Re: [PATCH v2 2/2] libatomic: Enable LSE128 128-bit atomics for armv9.4-a

[Richard Earnshaw <Richard.Earnshaw@foss.arm.com>]

On 13/11/2023 11:37, Victor Do Nascimento wrote:
> The armv9.4-a architectural revision adds three new atomic operations
> associated with the LSE128 feature:
> 
>    * LDCLRP - Atomic AND NOT (bitclear) of a location with 128-bit
>    value held in a pair of registers, with original data loaded into
>    the same 2 registers.
>    * LDSETP - Atomic OR (bitset) of a location with 128-bit value held
>    in a pair of registers, with original data loaded into the same 2
>    registers.
>    * SWPP - Atomic swap of one 128-bit value with 128-bit value held
>    in a pair of registers.
> 
> This patch adds the logic required to make use of these when the
> architectural feature is present and a suitable assembler available.
> 
> In order to do this, the following changes are made:
> 
>    1. Add a configure-time check to check for LSE128 support in the
>    assembler.
>    2. Edit host-config.h so that when N == 16, nifunc = 2.
>    3. Where available due to LSE128, implement the second ifunc, making
>    use of the novel instructions.
>    4. For atomic functions unable to make use of these new
>    instructions, define a new alias which causes the _i1 function
>    variant to point ahead to the corresponding _i2 implementation.
> 
> libatomic/ChangeLog:
> 
> 	* Makefile.am (AM_CPPFLAGS): add conditional setting of
> 	-DHAVE_FEAT_LSE128.
> 	* acinclude.m4 (LIBAT_TEST_FEAT_LSE128): New.
> 	* config/linux/aarch64/atomic_16.S (LSE128): New macro
> 	definition.
> 	(libat_exchange_16): New LSE128 variant.
> 	(libat_fetch_or_16): Likewise.
> 	(libat_or_fetch_16): Likewise.
> 	(libat_fetch_and_16): Likewise.
> 	(libat_and_fetch_16): Likewise.
> 	* config/linux/aarch64/host-config.h (IFUNC_COND_2): New.
> 	(IFUNC_NCOND): Add operand size checking.
> 	(has_lse2): Renamed from `ifunc1`.
> 	(has_lse128): New.
> 	(HAS_LSE128): Likewise.
> 	* libatomic/configure.ac: Add call to LIBAT_TEST_FEAT_LSE128.
> 	* configure (ac_subst_vars): Regenerated via autoreconf.
> 	* libatomic/Makefile.in: Likewise.
> 	* libatomic/auto-config.h.in: Likewise.
> ---
>   libatomic/Makefile.am                        |   3 +
>   libatomic/Makefile.in                        |   1 +
>   libatomic/acinclude.m4                       |  19 +++
>   libatomic/auto-config.h.in                   |   3 +
>   libatomic/config/linux/aarch64/atomic_16.S   | 170 ++++++++++++++++++-
>   libatomic/config/linux/aarch64/host-config.h |  27 ++-
>   libatomic/configure                          |  59 ++++++-
>   libatomic/configure.ac                       |   1 +
>   8 files changed, 274 insertions(+), 9 deletions(-)
> 
> diff --git a/libatomic/Makefile.am b/libatomic/Makefile.am
> index c0b8dea5037..24e843db67d 100644
> --- a/libatomic/Makefile.am
> +++ b/libatomic/Makefile.am
> @@ -130,6 +130,9 @@ libatomic_la_LIBADD = $(foreach s,$(SIZES),$(addsuffix _$(s)_.lo,$(SIZEOBJS)))
>   ## On a target-specific basis, include alternates to be selected by IFUNC.
>   if HAVE_IFUNC
>   if ARCH_AARCH64_LINUX
> +if ARCH_AARCH64_HAVE_LSE128
> +AM_CPPFLAGS	     = -DHAVE_FEAT_LSE128
> +endif
>   IFUNC_OPTIONS	     = -march=armv8-a+lse
