[RFC] c++, i386, arm, aarch64, libgcc: std::bfloat16_t and __bf16 arithmetic support

Message ID YzXABvJX2wl3gHkK@tucnak
State New, archived
Headers
Series [RFC] c++, i386, arm, aarch64, libgcc: std::bfloat16_t and __bf16 arithmetic support |

Commit Message

Jakub Jelinek Sept. 29, 2022, 3:55 p.m. UTC
  Hi!

Here is more complete patch to add std::bfloat16_t support on
x86, AArch64 and (only partially) on ARM 32-bit.  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.
In C by default (unless x86 -fexcess-precision=16) we use float excess
precision for BFmode, so truncate only on explicit casts and assignments.
In C++ unfortunately (but that is the case of also _Float16) we don't
support excess precision yet which means that for
__bf16 (__bf16 a, __bf16 b, __bf16 c, __bf16 d) { return a * b + c * d; }
we do a lot of conversions.
The aarch64 part is untested but has a chance of working (IMHO),
though I'd appreciate if ARM maintainers could decide whether it is
acceptable for them that __bf16 changes mangling and will allow arithmetics
and conversions.
The arm part is partial, libgcc side is missing as the target doesn't really
seem to use soft-fp right now.  Perhaps the config/arm/ changes can be
left out from the patch (thus keep ARM 32-bit __bf16 as before) and support
for it can be done at some later time.

Thoughts on this?

2022-09-29  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.
	* 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.
	* config/arm/arm.h (arm_bf16_type_node): Remove.
	(arm_bf16_ptr_type_node): Adjust comment.
	* config/arm/arm.cc (TARGET_INVALID_UNARY_OP,
	TARGET_INVALID_BINARY_OP): Don't redefine.
	(arm_mangle_type): Mangle BFmode as DFb16_.
	(arm_invalid_conversion): Only reject BF <-> HF conversions if
	HFmode is non-IEEE format.
	(arm_invalid_unary_op, arm_invalid_binary_op): Remove.
	* config/arm/arm-builtins.cc (arm_bf16_type_node): Remove.
	(arm_simd_builtin_std_type): Use bfloat16_type_node rather than
	arm_bf16_type_node.
	(arm_init_simd_builtin_types): Likewise.
	(arm_init_simd_builtin_scalar_types): Likewise.
	(arm_init_bf16_types): Likewise.
	* config/i386/i386.cc (ix86_mangle_type): Mangle BFmode as DFb16_.
	(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.
	* config/i386/i386-builtin-types.def (BFLOAT16): Likewise.
	* config/aarch64/aarch64.h (aarch64_bf16_type_node): Remove.
	(aarch64_bf16_ptr_type_node): Adjust comment.
	* config/aarch64/aarch64.cc (aarch64_gimplify_va_arg_expr): Use
	bfloat16_type_node rather than aarch64_bf16_type_node.
	(aarch64_mangle_type): Mangle BFmode as DFb16_.
	(aarch64_invalid_conversion, aarch64_invalid_unary_op): Remove.
	aarch64_invalid_binary_op): Remove BFmode related rejections.
	(TARGET_INVALID_CONVERSION, TARGET_INVALID_UNARY_OP): Don't redefine.
	* config/aarch64/aarch64-builtins.cc (aarch64_bf16_type_node): Remove.
	(aarch64_int_or_fp_type): Use bfloat16_type_node rather than
	aarch64_bf16_type_node.
	(aarch64_init_simd_builtin_types, aarch64_init_bf16_types): Likewise.
	* config/aarch64/aarch64-sve-builtins.def (svbfloat16_t): Likewise.
gcc/c-family/
	* c-cppbuiltin.cc (c_cpp_builtins): If bfloat16_type_node,
	predefine for C++ __BFLT16_*__ macros and for C++23 also
	__STDCPP_BFLOAT16_T__.
	* c-lex.cc (interpret_float): Handle CPP_N_BFLOAT16 for C++.
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.
libcpp/
	* include/cpplib.h (CPP_N_BFLOAT16): Define.
	* expr.cc (interpret_float_suffix): Handle bf16 and BF16 suffixes for
	C++.
libgcc/
	* config/arm/sfp-machine.h (_FP_NANFRAC_B): Define.
	* config/aarch64/t-softfp (softfp_extensions): Add bfsf.
	(softfp_truncations): Add tfbf dfbf sfbf hfbf.
	* config/aarch64/libgcc-softfp.ver (GCC_13.0.0): Export
	__extendbfsf2 and __trunc{s,d,t,h}fbf2.
	* config/aarch64/sfp-machine.h (_FP_NANFRAC_B): Define.
	* config/i386/t-softfp (softfp_extensions): Add bfsf.
	(softfp_truncations): Add tfbf xfbf dfbf sfbf hfbf.
	* 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 DFb16_.
	* testsuite/demangle-expected (_Z3xxxDFb16_): New test.


	Jakub
  

Comments

Jason Merrill Sept. 30, 2022, 1:49 p.m. UTC | #1
On 9/29/22 11:55, Jakub Jelinek wrote:
> Hi!
> 
> Here is more complete patch to add std::bfloat16_t support on
> x86, AArch64 and (only partially) on ARM 32-bit.  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.
> In C by default (unless x86 -fexcess-precision=16) we use float excess
> precision for BFmode, so truncate only on explicit casts and assignments.
> In C++ unfortunately (but that is the case of also _Float16) we don't
> support excess precision yet which means that for
> __bf16 (__bf16 a, __bf16 b, __bf16 c, __bf16 d) { return a * b + c * d; }
> we do a lot of conversions.

The comment from Apple on the ABI mangling proposal suggests to me that 
we might want to delay enabling C++ std::bfloat16_t (i.e. defining 
__STDCPP_BFLOAT16_T__) until we have that excess precision support?

"Steve [Cannon] is concerned that adding this type as an arithmetic type 
might serve to be an attractive nuisance. Because the precision of 
bfloat16 is so limited, controlling when truncation back to bfloat16 
occurs is of paramount practical importance to bfloat16 users. The 
normal semantics of an arithmetic type in C and C++ encourage the 
independent evaluation of operations, which would require an implicit 
truncation back to bfloat16 on every intermediate result. That would 
have catastrophic effects on both the precision and the performance of 
typical bfloat16 code. For example, on the performance side, typical 
hardware support is built around complex fused operations (e.g. float32 
+= bfloat16 * bfloat16 + bfloat16 * bfloat16, with all intermediate 
results computed in float32) that it would not be correct to 
pattern-match from independent operations.

Now, C and C++ do allow excess precision evaluation (C 6.5p8; C++ 
[expr.pre]p6), and Steve and I think that that might fix this problem. 
But we'd really need to force excess precision evaluation in order to 
get acceptable results; otherwise, allowing arithmetic is really just 
encouraging people to write code that is effectively incorrect. And even 
then there's definitely risk that someone might e.g. accumulate the 
intermediate results of a loop in std::bfloat16_t instead of in float."

> The aarch64 part is untested but has a chance of working (IMHO),
> though I'd appreciate if ARM maintainers could decide whether it is
> acceptable for them that __bf16 changes mangling and will allow arithmetics
> and conversions.
> The arm part is partial, libgcc side is missing as the target doesn't really
> seem to use soft-fp right now.  Perhaps the config/arm/ changes can be
> left out from the patch (thus keep ARM 32-bit __bf16 as before) and support
> for it can be done at some later time.
> 
> Thoughts on this?
> 
> 2022-09-29  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.
> 	* 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.
> 	* config/arm/arm.h (arm_bf16_type_node): Remove.
> 	(arm_bf16_ptr_type_node): Adjust comment.
> 	* config/arm/arm.cc (TARGET_INVALID_UNARY_OP,
> 	TARGET_INVALID_BINARY_OP): Don't redefine.
> 	(arm_mangle_type): Mangle BFmode as DFb16_.

If we're using DF32x for _Float32x, maybe we want DF16b for bfloat16?

