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authorH.J. Lu <hjl.tools@gmail.com>2022-02-07 05:55:15 -0800
committerH.J. Lu <hjl.tools@gmail.com>2022-02-08 15:58:56 -0800
commit3d9f171bfb5325bd5f427e9fc386453358c6e840 (patch)
tree5caeddafa6cb494bbe102c34f7f2ee630f5d83cf
parentdc98eeeb952f59bdbd51da0409e732756fe30170 (diff)
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x86-64: Optimize bzero
memset with zero as the value to set is by far the majority value (99%+ for Python3 and GCC). bzero can be slightly more optimized for this case by using a zero-idiom xor for broadcasting the set value to a register (vector or GPR). Co-developed-by: Noah Goldstein <goldstein.w.n@gmail.com>
-rw-r--r--sysdeps/x86_64/memset.S8
-rw-r--r--sysdeps/x86_64/multiarch/Makefile1
-rw-r--r--sysdeps/x86_64/multiarch/bzero.c106
-rw-r--r--sysdeps/x86_64/multiarch/ifunc-impl-list.c42
-rw-r--r--sysdeps/x86_64/multiarch/memset-avx2-unaligned-erms-rtm.S1
-rw-r--r--sysdeps/x86_64/multiarch/memset-avx2-unaligned-erms.S6
-rw-r--r--sysdeps/x86_64/multiarch/memset-avx512-unaligned-erms.S3
-rw-r--r--sysdeps/x86_64/multiarch/memset-evex-unaligned-erms.S3
-rw-r--r--sysdeps/x86_64/multiarch/memset-sse2-unaligned-erms.S1
-rw-r--r--sysdeps/x86_64/multiarch/memset-vec-unaligned-erms.S110
10 files changed, 256 insertions, 25 deletions
diff --git a/sysdeps/x86_64/memset.S b/sysdeps/x86_64/memset.S
index 3f0517bbfc..af26e9cedc 100644
--- a/sysdeps/x86_64/memset.S
+++ b/sysdeps/x86_64/memset.S
@@ -35,6 +35,9 @@
punpcklwd %xmm0, %xmm0; \
pshufd $0, %xmm0, %xmm0
+# define BZERO_ZERO_VEC0() \
+ pxor %xmm0, %xmm0
+
# define WMEMSET_SET_VEC0_AND_SET_RETURN(d, r) \
movd d, %xmm0; \
pshufd $0, %xmm0, %xmm0; \
@@ -53,6 +56,10 @@
# define MEMSET_SYMBOL(p,s) memset
#endif
+#ifndef BZERO_SYMBOL
+# define BZERO_SYMBOL(p,s) __bzero
+#endif
+
#ifndef WMEMSET_SYMBOL
# define WMEMSET_CHK_SYMBOL(p,s) p
# define WMEMSET_SYMBOL(p,s) __wmemset
@@ -63,6 +70,7 @@
libc_hidden_builtin_def (memset)
#if IS_IN (libc)
+weak_alias (__bzero, bzero)
libc_hidden_def (__wmemset)
weak_alias (__wmemset, wmemset)
libc_hidden_weak (wmemset)
diff --git a/sysdeps/x86_64/multiarch/Makefile b/sysdeps/x86_64/multiarch/Makefile
index 4274bfdd0d..e7b413edad 100644
--- a/sysdeps/x86_64/multiarch/Makefile
+++ b/sysdeps/x86_64/multiarch/Makefile
@@ -1,6 +1,7 @@
ifeq ($(subdir),string)
sysdep_routines += \
+ bzero \
memchr-avx2 \
memchr-avx2-rtm \
memchr-evex \
diff --git a/sysdeps/x86_64/multiarch/bzero.c b/sysdeps/x86_64/multiarch/bzero.c
new file mode 100644
index 0000000000..58a14b2c33
--- /dev/null
+++ b/sysdeps/x86_64/multiarch/bzero.c
@@ -0,0 +1,106 @@
+/* Multiple versions of bzero.
+ All versions must be listed in ifunc-impl-list.c.
+ 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.
