functions missing for complex; special-functions complete (also applies to std::valarray)?
>
> I want to add such things in my math-lib, as far as possible everything constexpr. I also want to provide additional classes for dual and splitcomplex numbers (i²=0, i²=1, but it is far from complete - because it is quite extensive). Maybe these could also be included in boost. To do this, however, it would be necessary to convert the boost-math-lib to C++20, since some functions (or the distinction between dual, complex and splitcomplex - classes/functions) is only possible with concepts (otherwise unreasonable effort). I also need some additional typetraits.

If you want to provide implementations for any complex valued special 
functions we can take care of the algorithm overload selection - 
enable_if will do fine, there's no need for concepts just yet.

Best John.

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