> 	(arm_invalid_conversion): Only reject BF <-> HF conversions if
> 	HFmode is non-IEEE format.
> 	(arm_invalid_unary_op, arm_invalid_binary_op): Remove.
> 	* config/arm/arm-builtins.cc (arm_bf16_type_node): Remove.
> 	(arm_simd_builtin_std_type): Use bfloat16_type_node rather than
> 	arm_bf16_type_node.
> 	(arm_init_simd_builtin_types): Likewise.
> 	(arm_init_simd_builtin_scalar_types): Likewise.
> 	(arm_init_bf16_types): Likewise.
> 	* config/i386/i386.cc (ix86_mangle_type): Mangle BFmode as DFb16_.
> 	(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.
> 	* config/i386/i386-builtin-types.def (BFLOAT16): Likewise.
> 	* config/aarch64/aarch64.h (aarch64_bf16_type_node): Remove.
> 	(aarch64_bf16_ptr_type_node): Adjust comment.
> 	* config/aarch64/aarch64.cc (aarch64_gimplify_va_arg_expr): Use
> 	bfloat16_type_node rather than aarch64_bf16_type_node.
> 	(aarch64_mangle_type): Mangle BFmode as DFb16_.
> 	(aarch64_invalid_conversion, aarch64_invalid_unary_op): Remove.
> 	aarch64_invalid_binary_op): Remove BFmode related rejections.
> 	(TARGET_INVALID_CONVERSION, TARGET_INVALID_UNARY_OP): Don't redefine.
> 	* config/aarch64/aarch64-builtins.cc (aarch64_bf16_type_node): Remove.
> 	(aarch64_int_or_fp_type): Use bfloat16_type_node rather than
> 	aarch64_bf16_type_node.
> 	(aarch64_init_simd_builtin_types, aarch64_init_bf16_types): Likewise.
> 	* config/aarch64/aarch64-sve-builtins.def (svbfloat16_t): Likewise.
> gcc/c-family/
> 	* c-cppbuiltin.cc (c_cpp_builtins): If bfloat16_type_node,
> 	predefine for C++ __BFLT16_*__ macros and for C++23 also
> 	__STDCPP_BFLOAT16_T__.
> 	* c-lex.cc (interpret_float): Handle CPP_N_BFLOAT16 for C++.
> 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.
> libcpp/
> 	* include/cpplib.h (CPP_N_BFLOAT16): Define.
> 	* expr.cc (interpret_float_suffix): Handle bf16 and BF16 suffixes for
> 	C++.
> libgcc/
> 	* config/arm/sfp-machine.h (_FP_NANFRAC_B): Define.
> 	* config/aarch64/t-softfp (softfp_extensions): Add bfsf.
> 	(softfp_truncations): Add tfbf dfbf sfbf hfbf.
> 	* config/aarch64/libgcc-softfp.ver (GCC_13.0.0): Export
> 	__extendbfsf2 and __trunc{s,d,t,h}fbf2.
> 	* config/aarch64/sfp-machine.h (_FP_NANFRAC_B): Define.
> 	* config/i386/t-softfp (softfp_extensions): Add bfsf.
> 	(softfp_truncations): Add tfbf xfbf dfbf sfbf hfbf.
> 	* 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 DFb16_.
> 	* testsuite/demangle-expected (_Z3xxxDFb16_): New test.
> 
> --- gcc/tree-core.h.jj	2022-09-29 09:13:25.717718458 +0200
> +++ gcc/tree-core.h	2022-09-29 12:40:17.417778754 +0200
> @@ -665,6 +665,9 @@ enum tree_index {
>     TI_DOUBLE_TYPE,
>     TI_LONG_DOUBLE_TYPE,
>   
> +  /* __bf16 type if supported (used in C++ as std::bfloat16_t).  */
> +  TI_BFLOAT16_TYPE,
> +
>     /* The _FloatN and _FloatNx types must be consecutive, and in the
>        same sequence as the corresponding complex types, which must also
>        be consecutive; _FloatN must come before _FloatNx; the order must
> --- gcc/tree.h.jj	2022-09-29 09:13:25.720718416 +0200
> +++ gcc/tree.h	2022-09-29 12:40:17.416778768 +0200
> @@ -4285,6 +4285,7 @@ tree_strip_any_location_wrapper (tree ex
>   #define float_type_node			global_trees[TI_FLOAT_TYPE]
>   #define double_type_node		global_trees[TI_DOUBLE_TYPE]
>   #define long_double_type_node		global_trees[TI_LONG_DOUBLE_TYPE]
> +#define bfloat16_type_node		global_trees[TI_BFLOAT16_TYPE]
>   
>   /* Nodes for particular _FloatN and _FloatNx types in sequence.  */
>   #define FLOATN_TYPE_NODE(IDX)		global_trees[TI_FLOATN_TYPE_FIRST + (IDX)]
> --- gcc/tree.cc.jj	2022-09-29 09:13:31.328641080 +0200
> +++ gcc/tree.cc	2022-09-29 12:40:17.400778985 +0200
> @@ -7711,7 +7711,7 @@ excess_precision_type (tree type)
>       = (flag_excess_precision == EXCESS_PRECISION_FAST
>          ? EXCESS_PRECISION_TYPE_FAST
>          : (flag_excess_precision == EXCESS_PRECISION_FLOAT16
> -	  ? EXCESS_PRECISION_TYPE_FLOAT16 :EXCESS_PRECISION_TYPE_STANDARD));
> +	  ? EXCESS_PRECISION_TYPE_FLOAT16 : EXCESS_PRECISION_TYPE_STANDARD));
>   
>     enum flt_eval_method target_flt_eval_method
>       = targetm.c.excess_precision (requested_type);
> @@ -7736,6 +7736,9 @@ excess_precision_type (tree type)
>     machine_mode float16_type_mode = (float16_type_node
>   				    ? TYPE_MODE (float16_type_node)
>   				    : VOIDmode);
> +  machine_mode bfloat16_type_mode = (bfloat16_type_node
> +				     ? TYPE_MODE (bfloat16_type_node)
> +				     : VOIDmode);
>     machine_mode float_type_mode = TYPE_MODE (float_type_node);
>     machine_mode double_type_mode = TYPE_MODE (double_type_node);
>   
> @@ -7747,16 +7750,19 @@ excess_precision_type (tree type)
>   	switch (target_flt_eval_method)
>   	  {
>   	  case FLT_EVAL_METHOD_PROMOTE_TO_FLOAT:
> -	    if (type_mode == float16_type_mode)
> +	    if (type_mode == float16_type_mode
> +		|| type_mode == bfloat16_type_mode)
>   	      return float_type_node;
>   	    break;
>   	  case FLT_EVAL_METHOD_PROMOTE_TO_DOUBLE:
>   	    if (type_mode == float16_type_mode
> +		|| type_mode == bfloat16_type_mode
>   		|| type_mode == float_type_mode)
>   	      return double_type_node;
>   	    break;
>   	  case FLT_EVAL_METHOD_PROMOTE_TO_LONG_DOUBLE:
>   	    if (type_mode == float16_type_mode
> +		|| type_mode == bfloat16_type_mode
>   		|| type_mode == float_type_mode
>   		|| type_mode == double_type_mode)
>   	      return long_double_type_node;
> @@ -7774,16 +7780,19 @@ excess_precision_type (tree type)
>   	switch (target_flt_eval_method)
>   	  {
>   	  case FLT_EVAL_METHOD_PROMOTE_TO_FLOAT:
> -	    if (type_mode == float16_type_mode)
> +	    if (type_mode == float16_type_mode
> +		|| type_mode == bfloat16_type_mode)
>   	      return complex_float_type_node;
>   	    break;
>   	  case FLT_EVAL_METHOD_PROMOTE_TO_DOUBLE:
>   	    if (type_mode == float16_type_mode
> +		|| type_mode == bfloat16_type_mode
>   		|| type_mode == float_type_mode)
>   	      return complex_double_type_node;
>   	    break;
>   	  case FLT_EVAL_METHOD_PROMOTE_TO_LONG_DOUBLE:
>   	    if (type_mode == float16_type_mode
> +		|| type_mode == bfloat16_type_mode
>   		|| type_mode == float_type_mode
>   		|| type_mode == double_type_mode)
>   	      return complex_long_double_type_node;
> --- gcc/expmed.h.jj	2022-07-26 10:32:23.681271790 +0200
> +++ gcc/expmed.h	2022-09-29 15:18:46.457023535 +0200
> @@ -707,6 +707,8 @@ extern rtx expand_variable_shift (enum t
>   				  rtx, tree, rtx, int);
>   extern rtx expand_shift (enum tree_code, machine_mode, rtx, poly_int64, rtx,
>   			 int);
> +extern rtx maybe_expand_shift (enum tree_code, machine_mode, rtx, int, rtx,
> +			       int);
>   #ifdef GCC_OPTABS_H
>   extern rtx expand_divmod (int, enum tree_code, machine_mode, rtx, rtx,
>   			  rtx, int, enum optab_methods = OPTAB_LIB_WIDEN);
> --- gcc/expmed.cc.jj	2022-08-31 10:20:20.000000000 +0200
> +++ gcc/expmed.cc	2022-09-29 15:17:52.224769673 +0200
> @@ -2705,7 +2705,7 @@ expand_shift (enum tree_code code, machi
>   
>   /* Likewise, but return 0 if that cannot be done.  */
>   
> -static rtx
> +rtx
>   maybe_expand_shift (enum tree_code code, machine_mode mode, rtx shifted,
>   		    int amount, rtx target, int unsignedp)
>   {
> --- gcc/expr.cc.jj	2022-09-09 09:50:35.228575531 +0200
> +++ gcc/expr.cc	2022-09-29 17:09:46.716352938 +0200
> @@ -344,7 +344,11 @@ convert_mode_scalar (rtx to, rtx from, i
>         gcc_assert ((GET_MODE_PRECISION (from_mode)
>   		   != GET_MODE_PRECISION (to_mode))
>   		  || (DECIMAL_FLOAT_MODE_P (from_mode)
> -		      != DECIMAL_FLOAT_MODE_P (to_mode)));
> +		      != DECIMAL_FLOAT_MODE_P (to_mode))
> +		  || (REAL_MODE_FORMAT (from_mode) == &arm_bfloat_half_format
> +		      && REAL_MODE_FORMAT (to_mode) == &ieee_half_format)
> +		  || (REAL_MODE_FORMAT (to_mode) == &arm_bfloat_half_format
> +		      && REAL_MODE_FORMAT (from_mode) == &ieee_half_format));
>   
>         if (GET_MODE_PRECISION (from_mode) == GET_MODE_PRECISION (to_mode))
>   	/* Conversion between decimal float and binary float, same size.  */
> @@ -364,6 +368,150 @@ convert_mode_scalar (rtx to, rtx from, i
>   	  return;
>   	}
>   
> +#ifdef HAVE_SFmode
> +      if (REAL_MODE_FORMAT (from_mode) == &arm_bfloat_half_format
> +	  && REAL_MODE_FORMAT (SFmode) == &ieee_single_format)
> +	{
> +	  if (GET_MODE_PRECISION (to_mode) > GET_MODE_PRECISION (SFmode))
> +	    {
> +	      /* To cut down on libgcc size, implement
> +		 BFmode -> {DF,XF,TF}mode conversions by
> +		 BFmode -> SFmode -> {DF,XF,TF}mode conversions.  */
> +	      rtx temp = gen_reg_rtx (SFmode);
> +	      convert_mode_scalar (temp, from, unsignedp);
> +	      convert_mode_scalar (to, temp, unsignedp);
> +	      return;
> +	    }
> +	  if (REAL_MODE_FORMAT (to_mode) == &ieee_half_format)
> +	    {
> +	      /* Similarly, implement BFmode -> HFmode as
> +		 BFmode -> SFmode -> HFmode conversion where SFmode
> +		 has superset of BFmode values.  We don't need
> +		 to handle sNaNs by raising exception and turning
> +		 into into qNaN though, as that can be done in the
> +		 SFmode -> HFmode conversion too.  */
> +	      rtx temp = gen_reg_rtx (SFmode);
> +	      int save_flag_finite_math_only = flag_finite_math_only;
> +	      flag_finite_math_only = true;
> +	      convert_mode_scalar (temp, from, unsignedp);
> +	      flag_finite_math_only = save_flag_finite_math_only;
> +	      convert_mode_scalar (to, temp, unsignedp);
> +	      return;
> +	    }
> +	  if (to_mode == SFmode
> +	      && !HONOR_NANS (from_mode)
> +	      && !HONOR_NANS (to_mode)
> +	      && optimize_insn_for_speed_p ())
> +	    {
> +	      /* If we don't expect sNaNs, for BFmode -> SFmode we can just
> +		 shift the bits up.  */
> +	      machine_mode fromi_mode, toi_mode;
> +	      if (int_mode_for_size (GET_MODE_BITSIZE (from_mode),
> +				     0).exists (&fromi_mode)
> +		  && int_mode_for_size (GET_MODE_BITSIZE (to_mode),
> +					0).exists (&toi_mode))
> +		{
> +		  start_sequence ();
> +		  rtx fromi = lowpart_subreg (fromi_mode, from, from_mode);
> +		  rtx tof = NULL_RTX;
> +		  if (fromi)
> +		    {
> +		      rtx toi = gen_reg_rtx (toi_mode);
> +		      convert_mode_scalar (toi, fromi, 1);
> +		      toi
> +			= maybe_expand_shift (LSHIFT_EXPR, toi_mode, toi,
> +					      GET_MODE_PRECISION (to_mode)
> +					      - GET_MODE_PRECISION (from_mode),
> +					      NULL_RTX, 1);
> +		      if (toi)
> +			{
> +			  tof = lowpart_subreg (to_mode, toi, toi_mode);
> +			  if (tof)
> +			    emit_move_insn (to, tof);
> +			}
> +		    }
> +		  insns = get_insns ();
> +		  end_sequence ();
> +		  if (tof)
> +		    {
> +		      emit_insn (insns);
> +		      return;
> +		    }
> +		}
> +	    }
> +	}
> +      if (REAL_MODE_FORMAT (from_mode) == &ieee_single_format
> +	  && REAL_MODE_FORMAT (to_mode) == &arm_bfloat_half_format
> +	  && !HONOR_NANS (from_mode)
> +	  && !HONOR_NANS (to_mode)
> +	  && !flag_rounding_math
> +	  && optimize_insn_for_speed_p ())
> +	{
> +	  /* If we don't expect qNaNs nor sNaNs and can assume rounding
> +	     to nearest, we can expand the conversion inline as
> +	     (fromi + 0x7fff + ((fromi >> 16) & 1)) >> 16.  */
> +	  machine_mode fromi_mode, toi_mode;
> +	  if (int_mode_for_size (GET_MODE_BITSIZE (from_mode),
> +				 0).exists (&fromi_mode)
> +	      && int_mode_for_size (GET_MODE_BITSIZE (to_mode),
> +				    0).exists (&toi_mode))
> +	    {
> +	      start_sequence ();
> +	      rtx fromi = lowpart_subreg (fromi_mode, from, from_mode);
> +	      rtx tof = NULL_RTX;
> +	      do
> +		{
> +		  if (!fromi)
> +		    break;
> +		  int shift = (GET_MODE_PRECISION (from_mode)
> +			       - GET_MODE_PRECISION (to_mode));
> +		  rtx temp1
> +		    = maybe_expand_shift (RSHIFT_EXPR, fromi_mode, fromi,
> +					  shift, NULL_RTX, 1);
> +		  if (!temp1)
> +		    break;
> +		  rtx temp2
> +		    = expand_binop (fromi_mode, and_optab, temp1, const1_rtx,
> +				    NULL_RTX, 1, OPTAB_DIRECT);
> +		  if (!temp2)
> +		    break;
> +		  rtx temp3
> +		    = expand_binop (fromi_mode, add_optab, fromi,
> +				    gen_int_mode ((HOST_WIDE_INT_1U
> +						   << (shift - 1)) - 1,
> +						  fromi_mode), NULL_RTX,
> +				    1, OPTAB_DIRECT);
> +		  if (!temp3)
> +		    break;
> +		  rtx temp4
> +		    = expand_binop (fromi_mode, add_optab, temp3, temp2,
> +				    NULL_RTX, 1, OPTAB_DIRECT);
> +		  if (!temp4)
> +		    break;
> +		  rtx temp5 = maybe_expand_shift (RSHIFT_EXPR, fromi_mode,
> +						  temp4, shift, NULL_RTX, 1);
> +		  if (!temp5)
> +		    break;
> +		  rtx temp6 = lowpart_subreg (toi_mode, temp5, fromi_mode);
> +		  if (!temp6)
> +		    break;
> +		  tof = lowpart_subreg (to_mode, force_reg (toi_mode, temp6),
> +					toi_mode);
> +		  if (tof)
> +		    emit_move_insn (to, tof);
> +		}
> +	      while (0);
> +	      insns = get_insns ();
> +	      end_sequence ();
> +	      if (tof)
> +		{
> +		  emit_insn (insns);
> +		  return;
> +		}
> +	    }
> +	}
> +#endif
> +
>         /* Otherwise use a libcall.  */
>         libcall = convert_optab_libfunc (tab, to_mode, from_mode);
>   
> --- gcc/config/arm/arm.h.jj	2022-09-29 09:13:25.709718568 +0200
> +++ gcc/config/arm/arm.h	2022-09-29 12:40:17.401778971 +0200
> @@ -78,9 +78,8 @@ extern void (*arm_lang_output_object_att
>      the backend.  Defined in arm-builtins.cc.  */
>   extern tree arm_fp16_type_node;
>   
> -/* This type is the user-visible __bf16.  We need it in a few places in
> -   the backend.  Defined in arm-builtins.cc.  */
> -extern tree arm_bf16_type_node;
> +/* The user-visible __bf16 uses bfloat16_type_node, but for pointer to that
> +   use backend specific tree.  Defined in arm-builtins.cc.  */
>   extern tree arm_bf16_ptr_type_node;
>   
>   
> --- gcc/config/arm/arm.cc.jj	2022-09-29 09:13:25.709718568 +0200
> +++ gcc/config/arm/arm.cc	2022-09-29 15:33:07.997170885 +0200
> @@ -688,12 +688,6 @@ static const struct attribute_spec arm_a
>   #undef TARGET_INVALID_CONVERSION
>   #define TARGET_INVALID_CONVERSION arm_invalid_conversion
>   
> -#undef TARGET_INVALID_UNARY_OP
> -#define TARGET_INVALID_UNARY_OP arm_invalid_unary_op
> -
> -#undef TARGET_INVALID_BINARY_OP
> -#define TARGET_INVALID_BINARY_OP arm_invalid_binary_op
> -
>   #undef TARGET_ATOMIC_ASSIGN_EXPAND_FENV
>   #define TARGET_ATOMIC_ASSIGN_EXPAND_FENV arm_atomic_assign_expand_fenv
>   
> @@ -30360,7 +30354,7 @@ arm_mangle_type (const_tree type)
>     if (TREE_CODE (type) == REAL_TYPE && TYPE_PRECISION (type) == 16)
>       {
>         if (TYPE_MODE (type) == BFmode)
> -	return "u6__bf16";
> +	return "DFb16_";
>         else
>   	return "Dh";
>       }
> @@ -33996,47 +33990,22 @@ arm_invalid_conversion (const_tree fromt
>   {
>     if (element_mode (fromtype) != element_mode (totype))
>       {
> -      /* Do no allow conversions to/from BFmode scalar types.  */
> -      if (TYPE_MODE (fromtype) == BFmode)
> -	return N_("invalid conversion from type %<bfloat16_t%>");
> -      if (TYPE_MODE (totype) == BFmode)
> -	return N_("invalid conversion to type %<bfloat16_t%>");
> +      /* Do no allow conversions from BFmode to non-ieee HFmode
> +	 scalar types or vice versa.  */
> +      if (TYPE_MODE (fromtype) == BFmode
> +	  && TYPE_MODE (totype) == HFmode
> +	  && arm_fp16_format == ARM_FP16_FORMAT_ALTERNATIVE)
> +	return N_("invalid conversion from type %<bfloat16_t%> to %<__fp16%>");
> +      if (TYPE_MODE (totype) == BFmode
> +	  && TYPE_MODE (fromtype) == HFmode
> +	  && arm_fp16_format == ARM_FP16_FORMAT_ALTERNATIVE)
> +	return N_("invalid conversion to type %<bfloat16_t%> from %<__fp16%>");
>       }
>   
>     /* Conversion allowed.  */
>     return NULL;
>   }
>   
> -/* Return the diagnostic message string if the unary operation OP is
> -   not permitted on TYPE, NULL otherwise.  */
> -
> -static const char *
> -arm_invalid_unary_op (int op, const_tree type)
> -{
> -  /* Reject all single-operand operations on BFmode except for &.  */
> -  if (element_mode (type) == BFmode && op != ADDR_EXPR)
> -    return N_("operation not permitted on type %<bfloat16_t%>");
> -
> -  /* Operation allowed.  */
> -  return NULL;
> -}
> -
> -/* Return the diagnostic message string if the binary operation OP is
> -   not permitted on TYPE1 and TYPE2, NULL otherwise.  */
> -
> -static const char *
> -arm_invalid_binary_op (int op ATTRIBUTE_UNUSED, const_tree type1,
> -			   const_tree type2)
> -{
> -  /* Reject all 2-operand operations on BFmode.  */
> -  if (element_mode (type1) == BFmode
> -      || element_mode (type2) == BFmode)
> -    return N_("operation not permitted on type %<bfloat16_t%>");
> -
> -  /* Operation allowed.  */
> -  return NULL;
> -}
> -
>   /* Implement TARGET_CAN_CHANGE_MODE_CLASS.
>   
>      In VFPv1, VFP registers could only be accessed in the mode they were
> --- gcc/config/arm/arm-builtins.cc.jj	2022-09-29 09:13:25.681718954 +0200
> +++ gcc/config/arm/arm-builtins.cc	2022-09-29 12:40:17.405778917 +0200
> @@ -1370,7 +1370,6 @@ struct arm_simd_type_info arm_simd_types
>   tree arm_fp16_type_node = NULL_TREE;
>   
>   /* Back-end node type for brain float (bfloat) types.  */
> -tree arm_bf16_type_node = NULL_TREE;
>   tree arm_bf16_ptr_type_node = NULL_TREE;
>   
>   static tree arm_simd_intOI_type_node = NULL_TREE;
> @@ -1459,7 +1458,7 @@ arm_simd_builtin_std_type (machine_mode
>       case E_DFmode:
>         return double_type_node;
>       case E_BFmode:
> -      return arm_bf16_type_node;
> +      return bfloat16_type_node;
>       default:
>         gcc_unreachable ();
>       }
> @@ -1570,9 +1569,9 @@ arm_init_simd_builtin_types (void)
>     arm_simd_types[Float32x4_t].eltype = float_type_node;
>   
>     /* Init Bfloat vector types with underlying __bf16 scalar type.  */
> -  arm_simd_types[Bfloat16x2_t].eltype = arm_bf16_type_node;
> -  arm_simd_types[Bfloat16x4_t].eltype = arm_bf16_type_node;
> -  arm_simd_types[Bfloat16x8_t].eltype = arm_bf16_type_node;
> +  arm_simd_types[Bfloat16x2_t].eltype = bfloat16_type_node;
> +  arm_simd_types[Bfloat16x4_t].eltype = bfloat16_type_node;
> +  arm_simd_types[Bfloat16x8_t].eltype = bfloat16_type_node;
>   
>     for (i = 0; i < nelts; i++)
>       {
> @@ -1658,7 +1657,7 @@ arm_init_simd_builtin_scalar_types (void
>   					     "__builtin_neon_df");
>     (*lang_hooks.types.register_builtin_type) (intTI_type_node,
>   					     "__builtin_neon_ti");
> -  (*lang_hooks.types.register_builtin_type) (arm_bf16_type_node,
> +  (*lang_hooks.types.register_builtin_type) (bfloat16_type_node,
>                                                "__builtin_neon_bf");
>     /* Unsigned integer types for various mode sizes.  */
>     (*lang_hooks.types.register_builtin_type) (unsigned_intQI_type_node,
> @@ -1797,13 +1796,13 @@ arm_init_builtin (unsigned int fcode, ar
>   static void
>   arm_init_bf16_types (void)
>   {
> -  arm_bf16_type_node = make_node (REAL_TYPE);
> -  TYPE_PRECISION (arm_bf16_type_node) = 16;
> -  SET_TYPE_MODE (arm_bf16_type_node, BFmode);
> -  layout_type (arm_bf16_type_node);
> +  bfloat16_type_node = make_node (REAL_TYPE);
> +  TYPE_PRECISION (bfloat16_type_node) = 16;
> +  SET_TYPE_MODE (bfloat16_type_node, BFmode);
> +  layout_type (bfloat16_type_node);
>   
> -  lang_hooks.types.register_builtin_type (arm_bf16_type_node, "__bf16");
> -  arm_bf16_ptr_type_node = build_pointer_type (arm_bf16_type_node);
> +  lang_hooks.types.register_builtin_type (bfloat16_type_node, "__bf16");
> +  arm_bf16_ptr_type_node = build_pointer_type (bfloat16_type_node);
>   }
>   
>   /* Set up ACLE builtins, even builtins for instructions that are not
> --- gcc/config/i386/i386.cc.jj	2022-09-29 12:03:12.073350093 +0200
> +++ gcc/config/i386/i386.cc	2022-09-29 12:40:17.409778863 +0200
> @@ -22728,7 +22728,7 @@ ix86_mangle_type (const_tree type)
>     switch (TYPE_MODE (type))
>       {
>       case E_BFmode:
> -      return "u6__bf16";
> +      return "DFb16_";
>       case E_HFmode:
>         /* _Float16 is "DF16_".
>   	 Align with clang's decision in https://reviews.llvm.org/D33719. */
> @@ -22747,55 +22747,6 @@ ix86_mangle_type (const_tree type)
>       }
>   }
>   
> -/* Return the diagnostic message string if conversion from FROMTYPE to
> -   TOTYPE is not allowed, NULL otherwise.  */
> -
> -static const char *
> -ix86_invalid_conversion (const_tree fromtype, const_tree totype)
> -{
> -  if (element_mode (fromtype) != element_mode (totype))
> -    {
> -      /* Do no allow conversions to/from BFmode scalar types.  */
> -      if (TYPE_MODE (fromtype) == BFmode)
> -	return N_("invalid conversion from type %<__bf16%>");
> -      if (TYPE_MODE (totype) == BFmode)
> -	return N_("invalid conversion to type %<__bf16%>");
> -    }
> -
> -  /* Conversion allowed.  */
> -  return NULL;
> -}
> -
> -/* Return the diagnostic message string if the unary operation OP is
> -   not permitted on TYPE, NULL otherwise.  */
> -
> -static const char *
> -ix86_invalid_unary_op (int op, const_tree type)
> -{
> -  /* Reject all single-operand operations on BFmode except for &.  */
> -  if (element_mode (type) == BFmode && op != ADDR_EXPR)
> -    return N_("operation not permitted on type %<__bf16%>");
> -
> -  /* Operation allowed.  */
> -  return NULL;
> -}
> -
> -/* Return the diagnostic message string if the binary operation OP is
> -   not permitted on TYPE1 and TYPE2, NULL otherwise.  */
> -
> -static const char *
> -ix86_invalid_binary_op (int op ATTRIBUTE_UNUSED, const_tree type1,
> -			   const_tree type2)
> -{
> -  /* Reject all 2-operand operations on BFmode.  */
> -  if (element_mode (type1) == BFmode
> -      || element_mode (type2) == BFmode)
> -    return N_("operation not permitted on type %<__bf16%>");
> -
> -  /* Operation allowed.  */
> -  return NULL;
> -}
> -
>   static GTY(()) tree ix86_tls_stack_chk_guard_decl;
>   
>   static tree
> @@ -24853,15 +24804,6 @@ ix86_libgcc_floating_mode_supported_p
>   #undef TARGET_MANGLE_TYPE
>   #define TARGET_MANGLE_TYPE ix86_mangle_type
>   
> -#undef TARGET_INVALID_CONVERSION
> -#define TARGET_INVALID_CONVERSION ix86_invalid_conversion
> -
> -#undef TARGET_INVALID_UNARY_OP
> -#define TARGET_INVALID_UNARY_OP ix86_invalid_unary_op
> -
> -#undef TARGET_INVALID_BINARY_OP
> -#define TARGET_INVALID_BINARY_OP ix86_invalid_binary_op
> -
>   #undef TARGET_STACK_PROTECT_GUARD
>   #define TARGET_STACK_PROTECT_GUARD ix86_stack_protect_guard
>   
> --- gcc/config/i386/i386-builtins.cc.jj	2022-09-29 09:13:25.710718554 +0200
> +++ gcc/config/i386/i386-builtins.cc	2022-09-29 12:40:17.406778903 +0200
> @@ -126,7 +126,6 @@ BDESC_VERIFYS (IX86_BUILTIN_MAX,
>   static GTY(()) tree ix86_builtin_type_tab[(int) IX86_BT_LAST_CPTR + 1];
>   
>   tree ix86_float16_type_node = NULL_TREE;
> -tree ix86_bf16_type_node = NULL_TREE;
>   tree ix86_bf16_ptr_type_node = NULL_TREE;
>   
>   /* Retrieve an element from the above table, building some of
> @@ -1372,16 +1371,15 @@ ix86_register_float16_builtin_type (void
>   static void
>   ix86_register_bf16_builtin_type (void)
>   {
> -  ix86_bf16_type_node = make_node (REAL_TYPE);
> -  TYPE_PRECISION (ix86_bf16_type_node) = 16;
> -  SET_TYPE_MODE (ix86_bf16_type_node, BFmode);
> -  layout_type (ix86_bf16_type_node);
> +  bfloat16_type_node = make_node (REAL_TYPE);
> +  TYPE_PRECISION (bfloat16_type_node) = 16;
> +  SET_TYPE_MODE (bfloat16_type_node, BFmode);
> +  layout_type (bfloat16_type_node);
>   
>     if (!maybe_get_identifier ("__bf16") && TARGET_SSE2)
>       {
> -      lang_hooks.types.register_builtin_type (ix86_bf16_type_node,
> -					    "__bf16");
> -      ix86_bf16_ptr_type_node = build_pointer_type (ix86_bf16_type_node);
> +      lang_hooks.types.register_builtin_type (bfloat16_type_node, "__bf16");
> +      ix86_bf16_ptr_type_node = build_pointer_type (bfloat16_type_node);
>       }
>   }
>   
> --- gcc/config/i386/i386-builtin-types.def.jj	2022-09-29 09:13:25.709718568 +0200
> +++ gcc/config/i386/i386-builtin-types.def	2022-09-29 12:40:17.406778903 +0200
> @@ -69,7 +69,7 @@ DEF_PRIMITIVE_TYPE (UINT16, short_unsign
>   DEF_PRIMITIVE_TYPE (INT64, long_long_integer_type_node)
>   DEF_PRIMITIVE_TYPE (UINT64, long_long_unsigned_type_node)
>   DEF_PRIMITIVE_TYPE (FLOAT16, ix86_float16_type_node)
> -DEF_PRIMITIVE_TYPE (BFLOAT16, ix86_bf16_type_node)
> +DEF_PRIMITIVE_TYPE (BFLOAT16, bfloat16_type_node)
>   DEF_PRIMITIVE_TYPE (FLOAT, float_type_node)
>   DEF_PRIMITIVE_TYPE (DOUBLE, double_type_node)
>   DEF_PRIMITIVE_TYPE (FLOAT80, float80_type_node)
> --- gcc/config/aarch64/aarch64.h.jj	2022-09-29 09:13:25.680718968 +0200
> +++ gcc/config/aarch64/aarch64.h	2022-09-29 12:40:17.409778863 +0200
> @@ -1337,9 +1337,8 @@ extern const char *aarch64_rewrite_mcpu
>   extern GTY(()) tree aarch64_fp16_type_node;
>   extern GTY(()) tree aarch64_fp16_ptr_type_node;
>   
> -/* This type is the user-visible __bf16, and a pointer to that type.  Defined
> -   in aarch64-builtins.cc.  */
> -extern GTY(()) tree aarch64_bf16_type_node;
> +/* Pointer to the user-visible __bf16 type.  __bf16 itself is generic
> +   bfloat16_type_node.  Defined in aarch64-builtins.cc.  */
>   extern GTY(()) tree aarch64_bf16_ptr_type_node;
>   
>   /* The generic unwind code in libgcc does not initialize the frame pointer.
> --- gcc/config/aarch64/aarch64.cc.jj	2022-09-29 09:13:25.680718968 +0200
> +++ gcc/config/aarch64/aarch64.cc	2022-09-29 12:40:17.413778808 +0200
> @@ -19741,7 +19741,7 @@ aarch64_gimplify_va_arg_expr (tree valis
>   	  field_ptr_t = aarch64_fp16_ptr_type_node;
>   	  break;
>   	case E_BFmode:
> -	  field_t = aarch64_bf16_type_node;
> +	  field_t = bfloat16_type_node;
>   	  field_ptr_t = aarch64_bf16_ptr_type_node;
>   	  break;
>   	case E_V2SImode:
> @@ -20645,7 +20645,7 @@ aarch64_mangle_type (const_tree type)
>     if (TREE_CODE (type) == REAL_TYPE && TYPE_PRECISION (type) == 16)
>       {
>         if (TYPE_MODE (type) == BFmode)
> -	return "u6__bf16";
> +	return "DFb16_";
>         else
>   	return "Dh";
>       }
> @@ -26820,39 +26820,6 @@ aarch64_stack_protect_guard (void)
>     return NULL_TREE;
>   }
>   
> -/* Return the diagnostic message string if conversion from FROMTYPE to
> -   TOTYPE is not allowed, NULL otherwise.  */
> -
> -static const char *
> -aarch64_invalid_conversion (const_tree fromtype, const_tree totype)
> -{
> -  if (element_mode (fromtype) != element_mode (totype))
> -    {
> -      /* Do no allow conversions to/from BFmode scalar types.  */
> -      if (TYPE_MODE (fromtype) == BFmode)
> -	return N_("invalid conversion from type %<bfloat16_t%>");
> -      if (TYPE_MODE (totype) == BFmode)
> -	return N_("invalid conversion to type %<bfloat16_t%>");
> -    }
> -
> -  /* Conversion allowed.  */
> -  return NULL;
> -}
> -
> -/* Return the diagnostic message string if the unary operation OP is
> -   not permitted on TYPE, NULL otherwise.  */
> -
> -static const char *
> -aarch64_invalid_unary_op (int op, const_tree type)
> -{
> -  /* Reject all single-operand operations on BFmode except for &.  */
> -  if (element_mode (type) == BFmode && op != ADDR_EXPR)
> -    return N_("operation not permitted on type %<bfloat16_t%>");
> -
> -  /* Operation allowed.  */
> -  return NULL;
> -}
> -
>   /* Return the diagnostic message string if the binary operation OP is
>      not permitted on TYPE1 and TYPE2, NULL otherwise.  */
>   
> @@ -26860,11 +26827,6 @@ static const char *
>   aarch64_invalid_binary_op (int op ATTRIBUTE_UNUSED, const_tree type1,
>   			   const_tree type2)
>   {
> -  /* Reject all 2-operand operations on BFmode.  */
> -  if (element_mode (type1) == BFmode
> -      || element_mode (type2) == BFmode)
> -    return N_("operation not permitted on type %<bfloat16_t%>");
> -
>     if (VECTOR_TYPE_P (type1)
>         && VECTOR_TYPE_P (type2)
>         && !TYPE_INDIVISIBLE_P (type1)
> @@ -27461,12 +27423,6 @@ aarch64_libgcc_floating_mode_supported_p
>   #undef TARGET_MANGLE_TYPE
>   #define TARGET_MANGLE_TYPE aarch64_mangle_type
>   
> -#undef TARGET_INVALID_CONVERSION
> -#define TARGET_INVALID_CONVERSION aarch64_invalid_conversion
> -
> -#undef TARGET_INVALID_UNARY_OP
> -#define TARGET_INVALID_UNARY_OP aarch64_invalid_unary_op
> -
>   #undef TARGET_INVALID_BINARY_OP
>   #define TARGET_INVALID_BINARY_OP aarch64_invalid_binary_op
>   
> --- gcc/config/aarch64/aarch64-builtins.cc.jj	2022-09-29 09:13:25.676719023 +0200
> +++ gcc/config/aarch64/aarch64-builtins.cc	2022-09-29 12:40:17.410778849 +0200
> @@ -918,7 +918,6 @@ tree aarch64_fp16_type_node = NULL_TREE;
>   tree aarch64_fp16_ptr_type_node = NULL_TREE;
>   
>   /* Back-end node type for brain float (bfloat) types.  */
> -tree aarch64_bf16_type_node = NULL_TREE;
>   tree aarch64_bf16_ptr_type_node = NULL_TREE;
>   
>   /* Wrapper around add_builtin_function.  NAME is the name of the built-in
> @@ -1010,7 +1009,7 @@ aarch64_int_or_fp_type (machine_mode mod
>       case E_DFmode:
>         return double_type_node;
>       case E_BFmode:
> -      return aarch64_bf16_type_node;
> +      return bfloat16_type_node;
>       default:
>         gcc_unreachable ();
>       }
> @@ -1124,8 +1123,8 @@ aarch64_init_simd_builtin_types (void)
>     aarch64_simd_types[Float64x2_t].eltype = double_type_node;
>   
>     /* Init Bfloat vector types with underlying __bf16 type.  */
> -  aarch64_simd_types[Bfloat16x4_t].eltype = aarch64_bf16_type_node;
> -  aarch64_simd_types[Bfloat16x8_t].eltype = aarch64_bf16_type_node;
> +  aarch64_simd_types[Bfloat16x4_t].eltype = bfloat16_type_node;
> +  aarch64_simd_types[Bfloat16x8_t].eltype = bfloat16_type_node;
>   
>     for (i = 0; i < nelts; i++)
>       {
> @@ -1197,7 +1196,7 @@ aarch64_init_simd_builtin_scalar_types (
>   					     "__builtin_aarch64_simd_poly128");
>     (*lang_hooks.types.register_builtin_type) (intTI_type_node,
>   					     "__builtin_aarch64_simd_ti");
> -  (*lang_hooks.types.register_builtin_type) (aarch64_bf16_type_node,
> +  (*lang_hooks.types.register_builtin_type) (bfloat16_type_node,
>   					     "__builtin_aarch64_simd_bf");
>     /* Unsigned integer types for various mode sizes.  */
>     (*lang_hooks.types.register_builtin_type) (unsigned_intQI_type_node,
> @@ -1682,13 +1681,13 @@ aarch64_init_fp16_types (void)
>   static void
>   aarch64_init_bf16_types (void)
>   {
> -  aarch64_bf16_type_node = make_node (REAL_TYPE);
> -  TYPE_PRECISION (aarch64_bf16_type_node) = 16;
> -  SET_TYPE_MODE (aarch64_bf16_type_node, BFmode);
> -  layout_type (aarch64_bf16_type_node);
> +  bfloat16_type_node = make_node (REAL_TYPE);
> +  TYPE_PRECISION (bfloat16_type_node) = 16;
> +  SET_TYPE_MODE (bfloat16_type_node, BFmode);
> +  layout_type (bfloat16_type_node);
>   
> -  lang_hooks.types.register_builtin_type (aarch64_bf16_type_node, "__bf16");
> -  aarch64_bf16_ptr_type_node = build_pointer_type (aarch64_bf16_type_node);
> +  lang_hooks.types.register_builtin_type (bfloat16_type_node, "__bf16");
> +  aarch64_bf16_ptr_type_node = build_pointer_type (bfloat16_type_node);
>   }
>   
>   /* Pointer authentication builtins that will become NOP on legacy platform.
> --- gcc/config/aarch64/aarch64-sve-builtins.def.jj	2022-09-29 09:13:25.676719023 +0200
> +++ gcc/config/aarch64/aarch64-sve-builtins.def	2022-09-29 12:40:17.413778808 +0200
> @@ -61,7 +61,7 @@ DEF_SVE_MODE (u64offset, none, svuint64_
>   DEF_SVE_MODE (vnum, none, none, vectors)
>   
>   DEF_SVE_TYPE (svbool_t, 10, __SVBool_t, boolean_type_node)
> -DEF_SVE_TYPE (svbfloat16_t, 14, __SVBfloat16_t, aarch64_bf16_type_node)
> +DEF_SVE_TYPE (svbfloat16_t, 14, __SVBfloat16_t, bfloat16_type_node)
>   DEF_SVE_TYPE (svfloat16_t, 13, __SVFloat16_t, aarch64_fp16_type_node)
>   DEF_SVE_TYPE (svfloat32_t, 13, __SVFloat32_t, float_type_node)
>   DEF_SVE_TYPE (svfloat64_t, 13, __SVFloat64_t, double_type_node)
> --- gcc/c-family/c-cppbuiltin.cc.jj	2022-09-29 09:13:25.675719037 +0200
> +++ gcc/c-family/c-cppbuiltin.cc	2022-09-29 12:40:17.416778768 +0200
> @@ -1264,6 +1264,13 @@ c_cpp_builtins (cpp_reader *pfile)
>         builtin_define_float_constants (prefix, ggc_strdup (csuffix), "%s",
>   				      csuffix, FLOATN_NX_TYPE_NODE (i));
>       }
> +  if (bfloat16_type_node && c_dialect_cxx ())
> +    {
> +      if (cxx_dialect > cxx20)
> +	cpp_define (pfile, "__STDCPP_BFLOAT16_T__=1");
> +      builtin_define_float_constants ("BFLT16", "BF16", "%s",
> +				      "BF16", bfloat16_type_node);
> +    }
>   
>     /* For float.h.  */
>     if (targetm.decimal_float_supported_p ())
> --- gcc/c-family/c-lex.cc.jj	2022-09-29 09:13:25.675719037 +0200
> +++ gcc/c-family/c-lex.cc	2022-09-29 12:40:17.416778768 +0200
> @@ -995,6 +995,19 @@ interpret_float (const cpp_token *token,
>   	  pedwarn (input_location, OPT_Wpedantic,
>   		   "non-standard suffix on floating constant");
>         }
> +    else if ((flags & CPP_N_BFLOAT16) != 0 && c_dialect_cxx ())
> +      {
> +	type = bfloat16_type_node;
> +	if (type == NULL_TREE)
> +	  {
> +	    error ("unsupported non-standard suffix on floating constant");
> +	    return error_mark_node;
> +	  }
> +	if (cxx_dialect < cxx23)
> +	  pedwarn (input_location, OPT_Wpedantic,
> +		   "%<bf16%> or %<BF16%> suffix on floating constant only "
> +		   "available with %<-std=c++2b%> or %<-std=gnu++2b%>");
> +      }
>       else if ((flags & CPP_N_WIDTH) == CPP_N_LARGE)
>         type = long_double_type_node;
>       else if ((flags & CPP_N_WIDTH) == CPP_N_SMALL
> --- gcc/cp/cp-tree.h.jj	2022-09-29 09:13:31.164643341 +0200
> +++ gcc/cp/cp-tree.h	2022-09-29 12:40:17.414778795 +0200
> @@ -8714,6 +8714,8 @@ extended_float_type_p (tree type)
>     for (int i = 0; i < NUM_FLOATN_NX_TYPES; ++i)
>       if (type == FLOATN_TYPE_NODE (i))
>         return true;
> +  if (type == bfloat16_type_node)
> +    return true;
>     return false;
>   }
>   
> --- gcc/cp/typeck.cc.jj	2022-09-29 09:13:25.716718472 +0200
> +++ gcc/cp/typeck.cc	2022-09-29 12:40:17.415778781 +0200
> @@ -293,6 +293,10 @@ cp_compare_floating_point_conversion_ran
>         if (mv2 == FLOATN_NX_TYPE_NODE (i))
>   	extended2 = i + 1;
>       }
> +  if (mv1 == bfloat16_type_node)
> +    extended1 = true;
> +  if (mv2 == bfloat16_type_node)
> +    extended2 = true;
>     if (extended2 && !extended1)
>       {
>         int ret = cp_compare_floating_point_conversion_ranks (t2, t1);
> @@ -390,7 +394,9 @@ cp_compare_floating_point_conversion_ran
>     if (cnt > 1 && mv2 == long_double_type_node)
>       return -2;
>     /* Otherwise, they have equal rank, but extended types
> -     (other than std::bfloat16_t) have higher subrank.  */
> +     (other than std::bfloat16_t) have higher subrank.
> +     std::bfloat16_t shouldn't have equal rank to any standard
> +     floating point type.  */
>     return 1;
>   }
>   
> --- libcpp/include/cpplib.h.jj	2022-09-08 13:01:19.853771383 +0200
> +++ libcpp/include/cpplib.h	2022-09-28 19:06:59.615380690 +0200
> @@ -1275,6 +1275,7 @@ struct cpp_num
>   #define CPP_N_USERDEF	0x1000000 /* C++11 user-defined literal.  */
>   
>   #define CPP_N_SIZE_T	0x2000000 /* C++23 size_t literal.  */
> +#define CPP_N_BFLOAT16	0x4000000 /* std::bfloat16_t type.  */
>   
>   #define CPP_N_WIDTH_FLOATN_NX	0xF0000000 /* _FloatN / _FloatNx value
>   					      of N, divided by 16.  */
> --- libcpp/expr.cc.jj	2022-09-27 08:03:27.119982735 +0200
> +++ libcpp/expr.cc	2022-09-28 17:55:36.667177540 +0200
> @@ -91,10 +91,10 @@ interpret_float_suffix (cpp_reader *pfil
>     size_t orig_len = len;
>     const uchar *orig_s = s;
>     size_t flags;
> -  size_t f, d, l, w, q, i, fn, fnx, fn_bits;
> +  size_t f, d, l, w, q, i, fn, fnx, fn_bits, bf16;
>   
>     flags = 0;
> -  f = d = l = w = q = i = fn = fnx = fn_bits = 0;
> +  f = d = l = w = q = i = fn = fnx = fn_bits = bf16 = 0;
>   
>     /* The following decimal float suffixes, from TR 24732:2009, TS
>        18661-2:2015 and C2X, are supported:
> @@ -131,7 +131,8 @@ interpret_float_suffix (cpp_reader *pfil
>        w, W - machine-specific type such as __float80 (GNU extension).
>        q, Q - machine-specific type such as __float128 (GNU extension).
>        fN, FN - _FloatN (TS 18661-3:2015).
> -     fNx, FNx - _FloatNx (TS 18661-3:2015).  */
> +     fNx, FNx - _FloatNx (TS 18661-3:2015).
> +     bf16, BF16 - std::bfloat16_t (ISO C++23).  */
>   
>     /* Process decimal float suffixes, which are two letters starting
>        with d or D.  Order and case are significant.  */
> @@ -239,6 +240,20 @@ interpret_float_suffix (cpp_reader *pfil
>   		fn++;
>   	    }
>   	  break;
> +	case 'b': case 'B':
> +	  if (len > 2
> +	      /* Except for bf16 / BF16 where case is significant.  */
> +	      && s[1] == (s[0] == 'b' ? 'f' : 'F')
> +	      && s[2] == '1'
> +	      && s[3] == '6'
> +	      && CPP_OPTION (pfile, cplusplus))
> +	    {
> +	      bf16++;
> +	      len -= 3;
> +	      s += 3;
> +	      break;
> +	    }
> +	  return 0;
>   	case 'd': case 'D': d++; break;
>   	case 'l': case 'L': l++; break;
>   	case 'w': case 'W': w++; break;
> @@ -257,7 +272,7 @@ interpret_float_suffix (cpp_reader *pfil
>        of N larger than can be represented in the return value.  The
>        caller is responsible for rejecting _FloatN suffixes where
>        _FloatN is not supported on the chosen target.  */
> -  if (f + d + l + w + q + fn + fnx > 1 || i > 1)
> +  if (f + d + l + w + q + fn + fnx + bf16 > 1 || i > 1)
>       return 0;
>     if (fn_bits > CPP_FLOATN_MAX)
>       return 0;
> @@ -295,6 +310,7 @@ interpret_float_suffix (cpp_reader *pfil
>   	     q ? CPP_N_MD_Q :
>   	     fn ? CPP_N_FLOATN | (fn_bits << CPP_FLOATN_SHIFT) :
>   	     fnx ? CPP_N_FLOATNX | (fn_bits << CPP_FLOATN_SHIFT) :
> +	     bf16 ? CPP_N_BFLOAT16 :
>   	     CPP_N_DEFAULT));
>   }
>   
> --- libgcc/config/arm/sfp-machine.h.jj	2020-01-12 11:54:38.615380187 +0100
> +++ libgcc/config/arm/sfp-machine.h	2022-09-28 19:02:51.922710542 +0200
> @@ -22,6 +22,7 @@ typedef int __gcc_CMPtype __attribute__
>   /* According to RTABI, QNAN is only with the most significant bit of the
>      significand set, and all other significand bits zero.  */
>   #define _FP_NANFRAC_H		_FP_QNANBIT_H
> +#define _FP_NANFRAC_B		_FP_QNANBIT_B
>   #define _FP_NANFRAC_S		_FP_QNANBIT_S
>   #define _FP_NANFRAC_D		_FP_QNANBIT_D, 0
>   #define _FP_NANFRAC_Q		_FP_QNANBIT_Q, 0, 0, 0
> --- libgcc/config/aarch64/t-softfp.jj	2020-09-29 11:32:02.988602194 +0200
> +++ libgcc/config/aarch64/t-softfp	2022-09-28 18:59:43.381246466 +0200
> @@ -1,7 +1,7 @@
>   softfp_float_modes := tf
>   softfp_int_modes := si di ti
> -softfp_extensions := sftf dftf hftf
> -softfp_truncations := tfsf tfdf tfhf
> +softfp_extensions := sftf dftf hftf bfsf
> +softfp_truncations := tfsf tfdf tfhf tfbf dfbf sfbf hfbf
>   softfp_exclude_libgcc2 := n
>   softfp_extras := fixhfti fixunshfti floattihf floatuntihf
>   
> --- libgcc/config/aarch64/libgcc-softfp.ver.jj	2022-01-11 23:11:23.691271871 +0100
> +++ libgcc/config/aarch64/libgcc-softfp.ver	2022-09-28 19:00:36.050537146 +0200
> @@ -26,3 +26,12 @@ GCC_11.0 {
>     __mulhc3
>     __trunctfhf2
>   }
> +
> +%inherit GCC_13.0.0 GCC_11.0.0
> +GCC_13.0.0 {
> +  __extendbfsf2
> +  __truncdfbf2
> +  __truncsfbf2
> +  __trunctfbf2
> +  __trunchfbf2
> +}
> --- libgcc/config/aarch64/sfp-machine.h.jj	2022-01-11 23:11:23.691271871 +0100
> +++ libgcc/config/aarch64/sfp-machine.h	2022-09-28 19:02:10.303270053 +0200
> @@ -43,6 +43,7 @@ typedef int __gcc_CMPtype __attribute__
>   #define _FP_DIV_MEAT_Q(R,X,Y)	_FP_DIV_MEAT_2_udiv(Q,R,X,Y)
>   
>   #define _FP_NANFRAC_H		((_FP_QNANBIT_H << 1) - 1)
> +#define _FP_NANFRAC_B		((_FP_QNANBIT_B << 1) - 1)
>   #define _FP_NANFRAC_S		((_FP_QNANBIT_S << 1) - 1)
>   #define _FP_NANFRAC_D		((_FP_QNANBIT_D << 1) - 1)
>   #define _FP_NANFRAC_Q		((_FP_QNANBIT_Q << 1) - 1), -1
> --- libgcc/config/i386/t-softfp.jj	2022-09-23 09:02:31.759659479 +0200
> +++ libgcc/config/i386/t-softfp	2022-09-28 18:58:09.114520943 +0200
> @@ -6,8 +6,9 @@ LIB2FUNCS_EXCLUDE += $(libgcc2-hf-functi
>   libgcc2-hf-extras = $(addsuffix .c, $(libgcc2-hf-functions))
>   LIB2ADD += $(addprefix $(srcdir)/config/i386/, $(libgcc2-hf-extras))
>   
> -softfp_extensions := hfsf hfdf hftf hfxf sfdf sftf dftf xftf
> -softfp_truncations := tfhf xfhf dfhf sfhf tfsf dfsf tfdf tfxf
> +softfp_extensions := hfsf hfdf hftf hfxf sfdf sftf dftf xftf bfsf
> +softfp_truncations := tfhf xfhf dfhf sfhf tfsf dfsf tfdf tfxf \
> +		      tfbf xfbf dfbf sfbf hfbf
>   
>   softfp_extras += eqhf2
>   
> @@ -20,6 +21,7 @@ CFLAGS-truncsfhf2.c += -msse2
>   CFLAGS-truncdfhf2.c += -msse2
>   CFLAGS-truncxfhf2.c += -msse2
>   CFLAGS-trunctfhf2.c += -msse2
> +CFLAGS-trunchfbf2.c += -msse2
>   
>   CFLAGS-eqhf2.c += -msse2
>   CFLAGS-_divhc3.c += -msse2
> --- libgcc/config/i386/libgcc-glibc.ver.jj	2022-09-23 09:02:31.746659658 +0200
> +++ libgcc/config/i386/libgcc-glibc.ver	2022-09-28 18:58:09.114520943 +0200
> @@ -214,3 +214,13 @@ GCC_12.0.0 {
>     __trunctfhf2
>     __truncxfhf2
>   }
> +
> +%inherit GCC_13.0.0 GCC_12.0.0
> +GCC_13.0.0 {
> +  __extendbfsf2
> +  __truncdfbf2
> +  __truncsfbf2
> +  __trunctfbf2
> +  __truncxfbf2
> +  __trunchfbf2
> +}
> --- libgcc/config/i386/sfp-machine.h.jj	2022-09-23 09:02:31.747659644 +0200
> +++ libgcc/config/i386/sfp-machine.h	2022-09-28 18:58:09.114520943 +0200
> @@ -18,6 +18,7 @@ typedef int __gcc_CMPtype __attribute__
>   #define _FP_QNANNEGATEDP 0
>   
>   #define _FP_NANSIGN_H		1
> +#define _FP_NANSIGN_B		1
>   #define _FP_NANSIGN_S		1
>   #define _FP_NANSIGN_D		1
>   #define _FP_NANSIGN_E		1
> --- libgcc/config/i386/64/sfp-machine.h.jj	2022-09-23 09:02:31.700660291 +0200
> +++ libgcc/config/i386/64/sfp-machine.h	2022-09-28 18:58:09.114520943 +0200
> @@ -14,6 +14,7 @@ typedef unsigned int UTItype __attribute
>   #define _FP_DIV_MEAT_Q(R,X,Y)   _FP_DIV_MEAT_2_udiv(Q,R,X,Y)
>   
>   #define _FP_NANFRAC_H		_FP_QNANBIT_H
> +#define _FP_NANFRAC_B		_FP_QNANBIT_B
>   #define _FP_NANFRAC_S		_FP_QNANBIT_S
>   #define _FP_NANFRAC_D		_FP_QNANBIT_D
>   #define _FP_NANFRAC_E		_FP_QNANBIT_E, 0
> --- libgcc/config/i386/32/sfp-machine.h.jj	2022-09-23 09:02:31.683660526 +0200
> +++ libgcc/config/i386/32/sfp-machine.h	2022-09-28 18:58:09.115520929 +0200
> @@ -87,6 +87,7 @@
>   #define _FP_DIV_MEAT_Q(R,X,Y)   _FP_DIV_MEAT_4_udiv(Q,R,X,Y)
>   
>   #define _FP_NANFRAC_H		_FP_QNANBIT_H
> +#define _FP_NANFRAC_B		_FP_QNANBIT_B
>   #define _FP_NANFRAC_S		_FP_QNANBIT_S
>   #define _FP_NANFRAC_D		_FP_QNANBIT_D, 0
>   /* Even if XFmode is 12byte,  we have to pad it to
> --- libgcc/soft-fp/brain.h.jj	2022-09-28 18:58:09.113520956 +0200
> +++ libgcc/soft-fp/brain.h	2022-09-28 18:58:09.113520956 +0200
> @@ -0,0 +1,172 @@
> +/* Software floating-point emulation.
> +   Definitions for Brain Floating Point format (bfloat16).
> +   Copyright (C) 1997-2022 Free Software Foundation, Inc.
> +   This file is part of the GNU C Library.
> +
> +   The GNU C Library is free software; you can redistribute it and/or
> +   modify it under the terms of the GNU Lesser General Public
> +   License as published by the Free Software Foundation; either
> +   version 2.1 of the License, or (at your option) any later version.
> +
> +   In addition to the permissions in the GNU Lesser General Public
> +   License, the Free Software Foundation gives you unlimited
> +   permission to link the compiled version of this file into
> +   combinations with other programs, and to distribute those
> +   combinations without any restriction coming from the use of this
> +   file.  (The Lesser General Public License restrictions do apply in
> +   other respects; for example, they cover modification of the file,
> +   and distribution when not linked into a combine executable.)
> +
> +   The GNU C Library is distributed in the hope that it will be useful,
> +   but WITHOUT ANY WARRANTY; without even the implied warranty of
> +   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
> +   Lesser General Public License for more details.
> +
> +   You should have received a copy of the GNU Lesser General Public
> +   License along with the GNU C Library; if not, see
> +   <https://www.gnu.org/licenses/>.  */
> +
> +#ifndef SOFT_FP_BRAIN_H
> +#define SOFT_FP_BRAIN_H	1
> +
> +#if _FP_W_TYPE_SIZE < 32
> +# error "Here's a nickel kid.  Go buy yourself a real computer."
> +#endif
> +
> +#define _FP_FRACTBITS_B		(_FP_W_TYPE_SIZE)
> +
> +#define _FP_FRACTBITS_DW_B	(_FP_W_TYPE_SIZE)
> +
> +#define _FP_FRACBITS_B		8
> +#define _FP_FRACXBITS_B		(_FP_FRACTBITS_B - _FP_FRACBITS_B)
> +#define _FP_WFRACBITS_B		(_FP_WORKBITS + _FP_FRACBITS_B)
> +#define _FP_WFRACXBITS_B	(_FP_FRACTBITS_B - _FP_WFRACBITS_B)
> +#define _FP_EXPBITS_B		8
> +#define _FP_EXPBIAS_B		127
> +#define _FP_EXPMAX_B		255
> +
> +#define _FP_QNANBIT_B		((_FP_W_TYPE) 1 << (_FP_FRACBITS_B-2))
> +#define _FP_QNANBIT_SH_B	((_FP_W_TYPE) 1 << (_FP_FRACBITS_B-2+_FP_WORKBITS))
> +#define _FP_IMPLBIT_B		((_FP_W_TYPE) 1 << (_FP_FRACBITS_B-1))
> +#define _FP_IMPLBIT_SH_B	((_FP_W_TYPE) 1 << (_FP_FRACBITS_B-1+_FP_WORKBITS))
> +#define _FP_OVERFLOW_B		((_FP_W_TYPE) 1 << (_FP_WFRACBITS_B))
> +
> +#define _FP_WFRACBITS_DW_B	(2 * _FP_WFRACBITS_B)
> +#define _FP_WFRACXBITS_DW_B	(_FP_FRACTBITS_DW_B - _FP_WFRACBITS_DW_B)
> +#define _FP_HIGHBIT_DW_B	\
> +  ((_FP_W_TYPE) 1 << (_FP_WFRACBITS_DW_B - 1) % _FP_W_TYPE_SIZE)
> +
> +/* The implementation of _FP_MUL_MEAT_B and _FP_DIV_MEAT_B should be
> +   chosen by the target machine.  */
> +
> +typedef float BFtype __attribute__ ((mode (BF)));
> +
> +union _FP_UNION_B
> +{
> +  BFtype flt;
> +  struct _FP_STRUCT_LAYOUT
> +  {
> +#if __BYTE_ORDER == __BIG_ENDIAN
> +    unsigned sign : 1;
> +    unsigned exp  : _FP_EXPBITS_B;
> +    unsigned frac : _FP_FRACBITS_B - (_FP_IMPLBIT_B != 0);
> +#else
> +    unsigned frac : _FP_FRACBITS_B - (_FP_IMPLBIT_B != 0);
> +    unsigned exp  : _FP_EXPBITS_B;
> +    unsigned sign : 1;
> +#endif
> +  } bits;
> +};
> +
> +#define FP_DECL_B(X)		_FP_DECL (1, X)
> +#define FP_UNPACK_RAW_B(X, val)	_FP_UNPACK_RAW_1 (B, X, (val))
> +#define FP_UNPACK_RAW_BP(X, val)	_FP_UNPACK_RAW_1_P (B, X, (val))
> +#define FP_PACK_RAW_B(val, X)	_FP_PACK_RAW_1 (B, (val), X)
> +#define FP_PACK_RAW_BP(val, X)			\
> +  do						\
> +    {						\
> +      if (!FP_INHIBIT_RESULTS)			\
> +	_FP_PACK_RAW_1_P (B, (val), X);		\
> +    }						\
> +  while (0)
> +
> +#define FP_UNPACK_B(X, val)			\
> +  do						\
> +    {						\
> +      _FP_UNPACK_RAW_1 (B, X, (val));		\
> +      _FP_UNPACK_CANONICAL (B, 1, X);		\
> +    }						\
> +  while (0)
> +
> +#define FP_UNPACK_BP(X, val)			\
> +  do						\
> +    {						\
> +      _FP_UNPACK_RAW_1_P (B, X, (val));		\
> +      _FP_UNPACK_CANONICAL (B, 1, X);		\
> +    }						\
> +  while (0)
> +
> +#define FP_UNPACK_SEMIRAW_B(X, val)		\
> +  do						\
> +    {						\
> +      _FP_UNPACK_RAW_1 (B, X, (val));		\
> +      _FP_UNPACK_SEMIRAW (B, 1, X);		\
> +    }						\
> +  while (0)
> +
> +#define FP_UNPACK_SEMIRAW_BP(X, val)		\
> +  do						\
> +    {						\
> +      _FP_UNPACK_RAW_1_P (B, X, (val));		\
> +      _FP_UNPACK_SEMIRAW (B, 1, X);		\
> +    }						\
> +  while (0)
> +
> +#define FP_PACK_B(val, X)			\
> +  do						\
> +    {						\
> +      _FP_PACK_CANONICAL (B, 1, X);		\
> +      _FP_PACK_RAW_1 (B, (val), X);		\
> +    }						\
> +  while (0)
> +
> +#define FP_PACK_BP(val, X)			\
> +  do						\
> +    {						\
> +      _FP_PACK_CANONICAL (B, 1, X);		\
> +      if (!FP_INHIBIT_RESULTS)			\
> +	_FP_PACK_RAW_1_P (B, (val), X);		\
> +    }						\
> +  while (0)
> +
> +#define FP_PACK_SEMIRAW_B(val, X)		\
> +  do						\
> +    {						\
> +      _FP_PACK_SEMIRAW (B, 1, X);		\
> +      _FP_PACK_RAW_1 (B, (val), X);		\
> +    }						\
> +  while (0)
> +
> +#define FP_PACK_SEMIRAW_BP(val, X)		\
> +  do						\
> +    {						\
> +      _FP_PACK_SEMIRAW (B, 1, X);		\
> +      if (!FP_INHIBIT_RESULTS)			\
> +	_FP_PACK_RAW_1_P (B, (val), X);		\
> +    }						\
> +  while (0)
> +
> +#define FP_TO_INT_B(r, X, rsz, rsg)	_FP_TO_INT (B, 1, (r), X, (rsz), (rsg))
> +#define FP_TO_INT_ROUND_B(r, X, rsz, rsg)	\
> +  _FP_TO_INT_ROUND (B, 1, (r), X, (rsz), (rsg))
> +#define FP_FROM_INT_B(X, r, rs, rt)	_FP_FROM_INT (B, 1, X, (r), (rs), rt)
> +
> +/* BFmode arithmetic is not implemented.  */
> +
> +#define _FP_FRAC_HIGH_B(X)	_FP_FRAC_HIGH_1 (X)
> +#define _FP_FRAC_HIGH_RAW_B(X)	_FP_FRAC_HIGH_1 (X)
> +#define _FP_FRAC_HIGH_DW_B(X)	_FP_FRAC_HIGH_1 (X)
> +
> +#define FP_CMP_EQ_B(r, X, Y, ex)       _FP_CMP_EQ (B, 1, (r), X, Y, (ex))
> +
> +#endif /* !SOFT_FP_BRAIN_H */
> --- libgcc/soft-fp/truncsfbf2.c.jj	2022-09-28 18:58:09.113520956 +0200
> +++ libgcc/soft-fp/truncsfbf2.c	2022-09-28 18:58:09.113520956 +0200
> @@ -0,0 +1,48 @@
> +/* Software floating-point emulation.
> +   Truncate IEEE single into bfloat16.
> +   Copyright (C) 2022 Free Software Foundation, Inc.
> +   This file is part of the GNU C Library.
> +
> +   The GNU C Library is free software; you can redistribute it and/or
> +   modify it under the terms of the GNU Lesser General Public
> +   License as published by the Free Software Foundation; either
> +   version 2.1 of the License, or (at your option) any later version.
> +
> +   In addition to the permissions in the GNU Lesser General Public
> +   License, the Free Software Foundation gives you unlimited
> +   permission to link the compiled version of this file into
> +   combinations with other programs, and to distribute those
> +   combinations without any restriction coming from the use of this
> +   file.  (The Lesser General Public License restrictions do apply in
> +   other respects; for example, they cover modification of the file,
> +   and distribution when not linked into a combine executable.)
> +
> +   The GNU C Library is distributed in the hope that it will be useful,
> +   but WITHOUT ANY WARRANTY; without even the implied warranty of
> +   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
> +   Lesser General Public License for more details.
> +
> +   You should have received a copy of the GNU Lesser General Public
> +   License along with the GNU C Library; if not, see
> +   <http://www.gnu.org/licenses/>.  */
> +
> +#include "soft-fp.h"
> +#include "brain.h"
> +#include "single.h"
> +
> +BFtype
> +__truncsfbf2 (SFtype a)
> +{
> +  FP_DECL_EX;
> +  FP_DECL_S (A);
> +  FP_DECL_B (R);
> +  BFtype r;
> +
> +  FP_INIT_ROUNDMODE;
> +  FP_UNPACK_SEMIRAW_S (A, a);
> +  FP_TRUNC (B, S, 1, 1, R, A);
> +  FP_PACK_SEMIRAW_B (r, R);
> +  FP_HANDLE_EXCEPTIONS;
> +
> +  return r;
> +}
> --- libgcc/soft-fp/truncdfbf2.c.jj	2022-09-28 18:58:09.114520943 +0200
> +++ libgcc/soft-fp/truncdfbf2.c	2022-09-28 18:58:09.114520943 +0200
> @@ -0,0 +1,52 @@
> +/* Software floating-point emulation.
> +   Truncate IEEE double into bfloat16.
> +   Copyright (C) 2022 Free Software Foundation, Inc.
> +   This file is part of the GNU C Library.
> +
> +   The GNU C Library is free software; you can redistribute it and/or
> +   modify it under the terms of the GNU Lesser General Public
> +   License as published by the Free Software Foundation; either
> +   version 2.1 of the License, or (at your option) any later version.
> +
> +   In addition to the permissions in the GNU Lesser General Public
> +   License, the Free Software Foundation gives you unlimited
> +   permission to link the compiled version of this file into
> +   combinations with other programs, and to distribute those
> +   combinations without any restriction coming from the use of this
> +   file.  (The Lesser General Public License restrictions do apply in
> +   other respects; for example, they cover modification of the file,
> +   and distribution when not linked into a combine executable.)
> +
> +   The GNU C Library is distributed in the hope that it will be useful,
> +   but WITHOUT ANY WARRANTY; without even the implied warranty of
> +   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
> +   Lesser General Public License for more details.
> +
> +   You should have received a copy of the GNU Lesser General Public
> +   License along with the GNU C Library; if not, see
> +   <http://www.gnu.org/licenses/>.  */
> +
> +#include "soft-fp.h"
> +#include "brain.h"
> +#include "double.h"
> +
> +BFtype
> +__truncdfbf2 (DFtype a)
> +{
> +  FP_DECL_EX;
> +  FP_DECL_D (A);
> +  FP_DECL_B (R);
> +  BFtype r;
> +
> +  FP_INIT_ROUNDMODE;
> +  FP_UNPACK_SEMIRAW_D (A, a);
> +#if _FP_W_TYPE_SIZE < _FP_FRACBITS_D
> +  FP_TRUNC (B, D, 1, 2, R, A);
> +#else
> +  FP_TRUNC (B, D, 1, 1, R, A);
> +#endif
> +  FP_PACK_SEMIRAW_B (r, R);
> +  FP_HANDLE_EXCEPTIONS;
> +
> +  return r;
> +}
> --- libgcc/soft-fp/truncxfbf2.c.jj	2022-09-28 18:58:09.113520956 +0200
> +++ libgcc/soft-fp/truncxfbf2.c	2022-09-28 18:58:09.113520956 +0200
> @@ -0,0 +1,52 @@
> +/* Software floating-point emulation.
> +   Truncate IEEE extended into bfloat16.
> +   Copyright (C) 2022 Free Software Foundation, Inc.
> +   This file is part of the GNU C Library.
> +
> +   The GNU C Library is free software; you can redistribute it and/or
> +   modify it under the terms of the GNU Lesser General Public
> +   License as published by the Free Software Foundation; either
> +   version 2.1 of the License, or (at your option) any later version.
> +
> +   In addition to the permissions in the GNU Lesser General Public
> +   License, the Free Software Foundation gives you unlimited
> +   permission to link the compiled version of this file into
> +   combinations with other programs, and to distribute those
> +   combinations without any restriction coming from the use of this
> +   file.  (The Lesser General Public License restrictions do apply in
> +   other respects; for example, they cover modification of the file,
> +   and distribution when not linked into a combine executable.)
> +
> +   The GNU C Library is distributed in the hope that it will be useful,
> +   but WITHOUT ANY WARRANTY; without even the implied warranty of
> +   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
> +   Lesser General Public License for more details.
> +
> +   You should have received a copy of the GNU Lesser General Public
> +   License along with the GNU C Library; if not, see
> +   <http://www.gnu.org/licenses/>.  */
> +
> +#include "soft-fp.h"
> +#include "brain.h"
> +#include "extended.h"
> +
> +BFtype
> +__truncxfbf2 (XFtype a)
> +{
> +  FP_DECL_EX;
> +  FP_DECL_E (A);
> +  FP_DECL_B (R);
> +  BFtype r;
> +
> +  FP_INIT_ROUNDMODE;
> +  FP_UNPACK_SEMIRAW_E (A, a);
> +#if _FP_W_TYPE_SIZE < 64
> +  FP_TRUNC (B, E, 1, 4, R, A);
> +#else
> +  FP_TRUNC (B, E, 1, 2, R, A);
> +#endif
> +  FP_PACK_SEMIRAW_B (r, R);
> +  FP_HANDLE_EXCEPTIONS;
> +
> +  return r;
> +}
> --- libgcc/soft-fp/trunctfbf2.c.jj	2022-09-28 18:58:09.114520943 +0200
> +++ libgcc/soft-fp/trunctfbf2.c	2022-09-28 18:58:09.114520943 +0200
> @@ -0,0 +1,52 @@
> +/* Software floating-point emulation.
> +   Truncate IEEE quad into bfloat16.
> +   Copyright (C) 2022 Free Software Foundation, Inc.
> +   This file is part of the GNU C Library.
> +
> +   The GNU C Library is free software; you can redistribute it and/or
> +   modify it under the terms of the GNU Lesser General Public
> +   License as published by the Free Software Foundation; either
> +   version 2.1 of the License, or (at your option) any later version.
> +
> +   In addition to the permissions in the GNU Lesser General Public
> +   License, the Free Software Foundation gives you unlimited
> +   permission to link the compiled version of this file into
> +   combinations with other programs, and to distribute those
> +   combinations without any restriction coming from the use of this
> +   file.  (The Lesser General Public License restrictions do apply in
> +   other respects; for example, they cover modification of the file,
> +   and distribution when not linked into a combine executable.)
> +
> +   The GNU C Library is distributed in the hope that it will be useful,
> +   but WITHOUT ANY WARRANTY; without even the implied warranty of
> +   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
> +   Lesser General Public License for more details.
> +
> +   You should have received a copy of the GNU Lesser General Public
> +   License along with the GNU C Library; if not, see
> +   <https://www.gnu.org/licenses/>.  */
> +
> +#include "soft-fp.h"
> +#include "brain.h"
> +#include "quad.h"
> +
> +BFtype
> +__trunctfbf2 (TFtype a)
> +{
> +  FP_DECL_EX;
> +  FP_DECL_Q (A);
> +  FP_DECL_B (R);
> +  BFtype r;
> +
> +  FP_INIT_ROUNDMODE;
> +  FP_UNPACK_SEMIRAW_Q (A, a);
> +#if _FP_W_TYPE_SIZE < 64
> +  FP_TRUNC (B, Q, 1, 4, R, A);
> +#else
> +  FP_TRUNC (B, Q, 1, 2, R, A);
> +#endif
> +  FP_PACK_SEMIRAW_B (r, R);
> +  FP_HANDLE_EXCEPTIONS;
> +
> +  return r;
> +}
> --- libgcc/soft-fp/trunchfbf2.c.jj	2022-09-28 18:58:09.114520943 +0200
> +++ libgcc/soft-fp/trunchfbf2.c	2022-09-28 18:58:09.114520943 +0200
> @@ -0,0 +1,58 @@
> +/* Software floating-point emulation.
> +   Truncate IEEE half into bfloat16.
> +   Copyright (C) 2022 Free Software Foundation, Inc.
> +   This file is part of the GNU C Library.
> +
> +   The GNU C Library is free software; you can redistribute it and/or
> +   modify it under the terms of the GNU Lesser General Public
> +   License as published by the Free Software Foundation; either
> +   version 2.1 of the License, or (at your option) any later version.
> +
> +   In addition to the permissions in the GNU Lesser General Public
> +   License, the Free Software Foundation gives you unlimited
> +   permission to link the compiled version of this file into
> +   combinations with other programs, and to distribute those
> +   combinations without any restriction coming from the use of this
> +   file.  (The Lesser General Public License restrictions do apply in
> +   other respects; for example, they cover modification of the file,
> +   and distribution when not linked into a combine executable.)
> +
> +   The GNU C Library is distributed in the hope that it will be useful,
> +   but WITHOUT ANY WARRANTY; without even the implied warranty of
> +   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
> +   Lesser General Public License for more details.
> +
> +   You should have received a copy of the GNU Lesser General Public
> +   License along with the GNU C Library; if not, see
> +   <http://www.gnu.org/licenses/>.  */
> +
> +#include "soft-fp.h"
> +#include "brain.h"
> +#include "half.h"
> +#include "single.h"
> +
> +/* BFtype and HFtype are unordered, neither is a superset or subset
> +   of each other.  Convert HFtype to SFtype (lossless) and then
> +   truncate to BFtype.  */
> +
> +BFtype
> +__trunchfbf2 (HFtype a)
> +{
> +  FP_DECL_EX;
> +  FP_DECL_H (A);
> +  FP_DECL_S (B);
> +  FP_DECL_B (R);
> +  SFtype b;
> +  BFtype r;
> +
> +  FP_INIT_ROUNDMODE;
> +  FP_UNPACK_RAW_H (A, a);
> +  FP_EXTEND (S, H, 1, 1, B, A);
> +  FP_PACK_RAW_S (b, B);
> +  FP_UNPACK_SEMIRAW_S (B, b);
> +  FP_TRUNC (B, S, 1, 1, R, B);
> +  FP_PACK_SEMIRAW_B (r, R);
> +  FP_HANDLE_EXCEPTIONS;
> +
> +  return r;
> +}
> --- libgcc/soft-fp/truncbfhf2.c.jj	2022-09-28 18:58:09.113520956 +0200
> +++ libgcc/soft-fp/truncbfhf2.c	2022-09-28 18:58:09.113520956 +0200
> @@ -0,0 +1,75 @@
> +/* Software floating-point emulation.
> +   Truncate bfloat16 into IEEE half.
> +   Copyright (C) 2022 Free Software Foundation, Inc.
> +   This file is part of the GNU C Library.
> +
> +   The GNU C Library is free software; you can redistribute it and/or
> +   modify it under the terms of the GNU Lesser General Public
> +   License as published by the Free Software Foundation; either
> +   version 2.1 of the License, or (at your option) any later version.
> +
> +   In addition to the permissions in the GNU Lesser General Public
> +   License, the Free Software Foundation gives you unlimited
> +   permission to link the compiled version of this file into
> +   combinations with other programs, and to distribute those
> +   combinations without any restriction coming from the use of this
> +   file.  (The Lesser General Public License restrictions do apply in
> +   other respects; for example, they cover modification of the file,
> +   and distribution when not linked into a combine executable.)
> +
> +   The GNU C Library is distributed in the hope that it will be useful,
> +   but WITHOUT ANY WARRANTY; without even the implied warranty of
> +   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
> +   Lesser General Public License for more details.
> +
> +   You should have received a copy of the GNU Lesser General Public
> +   License along with the GNU C Library; if not, see
> +   <http://www.gnu.org/licenses/>.  */
> +
> +#include "soft-fp.h"
> +#include "half.h"
> +#include "brain.h"
> +#include "single.h"
> +
> +/* BFtype and HFtype are unordered, neither is a superset or subset
> +   of each other.  Convert BFtype to SFtype (lossless) and then
> +   truncate to HFtype.  */
> +
> +HFtype
> +__truncbfhf2 (BFtype a)
> +{
> +  FP_DECL_EX;
> +  FP_DECL_H (A);
> +  FP_DECL_S (B);
> +  FP_DECL_B (R);
> +  SFtype b;
> +  HFtype r;
> +
> +  FP_INIT_ROUNDMODE;
> +  /* Optimize BFtype to SFtype conversion to simple left shift
> +     by 16 if possible, we don't need to raise exceptions on sNaN
> +     here as the SFtype to HFtype truncation should do that too.  */
> +  if (sizeof (BFtype) == 2
> +      && sizeof (unsigned short) == 2
> +      && sizeof (SFtype) == 4
> +      && sizeof (unsigned int) == 4)
> +    {
> +      union { BFtype a; unsigned short b; } u1;
> +      union { SFtype a; unsigned int b; } u2;
> +      u1.a = a;
> +      u2.b = (u1.b << 8) << 8;
> +      b = u2.a;
> +    }
> +  else
> +    {
> +      FP_UNPACK_RAW_B (A, a);
> +      FP_EXTEND (S, B, 1, 1, B, A);
> +      FP_PACK_RAW_S (b, B);
> +    }
> +  FP_UNPACK_SEMIRAW_S (B, b);
> +  FP_TRUNC (H, S, 1, 1, R, B);
> +  FP_PACK_SEMIRAW_H (r, R);
> +  FP_HANDLE_EXCEPTIONS;
> +
> +  return r;
> +}
> --- libgcc/soft-fp/extendbfsf2.c.jj	2022-09-28 18:58:09.114520943 +0200
> +++ libgcc/soft-fp/extendbfsf2.c	2022-09-28 18:58:09.114520943 +0200
> @@ -0,0 +1,49 @@
> +/* Software floating-point emulation.
> +   Return an bfloat16 converted to IEEE single
> +   Copyright (C) 2022 Free Software Foundation, Inc.
> +   This file is part of the GNU C Library.
> +
> +   The GNU C Library is free software; you can redistribute it and/or
> +   modify it under the terms of the GNU Lesser General Public
> +   License as published by the Free Software Foundation; either
> +   version 2.1 of the License, or (at your option) any later version.
> +
> +   In addition to the permissions in the GNU Lesser General Public
> +   License, the Free Software Foundation gives you unlimited
> +   permission to link the compiled version of this file into
> +   combinations with other programs, and to distribute those
> +   combinations without any restriction coming from the use of this
> +   file.  (The Lesser General Public License restrictions do apply in
> +   other respects; for example, they cover modification of the file,
> +   and distribution when not linked into a combine executable.)
> +
> +   The GNU C Library is distributed in the hope that it will be useful,
> +   but WITHOUT ANY WARRANTY; without even the implied warranty of
> +   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
> +   Lesser General Public License for more details.
> +
> +   You should have received a copy of the GNU Lesser General Public
> +   License along with the GNU C Library; if not, see
> +   <http://www.gnu.org/licenses/>.  */
> +
> +#define FP_NO_EXACT_UNDERFLOW
> +#include "soft-fp.h"
> +#include "brain.h"
> +#include "single.h"
> +
> +SFtype
> +__extendbfsf2 (BFtype a)
> +{
> +  FP_DECL_EX;
> +  FP_DECL_B (A);
> +  FP_DECL_S (R);
> +  SFtype r;
> +
> +  FP_INIT_EXCEPTIONS;
> +  FP_UNPACK_RAW_B (A, a);
> +  FP_EXTEND (S, B, 1, 1, R, A);
> +  FP_PACK_RAW_S (r, R);
> +  FP_HANDLE_EXCEPTIONS;
> +
> +  return r;
> +}
> --- libiberty/cp-demangle.h.jj	2022-09-27 08:03:27.142982423 +0200
> +++ libiberty/cp-demangle.h	2022-09-29 12:42:47.291727886 +0200
> @@ -180,7 +180,7 @@ d_advance (struct d_info *di, int i)
>   extern const struct demangle_operator_info cplus_demangle_operators[];
>   #endif
>   
> -#define D_BUILTIN_TYPE_COUNT (35)
> +#define D_BUILTIN_TYPE_COUNT (36)
>   
>   CP_STATIC_IF_GLIBCPP_V3
>   const struct demangle_builtin_type_info
> --- libiberty/cp-demangle.c.jj	2022-09-27 08:03:27.141982437 +0200
> +++ libiberty/cp-demangle.c	2022-09-29 13:04:57.083526204 +0200
> @@ -2489,6 +2489,7 @@ cplus_demangle_builtin_types[D_BUILTIN_T
>     /* 33 */ { NL ("decltype(nullptr)"),	NL ("decltype(nullptr)"),
>   	     D_PRINT_DEFAULT },
>     /* 34 */ { NL ("_Float"),	NL ("_Float"),		D_PRINT_FLOAT },
> +  /* 35 */ { NL ("std::bfloat16_t"), NL ("std::bfloat16_t"), D_PRINT_FLOAT },
>   };
>   
>   CP_STATIC_IF_GLIBCPP_V3
> @@ -2753,8 +2754,20 @@ cplus_demangle_type (struct d_info *di)
>   
>   	case 'F':
>   	  /* DF<number>_ - _Float<number>.
> -	     DF<number>x - _Float<number>x.  */
> +	     DF<number>x - _Float<number>x
> +	     DFb16_ - std::bfloat16_t.  */
>   	  {
> +	    if (d_peek_char (di) == 'b')
> +	      {
> +		d_advance (di, 1);
> +		if (d_number (di) != 16 || d_peek_char (di) != '_')
> +		  return NULL;
> +		d_advance (di, 1);
> +		ret = d_make_builtin_type (di,
> +					   &cplus_demangle_builtin_types[35]);
> +		di->expansion += ret->u.s_builtin.type->len;
> +		break;
> +	      }
>   	    int arg = d_number (di);
>   	    char buf[12];
>   	    char suffix = 0;
> --- libiberty/testsuite/demangle-expected.jj	2022-09-27 08:03:27.168982071 +0200
> +++ libiberty/testsuite/demangle-expected	2022-09-29 12:49:02.181597532 +0200
> @@ -1249,6 +1249,10 @@ xxx
>   _Z3xxxDF32xDF64xDF128xCDF32xVb
>   xxx(_Float32x, _Float64x, _Float128x, _Float32x _Complex, bool volatile)
>   xxx
> +--format=auto --no-params
> +_Z3xxxDFb16_
> +xxx(std::bfloat16_t)
> +xxx
>   # https://sourceware.org/bugzilla/show_bug.cgi?id=16817
>   --format=auto --no-params
>   _QueueNotification_QueueController__$4PPPPPPPM_A_INotice___Z
> 
> 	Jakub
>
  