>   libatomic_la_LIBADD += $(foreach s,$(SIZES),$(addsuffix _$(s)_1_.lo,$(SIZEOBJS)))
>   libatomic_la_SOURCES += atomic_16.S
> diff --git a/libatomic/Makefile.in b/libatomic/Makefile.in
> index dc2330b91fd..cd48fa21334 100644
> --- a/libatomic/Makefile.in
> +++ b/libatomic/Makefile.in
> @@ -452,6 +452,7 @@ M_SRC = $(firstword $(filter %/$(M_FILE), $(all_c_files)))
>   libatomic_la_LIBADD = $(foreach s,$(SIZES),$(addsuffix \
>   	_$(s)_.lo,$(SIZEOBJS))) $(am__append_1) $(am__append_3) \
>   	$(am__append_4) $(am__append_5)
> +@ARCH_AARCH64_HAVE_LSE128_TRUE@@ARCH_AARCH64_LINUX_TRUE@@HAVE_IFUNC_TRUE@AM_CPPFLAGS = -DHAVE_FEAT_LSE128
>   @ARCH_AARCH64_LINUX_TRUE@@HAVE_IFUNC_TRUE@IFUNC_OPTIONS = -march=armv8-a+lse
>   @ARCH_ARM_LINUX_TRUE@@HAVE_IFUNC_TRUE@IFUNC_OPTIONS = -march=armv7-a+fp -DHAVE_KERNEL64
>   @ARCH_I386_TRUE@@HAVE_IFUNC_TRUE@IFUNC_OPTIONS = -march=i586
> diff --git a/libatomic/acinclude.m4 b/libatomic/acinclude.m4
> index f35ab5b60a5..4197db8f404 100644
> --- a/libatomic/acinclude.m4
> +++ b/libatomic/acinclude.m4
> @@ -83,6 +83,25 @@ AC_DEFUN([LIBAT_TEST_ATOMIC_BUILTIN],[
>     ])
>   ])
>   
> +dnl
> +dnl Test if the host assembler supports armv9.4-a LSE128 isns.
> +dnl
> +AC_DEFUN([LIBAT_TEST_FEAT_LSE128],[
> +  AC_CACHE_CHECK([for armv9.4-a LSE128 insn support],
> +    [libat_cv_have_feat_lse128],[
> +    AC_LANG_CONFTEST([AC_LANG_PROGRAM([],[asm(".arch armv9-a+lse128")])])
> +    if AC_TRY_EVAL(ac_link); then
> +      eval libat_cv_have_feat_lse128=yes
> +    else
> +      eval libat_cv_have_feat_lse128=no
> +    fi
> +    rm -f conftest*
> +  ])
> +  LIBAT_DEFINE_YESNO([HAVE_FEAT_LSE128], [$libat_cv_have_feat_lse128],
> +	[Have LSE128 support for 16 byte integers.])
> +  AM_CONDITIONAL([ARCH_AARCH64_HAVE_LSE128], [test x$libat_cv_have_feat_lse128 = xyes])
> +])
> +
>   dnl
>   dnl Test if we have __atomic_load and __atomic_store for mode $1, size $2
>   dnl
> diff --git a/libatomic/auto-config.h.in b/libatomic/auto-config.h.in
> index ab3424a759e..7c78933b07d 100644
> --- a/libatomic/auto-config.h.in
> +++ b/libatomic/auto-config.h.in
> @@ -105,6 +105,9 @@
>   /* Define to 1 if you have the <dlfcn.h> header file. */
>   #undef HAVE_DLFCN_H
>   
> +/* Have LSE128 support for 16 byte integers. */
> +#undef HAVE_FEAT_LSE128
> +
>   /* Define to 1 if you have the <fenv.h> header file. */
>   #undef HAVE_FENV_H
>   
> diff --git a/libatomic/config/linux/aarch64/atomic_16.S b/libatomic/config/linux/aarch64/atomic_16.S
> index 3f6225830e6..44a773031f8 100644
> --- a/libatomic/config/linux/aarch64/atomic_16.S
> +++ b/libatomic/config/linux/aarch64/atomic_16.S
> @@ -34,10 +34,14 @@
>      writes, this will be true when using atomics in actual code.
>   
>      The libat_<op>_16 entry points are ARMv8.0.
> -   The libat_<op>_16_i1 entry points are used when LSE2 is available.  */
> -
> +   The libat_<op>_16_i1 entry points are used when LSE128 is available.
> +   The libat_<op>_16_i2 entry points are used when LSE2 is available.  */
>   
> +#if HAVE_FEAT_LSE128
> +	.arch	armv8-a+lse128

Shouldn't this match the test we run during configure?  ie 
armv9-a+lse128?  I'm not sure which is preferable, but it seems odd for 
them not to be the same.