+
+ 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/>. */
+
+/* Define multiple versions only for the definition in libc. */
+#if IS_IN (libc)
+# define __bzero __redirect___bzero
+# include <string.h>
+# undef __bzero
+
+# define SYMBOL_NAME __bzero
+# include <init-arch.h>
+
+extern __typeof (REDIRECT_NAME) OPTIMIZE1 (sse2_unaligned)
+ attribute_hidden;
+extern __typeof (REDIRECT_NAME) OPTIMIZE1 (sse2_unaligned_erms)
+ attribute_hidden;
+extern __typeof (REDIRECT_NAME) OPTIMIZE1 (avx2_unaligned) attribute_hidden;
+extern __typeof (REDIRECT_NAME) OPTIMIZE1 (avx2_unaligned_erms)
+ attribute_hidden;
+extern __typeof (REDIRECT_NAME) OPTIMIZE1 (avx2_unaligned_rtm)
+ attribute_hidden;
+extern __typeof (REDIRECT_NAME) OPTIMIZE1 (avx2_unaligned_erms_rtm)
+ attribute_hidden;
+extern __typeof (REDIRECT_NAME) OPTIMIZE1 (evex_unaligned)
+ attribute_hidden;
+extern __typeof (REDIRECT_NAME) OPTIMIZE1 (evex_unaligned_erms)
+ attribute_hidden;
+extern __typeof (REDIRECT_NAME) OPTIMIZE1 (avx512_unaligned)
+ attribute_hidden;
+extern __typeof (REDIRECT_NAME) OPTIMIZE1 (avx512_unaligned_erms)
+ attribute_hidden;
+
+static inline void *
+IFUNC_SELECTOR (void)
+{
+ const struct cpu_features* cpu_features = __get_cpu_features ();
+
+ if (CPU_FEATURE_USABLE_P (cpu_features, AVX512F)
+ && !CPU_FEATURES_ARCH_P (cpu_features, Prefer_No_AVX512))
+ {
+ if (CPU_FEATURE_USABLE_P (cpu_features, AVX512VL)
+ && CPU_FEATURE_USABLE_P (cpu_features, AVX512BW)
+ && CPU_FEATURE_USABLE_P (cpu_features, BMI2))
+ {
+ if (CPU_FEATURE_USABLE_P (cpu_features, ERMS))
+ return OPTIMIZE1 (avx512_unaligned_erms);
+
+ return OPTIMIZE1 (avx512_unaligned);
+ }
+ }
+
+ if (CPU_FEATURE_USABLE_P (cpu_features, AVX2))
+ {
+ if (CPU_FEATURE_USABLE_P (cpu_features, AVX512VL)
+ && CPU_FEATURE_USABLE_P (cpu_features, AVX512BW)
+ && CPU_FEATURE_USABLE_P (cpu_features, BMI2))
+ {
+ if (CPU_FEATURE_USABLE_P (cpu_features, ERMS))
+ return OPTIMIZE1 (evex_unaligned_erms);
+
+ return OPTIMIZE1 (evex_unaligned);
+ }
+
+ if (CPU_FEATURE_USABLE_P (cpu_features, RTM))
+ {
+ if (CPU_FEATURE_USABLE_P (cpu_features, ERMS))
+ return OPTIMIZE1 (avx2_unaligned_erms_rtm);
+
+ return OPTIMIZE1 (avx2_unaligned_rtm);
+ }
+
+ if (!CPU_FEATURES_ARCH_P (cpu_features, Prefer_No_VZEROUPPER))
+ {
+ if (CPU_FEATURE_USABLE_P (cpu_features, ERMS))
+ return OPTIMIZE1 (avx2_unaligned_erms);
+
+ return OPTIMIZE1 (avx2_unaligned);
+ }
+ }
+
+ if (CPU_FEATURE_USABLE_P (cpu_features, ERMS))
+ return OPTIMIZE1 (sse2_unaligned_erms);
+
