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The GNU Fortran compiler implements ISO/IEC 1539:1997 (Fortran 95). As such, it can also compile essentially all standard-compliant Fortran 90 and Fortran 77 programs. It also supports the ISO/IEC TR-15581 enhancements to allocatable arrays.
GNU Fortran also have a partial support for ISO/IEC 1539-1:2004 (Fortran
2003), ISO/IEC 1539-1:2010 (Fortran 2008), the Technical Specification
Further Interoperability of Fortran with C (ISO/IEC TS 29113:2012).
Full support of those standards and future Fortran standards is planned.
The current status of the support is can be found in the
Fortran 2003 status, Fortran 2008 status, TS 29113 status
and TS 18508 status sections of the documentation.
Additionally, the GNU Fortran compilers supports the OpenMP specification (version 4.0 and most of the features of the 4.5 version, http://openmp.org/wp/openmp-specifications/). There also is initial support for the OpenACC specification (targeting version 2.0, http://www.openacc.org/). Note that this is an experimental feature, incomplete, and subject to change in future versions of GCC. See https://gcc.gnu.org/wiki/OpenACC for more information.