Jakub Jelinek Sept. 30, 2022, 2:08 p.m. UTC | #2
On Fri, Sep 30, 2022 at 09:49:08AM -0400, Jason Merrill wrote:
> The comment from Apple on the ABI mangling proposal suggests to me that we
> might want to delay enabling C++ std::bfloat16_t (i.e. defining
> __STDCPP_BFLOAT16_T__) until we have that excess precision support?

I saw that comment.  We have similar problem with _Float16 too, where C++
effectively right now works as when one uses -fexcess-precision=16 in C
(which isn't default).
I can see how hard would it be to add EXCESS_PRECISION_EXPR support to C++
FE.

> > 	* config/arm/arm.cc (TARGET_INVALID_UNARY_OP,
> > 	TARGET_INVALID_BINARY_OP): Don't redefine.
> > 	(arm_mangle_type): Mangle BFmode as DFb16_.
> 
> If we're using DF32x for _Float32x, maybe we want DF16b for bfloat16?

Perhaps, I just followed what was in the pull request.  Can change it.

Anyway, overnight testing found some missing CFLAGS-*.c += -msse2
lines in libgcc/config/i386/t-softfp and some i386 tests that were testing
the inability to cast or use __bf16 in expressions, so have adjusted that
too.
What isn't in the patch but I think we'll need to also change are some
minimal set of __builtin_*bf16 builtins.  Seems for _Float16, GCC provides
all the __builtin_*f16 (and for C/ObjC even with *f16 names), but there is
no glibc support for any of that, so builtins that are expanded by the
compiler are fine, but what should be fall back to libm won't work.
Maybe at least for now it is acceptable to implement most <cmath> and
<complex> std::float16_t and std::bfloat16_t overloads with using
__builtin_*f and explicitly narrow down, but I think at least nextafter
(and apparently nexttoward as an alias for it for extended floating
point types) needs to be specific for the particular floating point format.
And, while e.g. most of bfloat16_t stuff in numeric_limits can be done
using say (__bf16) __builtin_nanf ("") and similar, at least for sNaN
I'm afraid there is no replacement, as it needs to be constexpr and so
we can't use union type punning to get signaling NaN value.  So we'll
need at least __builtin_nansbf16, maybe __builtin_huge_valbf16 and some
others for start.

2022-09-30  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.
	* 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.
	* config/arm/arm.h (arm_bf16_type_node): Remove.
	(arm_bf16_ptr_type_node): Adjust comment.
	* config/arm/arm.cc (TARGET_INVALID_UNARY_OP,
	TARGET_INVALID_BINARY_OP): Don't redefine.
	(arm_mangle_type): Mangle BFmode as DFb16_.
	(arm_invalid_conversion): Only reject BF <-> HF conversions if
	HFmode is non-IEEE format.
	(arm_invalid_unary_op, arm_invalid_binary_op): Remove.
	* config/arm/arm-builtins.cc (arm_bf16_type_node): Remove.
	(arm_simd_builtin_std_type): Use bfloat16_type_node rather than
	arm_bf16_type_node.
	(arm_init_simd_builtin_types): Likewise.
	(arm_init_simd_builtin_scalar_types): Likewise.
	(arm_init_bf16_types): Likewise.
	* config/i386/i386.cc (ix86_mangle_type): Mangle BFmode as DFb16_.
	(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.
	* config/i386/i386-builtin-types.def (BFLOAT16): Likewise.
	* config/aarch64/aarch64.h (aarch64_bf16_type_node): Remove.
	(aarch64_bf16_ptr_type_node): Adjust comment.
	* config/aarch64/aarch64.cc (aarch64_gimplify_va_arg_expr): Use
	bfloat16_type_node rather than aarch64_bf16_type_node.
	(aarch64_mangle_type): Mangle BFmode as DFb16_.
	(aarch64_invalid_conversion, aarch64_invalid_unary_op): Remove.
	aarch64_invalid_binary_op): Remove BFmode related rejections.
	(TARGET_INVALID_CONVERSION, TARGET_INVALID_UNARY_OP): Don't redefine.
	* config/aarch64/aarch64-builtins.cc (aarch64_bf16_type_node): Remove.
	(aarch64_int_or_fp_type): Use bfloat16_type_node rather than
	aarch64_bf16_type_node.
	(aarch64_init_simd_builtin_types, aarch64_init_bf16_types): Likewise.
	* config/aarch64/aarch64-sve-builtins.def (svbfloat16_t): Likewise.
gcc/c-family/
	* c-cppbuiltin.cc (c_cpp_builtins): If bfloat16_type_node,
	predefine for C++ __BFLT16_*__ macros and for C++23 also
	__STDCPP_BFLOAT16_T__.
	* c-lex.cc (interpret_float): Handle CPP_N_BFLOAT16 for C++.
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/
	* 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/arm/sfp-machine.h (_FP_NANFRAC_B): Define.
	* config/aarch64/t-softfp (softfp_extensions): Add bfsf.
	(softfp_truncations): Add tfbf dfbf sfbf hfbf.
	* config/aarch64/libgcc-softfp.ver (GCC_13.0.0): Export
	__extendbfsf2 and __trunc{s,d,t,h}fbf2.
	* config/aarch64/sfp-machine.h (_FP_NANFRAC_B): Define.
	* 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 DFb16_.
	* testsuite/demangle-expected (_Z3xxxDFb16_): New test.

--- gcc/tree-core.h.jj	2022-09-29 09:13:25.717718458 +0200
+++ gcc/tree-core.h	2022-09-29 12:40:17.417778754 +0200
@@ -665,6 +665,9 @@ enum tree_index {
   TI_DOUBLE_TYPE,
   TI_LONG_DOUBLE_TYPE,
 
+  /* __bf16 type if supported (used in C++ as std::bfloat16_t).  */
+  TI_BFLOAT16_TYPE,
+
   /* The _FloatN and _FloatNx types must be consecutive, and in the
      same sequence as the corresponding complex types, which must also
      be consecutive; _FloatN must come before _FloatNx; the order must
--- gcc/tree.h.jj	2022-09-29 09:13:25.720718416 +0200
+++ gcc/tree.h	2022-09-29 12:40:17.416778768 +0200
@@ -4285,6 +4285,7 @@ tree_strip_any_location_wrapper (tree ex
 #define float_type_node			global_trees[TI_FLOAT_TYPE]
 #define double_type_node		global_trees[TI_DOUBLE_TYPE]
 #define long_double_type_node		global_trees[TI_LONG_DOUBLE_TYPE]
+#define bfloat16_type_node		global_trees[TI_BFLOAT16_TYPE]
 
 /* Nodes for particular _FloatN and _FloatNx types in sequence.  */
 #define FLOATN_TYPE_NODE(IDX)		global_trees[TI_FLOATN_TYPE_FIRST + (IDX)]
--- gcc/tree.cc.jj	2022-09-29 09:13:31.328641080 +0200
+++ gcc/tree.cc	2022-09-29 12:40:17.400778985 +0200
@@ -7711,7 +7711,7 @@ excess_precision_type (tree type)
     = (flag_excess_precision == EXCESS_PRECISION_FAST
        ? EXCESS_PRECISION_TYPE_FAST
        : (flag_excess_precision == EXCESS_PRECISION_FLOAT16
-	  ? EXCESS_PRECISION_TYPE_FLOAT16 :EXCESS_PRECISION_TYPE_STANDARD));
+	  ? EXCESS_PRECISION_TYPE_FLOAT16 : EXCESS_PRECISION_TYPE_STANDARD));
 
   enum flt_eval_method target_flt_eval_method
     = targetm.c.excess_precision (requested_type);
@@ -7736,6 +7736,9 @@ excess_precision_type (tree type)
   machine_mode float16_type_mode = (float16_type_node
 				    ? TYPE_MODE (float16_type_node)
 				    : VOIDmode);
+  machine_mode bfloat16_type_mode = (bfloat16_type_node
+				     ? TYPE_MODE (bfloat16_type_node)
+				     : VOIDmode);
   machine_mode float_type_mode = TYPE_MODE (float_type_node);
   machine_mode double_type_mode = TYPE_MODE (double_type_node);
 
@@ -7747,16 +7750,19 @@ excess_precision_type (tree type)
 	switch (target_flt_eval_method)
 	  {
 	  case FLT_EVAL_METHOD_PROMOTE_TO_FLOAT:
-	    if (type_mode == float16_type_mode)
+	    if (type_mode == float16_type_mode
+		|| type_mode == bfloat16_type_mode)
 	      return float_type_node;
 	    break;
 	  case FLT_EVAL_METHOD_PROMOTE_TO_DOUBLE:
 	    if (type_mode == float16_type_mode
+		|| type_mode == bfloat16_type_mode
 		|| type_mode == float_type_mode)
 	      return double_type_node;
 	    break;
 	  case FLT_EVAL_METHOD_PROMOTE_TO_LONG_DOUBLE:
 	    if (type_mode == float16_type_mode
+		|| type_mode == bfloat16_type_mode
 		|| type_mode == float_type_mode
 		|| type_mode == double_type_mode)
 	      return long_double_type_node;
@@ -7774,16 +7780,19 @@ excess_precision_type (tree type)
 	switch (target_flt_eval_method)
 	  {
 	  case FLT_EVAL_METHOD_PROMOTE_TO_FLOAT:
-	    if (type_mode == float16_type_mode)
+	    if (type_mode == float16_type_mode
+		|| type_mode == bfloat16_type_mode)
 	      return complex_float_type_node;
 	    break;
 	  case FLT_EVAL_METHOD_PROMOTE_TO_DOUBLE:
 	    if (type_mode == float16_type_mode
+		|| type_mode == bfloat16_type_mode
 		|| type_mode == float_type_mode)
 	      return complex_double_type_node;
 	    break;
 	  case FLT_EVAL_METHOD_PROMOTE_TO_LONG_DOUBLE:
 	    if (type_mode == float16_type_mode
+		|| type_mode == bfloat16_type_mode
 		|| type_mode == float_type_mode
 		|| type_mode == double_type_mode)
 	      return complex_long_double_type_node;
--- gcc/expmed.h.jj	2022-07-26 10:32:23.681271790 +0200
+++ gcc/expmed.h	2022-09-29 15:18:46.457023535 +0200
@@ -707,6 +707,8 @@ extern rtx expand_variable_shift (enum t
 				  rtx, tree, rtx, int);
 extern rtx expand_shift (enum tree_code, machine_mode, rtx, poly_int64, rtx,
 			 int);
+extern rtx maybe_expand_shift (enum tree_code, machine_mode, rtx, int, rtx,
+			       int);
 #ifdef GCC_OPTABS_H
 extern rtx expand_divmod (int, enum tree_code, machine_mode, rtx, rtx,
 			  rtx, int, enum optab_methods = OPTAB_LIB_WIDEN);
--- gcc/expmed.cc.jj	2022-08-31 10:20:20.000000000 +0200
+++ gcc/expmed.cc	2022-09-29 15:17:52.224769673 +0200
@@ -2705,7 +2705,7 @@ expand_shift (enum tree_code code, machi
 
 /* Likewise, but return 0 if that cannot be done.  */
 
-static rtx
+rtx
 maybe_expand_shift (enum tree_code code, machine_mode mode, rtx shifted,
 		    int amount, rtx target, int unsignedp)
 {
--- gcc/expr.cc.jj	2022-09-09 09:50:35.228575531 +0200
+++ gcc/expr.cc	2022-09-29 17:09:46.716352938 +0200
@@ -344,7 +344,11 @@ convert_mode_scalar (rtx to, rtx from, i
       gcc_assert ((GET_MODE_PRECISION (from_mode)
 		   != GET_MODE_PRECISION (to_mode))
 		  || (DECIMAL_FLOAT_MODE_P (from_mode)
-		      != DECIMAL_FLOAT_MODE_P (to_mode)));
+		      != DECIMAL_FLOAT_MODE_P (to_mode))
+		  || (REAL_MODE_FORMAT (from_mode) == &arm_bfloat_half_format
+		      && REAL_MODE_FORMAT (to_mode) == &ieee_half_format)
+		  || (REAL_MODE_FORMAT (to_mode) == &arm_bfloat_half_format
+		      && REAL_MODE_FORMAT (from_mode) == &ieee_half_format));
 
       if (GET_MODE_PRECISION (from_mode) == GET_MODE_PRECISION (to_mode))
 	/* Conversion between decimal float and binary float, same size.  */
@@ -364,6 +368,150 @@ convert_mode_scalar (rtx to, rtx from, i
 	  return;
 	}
 
+#ifdef HAVE_SFmode
+      if (REAL_MODE_FORMAT (from_mode) == &arm_bfloat_half_format
+	  && REAL_MODE_FORMAT (SFmode) == &ieee_single_format)
+	{
+	  if (GET_MODE_PRECISION (to_mode) > GET_MODE_PRECISION (SFmode))
+	    {
+	      /* To cut down on libgcc size, implement
+		 BFmode -> {DF,XF,TF}mode conversions by
+		 BFmode -> SFmode -> {DF,XF,TF}mode conversions.  */
+	      rtx temp = gen_reg_rtx (SFmode);
+	      convert_mode_scalar (temp, from, unsignedp);
+	      convert_mode_scalar (to, temp, unsignedp);
+	      return;
+	    }
+	  if (REAL_MODE_FORMAT (to_mode) == &ieee_half_format)
+	    {
+	      /* Similarly, implement BFmode -> HFmode as
+		 BFmode -> SFmode -> HFmode conversion where SFmode
+		 has superset of BFmode values.  We don't need
+		 to handle sNaNs by raising exception and turning
+		 into into qNaN though, as that can be done in the
+		 SFmode -> HFmode conversion too.  */
+	      rtx temp = gen_reg_rtx (SFmode);
+	      int save_flag_finite_math_only = flag_finite_math_only;
+	      flag_finite_math_only = true;
+	      convert_mode_scalar (temp, from, unsignedp);
+	      flag_finite_math_only = save_flag_finite_math_only;
+	      convert_mode_scalar (to, temp, unsignedp);
+	      return;
+	    }
+	  if (to_mode == SFmode
+	      && !HONOR_NANS (from_mode)
+	      && !HONOR_NANS (to_mode)
+	      && optimize_insn_for_speed_p ())
+	    {
+	      /* If we don't expect sNaNs, for BFmode -> SFmode we can just
+		 shift the bits up.  */
+	      machine_mode fromi_mode, toi_mode;
+	      if (int_mode_for_size (GET_MODE_BITSIZE (from_mode),
+				     0).exists (&fromi_mode)
+		  && int_mode_for_size (GET_MODE_BITSIZE (to_mode),
+					0).exists (&toi_mode))
+		{
+		  start_sequence ();
+		  rtx fromi = lowpart_subreg (fromi_mode, from, from_mode);
+		  rtx tof = NULL_RTX;
+		  if (fromi)
+		    {
+		      rtx toi = gen_reg_rtx (toi_mode);
+		      convert_mode_scalar (toi, fromi, 1);
+		      toi
+			= maybe_expand_shift (LSHIFT_EXPR, toi_mode, toi,
+					      GET_MODE_PRECISION (to_mode)
+					      - GET_MODE_PRECISION (from_mode),
+					      NULL_RTX, 1);
+		      if (toi)
+			{
+			  tof = lowpart_subreg (to_mode, toi, toi_mode);
+			  if (tof)
+			    emit_move_insn (to, tof);
+			}
+		    }
+		  insns = get_insns ();
+		  end_sequence ();
+		  if (tof)
+		    {
+		      emit_insn (insns);
+		      return;
+		    }
+		}
+	    }
+	}
+      if (REAL_MODE_FORMAT (from_mode) == &ieee_single_format
+	  && REAL_MODE_FORMAT (to_mode) == &arm_bfloat_half_format
+	  && !HONOR_NANS (from_mode)
+	  && !HONOR_NANS (to_mode)
+	  && !flag_rounding_math
+	  && optimize_insn_for_speed_p ())
+	{
+	  /* If we don't expect qNaNs nor sNaNs and can assume rounding
+	     to nearest, we can expand the conversion inline as
+	     (fromi + 0x7fff + ((fromi >> 16) & 1)) >> 16.  */
+	  machine_mode fromi_mode, toi_mode;
+	  if (int_mode_for_size (GET_MODE_BITSIZE (from_mode),
+				 0).exists (&fromi_mode)
+	      && int_mode_for_size (GET_MODE_BITSIZE (to_mode),
+				    0).exists (&toi_mode))
+	    {
+	      start_sequence ();
+	      rtx fromi = lowpart_subreg (fromi_mode, from, from_mode);
+	      rtx tof = NULL_RTX;
+	      do
+		{
+		  if (!fromi)
+		    break;
+		  int shift = (GET_MODE_PRECISION (from_mode)
+			       - GET_MODE_PRECISION (to_mode));
+		  rtx temp1
+		    = maybe_expand_shift (RSHIFT_EXPR, fromi_mode, fromi,
+					  shift, NULL_RTX, 1);
+		  if (!temp1)
+		    break;
+		  rtx temp2
+		    = expand_binop (fromi_mode, and_optab, temp1, const1_rtx,
+				    NULL_RTX, 1, OPTAB_DIRECT);
+		  if (!temp2)
+		    break;
+		  rtx temp3
+		    = expand_binop (fromi_mode, add_optab, fromi,
+				    gen_int_mode ((HOST_WIDE_INT_1U
+						   << (shift - 1)) - 1,
+						  fromi_mode), NULL_RTX,
+				    1, OPTAB_DIRECT);
+		  if (!temp3)
+		    break;
+		  rtx temp4
+		    = expand_binop (fromi_mode, add_optab, temp3, temp2,
+				    NULL_RTX, 1, OPTAB_DIRECT);
+		  if (!temp4)
+		    break;
+		  rtx temp5 = maybe_expand_shift (RSHIFT_EXPR, fromi_mode,
+						  temp4, shift, NULL_RTX, 1);
+		  if (!temp5)
+		    break;
+		  rtx temp6 = lowpart_subreg (toi_mode, temp5, fromi_mode);
+		  if (!temp6)
+		    break;
+		  tof = lowpart_subreg (to_mode, force_reg (toi_mode, temp6),
+					toi_mode);
+		  if (tof)
+		    emit_move_insn (to, tof);
+		}
+	      while (0);
+	      insns = get_insns ();
+	      end_sequence ();
+	      if (tof)
+		{
+		  emit_insn (insns);
+		  return;
+		}
+	    }
+	}
+#endif
+
       /* Otherwise use a libcall.  */
       libcall = convert_optab_libfunc (tab, to_mode, from_mode);
 