> +#else
>   	.arch	armv8-a+lse
> +#endif
>   
>   #define ENTRY(name, feat)		\
>   	ENTRY1(name, feat)
> @@ -66,7 +70,8 @@ name##feat:				\
>   	.set alias##from, alias##to;
>   
>   #define CORE
> -#define LSE2	_i1
> +#define LSE128	_i1
> +#define LSE2	_i2
>   
>   #define res0 x0
>   #define res1 x1
> @@ -201,6 +206,31 @@ ENTRY (libat_exchange_16, CORE)
>   END (libat_exchange_16, CORE)
>   
>   
> +#if HAVE_FEAT_LSE128
> +ENTRY (libat_exchange_16, LSE128)
> +	mov	tmp0, x0
> +	mov	res0, in0
> +	mov	res1, in1
> +	cbnz	w4, 1f
> +
> +	/* RELAXED.  */
> +	swpp	res0, res1, [tmp0]
> +	ret
> +1:
> +	cmp	w4, ACQUIRE
> +	b.hi	2f
> +
> +	/* ACQUIRE/CONSUME.  */
> +	swppa	res0, res1, [tmp0]
> +	ret
> +
> +	/* RELEASE/ACQ_REL/SEQ_CST.  */
> +2:	swppal	res0, res1, [tmp0]
> +	ret
> +END (libat_exchange_16, LSE128)
> +#endif
> +
> +
>   ENTRY (libat_compare_exchange_16, CORE)
>   	ldp	exp0, exp1, [x1]
>   	cbz	w4, 3f
> @@ -389,6 +419,31 @@ ENTRY (libat_fetch_or_16, CORE)
>   END (libat_fetch_or_16, CORE)
>   
>   
> +#if HAVE_FEAT_LSE128
> +ENTRY (libat_fetch_or_16, LSE128)
> +	mov	tmp0, x0
> +	mov	res0, in0
> +	mov	res1, in1
> +	cbnz	w4, 1f
> +
> +	/* RELAXED.  */
> +	ldsetp	res0, res1, [tmp0]
> +	ret
> +1:
> +	cmp	w4, ACQUIRE
> +	b.hi	2f
> +
> +	/* ACQUIRE/CONSUME.  */
> +	ldsetpa	res0, res1, [tmp0]
> +	ret
> +
> +	/* RELEASE/ACQ_REL/SEQ_CST.  */
> +2:	ldsetpal	res0, res1, [tmp0]
> +	ret
> +END (libat_fetch_or_16, LSE128)
> +#endif
> +
> +
>   ENTRY (libat_or_fetch_16, CORE)
>   	mov	x5, x0
>   	cbnz	w4, 2f
> @@ -411,6 +466,36 @@ ENTRY (libat_or_fetch_16, CORE)
>   END (libat_or_fetch_16, CORE)
>   
>   
> +#if HAVE_FEAT_LSE128
> +ENTRY (libat_or_fetch_16, LSE128)
> +	cbnz	w4, 1f
> +	mov	tmp0, in0
> +	mov	tmp1, in1
> +
> +	/* RELAXED.  */
> +	ldsetp	in0, in1, [x0]
> +	orr	res0, in0, tmp0
> +	orr	res1, in1, tmp1
> +	ret
> +1:
> +	cmp	w4, ACQUIRE
> +	b.hi	2f
> +
> +	/* ACQUIRE/CONSUME.  */
> +	ldsetpa	in0, in1, [x0]
> +	orr	res0, in0, tmp0
> +	orr	res1, in1, tmp1
> +	ret
> +
> +	/* RELEASE/ACQ_REL/SEQ_CST.  */
> +2:	ldsetpal	in0, in1, [x0]
> +	orr	res0, in0, tmp0
> +	orr	res1, in1, tmp1
> +	ret
> +END (libat_or_fetch_16, LSE128)
> +#endif
> +
> +
>   ENTRY (libat_fetch_and_16, CORE)
>   	mov	x5, x0
>   	cbnz	w4, 2f
> @@ -433,6 +518,32 @@ ENTRY (libat_fetch_and_16, CORE)
>   END (libat_fetch_and_16, CORE)
>   
>   
> +#if HAVE_FEAT_LSE128
> +ENTRY (libat_fetch_and_16, LSE128)
> +	mov	tmp0, x0
> +	mvn	res0, in0
> +	mvn	res1, in1
> +	cbnz	w4, 1f
> +
> +	/* RELAXED.  */
> +	ldclrp	res0, res1, [tmp0]
> +	ret
> +
> +1:
> +	cmp	w4, ACQUIRE
> +	b.hi	2f
> +
> +	/* ACQUIRE/CONSUME.  */
> +	ldclrpa res0, res1, [tmp0]
> +	ret
> +
> +	/* RELEASE/ACQ_REL/SEQ_CST.  */
> +2:	ldclrpal	res0, res1, [tmp0]
> +	ret
> +END (libat_fetch_and_16, LSE128)
> +#endif
> +
> +
>   ENTRY (libat_and_fetch_16, CORE)
>   	mov	x5, x0
>   	cbnz	w4, 2f
> @@ -455,6 +566,37 @@ ENTRY (libat_and_fetch_16, CORE)
>   END (libat_and_fetch_16, CORE)
>   
>   
> +#if HAVE_FEAT_LSE128
> +ENTRY (libat_and_fetch_16, LSE128)
> +	mvn	tmp0, in0
> +	mvn	tmp0, in1
