Here is a complete patch to add std::bfloat16_t support on
x86 (AArch64 and ARM left for later).  Almost no BFmode optabs
are added by the patch, so for binops/unops it extends to SFmode
first and then truncates back to BFmode.
For {HF,SF,DF,XF,TF}mode -> BFmode conversions libgcc has implementations
of all those conversions so that we avoid double rounding, for
BFmode -> {DF,XF,TF}mode conversions to avoid growing libgcc too much
it emits BFmode -> SFmode conversion first and then converts to the even
wider mode, neither step should be imprecise.
For BFmode -> HFmode, it first emits a precise BFmode -> SFmode conversion
and then SFmode -> HFmode, because neither format is subset or superset
of the other, while SFmode is superset of both.
expr.cc then contains a -ffast-math optimization of the BF -> SF and
SF -> BF conversions if we don't optimize for space (and for the latter
if -frounding-math isn't enabled either).
For x86, perhaps truncsfbf2 optab could be defined for TARGET_AVX512BF16
but IMNSHO should FAIL if !flag_finite_math || flag_rounding_math
|| !flag_unsafe_math_optimizations, because I think the insn doesn't
raise on sNaNs, hardcodes round to nearest and flushes denormals to zero.
By default (unless x86 -fexcess-precision=16) we use float excess
precision for BFmode, so truncate only on explicit casts and assignments.
The patch introduces a single __bf16 builtin - __builtin_nansf16b,
because (__bf16) __builtin_nansf ("") will drop the sNaN into qNaN,
and uses f16b suffix instead of bf16 because there would be ambiguity on
log vs. logb - __builtin_logbf16 could be either log with bf16 suffix
or logb with f16 suffix.  In other cases libstdc++ should mostly use
__builtin_*f for std::bfloat16_t overloads (we have a problem with
std::nextafter though but that one we have also for std::float16_t).

2022-10-14  Jakub Jelinek  <jakub@redhat.com>

gcc/
	* tree-core.h (enum tree_index): Add TI_BFLOAT16_TYPE.
	* tree.h (bfloat16_type_node): Define.
	* tree.cc (excess_precision_type): Promote bfloat16_type_mode
	like float16_type_mode.
	(build_common_tree_nodes): Initialize bfloat16_type_node if
	BFmode is supported.
	* expmed.h (maybe_expand_shift): Declare.
	* expmed.cc (maybe_expand_shift): No longer static.
	* expr.cc (convert_mode_scalar): Don't ICE on BF -> HF or HF -> BF
	conversions.  If there is no optab, handle BF -> {DF,XF,TF,HF}
	conversions as separate BF -> SF -> {DF,XF,TF,HF} conversions, add
	-ffast-math generic implementation for BF -> SF and SF -> BF
	conversions.
	* builtin-types.def (BT_BFLOAT16, BT_FN_BFLOAT16_CONST_STRING): New.
	* builtins.def (BUILT_IN_NANSF16B): New builtin.
	* fold-const-call.cc (fold_const_call): Handle CFN_BUILT_IN_NANSF16B.
	* config/i386/i386.cc (classify_argument): Handle E_BCmode.
	(ix86_libgcc_floating_mode_supported_p): Also return true for BFmode
	for -msse2.
	(ix86_mangle_type): Mangle BFmode as DF16b.
	(ix86_invalid_conversion, ix86_invalid_unary_op,
	ix86_invalid_binary_op): Remove.
	(TARGET_INVALID_CONVERSION, TARGET_INVALID_UNARY_OP,
	TARGET_INVALID_BINARY_OP): Don't redefine.
	* config/i386/i386-builtins.cc (ix86_bf16_type_node): Remove.
	(ix86_register_bf16_builtin_type): Use bfloat16_type_node rather than
	ix86_bf16_type_node, only create it if still NULL.
	* config/i386/i386-builtin-types.def (BFLOAT16): Likewise.
	* config/i386/i386.md (cbranchbf4, cstorebf4): New expanders.
gcc/c-family/
	* c-cppbuiltin.cc (c_cpp_builtins): If bfloat16_type_node,
	predefine __BFLT16_*__ macros and for C++23 also
	__STDCPP_BFLOAT16_T__.  Predefine bfloat16_type_node related
	macros for -fbuilding-libgcc.
	* c-lex.cc (interpret_float): Handle CPP_N_BFLOAT16.
gcc/c/
	* c-typeck.cc (convert_arguments): Don't promote __bf16 to
	double.
gcc/cp/
	* cp-tree.h (extended_float_type_p): Return true for
	bfloat16_type_node.
	* typeck.cc (cp_compare_floating_point_conversion_ranks): Set
	extended{1,2} if mv{1,2} is bfloat16_type_node.  Adjust comment.
gcc/testsuite/
	* lib/target-supports.exp (check_effective_target_bfloat16,
	check_effective_target_bfloat16_runtime, add_options_for_bfloat16):
	New.
	* gcc.dg/torture/bfloat16-basic.c: New test.
	* gcc.dg/torture/bfloat16-builtin.c: New test.
	* gcc.dg/torture/bfloat16-builtin-issignaling-1.c: New test.
	* gcc.dg/torture/bfloat16-complex.c: New test.
	* gcc.dg/torture/builtin-issignaling-1.c: Allow to be includable
	from bfloat16-builtin-issignaling-1.c.
	* gcc.dg/torture/floatn-basic.h: Allow to be includable from
	bfloat16-basic.c.
	* gcc.target/i386/vect-bfloat16-typecheck_2.c: Adjust expected
	diagnostics.
	* gcc.target/i386/sse2-bfloat16-scalar-typecheck.c: Likewise.
	* gcc.target/i386/vect-bfloat16-typecheck_1.c: Likewise.
	* g++.target/i386/bfloat_cpp_typecheck.C: Likewise.
libcpp/
	* include/cpplib.h (CPP_N_BFLOAT16): Define.
	* expr.cc (interpret_float_suffix): Handle bf16 and BF16 suffixes for
	C++.
libgcc/
	* config/i386/t-softfp (softfp_extensions): Add bfsf.
	(softfp_truncations): Add tfbf xfbf dfbf sfbf hfbf.
	(CFLAGS-extendbfsf2.c, CFLAGS-truncsfbf2.c, CFLAGS-truncdfbf2.c,
	CFLAGS-truncxfbf2.c, CFLAGS-trunctfbf2.c, CFLAGS-trunchfbf2.c): Add
	-msse2.
	* config/i386/libgcc-glibc.ver (GCC_13.0.0): Export
	__extendbfsf2 and __trunc{s,d,x,t,h}fbf2.
	* config/i386/sfp-machine.h (_FP_NANSIGN_B): Define.
	* config/i386/64/sfp-machine.h (_FP_NANFRAC_B): Define.
	* config/i386/32/sfp-machine.h (_FP_NANFRAC_B): Define.
	* soft-fp/brain.h: New file.
	* soft-fp/truncsfbf2.c: New file.
	* soft-fp/truncdfbf2.c: New file.
	* soft-fp/truncxfbf2.c: New file.
	* soft-fp/trunctfbf2.c: New file.
	* soft-fp/trunchfbf2.c: New file.
	* soft-fp/truncbfhf2.c: New file.
	* soft-fp/extendbfsf2.c: New file.
libiberty/
	* cp-demangle.h (D_BUILTIN_TYPE_COUNT): Increment.
	* cp-demangle.c (cplus_demangle_builtin_types): Add std::bfloat16_t
	entry.
	(cplus_demangle_type): Demangle DF16b.
	* testsuite/demangle-expected (_Z3xxxDF16b): New test.