--- gcc/config/arm/arm.h.jj	2022-09-29 09:13:25.709718568 +0200
+++ gcc/config/arm/arm.h	2022-09-29 12:40:17.401778971 +0200
@@ -78,9 +78,8 @@ extern void (*arm_lang_output_object_att
    the backend.  Defined in arm-builtins.cc.  */
 extern tree arm_fp16_type_node;
 
-/* This type is the user-visible __bf16.  We need it in a few places in
-   the backend.  Defined in arm-builtins.cc.  */
-extern tree arm_bf16_type_node;
+/* The user-visible __bf16 uses bfloat16_type_node, but for pointer to that
+   use backend specific tree.  Defined in arm-builtins.cc.  */
 extern tree arm_bf16_ptr_type_node;
 
 
--- gcc/config/arm/arm.cc.jj	2022-09-29 09:13:25.709718568 +0200
+++ gcc/config/arm/arm.cc	2022-09-29 15:33:07.997170885 +0200
@@ -688,12 +688,6 @@ static const struct attribute_spec arm_a
 #undef TARGET_INVALID_CONVERSION
 #define TARGET_INVALID_CONVERSION arm_invalid_conversion
 
-#undef TARGET_INVALID_UNARY_OP
-#define TARGET_INVALID_UNARY_OP arm_invalid_unary_op
-
-#undef TARGET_INVALID_BINARY_OP
-#define TARGET_INVALID_BINARY_OP arm_invalid_binary_op
-
 #undef TARGET_ATOMIC_ASSIGN_EXPAND_FENV
 #define TARGET_ATOMIC_ASSIGN_EXPAND_FENV arm_atomic_assign_expand_fenv
 
@@ -30360,7 +30354,7 @@ arm_mangle_type (const_tree type)
   if (TREE_CODE (type) == REAL_TYPE && TYPE_PRECISION (type) == 16)
     {
       if (TYPE_MODE (type) == BFmode)
-	return "u6__bf16";
+	return "DFb16_";
       else
 	return "Dh";
     }
@@ -33996,47 +33990,22 @@ arm_invalid_conversion (const_tree fromt
 {
   if (element_mode (fromtype) != element_mode (totype))
     {
-      /* Do no allow conversions to/from BFmode scalar types.  */
-      if (TYPE_MODE (fromtype) == BFmode)
-	return N_("invalid conversion from type %<bfloat16_t%>");
-      if (TYPE_MODE (totype) == BFmode)
-	return N_("invalid conversion to type %<bfloat16_t%>");
+      /* Do no allow conversions from BFmode to non-ieee HFmode
+	 scalar types or vice versa.  */
+      if (TYPE_MODE (fromtype) == BFmode
+	  && TYPE_MODE (totype) == HFmode
+	  && arm_fp16_format == ARM_FP16_FORMAT_ALTERNATIVE)
+	return N_("invalid conversion from type %<bfloat16_t%> to %<__fp16%>");
+      if (TYPE_MODE (totype) == BFmode
+	  && TYPE_MODE (fromtype) == HFmode
+	  && arm_fp16_format == ARM_FP16_FORMAT_ALTERNATIVE)
+	return N_("invalid conversion to type %<bfloat16_t%> from %<__fp16%>");
     }
 
   /* Conversion allowed.  */
   return NULL;
 }
 
-/* Return the diagnostic message string if the unary operation OP is
-   not permitted on TYPE, NULL otherwise.  */
-
-static const char *
-arm_invalid_unary_op (int op, const_tree type)
-{
-  /* Reject all single-operand operations on BFmode except for &.  */
-  if (element_mode (type) == BFmode && op != ADDR_EXPR)
-    return N_("operation not permitted on type %<bfloat16_t%>");
-
-  /* Operation allowed.  */
-  return NULL;
-}
-
-/* Return the diagnostic message string if the binary operation OP is
-   not permitted on TYPE1 and TYPE2, NULL otherwise.  */
-
-static const char *
-arm_invalid_binary_op (int op ATTRIBUTE_UNUSED, const_tree type1,
-			   const_tree type2)
-{
-  /* Reject all 2-operand operations on BFmode.  */
-  if (element_mode (type1) == BFmode
-      || element_mode (type2) == BFmode)
-    return N_("operation not permitted on type %<bfloat16_t%>");
-
-  /* Operation allowed.  */
-  return NULL;
-}
-
 /* Implement TARGET_CAN_CHANGE_MODE_CLASS.
 
    In VFPv1, VFP registers could only be accessed in the mode they were
--- gcc/config/arm/arm-builtins.cc.jj	2022-09-29 09:13:25.681718954 +0200
+++ gcc/config/arm/arm-builtins.cc	2022-09-29 12:40:17.405778917 +0200
@@ -1370,7 +1370,6 @@ struct arm_simd_type_info arm_simd_types
 tree arm_fp16_type_node = NULL_TREE;
 
 /* Back-end node type for brain float (bfloat) types.  */
-tree arm_bf16_type_node = NULL_TREE;
 tree arm_bf16_ptr_type_node = NULL_TREE;
 
 static tree arm_simd_intOI_type_node = NULL_TREE;
@@ -1459,7 +1458,7 @@ arm_simd_builtin_std_type (machine_mode
     case E_DFmode:
       return double_type_node;
     case E_BFmode:
-      return arm_bf16_type_node;
+      return bfloat16_type_node;
     default:
       gcc_unreachable ();
     }
@@ -1570,9 +1569,9 @@ arm_init_simd_builtin_types (void)
   arm_simd_types[Float32x4_t].eltype = float_type_node;
 
   /* Init Bfloat vector types with underlying __bf16 scalar type.  */
-  arm_simd_types[Bfloat16x2_t].eltype = arm_bf16_type_node;
-  arm_simd_types[Bfloat16x4_t].eltype = arm_bf16_type_node;
-  arm_simd_types[Bfloat16x8_t].eltype = arm_bf16_type_node;
+  arm_simd_types[Bfloat16x2_t].eltype = bfloat16_type_node;
+  arm_simd_types[Bfloat16x4_t].eltype = bfloat16_type_node;
+  arm_simd_types[Bfloat16x8_t].eltype = bfloat16_type_node;
 
   for (i = 0; i < nelts; i++)
     {
@@ -1658,7 +1657,7 @@ arm_init_simd_builtin_scalar_types (void
 					     "__builtin_neon_df");
   (*lang_hooks.types.register_builtin_type) (intTI_type_node,
 					     "__builtin_neon_ti");
-  (*lang_hooks.types.register_builtin_type) (arm_bf16_type_node,
+  (*lang_hooks.types.register_builtin_type) (bfloat16_type_node,
                                              "__builtin_neon_bf");
   /* Unsigned integer types for various mode sizes.  */
   (*lang_hooks.types.register_builtin_type) (unsigned_intQI_type_node,
@@ -1797,13 +1796,13 @@ arm_init_builtin (unsigned int fcode, ar
 static void
 arm_init_bf16_types (void)
 {
-  arm_bf16_type_node = make_node (REAL_TYPE);
-  TYPE_PRECISION (arm_bf16_type_node) = 16;
-  SET_TYPE_MODE (arm_bf16_type_node, BFmode);
-  layout_type (arm_bf16_type_node);
+  bfloat16_type_node = make_node (REAL_TYPE);
+  TYPE_PRECISION (bfloat16_type_node) = 16;
+  SET_TYPE_MODE (bfloat16_type_node, BFmode);
+  layout_type (bfloat16_type_node);
 
-  lang_hooks.types.register_builtin_type (arm_bf16_type_node, "__bf16");
-  arm_bf16_ptr_type_node = build_pointer_type (arm_bf16_type_node);
+  lang_hooks.types.register_builtin_type (bfloat16_type_node, "__bf16");
+  arm_bf16_ptr_type_node = build_pointer_type (bfloat16_type_node);
 }
 
 /* Set up ACLE builtins, even builtins for instructions that are not
--- gcc/config/i386/i386.cc.jj	2022-09-29 12:03:12.073350093 +0200
+++ gcc/config/i386/i386.cc	2022-09-29 12:40:17.409778863 +0200
@@ -22728,7 +22728,7 @@ ix86_mangle_type (const_tree type)
   switch (TYPE_MODE (type))
     {
     case E_BFmode:
-      return "u6__bf16";
+      return "DFb16_";
     case E_HFmode:
       /* _Float16 is "DF16_".
 	 Align with clang's decision in https://reviews.llvm.org/D33719. */
@@ -22747,55 +22747,6 @@ ix86_mangle_type (const_tree type)
     }
 }
 
-/* Return the diagnostic message string if conversion from FROMTYPE to
-   TOTYPE is not allowed, NULL otherwise.  */
-
-static const char *
-ix86_invalid_conversion (const_tree fromtype, const_tree totype)
-{
-  if (element_mode (fromtype) != element_mode (totype))
-    {
-      /* Do no allow conversions to/from BFmode scalar types.  */
-      if (TYPE_MODE (fromtype) == BFmode)
-	return N_("invalid conversion from type %<__bf16%>");
-      if (TYPE_MODE (totype) == BFmode)
-	return N_("invalid conversion to type %<__bf16%>");
-    }
-
-  /* Conversion allowed.  */
-  return NULL;
-}
-
-/* Return the diagnostic message string if the unary operation OP is
-   not permitted on TYPE, NULL otherwise.  */
-
-static const char *
-ix86_invalid_unary_op (int op, const_tree type)
-{
-  /* Reject all single-operand operations on BFmode except for &.  */
-  if (element_mode (type) == BFmode && op != ADDR_EXPR)
-    return N_("operation not permitted on type %<__bf16%>");
-
-  /* Operation allowed.  */
-  return NULL;
-}
-
-/* Return the diagnostic message string if the binary operation OP is
-   not permitted on TYPE1 and TYPE2, NULL otherwise.  */
-
-static const char *
-ix86_invalid_binary_op (int op ATTRIBUTE_UNUSED, const_tree type1,
-			   const_tree type2)
-{
-  /* Reject all 2-operand operations on BFmode.  */
-  if (element_mode (type1) == BFmode
-      || element_mode (type2) == BFmode)
-    return N_("operation not permitted on type %<__bf16%>");
-
-  /* Operation allowed.  */
-  return NULL;
-}
-
 static GTY(()) tree ix86_tls_stack_chk_guard_decl;
 
 static tree
@@ -24853,15 +24804,6 @@ ix86_libgcc_floating_mode_supported_p
 #undef TARGET_MANGLE_TYPE
 #define TARGET_MANGLE_TYPE ix86_mangle_type
 
-#undef TARGET_INVALID_CONVERSION
-#define TARGET_INVALID_CONVERSION ix86_invalid_conversion
-
-#undef TARGET_INVALID_UNARY_OP
-#define TARGET_INVALID_UNARY_OP ix86_invalid_unary_op
-
-#undef TARGET_INVALID_BINARY_OP
-#define TARGET_INVALID_BINARY_OP ix86_invalid_binary_op
-
 #undef TARGET_STACK_PROTECT_GUARD
 #define TARGET_STACK_PROTECT_GUARD ix86_stack_protect_guard
 
--- gcc/config/i386/i386-builtins.cc.jj	2022-09-29 09:13:25.710718554 +0200
+++ gcc/config/i386/i386-builtins.cc	2022-09-29 12:40:17.406778903 +0200
@@ -126,7 +126,6 @@ BDESC_VERIFYS (IX86_BUILTIN_MAX,
 static GTY(()) tree ix86_builtin_type_tab[(int) IX86_BT_LAST_CPTR + 1];
 
 tree ix86_float16_type_node = NULL_TREE;
-tree ix86_bf16_type_node = NULL_TREE;
 tree ix86_bf16_ptr_type_node = NULL_TREE;
 
 /* Retrieve an element from the above table, building some of
@@ -1372,16 +1371,15 @@ ix86_register_float16_builtin_type (void
 static void
 ix86_register_bf16_builtin_type (void)
 {
-  ix86_bf16_type_node = make_node (REAL_TYPE);
-  TYPE_PRECISION (ix86_bf16_type_node) = 16;
-  SET_TYPE_MODE (ix86_bf16_type_node, BFmode);
-  layout_type (ix86_bf16_type_node);
+  bfloat16_type_node = make_node (REAL_TYPE);
+  TYPE_PRECISION (bfloat16_type_node) = 16;
+  SET_TYPE_MODE (bfloat16_type_node, BFmode);
+  layout_type (bfloat16_type_node);
 
   if (!maybe_get_identifier ("__bf16") && TARGET_SSE2)
     {
-      lang_hooks.types.register_builtin_type (ix86_bf16_type_node,
-					    "__bf16");
-      ix86_bf16_ptr_type_node = build_pointer_type (ix86_bf16_type_node);
+      lang_hooks.types.register_builtin_type (bfloat16_type_node, "__bf16");
+      ix86_bf16_ptr_type_node = build_pointer_type (bfloat16_type_node);
     }
 }
 
--- gcc/config/i386/i386-builtin-types.def.jj	2022-09-29 09:13:25.709718568 +0200
+++ gcc/config/i386/i386-builtin-types.def	2022-09-29 12:40:17.406778903 +0200
@@ -69,7 +69,7 @@ DEF_PRIMITIVE_TYPE (UINT16, short_unsign
 DEF_PRIMITIVE_TYPE (INT64, long_long_integer_type_node)
 DEF_PRIMITIVE_TYPE (UINT64, long_long_unsigned_type_node)
 DEF_PRIMITIVE_TYPE (FLOAT16, ix86_float16_type_node)
-DEF_PRIMITIVE_TYPE (BFLOAT16, ix86_bf16_type_node)
+DEF_PRIMITIVE_TYPE (BFLOAT16, bfloat16_type_node)
 DEF_PRIMITIVE_TYPE (FLOAT, float_type_node)
 DEF_PRIMITIVE_TYPE (DOUBLE, double_type_node)
 DEF_PRIMITIVE_TYPE (FLOAT80, float80_type_node)
--- gcc/config/aarch64/aarch64.h.jj	2022-09-29 09:13:25.680718968 +0200
+++ gcc/config/aarch64/aarch64.h	2022-09-29 12:40:17.409778863 +0200
@@ -1337,9 +1337,8 @@ extern const char *aarch64_rewrite_mcpu
 extern GTY(()) tree aarch64_fp16_type_node;
 extern GTY(()) tree aarch64_fp16_ptr_type_node;
 
-/* This type is the user-visible __bf16, and a pointer to that type.  Defined
-   in aarch64-builtins.cc.  */
-extern GTY(()) tree aarch64_bf16_type_node;
+/* Pointer to the user-visible __bf16 type.  __bf16 itself is generic
+   bfloat16_type_node.  Defined in aarch64-builtins.cc.  */
 extern GTY(()) tree aarch64_bf16_ptr_type_node;
 
 /* The generic unwind code in libgcc does not initialize the frame pointer.
--- gcc/config/aarch64/aarch64.cc.jj	2022-09-29 09:13:25.680718968 +0200
+++ gcc/config/aarch64/aarch64.cc	2022-09-29 12:40:17.413778808 +0200
@@ -19741,7 +19741,7 @@ aarch64_gimplify_va_arg_expr (tree valis
 	  field_ptr_t = aarch64_fp16_ptr_type_node;
 	  break;
 	case E_BFmode:
-	  field_t = aarch64_bf16_type_node;
+	  field_t = bfloat16_type_node;
 	  field_ptr_t = aarch64_bf16_ptr_type_node;
 	  break;
 	case E_V2SImode:
@@ -20645,7 +20645,7 @@ aarch64_mangle_type (const_tree type)
   if (TREE_CODE (type) == REAL_TYPE && TYPE_PRECISION (type) == 16)
     {
       if (TYPE_MODE (type) == BFmode)
-	return "u6__bf16";
+	return "DFb16_";
       else
 	return "Dh";
     }
@@ -26820,39 +26820,6 @@ aarch64_stack_protect_guard (void)
   return NULL_TREE;
 }
 
-/* Return the diagnostic message string if conversion from FROMTYPE to
-   TOTYPE is not allowed, NULL otherwise.  */
-
-static const char *
-aarch64_invalid_conversion (const_tree fromtype, const_tree totype)
-{
-  if (element_mode (fromtype) != element_mode (totype))
-    {
-      /* Do no allow conversions to/from BFmode scalar types.  */
-      if (TYPE_MODE (fromtype) == BFmode)
-	return N_("invalid conversion from type %<bfloat16_t%>");
-      if (TYPE_MODE (totype) == BFmode)
-	return N_("invalid conversion to type %<bfloat16_t%>");
-    }
-
-  /* Conversion allowed.  */
-  return NULL;
-}
-
-/* Return the diagnostic message string if the unary operation OP is
-   not permitted on TYPE, NULL otherwise.  */
-
-static const char *
-aarch64_invalid_unary_op (int op, const_tree type)
-{
-  /* Reject all single-operand operations on BFmode except for &.  */
-  if (element_mode (type) == BFmode && op != ADDR_EXPR)
-    return N_("operation not permitted on type %<bfloat16_t%>");
-
-  /* Operation allowed.  */
-  return NULL;
-}
-
 /* Return the diagnostic message string if the binary operation OP is
    not permitted on TYPE1 and TYPE2, NULL otherwise.  */
 
@@ -26860,11 +26827,6 @@ static const char *
 aarch64_invalid_binary_op (int op ATTRIBUTE_UNUSED, const_tree type1,
 			   const_tree type2)
 {
-  /* Reject all 2-operand operations on BFmode.  */
-  if (element_mode (type1) == BFmode
-      || element_mode (type2) == BFmode)
-    return N_("operation not permitted on type %<bfloat16_t%>");
-
   if (VECTOR_TYPE_P (type1)
       && VECTOR_TYPE_P (type2)
       && !TYPE_INDIVISIBLE_P (type1)
@@ -27461,12 +27423,6 @@ aarch64_libgcc_floating_mode_supported_p
 #undef TARGET_MANGLE_TYPE
 #define TARGET_MANGLE_TYPE aarch64_mangle_type
 
-#undef TARGET_INVALID_CONVERSION
-#define TARGET_INVALID_CONVERSION aarch64_invalid_conversion
-
-#undef TARGET_INVALID_UNARY_OP
-#define TARGET_INVALID_UNARY_OP aarch64_invalid_unary_op
-
 #undef TARGET_INVALID_BINARY_OP
 #define TARGET_INVALID_BINARY_OP aarch64_invalid_binary_op
 
--- gcc/config/aarch64/aarch64-builtins.cc.jj	2022-09-29 09:13:25.676719023 +0200
+++ gcc/config/aarch64/aarch64-builtins.cc	2022-09-29 12:40:17.410778849 +0200
@@ -918,7 +918,6 @@ tree aarch64_fp16_type_node = NULL_TREE;
 tree aarch64_fp16_ptr_type_node = NULL_TREE;
 
 /* Back-end node type for brain float (bfloat) types.  */
-tree aarch64_bf16_type_node = NULL_TREE;
 tree aarch64_bf16_ptr_type_node = NULL_TREE;
 
 /* Wrapper around add_builtin_function.  NAME is the name of the built-in
@@ -1010,7 +1009,7 @@ aarch64_int_or_fp_type (machine_mode mod
     case E_DFmode:
       return double_type_node;
     case E_BFmode:
-      return aarch64_bf16_type_node;
+      return bfloat16_type_node;
     default:
       gcc_unreachable ();
     }
@@ -1124,8 +1123,8 @@ aarch64_init_simd_builtin_types (void)
   aarch64_simd_types[Float64x2_t].eltype = double_type_node;
 
   /* Init Bfloat vector types with underlying __bf16 type.  */
-  aarch64_simd_types[Bfloat16x4_t].eltype = aarch64_bf16_type_node;
-  aarch64_simd_types[Bfloat16x8_t].eltype = aarch64_bf16_type_node;
+  aarch64_simd_types[Bfloat16x4_t].eltype = bfloat16_type_node;
+  aarch64_simd_types[Bfloat16x8_t].eltype = bfloat16_type_node;
 
   for (i = 0; i < nelts; i++)
     {
@@ -1197,7 +1196,7 @@ aarch64_init_simd_builtin_scalar_types (
 					     "__builtin_aarch64_simd_poly128");
   (*lang_hooks.types.register_builtin_type) (intTI_type_node,
 					     "__builtin_aarch64_simd_ti");
-  (*lang_hooks.types.register_builtin_type) (aarch64_bf16_type_node,
+  (*lang_hooks.types.register_builtin_type) (bfloat16_type_node,
 					     "__builtin_aarch64_simd_bf");
   /* Unsigned integer types for various mode sizes.  */
   (*lang_hooks.types.register_builtin_type) (unsigned_intQI_type_node,
@@ -1682,13 +1681,13 @@ aarch64_init_fp16_types (void)
 static void
 aarch64_init_bf16_types (void)
 {
-  aarch64_bf16_type_node = make_node (REAL_TYPE);
-  TYPE_PRECISION (aarch64_bf16_type_node) = 16;
-  SET_TYPE_MODE (aarch64_bf16_type_node, BFmode);
-  layout_type (aarch64_bf16_type_node);
+  bfloat16_type_node = make_node (REAL_TYPE);
+  TYPE_PRECISION (bfloat16_type_node) = 16;
+  SET_TYPE_MODE (bfloat16_type_node, BFmode);
+  layout_type (bfloat16_type_node);
 
-  lang_hooks.types.register_builtin_type (aarch64_bf16_type_node, "__bf16");
-  aarch64_bf16_ptr_type_node = build_pointer_type (aarch64_bf16_type_node);
+  lang_hooks.types.register_builtin_type (bfloat16_type_node, "__bf16");
+  aarch64_bf16_ptr_type_node = build_pointer_type (bfloat16_type_node);
 }
 
 /* Pointer authentication builtins that will become NOP on legacy platform.
--- gcc/config/aarch64/aarch64-sve-builtins.def.jj	2022-09-29 09:13:25.676719023 +0200
+++ gcc/config/aarch64/aarch64-sve-builtins.def	2022-09-29 12:40:17.413778808 +0200
@@ -61,7 +61,7 @@ DEF_SVE_MODE (u64offset, none, svuint64_
 DEF_SVE_MODE (vnum, none, none, vectors)
 
 DEF_SVE_TYPE (svbool_t, 10, __SVBool_t, boolean_type_node)
-DEF_SVE_TYPE (svbfloat16_t, 14, __SVBfloat16_t, aarch64_bf16_type_node)
+DEF_SVE_TYPE (svbfloat16_t, 14, __SVBfloat16_t, bfloat16_type_node)
 DEF_SVE_TYPE (svfloat16_t, 13, __SVFloat16_t, aarch64_fp16_type_node)
 DEF_SVE_TYPE (svfloat32_t, 13, __SVFloat32_t, float_type_node)
 DEF_SVE_TYPE (svfloat64_t, 13, __SVFloat64_t, double_type_node)
--- gcc/c-family/c-cppbuiltin.cc.jj	2022-09-29 09:13:25.675719037 +0200
+++ gcc/c-family/c-cppbuiltin.cc	2022-09-29 12:40:17.416778768 +0200
@@ -1264,6 +1264,13 @@ c_cpp_builtins (cpp_reader *pfile)
       builtin_define_float_constants (prefix, ggc_strdup (csuffix), "%s",
 				      csuffix, FLOATN_NX_TYPE_NODE (i));
     }
+  if (bfloat16_type_node && c_dialect_cxx ())
+    {
+      if (cxx_dialect > cxx20)
+	cpp_define (pfile, "__STDCPP_BFLOAT16_T__=1");
+      builtin_define_float_constants ("BFLT16", "BF16", "%s",
+				      "BF16", bfloat16_type_node);
+    }
 
   /* For float.h.  */
   if (targetm.decimal_float_supported_p ())
--- gcc/c-family/c-lex.cc.jj	2022-09-29 09:13:25.675719037 +0200
+++ gcc/c-family/c-lex.cc	2022-09-29 12:40:17.416778768 +0200
@@ -995,6 +995,19 @@ interpret_float (const cpp_token *token,
 	  pedwarn (input_location, OPT_Wpedantic,
 		   "non-standard suffix on floating constant");
       }
+    else if ((flags & CPP_N_BFLOAT16) != 0 && c_dialect_cxx ())
+      {
+	type = bfloat16_type_node;
+	if (type == NULL_TREE)
+	  {
+	    error ("unsupported non-standard suffix on floating constant");
+	    return error_mark_node;
+	  }
+	if (cxx_dialect < cxx23)
+	  pedwarn (input_location, OPT_Wpedantic,
+		   "%<bf16%> or %<BF16%> suffix on floating constant only "
+		   "available with %<-std=c++2b%> or %<-std=gnu++2b%>");
+      }
     else if ((flags & CPP_N_WIDTH) == CPP_N_LARGE)
       type = long_double_type_node;
     else if ((flags & CPP_N_WIDTH) == CPP_N_SMALL
--- gcc/cp/cp-tree.h.jj	2022-09-29 09:13:31.164643341 +0200
+++ gcc/cp/cp-tree.h	2022-09-29 12:40:17.414778795 +0200
@@ -8714,6 +8714,8 @@ extended_float_type_p (tree type)
   for (int i = 0; i < NUM_FLOATN_NX_TYPES; ++i)
     if (type == FLOATN_TYPE_NODE (i))
       return true;
+  if (type == bfloat16_type_node)
+    return true;
   return false;
 }
 
--- gcc/cp/typeck.cc.jj	2022-09-29 09:13:25.716718472 +0200
+++ gcc/cp/typeck.cc	2022-09-29 12:40:17.415778781 +0200
@@ -293,6 +293,10 @@ cp_compare_floating_point_conversion_ran
       if (mv2 == FLOATN_NX_TYPE_NODE (i))
 	extended2 = i + 1;
     }
+  if (mv1 == bfloat16_type_node)
+    extended1 = true;
+  if (mv2 == bfloat16_type_node)
+    extended2 = true;
   if (extended2 && !extended1)
     {
       int ret = cp_compare_floating_point_conversion_ranks (t2, t1);
@@ -390,7 +394,9 @@ cp_compare_floating_point_conversion_ran
   if (cnt > 1 && mv2 == long_double_type_node)
     return -2;
   /* Otherwise, they have equal rank, but extended types
-     (other than std::bfloat16_t) have higher subrank.  */
+     (other than std::bfloat16_t) have higher subrank.
+     std::bfloat16_t shouldn't have equal rank to any standard
+     floating point type.  */
   return 1;
 }
 
--- gcc/testsuite/gcc.target/i386/vect-bfloat16-typecheck_2.c.jj	2022-08-19 23:26:22.656373568 +0200
+++ gcc/testsuite/gcc.target/i386/vect-bfloat16-typecheck_2.c	2022-09-30 01:37:41.092709166 +0200
@@ -45,19 +45,19 @@ __m256bf16 footest (__m256bf16 vector0)
   __m256bf16 vector2_1 = {};
   __m256bf16 vector2_2 = { glob_bfloat };
   __m256bf16 vector2_3 = { glob_bfloat, glob_bfloat, glob_bfloat, glob_bfloat };
-  __m256bf16 vector2_4 = { 0 }; /* { dg-error {invalid conversion to type '__bf16'} } */
-  __m256bf16 vector2_5 = { 0.1 }; /* { dg-error {invalid conversion to type '__bf16'} } */
-  __m256bf16 vector2_6 = { is_a_float16 }; /* { dg-error {invalid conversion to type '__bf16'} } */
-  __m256bf16 vector2_7 = { is_a_float }; /* { dg-error {invalid conversion to type '__bf16'} } */
-  __m256bf16 vector2_8 = { is_an_int }; /* { dg-error {invalid conversion to type '__bf16'} } */
-  __m256bf16 vector2_9 = { is_a_short_int }; /* { dg-error {invalid conversion to type '__bf16'} } */
-  __m256bf16 vector2_10 = { 0.0, 0, is_a_short_int, is_a_float }; /* { dg-error "invalid conversion to type '__bf16'" } */
-
-  __v8si initi_2_1 = { glob_bfloat };   /* { dg-error {invalid conversion from type '__bf16'} } */
-  __m256 initi_2_2 = { glob_bfloat }; /* { dg-error {invalid conversion from type '__bf16'} } */
-  __m256h initi_2_3 = { glob_bfloat }; /* { dg-error {invalid conversion from type '__bf16'} } */
-  __m256i initi_2_5 = { glob_bfloat };   /* { dg-error {invalid conversion from type '__bf16'} } */
-  __v16hi initi_2_6 = { glob_bfloat };   /* { dg-error {invalid conversion from type '__bf16'} } */
+  __m256bf16 vector2_4 = { 0 };
+  __m256bf16 vector2_5 = { 0.1 };
+  __m256bf16 vector2_6 = { is_a_float16 };
+  __m256bf16 vector2_7 = { is_a_float };
+  __m256bf16 vector2_8 = { is_an_int };
+  __m256bf16 vector2_9 = { is_a_short_int };
+  __m256bf16 vector2_10 = { 0.0, 0, is_a_short_int, is_a_float };
+
+  __v8si initi_2_1 = { glob_bfloat };
+  __m256 initi_2_2 = { glob_bfloat };
+  __m256h initi_2_3 = { glob_bfloat };
+  __m256i initi_2_5 = { glob_bfloat };
+  __v16hi initi_2_6 = { glob_bfloat };
 
   /* Assignments to/from vectors.  */
 
@@ -79,25 +79,25 @@ __m256bf16 footest (__m256bf16 vector0)
   /* Assignments to/from elements.  */
 
   vector2_3[0] = glob_bfloat;
-  vector2_3[0] = is_an_int; /* { dg-error {invalid conversion to type '__bf16'} } */
-  vector2_3[0] = is_a_short_int; /* { dg-error {invalid conversion to type '__bf16'} } */
-  vector2_3[0] = is_a_float; /* { dg-error {invalid conversion to type '__bf16'} } */
-  vector2_3[0] = is_a_float16; /* { dg-error {invalid conversion to type '__bf16'} } */
-  vector2_3[0] = 0; /* { dg-error {invalid conversion to type '__bf16'} } */
-  vector2_3[0] = 0.1; /* { dg-error {invalid conversion to type '__bf16'} } */
+  vector2_3[0] = is_an_int;
+  vector2_3[0] = is_a_short_int;
+  vector2_3[0] = is_a_float;
+  vector2_3[0] = is_a_float16;
+  vector2_3[0] = 0;
+  vector2_3[0] = 0.1;
 
   glob_bfloat = vector2_3[0];
-  is_an_int = vector2_3[0]; /* { dg-error {invalid conversion from type '__bf16'} } */
-  is_a_short_int = vector2_3[0]; /* { dg-error {invalid conversion from type '__bf16'} } */
-  is_a_float = vector2_3[0]; /* { dg-error {invalid conversion from type '__bf16'} } */
-  is_a_float16 = vector2_3[0]; /* { dg-error {invalid conversion from type '__bf16'} } */
+  is_an_int = vector2_3[0];
+  is_a_short_int = vector2_3[0];
+  is_a_float = vector2_3[0];
+  is_a_float16 = vector2_3[0];
 
   /* Compound literals.  */
 
   (__m256bf16) {};
 
-  (__m256bf16) { 0 }; /* { dg-error {invalid conversion to type '__bf16'} } */
-  (__m256bf16) { 0.1 }; /* { dg-error {invalid conversion to type '__bf16'} } */
+  (__m256bf16) { 0 };
+  (__m256bf16) { 0.1 };
   (__m256bf16) { is_a_float_vec }; /* { dg-error {incompatible types when initializing type '__bf16' using type '__m256'} } */
   (__m256bf16) { is_an_int_vec }; /* { dg-error {incompatible types when initializing type '__bf16' using type '__v8si'} } */
   (__m256bf16) { is_a_long_int_pair }; /* { dg-error {incompatible types when initializing type '__bf16' using type '__m256i'} } */
@@ -176,16 +176,16 @@ __m256bf16 footest (__m256bf16 vector0)
   bfloat_ptr = &bfloat_ptr3[1];
 
   /* Simple comparison.  */
-  vector0 > glob_bfloat_vec; /* { dg-error {operation not permitted on type '__bf16'} } */
-  glob_bfloat_vec == vector0; /* { dg-error {operation not permitted on type '__bf16'} } */
-  vector0 > is_a_float_vec; /* { dg-error {operation not permitted on type '__bf16'} } */
-  is_a_float_vec == vector0; /* { dg-error {operation not permitted on type '__bf16'} } */
-  vector0 > 0; /* { dg-error {operation not permitted on type '__bf16'} } */
-  0 == vector0; /* { dg-error {operation not permitted on type '__bf16'} } */
-  vector0 > 0.1; /* { dg-error {operation not permitted on type '__bf16'} } */
-  0.1 == vector0; /* { dg-error {operation not permitted on type '__bf16'} } */
-  vector0 > is_an_int_vec; /* { dg-error {operation not permitted on type '__bf16'} } */
-  is_an_int_vec == vector0; /* { dg-error {operation not permitted on type '__bf16'} } */
+  vector0 > glob_bfloat_vec;
+  glob_bfloat_vec == vector0;
+  vector0 > is_a_float_vec; /* { dg-error {comparing vectors with different element types} } */
+  is_a_float_vec == vector0; /* { dg-error {comparing vectors with different element types} } */
+  vector0 > 0;
+  0 == vector0;
+  vector0 > 0.1; /* { dg-error {conversion of scalar 'double' to vector '__m256bf16'} } */
+  0.1 == vector0; /* { dg-error {conversion of scalar 'double' to vector '__m256bf16'} } */
+  vector0 > is_an_int_vec; /* { dg-error {comparing vectors with different element types} } */
+  is_an_int_vec == vector0; /* { dg-error {comparing vectors with different element types} } */
 