> +	cbnz	w4, 1f
> +
> +	/* RELAXED.  */
> +	ldclrp	tmp0, tmp1, [x0]
> +	and	res0, tmp0, in0
> +	and	res1, tmp1, in1
> +	ret
> +
> +1:
> +	cmp	w4, ACQUIRE
> +	b.hi	2f
> +
> +	/* ACQUIRE/CONSUME.  */
> +	ldclrpa tmp0, tmp1, [x0]
> +	and	res0, tmp0, in0
> +	and	res1, tmp1, in1
> +	ret
> +
> +	/* RELEASE/ACQ_REL/SEQ_CST.  */
> +2:	ldclrpal	tmp0, tmp1, [x5]
> +	and	res0, tmp0, in0
> +	and	res1, tmp1, in1
> +	ret
> +END (libat_and_fetch_16, LSE128)
> +#endif
> +
> +
>   ENTRY (libat_fetch_xor_16, CORE)
>   	mov	x5, x0
>   	cbnz	w4, 2f
> @@ -560,6 +702,28 @@ ENTRY (libat_test_and_set_16, CORE)
>   END (libat_test_and_set_16, CORE)
>   
>   
> +/* Alias entry points which are the same in LSE2 and LSE128.  */
> +
> +#if !HAVE_FEAT_LSE128
> +ALIAS (libat_exchange_16, LSE128, LSE2)
> +ALIAS (libat_fetch_or_16, LSE128, LSE2)
> +ALIAS (libat_fetch_and_16, LSE128, LSE2)
> +ALIAS (libat_or_fetch_16, LSE128, LSE2)
> +ALIAS (libat_and_fetch_16, LSE128, LSE2)
> +#endif
> +ALIAS (libat_load_16, LSE128, LSE2)
> +ALIAS (libat_store_16, LSE128, LSE2)
> +ALIAS (libat_compare_exchange_16, LSE128, LSE2)
> +ALIAS (libat_fetch_add_16, LSE128, LSE2)
> +ALIAS (libat_add_fetch_16, LSE128, LSE2)
> +ALIAS (libat_fetch_sub_16, LSE128, LSE2)
> +ALIAS (libat_sub_fetch_16, LSE128, LSE2)
> +ALIAS (libat_fetch_xor_16, LSE128, LSE2)
> +ALIAS (libat_xor_fetch_16, LSE128, LSE2)
> +ALIAS (libat_fetch_nand_16, LSE128, LSE2)
> +ALIAS (libat_nand_fetch_16, LSE128, LSE2)
> +ALIAS (libat_test_and_set_16, LSE128, LSE2)
> +
>   /* Alias entry points which are the same in baseline and LSE2.  */
>   
>   ALIAS (libat_exchange_16, LSE2, CORE)
> diff --git a/libatomic/config/linux/aarch64/host-config.h b/libatomic/config/linux/aarch64/host-config.h
> index 30ef21c7715..d873e91b1c9 100644
> --- a/libatomic/config/linux/aarch64/host-config.h
> +++ b/libatomic/config/linux/aarch64/host-config.h
> @@ -26,14 +26,17 @@
>   
>   #ifdef HWCAP_USCAT
>   # if N == 16
> -#  define IFUNC_COND_1	(ifunc1 (hwcap))
> +#  define IFUNC_COND_1		(has_lse128 (hwcap))
> +#  define IFUNC_COND_2		(has_lse2 (hwcap))
> +#  define IFUNC_NCOND(N)	2
>   # else
> -#  define IFUNC_COND_1	(hwcap & HWCAP_ATOMICS)
> +#  define IFUNC_COND_1		(hwcap & HWCAP_ATOMICS)
> +#  define IFUNC_NCOND(N)	1
>   # endif
>   #else
>   #  define IFUNC_COND_1	(false)
> +#  define IFUNC_NCOND(N)	1
>   #endif
> -#define IFUNC_NCOND(N)	(1)
>   
>   #endif /* HAVE_IFUNC */
>   
> @@ -56,7 +59,7 @@
>   #define MIDR_PARTNUM(midr)	(((midr) >> 4) & 0xfff)
>   
>   static inline bool
> -ifunc1 (unsigned long hwcap)
> +has_lse2 (unsigned long hwcap)
>   {
>     if (hwcap & HWCAP_USCAT)
>       return true;
> @@ -69,6 +72,22 @@ ifunc1 (unsigned long hwcap)
>       return true;
>     return false;
>   }
> +
> +/* LSE128 atomic support encoded in ID_AA64ISAR0_EL1.Atomic,
> +   bits[23:20].  The expected value is 0b0011.  Check that.  */
> +#define HAS_LSE128() ({						\
> +  unsigned long val;						\
> +  asm volatile ("mrs %0, ID_AA64ISAR0_EL1" : "=r" (val));	\
> +  (val & 0xf00000) >= 0x300000;					\
> +    })
> +