+ return OPTIMIZE1 (sse2_unaligned);
+}
+
+libc_ifunc_redirected (__redirect___bzero, __bzero, IFUNC_SELECTOR ());
+
+weak_alias (__bzero, bzero)
+#endif
diff --git a/sysdeps/x86_64/multiarch/ifunc-impl-list.c b/sysdeps/x86_64/multiarch/ifunc-impl-list.c
index 68a56797d4..a594f4176e 100644
--- a/sysdeps/x86_64/multiarch/ifunc-impl-list.c
+++ b/sysdeps/x86_64/multiarch/ifunc-impl-list.c
@@ -300,6 +300,48 @@ __libc_ifunc_impl_list (const char *name, struct libc_ifunc_impl *array,
__memset_avx512_no_vzeroupper)
)
+ /* Support sysdeps/x86_64/multiarch/bzero.c. */
+ IFUNC_IMPL (i, name, bzero,
+ IFUNC_IMPL_ADD (array, i, bzero, 1,
+ __bzero_sse2_unaligned)
+ IFUNC_IMPL_ADD (array, i, bzero, 1,
+ __bzero_sse2_unaligned_erms)
+ IFUNC_IMPL_ADD (array, i, bzero,
+ CPU_FEATURE_USABLE (AVX2),
+ __bzero_avx2_unaligned)
+ IFUNC_IMPL_ADD (array, i, bzero,
+ CPU_FEATURE_USABLE (AVX2),
+ __bzero_avx2_unaligned_erms)
+ IFUNC_IMPL_ADD (array, i, bzero,
+ (CPU_FEATURE_USABLE (AVX2)
+ && CPU_FEATURE_USABLE (RTM)),
+ __bzero_avx2_unaligned_rtm)
+ IFUNC_IMPL_ADD (array, i, bzero,
+ (CPU_FEATURE_USABLE (AVX2)
+ && CPU_FEATURE_USABLE (RTM)),
+ __bzero_avx2_unaligned_erms_rtm)
+ IFUNC_IMPL_ADD (array, i, bzero,
+ (CPU_FEATURE_USABLE (AVX512VL)
+ && CPU_FEATURE_USABLE (AVX512BW)
+ && CPU_FEATURE_USABLE (BMI2)),
+ __bzero_evex_unaligned)
+ IFUNC_IMPL_ADD (array, i, bzero,
+ (CPU_FEATURE_USABLE (AVX512VL)
+ && CPU_FEATURE_USABLE (AVX512BW)
+ && CPU_FEATURE_USABLE (BMI2)),
+ __bzero_evex_unaligned_erms)
+ IFUNC_IMPL_ADD (array, i, bzero,
+ (CPU_FEATURE_USABLE (AVX512VL)
+ && CPU_FEATURE_USABLE (AVX512BW)
+ && CPU_FEATURE_USABLE (BMI2)),
+ __bzero_avx512_unaligned_erms)
+ IFUNC_IMPL_ADD (array, i, bzero,
+ (CPU_FEATURE_USABLE (AVX512VL)
+ && CPU_FEATURE_USABLE (AVX512BW)
+ && CPU_FEATURE_USABLE (BMI2)),
+ __bzero_avx512_unaligned)
+ )
+
/* Support sysdeps/x86_64/multiarch/rawmemchr.c. */
IFUNC_IMPL (i, name, rawmemchr,
IFUNC_IMPL_ADD (array, i, rawmemchr,
diff --git a/sysdeps/x86_64/multiarch/memset-avx2-unaligned-erms-rtm.S b/sysdeps/x86_64/multiarch/memset-avx2-unaligned-erms-rtm.S
index 8ac3e479bb..5a5ee6f672 100644
--- a/sysdeps/x86_64/multiarch/memset-avx2-unaligned-erms-rtm.S
+++ b/sysdeps/x86_64/multiarch/memset-avx2-unaligned-erms-rtm.S
@@ -5,6 +5,7 @@
#define SECTION(p) p##.avx.rtm
#define MEMSET_SYMBOL(p,s) p##_avx2_##s##_rtm
+#define BZERO_SYMBOL(p,s) p##_avx2_##s##_rtm
#define WMEMSET_SYMBOL(p,s) p##_avx2_##s##_rtm
#include "memset-avx2-unaligned-erms.S"
diff --git a/sysdeps/x86_64/multiarch/memset-avx2-unaligned-erms.S b/sysdeps/x86_64/multiarch/memset-avx2-unaligned-erms.S
index c0bf2875d0..a093a2831f 100644
--- a/sysdeps/x86_64/multiarch/memset-avx2-unaligned-erms.S
+++ b/sysdeps/x86_64/multiarch/memset-avx2-unaligned-erms.S
@@ -14,6 +14,9 @@
vmovd d, %xmm0; \
movq r, %rax;
+# define BZERO_ZERO_VEC0() \
+ vpxor %xmm0, %xmm0, %xmm0
+
# define WMEMSET_SET_VEC0_AND_SET_RETURN(d, r) \
MEMSET_SET_VEC0_AND_SET_RETURN(d, r)
@@ -29,6 +32,9 @@
# ifndef MEMSET_SYMBOL
# define MEMSET_SYMBOL(p,s) p##_avx2_##s
# endif
+# ifndef BZERO_SYMBOL
+# define BZERO_SYMBOL(p,s) p##_avx2_##s
+# endif
# ifndef WMEMSET_SYMBOL
# define WMEMSET_SYMBOL(p,s) p##_avx2_##s
# endif
diff --git a/sysdeps/x86_64/multiarch/memset-avx512-unaligned-erms.S b/sysdeps/x86_64/multiarch/memset-avx512-unaligned-erms.S
index 5241216a77..727c92133a 100644
--- a/sysdeps/x86_64/multiarch/memset-avx512-unaligned-erms.S
+++ b/sysdeps/x86_64/multiarch/memset-avx512-unaligned-erms.S
@@ -19,6 +19,9 @@
vpbroadcastb d, %VEC0; \
movq r, %rax
+# define BZERO_ZERO_VEC0() \
+ vpxorq %XMM0, %XMM0, %XMM0
+
# define WMEMSET_SET_VEC0_AND_SET_RETURN(d, r) \
vpbroadcastd d, %VEC0; \
movq r, %rax
diff --git a/sysdeps/x86_64/multiarch/memset-evex-unaligned-erms.S b/sysdeps/x86_64/multiarch/memset-evex-unaligned-erms.S
index 6370021506..5d8fa78f05 100644
--- a/sysdeps/x86_64/multiarch/memset-evex-unaligned-erms.S
+++ b/sysdeps/x86_64/multiarch/memset-evex-unaligned-erms.S
@@ -19,6 +19,9 @@
vpbroadcastb d, %VEC0; \
movq r, %rax
+# define BZERO_ZERO_VEC0() \
+ vpxorq %XMM0, %XMM0, %XMM0
+
# define WMEMSET_SET_VEC0_AND_SET_RETURN(d, r) \
vpbroadcastd d, %VEC0; \
movq r, %rax
diff --git a/sysdeps/x86_64/multiarch/memset-sse2-unaligned-erms.S b/sysdeps/x86_64/multiarch/memset-sse2-unaligned-erms.S
index 8a6f0c561a..329c58ee46 100644
--- a/sysdeps/x86_64/multiarch/memset-sse2-unaligned-erms.S
+++ b/sysdeps/x86_64/multiarch/memset-sse2-unaligned-erms.S
@@ -22,6 +22,7 @@
#if IS_IN (libc)
# define MEMSET_SYMBOL(p,s) p##_sse2_##s
+# define BZERO_SYMBOL(p,s) MEMSET_SYMBOL (p, s)
# define WMEMSET_SYMBOL(p,s) p##_sse2_##s
# ifdef SHARED
diff --git a/sysdeps/x86_64/multiarch/memset-vec-unaligned-erms.S b/sysdeps/x86_64/multiarch/memset-vec-unaligned-erms.S
index 1b502b78e4..7c94fcdae1 100644
--- a/sysdeps/x86_64/multiarch/memset-vec-unaligned-erms.S
+++ b/sysdeps/x86_64/multiarch/memset-vec-unaligned-erms.S
@@ -26,6 +26,10 @@
#include <sysdep.h>
+#ifndef BZERO_SYMBOL
+# define BZERO_SYMBOL(p,s) MEMSET_SYMBOL (p, s)
+#endif
+
#ifndef MEMSET_CHK_SYMBOL
# define MEMSET_CHK_SYMBOL(p,s) MEMSET_SYMBOL(p, s)
#endif
@@ -87,6 +91,18 @@
# define XMM_SMALL 0
#endif
+#ifdef USE_LESS_VEC_MASK_STORE
+# define SET_REG64 rcx
+# define SET_REG32 ecx
+# define SET_REG16 cx
+# define SET_REG8 cl
+#else
+# define SET_REG64 rsi
+# define SET_REG32 esi
+# define SET_REG16 si
+# define SET_REG8 sil
+#endif
+
#define PAGE_SIZE 4096
/* Macro to calculate size of small memset block for aligning
@@ -98,18 +114,6 @@
# error SECTION is not defined!
#endif
- .section SECTION(.text),"ax",@progbits
-#if VEC_SIZE == 16 && IS_IN (libc)
-ENTRY (__bzero)
- mov %RDI_LP, %RAX_LP /* Set return value. */
- mov %RSI_LP, %RDX_LP /* Set n. */
- xorl %esi, %esi
- pxor %XMM0, %XMM0
- jmp L(entry_from_bzero)
-END (__bzero)
-weak_alias (__bzero, bzero)
-#endif
-
#if IS_IN (libc)
# if defined SHARED
ENTRY_CHK (WMEMSET_CHK_SYMBOL (__wmemset_chk, unaligned))
@@ -123,12 +127,37 @@ ENTRY (WMEMSET_SYMBOL (__wmemset, unaligned))
WMEMSET_SET_VEC0_AND_SET_RETURN (%esi, %rdi)
WMEMSET_VDUP_TO_VEC0_LOW()
cmpq $VEC_SIZE, %rdx
- jb L(less_vec_no_vdup)
+ jb L(less_vec_from_wmemset)
WMEMSET_VDUP_TO_VEC0_HIGH()
jmp L(entry_from_wmemset)
END (WMEMSET_SYMBOL (__wmemset, unaligned))
#endif
+ENTRY (BZERO_SYMBOL(__bzero, unaligned))
+#if VEC_SIZE > 16
+ BZERO_ZERO_VEC0 ()
+#endif
+ mov %RDI_LP, %RAX_LP
+ mov %RSI_LP, %RDX_LP
+#ifndef USE_LESS_VEC_MASK_STORE
+ xorl %esi, %esi
+#endif
+ cmp $VEC_SIZE, %RDX_LP
+ jb L(less_vec_no_vdup)
+#ifdef USE_LESS_VEC_MASK_STORE
+ xorl %esi, %esi
+#endif
+#if VEC_SIZE <= 16
+ BZERO_ZERO_VEC0 ()
+#endif
+ cmp $(VEC_SIZE * 2), %RDX_LP
+ ja L(more_2x_vec)
+ /* From VEC and to 2 * VEC. No branch when size == VEC_SIZE. */
+ VMOVU %VEC(0), (%rdi)
+ VMOVU %VEC(0), (VEC_SIZE * -1)(%rdi, %rdx)
+ VZEROUPPER_RETURN
+END (BZERO_SYMBOL(__bzero, unaligned))
+
#if defined SHARED && IS_IN (libc)
ENTRY_CHK (MEMSET_CHK_SYMBOL (__memset_chk, unaligned))
cmp %RDX_LP, %RCX_LP
@@ -142,7 +171,6 @@ ENTRY (MEMSET_SYMBOL (__memset, unaligned))
/* Clear the upper 32 bits. */
mov %edx, %edx
# endif
-L(entry_from_bzero):
cmpq $VEC_SIZE, %rdx
jb L(less_vec)
MEMSET_VDUP_TO_VEC0_HIGH()
@@ -187,6 +215,31 @@ END (__memset_erms)
END (MEMSET_SYMBOL (__memset, erms))
# endif
+ENTRY_P2ALIGN (BZERO_SYMBOL(__bzero, unaligned_erms), 6)
+# if VEC_SIZE > 16
+ BZERO_ZERO_VEC0 ()
+# endif
+ mov %RDI_LP, %RAX_LP
+ mov %RSI_LP, %RDX_LP
+# ifndef USE_LESS_VEC_MASK_STORE
+ xorl %esi, %esi
+# endif
+ cmp $VEC_SIZE, %RDX_LP
+ jb L(less_vec_no_vdup)
+# ifdef USE_LESS_VEC_MASK_STORE
+ xorl %esi, %esi
+# endif
+# if VEC_SIZE <= 16
+ BZERO_ZERO_VEC0 ()
+# endif
+ cmp $(VEC_SIZE * 2), %RDX_LP
+ ja L(stosb_more_2x_vec)
+ /* From VEC and to 2 * VEC. No branch when size == VEC_SIZE. */
+ VMOVU %VEC(0), (%rdi)
+ VMOVU %VEC(0), (VEC_SIZE * -1)(%rdi, %rdx)
+ VZEROUPPER_RETURN
+END (BZERO_SYMBOL(__bzero, unaligned_erms))
+
# if defined SHARED && IS_IN (libc)
ENTRY_CHK (MEMSET_CHK_SYMBOL (__memset_chk, unaligned_erms))
cmp %RDX_LP, %RCX_LP
@@ -229,6 +282,7 @@ L(last_2x_vec):
.p2align 4,, 10
L(less_vec):
L(less_vec_no_vdup):
+L(less_vec_from_wmemset):
/* Less than 1 VEC. */
# if VEC_SIZE != 16 && VEC_SIZE != 32 && VEC_SIZE != 64
# error Unsupported VEC_SIZE!
@@ -374,8 +428,11 @@ L(less_vec):
/* Broadcast esi to partial register (i.e VEC_SIZE == 32 broadcast to
xmm). This is only does anything for AVX2. */
MEMSET_VDUP_TO_VEC0_LOW ()
+L(less_vec_from_wmemset):
+#if VEC_SIZE > 16
L(less_vec_no_vdup):
#endif
+#endif
L(cross_page):
#if VEC_SIZE > 32
cmpl $32, %edx
@@ -386,7 +443,10 @@ L(cross_page):
jge L(between_16_31)
#endif
#ifndef USE_XMM_LESS_VEC
- MOVQ %XMM0, %rcx
+ MOVQ %XMM0, %SET_REG64
+#endif
+#if VEC_SIZE <= 16
+L(less_vec_no_vdup):
#endif
cmpl $8, %edx
jge L(between_8_15)
@@ -395,7 +455,7 @@ L(cross_page):
cmpl $1, %edx
jg L(between_2_3)
jl L(between_0_0)
- movb %sil, (%LESS_VEC_REG)
+ movb %SET_REG8, (%LESS_VEC_REG)
L(between_0_0):
ret
@@ -428,8 +488,8 @@ L(between_8_15):
MOVQ %XMM0, (%rdi)
MOVQ %XMM0, -8(%rdi, %rdx)
#else
- movq %rcx, (%LESS_VEC_REG)
- movq %rcx, -8(%LESS_VEC_REG, %rdx)
+ movq %SET_REG64, (%LESS_VEC_REG)
+ movq %SET_REG64, -8(%LESS_VEC_REG, %rdx)
#endif
ret
@@ -442,8 +502,8 @@ L(between_4_7):
MOVD %XMM0, (%rdi)
MOVD %XMM0, -4(%rdi, %rdx)
#else
- movl %ecx, (%LESS_VEC_REG)
- movl %ecx, -4(%LESS_VEC_REG, %rdx)
+ movl %SET_REG32, (%LESS_VEC_REG)
+ movl %SET_REG32, -4(%LESS_VEC_REG, %rdx)
#endif
ret
@@ -452,12 +512,12 @@ L(between_4_7):
L(between_2_3):
/* From 2 to 3. No branch when size == 2. */
#ifdef USE_XMM_LESS_VEC
- movb %sil, (%rdi)
- movb %sil, 1(%rdi)
- movb %sil, -1(%rdi, %rdx)
+ movb %SET_REG8, (%rdi)
+ movb %SET_REG8, 1(%rdi)
+ movb %SET_REG8, -1(%rdi, %rdx)
#else
- movw %cx, (%LESS_VEC_REG)
- movb %sil, -1(%LESS_VEC_REG, %rdx)
+ movw %SET_REG16, (%LESS_VEC_REG)
+ movb %SET_REG8, -1(%LESS_VEC_REG, %rdx)
#endif
ret
END (MEMSET_SYMBOL (__memset, unaligned_erms))