   /* Pointer comparison.  */
 
@@ -224,24 +224,24 @@ __m256bf16 footest (__m256bf16 vector0)
 
   /* Unary operators.  */
 
-  +vector0; /* { dg-error {operation not permitted on type '__bf16'} } */
-  -vector0; /* { dg-error {operation not permitted on type '__bf16'} } */
-  ~vector0; /* { dg-error {operation not permitted on type '__bf16'} } */
-  !vector0; /* { dg-error {operation not permitted on type '__bf16'} } */
+  +vector0;
+  -vector0;
+  ~vector0; /* { dg-error {wrong type argument to bit-complement} } */
+  !vector0; /* { dg-error {wrong type argument to unary exclamation mark} } */
   *vector0; /* { dg-error {invalid type argument of unary '\*'} } */
-  __real vector0; /* { dg-error {operation not permitted on type '__bf16'} } */
-  __imag vector0; /* { dg-error {operation not permitted on type '__bf16'} } */
-  ++vector0; /* { dg-error {operation not permitted on type '__bf16'} } */
-  --vector0; /* { dg-error {operation not permitted on type '__bf16'} } */
-  vector0++; /* { dg-error {operation not permitted on type '__bf16'} } */
-  vector0--; /* { dg-error {operation not permitted on type '__bf16'} } */
+  __real vector0; /* { dg-error {wrong type argument to __real} } */
+  __imag vector0; /* { dg-error {wrong type argument to __imag} } */
+  ++vector0;
+  --vector0;
+  vector0++;
+  vector0--;
 
   /* Binary arithmetic operations.  */
 
-  vector0 = glob_bfloat_vec + *bfloat_ptr; /* { dg-error {operation not permitted on type '__bf16'} } */
-  vector0 = glob_bfloat_vec + 0.1; /* { dg-error {operation not permitted on type '__bf16'} } */
-  vector0 = glob_bfloat_vec + 0; /* { dg-error {operation not permitted on type '__bf16'} } */
-  vector0 = glob_bfloat_vec + is_a_float_vec; /* { dg-error {operation not permitted on type '__bf16'} } */
+  vector0 = glob_bfloat_vec + *bfloat_ptr;
+  vector0 = glob_bfloat_vec + 0.1; /* { dg-error {conversion of scalar 'double' to vector '__m256bf16'} } */
+  vector0 = glob_bfloat_vec + 0;
+  vector0 = glob_bfloat_vec + is_a_float_vec; /* { dg-error {invalid operands to binary \+} } */
 
   return vector0;
 }
--- gcc/testsuite/gcc.target/i386/sse2-bfloat16-scalar-typecheck.c.jj	2022-08-27 23:01:28.323565905 +0200
+++ gcc/testsuite/gcc.target/i386/sse2-bfloat16-scalar-typecheck.c	2022-09-30 01:22:54.886600717 +0200
@@ -12,8 +12,8 @@ double is_a_double;
 
 float *float_ptr;
 
-__bf16 foo1 (void) { return (__bf16) 0x1234; } /* { dg-error {invalid conversion to type '__bf16'} } */
-__bf16 foo2 (void) { return (__bf16) (short) 0x1234; } /* { dg-error {invalid conversion to type '__bf16'} } */
+__bf16 foo1 (void) { return (__bf16) 0x1234; }
+__bf16 foo2 (void) { return (__bf16) (short) 0x1234; }
 
 __bf16 footest (__bf16 scalar0)
 {
@@ -22,87 +22,87 @@ __bf16 footest (__bf16 scalar0)
 
   __bf16 scalar1_1;
   __bf16 scalar1_2 = glob_bfloat;
-  __bf16 scalar1_3 = 0;   /* { dg-error {invalid conversion to type '__bf16'} } */
-  __bf16 scalar1_4 = 0.1; /* { dg-error {invalid conversion to type '__bf16'} } */
-  __bf16 scalar1_5 = is_a_float; /* { dg-error {invalid conversion to type '__bf16'} } */
-  __bf16 scalar1_6 = is_an_int;  /* { dg-error {invalid conversion to type '__bf16'} } */
-  __bf16 scalar1_7 = is_a_float16; /* { dg-error {invalid conversion to type '__bf16'} } */
-  __bf16 scalar1_8 = is_a_double; /* { dg-error {invalid conversion to type '__bf16'} } */
-  __bf16 scalar1_9 = is_a_short_int; /* { dg-error {invalid conversion to type '__bf16'} } */
-
-  int initi_1_1 = glob_bfloat; /* { dg-error {invalid conversion from type '__bf16'} } */
-  float initi_1_2 = glob_bfloat; /* { dg-error {invalid conversion from type '__bf16'} } */
-  _Float16 initi_1_3 = glob_bfloat; /* { dg-error {invalid conversion from type '__bf16'} } */
-  short initi_1_4 = glob_bfloat; /* { dg-error {invalid conversion from type '__bf16'} } */
-  double initi_1_5 = glob_bfloat; /* { dg-error {invalid conversion from type '__bf16'} } */
+  __bf16 scalar1_3 = 0;
+  __bf16 scalar1_4 = 0.1;
+  __bf16 scalar1_5 = is_a_float;
+  __bf16 scalar1_6 = is_an_int;
+  __bf16 scalar1_7 = is_a_float16;
+  __bf16 scalar1_8 = is_a_double;
+  __bf16 scalar1_9 = is_a_short_int;
+
+  int initi_1_1 = glob_bfloat;
+  float initi_1_2 = glob_bfloat;
+  _Float16 initi_1_3 = glob_bfloat;
+  short initi_1_4 = glob_bfloat;
+  double initi_1_5 = glob_bfloat;
 
   __bf16 scalar2_1 = {};
   __bf16 scalar2_2 = { glob_bfloat };
-  __bf16 scalar2_3 = { 0 }; /* { dg-error {invalid conversion to type '__bf16'} } */
-  __bf16 scalar2_4 = { 0.1 }; /* { dg-error {invalid conversion to type '__bf16'} } */
-  __bf16 scalar2_5 = { is_a_float }; /* { dg-error {invalid conversion to type '__bf16'} } */
-  __bf16 scalar2_6 = { is_an_int }; /* { dg-error {invalid conversion to type '__bf16'} } */
-  __bf16 scalar2_7 = { is_a_float16 }; /* { dg-error {invalid conversion to type '__bf16'} } */
-  __bf16 scalar2_8 = { is_a_double }; /* { dg-error {invalid conversion to type '__bf16'} } */
-  __bf16 scalar2_9 = { is_a_short_int }; /* { dg-error {invalid conversion to type '__bf16'} } */
-
-  int initi_2_1 = { glob_bfloat }; /* { dg-error {invalid conversion from type '__bf16'} } */
-  float initi_2_2 = { glob_bfloat }; /* { dg-error {invalid conversion from type '__bf16'} } */
-  _Float16 initi_2_3 = { glob_bfloat }; /* { dg-error {invalid conversion from type '__bf16'} } */
-  short initi_2_4 = { glob_bfloat }; /* { dg-error {invalid conversion from type '__bf16'} } */
-  double initi_2_5 = { glob_bfloat }; /* { dg-error {invalid conversion from type '__bf16'} } */
+  __bf16 scalar2_3 = { 0 };
+  __bf16 scalar2_4 = { 0.1 };
+  __bf16 scalar2_5 = { is_a_float };
+  __bf16 scalar2_6 = { is_an_int };
+  __bf16 scalar2_7 = { is_a_float16 };
+  __bf16 scalar2_8 = { is_a_double };
+  __bf16 scalar2_9 = { is_a_short_int };
+
+  int initi_2_1 = { glob_bfloat };
+  float initi_2_2 = { glob_bfloat };
+  _Float16 initi_2_3 = { glob_bfloat };
+  short initi_2_4 = { glob_bfloat };
+  double initi_2_5 = { glob_bfloat };
 
   /* Assignments.  */
 
   glob_bfloat = glob_bfloat;
-  glob_bfloat = 0;   /* { dg-error {invalid conversion to type '__bf16'} } */
-  glob_bfloat = 0.1; /* { dg-error {invalid conversion to type '__bf16'} } */
-  glob_bfloat = is_a_float; /* { dg-error {invalid conversion to type '__bf16'} } */
-  glob_bfloat = is_an_int; /* { dg-error {invalid conversion to type '__bf16'} } */
-  glob_bfloat = is_a_float16; /* { dg-error {invalid conversion to type '__bf16'} } */
-  glob_bfloat = is_a_double; /* { dg-error {invalid conversion to type '__bf16'} } */
-  glob_bfloat = is_a_short_int; /* { dg-error {invalid conversion to type '__bf16'} } */
-
-  is_an_int = glob_bfloat; /* { dg-error {invalid conversion from type '__bf16'} } */
-  is_a_float = glob_bfloat; /* { dg-error {invalid conversion from type '__bf16'} } */
-  is_a_float16 = glob_bfloat; /* { dg-error {invalid conversion from type '__bf16'} } */
-  is_a_double = glob_bfloat; /* { dg-error {invalid conversion from type '__bf16'} } */
-  is_a_short_int = glob_bfloat; /* { dg-error {invalid conversion from type '__bf16'} } */
+  glob_bfloat = 0;
+  glob_bfloat = 0.1;
+  glob_bfloat = is_a_float;
+  glob_bfloat = is_an_int;
+  glob_bfloat = is_a_float16;
+  glob_bfloat = is_a_double;
+  glob_bfloat = is_a_short_int;
+
+  is_an_int = glob_bfloat;
+  is_a_float = glob_bfloat;
+  is_a_float16 = glob_bfloat;
+  is_a_double = glob_bfloat;
+  is_a_short_int = glob_bfloat;
 
   /* Casting.  */
 
   (void) glob_bfloat;
   (__bf16) glob_bfloat;
 
-  (int) glob_bfloat; /* { dg-error {invalid conversion from type '__bf16'} } */
-  (float) glob_bfloat; /* { dg-error {invalid conversion from type '__bf16'} } */
-  (_Float16) glob_bfloat; /* { dg-error {invalid conversion from type '__bf16'} } */
-  (double) glob_bfloat; /* { dg-error {invalid conversion from type '__bf16'} } */
-  (short) glob_bfloat; /* { dg-error {invalid conversion from type '__bf16'} } */
-
-  (__bf16) is_an_int; /* { dg-error {invalid conversion to type '__bf16'} } */
-  (__bf16) is_a_float; /* { dg-error {invalid conversion to type '__bf16'} } */
-  (__bf16) is_a_float16; /* { dg-error {invalid conversion to type '__bf16'} } */
-  (__bf16) is_a_double; /* { dg-error {invalid conversion to type '__bf16'} } */
-  (__bf16) is_a_short_int; /* { dg-error {invalid conversion to type '__bf16'} } */
+  (int) glob_bfloat;
+  (float) glob_bfloat;
+  (_Float16) glob_bfloat;
+  (double) glob_bfloat;
+  (short) glob_bfloat;
+
+  (__bf16) is_an_int;
+  (__bf16) is_a_float;
+  (__bf16) is_a_float16;
+  (__bf16) is_a_double;
+  (__bf16) is_a_short_int;
 
   /* Compound literals.  */
 
   (__bf16) {};
   (__bf16) { glob_bfloat };
-  (__bf16) { 0 }; /* { dg-error {invalid conversion to type '__bf16'} } */
-  (__bf16) { 0.1 }; /* { dg-error {invalid conversion to type '__bf16'} } */
-  (__bf16) { is_a_float }; /* { dg-error {invalid conversion to type '__bf16'} } */
-  (__bf16) { is_an_int }; /* { dg-error {invalid conversion to type '__bf16'} } */
-  (__bf16) { is_a_float16 }; /* { dg-error {invalid conversion to type '__bf16'} } */
-  (__bf16) { is_a_double }; /* { dg-error {invalid conversion to type '__bf16'} } */
-  (__bf16) { is_a_short_int }; /* { dg-error {invalid conversion to type '__bf16'} } */
-
-  (int) { glob_bfloat }; /* { dg-error {invalid conversion from type '__bf16'} } */
-  (float) { glob_bfloat }; /* { dg-error {invalid conversion from type '__bf16'} } */
-  (_Float16) { glob_bfloat }; /* { dg-error {invalid conversion from type '__bf16'} } */
-  (double) { glob_bfloat }; /* { dg-error {invalid conversion from type '__bf16'} } */
-  (short) { glob_bfloat }; /* { dg-error {invalid conversion from type '__bf16'} } */
+  (__bf16) { 0 };
+  (__bf16) { 0.1 };
+  (__bf16) { is_a_float };
+  (__bf16) { is_an_int };
+  (__bf16) { is_a_float16 };
+  (__bf16) { is_a_double };
+  (__bf16) { is_a_short_int };
+
+  (int) { glob_bfloat };
+  (float) { glob_bfloat };
+  (_Float16) { glob_bfloat };
+  (double) { glob_bfloat };
+  (short) { glob_bfloat };
 
   /* Arrays and Structs.  */
 
@@ -145,16 +145,16 @@ __bf16 footest (__bf16 scalar0)
   bfloat_ptr = &bfloat_ptr3[1];
 
   /* Simple comparison.  */
-  scalar0 > glob_bfloat; /* { dg-error {operation not permitted on type '__bf16'} } */
-  glob_bfloat == scalar0; /* { dg-error {operation not permitted on type '__bf16'} } */
-  scalar0 > is_a_float; /* { dg-error {operation not permitted on type '__bf16'} } */
-  is_a_float == scalar0; /* { dg-error {operation not permitted on type '__bf16'} } */
-  scalar0 > 0; /* { dg-error {operation not permitted on type '__bf16'} } */
-  0 == scalar0; /* { dg-error {operation not permitted on type '__bf16'} } */
-  scalar0 > 0.1; /* { dg-error {operation not permitted on type '__bf16'} } */
-  0.1 == scalar0; /* { dg-error {operation not permitted on type '__bf16'} } */
-  scalar0 > is_an_int; /* { dg-error {operation not permitted on type '__bf16'} } */
-  is_an_int == scalar0; /* { dg-error {operation not permitted on type '__bf16'} } */
+  scalar0 > glob_bfloat;
+  glob_bfloat == scalar0;
+  scalar0 > is_a_float;
+  is_a_float == scalar0;
+  scalar0 > 0;
+  0 == scalar0;
+  scalar0 > 0.1;
+  0.1 == scalar0;
+  scalar0 > is_an_int;
+  is_an_int == scalar0;
 
   /* Pointer comparison.  */
 
@@ -174,41 +174,41 @@ __bf16 footest (__bf16 scalar0)
   /* Conditional expressions.  */
 
   0 ? scalar0 : scalar0;
-  0 ? scalar0 : is_a_float; /* { dg-error {invalid conversion from type '__bf16'} } */
-  0 ? is_a_float : scalar0; /* { dg-error {invalid conversion from type '__bf16'} } */
-  0 ? scalar0 : 0; /* { dg-error {invalid conversion to type '__bf16'} } */
-  0 ? 0 : scalar0; /* { dg-error {invalid conversion to type '__bf16'} } */
-  0 ? 0.1 : scalar0; /* { dg-error {invalid conversion from type '__bf16'} } */
-  0 ? scalar0 : 0.1; /* { dg-error {invalid conversion from type '__bf16'} } */
+  0 ? scalar0 : is_a_float;
+  0 ? is_a_float : scalar0;
+  0 ? scalar0 : 0;
+  0 ? 0 : scalar0;
+  0 ? 0.1 : scalar0;
+  0 ? scalar0 : 0.1;
   0 ? bfloat_ptr : bfloat_ptr2;
   0 ? bfloat_ptr : float_ptr; /* { dg-warning {pointer type mismatch in conditional expression} } */
   0 ? float_ptr : bfloat_ptr; /* { dg-warning {pointer type mismatch in conditional expression} } */
 
-  scalar0 ? scalar0 : scalar0; /* { dg-error {operation not permitted on type '__bf16'} } */
-  scalar0 ? is_a_float : scalar0; /* { dg-error {operation not permitted on type '__bf16'} } */
-  scalar0 ? scalar0 : is_a_float; /* { dg-error {operation not permitted on type '__bf16'} } */
-  scalar0 ? is_a_float : is_a_float; /* { dg-error {operation not permitted on type '__bf16'} } */
+  scalar0 ? scalar0 : scalar0;
+  scalar0 ? is_a_float : scalar0;
+  scalar0 ? scalar0 : is_a_float;
+  scalar0 ? is_a_float : is_a_float;
 
   /* Unary operators.  */
 
-  +scalar0; /* { dg-error {operation not permitted on type '__bf16'} } */
-  -scalar0; /* { dg-error {operation not permitted on type '__bf16'} } */
-  ~scalar0; /* { dg-error {operation not permitted on type '__bf16'} } */
-  !scalar0; /* { dg-error {operation not permitted on type '__bf16'} } */
+  +scalar0;
+  -scalar0;
+  ~scalar0; /* { dg-error {wrong type argument to bit-complement} } */
+  !scalar0;
   *scalar0; /* { dg-error {invalid type argument of unary '\*'} } */
-  __real scalar0; /* { dg-error {operation not permitted on type '__bf16'} } */
-  __imag scalar0; /* { dg-error {operation not permitted on type '__bf16'} } */
-  ++scalar0; /* { dg-error {operation not permitted on type '__bf16'} } */
-  --scalar0; /* { dg-error {operation not permitted on type '__bf16'} } */
-  scalar0++; /* { dg-error {operation not permitted on type '__bf16'} } */
-  scalar0--; /* { dg-error {operation not permitted on type '__bf16'} } */
+  __real scalar0;
+  __imag scalar0;
+  ++scalar0;
+  --scalar0;
+  scalar0++;
+  scalar0--;
 
   /* Binary arithmetic operations.  */
 
-  scalar0 = glob_bfloat + *bfloat_ptr; /* { dg-error {operation not permitted on type '__bf16'} } */
-  scalar0 = glob_bfloat + 0.1; /* { dg-error {operation not permitted on type '__bf16'} } */
-  scalar0 = glob_bfloat + 0; /* { dg-error {operation not permitted on type '__bf16'} } */
-  scalar0 = glob_bfloat + is_a_float; /* { dg-error {operation not permitted on type '__bf16'} } */
+  scalar0 = glob_bfloat + *bfloat_ptr;
+  scalar0 = glob_bfloat + 0.1;
+  scalar0 = glob_bfloat + 0;
+  scalar0 = glob_bfloat + is_a_float;
 
   return scalar0;
 }
--- gcc/testsuite/gcc.target/i386/vect-bfloat16-typecheck_1.c.jj	2022-08-19 23:26:22.656373568 +0200
+++ gcc/testsuite/gcc.target/i386/vect-bfloat16-typecheck_1.c	2022-09-30 01:37:34.270800614 +0200
@@ -48,20 +48,20 @@ __m128bf16 footest (__m128bf16 vector0)
   __m128bf16 vector2_1 = {};
   __m128bf16 vector2_2 = { glob_bfloat };
   __m128bf16 vector2_3 = { glob_bfloat, glob_bfloat, glob_bfloat, glob_bfloat };
-  __m128bf16 vector2_4 = { 0 }; /* { dg-error {invalid conversion to type '__bf16'} } */
-  __m128bf16 vector2_5 = { 0.1 }; /* { dg-error {invalid conversion to type '__bf16'} } */
-  __m128bf16 vector2_6 = { is_a_float16 }; /* { dg-error {invalid conversion to type '__bf16'} } */
-  __m128bf16 vector2_7 = { is_a_float }; /* { dg-error {invalid conversion to type '__bf16'} } */
-  __m128bf16 vector2_8 = { is_an_int }; /* { dg-error {invalid conversion to type '__bf16'} } */
-  __m128bf16 vector2_9 = { is_a_short_int }; /* { dg-error {invalid conversion to type '__bf16'} } */
-  __m128bf16 vector2_10 = { 0.0, 0, is_a_short_int, is_a_float }; /* { dg-error {invalid conversion to type '__bf16'} } */
-
-  __v8si initi_2_1 = { glob_bfloat };   /* { dg-error {invalid conversion from type '__bf16'} } */
-  __m256 initi_2_2 = { glob_bfloat }; /* { dg-error {invalid conversion from type '__bf16'} } */
-  __m128h initi_2_3 = { glob_bfloat }; /* { dg-error {invalid conversion from type '__bf16'} } */
-  __m128 initi_2_4 = { glob_bfloat }; /* { dg-error {invalid conversion from type '__bf16'} } */
-  __v4si initi_2_5 = { glob_bfloat };   /* { dg-error {invalid conversion from type '__bf16'} } */
-  __v4hi initi_2_6 = { glob_bfloat };   /* { dg-error {invalid conversion from type '__bf16'} } */
+  __m128bf16 vector2_4 = { 0 };
+  __m128bf16 vector2_5 = { 0.1 };
+  __m128bf16 vector2_6 = { is_a_float16 };
+  __m128bf16 vector2_7 = { is_a_float };
+  __m128bf16 vector2_8 = { is_an_int };
+  __m128bf16 vector2_9 = { is_a_short_int };
+  __m128bf16 vector2_10 = { 0.0, 0, is_a_short_int, is_a_float };
+
+  __v8si initi_2_1 = { glob_bfloat };
+  __m256 initi_2_2 = { glob_bfloat };
+  __m128h initi_2_3 = { glob_bfloat };
+  __m128 initi_2_4 = { glob_bfloat };
+  __v4si initi_2_5 = { glob_bfloat };
+  __v4hi initi_2_6 = { glob_bfloat };
 
   /* Assignments to/from vectors.  */
 
@@ -85,25 +85,25 @@ __m128bf16 footest (__m128bf16 vector0)
   /* Assignments to/from elements.  */
 
   vector2_3[0] = glob_bfloat;
-  vector2_3[0] = is_an_int; /* { dg-error {invalid conversion to type '__bf16'} } */
-  vector2_3[0] = is_a_short_int; /* { dg-error {invalid conversion to type '__bf16'} } */
-  vector2_3[0] = is_a_float; /* { dg-error {invalid conversion to type '__bf16'} } */
-  vector2_3[0] = is_a_float16; /* { dg-error {invalid conversion to type '__bf16'} } */
-  vector2_3[0] = 0; /* { dg-error {invalid conversion to type '__bf16'} } */
-  vector2_3[0] = 0.1; /* { dg-error {invalid conversion to type '__bf16'} } */
+  vector2_3[0] = is_an_int;
+  vector2_3[0] = is_a_short_int;
+  vector2_3[0] = is_a_float;
+  vector2_3[0] = is_a_float16;
+  vector2_3[0] = 0;
+  vector2_3[0] = 0.1;
 
   glob_bfloat = vector2_3[0];
-  is_an_int = vector2_3[0]; /* { dg-error {invalid conversion from type '__bf16'} } */
-  is_a_short_int = vector2_3[0]; /* { dg-error {invalid conversion from type '__bf16'} } */
-  is_a_float = vector2_3[0]; /* { dg-error {invalid conversion from type '__bf16'} } */
-  is_a_float16 = vector2_3[0]; /* { dg-error {invalid conversion from type '__bf16'} } */
+  is_an_int = vector2_3[0];
+  is_a_short_int = vector2_3[0];
+  is_a_float = vector2_3[0];
+  is_a_float16 = vector2_3[0];
 
   /* Compound literals.  */
 
   (__m128bf16) {};
 
-  (__m128bf16) { 0 }; /* { dg-error {invalid conversion to type '__bf16'} } */
-  (__m128bf16) { 0.1 }; /* { dg-error {invalid conversion to type '__bf16'} } */
+  (__m128bf16) { 0 };
+  (__m128bf16) { 0.1 };
   (__m128bf16) { is_a_float_vec }; /* { dg-error {incompatible types when initializing type '__bf16' using type '__m256'} } */
   (__m128bf16) { is_an_int_vec }; /* { dg-error {incompatible types when initializing type '__bf16' using type '__v8si'} } */
   (__m128bf16) { is_a_float_pair }; /* { dg-error {incompatible types when initializing type '__bf16' using type '__m128'} } */
@@ -186,16 +186,16 @@ __m128bf16 footest (__m128bf16 vector0)
   bfloat_ptr = &bfloat_ptr3[1];
 
   /* Simple comparison.  */
-  vector0 > glob_bfloat_vec; /* { dg-error {operation not permitted on type '__bf16'} } */
-  glob_bfloat_vec == vector0; /* { dg-error {operation not permitted on type '__bf16'} } */
-  vector0 > is_a_float_vec; /* { dg-error {operation not permitted on type '__bf16'} } */
-  is_a_float_vec == vector0; /* { dg-error {operation not permitted on type '__bf16'} } */
-  vector0 > 0; /* { dg-error {operation not permitted on type '__bf16'} } */
-  0 == vector0; /* { dg-error {operation not permitted on type '__bf16'} } */
-  vector0 > 0.1; /* { dg-error {operation not permitted on type '__bf16'} } */
-  0.1 == vector0; /* { dg-error {operation not permitted on type '__bf16'} } */
-  vector0 > is_an_int_vec; /* { dg-error {operation not permitted on type '__bf16'} } */
-  is_an_int_vec == vector0; /* { dg-error {operation not permitted on type '__bf16'} } */
+  vector0 > glob_bfloat_vec;
+  glob_bfloat_vec == vector0;
+  vector0 > is_a_float_vec; /* { dg-error {comparing vectors with different element types} } */
+  is_a_float_vec == vector0; /* { dg-error {comparing vectors with different element types} } */
+  vector0 > 0;
+  0 == vector0;
+  vector0 > 0.1; /* { dg-error {conversion of scalar 'double' to vector '__m128bf16'} } */
+  0.1 == vector0; /* { dg-error {conversion of scalar 'double' to vector '__m128bf16'} } */
+  vector0 > is_an_int_vec; /* { dg-error {comparing vectors with different element types} } */
+  is_an_int_vec == vector0; /* { dg-error {comparing vectors with different element types} } */
 
   /* Pointer comparison.  */
 
@@ -234,24 +234,24 @@ __m128bf16 footest (__m128bf16 vector0)
 
   /* Unary operators.  */
 
-  +vector0; /* { dg-error {operation not permitted on type '__bf16'} } */
-  -vector0; /* { dg-error {operation not permitted on type '__bf16'} } */
-  ~vector0; /* { dg-error {operation not permitted on type '__bf16'} } */
-  !vector0; /* { dg-error {operation not permitted on type '__bf16'} } */
+  +vector0;
+  -vector0;
+  ~vector0; /* { dg-error {wrong type argument to bit-complement} } */
+  !vector0; /* { dg-error {wrong type argument to unary exclamation mark} } */
   *vector0; /* { dg-error {invalid type argument of unary '\*'} } */
-  __real vector0; /* { dg-error {operation not permitted on type '__bf16'} } */
-  __imag vector0; /* { dg-error {operation not permitted on type '__bf16'} } */
-  ++vector0; /* { dg-error {operation not permitted on type '__bf16'} } */
-  --vector0; /* { dg-error {operation not permitted on type '__bf16'} } */
-  vector0++; /* { dg-error {operation not permitted on type '__bf16'} } */
-  vector0--; /* { dg-error {operation not permitted on type '__bf16'} } */
+  __real vector0; /* { dg-error {wrong type argument to __real} } */
+  __imag vector0; /* { dg-error {wrong type argument to __imag} } */
+  ++vector0;
+  --vector0;
+  vector0++;
+  vector0--;
 
   /* Binary arithmetic operations.  */
 
-  vector0 = glob_bfloat_vec + *bfloat_ptr; /* { dg-error {operation not permitted on type '__bf16'} } */
-  vector0 = glob_bfloat_vec + 0.1; /* { dg-error {operation not permitted on type '__bf16'} } */
-  vector0 = glob_bfloat_vec + 0; /* { dg-error {operation not permitted on type '__bf16'} } */
-  vector0 = glob_bfloat_vec + is_a_float_vec; /* { dg-error {operation not permitted on type '__bf16'} } */
+  vector0 = glob_bfloat_vec + *bfloat_ptr;
+  vector0 = glob_bfloat_vec + 0.1; /* { dg-error {conversion of scalar 'double' to vector '__m128bf16'} } */
+  vector0 = glob_bfloat_vec + 0;
+  vector0 = glob_bfloat_vec + is_a_float_vec; /* { dg-error {invalid operands to binary \+} } */
 
   return vector0;
 }
--- gcc/testsuite/g++.target/i386/bfloat_cpp_typecheck.C.jj	2022-08-16 23:06:21.395321891 +0200
+++ gcc/testsuite/g++.target/i386/bfloat_cpp_typecheck.C	2022-09-30 01:39:06.137569307 +0200
@@ -5,6 +5,6 @@ void foo (void)
 {
   __bf16 (); /* { dg-bogus {invalid conversion to type '__bf16'} } */
   __bf16 a = __bf16(); /* { dg-bogus {invalid conversion to type '__bf16'} } */
-  __bf16 (0x1234); /* { dg-error {invalid conversion to type '__bf16'} } */
-  __bf16 (0.1); /* { dg-error {invalid conversion to type '__bf16'} } */
+  __bf16 (0x1234); /* { dg-bogus {invalid conversion to type '__bf16'} } */
+  __bf16 (0.1); /* { dg-bogus {invalid conversion to type '__bf16'} } */
 }
--- libcpp/include/cpplib.h.jj	2022-09-08 13:01:19.853771383 +0200
+++ libcpp/include/cpplib.h	2022-09-28 19:06:59.615380690 +0200
@@ -1275,6 +1275,7 @@ struct cpp_num
 #define CPP_N_USERDEF	0x1000000 /* C++11 user-defined literal.  */
 
 #define CPP_N_SIZE_T	0x2000000 /* C++23 size_t literal.  */
+#define CPP_N_BFLOAT16	0x4000000 /* std::bfloat16_t type.  */
 
 #define CPP_N_WIDTH_FLOATN_NX	0xF0000000 /* _FloatN / _FloatNx value
 					      of N, divided by 16.  */
--- libcpp/expr.cc.jj	2022-09-27 08:03:27.119982735 +0200
+++ libcpp/expr.cc	2022-09-28 17:55:36.667177540 +0200
@@ -91,10 +91,10 @@ interpret_float_suffix (cpp_reader *pfil
   size_t orig_len = len;
   const uchar *orig_s = s;
   size_t flags;
-  size_t f, d, l, w, q, i, fn, fnx, fn_bits;
+  size_t f, d, l, w, q, i, fn, fnx, fn_bits, bf16;
 
   flags = 0;
-  f = d = l = w = q = i = fn = fnx = fn_bits = 0;
+  f = d = l = w = q = i = fn = fnx = fn_bits = bf16 = 0;
 
   /* The following decimal float suffixes, from TR 24732:2009, TS
      18661-2:2015 and C2X, are supported:
@@ -131,7 +131,8 @@ interpret_float_suffix (cpp_reader *pfil
      w, W - machine-specific type such as __float80 (GNU extension).
      q, Q - machine-specific type such as __float128 (GNU extension).
      fN, FN - _FloatN (TS 18661-3:2015).
-     fNx, FNx - _FloatNx (TS 18661-3:2015).  */
+     fNx, FNx - _FloatNx (TS 18661-3:2015).
+     bf16, BF16 - std::bfloat16_t (ISO C++23).  */
 
   /* Process decimal float suffixes, which are two letters starting
      with d or D.  Order and case are significant.  */
@@ -239,6 +240,20 @@ interpret_float_suffix (cpp_reader *pfil
 		fn++;
 	    }
 	  break;
+	case 'b': case 'B':
+	  if (len > 2
+	      /* Except for bf16 / BF16 where case is significant.  */
+	      && s[1] == (s[0] == 'b' ? 'f' : 'F')
+	      && s[2] == '1'
+	      && s[3] == '6'
+	      && CPP_OPTION (pfile, cplusplus))
+	    {
+	      bf16++;
+	      len -= 3;
+	      s += 3;
+	      break;
+	    }
+	  return 0;
 	case 'd': case 'D': d++; break;
 	case 'l': case 'L': l++; break;
 	case 'w': case 'W': w++; break;
@@ -257,7 +272,7 @@ interpret_float_suffix (cpp_reader *pfil
      of N larger than can be represented in the return value.  The
      caller is responsible for rejecting _FloatN suffixes where
      _FloatN is not supported on the chosen target.  */
-  if (f + d + l + w + q + fn + fnx > 1 || i > 1)
+  if (f + d + l + w + q + fn + fnx + bf16 > 1 || i > 1)
     return 0;
   if (fn_bits > CPP_FLOATN_MAX)
     return 0;
@@ -295,6 +310,7 @@ interpret_float_suffix (cpp_reader *pfil
 	     q ? CPP_N_MD_Q :
 	     fn ? CPP_N_FLOATN | (fn_bits << CPP_FLOATN_SHIFT) :
 	     fnx ? CPP_N_FLOATNX | (fn_bits << CPP_FLOATN_SHIFT) :
+	     bf16 ? CPP_N_BFLOAT16 :
 	     CPP_N_DEFAULT));
 }
 
--- libgcc/config/arm/sfp-machine.h.jj	2020-01-12 11:54:38.615380187 +0100
+++ libgcc/config/arm/sfp-machine.h	2022-09-28 19:02:51.922710542 +0200
@@ -22,6 +22,7 @@ typedef int __gcc_CMPtype __attribute__
 /* According to RTABI, QNAN is only with the most significant bit of the
    significand set, and all other significand bits zero.  */
 #define _FP_NANFRAC_H		_FP_QNANBIT_H
+#define _FP_NANFRAC_B		_FP_QNANBIT_B
 #define _FP_NANFRAC_S		_FP_QNANBIT_S
 #define _FP_NANFRAC_D		_FP_QNANBIT_D, 0
 #define _FP_NANFRAC_Q		_FP_QNANBIT_Q, 0, 0, 0
--- libgcc/config/aarch64/t-softfp.jj	2020-09-29 11:32:02.988602194 +0200
+++ libgcc/config/aarch64/t-softfp	2022-09-28 18:59:43.381246466 +0200
@@ -1,7 +1,7 @@
 softfp_float_modes := tf
 softfp_int_modes := si di ti
-softfp_extensions := sftf dftf hftf
-softfp_truncations := tfsf tfdf tfhf
+softfp_extensions := sftf dftf hftf bfsf
+softfp_truncations := tfsf tfdf tfhf tfbf dfbf sfbf hfbf
 softfp_exclude_libgcc2 := n
 softfp_extras := fixhfti fixunshfti floattihf floatuntihf
 
--- libgcc/config/aarch64/libgcc-softfp.ver.jj	2022-01-11 23:11:23.691271871 +0100
+++ libgcc/config/aarch64/libgcc-softfp.ver	2022-09-28 19:00:36.050537146 +0200
@@ -26,3 +26,12 @@ GCC_11.0 {
   __mulhc3
   __trunctfhf2
 }
+
+%inherit GCC_13.0.0 GCC_11.0.0
+GCC_13.0.0 {
+  __extendbfsf2
+  __truncdfbf2
+  __truncsfbf2
+  __trunctfbf2
+  __trunchfbf2
+}
--- libgcc/config/aarch64/sfp-machine.h.jj	2022-01-11 23:11:23.691271871 +0100
+++ libgcc/config/aarch64/sfp-machine.h	2022-09-28 19:02:10.303270053 +0200
@@ -43,6 +43,7 @@ typedef int __gcc_CMPtype __attribute__
 #define _FP_DIV_MEAT_Q(R,X,Y)	_FP_DIV_MEAT_2_udiv(Q,R,X,Y)
 