The pseudo-code for this register reads:

if PSTATE.EL == EL0 then
   if IsFeatureImplemented(FEAT_IDST) then
     if EL2Enabled() && HCR_EL2.TGE == '1' then
       AArch64.SystemAccessTrap(EL2, 0x18);
     else
       AArch64.SystemAccessTrap(EL1, 0x18);
   else
     UNDEFINED;
...

So this instruction may result in SIGILL if run on cores without 
FEAT_IDST.  SystemAccessTrap just punts the problem up to the kernel or 
hypervisor as well.

I think we need a hwcap bit to work this out, which is the preferred way 
on Linux anyway.  Something like this? :) 
https://lore.kernel.org/linux-arm-kernel/20231003124544.858804-2-joey.gouly@arm.com/T/



> +static inline bool
> +has_lse128 (unsigned long hwcap)
> +{
> +  if (has_lse2 (hwcap) && HAS_LSE128 ())

Why does this need to test for LSE2, surely that's mandatory if LSE128 
is implemented.

> +    return true;
> +  return false;
> +}
>   #endif
>   
>   #include_next <host-config.h>
> diff --git a/libatomic/configure b/libatomic/configure
> index d579bab96f8..ee3bbb97d69 100755
> --- a/libatomic/configure
> +++ b/libatomic/configure
> @@ -657,6 +657,8 @@ LIBAT_BUILD_VERSIONED_SHLIB_TRUE
>   OPT_LDFLAGS
>   SECTION_LDFLAGS
>   SYSROOT_CFLAGS_FOR_TARGET
> +ARCH_AARCH64_HAVE_LSE128_FALSE
> +ARCH_AARCH64_HAVE_LSE128_TRUE
>   enable_aarch64_lse
>   libtool_VERSION
>   ENABLE_DARWIN_AT_RPATH_FALSE
> @@ -11456,7 +11458,7 @@ else
>     lt_dlunknown=0; lt_dlno_uscore=1; lt_dlneed_uscore=2
>     lt_status=$lt_dlunknown
>     cat > conftest.$ac_ext <<_LT_EOF
> -#line 11459 "configure"
> +#line 11461 "configure"
>   #include "confdefs.h"
>   
>   #if HAVE_DLFCN_H
> @@ -11562,7 +11564,7 @@ else
>     lt_dlunknown=0; lt_dlno_uscore=1; lt_dlneed_uscore=2
>     lt_status=$lt_dlunknown
>     cat > conftest.$ac_ext <<_LT_EOF
> -#line 11565 "configure"
> +#line 11567 "configure"
>   #include "confdefs.h"
>   
>   #if HAVE_DLFCN_H
> @@ -11926,6 +11928,55 @@ ac_link='$CC -o conftest$ac_exeext $CFLAGS $CPPFLAGS $LDFLAGS conftest.$ac_ext $
>   ac_compiler_gnu=$ac_cv_c_compiler_gnu
>   
>   
> +
> +  { $as_echo "$as_me:${as_lineno-$LINENO}: checking for armv9.4-a LSE128 insn support" >&5
> +$as_echo_n "checking for armv9.4-a LSE128 insn support... " >&6; }
> +if ${libat_cv_have_feat_lse128+:} false; then :
