Here is another patch to complete __gnu_debug::basic_string<> Standard 
conformity. This one is adding the missing compare overloads.

I also would like to propose to change how __gnu_debug::basic_string<> 
is tested. I considered activating <bits/basic_string.h> checks when 
_GLIBCXX_ASSERTIONS is defined but it turns out that to do so this 
light-debug mode should then also consider _GLIBCXX_DEBUG_PEDANTIC. I 
prefer to avoid this.

So I restored previous behavior. I'm now checking for the 
_GLIBCXX_TEST_DEBUG_STRING macro to force usage of <debug/string>. This 
way I am testing it using:

make check-debug CXXFLAGS=-D_GLIBCXX_TEST_DEBUG_STRING

     libstdc++: Add __gnu_debug::basic_string<>::compare overloads

     Rather than adding those implementations we are ading a:
     using _Base::compare;

     so that any compare method not implemented at __gnu_debug::basic_string
     level are injected from the base class.

     Also review how __gnu_debug::basic_string is tested. Now require to 
define
     _GLIBCXX_TEST_DEBUG_STRING when running 'make check-debug'.

     libstdc++-v3/ChangeLog

             * include/debug/string: Add using _Base::compare.
             (__gnu_debug::basic_string<>::compare(const 
basic_string<>&)): Remove.
             (__gnu_debug::basic_string<>::compare(size_type, size_type, 
const basic_string<>&)):
             Remove.
             (__gnu_debug::basic_string<>::compare(size_type, size_type, 
const basic_string<>&,
             size_type, size_type)): Remove.
             * testsuite/util/testsuite_string.h 
[_GLIBCXX_TEST_DEBUG_STRING]: Include <debug/string>.
             * 
testsuite/21_strings/basic_string/operations/compare/char/1.cc: Include 
testsuite_string.h
             and use __gnu_test::string.
             * 
testsuite/21_strings/basic_string/operations/compare/char/13650.cc: 
Likewise.
             * 
testsuite/21_strings/basic_string/operations/compare/char/2.cc: Likewise.
             * 
testsuite/21_strings/basic_string/operations/rfind/char/1.cc: Likewise.
             * 
testsuite/21_strings/basic_string/operations/rfind/char/2.cc: Likewise.
             * 
testsuite/21_strings/basic_string/operations/rfind/char/3.cc: Likewise.
             * 
testsuite/21_strings/basic_string/operations/compare/wchar_t/1.cc: 
Include testsuite_string.h
             and use __gnu_test::wstring.
             * 
testsuite/21_strings/basic_string/operations/compare/wchar_t/13650.cc: 
Likewise.
             * 
testsuite/21_strings/basic_string/operations/compare/wchar_t/2.cc: Likewise.

Tested under Linux x86_64.

Ok to commit ?

François