 #define _FP_NANFRAC_H		((_FP_QNANBIT_H << 1) - 1)
+#define _FP_NANFRAC_B		((_FP_QNANBIT_B << 1) - 1)
 #define _FP_NANFRAC_S		((_FP_QNANBIT_S << 1) - 1)
 #define _FP_NANFRAC_D		((_FP_QNANBIT_D << 1) - 1)
 #define _FP_NANFRAC_Q		((_FP_QNANBIT_Q << 1) - 1), -1
--- libgcc/config/i386/t-softfp.jj	2022-09-23 09:02:31.759659479 +0200
+++ libgcc/config/i386/t-softfp	2022-09-29 22:42:26.554156219 +0200
@@ -6,8 +6,9 @@ LIB2FUNCS_EXCLUDE += $(libgcc2-hf-functi
 libgcc2-hf-extras = $(addsuffix .c, $(libgcc2-hf-functions))
 LIB2ADD += $(addprefix $(srcdir)/config/i386/, $(libgcc2-hf-extras))
 
-softfp_extensions := hfsf hfdf hftf hfxf sfdf sftf dftf xftf
-softfp_truncations := tfhf xfhf dfhf sfhf tfsf dfsf tfdf tfxf
+softfp_extensions := hfsf hfdf hftf hfxf sfdf sftf dftf xftf bfsf
+softfp_truncations := tfhf xfhf dfhf sfhf tfsf dfsf tfdf tfxf \
+		      tfbf xfbf dfbf sfbf hfbf
 
 softfp_extras += eqhf2
 
@@ -15,11 +16,17 @@ CFLAGS-extendhfsf2.c += -msse2
 CFLAGS-extendhfdf2.c += -msse2
 CFLAGS-extendhftf2.c += -msse2
 CFLAGS-extendhfxf2.c += -msse2
+CFLAGS-extendbfsf2.c += -msse2
 
 CFLAGS-truncsfhf2.c += -msse2
 CFLAGS-truncdfhf2.c += -msse2
 CFLAGS-truncxfhf2.c += -msse2
 CFLAGS-trunctfhf2.c += -msse2
+CFLAGS-truncsfbf2.c += -msse2
+CFLAGS-truncdfbf2.c += -msse2
+CFLAGS-truncxfbf2.c += -msse2
+CFLAGS-trunctfbf2.c += -msse2
+CFLAGS-trunchfbf2.c += -msse2
 
 CFLAGS-eqhf2.c += -msse2
 CFLAGS-_divhc3.c += -msse2
--- libgcc/config/i386/libgcc-glibc.ver.jj	2022-09-23 09:02:31.746659658 +0200
+++ libgcc/config/i386/libgcc-glibc.ver	2022-09-28 18:58:09.114520943 +0200
@@ -214,3 +214,13 @@ GCC_12.0.0 {
   __trunctfhf2
   __truncxfhf2
 }
+
+%inherit GCC_13.0.0 GCC_12.0.0
+GCC_13.0.0 {
+  __extendbfsf2
+  __truncdfbf2
+  __truncsfbf2
+  __trunctfbf2
+  __truncxfbf2
+  __trunchfbf2
+}
--- libgcc/config/i386/sfp-machine.h.jj	2022-09-23 09:02:31.747659644 +0200
+++ libgcc/config/i386/sfp-machine.h	2022-09-28 18:58:09.114520943 +0200
@@ -18,6 +18,7 @@ typedef int __gcc_CMPtype __attribute__
 #define _FP_QNANNEGATEDP 0
 
 #define _FP_NANSIGN_H		1
+#define _FP_NANSIGN_B		1
 #define _FP_NANSIGN_S		1
 #define _FP_NANSIGN_D		1
 #define _FP_NANSIGN_E		1
--- libgcc/config/i386/64/sfp-machine.h.jj	2022-09-23 09:02:31.700660291 +0200
+++ libgcc/config/i386/64/sfp-machine.h	2022-09-28 18:58:09.114520943 +0200
@@ -14,6 +14,7 @@ typedef unsigned int UTItype __attribute
 #define _FP_DIV_MEAT_Q(R,X,Y)   _FP_DIV_MEAT_2_udiv(Q,R,X,Y)
 
 #define _FP_NANFRAC_H		_FP_QNANBIT_H
+#define _FP_NANFRAC_B		_FP_QNANBIT_B
 #define _FP_NANFRAC_S		_FP_QNANBIT_S
 #define _FP_NANFRAC_D		_FP_QNANBIT_D
 #define _FP_NANFRAC_E		_FP_QNANBIT_E, 0
--- libgcc/config/i386/32/sfp-machine.h.jj	2022-09-23 09:02:31.683660526 +0200
+++ libgcc/config/i386/32/sfp-machine.h	2022-09-28 18:58:09.115520929 +0200
@@ -87,6 +87,7 @@
 #define _FP_DIV_MEAT_Q(R,X,Y)   _FP_DIV_MEAT_4_udiv(Q,R,X,Y)
 
 #define _FP_NANFRAC_H		_FP_QNANBIT_H
+#define _FP_NANFRAC_B		_FP_QNANBIT_B
 #define _FP_NANFRAC_S		_FP_QNANBIT_S
 #define _FP_NANFRAC_D		_FP_QNANBIT_D, 0
 /* Even if XFmode is 12byte,  we have to pad it to
--- libgcc/soft-fp/brain.h.jj	2022-09-28 18:58:09.113520956 +0200
+++ libgcc/soft-fp/brain.h	2022-09-28 18:58:09.113520956 +0200
@@ -0,0 +1,172 @@
+/* Software floating-point emulation.
+   Definitions for Brain Floating Point format (bfloat16).
+   Copyright (C) 1997-2022 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   In addition to the permissions in the GNU Lesser General Public
+   License, the Free Software Foundation gives you unlimited
+   permission to link the compiled version of this file into
+   combinations with other programs, and to distribute those
+   combinations without any restriction coming from the use of this
+   file.  (The Lesser General Public License restrictions do apply in
+   other respects; for example, they cover modification of the file,
+   and distribution when not linked into a combine executable.)
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <https://www.gnu.org/licenses/>.  */
+
+#ifndef SOFT_FP_BRAIN_H
+#define SOFT_FP_BRAIN_H	1
+
+#if _FP_W_TYPE_SIZE < 32
+# error "Here's a nickel kid.  Go buy yourself a real computer."
+#endif
+
+#define _FP_FRACTBITS_B		(_FP_W_TYPE_SIZE)
+
+#define _FP_FRACTBITS_DW_B	(_FP_W_TYPE_SIZE)
+
+#define _FP_FRACBITS_B		8
+#define _FP_FRACXBITS_B		(_FP_FRACTBITS_B - _FP_FRACBITS_B)
+#define _FP_WFRACBITS_B		(_FP_WORKBITS + _FP_FRACBITS_B)
+#define _FP_WFRACXBITS_B	(_FP_FRACTBITS_B - _FP_WFRACBITS_B)
+#define _FP_EXPBITS_B		8
+#define _FP_EXPBIAS_B		127
+#define _FP_EXPMAX_B		255
+
+#define _FP_QNANBIT_B		((_FP_W_TYPE) 1 << (_FP_FRACBITS_B-2))
+#define _FP_QNANBIT_SH_B	((_FP_W_TYPE) 1 << (_FP_FRACBITS_B-2+_FP_WORKBITS))
+#define _FP_IMPLBIT_B		((_FP_W_TYPE) 1 << (_FP_FRACBITS_B-1))
+#define _FP_IMPLBIT_SH_B	((_FP_W_TYPE) 1 << (_FP_FRACBITS_B-1+_FP_WORKBITS))
+#define _FP_OVERFLOW_B		((_FP_W_TYPE) 1 << (_FP_WFRACBITS_B))
+
+#define _FP_WFRACBITS_DW_B	(2 * _FP_WFRACBITS_B)
+#define _FP_WFRACXBITS_DW_B	(_FP_FRACTBITS_DW_B - _FP_WFRACBITS_DW_B)
+#define _FP_HIGHBIT_DW_B	\
+  ((_FP_W_TYPE) 1 << (_FP_WFRACBITS_DW_B - 1) % _FP_W_TYPE_SIZE)
+
+/* The implementation of _FP_MUL_MEAT_B and _FP_DIV_MEAT_B should be
+   chosen by the target machine.  */
+
+typedef float BFtype __attribute__ ((mode (BF)));
+
+union _FP_UNION_B
+{
+  BFtype flt;
+  struct _FP_STRUCT_LAYOUT
+  {
+#if __BYTE_ORDER == __BIG_ENDIAN
+    unsigned sign : 1;
+    unsigned exp  : _FP_EXPBITS_B;
+    unsigned frac : _FP_FRACBITS_B - (_FP_IMPLBIT_B != 0);
+#else
+    unsigned frac : _FP_FRACBITS_B - (_FP_IMPLBIT_B != 0);
+    unsigned exp  : _FP_EXPBITS_B;
+    unsigned sign : 1;
+#endif
+  } bits;
+};
+
+#define FP_DECL_B(X)		_FP_DECL (1, X)
+#define FP_UNPACK_RAW_B(X, val)	_FP_UNPACK_RAW_1 (B, X, (val))
+#define FP_UNPACK_RAW_BP(X, val)	_FP_UNPACK_RAW_1_P (B, X, (val))
+#define FP_PACK_RAW_B(val, X)	_FP_PACK_RAW_1 (B, (val), X)
+#define FP_PACK_RAW_BP(val, X)			\
+  do						\
+    {						\
+      if (!FP_INHIBIT_RESULTS)			\
+	_FP_PACK_RAW_1_P (B, (val), X);		\
+    }						\
+  while (0)
+
+#define FP_UNPACK_B(X, val)			\
+  do						\
+    {						\
+      _FP_UNPACK_RAW_1 (B, X, (val));		\
+      _FP_UNPACK_CANONICAL (B, 1, X);		\
+    }						\
+  while (0)
+
+#define FP_UNPACK_BP(X, val)			\
+  do						\
+    {						\
+      _FP_UNPACK_RAW_1_P (B, X, (val));		\
+      _FP_UNPACK_CANONICAL (B, 1, X);		\
+    }						\
+  while (0)
+
+#define FP_UNPACK_SEMIRAW_B(X, val)		\
+  do						\
+    {						\
+      _FP_UNPACK_RAW_1 (B, X, (val));		\
+      _FP_UNPACK_SEMIRAW (B, 1, X);		\
+    }						\
+  while (0)
+
+#define FP_UNPACK_SEMIRAW_BP(X, val)		\
+  do						\
+    {						\
+      _FP_UNPACK_RAW_1_P (B, X, (val));		\
+      _FP_UNPACK_SEMIRAW (B, 1, X);		\
+    }						\
+  while (0)
+
+#define FP_PACK_B(val, X)			\
+  do						\
+    {						\
+      _FP_PACK_CANONICAL (B, 1, X);		\
+      _FP_PACK_RAW_1 (B, (val), X);		\
+    }						\
+  while (0)
+
+#define FP_PACK_BP(val, X)			\
+  do						\
+    {						\
+      _FP_PACK_CANONICAL (B, 1, X);		\
+      if (!FP_INHIBIT_RESULTS)			\
+	_FP_PACK_RAW_1_P (B, (val), X);		\
+    }						\
+  while (0)
+
+#define FP_PACK_SEMIRAW_B(val, X)		\
+  do						\
+    {						\
+      _FP_PACK_SEMIRAW (B, 1, X);		\
+      _FP_PACK_RAW_1 (B, (val), X);		\
+    }						\
+  while (0)
+
+#define FP_PACK_SEMIRAW_BP(val, X)		\
+  do						\
+    {						\
+      _FP_PACK_SEMIRAW (B, 1, X);		\
+      if (!FP_INHIBIT_RESULTS)			\
+	_FP_PACK_RAW_1_P (B, (val), X);		\
+    }						\
+  while (0)
+
+#define FP_TO_INT_B(r, X, rsz, rsg)	_FP_TO_INT (B, 1, (r), X, (rsz), (rsg))
+#define FP_TO_INT_ROUND_B(r, X, rsz, rsg)	\
+  _FP_TO_INT_ROUND (B, 1, (r), X, (rsz), (rsg))
+#define FP_FROM_INT_B(X, r, rs, rt)	_FP_FROM_INT (B, 1, X, (r), (rs), rt)
+
+/* BFmode arithmetic is not implemented.  */
+
+#define _FP_FRAC_HIGH_B(X)	_FP_FRAC_HIGH_1 (X)
+#define _FP_FRAC_HIGH_RAW_B(X)	_FP_FRAC_HIGH_1 (X)
+#define _FP_FRAC_HIGH_DW_B(X)	_FP_FRAC_HIGH_1 (X)
+
+#define FP_CMP_EQ_B(r, X, Y, ex)       _FP_CMP_EQ (B, 1, (r), X, Y, (ex))
+
+#endif /* !SOFT_FP_BRAIN_H */
--- libgcc/soft-fp/truncsfbf2.c.jj	2022-09-28 18:58:09.113520956 +0200
+++ libgcc/soft-fp/truncsfbf2.c	2022-09-28 18:58:09.113520956 +0200
@@ -0,0 +1,48 @@
+/* Software floating-point emulation.
+   Truncate IEEE single into bfloat16.
+   Copyright (C) 2022 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   In addition to the permissions in the GNU Lesser General Public
+   License, the Free Software Foundation gives you unlimited
+   permission to link the compiled version of this file into
+   combinations with other programs, and to distribute those
+   combinations without any restriction coming from the use of this
+   file.  (The Lesser General Public License restrictions do apply in
+   other respects; for example, they cover modification of the file,
+   and distribution when not linked into a combine executable.)
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <http://www.gnu.org/licenses/>.  */
+
+#include "soft-fp.h"
+#include "brain.h"
+#include "single.h"
+
+BFtype
+__truncsfbf2 (SFtype a)
+{
+  FP_DECL_EX;
+  FP_DECL_S (A);
+  FP_DECL_B (R);
+  BFtype r;
+
+  FP_INIT_ROUNDMODE;
+  FP_UNPACK_SEMIRAW_S (A, a);
+  FP_TRUNC (B, S, 1, 1, R, A);
+  FP_PACK_SEMIRAW_B (r, R);
+  FP_HANDLE_EXCEPTIONS;
+
+  return r;
+}
--- libgcc/soft-fp/truncdfbf2.c.jj	2022-09-28 18:58:09.114520943 +0200
+++ libgcc/soft-fp/truncdfbf2.c	2022-09-28 18:58:09.114520943 +0200
@@ -0,0 +1,52 @@
+/* Software floating-point emulation.
+   Truncate IEEE double into bfloat16.
+   Copyright (C) 2022 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   In addition to the permissions in the GNU Lesser General Public
+   License, the Free Software Foundation gives you unlimited
+   permission to link the compiled version of this file into
+   combinations with other programs, and to distribute those
+   combinations without any restriction coming from the use of this
+   file.  (The Lesser General Public License restrictions do apply in
+   other respects; for example, they cover modification of the file,
+   and distribution when not linked into a combine executable.)
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <http://www.gnu.org/licenses/>.  */
+
+#include "soft-fp.h"
+#include "brain.h"
+#include "double.h"
+
+BFtype
+__truncdfbf2 (DFtype a)
+{
+  FP_DECL_EX;
+  FP_DECL_D (A);
+  FP_DECL_B (R);
+  BFtype r;
+
+  FP_INIT_ROUNDMODE;
+  FP_UNPACK_SEMIRAW_D (A, a);
+#if _FP_W_TYPE_SIZE < _FP_FRACBITS_D
+  FP_TRUNC (B, D, 1, 2, R, A);
+#else
+  FP_TRUNC (B, D, 1, 1, R, A);
+#endif
+  FP_PACK_SEMIRAW_B (r, R);
+  FP_HANDLE_EXCEPTIONS;
+
+  return r;
+}
--- libgcc/soft-fp/truncxfbf2.c.jj	2022-09-28 18:58:09.113520956 +0200
+++ libgcc/soft-fp/truncxfbf2.c	2022-09-28 18:58:09.113520956 +0200
@@ -0,0 +1,52 @@
+/* Software floating-point emulation.
+   Truncate IEEE extended into bfloat16.
+   Copyright (C) 2022 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   In addition to the permissions in the GNU Lesser General Public
+   License, the Free Software Foundation gives you unlimited
+   permission to link the compiled version of this file into
+   combinations with other programs, and to distribute those
+   combinations without any restriction coming from the use of this
+   file.  (The Lesser General Public License restrictions do apply in
+   other respects; for example, they cover modification of the file,
+   and distribution when not linked into a combine executable.)
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <http://www.gnu.org/licenses/>.  */
+
+#include "soft-fp.h"
+#include "brain.h"
+#include "extended.h"
+
+BFtype
+__truncxfbf2 (XFtype a)
+{
+  FP_DECL_EX;
+  FP_DECL_E (A);
+  FP_DECL_B (R);
+  BFtype r;
+
+  FP_INIT_ROUNDMODE;
+  FP_UNPACK_SEMIRAW_E (A, a);
+#if _FP_W_TYPE_SIZE < 64
+  FP_TRUNC (B, E, 1, 4, R, A);
+#else
+  FP_TRUNC (B, E, 1, 2, R, A);
+#endif
+  FP_PACK_SEMIRAW_B (r, R);
+  FP_HANDLE_EXCEPTIONS;
+
+  return r;
+}
--- libgcc/soft-fp/trunctfbf2.c.jj	2022-09-28 18:58:09.114520943 +0200
+++ libgcc/soft-fp/trunctfbf2.c	2022-09-28 18:58:09.114520943 +0200
@@ -0,0 +1,52 @@
+/* Software floating-point emulation.
+   Truncate IEEE quad into bfloat16.
+   Copyright (C) 2022 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   In addition to the permissions in the GNU Lesser General Public
+   License, the Free Software Foundation gives you unlimited
+   permission to link the compiled version of this file into
+   combinations with other programs, and to distribute those
+   combinations without any restriction coming from the use of this
+   file.  (The Lesser General Public License restrictions do apply in
+   other respects; for example, they cover modification of the file,
+   and distribution when not linked into a combine executable.)
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <https://www.gnu.org/licenses/>.  */
+
+#include "soft-fp.h"
+#include "brain.h"
+#include "quad.h"
+
+BFtype
+__trunctfbf2 (TFtype a)
+{
+  FP_DECL_EX;
+  FP_DECL_Q (A);
+  FP_DECL_B (R);
+  BFtype r;
+
+  FP_INIT_ROUNDMODE;
+  FP_UNPACK_SEMIRAW_Q (A, a);
+#if _FP_W_TYPE_SIZE < 64
+  FP_TRUNC (B, Q, 1, 4, R, A);
+#else
+  FP_TRUNC (B, Q, 1, 2, R, A);
+#endif
+  FP_PACK_SEMIRAW_B (r, R);
+  FP_HANDLE_EXCEPTIONS;
+
+  return r;
+}
--- libgcc/soft-fp/trunchfbf2.c.jj	2022-09-28 18:58:09.114520943 +0200
+++ libgcc/soft-fp/trunchfbf2.c	2022-09-28 18:58:09.114520943 +0200
@@ -0,0 +1,58 @@
+/* Software floating-point emulation.
+   Truncate IEEE half into bfloat16.
+   Copyright (C) 2022 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   In addition to the permissions in the GNU Lesser General Public
+   License, the Free Software Foundation gives you unlimited
+   permission to link the compiled version of this file into
+   combinations with other programs, and to distribute those
+   combinations without any restriction coming from the use of this
+   file.  (The Lesser General Public License restrictions do apply in
+   other respects; for example, they cover modification of the file,
+   and distribution when not linked into a combine executable.)
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <http://www.gnu.org/licenses/>.  */
+
+#include "soft-fp.h"
+#include "brain.h"
+#include "half.h"
+#include "single.h"
+
+/* BFtype and HFtype are unordered, neither is a superset or subset
+   of each other.  Convert HFtype to SFtype (lossless) and then
+   truncate to BFtype.  */
+
+BFtype
+__trunchfbf2 (HFtype a)
+{
+  FP_DECL_EX;
+  FP_DECL_H (A);
+  FP_DECL_S (B);
+  FP_DECL_B (R);
+  SFtype b;
+  BFtype r;
+
+  FP_INIT_ROUNDMODE;
+  FP_UNPACK_RAW_H (A, a);
+  FP_EXTEND (S, H, 1, 1, B, A);
+  FP_PACK_RAW_S (b, B);
+  FP_UNPACK_SEMIRAW_S (B, b);
+  FP_TRUNC (B, S, 1, 1, R, B);
+  FP_PACK_SEMIRAW_B (r, R);
+  FP_HANDLE_EXCEPTIONS;
+
+  return r;
+}
--- libgcc/soft-fp/truncbfhf2.c.jj	2022-09-28 18:58:09.113520956 +0200
+++ libgcc/soft-fp/truncbfhf2.c	2022-09-28 18:58:09.113520956 +0200
@@ -0,0 +1,75 @@
+/* Software floating-point emulation.
+   Truncate bfloat16 into IEEE half.
+   Copyright (C) 2022 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   In addition to the permissions in the GNU Lesser General Public
+   License, the Free Software Foundation gives you unlimited
+   permission to link the compiled version of this file into
+   combinations with other programs, and to distribute those
+   combinations without any restriction coming from the use of this
+   file.  (The Lesser General Public License restrictions do apply in
+   other respects; for example, they cover modification of the file,
+   and distribution when not linked into a combine executable.)
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <http://www.gnu.org/licenses/>.  */
+
+#include "soft-fp.h"
+#include "half.h"
+#include "brain.h"
+#include "single.h"
+
+/* BFtype and HFtype are unordered, neither is a superset or subset
+   of each other.  Convert BFtype to SFtype (lossless) and then
+   truncate to HFtype.  */
+
+HFtype
+__truncbfhf2 (BFtype a)
+{
+  FP_DECL_EX;
+  FP_DECL_H (A);
+  FP_DECL_S (B);
+  FP_DECL_B (R);
+  SFtype b;
+  HFtype r;
+
+  FP_INIT_ROUNDMODE;
+  /* Optimize BFtype to SFtype conversion to simple left shift
+     by 16 if possible, we don't need to raise exceptions on sNaN
+     here as the SFtype to HFtype truncation should do that too.  */
+  if (sizeof (BFtype) == 2
+      && sizeof (unsigned short) == 2
+      && sizeof (SFtype) == 4
+      && sizeof (unsigned int) == 4)
+    {
+      union { BFtype a; unsigned short b; } u1;
+      union { SFtype a; unsigned int b; } u2;
+      u1.a = a;
+      u2.b = (u1.b << 8) << 8;
+      b = u2.a;
+    }
+  else
+    {
+      FP_UNPACK_RAW_B (A, a);
+      FP_EXTEND (S, B, 1, 1, B, A);
+      FP_PACK_RAW_S (b, B);
+    }
+  FP_UNPACK_SEMIRAW_S (B, b);
+  FP_TRUNC (H, S, 1, 1, R, B);
+  FP_PACK_SEMIRAW_H (r, R);
+  FP_HANDLE_EXCEPTIONS;
+
+  return r;
+}
--- libgcc/soft-fp/extendbfsf2.c.jj	2022-09-28 18:58:09.114520943 +0200
+++ libgcc/soft-fp/extendbfsf2.c	2022-09-28 18:58:09.114520943 +0200
@@ -0,0 +1,49 @@
+/* Software floating-point emulation.
+   Return an bfloat16 converted to IEEE single
+   Copyright (C) 2022 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   In addition to the permissions in the GNU Lesser General Public
+   License, the Free Software Foundation gives you unlimited
+   permission to link the compiled version of this file into
+   combinations with other programs, and to distribute those
+   combinations without any restriction coming from the use of this
+   file.  (The Lesser General Public License restrictions do apply in
+   other respects; for example, they cover modification of the file,
+   and distribution when not linked into a combine executable.)
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <http://www.gnu.org/licenses/>.  */
+
+#define FP_NO_EXACT_UNDERFLOW
+#include "soft-fp.h"
+#include "brain.h"
+#include "single.h"
+
+SFtype
+__extendbfsf2 (BFtype a)
+{
+  FP_DECL_EX;
+  FP_DECL_B (A);
+  FP_DECL_S (R);
+  SFtype r;
+
+  FP_INIT_EXCEPTIONS;
+  FP_UNPACK_RAW_B (A, a);
+  FP_EXTEND (S, B, 1, 1, R, A);
+  FP_PACK_RAW_S (r, R);
+  FP_HANDLE_EXCEPTIONS;
+
+  return r;
+}
--- libiberty/cp-demangle.h.jj	2022-09-27 08:03:27.142982423 +0200
+++ libiberty/cp-demangle.h	2022-09-29 12:42:47.291727886 +0200
@@ -180,7 +180,7 @@ d_advance (struct d_info *di, int i)
 extern const struct demangle_operator_info cplus_demangle_operators[];
 #endif
 
-#define D_BUILTIN_TYPE_COUNT (35)
+#define D_BUILTIN_TYPE_COUNT (36)
 
 CP_STATIC_IF_GLIBCPP_V3
 const struct demangle_builtin_type_info
--- libiberty/cp-demangle.c.jj	2022-09-27 08:03:27.141982437 +0200
+++ libiberty/cp-demangle.c	2022-09-29 13:04:57.083526204 +0200
@@ -2489,6 +2489,7 @@ cplus_demangle_builtin_types[D_BUILTIN_T
   /* 33 */ { NL ("decltype(nullptr)"),	NL ("decltype(nullptr)"),
 	     D_PRINT_DEFAULT },
   /* 34 */ { NL ("_Float"),	NL ("_Float"),		D_PRINT_FLOAT },
+  /* 35 */ { NL ("std::bfloat16_t"), NL ("std::bfloat16_t"), D_PRINT_FLOAT },
 };
 
 CP_STATIC_IF_GLIBCPP_V3
@@ -2753,8 +2754,20 @@ cplus_demangle_type (struct d_info *di)
 
 	case 'F':
 	  /* DF<number>_ - _Float<number>.
-	     DF<number>x - _Float<number>x.  */
+	     DF<number>x - _Float<number>x
+	     DFb16_ - std::bfloat16_t.  */
 	  {
+	    if (d_peek_char (di) == 'b')
+	      {
+		d_advance (di, 1);
+		if (d_number (di) != 16 || d_peek_char (di) != '_')
+		  return NULL;
+		d_advance (di, 1);
+		ret = d_make_builtin_type (di,
+					   &cplus_demangle_builtin_types[35]);
+		di->expansion += ret->u.s_builtin.type->len;
+		break;
+	      }
 	    int arg = d_number (di);
 	    char buf[12];
 	    char suffix = 0;
--- libiberty/testsuite/demangle-expected.jj	2022-09-27 08:03:27.168982071 +0200
+++ libiberty/testsuite/demangle-expected	2022-09-29 12:49:02.181597532 +0200
@@ -1249,6 +1249,10 @@ xxx
 _Z3xxxDF32xDF64xDF128xCDF32xVb
 xxx(_Float32x, _Float64x, _Float128x, _Float32x _Complex, bool volatile)
 xxx
+--format=auto --no-params
+_Z3xxxDFb16_
+xxx(std::bfloat16_t)
+xxx
 # https://sourceware.org/bugzilla/show_bug.cgi?id=16817
 --format=auto --no-params
 _QueueNotification_QueueController__$4PPPPPPPM_A_INotice___Z


	Jakub
  
Joseph Myers Sept. 30, 2022, 6:21 p.m. UTC | #3
On Fri, 30 Sep 2022, Jakub Jelinek via Gcc-patches wrote:

> What isn't in the patch but I think we'll need to also change are some
> minimal set of __builtin_*bf16 builtins.  Seems for _Float16, GCC provides
> all the __builtin_*f16 (and for C/ObjC even with *f16 names), but there is
> no glibc support for any of that, so builtins that are expanded by the
> compiler are fine, but what should be fall back to libm won't work.
> Maybe at least for now it is acceptable to implement most <cmath> and
> <complex> std::float16_t and std::bfloat16_t overloads with using
> __builtin_*f and explicitly narrow down, but I think at least nextafter
> (and apparently nexttoward as an alias for it for extended floating
> point types) needs to be specific for the particular floating point format.

C doesn't have nexttoward (the function whose second argument is always 
long double, independent of the type of the first argument) for any of the 
_FloatN or _FloatNx types; why does C++ have in (but with second argument 
the same type as the first?) for those types?

(C2x also doesn't have fmax or fmin for the _FloatN or _FloatNx types, but 
that's because the operations those are bound to are replaced in IEEE 
754-2019 by different max/min operations with different corresponding 
functions; glibc still provides the fmax and fmin operations for _FloatN 
and _FloatNx, as in TS 18661-3, as extensions.)

Providing a full set of _Float16 operations in glibc would be reasonable 
(modulo the issues with implications for the minimum GCC version for 
building glibc for a given architecture).  It's rather less clear that 
__bf16 operations would be appropriate.

There may also be double rounding considerations for implementing some 
functions (that are required to be correctly rounded) via operations on 
float; at least for fma (if the result of fmaf is half way between two 
representable values of the narrower type, but not exactly equal to the 
value of a*b+c).
  
Jakub Jelinek Sept. 30, 2022, 6:38 p.m. UTC | #4
On Fri, Sep 30, 2022 at 06:21:04PM +0000, Joseph Myers wrote:
> On Fri, 30 Sep 2022, Jakub Jelinek via Gcc-patches wrote:
> 
> > What isn't in the patch but I think we'll need to also change are some
> > minimal set of __builtin_*bf16 builtins.  Seems for _Float16, GCC provides
> > all the __builtin_*f16 (and for C/ObjC even with *f16 names), but there is
> > no glibc support for any of that, so builtins that are expanded by the
> > compiler are fine, but what should be fall back to libm won't work.
> > Maybe at least for now it is acceptable to implement most <cmath> and
> > <complex> std::float16_t and std::bfloat16_t overloads with using
> > __builtin_*f and explicitly narrow down, but I think at least nextafter
> > (and apparently nexttoward as an alias for it for extended floating
> > point types) needs to be specific for the particular floating point format.
> 
> C doesn't have nexttoward (the function whose second argument is always 
> long double, independent of the type of the first argument) for any of the 
> _FloatN or _FloatNx types; why does C++ have in (but with second argument 
> the same type as the first?) for those types?

No idea.
https://eel.is/c++draft/cmath.syn
has (since that std::float*_t/std::bfloat16_t paper)
constexpr floating-point-type nextafter(floating-point-type x, floating-point-type y);
constexpr float nextafterf(float x, float y);
constexpr long double nextafterl(long double x, long double y);

constexpr floating-point-type nexttoward(floating-point-type x, floating-point-type y);
constexpr float nexttowardf(float x, long double y);
constexpr long double nexttowardl(long double x, long double y);

That is certainly wrong for double, because it is a backwards incompatible
change, where
constexpr double nexttoward(double x, long double y);
is gone and
constexpr double nexttoward(double x, double y);
is added.
IMHO the nexttoward case just shouldn't be changed, so it should remain:
constexpr float nexttoward(float x, long double y);
constexpr double nexttoward(double x, long double y);
constexpr long double nexttoward(long double x, long double y);
constexpr float nexttowardf(float x, long double y);
constexpr long double nexttowardl(long double x, long double y);
Having
constexpr floating-point-type nexttoward(floating-point-type x, long double y);
would be problematic, because long double might have unordered floating
point rank to floating-point-type (say powerpc IBM extended long double
vs. std::float128_t), or could have smaller floating point rank (say if
it is IEEE double).
But like nexttowardl or nexttoward(long double, long double) aren't very
useful because they are the same thing as nextafterl or
nextafter(long double, long double), introducing other nexttoward overloads
doesn't seem useful.

	Jakub
  
Jonathan Wakely Sept. 30, 2022, 7:27 p.m. UTC | #5
On Fri, 30 Sept 2022 at 19:38, Jakub Jelinek <jakub@redhat.com> wrote:
>
> On Fri, Sep 30, 2022 at 06:21:04PM +0000, Joseph Myers wrote:
> > On Fri, 30 Sep 2022, Jakub Jelinek via Gcc-patches wrote:
> >
> > > What isn't in the patch but I think we'll need to also change are some
> > > minimal set of __builtin_*bf16 builtins.  Seems for _Float16, GCC provides
> > > all the __builtin_*f16 (and for C/ObjC even with *f16 names), but there is
> > > no glibc support for any of that, so builtins that are expanded by the
> > > compiler are fine, but what should be fall back to libm won't work.
> > > Maybe at least for now it is acceptable to implement most <cmath> and
> > > <complex> std::float16_t and std::bfloat16_t overloads with using
> > > __builtin_*f and explicitly narrow down, but I think at least nextafter
> > > (and apparently nexttoward as an alias for it for extended floating
> > > point types) needs to be specific for the particular floating point format.
> >
> > C doesn't have nexttoward (the function whose second argument is always
> > long double, independent of the type of the first argument) for any of the
> > _FloatN or _FloatNx types; why does C++ have in (but with second argument
> > the same type as the first?) for those types?
>
> No idea.
> https://eel.is/c++draft/cmath.syn
> has (since that std::float*_t/std::bfloat16_t paper)
> constexpr floating-point-type nextafter(floating-point-type x, floating-point-type y);
> constexpr float nextafterf(float x, float y);
> constexpr long double nextafterl(long double x, long double y);
>
> constexpr floating-point-type nexttoward(floating-point-type x, floating-point-type y);
> constexpr float nexttowardf(float x, long double y);
> constexpr long double nexttowardl(long double x, long double y);
>
> That is certainly wrong for double, because it is a backwards incompatible
> change, where
> constexpr double nexttoward(double x, long double y);
> is gone and
> constexpr double nexttoward(double x, double y);
> is added.
> IMHO the nexttoward case just shouldn't be changed, so it should remain:
> constexpr float nexttoward(float x, long double y);
> constexpr double nexttoward(double x, long double y);
> constexpr long double nexttoward(long double x, long double y);
> constexpr float nexttowardf(float x, long double y);
> constexpr long double nexttowardl(long double x, long double y);

Right, this is a defect. The author of P1467 reported that as an
accidental change (which we all missed). It should be in the LWG
issues list by Monday, and (I hope) will be voted Tentatively Ready
immediately.