> +  $as_echo_n "(cached) " >&6
> +else
> +
> +    cat confdefs.h - <<_ACEOF >conftest.$ac_ext
> +/* end confdefs.h.  */
> +
> +int
> +main ()
> +{
> +asm(".arch armv9-a+lse128")
> +  ;
> +  return 0;
> +}
> +_ACEOF
> +    if { { eval echo "\"\$as_me\":${as_lineno-$LINENO}: \"$ac_link\""; } >&5
> +  (eval $ac_link) 2>&5
> +  ac_status=$?
> +  $as_echo "$as_me:${as_lineno-$LINENO}: \$? = $ac_status" >&5
> +  test $ac_status = 0; }; then
> +      eval libat_cv_have_feat_lse128=yes
> +    else
> +      eval libat_cv_have_feat_lse128=no
> +    fi
> +    rm -f conftest*
> +
> +fi
> +{ $as_echo "$as_me:${as_lineno-$LINENO}: result: $libat_cv_have_feat_lse128" >&5
> +$as_echo "$libat_cv_have_feat_lse128" >&6; }
> +
> +  yesno=`echo $libat_cv_have_feat_lse128 | tr 'yesno' '1  0 '`
> +
> +cat >>confdefs.h <<_ACEOF
> +#define HAVE_FEAT_LSE128 $yesno
> +_ACEOF
> +
> +
> +   if test x$libat_cv_have_feat_lse128 = xyes; then
> +  ARCH_AARCH64_HAVE_LSE128_TRUE=
> +  ARCH_AARCH64_HAVE_LSE128_FALSE='#'
> +else
> +  ARCH_AARCH64_HAVE_LSE128_TRUE='#'
> +  ARCH_AARCH64_HAVE_LSE128_FALSE=
> +fi
> +
> +
>       ;;
>   esac
>   
> @@ -15989,6 +16040,10 @@ if test -z "${ENABLE_DARWIN_AT_RPATH_TRUE}" && test -z "${ENABLE_DARWIN_AT_RPATH
>     as_fn_error $? "conditional \"ENABLE_DARWIN_AT_RPATH\" was never defined.
>   Usually this means the macro was only invoked conditionally." "$LINENO" 5
>   fi
> +if test -z "${ARCH_AARCH64_HAVE_LSE128_TRUE}" && test -z "${ARCH_AARCH64_HAVE_LSE128_FALSE}"; then
> +  as_fn_error $? "conditional \"ARCH_AARCH64_HAVE_LSE128\" was never defined.
> +Usually this means the macro was only invoked conditionally." "$LINENO" 5
> +fi
>   
>   if test -z "${LIBAT_BUILD_VERSIONED_SHLIB_TRUE}" && test -z "${LIBAT_BUILD_VERSIONED_SHLIB_FALSE}"; then
>     as_fn_error $? "conditional \"LIBAT_BUILD_VERSIONED_SHLIB\" was never defined.
> diff --git a/libatomic/configure.ac b/libatomic/configure.ac
> index 5f2821ac3f4..b2fe68d7d0f 100644
> --- a/libatomic/configure.ac
> +++ b/libatomic/configure.ac
> @@ -169,6 +169,7 @@ AC_MSG_RESULT([$target_thread_file])
>   case "$target" in
>    *aarch64*)
>       ACX_PROG_CC_WARNING_OPTS([-march=armv8-a+lse],[enable_aarch64_lse])
> +    LIBAT_TEST_FEAT_LSE128()
>       ;;
>   esac
>   

R.