All, 

I have attached a new patch to 

https://gcc.gnu.org/bugzilla/show_bug.cgi?id=113152

which addresses the following issues.

PR113152 -- implement half-cycle trigonometric functions
PR113412 -- better error message for atan(y,x)
PR113413 -- implement atand(y,x)

The patch clocks in at 3488 lines, so will not be attached
here.   

There are a few items that may need some explanation.  First, some
(if not all) of the half-cycle functions are contained in ISO/IEC
TS 18661-4, IEEE754-2008, and now Fortran 2023.  The patch assumes
that an OS's libm may/will contain cospi(), etc. (see for example
FreeBSD's libm).  If these are not in libm, then fallback routines
are provided by libgfortran.  The fallback routines have seen limited
testing, so your mileage may vary.  Second, I have no idea what REAL17
entails; however, I provide untested routines in trigpi_fallback2.F90
where I use REAL(16) in the declarations (yikes).  Third, MPFR provides
half-cycle functions in version 4.2.0 (and later).  For simplicifation,
the patch checks for an adequate MPFR version, if an older version is
found fallback algorithms are used.  These have had limited testing.

The patch appears to pass regression testing. Hopefully, someone will
find time to test and commit the patch.  The remainder is an attempt
to write ChangeLog entries.

gcc/fortran:

        * gfortran.h (gfc_isym_id): Add GFC_ISYM_ACOSPI, GFC_ISYM_ASINPI,
        GFC_ISYM_ATANPI, GFC_ISYM_ATAN2PI, GFC_ISYM_COSPI, GFC_ISYM_SINPI, and
        GFC_ISYM_TANPI
        * intrinsic.cc (do_check): Whitespace and typo in comments.
        (add_functions): Add two-argument form of ATAND.  Add half-cycle 
        trigonometric functions ACOSPI, ASINPI, ATANPI, ATAN2PI, COSPI,
        SINPI, and TANPI.
        (sort_actual): Generate sensible error messages for two argument
        versions of ATAN, ATAND, and ATANPI.
        * intrinsic.h: New prototypes for gfc_simplify_acospi, 
        gfc_simplify_asinpi, gfc_simplify_atanpi, gfc_simplify_atan2pi,
        gfc_simplify_cospi, gfc_simplify_sinpi, gfc_simplify_tanpi,
        gfc_resolve_acospi, gfc_resolve_asinpi, gfc_resolve_atanpi,
        gfc_resolve_atan2pi, gfc_resolve_cospi, gfc_resolve_sinpi, and
        gfc_resolve_tanpi
        * intrinsic.texi: Document new functions ACOSPI, ASINPI, ATANPI,
        ATAN2PI, COSPI, SINPI, and TANPI.  Put the ATAN* family of functions
        in lexigraphical order.
        * iresolve.cc (gfc_resolve_acospi, gfc_resolve_asinpi,
        gfc_resolve_atanpi, gfc_resolve_atan2pi, gfc_resolve_cospi,
        gfc_resolve_sinpi, gfc_resolve_tanpi):  New functions.
        * simplify.cc (gfc_simplify_acospi, gfc_simplify_asinpi,
        gfc_simplify_atanpi, gfc_simplify_atan2pi, gfc_simplify_cospi,
        gfc_simplify_sinpi, gfc_simplify_tanpi): New functions.
        Introduce MPFR_HALF_CYCLE macros to use MPFR half-cycle functions
        if available.
        * trans-intrinsic.cc: Declare asinpi, acospi, atanpi, atan2pi, sinpi, 
        cospi, and tanpi as LIB_FUNCTION's.

libgfortran:

        *Makefile.am: New files trigpi.c, trigpi_fallback1.c, and
        trigpi_fallback2.F90
        * configure.ac: Check libm for float, double, and long double
        functions for asinpi, acospi, atanpi, atan2pi, sinpi, cospi, and
        tanpi
        * Makefile.in: Regenerated.
        * config.h.in: Ditto.
        * configure: Ditto.
        * gfortran.map: Add GFORTRAN_14 section to expose the library
        symbols.
        * trigpi.c: Fallback implementations of the half-cycle trigonometric
        functions.
        * trigpi_fallback1.c: Fallback functions for float, double, and
        long double routines if libm does provide them.
        * trigpi_fallback2.F90: REAL(16)/REAL(17?) fallback implementations
        of the half-cycle trigonometric functions.

-- 
Steve

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