middle-end, c++, i386, libgcc: std::bfloat16_t and __bf16 arithmetic support

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

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

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

13 files changed, 580 insertions, 2 deletions

diff --git a/libgcc/config/i386/32/sfp-machine.h b/libgcc/config/i386/32/sfp-machine.h
index e24cbc8..7b59ff5 100644
--- a/libgcc/config/i386/32/sfp-machine.h
+++ b/libgcc/config/i386/32/sfp-machine.h
@@ -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
diff --git a/libgcc/config/i386/64/sfp-machine.h b/libgcc/config/i386/64/sfp-machine.h
index e1c6166..1c8e8a5 100644
--- a/libgcc/config/i386/64/sfp-machine.h
+++ b/libgcc/config/i386/64/sfp-machine.h
@@ -14,6 +14,7 @@ typedef unsigned int UTItype __attribute__ ((mode (TI)));
 #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
diff --git a/libgcc/config/i386/libgcc-glibc.ver b/libgcc/config/i386/libgcc-glibc.ver
index 08ce814..64c07d4 100644
--- a/libgcc/config/i386/libgcc-glibc.ver
+++ b/libgcc/config/i386/libgcc-glibc.ver
@@ -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
+}
diff --git a/libgcc/config/i386/sfp-machine.h b/libgcc/config/i386/sfp-machine.h
index c451ae7..cc20c2c 100644
--- a/libgcc/config/i386/sfp-machine.h
+++ b/libgcc/config/i386/sfp-machine.h
@@ -18,6 +18,7 @@ typedef int __gcc_CMPtype __attribute__ ((mode (__libgcc_cmp_return__)));
 #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
diff --git a/libgcc/config/i386/t-softfp b/libgcc/config/i386/t-softfp
index fe2ad8a..69d0f81 100644
--- a/libgcc/config/i386/t-softfp
+++ b/libgcc/config/i386/t-softfp
@@ -6,8 +6,9 @@ LIB2FUNCS_EXCLUDE += $(libgcc2-hf-functions)
 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
diff --git a/libgcc/soft-fp/brain.h b/libgcc/soft-fp/brain.h
new file mode 100644
index 0000000..c8563ef
--- /dev/null
+++ b/libgcc/soft-fp/brain.h
@@ -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 */
diff --git a/libgcc/soft-fp/extendbfsf2.c b/libgcc/soft-fp/extendbfsf2.c
new file mode 100644
index 0000000..c534a41
--- /dev/null
+++ b/libgcc/soft-fp/extendbfsf2.c
@@ -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;
+}
diff --git a/libgcc/soft-fp/truncbfhf2.c b/libgcc/soft-fp/truncbfhf2.c
new file mode 100644
index 0000000..6b6e6b4
--- /dev/null
+++ b/libgcc/soft-fp/truncbfhf2.c
@@ -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;
+}
diff --git a/libgcc/soft-fp/truncdfbf2.c b/libgcc/soft-fp/truncdfbf2.c
new file mode 100644
index 0000000..dfa0b26
--- /dev/null
+++ b/libgcc/soft-fp/truncdfbf2.c
@@ -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;
+}
diff --git a/libgcc/soft-fp/trunchfbf2.c b/libgcc/soft-fp/trunchfbf2.c
new file mode 100644
index 0000000..f3d6501
--- /dev/null
+++ b/libgcc/soft-fp/trunchfbf2.c
@@ -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;
+}
diff --git a/libgcc/soft-fp/truncsfbf2.c b/libgcc/soft-fp/truncsfbf2.c
new file mode 100644
index 0000000..ccd90b6
--- /dev/null
+++ b/libgcc/soft-fp/truncsfbf2.c
@@ -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;
+}
diff --git a/libgcc/soft-fp/trunctfbf2.c b/libgcc/soft-fp/trunctfbf2.c
new file mode 100644
index 0000000..095c12e
--- /dev/null
+++ b/libgcc/soft-fp/trunctfbf2.c
@@ -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;
+}
diff --git a/libgcc/soft-fp/truncxfbf2.c b/libgcc/soft-fp/truncxfbf2.c
new file mode 100644
index 0000000..fbff063
--- /dev/null
+++ b/libgcc/soft-fp/truncxfbf2.c
@@ -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;
+}