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### 595. TR1/C++0x: `fabs(complex<T>)` redundant / wrongly specified

Section: 28.4.7 [complex.value.ops] Status: CD1 Submitter: Stefan Große Pawig Opened: 2006-09-24 Last modified: 2016-01-28

Priority: Not Prioritized

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Discussion:

TR1 introduced, in the C compatibility chapter, the function `fabs(complex<T>)`:

>     ----- SNIP -----
>     8.1.1 Synopsis                                [tr.c99.cmplx.syn]

>       namespace std {
>       namespace tr1 {
>     [...]
>       template<class T> complex<T> fabs(const complex<T>& x);
>       } // namespace tr1
>       } // namespace std

>     [...]

>     8.1.8 Function fabs                          [tr.c99.cmplx.fabs]

>     1 Effects: Behaves the same as C99 function cabs, defined in
>       subclause 7.3.8.1.
>     ----- SNIP -----

The current C++0X draft document (n2009.pdf) adopted this definition in chapter 26.3.1 (under the comment // 26.3.7 values) and 26.3.7/7.

But in C99 (ISO/IEC 9899:1999 as well as the 9899:TC2 draft document n1124), the referenced subclause reads

>     ----- SNIP -----
>     7.3.8.1 The cabs functions

>       Synopsis

>     1 #include <complex.h>
>       double cabs(double complex z);
>       float cabsf(float complex z);
>       long double cabsl(long double z);

>       Description

>     2 The cabs functions compute the complex absolute value (also called
>       norm, modulus, or magnitude) of z.

>       Returns

>     3 The cabs functions return the complex absolute value.
>     ----- SNIP -----

Note that the return type of the cabs*() functions is not a complex type. Thus, they are equivalent to the already well established template<class T> T abs(const complex<T>& x); (26.2.7/2 in ISO/IEC 14882:1998, 26.3.7/2 in the current draft document n2009.pdf).

So either the return value of fabs() is specified wrongly, or fabs() does not behave the same as C99's cabs*().

Possible Resolutions

This depends on the intention behind the introduction of fabs().

If the intention was to provide a /complex/ valued function that calculates the magnitude of its argument, this should be explicitly specified. In TR1, the categorization under "C compatibility" is definitely wrong, since C99 does not provide such a complex valued function.

Also, it remains questionable if such a complex valued function is really needed, since complex<T> supports construction and assignment from real valued arguments. There is no difference in observable behaviour between

>       complex<double> x, y;
>       y = fabs(x);
>       complex<double> z(fabs(x));

and

>       complex<double> x, y;
>       y = abs(x);
>       complex<double> z(abs(x));

If on the other hand the intention was to provide the intended functionality of C99, fabs() should be either declared deprecated or (for C++0X) removed from the standard, since the functionality is already provided by the corresponding overloads of abs().

[ Bellevue: ]

> Bill believes that `abs()` is a suitable overload. We should remove `fabs()`.

Proposed resolution:

Change the synopsis in 28.4.2 [complex.syn]:

>     template<class T> complex<T> fabs(const complex<T>&);

Remove 28.4.7 [complex.value.ops], p7:

>     template<class T> complex<T> fabs(const complex<T>& x);

> > -7- Effects: Behaves the same as C99 function `cabs`, defined in subclause 7.3.8.1.

[ Kona (2007): Change the return type of `fabs(complex)` to `T`. Proposed Disposition: Ready ]