> Having
> constexpr floating-point-type nexttoward(floating-point-type x, long double y);
> would be problematic, because long double might have unordered floating
> point rank to floating-point-type (say powerpc IBM extended long double
> vs. std::float128_t), or could have smaller floating point rank (say if
> it is IEEE double).
> But like nexttowardl or nexttoward(long double, long double) aren't very
> useful because they are the same thing as nextafterl or
> nextafter(long double, long double), introducing other nexttoward overloads
> doesn't seem useful.
>
>         Jakub
>
  

Patch

--- gcc/tree-core.h.jj	2022-09-29 09:13:25.717718458 +0200
+++ gcc/tree-core.h	2022-09-29 12:40:17.417778754 +0200
@@ -665,6 +665,9 @@  enum tree_index {
   TI_DOUBLE_TYPE,
   TI_LONG_DOUBLE_TYPE,
 
+  /* __bf16 type if supported (used in C++ as std::bfloat16_t).  */
+  TI_BFLOAT16_TYPE,
+
   /* The _FloatN and _FloatNx types must be consecutive, and in the
      same sequence as the corresponding complex types, which must also
      be consecutive; _FloatN must come before _FloatNx; the order must
--- gcc/tree.h.jj	2022-09-29 09:13:25.720718416 +0200
+++ gcc/tree.h	2022-09-29 12:40:17.416778768 +0200
@@ -4285,6 +4285,7 @@  tree_strip_any_location_wrapper (tree ex
 #define float_type_node			global_trees[TI_FLOAT_TYPE]
 #define double_type_node		global_trees[TI_DOUBLE_TYPE]
 #define long_double_type_node		global_trees[TI_LONG_DOUBLE_TYPE]
+#define bfloat16_type_node		global_trees[TI_BFLOAT16_TYPE]
 
 /* Nodes for particular _FloatN and _FloatNx types in sequence.  */
 #define FLOATN_TYPE_NODE(IDX)		global_trees[TI_FLOATN_TYPE_FIRST + (IDX)]
--- gcc/tree.cc.jj	2022-09-29 09:13:31.328641080 +0200
+++ gcc/tree.cc	2022-09-29 12:40:17.400778985 +0200
@@ -7711,7 +7711,7 @@  excess_precision_type (tree type)
     = (flag_excess_precision == EXCESS_PRECISION_FAST
        ? EXCESS_PRECISION_TYPE_FAST
        : (flag_excess_precision == EXCESS_PRECISION_FLOAT16
-	  ? EXCESS_PRECISION_TYPE_FLOAT16 :EXCESS_PRECISION_TYPE_STANDARD));
+	  ? EXCESS_PRECISION_TYPE_FLOAT16 : EXCESS_PRECISION_TYPE_STANDARD));
 
   enum flt_eval_method target_flt_eval_method
     = targetm.c.excess_precision (requested_type);
@@ -7736,6 +7736,9 @@  excess_precision_type (tree type)
   machine_mode float16_type_mode = (float16_type_node
 				    ? TYPE_MODE (float16_type_node)
 				    : VOIDmode);
+  machine_mode bfloat16_type_mode = (bfloat16_type_node
+				     ? TYPE_MODE (bfloat16_type_node)
+				     : VOIDmode);
   machine_mode float_type_mode = TYPE_MODE (float_type_node);
   machine_mode double_type_mode = TYPE_MODE (double_type_node);
 
@@ -7747,16 +7750,19 @@  excess_precision_type (tree type)
 	switch (target_flt_eval_method)
 	  {
 	  case FLT_EVAL_METHOD_PROMOTE_TO_FLOAT:
-	    if (type_mode == float16_type_mode)
+	    if (type_mode == float16_type_mode
+		|| type_mode == bfloat16_type_mode)
 	      return float_type_node;
 	    break;
 	  case FLT_EVAL_METHOD_PROMOTE_TO_DOUBLE:
 	    if (type_mode == float16_type_mode
+		|| type_mode == bfloat16_type_mode
 		|| type_mode == float_type_mode)
 	      return double_type_node;
 	    break;
 	  case FLT_EVAL_METHOD_PROMOTE_TO_LONG_DOUBLE:
 	    if (type_mode == float16_type_mode
+		|| type_mode == bfloat16_type_mode
 		|| type_mode == float_type_mode
 		|| type_mode == double_type_mode)
 	      return long_double_type_node;
@@ -7774,16 +7780,19 @@  excess_precision_type (tree type)
 	switch (target_flt_eval_method)
 	  {
 	  case FLT_EVAL_METHOD_PROMOTE_TO_FLOAT:
-	    if (type_mode == float16_type_mode)
+	    if (type_mode == float16_type_mode
+		|| type_mode == bfloat16_type_mode)
 	      return complex_float_type_node;
 	    break;
 	  case FLT_EVAL_METHOD_PROMOTE_TO_DOUBLE:
 	    if (type_mode == float16_type_mode
+		|| type_mode == bfloat16_type_mode
 		|| type_mode == float_type_mode)
 	      return complex_double_type_node;
 	    break;
 	  case FLT_EVAL_METHOD_PROMOTE_TO_LONG_DOUBLE:
 	    if (type_mode == float16_type_mode
+		|| type_mode == bfloat16_type_mode
 		|| type_mode == float_type_mode
 		|| type_mode == double_type_mode)
 	      return complex_long_double_type_node;
--- gcc/expmed.h.jj	2022-07-26 10:32:23.681271790 +0200
+++ gcc/expmed.h	2022-09-29 15:18:46.457023535 +0200
@@ -707,6 +707,8 @@  extern rtx expand_variable_shift (enum t
 				  rtx, tree, rtx, int);
 extern rtx expand_shift (enum tree_code, machine_mode, rtx, poly_int64, rtx,
 			 int);
+extern rtx maybe_expand_shift (enum tree_code, machine_mode, rtx, int, rtx,
+			       int);
 #ifdef GCC_OPTABS_H
 extern rtx expand_divmod (int, enum tree_code, machine_mode, rtx, rtx,
 			  rtx, int, enum optab_methods = OPTAB_LIB_WIDEN);
--- gcc/expmed.cc.jj	2022-08-31 10:20:20.000000000 +0200
+++ gcc/expmed.cc	2022-09-29 15:17:52.224769673 +0200
@@ -2705,7 +2705,7 @@  expand_shift (enum tree_code code, machi
 
 /* Likewise, but return 0 if that cannot be done.  */
 
-static rtx
+rtx
 maybe_expand_shift (enum tree_code code, machine_mode mode, rtx shifted,
 		    int amount, rtx target, int unsignedp)
 {
--- gcc/expr.cc.jj	2022-09-09 09:50:35.228575531 +0200
+++ gcc/expr.cc	2022-09-29 17:09:46.716352938 +0200
@@ -344,7 +344,11 @@  convert_mode_scalar (rtx to, rtx from, i
       gcc_assert ((GET_MODE_PRECISION (from_mode)
 		   != GET_MODE_PRECISION (to_mode))
 		  || (DECIMAL_FLOAT_MODE_P (from_mode)
-		      != DECIMAL_FLOAT_MODE_P (to_mode)));
+		      != DECIMAL_FLOAT_MODE_P (to_mode))
+		  || (REAL_MODE_FORMAT (from_mode) == &arm_bfloat_half_format
+		      && REAL_MODE_FORMAT (to_mode) == &ieee_half_format)
+		  || (REAL_MODE_FORMAT (to_mode) == &arm_bfloat_half_format
+		      && REAL_MODE_FORMAT (from_mode) == &ieee_half_format));
 
       if (GET_MODE_PRECISION (from_mode) == GET_MODE_PRECISION (to_mode))
 	/* Conversion between decimal float and binary float, same size.  */
@@ -364,6 +368,150 @@  convert_mode_scalar (rtx to, rtx from, i
 	  return;
 	}
 
+#ifdef HAVE_SFmode
+      if (REAL_MODE_FORMAT (from_mode) == &arm_bfloat_half_format
+	  && REAL_MODE_FORMAT (SFmode) == &ieee_single_format)
+	{
+	  if (GET_MODE_PRECISION (to_mode) > GET_MODE_PRECISION (SFmode))
+	    {
+	      /* To cut down on libgcc size, implement
+		 BFmode -> {DF,XF,TF}mode conversions by
+		 BFmode -> SFmode -> {DF,XF,TF}mode conversions.  */
+	      rtx temp = gen_reg_rtx (SFmode);
+	      convert_mode_scalar (temp, from, unsignedp);
+	      convert_mode_scalar (to, temp, unsignedp);
+	      return;
+	    }
+	  if (REAL_MODE_FORMAT (to_mode) == &ieee_half_format)
+	    {
+	      /* Similarly, implement BFmode -> HFmode as
+		 BFmode -> SFmode -> HFmode conversion where SFmode
+		 has superset of BFmode values.  We don't need
+		 to handle sNaNs by raising exception and turning
+		 into into qNaN though, as that can be done in the
+		 SFmode -> HFmode conversion too.  */
+	      rtx temp = gen_reg_rtx (SFmode);
+	      int save_flag_finite_math_only = flag_finite_math_only;
+	      flag_finite_math_only = true;
+	      convert_mode_scalar (temp, from, unsignedp);
+	      flag_finite_math_only = save_flag_finite_math_only;
+	      convert_mode_scalar (to, temp, unsignedp);
+	      return;
+	    }
+	  if (to_mode == SFmode
+	      && !HONOR_NANS (from_mode)
+	      && !HONOR_NANS (to_mode)
+	      && optimize_insn_for_speed_p ())
+	    {
+	      /* If we don't expect sNaNs, for BFmode -> SFmode we can just
+		 shift the bits up.  */
+	      machine_mode fromi_mode, toi_mode;
+	      if (int_mode_for_size (GET_MODE_BITSIZE (from_mode),
+				     0).exists (&fromi_mode)
+		  && int_mode_for_size (GET_MODE_BITSIZE (to_mode),
+					0).exists (&toi_mode))
+		{
+		  start_sequence ();
+		  rtx fromi = lowpart_subreg (fromi_mode, from, from_mode);
+		  rtx tof = NULL_RTX;
+		  if (fromi)
+		    {
+		      rtx toi = gen_reg_rtx (toi_mode);
+		      convert_mode_scalar (toi, fromi, 1);
+		      toi
+			= maybe_expand_shift (LSHIFT_EXPR, toi_mode, toi,
+					      GET_MODE_PRECISION (to_mode)
+					      - GET_MODE_PRECISION (from_mode),
+					      NULL_RTX, 1);
+		      if (toi)
+			{
+			  tof = lowpart_subreg (to_mode, toi, toi_mode);
+			  if (tof)
+			    emit_move_insn (to, tof);
+			}
+		    }
+		  insns = get_insns ();
+		  end_sequence ();
+		  if (tof)
+		    {
+		      emit_insn (insns);
+		      return;
+		    }
+		}
+	    }
+	}
+      if (REAL_MODE_FORMAT (from_mode) == &ieee_single_format
+	  && REAL_MODE_FORMAT (to_mode) == &arm_bfloat_half_format
+	  && !HONOR_NANS (from_mode)
+	  && !HONOR_NANS (to_mode)
+	  && !flag_rounding_math
+	  && optimize_insn_for_speed_p ())
+	{
+	  /* If we don't expect qNaNs nor sNaNs and can assume rounding
+	     to nearest, we can expand the conversion inline as
+	     (fromi + 0x7fff + ((fromi >> 16) & 1)) >> 16.  */
+	  machine_mode fromi_mode, toi_mode;
+	  if (int_mode_for_size (GET_MODE_BITSIZE (from_mode),
+				 0).exists (&fromi_mode)
+	      && int_mode_for_size (GET_MODE_BITSIZE (to_mode),
+				    0).exists (&toi_mode))
+	    {
+	      start_sequence ();
+	      rtx fromi = lowpart_subreg (fromi_mode, from, from_mode);
+	      rtx tof = NULL_RTX;
+	      do
+		{
+		  if (!fromi)
+		    break;
+		  int shift = (GET_MODE_PRECISION (from_mode)
+			       - GET_MODE_PRECISION (to_mode));
+		  rtx temp1
+		    = maybe_expand_shift (RSHIFT_EXPR, fromi_mode, fromi,
+					  shift, NULL_RTX, 1);
+		  if (!temp1)
+		    break;
+		  rtx temp2
+		    = expand_binop (fromi_mode, and_optab, temp1, const1_rtx,
+				    NULL_RTX, 1, OPTAB_DIRECT);
+		  if (!temp2)
+		    break;
+		  rtx temp3
+		    = expand_binop (fromi_mode, add_optab, fromi,
+				    gen_int_mode ((HOST_WIDE_INT_1U
+						   << (shift - 1)) - 1,
+						  fromi_mode), NULL_RTX,
+				    1, OPTAB_DIRECT);
+		  if (!temp3)
+		    break;
+		  rtx temp4
+		    = expand_binop (fromi_mode, add_optab, temp3, temp2,
+				    NULL_RTX, 1, OPTAB_DIRECT);
+		  if (!temp4)
+		    break;
+		  rtx temp5 = maybe_expand_shift (RSHIFT_EXPR, fromi_mode,
+						  temp4, shift, NULL_RTX, 1);
+		  if (!temp5)
+		    break;
+		  rtx temp6 = lowpart_subreg (toi_mode, temp5, fromi_mode);
+		  if (!temp6)
+		    break;
+		  tof = lowpart_subreg (to_mode, force_reg (toi_mode, temp6),
+					toi_mode);
+		  if (tof)
+		    emit_move_insn (to, tof);
+		}
+	      while (0);
+	      insns = get_insns ();
+	      end_sequence ();
+	      if (tof)
+		{
+		  emit_insn (insns);
+		  return;
+		}
+	    }
+	}
+#endif
+
       /* Otherwise use a libcall.  */
       libcall = convert_optab_libfunc (tab, to_mode, from_mode);
 
--- gcc/config/arm/arm.h.jj	2022-09-29 09:13:25.709718568 +0200
+++ gcc/config/arm/arm.h	2022-09-29 12:40:17.401778971 +0200
@@ -78,9 +78,8 @@  extern void (*arm_lang_output_object_att
    the backend.  Defined in arm-builtins.cc.  */
 extern tree arm_fp16_type_node;
 
-/* This type is the user-visible __bf16.  We need it in a few places in
-   the backend.  Defined in arm-builtins.cc.  */
-extern tree arm_bf16_type_node;
+/* The user-visible __bf16 uses bfloat16_type_node, but for pointer to that
+   use backend specific tree.  Defined in arm-builtins.cc.  */
 extern tree arm_bf16_ptr_type_node;
 
 
--- gcc/config/arm/arm.cc.jj	2022-09-29 09:13:25.709718568 +0200
+++ gcc/config/arm/arm.cc	2022-09-29 15:33:07.997170885 +0200
@@ -688,12 +688,6 @@  static const struct attribute_spec arm_a
 #undef TARGET_INVALID_CONVERSION
 #define TARGET_INVALID_CONVERSION arm_invalid_conversion
 
-#undef TARGET_INVALID_UNARY_OP
-#define TARGET_INVALID_UNARY_OP arm_invalid_unary_op
-
-#undef TARGET_INVALID_BINARY_OP
-#define TARGET_INVALID_BINARY_OP arm_invalid_binary_op
-
 #undef TARGET_ATOMIC_ASSIGN_EXPAND_FENV
 #define TARGET_ATOMIC_ASSIGN_EXPAND_FENV arm_atomic_assign_expand_fenv
 
@@ -30360,7 +30354,7 @@  arm_mangle_type (const_tree type)
   if (TREE_CODE (type) == REAL_TYPE && TYPE_PRECISION (type) == 16)
     {
       if (TYPE_MODE (type) == BFmode)
-	return "u6__bf16";
+	return "DFb16_";
       else
 	return "Dh";
     }
@@ -33996,47 +33990,22 @@  arm_invalid_conversion (const_tree fromt
 {
   if (element_mode (fromtype) != element_mode (totype))
     {
-      /* Do no allow conversions to/from BFmode scalar types.  */
-      if (TYPE_MODE (fromtype) == BFmode)
-	return N_("invalid conversion from type %<bfloat16_t%>");
-      if (TYPE_MODE (totype) == BFmode)
-	return N_("invalid conversion to type %<bfloat16_t%>");
+      /* Do no allow conversions from BFmode to non-ieee HFmode
+	 scalar types or vice versa.  */
+      if (TYPE_MODE (fromtype) == BFmode
+	  && TYPE_MODE (totype) == HFmode
+	  && arm_fp16_format == ARM_FP16_FORMAT_ALTERNATIVE)
+	return N_("invalid conversion from type %<bfloat16_t%> to %<__fp16%>");
+      if (TYPE_MODE (totype) == BFmode
+	  && TYPE_MODE (fromtype) == HFmode
+	  && arm_fp16_format == ARM_FP16_FORMAT_ALTERNATIVE)
+	return N_("invalid conversion to type %<bfloat16_t%> from %<__fp16%>");
     }
 
   /* Conversion allowed.  */
   return NULL;
 }
 
-/* Return the diagnostic message string if the unary operation OP is
-   not permitted on TYPE, NULL otherwise.  */
-
-static const char *
-arm_invalid_unary_op (int op, const_tree type)
-{
-  /* Reject all single-operand operations on BFmode except for &.  */
-  if (element_mode (type) == BFmode && op != ADDR_EXPR)
-    return N_("operation not permitted on type %<bfloat16_t%>");
-
-  /* Operation allowed.  */
-  return NULL;
-}
-
-/* Return the diagnostic message string if the binary operation OP is
-   not permitted on TYPE1 and TYPE2, NULL otherwise.  */
-
-static const char *
-arm_invalid_binary_op (int op ATTRIBUTE_UNUSED, const_tree type1,
-			   const_tree type2)
-{
-  /* Reject all 2-operand operations on BFmode.  */
-  if (element_mode (type1) == BFmode
-      || element_mode (type2) == BFmode)
-    return N_("operation not permitted on type %<bfloat16_t%>");
-
-  /* Operation allowed.  */
-  return NULL;
-}
-
 /* Implement TARGET_CAN_CHANGE_MODE_CLASS.
 
    In VFPv1, VFP registers could only be accessed in the mode they were
--- gcc/config/arm/arm-builtins.cc.jj	2022-09-29 09:13:25.681718954 +0200
+++ gcc/config/arm/arm-builtins.cc	2022-09-29 12:40:17.405778917 +0200
@@ -1370,7 +1370,6 @@  struct arm_simd_type_info arm_simd_types
 tree arm_fp16_type_node = NULL_TREE;
 
 /* Back-end node type for brain float (bfloat) types.  */
-tree arm_bf16_type_node = NULL_TREE;
 tree arm_bf16_ptr_type_node = NULL_TREE;
 
 static tree arm_simd_intOI_type_node = NULL_TREE;
@@ -1459,7 +1458,7 @@  arm_simd_builtin_std_type (machine_mode
     case E_DFmode:
       return double_type_node;
     case E_BFmode:
-      return arm_bf16_type_node;
+      return bfloat16_type_node;
     default:
       gcc_unreachable ();
     }
@@ -1570,9 +1569,9 @@  arm_init_simd_builtin_types (void)
   arm_simd_types[Float32x4_t].eltype = float_type_node;
 
   /* Init Bfloat vector types with underlying __bf16 scalar type.  */
-  arm_simd_types[Bfloat16x2_t].eltype = arm_bf16_type_node;
-  arm_simd_types[Bfloat16x4_t].eltype = arm_bf16_type_node;
-  arm_simd_types[Bfloat16x8_t].eltype = arm_bf16_type_node;
+  arm_simd_types[Bfloat16x2_t].eltype = bfloat16_type_node;
+  arm_simd_types[Bfloat16x4_t].eltype = bfloat16_type_node;
+  arm_simd_types[Bfloat16x8_t].eltype = bfloat16_type_node;
 
   for (i = 0; i < nelts; i++)
     {
@@ -1658,7 +1657,7 @@  arm_init_simd_builtin_scalar_types (void
 					     "__builtin_neon_df");
   (*lang_hooks.types.register_builtin_type) (intTI_type_node,
 					     "__builtin_neon_ti");
-  (*lang_hooks.types.register_builtin_type) (arm_bf16_type_node,
+  (*lang_hooks.types.register_builtin_type) (bfloat16_type_node,
                                              "__builtin_neon_bf");
   /* Unsigned integer types for various mode sizes.  */
   (*lang_hooks.types.register_builtin_type) (unsigned_intQI_type_node,
@@ -1797,13 +1796,13 @@  arm_init_builtin (unsigned int fcode, ar
 static void
 arm_init_bf16_types (void)
 {
-  arm_bf16_type_node = make_node (REAL_TYPE);
-  TYPE_PRECISION (arm_bf16_type_node) = 16;
-  SET_TYPE_MODE (arm_bf16_type_node, BFmode);
-  layout_type (arm_bf16_type_node);
+  bfloat16_type_node = make_node (REAL_TYPE);
+  TYPE_PRECISION (bfloat16_type_node) = 16;
+  SET_TYPE_MODE (bfloat16_type_node, BFmode);
+  layout_type (bfloat16_type_node);
 
-  lang_hooks.types.register_builtin_type (arm_bf16_type_node, "__bf16");
-  arm_bf16_ptr_type_node = build_pointer_type (arm_bf16_type_node);
+  lang_hooks.types.register_builtin_type (bfloat16_type_node, "__bf16");
+  arm_bf16_ptr_type_node = build_pointer_type (bfloat16_type_node);
 }
 
 /* Set up ACLE builtins, even builtins for instructions that are not
--- gcc/config/i386/i386.cc.jj	2022-09-29 12:03:12.073350093 +0200
+++ gcc/config/i386/i386.cc	2022-09-29 12:40:17.409778863 +0200
@@ -22728,7 +22728,7 @@  ix86_mangle_type (const_tree type)
   switch (TYPE_MODE (type))
     {
     case E_BFmode:
-      return "u6__bf16";
+      return "DFb16_";
     case E_HFmode:
       /* _Float16 is "DF16_".
 	 Align with clang's decision in https://reviews.llvm.org/D33719. */
@@ -22747,55 +22747,6 @@  ix86_mangle_type (const_tree type)
     }
 }
 
-/* Return the diagnostic message string if conversion from FROMTYPE to
-   TOTYPE is not allowed, NULL otherwise.  */
-
-static const char *
-ix86_invalid_conversion (const_tree fromtype, const_tree totype)
-{
-  if (element_mode (fromtype) != element_mode (totype))
-    {
-      /* Do no allow conversions to/from BFmode scalar types.  */
-      if (TYPE_MODE (fromtype) == BFmode)
-	return N_("invalid conversion from type %<__bf16%>");
-      if (TYPE_MODE (totype) == BFmode)
-	return N_("invalid conversion to type %<__bf16%>");
-    }
-
-  /* Conversion allowed.  */
-  return NULL;
-}
-
-/* Return the diagnostic message string if the unary operation OP is
-   not permitted on TYPE, NULL otherwise.  */
-
-static const char *
-ix86_invalid_unary_op (int op, const_tree type)
-{
-  /* Reject all single-operand operations on BFmode except for &.  */
-  if (element_mode (type) == BFmode && op != ADDR_EXPR)
-    return N_("operation not permitted on type %<__bf16%>");
-
-  /* Operation allowed.  */
-  return NULL;
-}
-
-/* Return the diagnostic message string if the binary operation OP is
-   not permitted on TYPE1 and TYPE2, NULL otherwise.  */
-
-static const char *
-ix86_invalid_binary_op (int op ATTRIBUTE_UNUSED, const_tree type1,
-			   const_tree type2)
-{
-  /* Reject all 2-operand operations on BFmode.  */
-  if (element_mode (type1) == BFmode
-      || element_mode (type2) == BFmode)
-    return N_("operation not permitted on type %<__bf16%>");
-
-  /* Operation allowed.  */
-  return NULL;
-}
-
 static GTY(()) tree ix86_tls_stack_chk_guard_decl;
 
 static tree
@@ -24853,15 +24804,6 @@  ix86_libgcc_floating_mode_supported_p
 #undef TARGET_MANGLE_TYPE
 #define TARGET_MANGLE_TYPE ix86_mangle_type
 
-#undef TARGET_INVALID_CONVERSION
-#define TARGET_INVALID_CONVERSION ix86_invalid_conversion
-
-#undef TARGET_INVALID_UNARY_OP
-#define TARGET_INVALID_UNARY_OP ix86_invalid_unary_op
-
-#undef TARGET_INVALID_BINARY_OP
-#define TARGET_INVALID_BINARY_OP ix86_invalid_binary_op
-
 #undef TARGET_STACK_PROTECT_GUARD
 #define TARGET_STACK_PROTECT_GUARD ix86_stack_protect_guard
 
--- gcc/config/i386/i386-builtins.cc.jj	2022-09-29 09:13:25.710718554 +0200
+++ gcc/config/i386/i386-builtins.cc	2022-09-29 12:40:17.406778903 +0200
@@ -126,7 +126,6 @@  BDESC_VERIFYS (IX86_BUILTIN_MAX,
 static GTY(()) tree ix86_builtin_type_tab[(int) IX86_BT_LAST_CPTR + 1];
 
 tree ix86_float16_type_node = NULL_TREE;
-tree ix86_bf16_type_node = NULL_TREE;
 tree ix86_bf16_ptr_type_node = NULL_TREE;
 
 /* Retrieve an element from the above table, building some of
@@ -1372,16 +1371,15 @@  ix86_register_float16_builtin_type (void
 static void
 ix86_register_bf16_builtin_type (void)
 {
-  ix86_bf16_type_node = make_node (REAL_TYPE);
-  TYPE_PRECISION (ix86_bf16_type_node) = 16;
-  SET_TYPE_MODE (ix86_bf16_type_node, BFmode);
-  layout_type (ix86_bf16_type_node);
+  bfloat16_type_node = make_node (REAL_TYPE);
+  TYPE_PRECISION (bfloat16_type_node) = 16;
+  SET_TYPE_MODE (bfloat16_type_node, BFmode);
+  layout_type (bfloat16_type_node);
 
   if (!maybe_get_identifier ("__bf16") && TARGET_SSE2)
     {
-      lang_hooks.types.register_builtin_type (ix86_bf16_type_node,
-					    "__bf16");
-      ix86_bf16_ptr_type_node = build_pointer_type (ix86_bf16_type_node);
+      lang_hooks.types.register_builtin_type (bfloat16_type_node, "__bf16");
+      ix86_bf16_ptr_type_node = build_pointer_type (bfloat16_type_node);
     }
 }
 
--- gcc/config/i386/i386-builtin-types.def.jj	2022-09-29 09:13:25.709718568 +0200
+++ gcc/config/i386/i386-builtin-types.def	2022-09-29 12:40:17.406778903 +0200
@@ -69,7 +69,7 @@  DEF_PRIMITIVE_TYPE (UINT16, short_unsign
 DEF_PRIMITIVE_TYPE (INT64, long_long_integer_type_node)
 DEF_PRIMITIVE_TYPE (UINT64, long_long_unsigned_type_node)
 DEF_PRIMITIVE_TYPE (FLOAT16, ix86_float16_type_node)
-DEF_PRIMITIVE_TYPE (BFLOAT16, ix86_bf16_type_node)
+DEF_PRIMITIVE_TYPE (BFLOAT16, bfloat16_type_node)
 DEF_PRIMITIVE_TYPE (FLOAT, float_type_node)
 DEF_PRIMITIVE_TYPE (DOUBLE, double_type_node)
 DEF_PRIMITIVE_TYPE (FLOAT80, float80_type_node)
--- gcc/config/aarch64/aarch64.h.jj	2022-09-29 09:13:25.680718968 +0200
+++ gcc/config/aarch64/aarch64.h	2022-09-29 12:40:17.409778863 +0200
@@ -1337,9 +1337,8 @@  extern const char *aarch64_rewrite_mcpu
 extern GTY(()) tree aarch64_fp16_type_node;
 extern GTY(()) tree aarch64_fp16_ptr_type_node;
 
-/* This type is the user-visible __bf16, and a pointer to that type.  Defined
-   in aarch64-builtins.cc.  */
-extern GTY(()) tree aarch64_bf16_type_node;
+/* Pointer to the user-visible __bf16 type.  __bf16 itself is generic
+   bfloat16_type_node.  Defined in aarch64-builtins.cc.  */
 extern GTY(()) tree aarch64_bf16_ptr_type_node;
 
 /* The generic unwind code in libgcc does not initialize the frame pointer.
--- gcc/config/aarch64/aarch64.cc.jj	2022-09-29 09:13:25.680718968 +0200
+++ gcc/config/aarch64/aarch64.cc	2022-09-29 12:40:17.413778808 +0200
@@ -19741,7 +19741,7 @@  aarch64_gimplify_va_arg_expr (tree valis
 	  field_ptr_t = aarch64_fp16_ptr_type_node;
 	  break;
 	case E_BFmode:
-	  field_t = aarch64_bf16_type_node;
+	  field_t = bfloat16_type_node;
 	  field_ptr_t = aarch64_bf16_ptr_type_node;
 	  break;
 	case E_V2SImode:
@@ -20645,7 +20645,7 @@  aarch64_mangle_type (const_tree type)
   if (TREE_CODE (type) == REAL_TYPE && TYPE_PRECISION (type) == 16)
     {
       if (TYPE_MODE (type) == BFmode)
-	return "u6__bf16";
+	return "DFb16_";
       else
 	return "Dh";
     }
@@ -26820,39 +26820,6 @@  aarch64_stack_protect_guard (void)
   return NULL_TREE;
 }
 
-/* Return the diagnostic message string if conversion from FROMTYPE to
-   TOTYPE is not allowed, NULL otherwise.  */
-
-static const char *
-aarch64_invalid_conversion (const_tree fromtype, const_tree totype)
-{
-  if (element_mode (fromtype) != element_mode (totype))
-    {
-      /* Do no allow conversions to/from BFmode scalar types.  */
-      if (TYPE_MODE (fromtype) == BFmode)
-	return N_("invalid conversion from type %<bfloat16_t%>");
-      if (TYPE_MODE (totype) == BFmode)
-	return N_("invalid conversion to type %<bfloat16_t%>");
-    }
-
-  /* Conversion allowed.  */
-  return NULL;
-}
-
-/* Return the diagnostic message string if the unary operation OP is
-   not permitted on TYPE, NULL otherwise.  */
-
-static const char *
-aarch64_invalid_unary_op (int op, const_tree type)
-{
-  /* Reject all single-operand operations on BFmode except for &.  */
-  if (element_mode (type) == BFmode && op != ADDR_EXPR)
-    return N_("operation not permitted on type %<bfloat16_t%>");
-
-  /* Operation allowed.  */
-  return NULL;
-}
-
 /* Return the diagnostic message string if the binary operation OP is
    not permitted on TYPE1 and TYPE2, NULL otherwise.  */
 
@@ -26860,11 +26827,6 @@  static const char *
 aarch64_invalid_binary_op (int op ATTRIBUTE_UNUSED, const_tree type1,
 			   const_tree type2)
 {
-  /* Reject all 2-operand operations on BFmode.  */
-  if (element_mode (type1) == BFmode
-      || element_mode (type2) == BFmode)
-    return N_("operation not permitted on type %<bfloat16_t%>");
-
   if (VECTOR_TYPE_P (type1)
       && VECTOR_TYPE_P (type2)
       && !TYPE_INDIVISIBLE_P (type1)
@@ -27461,12 +27423,6 @@  aarch64_libgcc_floating_mode_supported_p
 #undef TARGET_MANGLE_TYPE
 #define TARGET_MANGLE_TYPE aarch64_mangle_type
 
-#undef TARGET_INVALID_CONVERSION
-#define TARGET_INVALID_CONVERSION aarch64_invalid_conversion
-
-#undef TARGET_INVALID_UNARY_OP
-#define TARGET_INVALID_UNARY_OP aarch64_invalid_unary_op
-
 #undef TARGET_INVALID_BINARY_OP
 #define TARGET_INVALID_BINARY_OP aarch64_invalid_binary_op
 
--- gcc/config/aarch64/aarch64-builtins.cc.jj	2022-09-29 09:13:25.676719023 +0200
+++ gcc/config/aarch64/aarch64-builtins.cc	2022-09-29 12:40:17.410778849 +0200
@@ -918,7 +918,6 @@  tree aarch64_fp16_type_node = NULL_TREE;
 tree aarch64_fp16_ptr_type_node = NULL_TREE;
 
 /* Back-end node type for brain float (bfloat) types.  */
-tree aarch64_bf16_type_node = NULL_TREE;
 tree aarch64_bf16_ptr_type_node = NULL_TREE;
 
 /* Wrapper around add_builtin_function.  NAME is the name of the built-in
@@ -1010,7 +1009,7 @@  aarch64_int_or_fp_type (machine_mode mod
     case E_DFmode:
       return double_type_node;
     case E_BFmode:
-      return aarch64_bf16_type_node;
+      return bfloat16_type_node;
     default:
       gcc_unreachable ();
     }
@@ -1124,8 +1123,8 @@  aarch64_init_simd_builtin_types (void)
   aarch64_simd_types[Float64x2_t].eltype = double_type_node;
 
   /* Init Bfloat vector types with underlying __bf16 type.  */
-  aarch64_simd_types[Bfloat16x4_t].eltype = aarch64_bf16_type_node;
-  aarch64_simd_types[Bfloat16x8_t].eltype = aarch64_bf16_type_node;
+  aarch64_simd_types[Bfloat16x4_t].eltype = bfloat16_type_node;
+  aarch64_simd_types[Bfloat16x8_t].eltype = bfloat16_type_node;
 
   for (i = 0; i < nelts; i++)
     {
@@ -1197,7 +1196,7 @@  aarch64_init_simd_builtin_scalar_types (
 					     "__builtin_aarch64_simd_poly128");
   (*lang_hooks.types.register_builtin_type) (intTI_type_node,
 					     "__builtin_aarch64_simd_ti");
-  (*lang_hooks.types.register_builtin_type) (aarch64_bf16_type_node,
+  (*lang_hooks.types.register_builtin_type) (bfloat16_type_node,
 					     "__builtin_aarch64_simd_bf");
   /* Unsigned integer types for various mode sizes.  */
   (*lang_hooks.types.register_builtin_type) (unsigned_intQI_type_node,
@@ -1682,13 +1681,13 @@  aarch64_init_fp16_types (void)
 static void
 aarch64_init_bf16_types (void)
 {
-  aarch64_bf16_type_node = make_node (REAL_TYPE);
-  TYPE_PRECISION (aarch64_bf16_type_node) = 16;
-  SET_TYPE_MODE (aarch64_bf16_type_node, BFmode);
-  layout_type (aarch64_bf16_type_node);
+  bfloat16_type_node = make_node (REAL_TYPE);
+  TYPE_PRECISION (bfloat16_type_node) = 16;
+  SET_TYPE_MODE (bfloat16_type_node, BFmode);
+  layout_type (bfloat16_type_node);
 
-  lang_hooks.types.register_builtin_type (aarch64_bf16_type_node, "__bf16");
-  aarch64_bf16_ptr_type_node = build_pointer_type (aarch64_bf16_type_node);
+  lang_hooks.types.register_builtin_type (bfloat16_type_node, "__bf16");
+  aarch64_bf16_ptr_type_node = build_pointer_type (bfloat16_type_node);
 }
 
 /* Pointer authentication builtins that will become NOP on legacy platform.
--- gcc/config/aarch64/aarch64-sve-builtins.def.jj	2022-09-29 09:13:25.676719023 +0200
+++ gcc/config/aarch64/aarch64-sve-builtins.def	2022-09-29 12:40:17.413778808 +0200
@@ -61,7 +61,7 @@  DEF_SVE_MODE (u64offset, none, svuint64_
 DEF_SVE_MODE (vnum, none, none, vectors)
 
 DEF_SVE_TYPE (svbool_t, 10, __SVBool_t, boolean_type_node)
-DEF_SVE_TYPE (svbfloat16_t, 14, __SVBfloat16_t, aarch64_bf16_type_node)
+DEF_SVE_TYPE (svbfloat16_t, 14, __SVBfloat16_t, bfloat16_type_node)
 DEF_SVE_TYPE (svfloat16_t, 13, __SVFloat16_t, aarch64_fp16_type_node)
 DEF_SVE_TYPE (svfloat32_t, 13, __SVFloat32_t, float_type_node)
 DEF_SVE_TYPE (svfloat64_t, 13, __SVFloat64_t, double_type_node)
--- gcc/c-family/c-cppbuiltin.cc.jj	2022-09-29 09:13:25.675719037 +0200
+++ gcc/c-family/c-cppbuiltin.cc	2022-09-29 12:40:17.416778768 +0200
@@ -1264,6 +1264,13 @@  c_cpp_builtins (cpp_reader *pfile)
       builtin_define_float_constants (prefix, ggc_strdup (csuffix), "%s",
 				      csuffix, FLOATN_NX_TYPE_NODE (i));
     }
+  if (bfloat16_type_node && c_dialect_cxx ())
+    {
+      if (cxx_dialect > cxx20)
+	cpp_define (pfile, "__STDCPP_BFLOAT16_T__=1");
+      builtin_define_float_constants ("BFLT16", "BF16", "%s",
+				      "BF16", bfloat16_type_node);
+    }
 
   /* For float.h.  */
   if (targetm.decimal_float_supported_p ())
--- gcc/c-family/c-lex.cc.jj	2022-09-29 09:13:25.675719037 +0200
+++ gcc/c-family/c-lex.cc	2022-09-29 12:40:17.416778768 +0200
@@ -995,6 +995,19 @@  interpret_float (const cpp_token *token,
 	  pedwarn (input_location, OPT_Wpedantic,
 		   "non-standard suffix on floating constant");
       }
+    else if ((flags & CPP_N_BFLOAT16) != 0 && c_dialect_cxx ())
+      {
+	type = bfloat16_type_node;
+	if (type == NULL_TREE)
+	  {
+	    error ("unsupported non-standard suffix on floating constant");
+	    return error_mark_node;
+	  }
+	if (cxx_dialect < cxx23)
+	  pedwarn (input_location, OPT_Wpedantic,
+		   "%<bf16%> or %<BF16%> suffix on floating constant only "
+		   "available with %<-std=c++2b%> or %<-std=gnu++2b%>");
+      }
     else if ((flags & CPP_N_WIDTH) == CPP_N_LARGE)
       type = long_double_type_node;
     else if ((flags & CPP_N_WIDTH) == CPP_N_SMALL
--- gcc/cp/cp-tree.h.jj	2022-09-29 09:13:31.164643341 +0200
+++ gcc/cp/cp-tree.h	2022-09-29 12:40:17.414778795 +0200
@@ -8714,6 +8714,8 @@  extended_float_type_p (tree type)
   for (int i = 0; i < NUM_FLOATN_NX_TYPES; ++i)
     if (type == FLOATN_TYPE_NODE (i))
       return true;
+  if (type == bfloat16_type_node)
+    return true;
   return false;
 }
 
--- gcc/cp/typeck.cc.jj	2022-09-29 09:13:25.716718472 +0200
+++ gcc/cp/typeck.cc	2022-09-29 12:40:17.415778781 +0200
@@ -293,6 +293,10 @@  cp_compare_floating_point_conversion_ran
       if (mv2 == FLOATN_NX_TYPE_NODE (i))
 	extended2 = i + 1;
     }
+  if (mv1 == bfloat16_type_node)
+    extended1 = true;
+  if (mv2 == bfloat16_type_node)
+    extended2 = true;
   if (extended2 && !extended1)
     {
       int ret = cp_compare_floating_point_conversion_ranks (t2, t1);
@@ -390,7 +394,9 @@  cp_compare_floating_point_conversion_ran
   if (cnt > 1 && mv2 == long_double_type_node)
     return -2;
   /* Otherwise, they have equal rank, but extended types
-     (other than std::bfloat16_t) have higher subrank.  */
+     (other than std::bfloat16_t) have higher subrank.
+     std::bfloat16_t shouldn't have equal rank to any standard
+     floating point type.  */
   return 1;
 }
 
--- libcpp/include/cpplib.h.jj	2022-09-08 13:01:19.853771383 +0200
+++ libcpp/include/cpplib.h	2022-09-28 19:06:59.615380690 +0200
@@ -1275,6 +1275,7 @@  struct cpp_num
 #define CPP_N_USERDEF	0x1000000 /* C++11 user-defined literal.  */
 
 #define CPP_N_SIZE_T	0x2000000 /* C++23 size_t literal.  */
+#define CPP_N_BFLOAT16	0x4000000 /* std::bfloat16_t type.  */
 
 #define CPP_N_WIDTH_FLOATN_NX	0xF0000000 /* _FloatN / _FloatNx value
 					      of N, divided by 16.  */
--- libcpp/expr.cc.jj	2022-09-27 08:03:27.119982735 +0200
+++ libcpp/expr.cc	2022-09-28 17:55:36.667177540 +0200
@@ -91,10 +91,10 @@  interpret_float_suffix (cpp_reader *pfil
   size_t orig_len = len;
   const uchar *orig_s = s;
   size_t flags;
-  size_t f, d, l, w, q, i, fn, fnx, fn_bits;
+  size_t f, d, l, w, q, i, fn, fnx, fn_bits, bf16;
 
   flags = 0;
-  f = d = l = w = q = i = fn = fnx = fn_bits = 0;
+  f = d = l = w = q = i = fn = fnx = fn_bits = bf16 = 0;
 
   /* The following decimal float suffixes, from TR 24732:2009, TS
      18661-2:2015 and C2X, are supported:
@@ -131,7 +131,8 @@  interpret_float_suffix (cpp_reader *pfil
      w, W - machine-specific type such as __float80 (GNU extension).
      q, Q - machine-specific type such as __float128 (GNU extension).
      fN, FN - _FloatN (TS 18661-3:2015).
-     fNx, FNx - _FloatNx (TS 18661-3:2015).  */
+     fNx, FNx - _FloatNx (TS 18661-3:2015).
+     bf16, BF16 - std::bfloat16_t (ISO C++23).  */
 
   /* Process decimal float suffixes, which are two letters starting
      with d or D.  Order and case are significant.  */
@@ -239,6 +240,20 @@  interpret_float_suffix (cpp_reader *pfil
 		fn++;
 	    }
 	  break;
+	case 'b': case 'B':
+	  if (len > 2
+	      /* Except for bf16 / BF16 where case is significant.  */
+	      && s[1] == (s[0] == 'b' ? 'f' : 'F')
+	      && s[2] == '1'
+	      && s[3] == '6'
+	      && CPP_OPTION (pfile, cplusplus))
+	    {
+	      bf16++;
+	      len -= 3;
+	      s += 3;
+	      break;
+	    }
+	  return 0;
 	case 'd': case 'D': d++; break;
 	case 'l': case 'L': l++; break;
 	case 'w': case 'W': w++; break;
@@ -257,7 +272,7 @@  interpret_float_suffix (cpp_reader *pfil
      of N larger than can be represented in the return value.  The
      caller is responsible for rejecting _FloatN suffixes where
      _FloatN is not supported on the chosen target.  */
-  if (f + d + l + w + q + fn + fnx > 1 || i > 1)
+  if (f + d + l + w + q + fn + fnx + bf16 > 1 || i > 1)
     return 0;
   if (fn_bits > CPP_FLOATN_MAX)
     return 0;
@@ -295,6 +310,7 @@  interpret_float_suffix (cpp_reader *pfil
 	     q ? CPP_N_MD_Q :
 	     fn ? CPP_N_FLOATN | (fn_bits << CPP_FLOATN_SHIFT) :
 	     fnx ? CPP_N_FLOATNX | (fn_bits << CPP_FLOATN_SHIFT) :
+	     bf16 ? CPP_N_BFLOAT16 :
 	     CPP_N_DEFAULT));
 }
 
--- libgcc/config/arm/sfp-machine.h.jj	2020-01-12 11:54:38.615380187 +0100
+++ libgcc/config/arm/sfp-machine.h	2022-09-28 19:02:51.922710542 +0200
@@ -22,6 +22,7 @@  typedef int __gcc_CMPtype __attribute__
 /* According to RTABI, QNAN is only with the most significant bit of the
    significand set, and all other significand bits zero.  */
 #define _FP_NANFRAC_H		_FP_QNANBIT_H
+#define _FP_NANFRAC_B		_FP_QNANBIT_B
 #define _FP_NANFRAC_S		_FP_QNANBIT_S
 #define _FP_NANFRAC_D		_FP_QNANBIT_D, 0
 #define _FP_NANFRAC_Q		_FP_QNANBIT_Q, 0, 0, 0
--- libgcc/config/aarch64/t-softfp.jj	2020-09-29 11:32:02.988602194 +0200
+++ libgcc/config/aarch64/t-softfp	2022-09-28 18:59:43.381246466 +0200
@@ -1,7 +1,7 @@ 
 softfp_float_modes := tf
 softfp_int_modes := si di ti
-softfp_extensions := sftf dftf hftf
-softfp_truncations := tfsf tfdf tfhf
+softfp_extensions := sftf dftf hftf bfsf
+softfp_truncations := tfsf tfdf tfhf tfbf dfbf sfbf hfbf
 softfp_exclude_libgcc2 := n
 softfp_extras := fixhfti fixunshfti floattihf floatuntihf
 
--- libgcc/config/aarch64/libgcc-softfp.ver.jj	2022-01-11 23:11:23.691271871 +0100
+++ libgcc/config/aarch64/libgcc-softfp.ver	2022-09-28 19:00:36.050537146 +0200
@@ -26,3 +26,12 @@  GCC_11.0 {
   __mulhc3
   __trunctfhf2
 }
+
+%inherit GCC_13.0.0 GCC_11.0.0
+GCC_13.0.0 {
+  __extendbfsf2
+  __truncdfbf2
+  __truncsfbf2
+  __trunctfbf2
+  __trunchfbf2
+}
--- libgcc/config/aarch64/sfp-machine.h.jj	2022-01-11 23:11:23.691271871 +0100
+++ libgcc/config/aarch64/sfp-machine.h	2022-09-28 19:02:10.303270053 +0200
@@ -43,6 +43,7 @@  typedef int __gcc_CMPtype __attribute__
 #define _FP_DIV_MEAT_Q(R,X,Y)	_FP_DIV_MEAT_2_udiv(Q,R,X,Y)
 
 #define _FP_NANFRAC_H		((_FP_QNANBIT_H << 1) - 1)
+#define _FP_NANFRAC_B		((_FP_QNANBIT_B << 1) - 1)
 #define _FP_NANFRAC_S		((_FP_QNANBIT_S << 1) - 1)
 #define _FP_NANFRAC_D		((_FP_QNANBIT_D << 1) - 1)
 #define _FP_NANFRAC_Q		((_FP_QNANBIT_Q << 1) - 1), -1
--- libgcc/config/i386/t-softfp.jj	2022-09-23 09:02:31.759659479 +0200
+++ libgcc/config/i386/t-softfp	2022-09-28 18:58:09.114520943 +0200
@@ -6,8 +6,9 @@  LIB2FUNCS_EXCLUDE += $(libgcc2-hf-functi
 libgcc2-hf-extras = $(addsuffix .c, $(libgcc2-hf-functions))
 LIB2ADD += $(addprefix $(srcdir)/config/i386/, $(libgcc2-hf-extras))
 
-softfp_extensions := hfsf hfdf hftf hfxf sfdf sftf dftf xftf
-softfp_truncations := tfhf xfhf dfhf sfhf tfsf dfsf tfdf tfxf
+softfp_extensions := hfsf hfdf hftf hfxf sfdf sftf dftf xftf bfsf
+softfp_truncations := tfhf xfhf dfhf sfhf tfsf dfsf tfdf tfxf \
+		      tfbf xfbf dfbf sfbf hfbf
 
 softfp_extras += eqhf2
 
@@ -20,6 +21,7 @@  CFLAGS-truncsfhf2.c += -msse2
 CFLAGS-truncdfhf2.c += -msse2
 CFLAGS-truncxfhf2.c += -msse2
 CFLAGS-trunctfhf2.c += -msse2
+CFLAGS-trunchfbf2.c += -msse2
 
 CFLAGS-eqhf2.c += -msse2
 CFLAGS-_divhc3.c += -msse2
--- libgcc/config/i386/libgcc-glibc.ver.jj	2022-09-23 09:02:31.746659658 +0200
+++ libgcc/config/i386/libgcc-glibc.ver	2022-09-28 18:58:09.114520943 +0200
@@ -214,3 +214,13 @@  GCC_12.0.0 {
   __trunctfhf2
   __truncxfhf2
 }
+
+%inherit GCC_13.0.0 GCC_12.0.0
+GCC_13.0.0 {
+  __extendbfsf2
+  __truncdfbf2
+  __truncsfbf2
+  __trunctfbf2
+  __truncxfbf2
+  __trunchfbf2
+}
--- libgcc/config/i386/sfp-machine.h.jj	2022-09-23 09:02:31.747659644 +0200
+++ libgcc/config/i386/sfp-machine.h	2022-09-28 18:58:09.114520943 +0200
@@ -18,6 +18,7 @@  typedef int __gcc_CMPtype __attribute__
 #define _FP_QNANNEGATEDP 0
 
 #define _FP_NANSIGN_H		1
+#define _FP_NANSIGN_B		1
 #define _FP_NANSIGN_S		1
 #define _FP_NANSIGN_D		1
 #define _FP_NANSIGN_E		1
--- libgcc/config/i386/64/sfp-machine.h.jj	2022-09-23 09:02:31.700660291 +0200
+++ libgcc/config/i386/64/sfp-machine.h	2022-09-28 18:58:09.114520943 +0200
@@ -14,6 +14,7 @@  typedef unsigned int UTItype __attribute
 #define _FP_DIV_MEAT_Q(R,X,Y)   _FP_DIV_MEAT_2_udiv(Q,R,X,Y)
 
 #define _FP_NANFRAC_H		_FP_QNANBIT_H
+#define _FP_NANFRAC_B		_FP_QNANBIT_B
 #define _FP_NANFRAC_S		_FP_QNANBIT_S
 #define _FP_NANFRAC_D		_FP_QNANBIT_D
 #define _FP_NANFRAC_E		_FP_QNANBIT_E, 0
--- libgcc/config/i386/32/sfp-machine.h.jj	2022-09-23 09:02:31.683660526 +0200
+++ libgcc/config/i386/32/sfp-machine.h	2022-09-28 18:58:09.115520929 +0200
@@ -87,6 +87,7 @@ 
 #define _FP_DIV_MEAT_Q(R,X,Y)   _FP_DIV_MEAT_4_udiv(Q,R,X,Y)
 
 #define _FP_NANFRAC_H		_FP_QNANBIT_H
+#define _FP_NANFRAC_B		_FP_QNANBIT_B
 #define _FP_NANFRAC_S		_FP_QNANBIT_S
 #define _FP_NANFRAC_D		_FP_QNANBIT_D, 0
 /* Even if XFmode is 12byte,  we have to pad it to
--- libgcc/soft-fp/brain.h.jj	2022-09-28 18:58:09.113520956 +0200
+++ libgcc/soft-fp/brain.h	2022-09-28 18:58:09.113520956 +0200
@@ -0,0 +1,172 @@ 
+/* Software floating-point emulation.
+   Definitions for Brain Floating Point format (bfloat16).
+   Copyright (C) 1997-2022 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   In addition to the permissions in the GNU Lesser General Public
+   License, the Free Software Foundation gives you unlimited
+   permission to link the compiled version of this file into
+   combinations with other programs, and to distribute those
+   combinations without any restriction coming from the use of this
+   file.  (The Lesser General Public License restrictions do apply in
+   other respects; for example, they cover modification of the file,
+   and distribution when not linked into a combine executable.)
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <https://www.gnu.org/licenses/>.  */
+
+#ifndef SOFT_FP_BRAIN_H
+#define SOFT_FP_BRAIN_H	1
+
+#if _FP_W_TYPE_SIZE < 32
+# error "Here's a nickel kid.  Go buy yourself a real computer."
+#endif
+
+#define _FP_FRACTBITS_B		(_FP_W_TYPE_SIZE)
+
+#define _FP_FRACTBITS_DW_B	(_FP_W_TYPE_SIZE)
+
+#define _FP_FRACBITS_B		8
+#define _FP_FRACXBITS_B		(_FP_FRACTBITS_B - _FP_FRACBITS_B)
+#define _FP_WFRACBITS_B		(_FP_WORKBITS + _FP_FRACBITS_B)
+#define _FP_WFRACXBITS_B	(_FP_FRACTBITS_B - _FP_WFRACBITS_B)
+#define _FP_EXPBITS_B		8
+#define _FP_EXPBIAS_B		127
+#define _FP_EXPMAX_B		255
+
+#define _FP_QNANBIT_B		((_FP_W_TYPE) 1 << (_FP_FRACBITS_B-2))
+#define _FP_QNANBIT_SH_B	((_FP_W_TYPE) 1 << (_FP_FRACBITS_B-2+_FP_WORKBITS))
+#define _FP_IMPLBIT_B		((_FP_W_TYPE) 1 << (_FP_FRACBITS_B-1))
+#define _FP_IMPLBIT_SH_B	((_FP_W_TYPE) 1 << (_FP_FRACBITS_B-1+_FP_WORKBITS))
+#define _FP_OVERFLOW_B		((_FP_W_TYPE) 1 << (_FP_WFRACBITS_B))
+
+#define _FP_WFRACBITS_DW_B	(2 * _FP_WFRACBITS_B)
+#define _FP_WFRACXBITS_DW_B	(_FP_FRACTBITS_DW_B - _FP_WFRACBITS_DW_B)
+#define _FP_HIGHBIT_DW_B	\
+  ((_FP_W_TYPE) 1 << (_FP_WFRACBITS_DW_B - 1) % _FP_W_TYPE_SIZE)
+
+/* The implementation of _FP_MUL_MEAT_B and _FP_DIV_MEAT_B should be
+   chosen by the target machine.  */
+
+typedef float BFtype __attribute__ ((mode (BF)));
+
+union _FP_UNION_B
+{
+  BFtype flt;
+  struct _FP_STRUCT_LAYOUT
+  {
+#if __BYTE_ORDER == __BIG_ENDIAN
+    unsigned sign : 1;
+    unsigned exp  : _FP_EXPBITS_B;
+    unsigned frac : _FP_FRACBITS_B - (_FP_IMPLBIT_B != 0);
+#else
+    unsigned frac : _FP_FRACBITS_B - (_FP_IMPLBIT_B != 0);
+    unsigned exp  : _FP_EXPBITS_B;
+    unsigned sign : 1;
+#endif
+  } bits;
+};
+
+#define FP_DECL_B(X)		_FP_DECL (1, X)
+#define FP_UNPACK_RAW_B(X, val)	_FP_UNPACK_RAW_1 (B, X, (val))
+#define FP_UNPACK_RAW_BP(X, val)	_FP_UNPACK_RAW_1_P (B, X, (val))
+#define FP_PACK_RAW_B(val, X)	_FP_PACK_RAW_1 (B, (val), X)
+#define FP_PACK_RAW_BP(val, X)			\
+  do						\
+    {						\
+      if (!FP_INHIBIT_RESULTS)			\
+	_FP_PACK_RAW_1_P (B, (val), X);		\
+    }						\
+  while (0)
+
+#define FP_UNPACK_B(X, val)			\
+  do						\
+    {						\
+      _FP_UNPACK_RAW_1 (B, X, (val));		\
+      _FP_UNPACK_CANONICAL (B, 1, X);		\
+    }						\
+  while (0)
+
+#define FP_UNPACK_BP(X, val)			\
+  do						\
+    {						\
+      _FP_UNPACK_RAW_1_P (B, X, (val));		\
+      _FP_UNPACK_CANONICAL (B, 1, X);		\
+    }						\
+  while (0)
+
+#define FP_UNPACK_SEMIRAW_B(X, val)		\
+  do						\
+    {						\
+      _FP_UNPACK_RAW_1 (B, X, (val));		\
+      _FP_UNPACK_SEMIRAW (B, 1, X);		\
+    }						\
+  while (0)
+
+#define FP_UNPACK_SEMIRAW_BP(X, val)		\
+  do						\
+    {						\
+      _FP_UNPACK_RAW_1_P (B, X, (val));		\
+      _FP_UNPACK_SEMIRAW (B, 1, X);		\
+    }						\
+  while (0)
+
+#define FP_PACK_B(val, X)			\
+  do						\
+    {						\
+      _FP_PACK_CANONICAL (B, 1, X);		\
+      _FP_PACK_RAW_1 (B, (val), X);		\
+    }						\
+  while (0)
+
+#define FP_PACK_BP(val, X)			\
+  do						\
+    {						\
+      _FP_PACK_CANONICAL (B, 1, X);		\
+      if (!FP_INHIBIT_RESULTS)			\
+	_FP_PACK_RAW_1_P (B, (val), X);		\
+    }						\
+  while (0)
+
+#define FP_PACK_SEMIRAW_B(val, X)		\
+  do						\
+    {						\
+      _FP_PACK_SEMIRAW (B, 1, X);		\
+      _FP_PACK_RAW_1 (B, (val), X);		\
+    }						\
+  while (0)
+
+#define FP_PACK_SEMIRAW_BP(val, X)		\
+  do						\
+    {						\
+      _FP_PACK_SEMIRAW (B, 1, X);		\
+      if (!FP_INHIBIT_RESULTS)			\
+	_FP_PACK_RAW_1_P (B, (val), X);		\
+    }						\
+  while (0)
+
+#define FP_TO_INT_B(r, X, rsz, rsg)	_FP_TO_INT (B, 1, (r), X, (rsz), (rsg))
+#define FP_TO_INT_ROUND_B(r, X, rsz, rsg)	\
+  _FP_TO_INT_ROUND (B, 1, (r), X, (rsz), (rsg))
+#define FP_FROM_INT_B(X, r, rs, rt)	_FP_FROM_INT (B, 1, X, (r), (rs), rt)
+
+/* BFmode arithmetic is not implemented.  */
+
+#define _FP_FRAC_HIGH_B(X)	_FP_FRAC_HIGH_1 (X)
+#define _FP_FRAC_HIGH_RAW_B(X)	_FP_FRAC_HIGH_1 (X)
+#define _FP_FRAC_HIGH_DW_B(X)	_FP_FRAC_HIGH_1 (X)
+
+#define FP_CMP_EQ_B(r, X, Y, ex)       _FP_CMP_EQ (B, 1, (r), X, Y, (ex))
+
+#endif /* !SOFT_FP_BRAIN_H */
--- libgcc/soft-fp/truncsfbf2.c.jj	2022-09-28 18:58:09.113520956 +0200
+++ libgcc/soft-fp/truncsfbf2.c	2022-09-28 18:58:09.113520956 +0200
@@ -0,0 +1,48 @@ 
+/* Software floating-point emulation.
+   Truncate IEEE single into bfloat16.
+   Copyright (C) 2022 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   In addition to the permissions in the GNU Lesser General Public
+   License, the Free Software Foundation gives you unlimited
+   permission to link the compiled version of this file into
+   combinations with other programs, and to distribute those
+   combinations without any restriction coming from the use of this
+   file.  (The Lesser General Public License restrictions do apply in
+   other respects; for example, they cover modification of the file,
+   and distribution when not linked into a combine executable.)
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <http://www.gnu.org/licenses/>.  */
+
+#include "soft-fp.h"
+#include "brain.h"
+#include "single.h"
+
+BFtype
+__truncsfbf2 (SFtype a)
+{
+  FP_DECL_EX;
+  FP_DECL_S (A);
+  FP_DECL_B (R);
+  BFtype r;
+
+  FP_INIT_ROUNDMODE;
+  FP_UNPACK_SEMIRAW_S (A, a);
+  FP_TRUNC (B, S, 1, 1, R, A);
+  FP_PACK_SEMIRAW_B (r, R);
+  FP_HANDLE_EXCEPTIONS;
+
+  return r;
+}
--- libgcc/soft-fp/truncdfbf2.c.jj	2022-09-28 18:58:09.114520943 +0200
+++ libgcc/soft-fp/truncdfbf2.c	2022-09-28 18:58:09.114520943 +0200
@@ -0,0 +1,52 @@ 
+/* Software floating-point emulation.
+   Truncate IEEE double into bfloat16.
+   Copyright (C) 2022 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   In addition to the permissions in the GNU Lesser General Public
+   License, the Free Software Foundation gives you unlimited
+   permission to link the compiled version of this file into
+   combinations with other programs, and to distribute those
+   combinations without any restriction coming from the use of this
+   file.  (The Lesser General Public License restrictions do apply in
+   other respects; for example, they cover modification of the file,
+   and distribution when not linked into a combine executable.)
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <http://www.gnu.org/licenses/>.  */
+
+#include "soft-fp.h"
+#include "brain.h"
+#include "double.h"
+
+BFtype
+__truncdfbf2 (DFtype a)
+{
+  FP_DECL_EX;
+  FP_DECL_D (A);
+  FP_DECL_B (R);
+  BFtype r;
+
+  FP_INIT_ROUNDMODE;
+  FP_UNPACK_SEMIRAW_D (A, a);
+#if _FP_W_TYPE_SIZE < _FP_FRACBITS_D
+  FP_TRUNC (B, D, 1, 2, R, A);
+#else
+  FP_TRUNC (B, D, 1, 1, R, A);
+#endif
+  FP_PACK_SEMIRAW_B (r, R);
+  FP_HANDLE_EXCEPTIONS;
+
+  return r;
+}
--- libgcc/soft-fp/truncxfbf2.c.jj	2022-09-28 18:58:09.113520956 +0200
+++ libgcc/soft-fp/truncxfbf2.c	2022-09-28 18:58:09.113520956 +0200
@@ -0,0 +1,52 @@ 
+/* Software floating-point emulation.
+   Truncate IEEE extended into bfloat16.
+   Copyright (C) 2022 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   In addition to the permissions in the GNU Lesser General Public
+   License, the Free Software Foundation gives you unlimited
+   permission to link the compiled version of this file into
+   combinations with other programs, and to distribute those
+   combinations without any restriction coming from the use of this
+   file.  (The Lesser General Public License restrictions do apply in
+   other respects; for example, they cover modification of the file,
+   and distribution when not linked into a combine executable.)
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <http://www.gnu.org/licenses/>.  */
+
+#include "soft-fp.h"
+#include "brain.h"
+#include "extended.h"
+
+BFtype
+__truncxfbf2 (XFtype a)
+{
+  FP_DECL_EX;
+  FP_DECL_E (A);
+  FP_DECL_B (R);
+  BFtype r;
+
+  FP_INIT_ROUNDMODE;
+  FP_UNPACK_SEMIRAW_E (A, a);
+#if _FP_W_TYPE_SIZE < 64
+  FP_TRUNC (B, E, 1, 4, R, A);
+#else
+  FP_TRUNC (B, E, 1, 2, R, A);
+#endif
+  FP_PACK_SEMIRAW_B (r, R);
+  FP_HANDLE_EXCEPTIONS;
+
+  return r;
+}
--- libgcc/soft-fp/trunctfbf2.c.jj	2022-09-28 18:58:09.114520943 +0200
+++ libgcc/soft-fp/trunctfbf2.c	2022-09-28 18:58:09.114520943 +0200
@@ -0,0 +1,52 @@ 
+/* Software floating-point emulation.
+   Truncate IEEE quad into bfloat16.
+   Copyright (C) 2022 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   In addition to the permissions in the GNU Lesser General Public
+   License, the Free Software Foundation gives you unlimited
+   permission to link the compiled version of this file into
+   combinations with other programs, and to distribute those
+   combinations without any restriction coming from the use of this
+   file.  (The Lesser General Public License restrictions do apply in
+   other respects; for example, they cover modification of the file,
+   and distribution when not linked into a combine executable.)
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <https://www.gnu.org/licenses/>.  */
+
+#include "soft-fp.h"
+#include "brain.h"
+#include "quad.h"
+
+BFtype
+__trunctfbf2 (TFtype a)
+{
+  FP_DECL_EX;
+  FP_DECL_Q (A);
+  FP_DECL_B (R);
+  BFtype r;
+
+  FP_INIT_ROUNDMODE;
+  FP_UNPACK_SEMIRAW_Q (A, a);
+#if _FP_W_TYPE_SIZE < 64
+  FP_TRUNC (B, Q, 1, 4, R, A);
+#else
+  FP_TRUNC (B, Q, 1, 2, R, A);
+#endif
+  FP_PACK_SEMIRAW_B (r, R);
+  FP_HANDLE_EXCEPTIONS;
+
+  return r;
+}
--- libgcc/soft-fp/trunchfbf2.c.jj	2022-09-28 18:58:09.114520943 +0200
+++ libgcc/soft-fp/trunchfbf2.c	2022-09-28 18:58:09.114520943 +0200
@@ -0,0 +1,58 @@ 
+/* Software floating-point emulation.
+   Truncate IEEE half into bfloat16.
+   Copyright (C) 2022 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   In addition to the permissions in the GNU Lesser General Public
+   License, the Free Software Foundation gives you unlimited
+   permission to link the compiled version of this file into
+   combinations with other programs, and to distribute those
+   combinations without any restriction coming from the use of this
+   file.  (The Lesser General Public License restrictions do apply in
+   other respects; for example, they cover modification of the file,
+   and distribution when not linked into a combine executable.)
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <http://www.gnu.org/licenses/>.  */
+
+#include "soft-fp.h"
+#include "brain.h"
+#include "half.h"
+#include "single.h"
+
+/* BFtype and HFtype are unordered, neither is a superset or subset
+   of each other.  Convert HFtype to SFtype (lossless) and then
+   truncate to BFtype.  */
+
+BFtype
+__trunchfbf2 (HFtype a)
+{
+  FP_DECL_EX;
+  FP_DECL_H (A);
+  FP_DECL_S (B);
+  FP_DECL_B (R);
+  SFtype b;
+  BFtype r;
+
+  FP_INIT_ROUNDMODE;
+  FP_UNPACK_RAW_H (A, a);
+  FP_EXTEND (S, H, 1, 1, B, A);
+  FP_PACK_RAW_S (b, B);
+  FP_UNPACK_SEMIRAW_S (B, b);
+  FP_TRUNC (B, S, 1, 1, R, B);
+  FP_PACK_SEMIRAW_B (r, R);
+  FP_HANDLE_EXCEPTIONS;
+
+  return r;
+}
--- libgcc/soft-fp/truncbfhf2.c.jj	2022-09-28 18:58:09.113520956 +0200
+++ libgcc/soft-fp/truncbfhf2.c	2022-09-28 18:58:09.113520956 +0200
@@ -0,0 +1,75 @@ 
+/* Software floating-point emulation.
+   Truncate bfloat16 into IEEE half.
+   Copyright (C) 2022 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   In addition to the permissions in the GNU Lesser General Public
+   License, the Free Software Foundation gives you unlimited
+   permission to link the compiled version of this file into
+   combinations with other programs, and to distribute those
+   combinations without any restriction coming from the use of this
+   file.  (The Lesser General Public License restrictions do apply in
+   other respects; for example, they cover modification of the file,
+   and distribution when not linked into a combine executable.)
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <http://www.gnu.org/licenses/>.  */
+
+#include "soft-fp.h"
+#include "half.h"
+#include "brain.h"
+#include "single.h"
+
+/* BFtype and HFtype are unordered, neither is a superset or subset
+   of each other.  Convert BFtype to SFtype (lossless) and then
+   truncate to HFtype.  */
+
+HFtype
+__truncbfhf2 (BFtype a)
+{
+  FP_DECL_EX;
+  FP_DECL_H (A);
+  FP_DECL_S (B);
+  FP_DECL_B (R);
+  SFtype b;
+  HFtype r;
+
+  FP_INIT_ROUNDMODE;
+  /* Optimize BFtype to SFtype conversion to simple left shift
+     by 16 if possible, we don't need to raise exceptions on sNaN
+     here as the SFtype to HFtype truncation should do that too.  */
+  if (sizeof (BFtype) == 2
+      && sizeof (unsigned short) == 2
+      && sizeof (SFtype) == 4
+      && sizeof (unsigned int) == 4)
+    {
+      union { BFtype a; unsigned short b; } u1;
+      union { SFtype a; unsigned int b; } u2;
+      u1.a = a;
+      u2.b = (u1.b << 8) << 8;
+      b = u2.a;
+    }
+  else
+    {
+      FP_UNPACK_RAW_B (A, a);
+      FP_EXTEND (S, B, 1, 1, B, A);
+      FP_PACK_RAW_S (b, B);
+    }
+  FP_UNPACK_SEMIRAW_S (B, b);
+  FP_TRUNC (H, S, 1, 1, R, B);
+  FP_PACK_SEMIRAW_H (r, R);
+  FP_HANDLE_EXCEPTIONS;
+
+  return r;
+}
--- libgcc/soft-fp/extendbfsf2.c.jj	2022-09-28 18:58:09.114520943 +0200
+++ libgcc/soft-fp/extendbfsf2.c	2022-09-28 18:58:09.114520943 +0200
@@ -0,0 +1,49 @@ 
+/* Software floating-point emulation.
+   Return an bfloat16 converted to IEEE single
+   Copyright (C) 2022 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   In addition to the permissions in the GNU Lesser General Public
+   License, the Free Software Foundation gives you unlimited
+   permission to link the compiled version of this file into
+   combinations with other programs, and to distribute those
+   combinations without any restriction coming from the use of this
+   file.  (The Lesser General Public License restrictions do apply in
+   other respects; for example, they cover modification of the file,
+   and distribution when not linked into a combine executable.)
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <http://www.gnu.org/licenses/>.  */
+
+#define FP_NO_EXACT_UNDERFLOW
+#include "soft-fp.h"
+#include "brain.h"
+#include "single.h"
+
+SFtype
+__extendbfsf2 (BFtype a)
+{
+  FP_DECL_EX;
+  FP_DECL_B (A);
+  FP_DECL_S (R);
+  SFtype r;
+
+  FP_INIT_EXCEPTIONS;
+  FP_UNPACK_RAW_B (A, a);
+  FP_EXTEND (S, B, 1, 1, R, A);
+  FP_PACK_RAW_S (r, R);
+  FP_HANDLE_EXCEPTIONS;
+
+  return r;
+}
--- libiberty/cp-demangle.h.jj	2022-09-27 08:03:27.142982423 +0200
+++ libiberty/cp-demangle.h	2022-09-29 12:42:47.291727886 +0200
@@ -180,7 +180,7 @@  d_advance (struct d_info *di, int i)
 extern const struct demangle_operator_info cplus_demangle_operators[];
 #endif
 
-#define D_BUILTIN_TYPE_COUNT (35)
+#define D_BUILTIN_TYPE_COUNT (36)
 
 CP_STATIC_IF_GLIBCPP_V3
 const struct demangle_builtin_type_info
--- libiberty/cp-demangle.c.jj	2022-09-27 08:03:27.141982437 +0200
+++ libiberty/cp-demangle.c	2022-09-29 13:04:57.083526204 +0200
@@ -2489,6 +2489,7 @@  cplus_demangle_builtin_types[D_BUILTIN_T
   /* 33 */ { NL ("decltype(nullptr)"),	NL ("decltype(nullptr)"),
 	     D_PRINT_DEFAULT },
   /* 34 */ { NL ("_Float"),	NL ("_Float"),		D_PRINT_FLOAT },
+  /* 35 */ { NL ("std::bfloat16_t"), NL ("std::bfloat16_t"), D_PRINT_FLOAT },
 };
 
 CP_STATIC_IF_GLIBCPP_V3
@@ -2753,8 +2754,20 @@  cplus_demangle_type (struct d_info *di)
 
 	case 'F':
 	  /* DF<number>_ - _Float<number>.
-	     DF<number>x - _Float<number>x.  */
+	     DF<number>x - _Float<number>x
+	     DFb16_ - std::bfloat16_t.  */
 	  {
+	    if (d_peek_char (di) == 'b')
+	      {
+		d_advance (di, 1);
+		if (d_number (di) != 16 || d_peek_char (di) != '_')
+		  return NULL;
+		d_advance (di, 1);
+		ret = d_make_builtin_type (di,
+					   &cplus_demangle_builtin_types[35]);
+		di->expansion += ret->u.s_builtin.type->len;
+		break;
+	      }
 	    int arg = d_number (di);
 	    char buf[12];
 	    char suffix = 0;
--- libiberty/testsuite/demangle-expected.jj	2022-09-27 08:03:27.168982071 +0200
+++ libiberty/testsuite/demangle-expected	2022-09-29 12:49:02.181597532 +0200
@@ -1249,6 +1249,10 @@  xxx
 _Z3xxxDF32xDF64xDF128xCDF32xVb
 xxx(_Float32x, _Float64x, _Float128x, _Float32x _Complex, bool volatile)
 xxx
+--format=auto --no-params
+_Z3xxxDFb16_
+xxx(std::bfloat16_t)
+xxx
 # https://sourceware.org/bugzilla/show_bug.cgi?id=16817
 --format=auto --no-params
 _QueueNotification_QueueController__$4PPPPPPPM_A_INotice___Z