libstdc++/10689: pow(std::complex(0),1/3) returns (nan, nan) instead of 0.

[Daniel.Levine@jhuapl.edu]

>Number:         10689
>Category:       libstdc++
>Synopsis:       pow(std::complex(0),1/3) returns (nan, nan) instead of 0.
>Confidential:   no
>Severity:       non-critical
>Priority:       medium
>Responsible:    unassigned
>State:          open
>Class:          wrong-code
>Submitter-Id:   net
>Arrival-Date:   Thu May 08 18:16:00 UTC 2003
>Closed-Date:
>Last-Modified:
>Originator:     Daniel Levine
>Release:        gcc 3.2-7
>Organization:
>Environment:
Any.
>Description:
Executing the pow(0,y) function call for doubles correctly produces return values of 0 as long as y != 0.  Doing the same with the pow(std::complex<double>(0),y) will return (nan, nan).  This appears to be caused by the log(x) when x is 0 returning nan as it should.  Further exp() will never return 0 so some check needs to be implemented so pow(std::complex<double>(0),y) can return 0 when y != 0.

This problem is not specific to complex<double>.  Other complex floating point types would suffer from the same problem.

One final note, pow(std::complex<double>(0), 1) works because it triggers other code while pow(std::complex<double>(0), 1.0) fails.
>How-To-Repeat:
#include <iostream>
using namespace std;
complex<double> complexZero;
complex<double> cubeRootOf0 = pow(complexZero, 1.0/3.0);
cerr << cubeRootof0 << endl; // Should be 0.0;
complex<double> zeroToThe1.0 = pow(complexZero, 1.0);
cerr << zeroToThe1.0 << endl; // Should be 0.0;
complex<double> zeroToThe1 = pow(complexZero, 1);
cerr << zeroToThe1 << endl; // Is 0.0;
>Fix:

>Release-Note:
>Audit-Trail:
>Unformatted: